design of antenna-diversity transceivers for wireless ...is therefore an important principle that...

Design of antenna-diversity transceivers for wirelessconsumer productsCitation for published version (APA):Leijten, L. (2001). Design of antenna-diversity transceivers for wireless consumer products. Eindhoven:Technische Universiteit Eindhoven.

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Design of Antenna-DiversityTransceivers

for Wireless Consumer Products

Lukas Leijten

Design of Antenna-DiversityTransceivers

for Wireless Consumer Products

PROEFSCHRIFT

ter verkrijging van de graad van doctoraan de Technische Universiteit Eindhoven

op gezag van de Rector Magnificus, prof.dr. R.A. van Santen,voor een commissie aangewezen door het College voor Promoties,

in het openbaar te verdedigenop donderdag 6 september 2001 om 16.00 uur

door

Lukas Leijten

geboren te Woudenberg

Dit proefschrift is goedgekeurd door de promotoren:

prof.dr.ir. G. Brussaardenprof.dr.ir. W.M.G. van Bokhoven

Copromotor:dr.ir. M.H.A.J. Herben

The work described in this thesis has been carried outat the PHILIPS RESEARCH LABORATORIES Eindhoven,the Netherlands, as part of the Philips Research Programme.

CIP-gegevens Koninklijke Bibliotheek, Den HaagLeijten, L.Design of Antenna-Diversity Transceiversfor Wireless Consumer ProductsProefschrift Technische Universiteit Eindhoven,-Met lit. opg.,-Met samenvatting in het Nederlands.ISBN 90-74445-53-5Trefwoorden: antenna diversity, draadloze communicatie, DECT, radiokanaal, metingen,modellen, consumentenproductenSubject headings: antenna diversity, wireless communications, DECT, radio channel,measurements, models, consumer products

c©Koninklijke Philips Electronics N.V. 2001All rights are reserved.

Reproduction in whole or in part is prohibitedwithout the written consent of the copyright owner.

Aut nunquam tentes aut perfice∗

∗Ovidius, Ars amatoria 1, 389: Complete whatever you start or do not start at all.

Summary

Antenna-diversity implementations consist of two or more antennas and a circuit to com-bine the antenna signals in an optimum way. The performance of an antenna-diversitytransceiver is better than a standard transceiver with a single-antenna. This improve-ment cannot easily and inexpensively be obtained by other techniques. Antenna diversityis therefore an important principle that can be implemented in many wireless consumerproducts, like mobile phones and wireless networks.

In this Ph.D. thesis a procedure for the design of antenna-diversity transceivers forwireless consumer products is presented. This procedure leads to an antenna-diversityimplementation that is as best as possible with respect to the complexity of the total cir-cuit, the power dissipation, size, cost, and other relevant issues. The first step is to analyseantenna-diversity principles with simulations with respect to, e.g., efficiency, size and ra-diation pattern. The next step is to analyse these concepts for a multi-path environment toobtain quantities, like signal-to-noise ratio and bit-error rate. Finally, a prototype is builtand field tests are conducted to obtain its performance.

A simulation tool is selected and a measurement set-up is devised for this proce-dure. The simulation tool is based on the Finite Difference Time Domain method. Thefrequency-domain response of the radio channel including the antenna characteristics isobtained with the measurement set-up. Moreover, antenna-diversity transceivers can beinserted into this set-up to measure their performance and to compare them with eachother in a quantitative way.

Signals are spread in time when travelling through the radio channel. Usually anestimate of the spreading is obtained from wideband measurements or simulations. Inthis Ph.D. thesis a method is presented to obtain this estimate from narrowband measure-ments or simulations. The spreading obtained in this way is a more realistic measure forthe performance of an antenna-diversity receiver. The method is applied to analyse therelation between the bandwidth of the transmitted signals and the performance of antenna-diversity techniques. This analysis shows that the performance of all techniques reducesif the bandwidth is increased.

With the presented procedure a state-of-the-art antenna-diversity transceiver has beendesigned for implementation in a portable consumer product. This transceiver has beenbuilt and tested. It consists of a two-antenna space-diversity technique with a discreteequal-gain circuit to combine the signals, this circuit is implemented in its baseband part.The antenna-diversity transceiver has the ability to improve the signal-to-noise ratio witha factor of 5 relative to a standard single-antenna transceiver.

i

Contents

Summary i

Symbols and abbreviations viiList of symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiList of subscripts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ixAbbreviations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x

1 Introduction 11.1 Antenna-diversity in handsets . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Goal and approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.3 Background and achievements . . . . . . . . . . . . . . . . . . . . . . . 4

2 The indoor radio channel 92.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92.2 Digital European Cordless Telecommunications system . . . . . . . . . . 102.3 Characterisation of fading multi-path channels . . . . . . . . . . . . . . . 12

2.3.1 Classification of small-scale fading . . . . . . . . . . . . . . . . 132.3.2 WSSUS linear time-variant channel . . . . . . . . . . . . . . . . 152.3.3 Classification of the indoor DECT radio-channel . . . . . . . . . 16

2.4 Thevenin representation of antenna . . . . . . . . . . . . . . . . . . . . . 162.5 Time domain analysis using a Gaussian modulated sine source . . . . . . 17

2.5.1 Gaussian modulated sine source . . . . . . . . . . . . . . . . . . 182.6 Lowpass representation of transmitted and received bandpass signals . . . 202.7 Delay spread . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

2.7.1 Definition of delay spread . . . . . . . . . . . . . . . . . . . . . 222.8 Power delay profile and delay spread obtained with wideband pulses . . . 252.9 Power delay profile and delay spread obtained with narrowband pulses . . 262.10 Practical calculation of the delay spread . . . . . . . . . . . . . . . . . . 32

2.10.1 Power delay profile duration . . . . . . . . . . . . . . . . . . . . 322.10.2 Delay spread calculation based on received signal . . . . . . . . . 332.10.3 Mean delay spread obtained from the local delay spread . . . . . 34

2.11 Bit-error rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 362.11.1 Bit-error rate as a function of radio channel parameters . . . . . . 37

iii

iv Contents

2.12 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 402.12.1 Requirements for measurements and simulation methods . . . . . 42

3 Radio channel modelling 453.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 453.2 Path-loss models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 463.3 Statistical propagation models . . . . . . . . . . . . . . . . . . . . . . . 483.4 Analytical propagation models . . . . . . . . . . . . . . . . . . . . . . . 493.5 Ray-tracing propagation models . . . . . . . . . . . . . . . . . . . . . . 50

3.5.1 Ray-tracing algorithm . . . . . . . . . . . . . . . . . . . . . . . 513.6 Finite Difference Time Domain (FDTD) propagation model . . . . . . . . 53

3.6.1 Source ramp-up for frequency domain analysis . . . . . . . . . . 543.6.2 Source ramp-up and spurious . . . . . . . . . . . . . . . . . . . . 553.6.3 Gaussian modulated sine source . . . . . . . . . . . . . . . . . . 603.6.4 Implementation of delay spread calculations . . . . . . . . . . . . 63

3.7 Two- versus three- dimensional models . . . . . . . . . . . . . . . . . . 663.8 Finite Difference Time Domain versus ray-tracing . . . . . . . . . . . . . 673.9 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

4 Radio channel measurements 794.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 794.2 Measurement set-up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 804.3 Frequency transfer function . . . . . . . . . . . . . . . . . . . . . . . . . 824.4 Power delay profile obtained from measurements . . . . . . . . . . . . . 83

4.4.1 Aliasing and essentially band-limited signals . . . . . . . . . . . 854.4.2 Windowing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

4.5 Measurement accuracy . . . . . . . . . . . . . . . . . . . . . . . . . . . 894.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

5 Design of adaptive diversity implementations 935.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 935.2 Diversity implementations . . . . . . . . . . . . . . . . . . . . . . . . . 94

5.2.1 Space diversity . . . . . . . . . . . . . . . . . . . . . . . . . . . 945.2.2 Frequency diversity . . . . . . . . . . . . . . . . . . . . . . . . . 955.2.3 Polarisation diversity . . . . . . . . . . . . . . . . . . . . . . . . 965.2.4 Field-component diversity . . . . . . . . . . . . . . . . . . . . . 965.2.5 Angle diversity . . . . . . . . . . . . . . . . . . . . . . . . . . . 975.2.6 Time diversity . . . . . . . . . . . . . . . . . . . . . . . . . . . 985.2.7 Comparison of diversity implementations . . . . . . . . . . . . . 98

5.3 Diversity combining techniques . . . . . . . . . . . . . . . . . . . . . . 995.3.1 Switched combining . . . . . . . . . . . . . . . . . . . . . . . . 1005.3.2 Selective combining . . . . . . . . . . . . . . . . . . . . . . . . 1015.3.3 Equal-gain combining . . . . . . . . . . . . . . . . . . . . . . . 1025.3.4 Maximum-ratio combining . . . . . . . . . . . . . . . . . . . . . 109

5.4 Performance and comparison of diversity combining techniques . . . . . 111

Contents v

5.4.1 Measures of performance . . . . . . . . . . . . . . . . . . . . . . 1125.4.2 Diversity combining performance as a function of bandwidth . . . 1155.4.3 Selection of combining technique . . . . . . . . . . . . . . . . . 119

5.5 Equal-gain combiner with discrete phase shifter . . . . . . . . . . . . . . 1205.6 Equal-gain combining and body effects . . . . . . . . . . . . . . . . . . 1235.7 Adaptation speed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1255.8 Diversity and equalisers . . . . . . . . . . . . . . . . . . . . . . . . . . . 1265.9 Quality indicators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129

5.9.1 Quality signal and diversity performance . . . . . . . . . . . . . 1295.9.2 Out-of-band noise detection . . . . . . . . . . . . . . . . . . . . 131

5.10 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134

6 Practical diversity implementations 1376.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1376.2 DECT zero-IF transceiver . . . . . . . . . . . . . . . . . . . . . . . . . . 1396.3 IQ phase shifter at zero-IF . . . . . . . . . . . . . . . . . . . . . . . . . 142

6.3.1 Continuous phase shifter . . . . . . . . . . . . . . . . . . . . . . 1426.3.2 Discrete phase shifter . . . . . . . . . . . . . . . . . . . . . . . . 144

6.4 Selection circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1476.5 Combiner . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1496.6 Out-of-band noise detector . . . . . . . . . . . . . . . . . . . . . . . . . 1506.7 Controller . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1536.8 Full circuit implementation . . . . . . . . . . . . . . . . . . . . . . . . . 1536.9 Performance evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . 1586.10 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160

6.10.1 Current handheld diversity implementation . . . . . . . . . . . . 161

7 Conclusions 1637.1 Results obtained . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163

7.1.1 Selection of tools . . . . . . . . . . . . . . . . . . . . . . . . . . 1637.1.2 Designing and building the diversity receiver . . . . . . . . . . . 164

7.2 Recommendations for further research . . . . . . . . . . . . . . . . . . . 1667.3 Recent developments . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167

References 169

Samenvatting 177

Acknowledgments 179

Biography 181

Levensbeschrijving 183

Index 185

vi Contents

Symbols and abbreviations

Symbols

a (s−1) decay of Gaussian pulse or Gaussian windowA (V) amplitude (of a signal)br (s−1) bit rateB (Hz) bandwidthBER ( ) bit-error ratec (m/s) 299.792.458, . . . m/s, speed of light in vacuumC ( ) complex weighting factorD ( ) real weighting factor (adjustable amplitude)e 2.718281828 . . . , natural base of logarithmsEE (V/m) electric field strengthEr ensemble average over a small areaEt time average (of a signal)f (Hz) frequencyEf ( ) (far-field) antenna directivity pattern

Fourier transformation −1 inverse Fourier transformationg ( ) (antenna,array) gainh ( ) (channel) impulse responseh ( ) complex-valued lowpass equivalent of impulse response h

(s) Fourier transform of hi (A) currentI (V) in-phase (quadrature) component (of a signal)j imaginary unitEJ (A/m) (antenna) current distribution

k ( ) number of ramp-up periods (FDTD)L ( ) (transmission) lossm ( ) integer numbern ( ) integer numberM ( ) integer number (diversity branches)N ( ) integer number (detectable propagation paths, taps of equaliser)p ( ) probability density function

vii

viii Symbols and abbreviations

P (W) power delay profile, i.e. instantaneous power as a function of timeQ (V) (90) quadrature component (of a signal)r (m) distance or separation defined as |Er |Er (m) location vectorR () real part of impedance Z< real part of a complex-valued quantitys (V) real valued signals (V) complex-valued lowpass equivalent of a signal sS (W) time-averaged power (of a signal)S12 ( ) reverse transmission coefficient (of a two-port network)S21 ( ) forward transmission coefficient (of a two-port network)t (s) timeT (s) (symbol, time-slot, frame) duration or periodV (V) voltage

(Vs) Fourier transform of VW (m2) surface

( ) frequency domain Gaussian windowx (m) co-ordinate of (x, y, z) right-hand rectangular cartesian co-ordinate systemX () imaginary part of impedance Zy (m) co-ordinate of (x, y, z) right-hand rectangular cartesian co-ordinate systemz (m) co-ordinate of (x, y, z) right-hand rectangular cartesian co-ordinate systemZ () impedanceα ( ) attenuation factor of a multi-path component, real numberβ ( ) real numberγ ( ) signal-to-noise ratio0 ( ) reflection coefficientδ Dirac impulse function1r (m) cell size, length and width of the cell (FDTD)1t (s) time step size (FDTD, DFT)1 f (Hz) frequency step size (DFT)1ξ (rad) maximum absolute phase errorθ (rad) spherical angle of (φ, θ, r) right-hand spherical co-ordinate systemλ (m) wavelengthµ ( ) probabilityν (m/s) speed (of movement)ξ () phase shift (of a signal)π 3.141592654 . . .ρ ( ) loss factor (exponent)τ (s) (root mean squared) delay spreadτ (s) averaged delay spreadφ (rad) spherical angle of (φ, θ, r) right-hand spherical co-ordinate systemψ () phase (of a signal)

Symbols and abbreviations ix

Subscripts

0 carrier (wavelength, frequency), constant (value, number)r0 at a distance of r0 (from an antenna)30 at -30 dB points (bandwidth, duration)a antenna (voltage, impedance, separation)c coherence (bandwidth, time)b bit or symbold (propagation) delay (time)det detector (voltage)div diversity (gain)D Doppler (spread, frequency)eg equal gain combiningf frame (duration)g Gaussian pulse, equivalent to narrowband excitationi incidentin input (voltage, signal)m maximum (speed of movement)mr maximum-ratio combiningn integer index (within equations)ns noiseout output (voltage, signal)p pulse (spread, duration)q qualityr receive (state)rr array (gain)s time-slot (duration)se selective combiningsw switched combiningt transmit (state)tr transmission (loss)T threshold (voltage)w window (delay time)s/n (due to) signal-to-noise ratioδ Dirac pulse or equivalent to wideband excitationτ (due to) delay spread

x Symbols and abbreviations

Abbreviations

ADC Analogue-to-Digital ConverterAGC Automatic Gain ControlBB BaseBand part of receiverBER Bit-Error RateCDF Cumulative Distribution FunctionCDMA Code Division Multiple AccessCPU Central Processing UnitDAC Digital-to-Analogue ConverterdBm power in dB relative to 1 mWDC Direct CurrentDECT Digital European Cordless Telecommunication (standard/system)DFT Discrete Fourier TransformationDIFT Discrete Inverse Fourier TransformationEMC ElectroMagnetic CompatibilityFDTD Finite Difference Time Domain (method)FE Front-End part of receiverGFSK Gaussian Frequency Shift KeyingGms Gaussian modulated sine (source)GMSK Gaussian Minimum Shift KeyingGSM Global System for Mobile communicationIA DECT Installation AssistantIC Integrated CircuitIF Intermediate FrequencyIFT Inverse Fourier TransformationISI Inter-Symbol InterferenceLED Light Emitting DiodeLO Local OscillatorLOS Line-Of-SightOFDM Orthogonal Frequency Division Multiplexingopamp operational amplifierPACMAN Philips Adaptive aCtive Miniature ANtennasPC Personal ComputerPCB Printed Circuit BoardPDF Probability Density FunctionPDP Power Delay ProfilePHS Personal Handy-phone SystemPLL Phase Lock Loop (synthesiser)PML (Berenger’s) Perfectly Matched LayersPRLE Philips Research Laboratories EindhovenPSD Power Spectral DensityPSK Phase Shift KeyingQAM Quadrature Amplitude ModulationRF Radio-Frequency

Symbols and abbreviations xi

rms root-mean-squared (difference, error)RSSI Received Signal-Strength IndicatorRX receiverSAR Specific Absorption RateSAW Surface Acoustic WaveSNR Signal-to-Noise RatioSNIR Signal-to-Noise-plus-Interference RatioTDMA Time Division Multiple AccessTU/e Eindhoven University of TechnologyTX transmitterUMTS Universal Mobile Telecommunications SystemVCA Voltage Controlled AmplifierVCO Voltage Controlled OscillatorWSSUS Wide-Sense Stationary Uncorrelated ScatteringµC microcontroller

xii Symbols and abbreviations

Chapter 1

Introduction

1.1 Antenna-diversity in handsets

In 1999 Philips introduced two cordless telephones: the ‘Kala’ for the consumer marketand the ‘Zenia’ for the (semi-) professional market. Their radio interface is based on theDigital European Cordless Telecommunication (DECT) standard. The press release ofthe introduction stated the following:

‘The usable indoor range is maximised by two internal antennas, which are used incombination with fast switching technology to ensure good reception quality throughoutthe area served by the DECT network.’

Figure 1.1 shows the Kala DECT phone and Figure 1.2 shows a close-up of the inter-nal antennas. The good performance of the new telephones, as stated in the press release,has been verified by comparing them to a telephone with only one antenna (called ‘Onis’)[Gerritsen, 2000]. For this a user trial in a typical office environment has been done. Theresults are:

• indoor range increased from about 40 to 50 metres (+30%),

• total muted time reduced from 2.2% of the total time to 0.25% (-90%),

• number of audible clicks reduced from 4 per minute to 0.

The performance is expressed in user-observable quantities. The fact that the user isable to experience the improvement, means that this product is potentially attractive. Theimprovement is obtained by an implementation of the antenna-diversity principle.

Antenna-diversity implementations consist of two or more antennas and a circuit tocombine the antenna signals in an optimum way. The performance of an antenna-diversitytransceiver is better than a standard transceiver with a single-antenna. This improvementcannot easily and inexpensively be obtained by other techniques. Antenna diversity istherefore an important principle that can be implemented in many wireless consumerproducts, like mobile phones and wireless networks. In this Ph.D. thesis a procedure ispresented for the design of antenna-diversity transceivers for wireless consumer products.

1

2 Chapter 1. Introduction

Figure 1.1: Philips’ Kala DECT phone; its internal board, left side, and itsfront, right side.

Antenna 1

Antenna 2

Figure 1.2: Close-up of the antenna part of the Philips’ Kala, left side, and thearrangement of the two inverted-F antennas, right side.

1.2. Goal and approach 3

1.2 Goal and approach

The goal of the Ph.D. project was to define and verify a procedure to design adaptiveantenna-diversity implementations for portable wireless consumer products. This proce-dure leads to a diversity implementation that is as best as possible with respect to thecomplexity of the total circuit, the power dissipation, size, cost and other relevant issues.This procedure is verified by the design, implementation and characterisation of a state-of-the-art diversity receiver.

The ideas behind the procedure are illustrated in Figure 1.3. The design of an antenna-diversity implementation is divided into several steps. The first step is to analyse ideasand concepts with simulations for free-space conditions. Requirements, like efficiency,size and radiation pattern are analysed in this phase. The next step is to analyse the ideasand the concepts for a realistic multi-path environment, for example, that of a house oroffice. Quantities like diversity gain, outage and bit-error rate are evaluated in this phase.The characteristics of the multi-path environment are obtained by simulations or with themeasurement set-up. Next, a prototype is built and field tests are conducted to judge itsperformance. If the design still satisfies the requirements, a product implementation canbe made.

Free-spaceperformance

Ideas andconcepts

Simulationtools

Product

Field test

Chapter 4

set-upMeasurement

performanceMulti-path

Chapter 5

Chapter 3

Chapter 6

Prototype

Figure 1.3: Procedure for designing antenna-diversity systems with the refer-ences to the relevant chapters of this thesis. The procedure startswith ideas and concepts and ends with products.

During the design process the time for and the costs of every step increases expo-nentially. Basic ideas and concepts can be verified within days with computer models.The realisation of a prototype can last for months and expensive measurement equip-ment (e.g., network analyser or spectrum analyser) is needed. The implementation into aproduct is the most time-consuming and costly phase. The product must satisfy all legalrequirements (e.g., electromagnetic compatibility, safety) and a production line must beconverted or built for the manufacturing.


Figure 1.3 also shows which parts of the design process are considered in this thesiswith references to the chapters. This thesis focuses on the performance of diversity-system implementations in an indoor propagation environment (Chapter 5) and on thedesign and evaluation of a prototype (Chapter 6). As part of the procedure a model of theradio channel is chosen (Chapter 3) and a measurement set-up is devised (Chapter 4). Theimplementation into a product, the last step in Figure 1.3, is not considered. This step isthe responsibility of the set-maker (a product division or business unit within Philips).

This Ph.D. thesis limits itself to showing the feasibility and performance of state-of-the-art antenna-diversity implementations for wireless consumer products designed withthe proposed procedure. During the design process many new results have been obtainedwith respect to the relation between the bandwidth of the transmitted signals and theperformance of antenna-diversity implementations (Chapter 5).

In Europe a handset of the DECT system is often used as a replacement for the stan-dard phone with a cord. As a consequence, up to now a DECT phone is allowed to havea larger size than a mobile phone. A mobile phone is normally carried in a pocket incontrast to a cordless phone that is often placed on a table. The DECT phone has moreroom for the implementation of antenna diversity than a mobile phone. Therefore, the im-plementation of diversity in a DECT phone can be done in an easier way than in a mobilephone. The carrier frequencies of the DECT system are close to those of the UniversalMobile Telecommunications System (UMTS) [ETSI, 2000]. As a result the experienceobtained with implementing antenna-diversity in a DECT handset can be used to makesmaller implementations for the next generation mobile phones.

In this Ph.D. thesis the models and the measurement set-up are developed and testedwith the portable part of the DECT system, described in Section 2.2. The system param-eters of the DECT system will be used to illustrate all concepts and results. The modelsand measurement set-up, however, have also been used for other systems and applications,e.g. GSM, Blue-Tooth.

The diversity methods will only be considered for the receiver. Transmit-diversitysystems are only briefly discussed in this work (e.g., Section 5.6). The procedure andthe tools developed for it, however, are expected to be useful for the design of transmitantenna-diversity implementations.

1.3 Background and achievements

At the end of 1991 within the Philips Research Laboratories Eindhoven (PRLE) a projectwas initiated called Radio-Frequency Module Project. The aim of this project was toacquire the knowledge and capabilities to design Radio-Frequency (RF) modules. TheRF-module had been defined as the high-frequency part between antenna and basebandsignal-processing circuits. The high-frequency circuits are, for example, filters, mixers,oscillators, low noise amplifiers and power amplifiers. The concept of RF-modules wasnot new, this already existed in the professional and military markets. The idea of thisproject was to make RF-modules for consumer products, like portable and mobile phones.

At that time the manufacturers of consumer products designed the RF-circuits them-selves. Supplying RF-modules means that the producer does not need to have specific

1.3. Background and achievements 5

RF-design knowledge. The advantage for Philips is that the module can internally beoptimised to deliver an optimum performance with respect to cost, size and power dissi-pation. Such a module is an attractive product because of its added value. Today, in 2001,RF-modules exist, but the envisaged highly integrated RF-modules do not form a largepart of the market. A sub-part of the fully integrated RF-module, however, is sold in verylarge quantities as modules: power amplifiers for mobile phones.

At the beginning of 1992 the RF-module project focused on a wireless link at 2.5 GHzto send digital audio information from a compact disc player to a loudspeaker. The systemshould work inside a typical home. The project was called Homecast. At the same time attwo other places within Philips similar projects at other carrier frequencies, 900 MHz and5.8 GHz, were initiated. The project was officially terminated at the end of 1992 due to arearrangement of priorities within Philips, forced by the financial situation. All projects,however, resulted in working prototypes.

The different prototypes suffered from the same problem: multi-path fading. Due toreflections of the transmitted waves against (moving) objects the received signal largelyvaried as a function of time and place. These variations caused a distortion of the re-ceived signals. Within all projects, this problem was solved by putting more antennason the receiver to reduce the chance of a very low received signal power. At that timethe knowledge to design and optimise these antenna-diversity receivers was available forprofessional and military products. The characteristics of consumer products, especiallylow cost and small size, required different design and optimisation tools.

At the end of 1992 a new research project started: Philips Adaptive aCtive Minia-ture ANtennas (PACMAN). The idea was to make an adaptive antenna-diversity receiver,which has the ability to respond positively to statistical variations of the environment inwhich it operates. It was also believed that adaptive antenna-diversity receivers wouldbecome important in the future. Today, it seems that that has become true [Ephremides,2000], [Leyten and Dolmans, 2000a]:

• In 1999 Philips introduces a portable phone with antenna diversity, which has abetter performance than previous generations without antenna diversity (Section1.1).

• In 2000 the specifications of the Universal Mobile Telecommunications System(UMTS) includes multiple antennas for the handset [ETSI, 2000].

• Today, in 2001, the multi-antenna concept to combat multi-path fading is beingtransformed into the Space-Time coding concept, that makes use of multiple anten-nas and multi-path effects to increase channel capacity [Foschini, 1996].

The PACMAN project was carried out as a fundamental research project: from basicprinciples towards design tools and prototypes. In 1993 a co-operation with the Elec-tromagnetics Group of the Eindhoven University of Technology (TU/e) was set-up toprovide theoretical models for the design of adaptive diversity transceivers. In 1997 thisco-operation resulted in a Ph.D. thesis summarising the work [Dolmans, 1997b]. Thisthesis will frequently be cited due to the close relation with this work.

The work had been divided such that PRLE would take care of all practical aspects,like measurements and prototypes, the TU/e would provide theoretical models [Dolmans


and Leyten, 1999b], [Dolmans and Leyten, 1995]. This division of work would helpto protect the commercial interests of Philips in terms of patent applications and designmethods linked to state-of-the-art technology. The following patents have been granted toPhilips based on the work at PRLE:

• Two patents on the angle-scanning diversity principle and its implantation [Baltus,1998], [Baltus, 1999].

• A patent on a handset that can, by choice of the user, either optimise the quality ofthe communication link or minimise the specific absorption rate within the humanhead [Leyten, 2000].

• A patent on an antenna that is optimised for operation both close to and far awayfrom the human head or other objects [Leyten, 1998].

During the execution of the project a second application of diversity became apparent:the improvement of communication systems that were not designed to include diversity[Leyten and Dolmans, 2000a]. Inclusion of diversity results in an improvement of the linkbudget of a radio transmission system. This improvement can be in the order of 10 dB ora factor of 10. Therefore, the diversity gain can be used in several ways to make improvedproducts that are attractive for potential customers [Leyten and Dolmans, 2000a]:

• Reduction of the transmit power of a handheld, portable or mobile device, so thatits batteries will last longer (increased ’talk’ time) or can be made smaller and lessheavy.

• Increased data throughput by using the diversity gain to transmit more bits per trans-mitted symbol. In this case the existing infrastructure or network does not have tobe improved, because the diversity gain is used. This could speed up the transitionfrom the 2nd generation Global system for Mobile communication (GSM) into a2.5 generation system by using 8 Phase Shift Keying (8 PSK) with 3 bits per symbolinstead of Gaussian Minimum Shift Keying (GMSK) with 1 bit per symbol.

• Increased range of the product, e.g. to be able to use a portable phone in the back-yard or to be able to install less basestations to cover a certain area.

• Increased capacity by allowing more users within the area covered by a basestation.One way of achieving this is by using non-omnidirectional antenna patterns (at thebasestation or portable). The diversity algorithm switches between these patternsto maximise the signal-to-interference ratio.

• Improvement of the audible quality of the link, e.g. less ’clicks’ and ’mutes’.

• Increased dynamic range of the system. The maximum transmit power of the trans-mitter is normally specified, it is related to safety and interference limits. The noisefigure of modern receivers is quite low, about 4 dB. This results in an overall noisefigure of about 6 dB if antenna switch and filters are included. Lowering the noisefigure is not easy without an increase in power or cost. However, the 10 dB increasein dynamic range obtainable with diversity is more than can ever be obtained bylowering the noise figure.

1.3. Background and achievements 7

A combination of the above mentioned improvements can also be made. An example ofthis is the Philips Kala portable phone (Section 1.1).

The angle-scanning diversity receiver, described in Chapter 6, with two antennas is avery simple form of multi-antenna arrays for military and astronomy purposes [Smoldersand Haarlem, 1999]. The circuits and concepts in these different application fields show aremarkable similarity. Perhaps, the solutions and hardware developed for the large marketof communication products might find their way into high-tech multi-antenna products.At a higher level of abstraction the concepts of phased antenna arrays are also used inacoustic products in order to improve the quality of, for example, public-address andhands-free phone products. The microphones or loudspeakers of acoustic products areanalogous to the antennas of wireless products.

During a visit of a team of experts from the USA to Philips Research, the project onadvanced diversity techniques was considered to be a good example of industrial researchin this field [Ephremides, 2000]. This resulted in an invitation to present a summary ofthe work on the IEEE AP-S International Symposium and USNC/URSI National RadioScience Meeting [Leyten and Dolmans, 2000a].

This Ph.D. thesis summarises a large part of the work that has been done from 1992to 2001 at the PRLE with respect to adaptive antenna-diversity transceivers.

Chapter 2

The indoor radio channel

2.1 Introduction

In this Ph.D. thesis the application of antenna-diversity is focused on the Digital EuropeanCordless Telecommunication (DECT) system. Section 2.2 introduces the DECT systemwith its relevant details.

The antenna forms the interface to the radio channel by transforming electromagneticwaves to voltages and currents and vice versa. The relation between the electromagneticdomain and the circuit domain is elaborated in Section 2.4, in which the Thevenin circuitrepresentation of an antenna is introduced. The electromagnetic waves generated by theantenna carry the information from basestation to a portable product and vice versa. Atdifferent positions in the room the signals received by the antennas can vary significantly(fading) because of interfering reflections. Section 2.3 gives an overview and classifica-tion of fading effects.

In most communication systems the information in the form of bits or symbols ismodulated on a carrier frequency. This signal is transmitted through the radio channeltowards the receiver. Before the modulation, the symbols are shaped or filtered to reducethe harmonic content (Nyquist filtering). Popular communication systems like DECT andGSM use a Gaussian filter for this. The frequency spectrum of these systems has also aGaussian shape due to the applied modulation method. To model the time and frequencycharacteristics of these systems accurately, the Gaussian function is used in the time do-main simulations (Section 3.6.3) and as an anti-aliasing window (Section 4.4.2). Theproperties of the Gaussian function in the time and frequency domain and the Gaussianmodulated sine source are introduced in Section 2.5.

The effects of the radio channel on the transmitted symbols can be effectively mod-elled by using a lowpass representation (Section 2.6). In this representation the carrierfrequency is removed from the signal and channel descriptions. A complex envelope isintroduced to describe the transmitted and received signals.

At the receiver the reflected waves result in the reception of multiple copies of thetransmitted symbol with different arrival times. The symbol is spread over time and mightinterfere with adjacent symbols. This interference, called Inter-Symbol Interference (ISI),

9

10 Chapter 2. The indoor radio channel

can influence the Bit-Error Rate (BER) of a system.A measure of the amount of symbol spreading is delay spread (Section 2.7). The delay

spread is a wideband property of the radio channel. It can be obtained by using a channelsounder, a ray-tracing simulation method or a broadband network-analyser measurement.These methods use very short pulses to obtain the impulse response or Power Delay Pro-file (PDP) of the radio channel. The delay spread obtained with wideband pulses is calledwideband delay spread (Section 2.8). An overview of all delay-spread types defined inthis chapter is given in Table 2.2 of Section 2.12.

The results obtained with a wideband measurement set-up might not be applicableto a realistic, in most cases narrowband, communication system [Dolmans and Leyten,1999a]. For example, the antenna characteristics, like radiation and polarisation patterns,of a wideband antenna will differ from the small antennas used in hand-held devices.Preferably, a narrowband measurement set-up is devised so that available communicationcircuits and components, like power amplifiers, front-ends, filters, oscillators etc., can beused. In Section 2.9 the delay spread for narrowband pulses is derived. Its relation to thewideband delay spread is also derived.

The PDP is obtained from measurements or simulations. The PDP has therefore afinite resolution, a finite duration and a noise floor. The noise floor is caused by, forexample, the (thermal) noise present in the measurement set-up or the finite numericalaccuracy of a computer implementation of a simulation method. The wideband delayspread obtained from the PDP should be calculated such that measurement and simulationimperfections do not influence the result and such that it can be done in an efficient way(Section 2.10).

Delay spread and the amplitude variation of the received signal are important effectsthat influences the BER of a receiver. The noise floor of a receiver is fixed. When thereceived signal fluctuates due to multi-path fading, the Signal-to-Noise Ratio (SNR) willalso fluctuate. As a consequence, the BER will also fluctuate due to SNR fluctuations.The dependence of the BER on the SNR and on the delay spread is considered in Section2.11.

This chapter concludes with an overview of all obtained results and the main require-ments for a measurement set-up or a software simulator (Section 2.12.1). These require-ments are essential for obtaining relevant data for the design of antenna-diversity imple-mentations for communication systems.

2.2 Digital European Cordless Telecommunications sys-tem

The Digital European Cordless Telecommunications (DECT) system is chosen to illus-trate the principles and approaches for designing diversity algorithms for the handset.Other types of digital systems, like the Global System for Mobile communication (GSM)or Personal Handy-phone System (PHS) could also have been chosen. In this sectionthose characteristics of the DECT system are treated, that are relevant for the design of anantenna-diversity implementation. The details can be found in the system specifications[ETSI, 1992].

2.2. Digital European Cordless Telecommunications system 11

The DECT frequency band ranges from 1880 to 1900 MHz. This band is divided into10 channels with a bandwidth of 1728 kHz. The frequency of each carrier f0 is specifiedby:

f0 = 1.897344 109− n 1.728 106 Hz for n ∈ 0, 1, . . . , 9. (2.1)

The modulation form is Gaussian Frequency Shift Keying (GFSK) with a modulationindex of 0.5. This type of modulation form is also called Gaussian Minimum Shift Keying(GMSK). GMSK is also used in GSM. One of the main differences between DECT andGSM is the 3 dB bandwidth bit-time (BTb) product of the Gaussian filter, which is 0.5 forDECT. The bit duration Tb is defined as 1/br, in which br is the bit rate. The bit rate forDECT is 1152 kbit/s, which gives Tb=0.8681 µs.

Figure 2.1 shows the Power Spectral Density (PSD)∗ of one channel of the DECTsystem obtained from a computer model of the modulation method. By integration of thecurve of Figure 2.1 it is found that 99% of the energy is present in a bandwidth equal to1.04 br = 1198 kHz. This shows that the GFSK modulation of DECT has a reasonablygood spectral efficiency [Murota and Hirade, 1981].

−2 −1 0 1 2−60

−45

−30

−15

0

Offset from carrier, f−f0, (MHz)

Pow

er s

pect

ral d

ensi

ty (

dB)

Figure 2.1: Simulated power spectral density of DECT channel as a function ofthe frequency.

∗The PSD is an estimation of the frequency content of a signal based on a finite set of data. It has the propertythat its integral over the frequency band is equal to the power of the signal in that band. The PSD in this work iscalculated with Welch’s method [The MathWorks Inc., 1999].


The channel filters of many DECT receivers are Surface Acoustic Wave (SAW) filters.These filters have a filter curve that is close to an ideal rectangular filter [Samsung, 1999],[Murata, 2001]. The amount of noise power before detection is determined by the equiva-lent noise bandwidth of the channel filter [Shanmugam, 1985]. Integrating the SAW filtercurves results in an equivalent noise bandwidth Bns of about 1200 kHz, which is equal tothe 99% energy bandwidth of the DECT modulation.

The data stream between transmitter and receiver is organised in frames of 10 ms.Each frame is divided into 24 time slots of 0.417 ms. The first 12 time slots are used by thebasestation to transmit to the portables, one or more of the next 12 time slots can be usedby a portable to transmit to the basestation. For a DECT system the minimum input levelis -90 dBm for the receiver. The output level of the transmitter is 24 dBm (=250 mW).Table 2.1 summarises the characteristics of the DECT system that are relevant for thedesign of an antenna-diversity implementation.

Frequency band 1880-1900 MHz

Channel separation 1728 kHz

Equivalent noise bandwidth Bns 1200 kHz

Bit rate br 1152 kbit/s

Bit duration Tb 0.8681 µs

Frame duration T f 10 ms

Time-slot duration Ts 0.417 ms

Minimum input power level -90 dBm

Transmit power +24 dBm

Table 2.1: DECT system characteristics, that are relevant for the design of anantenna-diversity implementation.

2.3 Characterisation of fading multi-path channels

In indoor environments the main mechanisms behind electromagnetic wave propagationare absorption, reflection, diffraction and scattering by objects (like persons, walls, desks,etc.). The reflection of the waves results in a so-called multi-path environment or channel:the portable will receive the transmitted signal via different paths with different ampli-tudes and different arrival times or propagation delays. This is illustrated in Figure 2.2.At different positions in the room or at different time instances the received signals canvary significantly. This effect is called fading. Fading is the fluctuation of the amplitudeor envelope of a received signal as a function of time or distance.

Within a multi-path channel the time interval or travel distance over which the en-velope and phase of the signals varies is short; this is called small-scale fading. Themean signal strength of the signals averaged over a small area decreases with an increas-ing distance between receiver and transmitter. This effect is called large-scale fading.

2.3. Characterisation of fading multi-path channels 13

LOS

Figure 2.2: The received signal is the sum of the line-of-sight wave, specifiedby ’LOS’, and the waves reflected by walls and objects inside theroom.

Large-scale fading effects determine the area that can be covered by a basestation of acommunication system. As a consequence large-scale fading models, like the path-lossmodel of Section 3.2, are used for basestation planning. Small-scale fading effects andparameters will be considered in more detail in the next section. A special class of radio-channels, Wide-Sense Stationary Uncorrelated Scattering (WSSUS) channels, defined bythe previously introduced concepts is described in Section 2.3.2. In Section 2.3.3 it willbe demonstrated that the DECT radio-channel can be considered to be a WSSUS channelfor the transmission of symbols.

2.3.1 Classification of small-scale fading

Four different types of small-scale fading can be identified depending on the nature ofthe radio channel and the system parameters. The system parameters are the bandwidth Band the transmit duration, like symbol duration Tb, time-slot duration Ts or frame durationT f . The channel characteristics are time dispersion or frequency-selective fading due todelay spread and frequency dispersion or fast fading due to Doppler spread.

The delay spread τ is defined as the time for which the impulse response of the chan-nel is essentially non-zero. The coherence bandwidth Bc is a statistical measure of therange of frequencies over which the channel can be considered ’flat’. A flat radio channelpasses all spectral components with approximately equal gain and linear phase. Withinthe coherence bandwidth two frequency components of the channel transfer have an enve-lope or phase correlation. The coherence bandwidth is typically defined for a correlationof 0.5 and higher. The envelope and phase correlation functions can be calculated as a


function of the delay spread τ [Lee, 1982], [Jakes, 1994]. For example, an expression forthe envelope fading is [Lee, 1982]:

Bc ≈ 1

2πτ. (2.2)

The phase-correlation expression can be found elsewhere [Lee, 1982], [Jakes, 1994]. Therelation between the coherence bandwidth and the delay spread is not an exact relation;the impact of a particular radio channel on a transmitted signal must be derived frommeasurements or simulations. From the coherence bandwidth two types of small-scalefading can be identified:

• flat fading or frequency-non-selective fading: within the system bandwidth B theamplitude response is constant and the phase response is linear for the consideredradio channel, i.e. the coherence bandwidth Bc is greater than the bandwidth of thetransmitted signal B,

• time dispersion or frequency-selective fading: within the system bandwidth B theamplitude response is not constant and the phase response is non-linear for theconsidered radio channel, i.e. the coherence bandwidth Bc is smaller than the band-width of the transmitted signal B.

The Doppler spread BD is a measure of the spectral broadening caused by the timerate of change (movements) of the radio channel. It can be defined as the range of frequen-cies over which the received Doppler spectrum is essentially non-zero. BD can be relatedto the Doppler frequency fm of the maximum speed νm in the propagation environment:

fm = νm

λ0, (2.3)

BD = 2 fm, (2.4)

where λ0 is the wavelength of the carrier frequency. The coherence time is defined in asimilar way as the coherence bandwidth [Steele, 1994]. The coherence time tc is a mea-sure of the time duration over which the channel impulse response is essentially invariant.Within the coherence time two received signals have a strong potential for envelope orphase correlation. The envelope and phase correlation functions can be calculated as afunction of the coherence time. For example, an expression for the envelope fading is[Lee, 1982]:

tc ≈ 9

16π fm= 9λ0

16πνm. (2.5)

The phase-correlation expression can be found elsewhere [Lee, 1982], [Jakes, 1994]. Therelation between the coherence time and the maximum Doppler frequency is not an exactrelation; it should be derived from measurements or simulations. Based on the coherencetime two types of small-scale fading can be identified:

• slow fading: during the transmit time the gain response is constant and the phaseresponse is linear for the considered radio channel, i.e. the coherence time tc isgreater than the duration of the transmitted signal or symbol Tb,

2.3. Characterisation of fading multi-path channels 15

• frequency dispersion or fast fading: during the transmit time the gain response isnot constant and the phase response is non-linear for the considered radio channel,i.e. the coherence time tc is shorter than the duration of the transmitted signal orsymbol Tb.

Figure 2.3 summarises the classification of small-scale fading channels based on co-herence bandwidth Bc, coherence time tc, system bandwidth B and the symbol durationTb. Instead of the symbol duration also the frame or time-slot duration can be considered.The nomenclature differs from publication to publication and the classification can alsobe further refined [Steele, 1994]. Recent classifications include a third axis that is relatedto the spatial domain.

Bc

tc

B

Tb

Tb < tc

flat-flat frequency-flat

B > Bc

time-flatfrequency-

Tb < tc

non-flat

B > Bc

Tb > tc

B < Bc B < Bc

Tb > tc

flat

slow fast

selective

Figure 2.3: Small-scale fading classification based on coherence bandwidthBc, coherence time tc, system bandwidth B and the bit (symbol)duration Tb.

2.3.2 WSSUS linear time-variant channel

The general theory for linear time-variant channels is well explained in many publica-tions and textbooks, e.g. [Bello, 1963], [Proakis, 2000], [Lee, 1982], [Jakes, 1994]. Sucha channel can be modelled as a linear filter with a time-varying impulse response. In thissection a sub-class of these channels is considered: the Wide-Sense Stationary Uncorre-lated Scattering (WSSUS) channels. The two discriminating properties of these channelsare:

1. the fading statistics may be assumed approximately stationary for sufficiently longtime intervals (wide-sense stationary),

2. the channel may be approximately modelled as a continuum of uncorrelated scat-tering objects.


Frequency dispersion is not taken into account in the model. The effects of frequencydispersion are not a significant for narrowband communication systems, like DECT.

At a certain location Er the channel impulse response of a WSSUS channel hδ is writtenas the sum of Dirac impulses (e.g. [Rappaport, 1999], [Tholl, 1993]):

hδ(t, Er) =N(Er)∑

n=1

αn(Er) δ(t − td,n(Er)), (2.6)

where N(Er ) represents the number of detectable pulses at location Er and the nth pulse isdefined by its attenuation factor αn and its propagation delay td,n.

2.3.3 Classification of the indoor DECT radio-channel

The indoor radio channel for the DECT system can be classified with the DECT systemparameters given in Section 2.2 and the classification of small-scale fading of Section2.3.1. For this classification only the envelope fading will be considered. If phase fadingis also considered the classification will not be significantly different [Lee, 1982].

Previous measurements have shown that a maximum average delay spread of about100 ns can be encountered for indoor environments [Hashemi, 1993]. As a consequencethe coherence bandwidth becomes 1.6 MHz (Equation 2.2). According to Table 2.1 aDECT channel is about 1.2 MHz wide. The DECT radio channel can therefore be con-sidered neither flat nor frequency selective based on the classification of Figure 2.3.

The maximum (relative) speed due to movements of users and objects that can be ex-pected in an indoor environment is about 5 m/s (18 km/h). The wavelength correspondingto the DECT frequency band is about 0.16 m. With these values the coherence time is5.7 ms according to Equation 2.5. As a result, the fading can be considered slow for aaverage delay spread of about 100 ns and a bit duration of Tb = 0.87 µs or a time-slotduration of Ts = 0.4 ms (Table 2.1). During a frame, T f = 10 ms, the channel cannot beconsidered to be slow.

In this work the transmission of individual symbols is considered. In this case theDECT channel can be considered to be a very slowly fading or time-invariant channel.This channel is equivalent to the WSSUS channel.

2.4 Thevenin representation of antenna

The characteristics of the indoor radio channel are determined by the way the electromag-netic waves propagate through a building. These electromagnetic waves are generatedand received by antennas. Currently, in most communication systems the antenna is madefrom copper in the form of a wire, strip or patch. For these antennas the conductivityis very high and the approximation of a perfect conductor can be made. For a perfectlyconducting antenna the received voltage Vr is related to the electric field incident on theantenna EEi and the current distribution on the antenna surface W in the transmit state EJt

2.5. Time domain analysis using a Gaussian modulated sine source 17

[Dolmans and Leyten, 1995], [Dolmans, 1997b]:

Vr = −∫ ∫

W

EJt · EEi dW. (2.7)

This relation leads to the Thevenin representation of the antenna shown in Figure 2.4. Theantenna impedance Za is determined in the transmit state and is considered to be the samein the receive state.

Za

+Vr

−

Figure 2.4: Thevenin representation of an antenna.

With the aid of this equation the received voltage at the antenna terminals of mostmobile and portable communication products can be calculated. In order to do this, theincident electric field EEi must be determined from a simulation model or measurements[Dolmans and Leyten, 1995], [Dolmans, 1997a]. The received voltage can also be ob-tained from models or simulations (Chapter 3) or measurements (Chapter 4).

In the next chapters implementations with multiple antennas are considered. Themutual coupling between the antennas and between the antennas and other objects willbe neglected. This is allowed if an antenna is about a quarter wavelength separated fromother antennas or objects [van Leersum, 1995].

2.5 Time domain analysis using a Gaussian modulatedsine source

The form or envelope of the transmitted symbols in most communication systems resem-bles a Gaussian pulse. This pulse is obtained by filtering the square-wave digital signalswith a higher order low-pass Bessel filter. Modulation schemes based on this principleare called ’Gaussian’. Two examples are Gaussian Minimum Shift Keying (GMSK) usedfor the GSM system and Gaussian Frequency Shift Keying (GFSK) for the DECT system(Section 2.1). The filtered data-stream is modulated on a carrier frequency. The main lobeof the resulting high-frequency spectrum also resembles a Gaussian function (Figure 2.1).

Two additional advantages of the Gaussian shape become apparent in the analyticalevaluation of integrals involving exponential functions and in using it as window in theFourier transformation. The first advantage becomes clear in evaluating the integrals inthe expression of the delay spread when Gaussian pulses are used to characterise theradio-channel, Section 2.9. The second advantage has to do with using the Gaussianshape as a window in the Discrete Fourier transformation (DFT). A window is neededto transform the sampled frequency domain data to the time domain to obtain the power


delay profile. The Gaussian window exhibits an adjustable and relative good processingloss versus side-lobe level (Section 4.4.2).

The Gaussian shape is also used in the Finite Difference Time Domain (FDTD) analy-sis (Section 3.6.3) to prevent spurious frequencies by limiting the high frequency contentof the source.

2.5.1 Gaussian modulated sine source

The Gaussian pulse is defined by the following equation:

V (t) = A e−a2t2, (2.8)

where t is the time in s, A is the amplitude in V and a (> 0) is the pulse decay in s−1,which defines the slope of the Gaussian pulse. Its Fourier transformation

is defined as:

( f ) =

∫ ∞

−∞V (t) e− j2π f t dt . (2.9)

The Fourier transform of a Gaussian pulse

is also a Gaussian pulse:

( f ) = A

√π

ae−(π f

a

)2

, (2.10)

where f is the frequency in Hz. Figure 2.5 shows a Gaussian pulse and its Fourier trans-form.

−4 −2 0 2 40

1

Time (s)

Am

plitu

de (

V)

−1 −0.5 0 0.5 10

1

2

Frequency (Hz)

Am

plitu

de (

V)

Figure 2.5: The Gaussian pulse, left figure, and its Fourier transform, rightfigure, for A = 1 V and a = 1 s−1.

Modulating a sine source (carrier frequency) with a Gaussian pulse leads to the Gaus-sian modulated sine (Gms) source. The expression of a Gms source is obtained by multi-plying Equation 2.8 with a sine source with frequency f0:

V (t) = A e−a2t2cos(2π f0 t). (2.11)

2.5. Time domain analysis using a Gaussian modulated sine source 19

The bottom two subfigures of Figure 2.6 show the Gms source and its Fourier trans-form. As can be expected from basic Fourier theory, the frequency spectrum of the Gaus-sian pulse is shifted by the frequency of the sine source (carrier frequency), which is 5 Hzin Figure 2.6.

The power spectral density (PSD) (defined in Section 2.2) of the Gms source shownin Figure 2.6 resembles that of the main lobe of the DECT system shown in Figure 2.1.The other parts of the DECT PSD are lower than 30 dB. As a consequence, these partsdo not contribute much to the received signal. As a result the Gms source can be used inchannel sounding or simulations as an approximation of the signals of practical GFSK orGMSK communication systems.

−4 −2 0 2 4

−1

−0.5

0

0.5

1

Time (s)

Am

plitu

de (

V)

0 1 2 3 4 5 6 7−150

−100

−50

0

50

Frequency (Hz)

Pow

er s

pect

ral d

ensi

ty (

dB)

−4 −2 0 2 4

−1

−0.5

0

0.5

1

Time (s)

Am

plitu

de (

V)

0 1 2 3 4 5 6 7−150

−100

−50

0

50

Frequency (Hz)

Pow

er s

pect

ral d

ensi

ty (

dB)

Figure 2.6: The Gaussian pulse, top left, its PSD, top right, the Gms source,bottom left, and its PSD, bottom right, for A = 1 V, a = 1 s−1 andf0 = 5 Hz.

The Gms source of Equation 2.11 is not causal. Therefore, a sufficiently long delaytime td (propagation delay) is introduced to obtain a very small signal level at t = 0:

V (t) = A e−a2(t − td)2

cos(2π f0(t − td)). (2.12)


With Equation 2.9 the Fourier transform of the causal Gms source becomes:

( f ) = A

√π

2a

(

e−(π f − π f0

a

)2

+ e−(π f + π f0

a

)2 )e− j2π f td . (2.13)

The PSD of the Gms source is lower than that of the unmodulated Gaussian source (Figure2.6). By comparing Equation 2.10 with 2.13, the difference in amplitude at the carrierfrequencies− f0 and f0 is a factor of two, which is equal to 6 dB.

The simulations and measurements of the radio channel use the Gms source as theprobing signal to simulate the high frequency spectrum of a realistic communication sys-tem, like DECT. The -30 dB frequency bandwidth B30 is chosen to be equal to the band-width of the considered system. From the frequency domain expression of the Gms sourcegiven in Equation 2.13, this bandwidth can be expressed as a function of pulse decay a:

B30 = a

π

√6 ln(10) = 1.1831 a. (2.14)

In a similar way the -30 dB duration Tb,30 is chosen to be equal to a symbol (or bit)duration of the considered system. The duration of the Gaussian pulse for the -30 dBpoints can be expressed as a function of pulse decay a with Equation 2.12:

Tb,30 = 1

a

√6 ln(10) = 3.7169

a. (2.15)

The two equations show that, if the pulse decay a increases then the pulse duration willdecrease and the frequency bandwidth will increase.

2.6 Lowpass representation of transmitted and receivedbandpass signals

A real-valued signal s(t) with a frequency content concentrated in a narrow band of fre-quencies around a carrier frequency f0 can be expressed in the following form [Proakis,2000]:

s(t) = A(t) cos(2π f0t + ψ(t)), (2.16)

where A(t) denotes the amplitude and ψ(t) the phase. By expanding the cosine functionthe following expression is obtained:

s(t) = A(t) cos(ψ(t)) cos(2π f0t)− A(t) sin(ψ(t)) sin(2π f0t)

= I (t) cos(2π f0t)− Q(t) sin(2π f0t),(2.17)

where the signals I (t) and Q(t) are called the in-phase and quadrature components, re-spectively, of s(t):

I (t) = A(t) cos(ψ(t)), (2.18)

Q(t) = A(t) sin(ψ(t)). (2.19)

2.6. Lowpass representation of transmitted and received bandpass signals 21

The frequency content of the in-phase and quadrature components is concentrated atlow frequencies and, hence, these components are called lowpass signals. The definitionof the complex envelope s(t) of s(t) is based on the I and Q signals:

s(t) = A(t)e jψ(t) = I (t)+ j Q(t). (2.20)

The real-valued signal s(t) can be expressed in the complex envelope and the carrierfrequency:

s(t) = <

s(t)e j2π f0t, (2.21)

where< denotes taking the real part of a complex-valued quantity. The complex-valuedsignal s(t) is can be interpreted as a low-pass signal. Therefore, it is called the equivalentlowpass signal of s(t). The time-averaged power S of the signal s(t) is:

S = 1

2Et

|s(t)|2

, (2.22)

where Et denotes the time average and |s(t)| is the envelope, equal to A(t) of thesignal. This expression is used to obtain the average power of, for example, a transmittedsymbol. A transmitted symbol is a slowly time-varying envelope modulated on a highcarrier frequency.

In a similar way the impulse response h(t) of linear filter or system may be describedby a complex lowpass equivalent h(t):

h(t) = 2<

h(t)e j2π f0t. (2.23)

This equation is similar to Equation 2.21 except for a factor 2. The Power Delay Profile(PDP) P(t, Er ) is defined with the equivalent lowpass impulse response:

P(t, Er ) = |h(t, Er)|2. (2.24)

This PDP is measured at a specific location Er , it is therefore called the local PDP P(t, Er ).The mean PDP is obtained by averaging all the PDPs of the signals received over a smallarea:

P(t) = ErP(t, Er ), (2.25)

where Er means the ensemble average over a small area. The size of this area is deter-mined in Section 2.9.

The output of a bandpass system sout(t) to a bandpass input signal sin(t) can be ob-tained from the equivalent lowpass input signal sin(t) and the equivalent lowpass impulseresponse of the system h(t) [Proakis, 2000]:

sout(t) = <

sout(t)ej2π f0t

, (2.26)


with

sout(t) =∫ ∞

−∞h(t1)sin(t − t1) dt1. (2.27)

In this work the Gms source, defined by Equation 2.12 is the transmitted signal. Thissignal is transmitted through the radio channel defined by Equation 2.6. The equivalentlowpass channel response hg(t, Er) at location Er is:

hg(t, Er) =N(Er)∑

n=1

An(Er) e−a2(t − td,n(Er))2e− j2π f0 td,n(Er). (2.28)

This response is obtained by a convolution of Equation 2.6 and the complex (two-sided)equivalent of Equation 2.12. The amplitudes An(Er) include the attenuation factors αn(Er)of Equation 2.6 and the amplitude A of Equation 2.12. In a similar way the time delaystd,n(Er) include the delay of the Gaussian pulse td and the propagation delays of the radiochannel. The PDP of the channel response at location Er for the Gms source is obtainedfrom Equation 2.24:

Pg(t, Er) = |hg(t, Er)|2. (2.29)

2.7 Delay spread

Figure 2.7 shows an example of the received voltage as a function of time at some arbitrarychosen locations inside a simulated building. A Gms source (see for more details Section2.5) has been used for this simulation. The relation between the received electromagneticfield and the received voltage is given in Section 2.4. The signals at the locations consistof the Gaussian pulse that travelled in a straight line from the source to each observationpoint and of all the reflected Gaussian pulses that also arrive at these points.

From the figure, it is clear that the reflections inside the structure result in a deformedsignal at the receiver. This distortion, also called Inter-Symbol Interference (ISI), caninfluence the Bit-Error Rate (BER) of a system. In Section 2.7.1 the delay spread isintroduced as a measure of this distortion. The delay spread, which is a wideband prop-erty of the radio channel, can be obtained by with a channel sounder, ray-tracing methodor broadband network-analyser measurement techniques. These methods use very shortpulses, equivalent to large bandwidths, to find the PDP (impulse response) of the radiochannel. The delay spread of very wideband pulses is given in Section 2.8. The mea-surements and simulation in this work have a small bandwidth. In Section 2.9 the delayspread for narrowband pulses is derived. Its relation to the wideband delay spread is alsogiven.

2.7.1 Definition of delay spread

The radio channel at a location Er is characterised by its impulse response hδ(t, Er) givenin Equation 2.6. The impulse response is obtained by an excitation with wideband pulses.

2.7. Delay spread 23

0 50 100 150 200−0.4

−0.2

0

0.2

0.4

Rec

eive

d vo

ltage

(V

)

Time (ns)

d=0 m

0 50 100 150 200−30

−15

0

15

30

Rec

eive

d vo

ltage

(m

V)

Time (ns)

d=2.75 m

0 50 100 150 200−2

−1

0

1

2

Rec

eive

d vo

ltage

(m

V)

Time (ns)

d=4.85 m

0 50 100 150 200−100

−50

0

50

100

Rec

eive

d vo

ltage

(µV)

Time (ns)

d=10.8 m

Figure 2.7: Voltage as a function of time of the Gms source, top left, and thereceived voltage as a function of time at some arbitrary chosenlocations inside a simulated structure. The distance d to the sourceis specified in the figures. Note the different vertical scales of thefigures.

Figure 2.8 shows the envelopes of a simulated example of such an impulse response fortwo different bandwidths. Compared to Figure 2.7 the pulses are much smaller and do notoverlap.

To give a compact description of the indoor radio channel, it is convenient to extracta parameter from the PDP that gives an indication of the severity of a multi-path envi-ronment. For this the delay spread τ is introduced as the square root of the normalisedsecond central moment of the PDP [Bello, 1963]. Based on Equation 2.24 the local delayspread τ(Er) is defined as [Molisch, 1996]:

τ(Er) =

√√√√√√√√√√√√

∫ ∞

0

t −

∫ ∞

0t P(t, Er ) dt

∫ ∞

0P(t, Er ) dt

2

P(t, Er) dt

∫ ∞

0P(t, Er ) dt

. (2.30)


0 50 1000

0.1

0.2

0.3

0.4

Time (ns)R

ecei

ved

volta

ge (

V) T

p = 18.6 ns

0 50 1000

0.1

0.2

0.3

0.4

Time (ns)

Rec

eive

d vo

ltage

(V

) Tp = 3.72 ns

Figure 2.8: Envelope of a simulated impulse response obtained by excitationwith wideband pulses for two pulse duration values Tp.

In correspondence with this definition the delay spread is also referred to as the rms (root-mean-squared) delay spread. In a similar way the mean delay spread τ is defined basedon Equation 2.25:

τ =

√√√√√√√√√√√√

∫ ∞

0

t −

∫ ∞

0t P(t) dt

∫ ∞

0P(t) dt

2

P(t) dt

∫ ∞

0P(t) dt

. (2.31)

An intuitive explanation of the delay spread definition is that the pulses arriving at latetime instants will contribute the most to the delay spread. This increase of the contributionas a function of time is determined by the quadratic weight factor in the integrand ofEquations 2.30 and 2.31. This is in correspondence with the fact that these pulses willlead to ISI if the bit rate is too high. Therefore, the local and mean delay spread give anqualitative indication of the of the severity of a multi-path environment.

The equations of the delay spread do not include the propagation delay of the firstray or, in other words, the starting time of the PDP. Delay is a phenomenon for whichτ should be invariant. The propagation delay is, among other things, a function of thedistance between transmitter and receiver. In this case, τ should reflect how and not whenthe signals arrive at a certain observation point.

In this work it is assumed that the BER depends on the delay spread of the receivedsignals (Section 2.11). Typical values of the delay spread τ depend on the size and typeof building, existence or absence of a line-of-sight path, etc. [Hashemi, 1993].

The impulse response of the radio channel can be determined either with a wide-band measurement set-up, e.g. a channel sounder, or with a narrowband measurement,e.g. based on a network analyser [Tholl, 1993]. The results obtained with a widebandmeasurement set-up may not be representative for a practical, in most cases narrowband,

2.8. Power delay profile and delay spread obtained with wideband pulses 25

communication system [Dolmans and Leyten, 1999a]. For example, the antenna charac-teristics, like radiation and polarisation pattern, of a wideband antenna will differ fromthat of the small antennas used in hand-held devices. Preferably, a narrowband measure-ment set-up is used so that available communication circuits and components, like poweramplifiers, front-ends, filters, oscillators etc., can be used. The relation between widebandand narrowband measurements resulting in the wideband and narrowband delay spreadsτδ and τg will be further studied in the following sections.

2.8 Power delay profile and delay spread obtained withwideband pulses

Wideband pulses are used in simulations and measurements to obtain an approximationof the impulse response of the radio channel. For a linear time-invariant radio channel theimpulse response at a certain location Er can be written as Equation 2.6 [Rappaport, 1999],[Tholl, 1993]. Equation 2.25 defines the mean PDP of the impulse response:

Pδ(t) =N∑

n=1

A2n δ(t − td,n). (2.32)

In obtaining this expression it is assumed that the contributing pulses have constant am-plitudes and delay times in a small area. The size of this area is determined in Section2.9.

For the very wideband pulses (or Dirac impulses) the integrals in Equation 2.31 reduceto summations:

τδ =

√√√√√√√√√√

N∑

n=1

A2n

N∑

n=1

t2d,n A2

n −(

N∑

n=1

td,n A2n

)2

(N∑

n=1

A2n

)2

=

0 for N = 1

√√√√√√√√√√

N−1∑

m=1

N∑

n=m+1

(tm − tn)2 A2

m A2n

N∑

n=1

A2n

2 for N > 1.

(2.33)

The integrals have become summations due to the properties of the Dirac function. Thesevery short pulses and the associated expressions for the delay spread are encountered inmeasurements with a channel sounder or in simulations based on the ray-tracing method


(Section 3.5.1). The value of the delay spread obtained in this way is normally called thedelay spread of the radio channel. In this work it will be referred to as the wideband delayspread τδ .

2.9 Power delay profile and delay spread obtained withnarrowband pulses

Normally wideband pulses like those of Figure 2.8 are used to characterise the radiochannel. There is, however, a disadvantage of the wideband characterisation of the radiochannel. The results obtained might not be applicable to a realistic, in most cases nar-rowband, communication system. For example, the antenna characteristics, like radiationand polarisation pattern, of a wideband antenna will differ from the small and narrowbandantennas used in portable handsets. A narrowband measurement set-up can make use ofrealistic communication antennas. The PDPs of the signals of Figure 2.7 are shown inFigure 2.9. The pulses have a smaller bandwidth and, therefore, a longer time duration.In contrast to those shown in Figure 2.8, the pulses from the different propagation pathsoverlap.

0 50 100 150 200

−60

−40

−20

0

Pow

er (

dBm

)

Time (ns)

d=0 m

0 50 100 150 200−90

−70

−50

−30

−10

Pow

er (

dBm

)

Time (ns)

d=2.75 m

0 50 100 150 200−120

−100

−80

−60

−40

Pow

er (

dBm

)

Time (ns)

d=4.85 m

0 50 100 150 200−140

−120

−100

−80

−60

Pow

er (

dBm

)

Time (ns)

d=10.8 m

Figure 2.9: Power delay profiles of signals shown in Figure 2.7. The distanced to the source is specified in the figures. Note the different verticalscales of the figures.

2.9. Power delay profile and delay spread obtained with narrowband pulses 27

There are a few additional advantages of using narrowband pulses for radio-channelcharacterisation:

• Not only realistic antennas can be used but also the widely available narrowbandcomponents and circuits of commercial communication equipment.

• In this work a network analyser is used for obtaining the power delay profile. Thismethod is faster (sweep time) and has a better dynamic range if the measurementscan be done within a smaller bandwidth.

• The frequency resolution of a measurement is increased if the bandwidth is de-creased. For example, some network analysers have a maximum of 1601 frequencypoints per sweep. The alternative would be to increase the frequency resolutionby splitting the required bandwidth into several smaller bandwidths. This methodwill increase the measurement time because the network analyser has to do morefrequency sweeps.

Preventing an increase of the time needed for a measurement is important. The typicaltime needed for a measurement of the set-up described in this work (Chapter 4) is alreadyin the order of half a day.

The effect of the pulse bandwidth on the calculated delay-spread value will be anal-ysed for a Gaussian pulse shape. The analysis, however, can also be done for other pulseshapes. The PDP of a Gms source Pg(t, Er) at location Er is defined by Equations 2.28and 2.29. In contrast to the wideband pulses of Equation 2.6 the Gaussian pulses overlap,hence constructive and destructive interference between pulses will occur. For the meanPDP the impulse responses in a small area are averaged (Equation 2.25). The size of thisarea is determined at the end of this section. If the phases of the individual pulses areidentically, independently and uniformly distributed over [0, 2π] in this area, the pulsesmay be added on a power basis. In other words the constructive and destructive interfer-ence will cancel out when averaged over a small area. The assumption of the uniformphase distribution seems to be valid for an indoor multi-path environment. In such anenvironment many pulses that have travelled many wavelengths contribute to the powerdelay profile. The mean PDP obtained with a Gms Pg becomes:

Pg(t) =N∑

n=1

A2n e−2a2(t − td,n)

2. (2.34)

The mean delay spread of the Gms source is obtained by substituting Equation 2.34 inEquation 2.31. The resulting integrals can be evaluated in closed form (e.g. [Spiegel,1990]):

∫ ∞

0t Pg(t) dt = 1

2a

√π

2

N∑

n=1

td,n A2n, (2.35)

∫ ∞

0Pg(t) dt = 1

2a

√π

2

N∑

n=1

A2n, (2.36)


∫ ∞

0

t −

∫ ∞

0t Pg(t) dt

∫ ∞

0Pg(t) dt

2

Pg(t) dt

= 1

4a3

√π

2

N∑

n=1

A2n +

1

a

√π

2

N∑

n=1

t2d,n A2

n −

(N∑

n=1

td,n A2n

)2

N∑

n=1

A2n

.

(2.37)

Finally, the mean delay spread of the Gms source τg is obtained by evaluating Equation2.31 using the previous results:

τg =

12a for N = 1

√√√√√√√√√√

14a2 +

N−1∑

m=1

N∑

n=m+1

(td,m − td,n)2 A2

m A2n

N∑

n=1

A2n

2 for N > 1. (2.38)

This mean delay spread value will be referred to as mean narrowband delay spread τg .The equation shows that the mean narrowband delay τg of a single Gaussian pulse (noreflections) is equal to 1/(2a). Hereafter, this value will be called the pulse delay spreadτp:

τp = 1

2a. (2.39)

By using the definition of pulse delay spread and by comparing Equation 2.38 with Equa-tion 2.33 the following expression is obtained:

τδ =√τ 2

g − τ 2p . (2.40)

This equation gives a relationship between the mean delay spread of the radio channel τδand that of the channel excited with bandwidth-limited Gaussian pulses τg by means ofthe pulse delay spread of a Gms source τp. This relationship is a general one. The sameprocedure can be followed for a source with another envelope such as a rectangular ortriangular envelope. In the case of a rectangular envelope with amplitude A and durationTp, the pulse delay spread equals Tp/

√(12). For a triangular envelope, the pulse delay

spread is Tp/√(40).

Typical mean delay-spread values for an indoor environment are in the order of 10to 100 ns [Hashemi, 1993]. Equation 2.40 implies that for small bandwidths the meandelay spread is dominated by the pulse delay spread. Moreover, Equation 2.38 shows that


the delay spread of a single received Gaussian pulse is non-zero. This is an unexpectedresult, one would expect the delay spread to be zero in the absence of scatterers. Thissituation occurs, for example, in free space where no scatterers are present. A betterresult is obtained if the mean delay spread based on measurements or simulations withnarrowband pulses τg is corrected for the pulse delay spread τp with Equation 2.40. Dueto this correction the mean wideband delay spread τδ is obtained. By substituting Equation2.14 into 2.39 and by substituting the result in Equation 2.40 the following expression isobtained:

τδ =√τ 2

g − τ 2p =

√τ 2

g −3 ln(10)

2(πB30)2=√τ 2

g −0.35

B230

. (2.41)

This equation shows that the mean delay spread of a radio channel excited with Gaussianpulses τg , Equation 2.38, approaches that of a channel excited with wideband pulses τδ ,Equation 2.33, if the bandwidth B30 is increased.

Figure 2.10 shows the experimental verification of Equations 2.40 and 2.41 for anindoor radio channel with a centre frequency of 2.2 GHz. First the local PDPs in a planehave been obtained from measurements. Next, the local PDPs have been averaged over acircular area with a radius of 1/8 λ to obtain the mean PDP Pg(t) (Equation 2.34).

0 10 20 30 400

20

40

60

80

100

Bandwidth (MHz)

Del

ay s

prea

d (n

s)

τδ

τp

τg

Figure 2.10: Mean wideband delay spread τδ obtained from the mean narrow-band delay spread τg and pulse delay spread τp of a single Gaus-sian pulse, all as a function of the bandwidth.

The results of Figure 2.10 are derived from a non Line-Of-Sight (non-LOS) measure-ment with a bandwidth of 40 MHz. The results for the smaller bandwidths have beenobtained by changing the bandwidth of the Gaussian window before the inverse Fouriertransformation. This procedure is explained in Section 4.6. Here the results based on only


one measurement are given, but the validity of Equation 2.41 has also been verified fordata from other measurements.

Figure 2.10 shows that the mean wideband delay spread of the radio channel canbe obtained from narrowband measurements with Equation 2.41. A bandwidth of about7 MHz is sufficient to obtain the wideband delay spread value. During the measure-ments the bandwidth was limited to 40 MHz to obtain sufficient resolution at the lowerfrequencies. At 40 MHz the following values are obtained: τg = 22 ns, τp = 14 ns andτδ = 17 ns. According to Equation 2.41 the maximum measurement bandwidth shouldhave been more than 500 MHz to make τp small enough (less than 1 ns) to directly mea-sure the mean wideband delay spread (τg = τδ). Below 5 MHz the numerical accuracyand stability is limiting the accuracy. At 5 MHz, for example, τg and τp only differ 1.7%.This difference contains the information to calculate τδ with Equation 2.40. A part ofthis difference is also caused by errors, like the finite resolution and the noise floor of themeasurement equipment (Section 4.5) and the integration of the PDP.

The radius of the area over which the PDPs are averaged (Equation 2.25) has beendetermined by analysing the dependence of the mean delay spread on the radius of thisarea. Figure 2.11 shows the mean wideband delay spread τδ as a function of the radius.The curve is not smooth, because the observation points within the observation planehave a spacing of 1/16 λ. If the radius used for averaging is increased than the number ofobservation points within the area increases with integer numbers. This is also the reasonfor the small discontinuity at the beginning of the curve. First only 1 PDP falls within theaveraging area, if the radius of this area is increased suddenly 5 PDPs fall within the area.

0 0.2 0.4 0.6 0.8 10

10

20

30

40

Radius (λ)

Mea

n w

ideb

and

dela

y sp

read

(ns

)

Figure 2.11: Mean wideband delay spread τδ as a function of the radius thatdetermines the area for averaging the PDPs.

The curve shows that for a radius between approximately 0.1 λ and 0.5 λ the meanwideband delay spread has an almost constant value. For a radius larger than 0.5 λ the


delay spread starts to diverge from this value. In deriving Equation 2.34 it is assumedthat the effect of constructive and destructive interference between individual pulses iscancelled by averaging several PDPs. Figure 2.11, however, shows that the delay-spreadvalue obtained from a single PDP is close to that based on averaging many PDPs. Thereason for this is not clear and will be investigated in the future. Figure 2.11 also showsthat the delay-spread value suddenly changes when the radius is increased to about 0.6 λ.Further increasing the radius results in a delay-spread value that becomes also constant.This behaviour will also be investigated in the future.

The radius for calculating the mean PDP is chosen to be 1/8 λ. This choice is basedon the assumptions for the PDP at the beginning of this section and on the curve of Figure2.11. The averaging area is chosen to be small, such that the averaging is done for a smallnumber of PDPs. This reduces the time needed for the numerical calculations. Withinthe circular area defined by the radius with a length of 1/8 λ, 13 observation points arepresent.

The correction (Equation 2.41) is based on the mean delay spread. This means thatthe local responses of the radio channel are averaged over a small area to obtain the meanPDP (Equation 2.25). Figure 2.12 shows the mean PDP for two bandwidths: 7.5 and40 MHz. The PDPs look quite different. With Equation 2.40, however, the same value forthe mean wideband delay spread τd is obtained from both PDPs as can be seen in Figure2.10.

0 2 4 6−80

−60

−40

−20

0

Time (µs)

Nor

mal

ised

am

plitu

de (

dB)

B = 7.5 MHz

0 2 4 6−80

−60

−40

−20

0

Time (µs)

Nor

mal

ised

am

plitu

de (

dB)

B = 40 MHz

Figure 2.12: Mean power delay profile Pg(t) obtained from measurements withtwo Gaussian pulses with different bandwidths B.

With the relation derived in this section, narrowband measurements with typical com-munication antennas and other components can be converted to a meaningful quantity,the mean wideband delay spread, which is almost independent of the bandwidth of themeasurements.


2.10 Practical calculation of the delay spread

In practice the Power Delay Profile (PDP) is obtained from measurements or simulations.The PDP has therefore a finite resolution, a finite duration and a noise floor. The noisefloor is caused by the (thermal) noise present in the measurement set-up or the finitenumerical accuracy of a computer implementation of a simulation method. Based on thePDP, the delay spread is calculated. Many, about 5000 to 10000, PDPs are necessary toobtain relevant statistical information, like the mean value, the standard deviation or thecumulative distribution function. The processing of all PDPs requires a lot of computingpower in terms of CPU time and storage. Ways of relaxing the computer requirements aretherefore essential to obtain results within a reasonable amount of time. In the followingsections ways of minimising the error due to noise and ways of reducing the amount ofdata and processing are considered:

• Section 2.10.1, limitation of the duration of the PDP based on the indoor radio-channel characteristics,

• Section 2.10.2, calculation of the delay spread based on the received signal withoutdetermining the envelope,

• Section 2.10.3, calculation of the mean delay spread based on averaging the localdelay-spread values.

2.10.1 Power delay profile duration

The PDP decays as a function of time due to the decay of the contributing signals. Thesesignals decay due to the angular distribution of the power (propagation loss) and due toattenuation by objects. After a certain time delay the PDP drops below the noise leveldetermined by the measurement set-up or simulation tool. In that case the noise will bethe only contribution to the integrals in the delay spread calculation of Equation 2.30. Inthese integrals the received signals and noise are quadratically weighted with time. As aconsequence, if the PDP drops below the noise level, the noise will contribute more andmore to the delay-spread value as time increases. This will result in delay-spread valuesthat are too high. There are two ways of preventing this error:

1. setting a threshold level just above the noise level, which determines the minimumsignal level that is allowed to contribute to the delay spread [Rappaport, 1999],

2. limiting the duration of the PDP, so that the noise contribution to the delay spreadcan be neglected.

In this work the duration of the PDP is chosen as a criterion. There are two advantagesof this method. First, the time-domain numerical calculations can be stopped with theduration as a criterion. This is especially convenient in the Finite Difference Time Domain(FDTD) method, Section 3.6, which increases the duration of the PDP with a constanttime-step for each iteration. Second, the duration can be used to calculate the requiredfrequency resolution of the measurement set-up based on the reciprocity relation of theFourier transformation (Section 4.4).

2.10. Practical calculation of the delay spread 33

In this work the DECT communication system is considered. The system is designedfor communication inside houses and office buildings. The maximum separation betweena handset and the basestation is in the order of 100 m. Based on wave propagation with thespeed of light, 3 108 m/s, the travel time of the signals becomes 0.33 µs. To these traveltimes the DECT symbol duration of approximately 1 µs and the maximum expected PDPduration of about 0.5µs must be added. The expected PDP duration for indoor environ-ments can be obtained from simulations and measurements, for example, see Figure 4.5.As a consequence, the upper integration limit of the integrals in the definition of the delayspread (Equation 2.30 and 2.31) should be limited to about 2 µs for indoor environments.If the integration is continued well beyond this limit, the presence of noise will influencethe delay-spread value. The accuracy of this method has been verified with measurementsin indoor environments [Beek and Kerkhof, 1998].

2.10.2 Delay spread calculation based on received signal

The envelope of the received signal (Equation 2.24) forms the basis of the definition ofthe delay spread τ given in Equation 2.30. The signals obtained by the FDTD method(Section 3.6) contain both the envelope as well as the carrier frequency. As a consequencethe envelope should be determined from the simulated signals to calculate τ . In Figure2.13 an example is shown, in which the envelope and the modulated signal with a carrierfrequency f0 of 280 MHz are plotted.

0 25 50 75 100−250

−125

0

125

250

Time (ns)

Vol

tage

(V

)

0 25 50 75 100−250

−125

0

125

250

Time (ns)

Vol

tage

(V

)

Figure 2.13: Envelope of three Gaussian pulses, left part, and the modulatedversion with a carrier frequency of 280 MHz, right part. The pulsedecay of the pulses a is 2.5 108 s−1.

A calculation method for τ based on the received signal with the carrier frequencypresent (no filtering) is efficient. Due to the presence of the carrier frequency, however,the power of the (modulated) signal is less compared to the power of the envelope. For-tunately, the definitions of the local and mean delay spread given by Equations 2.30 and2.31, respectively, involves a normalisation on the average power of the delay profile.This normalisation results in identical delay-spread values for a calculation based on themodulated signal and that based on the envelope. For example, the numerically calculated


local narrowband delay spread τg is 21.6 ns for both curves in Figure 2.13. The is onlyvalid if the carrier frequency is not too low. In practical systems the number of periodsper pulse is in the order of 1000 or more. This number can be derived from, for example,Table 2.1). The delay spread can therefore directly be calculated from the received (mod-ulated) signals. This works only if the carrier frequency is sampled at sufficiently smallintervals. For the FDTD method the carrier frequency sampling is sufficient, because it isspecified by the Courant criterion (Section 3.6.4).

2.10.3 Mean delay spread obtained from the local delay spread

In the previous sections different delay-spread types have been introduced. An overviewis given in Table 2.2 of the last section of this Chapter (Section 2.12). In this section anew type of delay spread is introduced: the averaged delay spread τ .

The mean delay spread is obtained from averaging several PDPs over a small area(Equation 2.31). The PDPs within this area must be obtained and subsequently storedbefore the averaging can be done. Storing the PDP of every observation point results inabout 1000 real numbers per point. In experiments up to 10.000 observation points areconsidered to obtain accurate statistical results. As a consequence, the required memoryand CPU time are significant. A way of reducing both is to approximate the mean delayspread by averaging the local delay-spread values. This calculation results in the averageddelay spread τ :

τ = Er τ(Er). (2.42)

The averaged delay spread is not necessarily the same as as the mean delay spread basedon averaging the PDPs. However, it has been shown in [Molisch, 1996] that these twoquantities approach each other closely in a multi-path environment with enough contribut-ing paths. The left part of Figure 2.14 shows an example that verifies this assumption fordifferent bandwidths; the curves of the mean narrowband delay spread τg and the aver-aged delay spread τg are very close to each other. The curves are obtained following thesame procedure and for the same measurement data as those in Section 2.9. The curvesof the mean narrowband delay spread τg are therefore identical in Figures 2.10 and 2.14.The radius of the area for averaging the PDPs is chosen to be 1/8 λ (Section 2.9). Theradius of the area for averaging the local delay spread values according to Equation 2.42will be considered further below.

Based on these results, the following relationship is assumed to hold for an arbitrarybandwidth :

τg ≈ τg . (2.43)

Substituting Equation 2.43 into Equation 2.40 results in:

τδ ≈√τ 2

g − τ 2p =

√(Erτg(Er))2 − τ 2

p . (2.44)

With this relation the mean wideband delay-spread can be obtained from averaging thelocal narrowband delay spread values and then correcting for the pulse delay spread. The

2.10. Practical calculation of the delay spread 35

0 10 20 30 400

20

40

60

80

100

Bandwidth (MHz)

Del

ay s

prea

d (n

s)

τg

τg

−

0 10 20 30 400

10

20

30

40

Bandwidth (MHz)

Del

ay s

prea

d (n

s)

τδ

approximated τδ

Figure 2.14: Delay spread as a function of the bandwidth obtained from mea-surements. Left part: mean narrowband delay spread τg and aver-aged delay spread τg (Equation 2.43). Right part: associated meanwideband delay spread τδ and its approximation (Equation 2.44).

right part of Figure 2.14 shows the experimental verification of the relation. The curvesof τδ and its approximated value from Equation 2.44 are close to each other. In this casethe difference between both is about 7% for bandwidths larger than 10 MHz. For thenon-LOS measurement considered here, the root-mean-squared (rms) difference betweenτδ and its approximation is about 3.5 ns for 441 observation points. The accuracy ofthe measurement results, like the finite resolution and the noise floor of the measurementequipment (Section 4.5), will also contribute to the difference between the mean widebanddelay spread and its approximation. Again, the curves of the mean wideband delay spreadτδ in Figures 2.14 and Figure 2.10 are identical. The validity of Equation 2.44 has alsobeen verified for data from other measurements.

For the measurements and simulations of this thesis, the local delay-spread values ateach observation point are computed and stored as a single number. Averaging these localdelay-spread values will then result in the mean delay spread with Equation 2.44.

For the computation of the averaged delay spread the size of the averaging area hasto be determined (Equation 2.42). The size of this area is not necessarily the same as thatused for averaging the PDPs. This last area has been chosen to be 1/8 λ in Section 2.9. Theradius of the area for the averaged delay spread has been determined by the dependenceof the approximated mean wideband delay spread (Equation 2.44) on the radius of thisarea. This is shown in Figure 2.15 for a bandwidth of 10 MHz. The curve shows that for aradius smaller than approximately 0.2 λ and a radius larger than approximately 0.4 λ theapproximated mean delay spread has an almost stable value. The curve of Figure 2.15 isnot smooth, because the observation points within the observation plane have a spacingof 1/16 λ. If the radius used for averaging is increased than the number of observationpoints within the area increases with integer numbers.

For a radius with a length of 1/8 λ the approximated mean wideband delay-spreadvalue is very close to the mean wideband delay-spread value obtained with the procedureof Section 2.9. This length is therefore chosen for evaluating Equation 2.42. Within


0 0.2 0.4 0.6 0.8 10

10

20

30

40

Radius (λ)

App

roxi

mat

ed v

alue

(ns

)

Figure 2.15: Approximated mean wideband delay spread (Equation 2.44) as afunction of the radius that determines the area for averaging thelocal delay spread values for B30 = 10 MHz.

the circular area determined by this radius 13 observation points are present within themeasured data.

In Section 2.9 it has already been stated that the shape of the curve of Figure 2.11should be further investigated in the future. The same holds for the curve in Figure 2.15.

2.11 Bit-error rate

In this section the radio channel parameters will be related to the Bit-Error Rate (BER)of a communication system. The BER is a measure of the performance of a consideredcommunication system. The quantitative relation between radio-channel parameters andthe link performance or BER is not straightforward, although simple formulas have beenpublished, e.g. [Crohn, 1993], [Glance and Greenstein, 1983], [Chuang, 1987].

BER is a statistical measure derived from the transmission and reception of manysymbols. In this work deterministic models are used to obtain the PDP and the delayspread. In these models the radio channel is assumed to be stationary. As a consequence,at a fixed location the BER is constant. Fortunately, if the BER is averaged over a suf-ficiently large area, then the resulting BER is close the actual BER performance of thereceiver in that area [Molisch, 1996]. This approximation is valid if a large enough num-ber of multi-path components is present, such as in an indoor propagation environment.Therefore, in this Ph.D. thesis the BER will be expressed in terms of local quantities.

In Section 2.11.1 the BER of a DECT system will be given as a function of the signal-to-noise ratio and the wideband delay spread. This relation is a good approximation of

2.11. Bit-error rate 37

the behaviour of a ’typical’ DECT receiver in a multi-path environment. In Section 2.11.1the BER is made explicit by including the relevant DECT system parameters in the BERexpression.

If a more accurate analysis of a communication system is needed, the simulated ormeasured power delay profiles can be fed to a behavioural model of the receiver. Thisanalysis, however, is beyond the scope of this work. Figure 2.16 illustrates the differencesbetween the two approaches.

behaviouralmodel ofreceiver

(BER)extract

Sr (Er)calculate

t

power delay profile at Er

τδ(Er)

Pr (Er) Bit-Error Rate

Figure 2.16: Two methods for obtaining the Bit-Error Rate (BER) of a receiverat a certain location Er in a multi-path environment. The top methodis based on a behavioural model of the receiver. The bottom methodis based on an approximate relation between the BER and two pa-rameters extracted from the power delay profile, Sr and τδ .

2.11.1 Bit-error rate as a function of radio channel parameters

The BER is a complicated function of the received signals. It depends on the signalstrength and the distribution of the signals strength over time. The DECT communicationsystem needs a BER in the order of 10−3 for correct operation. For such a BER valuethe error correction implemented in the receiver can cope with the errors in such a waythat the perceived communication quality is still close to perfect. For higher BER val-ues the communication quality deteriorates rapidly; the system starts to mute which isexperienced as ’clicks’ by the user.

The relation between BER and radio channel parameters , like received signal strengthand delay spread, is different for every type of receiver. Moreover, the BER dependson a large number of parameters or even the complete PDP of the received signals. Inthis work the BER will be assumed to depend on two parameters derived from the PDP.The following two propagation effects that contribute to the BER of a system will beconsidered in this work [Jakes, 1994]:

1. errors due to envelope fading denoted as BERs/n,

2. errors caused by delay spread denoted as BERτ .


The total BER can be approximated by adding the BERs of the two propagation mecha-nisms [Jakes, 1994]:

BER = BERs/n + BERτ . (2.45)

This model assumes that the total BER behaviour of a receiver can be decomposed intothese two separate contributions.

The symbol time of a DECT symbol is much shorter than the coherence time of theradio channel (Section 2.3.3). It will be assumed that the phase shift of the signal can beestimated from the received signal without error. This corresponds to an ideal coherentdetection of the received signal. As a consequence the BER due to phase variations (ran-dom FM) is zero. Expressions for the contribution of the phase variations to the BER canbe derived for communication systems or propagation environments for which the phasevariations cannot be neglected [Proakis, 2000].

The DECT system uses a (GFSK) modulation (Section 2.2). The approximate BERonly due to envelope fading and thermal noise is given as [Wittneben and Kaltenschnee,1994] [Shanmugam, 1985]:

BERs/n(Er) = 1

2e−(

Sr (Er)2 Sns

)

, (2.46)

in which Sr (Er) is the received time-averaged signal power at position Er and Sns is thetime-averaged thermal noise power. The received signal power is a function of the fadingcharacteristics of the propagation environment. Figure 2.17 shows the BER as a functionof the Signal-to-Noise Ratio (SNR). The noise figure of the system is not taken into ac-count in the equations. For a non-ideal system the SNR at the antenna terminals mustbe increased with the noise figure to obtain the same BER as an ideal, noise free, system[Shanmugam, 1985]. The DECT system requires a BER of 10−3 or less. Figure 2.17shows that this requirement is achieved by a SNR of approximately 11 dB.

An adaptive diversity receiver, e.g., as described in Chapter 6, minimises the BER byreacting to the locally received signals. The performance of such a receiver, especially theirreducible BER, is closely linked to the local delay spread τδ(Er) [Molisch, 1996] definedin Equation 2.30. The relation between SNR and BER in the form of Equation 2.46 iswidely accepted. The relation between the BER and the delay spread is less obvious. Inthis work it will be assumed that the BER caused by the wideband delay spread for aDECT system is a function of the normalised delay spread τδ(Er)/Tb,30: [Crohn, 1993]:

BERτ (Er) = 1

2

(τδ(Er)Tb,30

)2

, (2.47)

where τδ(Er) is the local wideband delay spread defined by Equation 2.30 and Tb,30 is the-30 dB pulse duration or bit time. The validity of this equation is only established for asmall range of normalised delay-spread values; from approximately 0.01 up to 0.3 [Crohn,1993] [Glance and Greenstein, 1983] [Chuang, 1987]. Efforts to extend the validity of theequation are based on inclusion of the shape of the pulse and of the PDP in the normalisa-tion of the delay spread [Garber and Pursley, 1988]. The validity range of Equation 2.47

2.11. Bit-error rate 39

−10 −5 0 5 10 15 2010

−6

10−5

10−4

10−3

10−2

10−1

100

Signal to noise ratio (dB)

Bit−

erro

r ra

te

Figure 2.17: Bit-error rate as a function of signal-to-noise ratio, Equation 2.46.

expressed in BER is from 5 10−5 to 4.5 10−2. A typical DECT system can handle a BERup to 10−3. Above this limit the system does not work properly and the audio output willbe muted. Therefore, Equation 2.47 suffices to analyse the proper operation of a DECTsystem if the limit is set to 10−3.

With the obtained expressions for BERs/n, BERτ , the total BER can be written as(Equation 2.45):

BER(Er) = BERs/n(Er)+ BERτ (Er)

= 1

2e−(

Sr (Er)2 Sns

)

+ 1

2

(τδ(Er)Tb,30

)2

.

(2.48)

In Figure 2.18 the BER as a function of delay spread is plotted for five different valuesof the SNR. As the delay spread decreases the BER approaches a constant value, whichdepends on the SNR. If the delay spread dominates the BER then the resulting errorsare called irreducible errors. Irreducible errors can not be avoided by increasing thetransmitted power. The reflections that cause the delay spread do not depend on this, theydepend on the propagation environment (walls, closets, people, etc.). The SNR valueshave been chosen such that the associated BER values are round figures (10−5, 10−4, ...).The DECT system needs a BER of 10−3 or less, which is achieved for an SNR larger thanabout 11 dB and a delay spread value smaller than about 39 ns.

The measurements and simulation in this work are done with Gaussian pulses with alimited bandwidth. Before using Equation 2.47, the previously derived relations between


100

101

102

103

10−6

10−5

10−4

10−3

10−2

10−1

100

Delay spread τδ (ns)

Bit−

erro

r ra

te

5.1 dB

8.9 dB

11 dB

12 dB

13 dB

Figure 2.18: Bit-error rate for five different values of the signal-to-noise ratio,specified above each curve, as a function of delay spread τδ/Tb,30.

the delay spread τg of a bandwidth-limited system and τδ of the radio channel, Equations2.40 or 2.44, are used.

2.12 Conclusions

In this chapter the main characteristics of Digital European Cordless Telecommunication(DECT) system are introduced (Section 2.2). The DECT system is mainly used in indoorenvironments. The indoor environment is characterised by the nature of the small-scalefading of the received signals (Section 2.3). The DECT indoor channel can be classifiedas a Wide-Sense Stationary Uncorrelated Scattering (WSSUS) channel (Section 2.3.2).

To model the time and frequency characteristics of the DECT system, the Gaussianmodulated sine source is introduced in Section 2.5. The Gaussian function is also usedin time domain simulations (Section 3.6.3) and as an anti-aliasing window before thediscrete Fourier transformation (Section 4.4.2).

In this work the delay spread is used as a measure of the amount of symbol spreadingdue to reflections (Section 2.7). In several sections different delay-spread types are intro-duced. Table 2.2 gives an overview of all the delay-spread types, their symbols and how

2.12. Conclusions 41

they are obtained. Normally, the delay spread is interpreted as a wideband property of theradio channel based on the impulse response. In this work, this delay spread is thereforecalled wideband delay spread τδ (Section 2.8). In Section 2.9 the delay spread for narrow-band pulses τg is derived. Its relation to the wideband delay spread is also derived. Themeasurement set-up in this work is a narrowband set-up (Chapter 4). The derived relationis used to obtain the wideband delay spread from the narrowband measurement results.The advantage of a narrowband measurement set-up is that available and realistic com-munication circuits and components, like power amplifiers, front-ends, filters, oscillatorsetc., can be used.

Type Symbol Obtained from

local τ(Er) local PDP P(t, Er) (Equation 2.30)

mean τ mean PDP P(t) = Er P(t, Er) (Equation 2.31)

pulse τg single (Gaussian) pulse (Section 2.9)

wideband τδ(Er), τδ wideband radio-channel response (Section 2.8)

narrowband τg(Er), τg narrowband radio-channel response (Section 2.9)

averaged τδ, τg averaged local narrowband delay spread,

Er τδ(Er), Erτg(Er) (Section 2.10.3)

Table 2.2: Overview of different delay-spread types, their symbols and howthey are obtained. The wideband and narrowband delay spreadcan both be local quantities, τδ(Er) and τg(Er), respectively, or meanquantities obtained from the mean PDP, τδ and τg, respectively.The averaged delay spread can be obtained from averaging thelocal narrowband or the local wideband delay spread, τδ or τg ,respectively.

For the derivation of the relation between the narrowband and wideband delay spreadmeasurement results are used. The processing of these results supports two importantassumptions of the indoor radio channel: the phase distribution is uniform in a smallarea and the amplitude of the contributing pulses is constant in the same area. Theseassumptions are quite often used in publications, e.g., [Molisch, 1996] and [Rappaport,1999], in which these are derived from a reasoning based on physical grounds. In thiswork, quantitative results are obtained that support this reasoning. Moreover, a beginninghas been made to analyse the size of the circular area for which the phase distribution canbe considered uniform. The radius of this area is chosen to be 1/8 λ in this work. However,more research is needed to explain the behaviour of the delay spread as a function of thisradius (Figures 2.11 and 2.15).

The Power Delay Profile (PDP) gives the envelope of the received signal power as afunction of time. It forms the basis of many results within this work. In Section 2.10 apractical method is presented to obtain the wideband delay spread from the PDP. The PDPis terminated within the delay spread calculations after about 2 µs to prevent noise from


contributing the delay spread value and to speed up simulations. It is also shown that theenvelope does not have to be determined; the delay spread can also be obtained from thereceived signal with the carrier frequency still present.

In Section 2.10.3 it is demonstrated that the wideband delay spread can be obtainedfrom averaging the local narrowband delay-spread values and then correcting for the pulsedelay spread. This relation is convenient, because in some measurement set-ups andsimulation tools it is convenient to compute the local delay spread at the observation pointand to store this as a single number. The alternative would be to store a certain amount ofPDPs and then to compute the mean delay spread by averaging these PDPs. This wouldresult in more CPU time usage and higher memory requirements.

Finally, two parameters are introduced to assess the performance of a diversity imple-mentation: the delay spread and the Signal-to-Noise Ratio (SNR). The dependence of theBit-Error Rate (BER) on SNR and delay spread is given in Section 2.11.1.

2.12.1 Requirements for measurements and simulation methods

Based on the results presented in this chapter the main requirements for a measurementset-up or a software simulator can be defined in order to obtain relevant data for the designof smart antennas for communication systems. These requirements will be used to choosea simulation method, Chapter 3, and to devise a measurement set-up, Chapter 4. The mostimportant requirements are treated in detail below, they are summarised in Table 2.3.

Spatial resolution In Equation 2.7 of Section 2.4 the received voltage is given as anintegration of the antenna current distribution and the incident electric field over the an-tenna surface. The antennas in portable communication products are mostly wire or patchantennas with a length from about λ/4 to λ/2. To calculate the received voltage of theseantennas with Equation 2.7 a sufficient number of field points across the length of theantenna is necessary. In practice this means that the incident electric field must be knownwith intervals of about λ/10 (1.6 cm for DECT). The spatial resolution of about λ/10also suffices for the analysis of diversity systems, in which antennas are placed at shortdistances, e.g., (λ/4 to λ/2), from each other.

Duration Section 2.10 gives a required PDP duration of 2 µs for a DECT system in anindoor propagation environment.

Time resolution The time resolution should be sufficient for describing the power delayprofile (PDP). Similar to the spatial resolution, considered above, about 5 points per bitduration is sufficient. This is equivalent to about 10 points for one period of the Nyquistfrequency. If the carrier frequency, f0, of the received signal is present in the calculationof the delay spread (Section 2.10.2), then the resolution should be 10 points per period.For DECT the minimum resolution should be about 0.17 µs for the PDP and about 50 psfor the received signal with carrier.


Measurement speed The radio channel is time-varying due to movement of the re-ceiver or transmitter and due to movement of objects, like persons and cars. The mea-surement time should be smaller than the coherence time of the channel to keep track ofthe changes. In this work the measurements and simulations are done for a time-invariantradio channel. This has been achieved by measuring in environments without fast mov-ing objects and by keeping the antennas stationary during each measurement (Chapter 4).The simulations did not include any movement or time variation of the radio channel.

The movement of the user and of objects (mainly people) through the propagationenvironment is simulated by going (with the desired speed) through the data obtained atdifferent observation points. The assumption is that the results obtained for time-varyingradio channel are similar to those obtained by moving through a time-invariant channel.In section 4.1 this topic is elaborated in more detail for the measurement set-up used inthis work. The total measurement speed is determined by the measurement equipmentavailable.

Item General DECT

Spatial resolution ≤ λ/10 ≤ 1.6 cm

PDP duration – ≈ 2µs

Time resolution PDP ≤ 0.2 Tb ≤ 0.17µs

Time resolution signal ≤ 0.1 / f0 ≤ 50 ps

Measurement speed – –

Table 2.3: Requirements for a measurement set-up or computer simulationmodel in general terms and elaborated for the DECT system.

Chapter 3

Radio channel modelling

3.1 Introduction

The characteristics of the indoor propagation environment vary as a function of time dueto movement of people and objects, like computer monitors, keyboards, drawers, etc bypeople. This means that a experiment done a few days ago will have a different out-come than a recently done experiment. The inability to get detailed reproducible resultsfrom experiments is the main reason for developing a radio channel simulator based onfundamental (Maxwell’s) equations [Dolmans and Leyten, 1995], [Leyten and Dolmans,2000a]. A good simulator can also be used to test new ideas in an early stage, beforeimplementing them and testing them in practice.

The interaction between the electromagnetic fields and the antenna results in a signal-to-noise ratio at the terminals of the antenna, which greatly determines the performanceof the complete system. The details of this field interaction can not be studied with statis-tical experimental data. However, with a statistical analysis of diversity systems, generalquantities, like diversity gain and array gain, can be obtained [Lee, 1971], [Lee, 1972].

Models based on stochastic methods give the received signal variation at a certainlocation in the form of a probability density function (Section 3.3). These models are notcomplete; the mean received signal strength is not known. A path-loss model (Section3.2) can be used to predict the mean received signal strength. The combination of astochastic model with a path-loss model will give the received signal strength for a certaintype of antenna in a certain type of propagation environment (office, house, etc.). If theperformance of a system with other antennas or in other propagation environments is tobe studied, new measurements will be needed to obtain relevant statistical data.

Deterministic models do not have the limitations of the statistical and path-loss mod-els, but they are either very complex or require substantial computer resources even forsimple configurations. Deterministic models based on analytical methods are often lim-ited to only a few configurations (Section 3.4). The main advantage is that they are exactand results with high accuracies can easily be obtained. Analytical models are ideal tobenchmark the results of deterministic models based on numerical methods, like thosedescribed in Sections 3.5 and 3.6. For these numerical models it is difficult to obtain

45

46 Chapter 3. Radio channel modelling

an estimate of the accuracy of the result. The accuracy of the result is a function of themethod, the (cumulative) numerical errors and the uncertainties in the electromagneticproperties (dielectric constant) of the materials of the considered geometry. In order to re-duce the computational resources or to obtain a better resolution, analytical and numericalmethods are sometimes combined [Hosea, 1997], [Cerri, 1998], [Mangoud, 2000].

The ray-tracing method (Section 3.5), and the Finite Difference Time Domain (FDTD)method (Section 3.6) will only be applied to two-dimensional (2D) structures with cylin-drical wave propagation. However both are capable of modelling three-dimensional (3D)geometries. The advantage of simulating 2D structures is that relatively quick (in terms ofCPU time) results can be obtained for large structures. Moreover, several publications in-dicate that a 2D model suffices for indoor wave propagation modelling [Talbi and Delisle,1996], [Lauer, 1994]. This is further explained in Section 3.7.

This chapter ends with an overview of the features of the introduced propagation mod-els in Section 3.9. From this overview it is concluded that only the ray-tracing methodand the FDTD method are suitable for this work. In the same section a specific ver-sion of a ray-tracing model, the Installation Assistant [Cattell and van Dam, 1996], iscompared with an specific implementation of a higher-order FDTD method [Dolmans,1997a], [Dolmans, 1997b]. As a result from this comparison the FDTD version is chosenas the simulation tool for this work.

3.2 Path-loss models

Path-loss models are deterministic models that give the mean attenuation of the transmit-ted power as a function of position. Their application is straightforward. With a path-lossmodel the maximum allowable separation between transmitter and receiver is calculatedfor a specified transmit power and for a specified receiver sensitivity. The path-loss mod-els are frequently used to determine the cell size for portable and mobile communicationsystems.

Path-loss models predict the mean path attenuation. Statistical fluctuations aroundthe mean value as a function of time or location are not included. These fluctuationscan be obtained by measurements or by, for example, the statistical models of Section3.3. The local field-strength variations can be added to a path-loss model to obtain aprediction model incorporating all fading effects. In this section a well-known path-lossmodel for radio wave propagation is presented based on the radio transmission equation(also referred to as Friis transmission formula) [Rappaport, 1999], [Collin, 1985]. Thepath-loss model assumes a homogeneous radio path. The path-loss model presented inthis section is not unique; many other models are summarised in [Rappaport, 1999].

Figure 3.1 shows a receiving and transmitting antenna in free space. The relevant vari-ables are also specified in this figure. The relation between input power St and receivedpower Sr is given by the radio transmission equation:

Sr (r) = Stλ2

16π2r2gr(θr , φr ) gt(θt , φt ), (3.1)

where gr(θr , φr ) and gt(θt , φt) are the gains as a function of spherical angles (θr , φr )

3.2. Path-loss models 47

and (θt , φt), respectively, and of the receive and transmit antenna, respectively, r is thedistance between the centres of the antennas and λ is the wavelength. The sphericalangles (θr , φr ) and (θt , φt ) are defined with respect to a right-hand cartesian co-ordinatesystem with the centres of the antennas as origins. The gain of an antenna is defined asthe product of the efficiency times the directivity. The directivity is the electromagneticradiation (or sensitivity in the receive state) of the antenna as a function of spherical angle.The efficiency includes the effects of the polarisation mismatch between the antennas andthat of the reflection coefficients, 0r and 0t in Figure 3.1, between feed-line and thereceive and transmit antenna, respectively. For most mobile communication systems theefficiency of the antenna itself is high, as a consequence the gain is almost equal to thedirectivity.

Prθr , φr

θt , φt0t

0r

r

Pt

gt

gr

Figure 3.1: Transmission and reception.

The antenna gains gr and gt are defined for the far-field (or far-zone field) of bothantennas. As a result, the radio transmission equation may only be applied for antennaseparations that are large enough to guarantee that both antennas are in each others far-field zone.

The inverse exponent-law transmission-loss model is based on the radio transmissionequation (Equation 3.1) and the observation that the received signal power Sr can be fittedto an inverse exponent law as a function of the antenna separation r :

Sr (r) = Sr0

(r

r0

)−ρ, (3.2)

where Sr0 is a scaling factor defined as the power at r = r0. This factor depends on thetransmitted power, frequency, antenna heights and gains, antenna matching, etc. Path-loss is in this model proportional to r−ρ , where the loss factor ρ depends on the environ-ment. In indoor propagation environments a loss factor between 1.81 and 5.22 is reported,[Hashemi, 1993]. A number of investigators have used this model, because of its simplic-ity and its previous successful application to the mobile channel. The transmission-lossequation is mostly expressed in logarithmic form:

Sr (r) = Sr0 − 10 ρ log

(r

r0

)dBm, (3.3)


where Sr and Sr0 are expressed in dBm. The transmission loss L tr is defined as:

L tr (r) = 10 ρ log

(r

r0

)dB, (3.4)

where the antenna separation r is now equivalent to the distance.The transmission-loss model assumes a homogeneous propagation path. To charac-

terise the indoor propagation path with a single quantity like the loss factor ρ, there mustbe a sufficient number of walls, floors and obstacles along the path. During the Homecastproject [Stiphout, 1992] loss factor measurements were carried out at 2.5 GHz in resi-dential houses and at the Philips Research Laboratories in Eindhoven. The overall lossfactors were between 2.6 and 4.2.

It is not difficult to make a better prediction of transmission loss based on the radiotransmission equation (Equation 3.1). One of the most often used methods is to measurethe loss factor ρ and the wall attenuation in each room of a house or office. Then thetransmission-loss formula, Equation 3.4 is used within each room and discrete attenuationjumps between two rooms are introduced to account for the wall attenuation. This resultsin a partitioned transmission-loss model.

3.3 Statistical propagation models

In the previous section path-loss models have been reviewed. Path-loss models predictthe propagation loss between transmitter and receiver as a function of distance betweenthem. Local field-strength variations are not included in path-loss models. Models basedon statistical methods can be used to predict these local field strength variations. Thecombination of a path-loss model and a statistical model results in a propagation modelincorporating all fading effects.

Statistic methods are used to draw general conclusions from a large amount of data.These data are usually obtained by radio-channel measurements at a large number of po-sitions. By using statistic methods various properties of the channel can be described,like the probability density functions of received power and angle of arrival. Care mustbe taken not to apply the obtained statistical results to propagation environments or toantennas that are different from those used to generate the dataset. In most cases the prop-agation environment for which the probability density function is determined is specified,but the antennas used are mostly omitted. This can lead to erroneous results because thepolarisation properties, the size and the orientation of the antenna are important factors.As a consequence, the applicability of statistical models is limited.

Statistical methods can be used to derive some global quantities, like the mean re-ceived signal improvement (diversity gain), for a system with more than one antenna anda combining network [Lee, 1972], [Lee, 1971]. The improvement with respect to otherparameters, like delay spread or mean received signal power (array gain), can not easilybe derived. In that case, deterministic methods, like the ray-tracing method of Section 3.5or the FDTD method of Section 3.6 can be used.

The two most popular statistical fading distributions are the Rayleigh fading distri-bution and the Ricean fading distribution. These fading distributions are used to model

3.4. Analytical propagation models 49

the received signal fluctuations for a communication system in a certain environment.The relevant parameters of the probability density functions have to be obtained frommeasurements or deterministic models. The Rayleigh distribution is commonly used todescribe the statistical small-scale rapid time-varying nature of the envelope of the re-ceived signal in the absence of a strong received component (non line-of-sight situations).Its limitations, however, should be kept in mind:’The Rayleigh distribution is widely used to describe multi-path fading because of itselegant theoretical explanation and occasional empirical justifications’ [Hashemi, 1993].

The Rayleigh distribution can be derived from the envelope of the sum of two inde-pendent Gaussian noise signals. The Rayleigh fading distribution can be used to assessthe performance of a diversity system on a statistical basis. The common approach is tocalculate a new distribution function based on the considered diversity method and on aRayleigh distribution for each antenna, e.g., [Rappaport, 1999]. Depending on the an-tenna separation the correlation between the two signal distributions must be taken intoaccount, otherwise erroneous predictions could be made.

In the presence of a dominant stationary (non-fading) signal component (line-of-sight)the small-scale fading envelope obeys the Ricean fading distribution. For a very smalldominant signal component the Ricean distribution becomes the Rayleigh distribution.If a strong dominant signal component is present, then the Ricean probability densityfunction becomes a Gaussian probability density function.

3.4 Analytical propagation models

Analysing indoor environments based on analytical methods is complicated. The geom-etry of the structure has to be modelled with analytical expressions. This limits the com-plexity of the structures that can be modelled. However, once an analytical expression isobtained for a simple geometry it can be used for benchmarking numerical models.

The objective of the harmonic model presented in this section is to describe the signalfluctuations caused by local multi-path features that would occur in a single, highly reflec-tive, room. This results in a prediction of the local signal amplitude caused by constructiveand destructive interference. The harmonic model is based on the Green’s function tech-nique [Dolmans, 1997b]. A Green’s function describes the response of a configurationcaused by a unit-source excitation. A realistic antenna can be described by combinationof these unit sources. The electromagnetic field of an antenna can be found by integratingGreen’s function and the antenna current distribution over the surface of the antenna. Acomplete description of this analytical method can be found in [Dolmans, 1997b].

The Green’s function is found by using a harmonic analysis of highly reflective rooms.The configurations considered are shown in Figure 3.2. The method is not very flexible,the possible room configurations are restricted and the rooms can only contain one or twodielectric layers. However, it is possible to combine this method with other numerical oranalytical methods to model more complex configurations [Hosea, 1997]. Care must betaken that the numerical and analytic effort for combining these two methods is not morethan that of a complete (brute force) numerical method like the FDTD method (Section3.6).


dielectric material:

source:

Figure 3.2: Room configurations of the harmonic model [Dolmans, 1997b].One room with two (lossy) dielectric walls, top left, two roomsseparated by one (lossy) dielectric wall and, top right, room and(infinitely) long corridor separated by one (lossy) dielectric wall,bottom. The outside of the room is perfectly conducting.

Despite the limitations of the analytical models, they can be used as benchmarks fornumerical methods. With the harmonic model it is easy to obtain highly accurate fieldpredictions that can be used to verify the numerical results. For this purpose an estimateof the truncation error of the harmonic models is determined [Dolmans, 1997b].

3.5 Ray-tracing propagation models

A known electromagnetic field can be described by an expansion into plane waves withFourier theory [Stratton, 1941]. Finding an unknown electromagnetic field distributionwith a ray expansion technique is more difficult. In such a technique all the rays launchedby the source that contribute to the field in a certain point in space, should be found. Thisis difficult due to the diffraction property of electromagnetic fields. This property leads tonew diffracted rays. The ray-tracing method is illustrated in Figure 3.3. The strength andphase of these new rays depend on the curvature and surface properties of objects.

3.5. Ray-tracing propagation models 51

ray

raysdiffracted

source

reflected

object

Figure 3.3: Ray-tracing method.

In order to make a complete description of the fields with rays the generation ofdiffracted rays has also to be included in the model. This is particularly important forthe indoor environment in which objects are comparable to the wavelength of cordlessand cellular communication systems [Remley, 1998]. Taking into account a complete setof rays takes up too much computer resources and is too difficult to implement for arbi-trarily shaped objects. Therefore, in most cases the generation of additional rays is basedon approximate models of diffraction, in which a predetermined set of rays is generatedfor a limited set of obstacle shapes. A numerical method based on an algorithm that au-tomatically copes with diffraction of electromagnetic fields is the finite difference timedomain (FDTD) method (Section 3.6).

The ray-tracing propagation model presented further down does not include diffrac-tion effects. This is a first-order approximation in which the evolution of the rays isgoverned by the basic optical laws of reflection and refraction. Therefore, this methodis sometimes called the ray-optics method. Propagation models based on the ray-tracingalgorithm are deterministic and are reasonably fast.

3.5.1 Ray-tracing algorithm

In many textbooks the ray-tracing algorithm is very well explained. Here, the algorithmimplemented in the DECT Installation Assistant [Cattell and van Dam, 1996] is brieflyexplained. The following steps are illustrated in Figure 3.4.


reflected ray

ray:

cell

initial ray

internal ray

initial ray

grid: object: source:

Figure 3.4: Illustration of the ray-tracing algorithm for two initial rays.

1. The propagation environment is specified by defining the walls of the rooms andthe building and the objects inside. The (in this example two-dimensional) world ismapped onto a grid, consisting of cells of a convenient size.

2. Rays are launched from the source (transmitter) and the extent of travel is deter-mined by finding the nearest object intersected. If no object is found, the ray isconsidered to be terminated at the edge of the grid. Once the end of the ray hasbeen found then its contribution to each intersected cell within the grid is noted.Rays are generated for the full 360 around the transmitter. During propagationthrough the grid the intensity of the ray decreases in the same way as electromag-netic waves in free space.

3. If the ray does intersect with an object then it spawns two rays, the internal ray andthe reflected ray. These rays are dealt with in exactly the same manner as the initialrays. Before reflected and internal rays are generated, they are checked against theuser-specified threshold. If the intensity is less than the threshold, the ray will notbe spawned. As a consequence, propagation is not carried on indefinitely.

4. The contributions of all rays to a certain cell are used to calculate the field intensityand the delay spread inside the considered cell.

3.6. Finite Difference Time Domain (FDTD) propagation model 53

In this Ph.D. thesis the ray-tracing method will be compared with a two-dimensionalimplementation of the FDTD method (Section 3.8). As a consequence a two-dimensionalimplementation of the DECT Installation Assistant has been used.

In some implementations of the ray-tracing algorithm the amplitude and phase ofthe rays are constant within each cell. For the analysis of small diversity systems, thereceived signal must be known for antenna separations of less than a wavelength. As aresult the cells must have similar dimensions. Depending on the implementation of thealgorithm, the computer resources (CPU time and memory) for small cell-sizes could beconsiderable. For large geometries, like buildings or cities, the cell size is often largerthan one metre.

In the DECT Installation Assistant the pulses have zero width. Calculations are basedon summing rays that enter a cell with arrival times equivalent to the travelled distance.The implementation of the time delay spread calculation τδ in the ray-tracing algorithm isstraightforward by using Equation 2.33. The propagation delays td,n and the amplitudesAn are easily obtained from the simulation results. Calculations are done for each cell inthe form of post processing on the simulation results.

3.6 Finite Difference Time Domain (FDTD) propagationmodel

The Finite Difference Time Domain (FDTD) method can be seen as a direct numericalimplementation of Maxwell’s differential equations by approximating them by finite dif-ferences. The FDTD method was first proposed in 1966 [Yee, 1966]. Since then, manyscientists have contributed to the method by making it more efficient and accurate. Thishas resulted in numerous papers in many journals.

With the FDTD method, the temporal evolution of the electromagnetic field is cal-culated within a region of space by stepping through time. At each time step, the finitedifference approximations of Maxwell’s equations are used to calculate the evolution ofthe field components on a lattice of points (Yee cell) with the field components of previoussteps at nearby points (leap-frog scheme) [Kunz and Luebbers, 1993].

The standard first-order FDTD method is computationally intensive. The efficiencyof the FDTD method can be greatly increased by using higher-order schemes [Dolmans,1997a], [Dolmans, 1997b]. Then, a second/fourth-order (2,4) FDTD scheme can be usedwith the Berenger’s Perfectly Matched Layer (PML) technique to truncate the solutionmesh [Dolmans, 1997b]. The order of the FDTD scheme is denoted like (m, n), where mis the order of accuracy in time and n that in space. These numbers denote the order ofthe truncation error of the time or space approximation.

Turning on a source in the FDTD algorithm must be done smoothly with a ramp-up,otherwise the sudden change in source strength will introduce high-frequency componentsfor which the cell size is too large. This will result in incorrect field strength predictions.The source ramp-up is introduced in Section 3.6.1. The effect of source ramp-up onspurious frequency components is analysed in Section 3.6.2. This work has been donealready in 1997 [Leyten and Massey, 1997] [Dolmans, 1997a]. Later on a more in depthanalysis has been done based on sampling theory [Gurel and Oguz, 2000].


In Section 3.6.3 a Gaussian modulated sine source is introduced and implemented intothe FDTD algorithm. This source enables the simulation of Gaussian pulse propagation inmulti-path environments. From these simulations the time delay spread can be extracted,Section 3.6.4.

3.6.1 Source ramp-up for frequency domain analysis

The FDTD method constitutes a numerical implementation of the time-domain Maxwell’sequations for a certain frequency range (which depends on the cell size and the local ma-terial properties). Therefore, the time behaviour of a source should be correctly translatedinto the appropriate time behaviour of the electromagnetic fields [Dolmans, 1997a]. Ifonly one frequency is being considered, i.e. a frequency domain analysis, care must betaken not to generate other unwanted frequency components that can propagate in themesh. The unwanted frequency components are called spurious frequency components orspurious for short.

In real life, switching on a sinusoidal source results in a broad decaying frequencyspectrum, after some time only the fundamental frequency component will remain. Itmight be expected that switching on the source in the FDTD algorithm may exhibit thesame behaviour. This could lead to spurious responses of the FDTD algorithm, which isinvestigated in the next section.

The cell size in terms of wavelength determines the accuracy of the solution. A mea-sure for the accuracy is the grid dispersion error and the anisotropy [Dolmans, 1997a],[Dolmans, 1997b]. For accurate and stable results, these must be reduced to an accept-able level. In this section the cell size 1r is chosen to be λ/10. The cells are square, thismeans that the cell size determines both the width as well as the length. Once the cellsize has been determined the Courant criterion gives an upper limit for the time step size1t . For the equally spaced two-dimensional grid and the (2,4) FDTD scheme used in thissection the Courant criterion gives [Dolmans, 1997b]:

1t ≤ 61r

7√

2 c, (3.5)

where c is the speed of light in vacuum. In the numerical calculations the time step sizeis chosen to be equal to:

1t = 0.58931r

c, (3.6)

which is slightly below the upper limit of the Courant criterion given in the previousequation.

Source ramp-up is gradually increasing the amplitude of the source to a predeterminedamplitude. Here a cosine shape ramp-up will be chosen; other types, like Gaussian orexponential, may also be used, however they will not give significantly different numericalresults. The length of the cosine shaped ramp-up is defined in periods of the carrierfrequency. The following equation gives the voltage V of a sine source with a cosine


shape ramp-up :

V (n1t) =

A 12 (1− cos(π f n1t/k)) sin(2π f n1t) if n1t < kT

A sin(2π f n1t) if n1t ≥ kT, (3.7)

where A is the amplitude in V, 1t is the time step size, n is the time step number, k isthe total number of ramp-up periods, T is the time of one period and f is the frequency.The frequency is chosen to be 900 MHz, so one period corresponds to 1.11 ns. Figure 3.5shows four examples of cosine shape ramping with different lengths.

0 2 4 6 8−600

−300

0

300

600

Vol

tage

(V

)

Time (ns)

k = 0

0 2 4 6 8−600

−300

0

300

600

Vol

tage

(V

)

Time (ns)

k = 0.5

0 2 4 6 8−600

−300

0

300

600

Vol

tage

(V

)

Time (ns)

k = 1

0 2 4 6 8−600

−300

0

300

600

Vol

tage

(V

)

Time (ns)

k = 5

Figure 3.5: Cosine shape ramp-up of sinusoidal source. Solid line: sinusoidalsource with ramp-up. Dash-dot line: cosine shape ramp-up withoutsinusoidal modulation (envelope). In each figure the length of theramp-up in periods k is specified.

3.6.2 Source ramp-up and spurious

The objective of this section is to determine the influence of the source ramp-up on spu-rious. Spurious is also a function of cell size and time step size, but in this chapter theseparameters will remain constants. A sinusoidal source of 900 MHz is chosen for theanalysis.


For the analysis of the relation between source ramp-up and spurious, an empty mesh(no structure defined in it) of 250 by 250 cells is used. The frequency is 900 MHz, thecell width is λ/10 (i.e. 33 mm), the time step size is 65 ps (calculated with Equation 3.6)and the depth of the Perfectly Matched Layer (PML) regions, [Dolmans, 1997b], at theboundaries is chosen to be 6 cells.

A source is placed at cell position (50,25), two observation points are placed at cellpositions (50,50) and (200,200). The distance between observation points and the sourceis 25 cell widths (0.83 m) and 230.5 cell widths (7.68 m), respectively. When the source isswitched on, it will take some time for the electromagnetic field to arrive at the observationpoints. Therefore, the analysis of spurious at the observation points in this section will bedone taking into account an appropriate time delay. Figure 3.6 shows the spectrogram andthe Power Spectral Density (PSD) of the electric field Ez at the two observation points forthe source lacking a ramp-up.

−75

−50

−25

0

25

50

75

Time (µs)

Freq

uenc

y (G

Hz)

d=0.83 m, t >2.3 ns

0 0.2 0.4 0.60

2

4

6

−75

−50

−25

0

25

50

75

Time (µs)

Freq

uenc

y (G

Hz)

d=7.68 m, t >21 ns

0 0.2 0.4 0.60

2

4

6

0 2 4 6 8−150

−75

0

75

150

Frequency (GHz)

Pow

er s

pect

ral d

ensi

ty (

dB)

d=0.83 m0.33 µs ≤ t ≤ 0.65 µs

0 2 4 6 8−150

−75

0

75

150

Frequency (GHz)

Pow

er s

pect

ral d

ensi

ty (

dB)

d=7.68 m0.33 µs ≤ t ≤ 0.65 µs]

Figure 3.6: Spurious generated at 3.5 GHz and 6.5 GHz by switching on asource without ramp-up. The top two figures represent the spec-trograms and the bottom two figures represent the PSDs. In eachfigure the distance d from the observation point to the source isspecified. The spectrogram starts after the time delay that is spec-ified above the figures, the PSD is calculated for the time intervalspecified in the bottom two figures.


The PSD has already been introduced in Section 2.2. Here, the PSD is calculated in atime interval for which the field values remain constant. Thus the time interval is chosenwell after the source has been turned on; it is specified in Figure 3.6.

The spectrogram of a signal is obtained by splitting the signal into overlapping seg-ments and windowing these segments with a Hanning window. Finally, from each win-dowed segment the discrete Fourier transform is taken. From the final result only themagnitude is plotted, which is an estimate of the short-term, time-localised frequencycontent of the signal.

From the spectrograms of Figure 3.5 it becomes clear that a lot of spurious is gen-erated by switching on the source. These spurious frequencies excite two resonances at3.7 GHz and 6.5 GHz, which can be seen in the figures of the PSD. These resonancesare not physical, they occur because the mesh size and the time step size were based on afrequency of 900 MHz, they are far from optimal for higher frequencies.

The powers of the 900 MHz cylindrical wave at the different observation points shouldhave a difference in dB equal to ten times the logarithm of the quotient of the respectivedistances from the source (section 3.7):

10 log

(7.68

0.83

)= 9.7 dB. (3.8)

In Figure 3.6 the power at 900 MHz is 91.9 dB for d = 0.83 m and 82.3 dB for d =7.68 m. The power difference between these two observation points, 9.6 dB is very closeto the value predicted by Equation 3.8. The two spurious frequencies at 3.7 GHz and6.5 GHz are 12.9 dB and 10.9 dB, respectively, for d = 0.83 m and 16.6 dB and 10.6 dB,respectively, for d = 7.68 m. Therefore, they do not represent the amplitude of a physicalwave that propagates away from the source, but are definitely resonances.

The frequency of the resonances can approximately be related to the length of thediagonal of the mesh, which is 47 mm. This corresponds to half a wavelength at 3.2 GHzand a wavelength at 6.4 GHz. A possible explanation for the spurious at these frequenciesis that the (2.4) FDTD scheme has its maximum dispersion along the diagonal [Dolmans,1997a] [Dolmans, 1997b].

Figure 3.7 shows the frequency content of the electric field at one observation pointfor different time intervals. The time intervals are chosen after the moment of switchingon the source. The figure clearly shows the broad frequency spectrum resulting from theswitching action and the excitation of the two resonance frequencies.


0 2 4 6 8−100

−50

0

50

100

Frequency (GHz)

Pow

er s

pect

ral d

ensi

ty (

dB)

21 ns ≤ t ≤ 28 ns

0 2 4 6 8−100

−50

0

50

100

Frequency (GHz)

Pow

er s

pect

ral d

ensi

ty (

dB)

28 ns ≤ t ≤ 41 ns

0 2 4 6 8−100

−50

0

50

100

Frequency (GHz)

Pow

er s

pect

ral d

ensi

ty (

dB)

41 ns ≤ t ≤ 67 ns

0 2 4 6 8−100

−50

0

50

100

Frequency (GHz)

Pow

er s

pect

ral d

ensi

ty (

dB)

67 ns ≤ t ≤ 0.12 µs

Figure 3.7: Evolution of the frequency content of the electric field at the ob-servation point at d=7.68 m, the source has no ramp-up. In eachfigure the time interval is specified.


Figures 3.8 and 3.9 show the effect of a ramp-up of 5 periods (Section 3.6.1 and Figure3.5). The resonances have almost disappeared; some spurious effects are still visible. Theresonance are about 140 dB below the carrier frequency. This results in a dynamic rangeof also 140 dB.

−75

−50

−25

0

25

50

75

Time (µs)

Freq

uenc

y (G

Hz)

d=0.83 m, t >2.3 ns

0 0.2 0.4 0.60

2

4

6

−75

−50

−25

0

25

50

75

Time (µs)

Freq

uenc

y (G

Hz)

d=7.68 m, t >21 ns

0 0.2 0.4 0.60

2

4

6

0 2 4 6 8−150

−75

0

75

150

Frequency (GHz)

Pow

er s

pect

ral d

ensi

ty (

dB)

d=0.83 m0.33 µs ≤ t ≤ 0.65 µs

0 2 4 6 8−150

−75

0

75

150

Frequency (GHz)

Pow

er s

pect

ral d

ensi

ty (

dB)

d=7.68 m0.33 µs ≤ t ≤ 0.65 µs]

Figure 3.8: Spurious generated at 3.5 GHz and 6.5 GHz by switching on asource with a ramp-up of 5 periods. The top two figures representthe spectrograms and the bottom two figures represent the PSDs. Ineach figure the distance d from the observation point to the sourceis specified. The spectrogram starts after the time delay that is spec-ified above the figures, the PSD is calculated for the time intervalspecified in the bottom two figures.


0 2 4 6 8−100

−50

0

50

100

Frequency (GHz)P

ower

spe

ctra

l den

sity

(dB

)

21 ns ≤ t ≤ 28 ns

0 2 4 6 8−100

−50

0

50

100

Frequency (GHz)

Pow

er s

pect

ral d

ensi

ty (

dB)

28 ns ≤ t ≤ 41 ns

0 2 4 6 8−100

−50

0

50

100

Frequency (GHz)

Pow

er s

pect

ral d

ensi

ty (

dB)

41 ns ≤ t ≤ 67 ns

0 2 4 6 8−100

−50

0

50

100

Frequency (GHz)

Pow

er s

pect

ral d

ensi

ty (

dB)

67 ns ≤ t ≤ 0.12 µs

Figure 3.9: Evolution of the frequency content of the electric field at the obser-vation point at d=7.68 m, the source has a ramp-up of 5 periods.In each figure the time interval is specified.

Comparing the first picture of Figure 3.7 with the one of Figure 3.9 shows that rampingintroduces far less spurious. The initial amplitude with ramp-up is of course lower thanwithout ramping due to the gradual increase of the amplitude of the source with ramp-up.

Instead of using a cosine shape ramp-up other types of ramp-ups can be defined basedon classical windows, like Hanning, Hamming or Blackman [Gurel and Oguz, 2000]. Inthe next section a Gaussian envelope is introduced for exciting a modelled structure in theFDTD method. This Gaussian envelope can also be considered as a source ramp-up.

3.6.3 Gaussian modulated sine source

In the previous section the influence of source ramp-up on spurious has been analysed forfrequency domain simulations with FDTD. In this section the FDTD will be set up for theanalysis of narrowband communication systems. In some publications a Gaussian pulse isproposed for the analysis [Kunz and Luebbers, 1993]. By doing this all frequencies from0 Hz up to a certain cut-off frequency in the GHz range will be excited. Applying thismethod to analyse narrowband systems is not very efficient, because only a very smallfrequency band around a centre frequency should be included in the analysis. Excitingother frequencies may result into resonances and offsets that might influence the final


results. Therefore, in this section FDTD will be set up with a Gaussian modulated sine(Gms) source. This limits the excited frequencies to the frequencies of interest. TheGaussian envelope of the carrier frequency can be considered to be a window or sourceramp-up. The analysis of the previous section will therefore be applied again to determinethe parameters of the Gms source in order to avoid spurious. In this section the FDTDmain parameters are chosen equal to that of the previous section: f = 900 MHz, 1r =λ/10 and 1t = 0.58931r/c.

A time discretised version of the Gms source, Equation 2.12, is used for implementa-tion in the FDTD algorithm:

V (n1t) = A e−a2(n1t − β1t)2 cos(2π f n1t), 0 ≤ n ≤ 2β, (3.9)

where A is the amplitude, 1t is the time step size, n is the time step number, β is aparameter to make the pulse causal and finite: β1t = td , a is the pulse decay, f is thefrequency. The delay τ in the cosine function of Equation 2.12 has been omitted. Theparameter β also defines the duration of the Gaussian envelope, the pulse exists fromn1t = 0 until n1t = 2β1t . The Gaussian envelope has a value exp(−(aβ1t)2) downfrom the maximum value at the truncation times. A suitable truncation value is found for:

β = 4

a1t, (3.10)

then the value of the envelope at truncation is exp(−16) down from the maximum value.This corresponds to -139 dB (relative power), which suffices for most applications [Kunzand Luebbers, 1993]. The time discretised Gms source can now be written as:

V (n1t) = A e−(a n1t − 4)2 cos(2π f n1t), 0 ≤ n ≤ 8

a1t. (3.11)

In order to check that spurious frequencies are absent, two Gaussian modulated sinesources with pulse decay of 1e+09 and 1e+08, respectively, are used in an FDTD simula-tion with an empty mesh (same simulation as in Section 3.6.2). The two top pictures ofFigure 3.10 and 3.11 show the electric field strength as a function of time at two places inthe FDTD mesh at different distances from the source. The two bottom pictures show thePSD of the pulses for the specified time intervals. The length of the two time intervals iscentred around the pulse. The amplitude difference between the pulses at d = 0.83 m andat d = 7.68 m is equal to the transmission loss for two-dimensional geometries (section3.7 and Equation 3.8). Figure 3.10 shows a Gms pulse with the shortest duration, that hasbeen used in this work. The spurious frequencies are absent. Due to the short duration ofthe pulse, the carrier frequency (900 MHz) cannot be accurately determined. Figure 3.11shows a Gms pulse with a longer duration. The resulting dynamic range (bottom figures)is more than 160 dB. The power in the pulse is concentrated around the carrier frequency.It can be concluded that the Gms source does not result in spurious frequencies and thatthe dynamic range obtained is sufficient.


0 10 20 30 40−1.6

−0.8

0

0.8

1.6E

lect

ric fi

eld

(kV

/m)

Time (ns)

d=0.83 m

0 1 2 3 4 5 6 7 8−120

−80

−40

0

40

80

Frequency (GHz)

Pow

er s

pect

ral d

ensi

ty (

dB)

2.78 ns ≤ t ≤ 10.8 ns d=0.83 m

0 10 20 30 40−1.6

−0.8

0

0.8

1.6

Ele

ctric

fiel

d (k

V/m

)

Time (ns)

d=7.68 m

0 1 2 3 4 5 6 7 8−120

−80

−40

0

40

80

Frequency (GHz)

Pow

er s

pect

ral d

ensi

ty (

dB)

25.6 ns ≤ t ≤ 33.6 ns d=7.68 m

Figure 3.10: Top two pictures, electric field due to a Gms source at the specifieddistances d from the source for a = 109 s−1. Bottom two picturesthe associated PSDs for the specified time intervals.


0 25 50 75 100−1.6

−0.8

0

0.8

1.6E

lect

ric fi

eld

(kV

/m)

Time (ns)

d=0.83 m

0 1 2 3 4 5 6 7 8−120

−80

−40

0

40

80

Frequency (GHz)

Pow

er s

pect

ral d

ensi

ty (

dB)

2.78 ns ≤ t ≤ 82.8 ns d=0.83 m

0 25 50 75 100−1.6

−0.8

0

0.8

1.6

Ele

ctric

fiel

d (k

V/m

)

Time (ns)

d=7.68 m

0 1 2 3 4 5 6 7 8−120

−80

−40

0

40

80

Frequency (GHz)

Pow

er s

pect

ral d

ensi

ty (

dB)

25.6 ns ≤ t ≤ 106 ns d=7.68 m

Figure 3.11: Top two pictures, electric field due to a Gms source at the specifieddistances d from the source for a = 108 s−1. Bottom two picturesthe associated PSDs for the specified time intervals.

3.6.4 Implementation of delay spread calculations

The original FDTD code [Dolmans, 1997b] is capable of determining the maximum fieldstrength at a certain point in the mesh. For this work the delay spread must also be knownto analyse the performance of communication systems with antenna diversity. Conse-quently, for the calculation of delay spread τg Equation 2.30 is implemented in the FDTDalgorithm. The ray-tracing algorithms, however, use the wideband version τδ (Equation2.33).


The implementation of the delay-spread calculation in the FDTD algorithm is notstraightforward. It is not possible to store the simulation results of every grid point for allthe time steps during the simulation time. Storing the results for only one time step resultsin mega-bytes of data due to the many cells needed for accurate results. Storing the resultsfor many time steps is therefore impossible. Preferably, the integrations of Equation 2.30are done as ’running’ calculations that are updated for each time step. However, thisequation consists of several nested integrals; before the outer integral can be calculatedthe inner integrals must be known. Equation 2.30 can be rewritten as:

τg(Er) =

√√√√√√√

∫ ∞

0(t − t0)

2 P(t, Er ) dt∫ ∞

0P(t, Er ) dt

, (3.12)

with t0 a constant defined as:

t0 =

∫ ∞

0t P(t, Er ) dt

∫ ∞

0P(t, Er ) dt

. (3.13)

The integral in the numerator of Equation 3.12 can be written as:

∫ ∞

0(t − t0)

2 P(t, Er ) dt

=∫ ∞

0t2 P(t, Er ) dt − 2t0

∫ ∞

0t P(t, Er ) dt + t2

0

∫ ∞

0P(t, Er) dt .

(3.14)

With these equations the delay spread τg can obtained in every grid by only doing oneFDTD simulation run. The procedure is as follows:

1. the integrals∫ ∞

0t2 P(t, Er ) dt ,

∫ ∞

0t P(t, Er ) dt and

∫ ∞

0P(t, Er ) dt are evaluated for

each grid point (running updates),

2. to obtain τg for each grid point the Equations are evaluated in the following order:Equation 3.13, Equation 3.14 and finally Equation 3.12.

Calculating τg in this way only slightly increases the total amount of memory needed.The Gms source used in the FDTD simulator results in a Gaussian envelope on a

high frequency carrier. Fortunately, calculations based on only the envelope gives thesame results as calculations based on the envelope including the carrier frequency (Sec-tion 2.10.2). In order to be able to exploit this property, the signal including the carrierfrequency should be known at sufficiently close time intervals. According to the Courantcriterion, Equation 3.5, the time step size1t is a function of the cell size1r . This cell size1r is chosen to be λ0/10, with λ0 the wavelength corresponding to the carrier frequency


f0. Substituting this value into Equation 3.6 results in:

1t = 0.5893λ0

10 c= 0.05893

f0. (3.15)

As a result the time step size (or resolution) is sufficient according to Table 2.3 to beable to calculate the delay spread based on a modulated signal. The integration in thecalculation of τg with the FDTD method can be done with instantaneous field values.

Figure 3.12 shows the local narrowband delay spread τg(Er) for a Gms source in anempty grid (no structure present) with a carrier frequency of 900 MHz. a = 108 s−1.Based on Equations 2.40 and 2.39 the delay spread should be equal to τ p = 5 ns through-out the whole grid (τδ = 0 for a free-space environment). Figure 3.12 shows that anegligible error of less than 15 ps or 0.3 % is made in the calculation of τg . The accuracyof the delay spread calculation is related to the accuracy of the FDTD method [Dolmans,1997b].

4.985

4.99

4.995

5

5.005

5.01

5.015

0 1 2 3 4 5 6 70

1

2

3

4

5

6

7

x−position (m)

y−po

sitio

n (m

)

Narrowband delay spread (ns)

X

Figure 3.12: Local narrowband delay spread τg(Er) in ns for an empty grid ob-tained with the FDTD method. The ’X’ denotes the location of theGms source at (x, y) = (0.5 m, 1.33 m).


3.7 Two- versus three- dimensional models

The two-dimensional world is obtained by slicing the three-dimensional world. For prop-agation simulation the slicing is done parallel to the floor of a building through the middleof a room. In 2D and for free-space conditions, the wavefronts (equal phase trajectories)form concentric circles around a finite source at a large distance (far-field radiation con-dition). If the 2D geometry represents a 3D free-space condition, the wavefronts can beconsidered to be concentric cylindrical waves. The source in this case is a line source ofinfinite length. In both cases the total power in each wavefront must be a constant. There-fore, the power reduces proportional to the distance from the source. This in contrast towavefronts caused by finite sources at large distances in 3D (for free-space conditions),where the power reduces proportionally to the square of the distance. The field strengthin 2D structures reduces proportionally to the square root of the distance from the source.

The indoor propagation environment is a three-dimensional (3D) environment. There-fore, it seems that a 3D model would give the best simulation results. The computerrequirements, however, for 3D models are tremendous. A 3D FDTD implementationwritten in the C language and running on a Sun SparcStation would, for example, needa simulation time in the order of 8 105 s (this equals 9.26 days) for an empty room of12.18 m by 4.5 m by 3.5 m and a wavelength of 33 cm [Talbi and Delisle, 1996]. Theanalysis of the two-dimensional (2D) equivalent with a 2D FDTD code only needs 7031 s(this equals 1.95 hours). The continuous improvement of computers with respect to com-putational speed and memory size will enable the 3D structures to be analysed in the nearfuture.

The development of higher-order FDTD methods that require less computer power[Dolmans, 1997b] might accelerate the ability to simulate 3D structures. These higher-order methods require less cells per wavelength without sacrificing accuracy, this leadsto less storage and processing requirements. These methods are based on more complexexpressions, which require more CPU time to evaluate. The increase of processing time toevaluate these expressions might limit the performance improvement that can be obtained.For an efficient method a trade off between the complexity of the expressions and therequired number of cells per wavelength must be made. In this work already a higher-order, (2,4) instead of (2,2) [Dolmans, 1997b], FDTD method is used for the simulations.

Some research groups have compared measurements of 3D structures with 2D simu-lation results [Talbi and Delisle, 1996], [Lauer, 1994]. From their observations it seemsthat there are no important differences for a normal communication set-up with antennasthat are vertically polarised and that are omni-directional in azimuth. The power levelversus distance, the statistical power distribution and the power delay profiles from thesimulations show a good agreement with those obtained from measurements [Talbi andDelisle, 1996]. It is observed that there are small differences due to the fact that in the 2Dsimulations the objects have infinite heights and that the ground and floor reflections areabsent. However, for buildings with relative good reflecting floors and ceilings, e.g. rein-forced concrete, the difference between 2D simulations and measurements is very small[Lauer, 1994]. 2D simulations can therefore be used for the analysis of the wave propa-gation inside most buildings. The uncertainties in the location and dielectric properties ofthe modelled objects seem to contribute also to the observed small differences [Talbi and

3.8. Finite Difference Time Domain versus ray-tracing 67

Delisle, 1996].Although this work has been set up for a 3D simulation program, the results of only

2D simulations will be presented. The 3D simulation results for large structures willprobably be obtained in the future.

3.8 Finite Difference Time Domain versus ray-tracing

In the previous section two suitable methods for channel simulation have been identified:ray-tracing and Finite Difference Time Domain (FDTD). In this section two-dimensionalimplementations of these methods are compared; the DECT Installation Assistant, basedon the ray-tracing method, developed by Philips Research in Redhill [Cattell and vanDam, 1996] and the (2,4) FDTD method developed by Dolmans [Dolmans, 1997b].

It is easily verified that both methods also satisfy the requirements of Section 2.12.1.They can therefore be used for analysing communication systems. In many ray-tracingimplementations the loss factor ρ, Equation 3.4, is mostly chosen to be 2 as for sphericalwaves in free space. Especially for the comparison of this section a ’real’ two-dimensionalimplementation (ρ = 1) of a ray-tracing program has been made.

Figure 3.13 shows the two-dimensional configuration that is analysed by both meth-ods. It represents a part of a floor of the Eindhoven University of Technology (TU/e). Thewalls of the rooms have a thickness of 0.2 m, the dielectric constant is 4.5, the conductiv-ity is 0.1 S. The walls of the elevator have a conductivity of∞ S. The carrier frequencyof the source is 900 MHz. Figure 3.14 and 3.15 show the transmission loss L tr and localnarrowband delay spread τg(Er) of the complete configuration. These plots were generatedwith the (2,4) FDTD method with a Gms source with pulse decay a = 109 s−1. In Figure3.13 a line at y= 10.3 m is drawn, this line intersects the source. The received power anddelay spread obtained from the different simulations will be plotted along this line forcomparison, see Figures 3.16 through 3.22.


Source locationEnd of computational domain

XWall of roomSteel wall of elevator

X

32 m

0 m0 m x 32 m

y

10.3 m

Figure 3.13: Part of a floor of the TU/e chosen as the two-dimensional config-uration. The line at y = 10.3 m is used as an observation line tocompare the results of different simulations.


−120

−100

−80

−60

−40

−20

0

0 4 8 12 16 20 24 28 320

4

8

12

16

20

24

28

32

x−position (m)

y−po

sitio

n (m

)

Transmission loss (dB)

Figure 3.14: Transmission loss L tr(Er) inside the configuration of Figure 3.13obtained with the (2,4) FDTD method with a Gms source with pulsedecay a = 109 s−1.


10

20

30

40

50

60

70

0 4 8 12 16 20 24 28 320

4

8

12

16

20

24

28

32

x−position (m)

y−po

sitio

n (m

)Delay spread (ns)

Figure 3.15: Local narrowband delay spread τg(Er) inside the configuration ofFigure 3.13 obtained with the (2,4) FDTD method with a Gmssource with pulse decay a = 109 s−1.


Table 3.1 gives an overview of four different simulations and their main parameters.The simulations are listed in such an order that the frequency bandwidth increases. The(2,4) FDTD simulation with the sine source has the smallest bandwidth. The source isunmodulated, so there is only one frequency component present. The pulse duration ofsuch a source is infinite, as a result the delay spread is undefined. The FDTD simulationswith the Gms source have a frequency bandwidth B30 that is a function of pulse decaya given in Equation 2.14. The DECT Installation Assistant (IA) has a source that emitsDirac type of pulses (they have zero width). This means that the frequency bandwidth isinfinite. As an illustration of the change in signals as a function of frequency bandwidth,Figure 3.23 shows the time domain signal at one point in the configuration for the threedifferent FDTD simulations.

Method Source a (s−1) T30 (ns) B30 (MHz) Figure

FDTD sine 0 ∞ 0 3.16

FDTD Gms 108 37.2 118.3 3.17, 3.18

FDTD Gms 109 3.72 1183 3.19, 3.20

IA Dirac pulse ∞ 0 ∞ 3.21, 3.22

Table 3.1: Overview of the different simulations. IA = DECT Installation As-sistant, FDTD = (2,4) FDTD method, a is the pulse decay of theGms source (Equation 2.11), T30 is the pulse duration (Equation2.15) and B30 is the frequency bandwidth (Equation 2.14).

The small-scale variations in received power and delay spread decrease with increas-ing bandwidth or decreasing pulse duration. This can be observed by comparing figures3.16 through 3.22. The variations are caused by interference effects between the mainand reflected pulses. The IA uses pulses with zero duration, which is ideal to obtain theimpulse response of the radio channel.

The accuracy at the scale of a wavelength of this implementation of the ray-tracingmethod, however, is not very high. The IA has not been developed for analysing radiochannels in great detail, it is optimised towards simulation time to facilitate the planningof base stations in buildings. For this reason the diffraction effects are omitted in the IA,which can be observed between x = 5 m and x = 9 m in Figures 3.21 and 3.22. Herethe observation line intersects the perfectly conducting walls of the elevator, due to theabsence of diffraction no power is present in this region. As a result the delay spread iszero in this region. The inclusion of diffraction effects is particularly important for theindoor environment in which objects are comparable to the wavelength of cordless andcellular communication systems [Remley, 1998]. More generally the ray-tracing methodseems to become more elaborate if details of the structures become important, i.e. whenthe wave propagation is not quasi-optical [Lauer, 1994].

Second-order electromagnetic effects, like diffraction, are automatically included inthe results of the FDTD simulations. This can be observed in the same region (x = 5 mto x = 9 m) of Figures 3.16 through 3.20. In this case power is present due to the correct


modelled diffraction at the edges of the wall of the elevator. The power level, however, isvery low, which results in a high delay spread. The pulse delay spread, Equation 2.39, ofthe FDTD simulations with a = 108 s−1 and a = 109 s−1 is 5 ns and 0.5 ns, respectively.The delay spread is between approximately 10 ns and 70 ns. As a consequence, thesimulation results of the FDTD simulation with a = 109 s−1 approaches the impulseresponse of the radio channel the best.

0 4 8 12 16 20 24 28 32−120

−80

−40

0

40

x position (m)

Rec

eive

d po

wer

(dB

m)

Figure 3.16: Received power, (2,4) FDTD method, sine source.


0 4 8 12 16 20 24 28 32−120

−80

−40

0

40

x position (m)

Rec

eive

d po

wer

(dB

m)

Figure 3.17: Received power, (2,4) FDTD method, Gms source, a = 108 s−1.

0 4 8 12 16 20 24 28 320

20

40

60

80

x position (m)

Del

ay s

prea

d (n

s)

Figure 3.18: Delay spread, (2,4) FDTD method, Gms source, a = 108 s−1.


0 4 8 12 16 20 24 28 32−120

−80

−40

0

40

x position (m)

Rec

eive

d po

wer

(dB

m)

Figure 3.19: Received power, (2,4) FDTD method, Gms source, a = 109 s−1.

0 4 8 12 16 20 24 28 320

20

40

60

80

x position (m)

Del

ay s

prea

d (n

s)

Figure 3.20: Delay spread, (2,4) FDTD method, Gms source, a = 109 s−1.


0 4 8 12 16 20 24 28 32−120

−80

−40

0

40

x position (m)

Rec

eive

d po

wer

(dB

m)

Figure 3.21: Received power calculated, DECT Installation Assistant.

0 4 8 12 16 20 24 28 320

20

40

60

80

x position (m)

Del

ay s

prea

d (n

s)

Figure 3.22: Delay spread, DECT Installation Assistant.


25 75 125 175−10

−5

0

5

10

Time (ns)

Am

plitu

de (

V)

a=1e+09 s−1

75 125 175−10

−5

0

5

10

Time (ns)

Am

plitu

de (

V)

a=1e+08 s−1

25 75 125 175−15

−7.5

0

7.5

15

Time (ns)A

mpl

itude

(V

)

sine source

Figure 3.23: Received amplitude as a function of time at one point in the con-figuration for the three (2,4) FDTD simulations listed in Table 3.1.

3.9 Conclusions

In the previous sections several methods for propagation modelling have been introduced.This section gives a relative comparison of these models. From this comparison two deter-ministic methods seem able to predict the small-scale fading effects that are necessary formodelling diversity systems on a handset: ray-tracing and Finite Difference Time Domain(FDTD). Both methods also satisfy the requirements of Section 2.12.1.

Section 3.8 gives a comparison between two available two-dimensional implementa-tions of both methods: the DECT Installation Assistant developed by Philips Research inRedhill [Cattell and van Dam, 1996] and the (2,4) FDTD method developed by Dolmans[Dolmans, 1997b].

Table 3.2 ranks the different propagation models and methods with respect to fourcategories. These categories are related to analysing and predicting the small-scale fadingeffects. The four categories are:

• Resolution The resolution is related to the scale on which field values are obtained.This is important for diversity systems for handsets, for which antenna separationsof half a wavelength or less are required.

3.9. Conclusions 77

• Flexibility The flexibility is related to the ease with which different geometries canbe analysed or modified.

• Resources The resources are related to CPU time and storage requirements.

• Accuracy With ’accuracy’, the accuracy of the field predictions of the deterministicmodels is meant.

Model Section Resolution Flexibility Resources Accuracy

Path Loss 3.2 −− + ++Statistical 3.3 − − +Analytical 3.4 ++ −− 0 +IA 3.5 0 0 − 0

(2,4) FDTD 3.6 + ++ − 0

−− : unacceptable, − : unfavorable, 0 : neutral, + : favorable, ++ : excellent

Table 3.2: Relative comparison of different propagation modelling methods.IA stands for the DECT Installation Assistant.

The path-loss model and the statistical model are no deterministic models. For thiswork a deterministic model is required to analyse the interaction between objects, anten-nas and the electromagnetic fields [Leyten and Dolmans, 2000a]. The path-loss modelhas too little detail to obtain useful results for diversity systems. Statistical models arealso not suitable for this purpose as explained in Section 3.3.

The three remaining deterministic models are all potentially capable of modellingdiversity systems for handsets. The main disadvantages of the analytical method are thepoor flexibility of the method and the inability to analyse arbitrarily shaped geometries.As a consequence, only two methods remain: ray-tracing and FDTD.

A ray-tracing method requires less computer resources, but obtaining high resolutionresults might be difficult. An FDTD method is very flexible, but requires huge computerresources. The typical application of a ray-tracing method is prediction the received signalstrength in cities. In this case the resolution is in the order of metres and the objects(houses, buildings, etc.) are not modelled in detail. The typical application of the FDTDis the calculation of the electromagnetic fields in structures with dimensions of severalwavelengths. The structures are modelled in detail and the electromagnetic fields areobtained at small intervals.

The choice between ray-tracing and FDTD was determined by the implementationsof the methods that were available for this work at the time. The results of both imple-mentations have been shown in Section 3.8. The (2,4) FDTD implementation is thereforebetter. It will be used as the simulation tool in this Ph.D. thesis.

Chapter 4

Radio channel measurements

4.1 Introduction

The radio channel is time-varying due to movement of the receiver or transmitter and dueto movement of objects, like persons and cars. The measurement time should be smallerthan the coherence time of the channel to keep track of the changes. The DECT channelhas a coherence time of about 6 ms (Section 2.3.3). The time varying characteristics ofthis radio channel could be measured with a fast measurement set-up , e.g. based on asliding correlator [Bultitude, 1998]. In this work, however, a network analyser is used.The typical sweep time for the calibrated network analyser is 600 ms (1601 points persweep), which is much larger than the coherence time of the radio channel. Some time isalso needed to send the data from the network analyser to a computer, where it is storedfor further analysis. After that a new measurement is started. As a consequence themeasurements in this work are done for a slowly time-varying radio channel. This hasbeen achieved by measuring in environments without fast moving objects and by keepingthe antennas stationary during each sweep of the network analyser.

In order to design an adaptive diversity receiver, the speed of adaptation and thechange of relevant quantities as a function of time are needed. This is not present withinthe measured data set. The movement of the user and of objects (mainly people) throughthe propagation environment is simulated by going (with the desired speed) through thedata obtained at different observation points. The assumption is that the results obtainedfor time-varying radio channel are similar to those obtained by moving through a time-invariant channel.

Section 4.2 introduces the hardware of the measurement set-up. In section 4.3 thefrequency power transfer-function is introduced . In section 4.4 a procedure to obtain thePower Delay Profile (PDP) based on the frequency domain measurements is introduced.This procedure involves the derivation of a relation between the PDP and the measure-ments based on a Discrete Inverse Fourier Transformation (DIFT) (Section 4.4), someconsiderations with respect to aliasing (Section 4.4.1), and windowing (Section 4.4.2). InSection 4.5 the accuracy of the proposed measurement procedure is analysed.

79

80 Chapter 4. Radio channel measurements

Finally, Section 4.6 gives an overview of the measurement set-up and a summary ofthe procedure to obtain the power delay profile.

4.2 Measurement set-up

Figure 4.1 shows the measurement set-up. The main parts are an xy-table or scanner withcontroller, a network analyser, a pre-amplifier, a Personal Computer (PC), switch, cablesand antennas.

personal computer

switch

network analyser

receive antennatransmit antenna radio channel

pre-amplifier

x

y

xy-table controller

Figure 4.1: Measurement set-up.

• The xy-table moves an antenna through a plane located in the propagation environ-ment. The network analyser measures the frequency transfer-function between thetwo antennas for every position of the xy-table.

• The pre-amplifier increases the dynamic range of the measurement set-up loweringthe noise floor and amplifying the received signals. The pre-amplifier amplifies thesignals in only one direction (the arrow above it in Figure 4.1). Its location, i.e. atport 1 or 2 of the network analyser, determines which antenna receives and whichantenna transmits.

4.2. Measurement set-up 81

• The PC controls the measurement process and logs the data from the network anal-yser. The xy-table is capable of scanning a plane of 1.02 m by 0.82 m. The networkanalyser is capable of measuring from 0.3 MHz up to 6 GHz (the frequency rangecan easily be extended by substituting the network analyser with an other).

• The distance between the antennas is limited by the length of the cables. Two cableswith a length of 9 m are available. The distance and the location of the antennascan be varied to characterise different propagation situations, e.g. single room ormulti room.

• Different type of antennas and antenna orientations can be chosen for character-ising the propagation environment. The receive and transmit antenna types, theirorientation and their separation should be logged for every measurement, becausethese parameters influence the transfer function.

• The switch is controlled by the xy-table controller, which has a few extra outputsfor this purpose. The switch switches between two antennas for space, polarisation,etc. diversity measurements.

With this measurement set-up it is possible to measure the frequency transfer functionof the radio channel as a function of position. A detailed description of the measure-ment set-up and the data acquisition software can be found elsewhere [Beek and Kerkhof,1998].

In most cases the network analyser is calibrated at the ports of the S-parameter testset. For the measurement set-up of Figure 4.1, however, the calibration is done at theend of the cables that are used to connect the antennas. The advantage is that the thecharacteristics of the cables, connectors and the pre-amplifier are automatically taken intoaccount by the network analyser. Otherwise these characteristics have to be de-embeddedfrom the measured data. A minor disadvantage is that the cables and antennas can only bemounted after calibration, because the cables need to be connected to each other duringthe calibration procedure.

In Section 2.12.1 the requirements for a measurement setup are specified, Table 2.3.A typical measurement done for this work has the following characteristics:

• frequency range from 1.8 GHz to 2.2 GHz in 1601 points, resulting in a time dura-tion of 4 µs and a time resolution of 2.5 ns,

• resolution of 16 points per wavelength,

• measurement area of 5 by 5 wavelengths, resulting in 6400 observation points,

• dynamic range of network analyser of about 80 dB.

With these characteristics, the requirements of Table 2.3 are satisfied. The time resolutionfor the received signal is not applicable, because, with the network analyser the amplitudeand phase of the complex envelope (Section 2.6) are directly measured.


4.3 Frequency transfer function

After completion of the calibration procedure, the frequency transfer function of the radiochannel including the characteristics of the antennas is obtained. These characteristicsare: antenna impedance, polarisation, radiation pattern and gain (or efficiency). Thesequantities are included in the gains gr and gt of Equation 3.1. For the measurements,antennas are chosen that would typically also be used in a real communication system. Inthis way, the antenna radiation characteristics, like polarisation, radiation pattern and gainare automatically included in the measured data. Care must be taken with the inclusionof the antenna impedance. In Figure 4.2 it shown that the antenna impedance changes asa function of frequency. As a result, the reflection coefficients of the transmit and receiveantennas are also functions of the frequency [Gonzalez, 1997]:

0t( f ) = Z t( f )− 50

Z t( f )+ 50, (4.1)

0r ( f ) = Zr( f )− 50

Zr( f )+ 50. (4.2)

In these equations, feed lines have an impedance of 50 . Furthermore, it is assumedthat the impedances of the transmit and receive antenna, Z t and Zr , respectively, are notchanged due to mutual coupling.

1.5 1.75 2 2.25 2.50

150

300

450

Rt (

Ω)

Frequency (GHz)1.5 1.75 2 2.25 2.5

−300

−150

0

150

300 X

t (Ω

)

Frequency (GHz)

Figure 4.2: Real and imaginary part, Rt and X t respectively, of the measuredantenna impedance of a DECT antenna used in the measurementset-up shown in Figure 4.1.

Due to the changing antenna impedance the match of the antenna of Figure 4.2 canonly be acceptable in a limited frequency range, for example, 10 log(|0|2) < −10 dB.This is shown in Figure 4.3, in which the -10 dB bandwidth is approximately 250 MHz.Outside the matched frequency band the received and transmitted power are reduced sig-nificantly due to the antenna mismatch. As a result the measured radio-channel transfer isdeteriorated. By compensating for the mismatch of the antennas the radio-channel trans-fer can be determined for a broader frequency range. Moreover, in most communication

4.4. Power delay profile obtained from measurements 83

systems the antenna mismatch is compensated for by using an impedance matching net-work.

1.5 1.75 2 2.25 2.5−40

−30

−20

−10

0

Ret

urn

loss

(dB

)

Frequency (GHz)

Figure 4.3: Power magnitude of the 50 input reflection coefficient |0t |2, re-turn loss, based on the antenna impedance of Figure 4.2.

The characteristics of the radio channel and the differences between the antennas inpolarisation and radiation pattern are contained in the scattering parameters S21 or S12measured by the network analyser.

4.4 Power delay profile obtained from measurements

In the time domain the radio-channel is characterised by its PDP defined in Equation2.24. The PDP P(t) is based on the complex envelope of the equivalent lowpass impulseresponse of the radio channel h(t):

P(t) = |h(t)|2. (4.3)

The network analyser measures the frequency-domain response S21( f ) as a functionof the frequency between the receive and transmit antenna. The frequency transfer func-tion S21 is obtained with non-ideal antennas. These antennas have a limited frequency inwhich most of the electric power is converted to electromagnetic waves (previous section).However, the effects of this error for the PDP will be very small. The antenna mismatchis only significant at the lower and higher frequencies within its bandwidth (Figure 4.3).These frequencies will be suppressed by the window needed for a good inverse Fouriertransformation described in Section 4.4.2. As a result, the measured frequency responseS21( f ) is determined by the effects of the antenna characteristics and the response of theradio channel. With this response, diversity systems can be analysed for a certain type ofantenna, like a dipole antenna, and within a certain type of propagation environment, likethe indoor environment. The frequency response S21( f ) is measured for only positive


frequencies. With this response the PDP (Equation 4.3) can be expressed as:

P(t) = 2| −1 S21( f ) |2, (4.4)

where −1 denotes the Inverse Fourier Transformation (IFT):

h(t) = −1 ( f ) =

∫ ∞

0

( f ) e j2π f t d f. (4.5)

The IFT is applied to obtain the time domain response. The frequency response S21( f )is measured at a fixed number of equally-spaced discrete frequencies within the mea-surement bandwidth. As a result the Discrete Inverse Fourier Transformation (DIFT) isneeded to obtain the PDP. In this section expressions for the DIFT and Discrete FourierTransformation (DFT) are derived and compared to those implemented in MatLab [TheMathWorks Inc., 1999].

The channel response S21( f ) is measured with a fixed frequency interval1 f within afinite frequency band. For the discrete function the same symbol is used as its continuouscounterpart: S21(k) with k = 0, 1, 2, . . . , N − 1. With the aid of the trapezoidal rule theintegral in Equation 4.5 can be approximated:∫ ∞

0

( f ) e j2π f t d f

≈ 1 f

1

2

(0)+

N−2∑

k=1

(k) e j2πk1 f t + 1

2

(N − 1) e j2π(N − 1)1 f t

≈ 1 fN−1∑

k=0

(k) e j2πk1 f t . (4.6)

This equation is evaluated at discrete time intervals t = n1t with a computer. Forthe discrete function the same symbol is used as its continuous counterpart: h(n) withn = 0, 1, 2, . . . , N−1. By choosing the 1/N = 1t 1 f , the so-called reciprocity relation,the DIFT is obtained:

h(n) = 1 fN−1∑

k=0

(k) e

j2π

(kn

N

)

. (4.7)

In a similar way the DFT can be obtained by starting from the continuous Fourier trans-formation give in Equation 2.9:

(k) = 1t

N−1∑

k=0

h(n) e− j2π

(kn

N

)

. (4.8)

Table 4.1 summarises the relation between the frequency- and time-domain parameters ofthe DIFT and DFT.


Frequency domain Time domain

k=0,1,2, . . . ,N-1 n=0,1,2, . . . ,N-1

Frequency step = 1 f = 1N 1t Time step = 1t = 1

N 1 f

Bandwidth = N 1 f = 11t Duration = N 1t = 1

1 f

Table 4.1: Relationship between parameters of discrete Fourier transforma-tions.

In MatLab the DIFT and DFT are defined in a dimensionless way and the DIFT isimplemented with a division by N [The MathWorks Inc., 1999]. Therefore, the followingcorrections must be made after the computations [Siemons, 2000]:

‘Equation 4.7’ = N 1 f ‘MatLab DIFT’, (4.9)

‘Equation 4.8’ = 1t ‘MatLab DFT’. (4.10)

4.4.1 Aliasing and essentially band-limited signals

The data in the frequency domain are measured at discrete frequencies with fixed fre-quency steps. This so-called sampling in the frequency domain results in a repetition ofthe impulse response in the time domain after the IFT [Brigham, 1988]. This effect is sim-ilar to aliasing that occurs by the Fourier transformation if the sampling intervals in thetime domain were too large. The repetition time T is given by 1/1 f . In order to obtaina valid time representation the following condition, equivalent to the Shannon samplingtheorem [Brigham, 1988], should be satisfied:

1 f ≤ 1

T. (4.11)

A way of reducing the effect of aliasing is decreasing the frequency step. However, thisresults in a longer measurement time and larger data files which reduces the speed of themeasurement and the simulations.

The Agilent network analyser used in this work, HP 8753E [Hewlett Packard, 1998],has a maximum number of 1601 frequency points per frequency sweep. In this work themaximum bandwidth in a measurement is 400 MHz, this result in a frequency step 1 f of250 kHz. The corresponding repetition time is 4 µs. In Section 2.10.1 it is shown that thePDP duration is 2 µs for the DECT indoor environment. As a consequence, the effects ofaliasing can be neglected in this work.


Due to the rapid amplitude decay of the PDP (the time domain signal) the theory ofessentially band-limited signals applies [Shanmugam, 1985] [Briggs and Henson, 1995].This theory involves an uncertainty principle that states that both the time duration andbandwidth of a signal cannot be made arbitrarily small simultaneously [Papoulis, 1977].It is outside the scope of this work to estimate the error made by the DIFT. However, asdemonstrated in this section, the sampling theorem is satisfied and the frequency band-width is always scaled such that the PDP has a sufficient resolution with respect to thepulse width. This procedure is generally accepted as being accurate enough [Briggs andHenson, 1995].

4.4.2 Windowing

If a DIFT is applied to a signal then, from the continuum of possible time instances, onlythose that coincide with the basis of discrete equidistant time-instances will project onto asingle basis vector. All other time-instances will exhibit nonzero projections on the entirebasis set [Harris, 1978]. This is often referred to as spectral leakage. Spectral leakageoccurs for signals that contain frequencies that are non-periodic within the observationinterval. Although the amount of leakage is influenced by the sampling period, leakage isnot caused by the sampling. Windows are weighting functions applied to data to reducethe order of the discontinuity at the boundaries of the periodic extension. The result isthat a signal of arbitrary frequency will exhibit a significant projection only on those basisvectors corresponding to a frequency close to the signal frequency.

By applying a window the spectral leakage can be reduced at the expense of distortingthe obtained data with the imperfections of the window itself. For example, one of thoseimperfections is the sidelobe of the Fourier transform of the window. Windowing amountsto multiplying the data by a weighting function. The multiplication in the frequencydomain is equivalent to a convolution in the time domain. The result is that the timedomain spectrum of the window is present in the impulse response. The data from thenetwork analyser can be interpreted as the result of a rectangular window applied to theinfinite frequency interval. The time domain spectrum of a rectangular window is thesinc function. The sinc function has a highest sidelobe level of -13 dB [Harris, 1978].As a consequence the dynamic range in the time domain is limited to 13 dB due to therectangular window applied in the frequency domain. Another window with a lowersidelobe level will be applied to suppress the effects of the rectangular window.

Many figures of merit for windows exist [Harris, 1978]. In this work, the sidelobelevel and the worst-case processing loss are chosen to evaluate the performance of win-dows. The worst-case processing loss is a measure for the reduction of output signal-to-noise ratio as a result of windowing and of worst-case frequency location [Harris, 1978].This is related to the minimum detectable tone in broadband noise. Windows with aworst-case processing loss exceeding 3.8 dB are considered to be very poor windows. Atrade-off between processing loss and highest sidelobe level can be made.


Table 4.2 lists certain types of windows with their sidelobe level and processing loss.One of the listed windows is the Gaussian window:

( f ) = e

−(π f − π f0

a

)2

+ e−(π f + π f0

a

)2

. (4.12)

This expression is similar to that of the Gaussian modulated sine source 2.13. Thepulse decay a defines the highest sidelobe level and the processing loss of the Gaussianwindow. The smaller the processing loss, the higher the sidelobe level, Table 4.2. Bychanging the value of a a trade-off between the processing loss and sidelobe level canbe made depending on the application. The performance of a Gaussian window witha = 0.8886 B is comparable with that of a Hamming window (Table 4.2).

In this work the Gaussian window with a = 0.8886 B is chosen. Better windowsalso exist [Harris, 1978], for example, the Blackman-Harris window can be encounteredin other publications [Bultitude, 1998]. Many of these better windows are constructedwindows that are complex to evaluate [Harris, 1978]. The Gaussian window is chosenbecause it can be analytically evaluated, this and others aspects are already mentioned inSection 2.5. Windowing the frequency-domain transfer function with different windowwidths results in different amplitudes of the PDP. This effect could be taken into account inthe definition of the window by means of an bandwidth-depending multiplication factor.In this work, however, only normalised PDPs are considered.

Window type Sidelobe (dB) Process loss (dB)

Rectangular -13 3.92

Triangle -27 3.07

Gaussian a = 0.8886 B -42 3.14

a = 0.7405 B -55 3.40

a = 0.6347 B -69 3.73

Hamming -43 3.10

Table 4.2: Overview of windows [Harris, 1978]. The bandwidth B is definedin Hz.


2 2.1 2.2 2.3 2.4−60

−45

−30

−15

0

15

Frequency (GHz)N

orm

alis

ed p

ower

(dB

)

2 2.1 2.2 2.3 2.4−60

−45

−30

−15

0

15

Frequency (GHz)

Nor

mal

ised

pow

er (

dB)

Figure 4.4: Normalised power of the measured frequency-domain data, top fig-ure, and that of the data windowed with a Gaussian window witha = 0.8886 B, bottom figure.

Figure 4.4 shows the normalised power of the measured frequency-domain data andthat of the windowed data. Due to the windowing the values at the boundaries are sup-pressed by 27 dB. Figure 4.5 shows the time domain result, i.e., the power delay profile,for two values of a. This figure shows that increasing a reduces the time resolution.

The Gaussian window of Equation 4.12 is not causal. A sufficient long delay musttherefore be added to prevent the PDP from starting on the negative time axis. Thismethod similar to that used to make Gaussian modulated sine source causal (Equation2.12. Here, the delay of the window tw is chosen to be:

tw = 3

a. (4.13)

With this delay the window has a sufficiently small amplitude at t = 0.The most important quantities obtained from the PDP, like the received amplitude

and the delay spread are not a function of the propagation delay (Section 2.7.1). Thenumerical calculations, however, are implemented in a general way assuming the PDP tostart immediately after t = 0. With an extra delay, the PDP will start after the propagationdelay td , that is the time needed for the waves to travel from the transmitter to the receiver.

4.5. Measurement accuracy 89

0 200 400 600 800−80

−60

−40

−20

0

20

Time (ns)

Nor

mal

ised

pow

er (

dB)

a = 0.8886 B

0 200 400 600 800−80

−60

−40

−20

0

20

Time (ns)

Nor

mal

ised

pow

er (

dB)

a = 0.6347 B

Figure 4.5: Power delay profile of the measured frequency-domain data shownin Figure 4.4 for the specified values of a.

As a result in this work, like in Figure 4.5, the propagation delay is compensated for byimplementing it as a negative delay in the window.

When the two delay times are incorporated the Gaussian window becomes:

( f ) =

(

e−(π f − π f0

a

)2

− e−(π f + π f0

a

)2 )

ej2π f

(td − 3

a

). (4.14)

This equation is similar to Fourier transform of the Gaussian modulated sine source, Equa-tion 2.13.

4.5 Measurement accuracy

Before a measurement is made with the network analyser, an error-correction procedureis carried out with a set of calibration standards. Error correction is an accuracy enhance-ment procedure that removes systematic errors in the measurement set-up. The removalof the systematic errors is called calibration. After calibration only statistical errors con-tribute to the measurement accuracy. These errors are caused by oscillator drift, thermalnoise, mechanical vibrations, etc.


The contribution of the statistical errors to the accuracy can be modelled by insertingan equivalent noise source at the input of the network analyser. This noise source has aflat power spectral density within the measurement bandwidth. The standard deviationof the noise amplitude and phase in the frequency domain is specified in the user’s guide[Hewlett Packard, 1998]. The standard deviation of the noise amplitude is about 0.1 dBand that of the phase is about 1 degree for the dynamic range and power levels of themeasurements carried out in this work. In the complex plane these values define a circulararea centred around the value of the measured scattering parameter.

The effect of the noise source on the measured PDP is similar to the effect of a thermalnoise source. This means that noise floor with an average power level can be defined. Thislevel can be obtained with Parseval’s theorem [Shanmugam, 1985], which relates theaveraged power in the frequency domain to that in the time domain. Several simulationshave been done to study the time-domain noise floor. In these simulations noise is added toan ideal (constant) frequency transfer function. Then the procedure of the previous sectionis followed to obtain the PDP via a DIFT. The noise-source parameters have been chosenidentical to that specified in the user’s guide [Hewlett Packard, 1998]. The simulationsshow that the mean power level of the noise floor in the time domain is about -60 dBbelow the maximum of the PDP. This noise floor is also visible in the measured PDPs ofFigure 4.5 after 500 ns.

A different source of errors is the time resolution of the PDP. Figure 4.6 shows anenlarged PDP. The measurement bandwidth has been 400 MHz. The corresponding timeresolution is 2.5 ns, which can be observed in Figure 4.6. The PDP does not look smooth.It seems that a smaller time resolution would improve the PDP. Unfortunately, in thiswork bandwidths larger than 400 MHz have not been considered to prevent interferenceto and from communication systems. In the future larger bandwidths will be consideredat higher frequencies to study the accuracy and convergence of the PDP as a function ofbandwidth. An alternative is to improve the time resolution by using a window with lessprocessing loss, like the Blackman-Harris in [Bultitude, 1998].

0 50 100 150 200−40

−30

−20

−10

0

10

Time (ns)

Nor

mal

ised

pow

er (

dB)

Figure 4.6: Enlargement of the PDP of Figure 4.5 for a = 0.8886B.

4.6. Conclusions 91

Although the time resolution of the PDP seems not to be optimal, it might have a verysmall effect on the performance analysis of narrowband communication systems. Theresponse of the radio channel excited with a realistic pulse is obtained by a convolution ofthe pulse with the impulse response of the channel. The pulse duration, for example, ofthe DECT system is 0.8681 µs (Table 2.1). This is much larger than the 2.5 ns resolutionof the measured PDP. As a result, the shape of the curve obtained by the convolutionwill be determined for a large part by the DECT pulse shape. Improving the resolutionof the PDP might not be needed in this case. For the delay spread. however, the timeresolution of the PDP is important, because this quantity is directly obtained from theimpulse response (PDP) of the radio channel.

By analysing several PDPs, like that of Figure 4.6, the accuracy of the amplitudes ofthe PDP is estimated to be in the order of 1 dB. This value will be used in this work. Anaccuracy analysis based on very wideband measurements will give a better estimate of theaccuracy. This will be done in the future.

The results in this work obtained from measurements are similar to those from com-puter simulations (FDTD method) and those that can be found in the literature. Themeasurement procedure can therefore be considered to be accurate enough.

4.6 Conclusions

In this section a summary is given of the measurement procedures for obtaining the PowerDelay Profile (PDP). The PDP is obtained by carrying out the following steps:

1. Use the measurement set-up described in Section 4.2 to obtain the frequency trans-fer function S21 of the radio channel as a function of position. Check if the fre-quency step1 f is small enough to ensure that aliasing in the time domain is absent(Section 4.4.1).

2. Apply the Gaussian window with a = 0.8886 B to improve the time-domain trans-fer function and also add an appropriate delay to make the Gaussian pulse causal(Equation 4.13) and to have the PDP started at t = 0 (Equation 4.14):

( f ) =

(

e−(π f − π f0

a

)2

− e−(π f + π f0

a

)2 )

ej2π f

(td − 3

a

).

By changing the value of a the bandwidth also changes. This is done to obtaintime-domain data for different system bandwidths from a single measurement (e.g.Section 5.4.2 and Figure 5.22). The value of a should not be chosen higher than0.8886 B to prevent a distortion of the PDP due to an increased sidelobe level ofthe window.

3. Apply a discrete inverse Fourier transformation −1 (Equation 4.7) and calculate

the PDP P(t) with Equation 4.4:

P(t) = 2| −1 ( f ) S21( f ) |2. (4.15)


The accuracy of the PDP is about 1 dB (Section 4.5). In the future the accuracy willbe analysed in more detail by performing measurements with larger bandwidths. Thestatistical errors that remain after calibration of the network analyser result in a noisefloor at about -60 dB from the maximum of the PDP.

In the following chapter the PDP is used to analyse the delay spread and the perfor-mance of diversity systems.

Chapter 5

Design of adaptive diversityimplementations

5.1 Introduction

For portable and mobile communication systems the level or amplitude of the receivedsignal varies due to varying radio-channel characteristics. As a result the status of theradio channel itself is unknown and time varying. If the channel is in a deep fade thenerrors might occur in the reception of data. The received signal has a certain probabilityto fade below a threshold value. Within a diversity system one or more interfaces to theradio channel, diversity branches, are connected to a receiver. If the received signals fromeach diversity branch fade independently, then the probability that all received signals willfade below the threshold value is considerably reduced.

The signals at the output of the diversity circuits vary as a function of time and lo-cation. Circuits that are implemented to compensate for the imperfections of the radiochannel should therefore be adaptive. This chapter introduces the application of adaptivediversity techniques to indoor portable communication systems at frequencies around 1 to2 GHz (GSM, DECT). There are many ways of doing this, the most popular implementa-tions are summarised in Section 5.2. In Section 5.2.7 these different implementations arecompared. Space diversity seems to be the most favourable for a handset.

The received signals from the diversity branches are selected or combined before theyarrive at the detector. Again, many techniques of combining exist, they are summarisedin Section 5.3. The different combining techniques are compared for a space-diversityreceiver in Section 5.4. The measures for ranking them is the diversity gain and arraygain, which are introduced in the same section. Equal-gain combining is chosen as thebest performing combining technique with respect to circuit complexity.

The equal-gain combiner is in most studies an ideal one that has the ability to combinesignals with an arbitrary phase difference. For practical implementations a discrete phaseshifter with a fixed number of phase-shift values has some advantages. In Section 5.5 theperformance of the ideal equal-gain combiner is compared to a discrete one.

93

94 Chapter 5. Design of adaptive diversity implementations

Depending on the type of system the implementation of the diversity algorithm shouldbe fast enough to track the variations of the received signals. In Section 5.7 this is analysedfor two-phase equal-gain combiners with different response times. The speed of move-ment of the portable device is set to 5 km/h, which is comparable to the speed of a walkingperson. The following section, Section 5.6, addresses an additional advantage of equal-gain combining for a space diversity receiver. By using such a system during transmissionthe Specific Absorption Rate (SAR) within the human head can be reduced. Another wayof improving the performance of a receiver is the application of an equaliser. Section 5.8shortly describes the difference between diversity and equalisation. A diversity receivercombines the signals that are coming from the diversity branches, An adaptive receiverdoes this by changing the combination depending on some quality measure. In Section5.9 different quality signals are introduced and compared.

This chapter ends with an overview of all the choices that have been made for a di-versity system for handsets (Section 5.10). The resulting system is implemented in aprototype, which is described in detail in Chapter 6. The diversity methods will onlybe considered for the receiver. Transmit-diversity systems are only briefly discussed inthis work (e.g., Section 5.6). The procedure and the tools developed for it, however, areexpected to be useful for the design of transmit antenna-diversity implementations.

5.2 Diversity implementations

The objective of diversity is to provide a communication system with two or more pathsfrom transmitter to receiver across the radio channel so that the fading phenomena ofthese paths are as uncorrelated as possible. Continuously selecting the path with the bestsignal quality will result in an improved communication link. Different ways of accessingthe radio channel (diversity) are possible to obtain uncorrelated paths.

The application of diversity can also result in an improved signal-to-interference ratio.This aspect of diversity is not considered here. In the following sections the advantagesand disadvantages of basic diversity implementations are summarised.

5.2.1 Space diversity

Multiple receive (or transmit) antennas can be placed at different locations. Each antennawill receive the transmitted signals via different paths through the radio channel. Thereceived signals of the different antennas will therefore be mutually decorrelated. Theamount of decorrelation depends on the antenna separation. In most cases, a separationof approximately half a wavelength is sufficient [Jakes, 1994]. This principle of obtainingdecorrelated signals is called space diversity. Space diversity is illustrated in Figure 5.1.

A disadvantage of space diversity is the increased volume needed to contain multipleantennas. The attractiveness of this diversity implementation is its simplicity.

5.2. Diversity implementations 95

r1

r2

r3

Figure 5.1: Space diversity illustrated by three (identical) antennas separatedby distances r1, r2 and r3.

5.2.2 Frequency diversity

The fading characteristics of the radio channel are not the same for different carrier fre-quencies. Transmitting the information using different carrier frequencies may result inuncorrelated signals. This diversity implementation is called frequency diversity. It isillustrated in Figure 5.2. The frequency separation between the carrier frequencies deter-mines the amount of of decorrelation of the signals. The frequency separation, for whichsufficient decorrelation is obtained, is related to the coherence bandwidth (Section 2.3.1).

ampl

itude

frequencyf0,1 f0,2 f0,3

Figure 5.2: Frequency diversity illustrated by three carrier frequencies f0,1,f0,2 and f0,3, that are used for the radio link.

This form of diversity is not very efficient with respect to the use of the available band-width. In most implementations the signal is not simultaneously transmitted on severalcarrier frequencies but only on the one that will result in good transmission. This formof diversity is used in modern multi-carrier communication systems, like GSM or DECT.The hopping between different frequencies results in an increased circuit complexity.

The carrier frequency decorrelation is also exploited in modulation techniques, likeOrthogonal Frequency Division Multiplexing (OFDM) and in access techniques, likeCode Division Multiple Access (CDMA). A communication system based on these tech-niques is more robust against frequency selective fading or interfering transmitters.


5.2.3 Polarisation diversity

The polarisation of the electromagnetic fields has different orientations at different posi-tions. If a linear receive antenna is used, there will be a probability that the orientation orpolarisation of the antenna does not match the polarisation of the electromagnetic fields.This will result in a low received signal level. A differently oriented linear antenna willresult in a higher received signal level. Using multiple differently polarised antennas is away of obtaining uncorrelated signals. This implementation, called polarisation diversity,is relatively simple to implement. An implementation of polarisation diversity is shownin Figure 5.3. A disadvantage is the increased volume to contain the antennas.

x

z

yx

z

Figure 5.3: Polarisation diversity illustrated by two dipoles, one in the x direc-tion and one in the z direction.

For polarisation diversity the combination of horizontally and vertically polarised lin-ear antennas (monopole or dipole antennas) is quite often suggested. However, the hor-izontally polarised antenna has two large nulls in its directivity pattern in the horizontalplane. These nulls reduce the mean received power, because the power is predominantlytransmitted in the horizontal plane. A vertically polarised antenna is omnidirectional inthe horizontal plane, which results in a higher mean received power. Using two diversityantennas which have a certain angle with respect to the horizontal, e.g. 45 and -45 de-grees, results in a better performance than that of the horizontal-vertical implementation.This type of polarisation diversity is referred to as slanted polarisation diversity.

For mobile communication systems, like GSM, the transmitted signals are scatteredand reflected by many objects. In these system polarisation diversity seems to have aperformance close to that of space diversity [Sørensen, 1998], [Emmer, 1998].

5.2.4 Field-component diversity

At a certain location in a multi-path environment with many reflections the electric fieldstrength can be completely different from the magnetic field strength. This is similar tostanding waves occurring in resonators and transmission lines. For these standing wavesthe maximum of the electric field coincides with the minimum of the magnetic field andvice versa.

Using antennas that predominantly couple to only one of the field components canresult in uncorrelated signals. The advantage of this field-component diversity implemen-tation is that the antennas can be situated at the same location. Figure 5.4 shows two

5.2. Diversity implementations 97

Figure 5.4: Field-component diversity illustrated by two antennas, electricdipole and magnetic loop.

antennas that can be applied for field-component diversity. The major disadvantage is therelatively low efficiency of small antennas (including the matching circuits) that predom-inantly couple to the magnetic field. Especially in the frequency range from 1 to 5 GHzthe electric-field antennas have a better efficiency.

Directly summing the signals of an antenna that couples to the electric field (dipole)with one that couples the magnetic field (loop) can result in a ’diversity’ antenna with abetter output signal than a single antenna [Young, 2000]. In this case no additional signalprocessing is needed.

5.2.5 Angle diversity

Local variations of the electromagnetic field are the result of interference between twoor more reflected waves (Chapter 2). By using a directional antenna one of the reflectedwaves can be selected and the other ones can be suppressed. A good angle diversity im-plementation is established either if more than one directional antenna is used, illustratedin Figure 5.5, or if a directional antenna is used that can change its directivity pattern.

Figure 5.5: Angle diversity illustrated by three directional horn antennas, dot-ted lines indicate directivity patterns.

A significant advantage of using angle diversity is the reduction of the time delayspread due to the reduction of received (reflected) waves. This is an interesting feature,especially in environments or locations with high delay-spread values, like highly reflec-tive assembly halls or at the boundaries of communication cells.

A disadvantage of directional antennas is that they have to be large in terms of wave-lengths. For the mobile communications frequency range, approximately from 1 to 5


GHz, antennas are needed that are too large to fit in a handset. However, phased arrayscan also adaptively suppress undesired waves by means of null and beam steering. Thesmallest phased array consists of two antennas and a variable phase shifter. Space diver-sity using equal-gain or maximum-ratio combining constitutes a phased array (Section5.3).

5.2.6 Time diversity

The properties of the radio channel change as a function of time (Chapter 2). By trans-mitting a message two or more times on the same frequency across the radio channel,the probability of good reception is increased. Time diversity is illustrated in Figure 5.6.Increasing the time interval between the messages increases the decorrelation betweenthe received signal levels of the messages. A measure of this decorrelation is the coher-ence time (Section 2.3.1). This time diversity implementation, however, result in half theavailable bandwidth in terms of bytes per second. As a result, this implementation is notvery popular. At the moment it is only used in paging systems. The major advantage is ofcourse that no additional hardware is needed.

1011001101 1011001101td

Figure 5.6: Time diversity illustrated by a data block that is transmitted twicewith delay td .

In Time Division Multiple Access (TDMA) a derivative of time diversity is sometimesused. In TDMA system the information of the source is compressed and subsequentlytransmitted on a single carrier frequency together with the information of other sources.These information packages are called time slots. In the case of interference due to a timeslot of an adjacent communication cell, a different time slot on the same or on differentcarrier frequency can be chosen. This slot hopping results in an improved signal-to-interference ratio.

5.2.7 Comparison of diversity implementations

In the following table the previously described diversity implementations are ranked withrespect to three of their main design characteristics. The emphasis is on the suitabilityof the diversity implementation for indoor portable communications. For basestations orfor mobiles the ranking of the design characteristics of the different implementations willchange.

The size of the implementation is mainly determined by the size of the antenna system.It is assumed that additional circuitry can be integrated without significant increase in size.The performance is determined by the expected improvement in received mean power andby the expected reduction of delay spread. The efficiency is related to the radio channelcapacity needed for a certain diversity implementation.

5.3. Diversity combining techniques 99

Diversity implementation Size Performance Efficiency

Space − + 0

Frequency 0 + −−Frequency hopping 0 + 0

Polarisation, horizontal/vertical − − 0

Polarisation, slanted − + 0

Field-component − − 0

Angle with directional antennas −− ++ 0

Angle with adaptive beam steering − ++ 0

Time 0 + −−

−− : unacceptable, − : unfavorable, 0 : neutral, + : favorable, ++ : excellent

Table 5.1: Relative comparison of different diversity implementations for in-door communications.

From the table the angle diversity implementation with adaptive beam steering is cho-sen as the most favourable diversity form. Due to the size constraints of the handset,this type of diversity will be implemented as a two-antenna array. The angle diversityimplementation with adaptive beam steering is based on a space diversity implementa-tion. In Section 5.4, different combining techniques in combination with a space diversityimplementation are compared based on their performance.

5.3 Diversity combining techniques

In the previous section ways of obtaining uncorrelated transmission paths, diversity im-plementations, have been reviewed. This section will illustrate how these uncorrelatedpaths can be chosen or combined. The implementation examples are based on a spacediversity implementation. For planar antenna arrays a good decorrelation between thereceived signals is obtained for antenna separations of about 0.5 λ [Lee, 1971], [Lee,1972]. This antenna separation will therefore be used in the examples of the sections.The combining techniques can also be applied to all the other diversity implementations.

The implementation examples contain a microcontroller µC to process the qualitysignal sq and to control the combiner. The quality signal sq , which is a measure of thequality of the received diversity signal, is generated by the receiver. In this section thequality signal can be regarded as a measure of the Signal-to-Noise Ratio (SNR) at theantenna terminals. The relation between the SNR and the BER depends on the type ofsymbol detector. Section 5.9 deals with the generation and the definition of the qualitysignal in more detail. For simple combining schemes the microcontroller can be replacedby, for example, a discrete solution.


The diversity combining techniques presented in this section generate an output signalVout which is a based on the signals received by two antennas Vr,1 and Vr,2 at differentpositions. The received noise power at the antenna terminals, necessary to obtain the BER,is omitted in this section. The expressions for the output signal Vout can be considered tohave been normalised on the noise power received by only one antenna. As a consequencethe expressions show the improvement in the SNR. The received noise power and thecomparison of the diversity combining techniques is dicussed in Section 5.4. The receivedsignals Vr,1 and Vr,2 are functions of time. As a consequence Vout is also a function oftime. The time variations are caused by movement of the receiver or by movement ofpeople or other objects within the propagation environment.

The formulas of Vout are written such that operations, like switching and selection, canbe done in an instanteneous way. This is not a realistic assumption. Therefore, in Section5.7 the speed of the algorithms is reduced to a level that can be realised in hardwareimplementations.

5.3.1 Switched combining

In switched combining only one of the diversity signals is directed to one receiver. Theother diversity signals are not used. The quality of the different diversity signals cannotbe determined with only one receiver. As a consequence, switching between the diversitysignals is not done based on their quality; it is done based on a threshold level for thequality of the diversity signal that is being used for data reception. As long as the levelof this quality signal is sufficient nothing will happen. As soon as the level drops belowa certain predetermined threshold level one of the other diversity signals will be chosen.If the quality of the new diversity signal is also below threshold the next diversity signalwill be chosen. This will continue untill a diversity signal with sufficient quality is found.Swithed combining is illustrated in Figure 5.7.

RX

µCsq

Vr,1

Vr,2

Voutdata

Figure 5.7: Switched combiner, solid lines represent signal lines, dashed linesrepresent control lines, sq is the signal of the quality indicator.Building blocks from left to right: antennas, controlled switch, mi-crocontroller µC and receiver RX.


The operation of the algorithm can be summarised as follows:

Vout,2 =

Vr,1 if Vout,1 = Vr,1 and |Vout,1| ≥ VT

Vr,1 if Vout,1 = Vr,2 and |Vout,1| ≤ VT

Vr,2 if Vout,1 = Vr,2 and |Vout,1| ≥ VT

Vr,2 if Vout,1 = Vr,1 and |Vout,1| ≤ VT

, (5.1)

where, Vout,2 is the new output voltage, Vout,1 is the previous output voltage, Vr,1 andVr,2 are the received voltages of antenna 1 and 2, respectively and VT is a threshold valuerelated to the required BER. If the time needed to decide and switch is reduced to zero,then the diversity algorithm has the ability to continuously scan the antennas for a signalwith the required quality. In this case the switched diversity algorithm behaves like aselective combiner, which is presented in Section 5.3.2.

In a practical implementation continuously switching between the diversity signals isprevented by waiting a certain amount of time after each switching action. This resultsin hysteresis. Without hysteresis the switch might start oscillating between the diversitysignals. Hysteresis also prevents undesired short times between switching actions. If toomany switch actions per second occur, then the receiver might get out of lock with thetransmitter; this is called switching loss. Worst case, switching loss can result in loss oflarge blocks of data.

The value of the threshold level should be chosen with care. If this value is chosenin correspondence to a certain required BER, e.g. 10−3, then for other BER values thecombining will be suboptimal. Instead of using a fixed threshold level and also a fixedhysteresis, an adaptive update could optimise both quantities towards minimum switchingloss and maximum performance. This results in different settings as a function of timefor these quantities and hence a different behaviour as a function of time for the com-plete system. For example, close to a basestation the amount of switching actions canbe minimised, further away from the basestation the amount of switching actions couldbe increased to a point where the switching loss becomes unacceptable. More details onchoosing the threshold level and on hysteresis can be found in [Jakes, 1994].

5.3.2 Selective combining

In selective combining the best diversity signal is continuously selected and directed tothe output via a diversity switch. The operation can be described as:

Vout =

Vr,1 if |Vr,1| ≥ |Vr,2|Vr,2 if |Vr,2| > |Vr,1| , (5.2)

where Vout is the output voltage and Vr,1 and Vr,2 are the received voltages of antenna1 and 2, respectively. The principle of selective combining is illustrated in Figure 5.8for two antennas. In this figure the demodulated counterparts of the signals of the twodiversity branches are selected. Therefore, the output signal Vout is not shown.

Quality signals of each diversity input signal must be continuously available to selectthe best input signal. The easiest way of doing this is by using complete receivers for eachdiversity signal and derive the quality signals from the receivers. This implementation is


RX2

sq,1

sq,2

µC

Vr,1

Vr,2 data

RX1

Figure 5.8: Selective combiner, solid lines represent signal lines, dashed linesrepresent control lines, sq,1 and sq,2 are signals of the quality indi-cators. Building blocks from left to right: antennas receivers RX1and RX2, microcontroller µC and controlled switch.

shown in Figure 5.8. Depending on the type of quality signal only parts of receiversmay be needed to obtain a quality signal (Section 5.9). A selective diversity combiningtechnique has a better performance compared to a switched combining technique.

A hybrid form of the selective combining technique uses a well-defined preamblethat precedes the transmitted data [Almholt and Nielsen, 1996]. During the preamblethe different diversity signals are compared and the best signal is chosen for reception.During the remainder of the time slot no switching or scanning will be done. This is calleda select and stay strategy. The advantage is that only one receiver is needed instead oftwo or more. The disadvantages are a decrease of effective bandwidth due to an extendedpreamble and inability to select another diversity signal during the transmission of thedata. Depending on the type of communication system the performance of the select andstay strategy can be comparable to that of maximum-ratio combining [Reiter, 1999]. Inthe Philips Kala DECT-phone a select and stay strategy is used (Section 6.10.1).

For a selective combining technique, hysteresis is also useful to prevent undesiredshort times between switching actions. Short times between switching actions may resultin ’switching loss’ introduced in the previous section. An adaptive hysteresis might furtherimprove the dynamic behaviour and performance of a selective combining technique.

5.3.3 Equal-gain combining

Due to reflections of the waves inside a building the wavefronts of these waves will reachthe antennas of a communication system with arbitrary angles. This is illustrated in Fig-ure 5.9. The behaviour of the output signals of a multiple antenna system as a functionof angle of incidence φ (angle between direction of propagation and antennas) is welldescribed in literature on phased arrays [Collin, 1985]. Here the output signal of twoomni-directional antennas connected to a summing circuit will be considered for a plane(2-dimensional case).


Vout

y

x

ra

φ

+

Figure 5.9: Wavefront, indicated by solid lines, incident on two antennas con-nected to summing circuit +, ra is the antenna separation and φ isthe angle angle of incidence.

The amplitude of the output voltage of the summing circuit V in terms of antennaseparation ra and angle of incidence φ can be written as:

|Vout(φ)| = A

∣∣∣∣∣ 1+ ej

(2π

λra cos(φ)

) ∣∣∣∣∣ = 2A∣∣∣cos

(πλ

ra cos(φ))∣∣∣ , (5.3)

with A an arbitrary amplitude, which is identical for the signals of both antennas, andwith λ the wavelength of the carrier frequency. The wavefront is considered to be a plane;this only holds for waves that have travelled a sufficiently long distance from the sourceor from induced sources present in reflecting surfaces. Furthermore, in this chapter it isassumed that mutual coupling between the antennas can be neglected. This is a reasonableassumption for antenna separations of more than approximately λ/2 [van Leersum, 1995].It is clear that the output voltage Vout is a function of φ.

The maximum values of the amplitude, |Vout | = 2A and minimum values, |Vout | = 0are given by:

|Vout | = 0 for φ = arccos

((2n + 1)λ

2ra

)with

∣∣∣∣(2n + 1)λ

2ra

∣∣∣∣ ≤ 1, (5.4)

|Vout | = 2A for φ = arccos

(nλ

ra

)with

∣∣∣∣nλ

ra

∣∣∣∣ ≤ 1, (5.5)

where n is an integer. Apparently, the antenna system works as a spatial filter; it sup-presses and amplifies waves depending on their angle of incidence. This property is illus-trates in Figure 5.10 for different antenna spacings ra .


Figure 5.10: Normalised directivity patterns of two omni-directional antennasconnected as shown in Figure 5.9 for different antenna separationsra: λ/4, λ/2, λ, 1.5λ, 2λ, 5λ.

A spatial filter can prevent cases of destructive interference (where the output signalis too small for reliable detection) by simply eliminating a number of incident waves.This could also improve the time delay spread, because only a small set of incident wavescontribute to the output signal; the other waves are suppressed. By only adding the signalsof both antenna the directivity pattern of the spatial filter is fixed. It is not desired thata user should manually orient the antenna system to find the best orientation of the filterwith respect to the incident waves. Therefore, a controlled time delay td is introduced inone of the antenna paths as shown in Figure 5.11.

+ datatd

sqVout

Vr,2

Vr,1RX

Figure 5.11: Equal-gain combiner, solid lines represent signal lines, dashedlines represent control lines, sq is the signal of the quality indi-cator. Building blocks from left to right: antennas, controlled timedelay td , summing circuit + and receiver RX.


The amplitude of the output voltage of the summing circuit can be written as:

|Vout(φ, td)| = A

∣∣∣∣∣ 1+ ej

(2π

λra cos(φ)

)

ej

(2π tdc

λ

) ∣∣∣∣∣

= 2A

∣∣∣∣cos

(π

λra cos(φ)+ π tdc

λ

)∣∣∣∣ ,(5.6)

where c is the speed of propagation of electromagnetic waves in vacuum (≈ 3 · 108 m/s)and A is an arbitrary amplitude.

The quality signal sq generated by the receiver RX in Figure 5.11 has the same purposeas in the previous sections. It is used to control the time delay td in such a way thatthe output signal of the summing circuit is optimised to enable reliable detection by thereceiver. This combining technique is called equal-gain combining, because the antennasignals are amplified with amplifiers with identical gain factors. Due to the alignment intime of the two antenna signals the operation of selective combining can be described by[de Bot, 1993], [Green and Jensen, 2000]:

Vout = |Vr,1| + |Vr,2|√2

, (5.7)

where Vout is the output voltage and Vr,1 and Vr,2 are the received voltages of antenna 1and 2, respectively. It is assumed that the noise voltages from both antennas are uncor-related, such that they do not combine in phase. This results in the factor of

√2 in the

denominator.In Equation 5.3 the only degree of freedom (for a system with a fixed carrier fre-

quency) is the antenna separation ra . For portable communication systems like DECTand GSM the wavelength is in the order of 10 to 30 centimetres. The maximum sizes ofthe handsets for these systems are 20 centimetre or less. Therefore, if two antennas aremounted inside these handsets the separation will automatically be at most in the order ofa wavelength. As an example ra will now be chosen equal to λ/2 in Equation 5.6:

|Vout(φ, td)| = 2A

∣∣∣∣cos

(π

2cos(φ)+ π tdc

λ

)∣∣∣∣ . (5.8)

The controlled delay td can be replaced by a controlled phase shifter ξ , which is afunction of the frequency:

ξ( f ) = 2π tdc

λ= 2π td f, (5.9)

with f the carrier frequency. This equation clearly shows that if f changes then ξ shouldalso change. If the frequency content of the incident waves is small, replacing the con-trolled delay with a controlled phase shifter will not introduce large errors. The maximumabsolute phase error1ξ using a phase shifter depends on the maximum frequency devia-tion 1 f . In DECT the bandwidth for each channel is approximately 1 MHz (Table 2.1),which results in a 1 f of 0.5 MHz:

1ξ = 2π td1 f = 3.142 · 106td . (5.10)


Realistic values for td at 1900 MHz are between 0 and 1 ns (a phase-shift value of 360equals a delay of 0.53 ns). Substituting the maximum value of td in the previous equa-tion results in a negligible error 1ξ . For most narrowband communication systems thecontrolled time delay can be replaced by a controlled phase shifter.

Substituting Equation 5.9 in 5.8 gives:

|Vout(φ, ξ)| = 2A

∣∣∣∣cos

(π

2cos(φ)+ ξ

2

)∣∣∣∣ . (5.11)

This equation is based on an antenna separation of half a wavelength and represents theoutput voltage of the summing circuit for the 2-dimensional case. Figure 5.12 shows thereceived voltage as a function of φ (directivity pattern) for different combining phases ξ .

Figure 5.12: Normalised directivity patterns of two omni-directional antennasconnected as shown in Figure 5.11 with an antenna separation ra

of λ/2 for different combining phases ξ : 0, π/3, 2π/3, π , 4π/3,5π/3.

The (far-field zone) expression for the amplitude of the output voltage of the summingcircuit for the three-dimensional case with two identically oriented antennas with (far-field) antenna directivity pattern Ef (θ, φ) located on the x-axis with a separation of ra (ra

must be small in terms of wavelengths) is:

|Vout(θ, φ, ξ)| = A | Ef (θ, φ)|∣∣∣∣∣ 1+ e

j

(2π

λra sin(θ) cos(φ)

)

e jξ

∣∣∣∣∣

= 2A | Ef (θ, φ)|∣∣∣∣cos

(π

λra sin(θ) cos(φ)+ ξ

2

)∣∣∣∣ ,(5.12)

where the antenna without phase shifter is chosen as a reference for the phase, A is anarbitrary amplitude, no polarisation mismatch between the waves and the antennas is


assumed, mutual coupling between the antennas is neglected and θ and φ represent theangle from an observation point to the positive z-axis and to the xz-plane, respectively, ofa Cartesian xyz right-hand co-ordinate system.

As an example two parallel half-wavelength dipole antennas with a separation ra ofhalf a wavelength will be chosen. The configuration is shown in Figure 5.13. The direc-tivity | Ef (θ, φ)| of a dipole antenna is approximated by [Collin, 1985]:

| Ef (θ, φ)| =

∣∣∣∣∣∣∣

cos(π

2cos(θ)

)

sin(θ)

∣∣∣∣∣∣∣. (5.13)

Substituting ra and | Ef (θ, φ)| in Equation 5.12 results in:

|Vout(θ, φ, ξ)| = 2A

∣∣∣∣∣∣∣

cos(π

2cos(θ)

)

sin(θ)

∣∣∣∣∣∣∣

∣∣∣∣cos

(π

2sin(θ) cos(φ)+ ξ

2

)∣∣∣∣ . (5.14)

λ/2

z

y

x

λ/2

Figure 5.13: Two parallel half-wavelength dipole antennas with a separation ofhalf a wavelength.

Figure 5.14 shows a few normalised directivity patterns for the setup and orientationof Figure 5.13. It shows that choosing an appropriate phase difference ξ between the twoantennas results in a spatial filter that is capable of attenuating undesired or interferingsignals coming from a specific direction. This type of equal-gain combining can be usedwith an angle diversity implementation introduced in Section 5.2.5. The shape of thedirectivity pattern as a function of phase difference ξ does not change rapidly for thissmall phased array.

The two antennas can also be connected to more than one phase shifter. This resultsin the ability to constitute multiple different directivity patterns at the same time. Animplementation with two phase shifters, a dual equal-gain combiner is shown in Figure5.15.


Figure 5.14: Normalised directivity patterns of two parallel dipoles connectedas shown in Figure 5.11 with an antenna separation ra of λ/2 fordifferent combining phases ξ : 0, π/3, 2π/3, π , 4π/3, 5π/3.

data+sq,1

ξ1

+ξ2

sq,2

RX2

RX1

data

Figure 5.15: Equal-gain combiner with two phase shifters, solid lines representsignal lines, dashed lines represent control lines, sq,1 and sq,2 arethe signals of the quality indicators. Building blocks from left toright: antennas, controlled phase shifters ξ1 and ξ2, summing cir-cuits + and receivers RX1 and RX2.


5.3.4 Maximum-ratio combining

The maximum-ratio combining technique is the most optimal technique. In this techniquenot only a controlled phase difference, like in equal-gain combining, but also a controlledamplitude difference between two antennas is introduced. A symbolic representation ofa maximum-ratio combiner is shown in Figure 5.16. Due to the alignment of the phasesand amplitudes of the two antenna signals the operation of maximum-ratio combiningtechnique can be described by [de Bot, 1993], [Proakis, 2000]:

Vout =√|Vr,1|2 + |Vr,2|2, (5.15)

where Vout is the output voltage and Vr,1 and Vr,2 are the received voltages of antenna 1and 2, respectively.

Vout+td

Vr,1

Vr,2RX data

sq,1sq,2

Figure 5.16: Maximum-ratio combiner, solid lines represent signal lines, dashedlines represent control lines, sq,1 and sq,2 are signals of the qualityindicators. Building blocks from left to right: antennas, controlledamplifier, controlled time delay td , summing circuit+, receiver RX.

The quality signals sq,1 and sq,2 are generated by the receiver RX in Figure 5.16. Theyare used to control the amplitude D and the adjustable time delay td in such a way that theoutput signal of the summing circuit is good enough for reliable detection by the receiver.For the maximum-ratio combiner the level of the signal and that of the noise from eachdiversity branch must be determined. These and the corresponding quality signal(s) haveto be derived from only one input signal. This is one of the implementation difficultiesof the maximum-ratio combining technique that increases the complexity of the controlalgorithms and associated circuitry.

The (far-field zone) expression for the amplitude of the output voltage of the summingcircuit for the three dimensional case with two identically oriented antennas with (far-field) antenna directivity pattern Ef (θ, φ) located on the x-axis with a separation of ra (ra

must be small in terms of wavelengths) is:

|Vout(θ, φ, ξ)| = A | Ef (θ, φ)|∣∣∣∣∣ 1+ D e

j

(2π

λra sin(θ) cos(φ)

)

e jξ

∣∣∣∣∣ , (5.16)

where the antenna without phase shifter is chosen as a reference for the phase, A is anarbitrary amplitude, D is the amplitude of the controlled amplifier or attenuator with


0 ≤ D ≤ 1, a perfect polarisation match between the waves and the antennas is assumedand θ and φ represent the angle to the positive z-axis and to xz-plane, respectively, of aright-hand Cartesian xyz co-ordinate system.

Like in the previous section (Equation 5.8), two parallel half-wavelength dipole anten-nas with a separation ra of half a wavelength will be chosen (Figure 5.13). The directivity| Ef (θ, φ)| of a dipole antenna is given in Equation 5.13. Figures 5.17 and 5.18 show a fewnormalised directivity patterns for the setup and orientation of Figure 5.13. Figure 5.17shows the directivity patterns for D = 0.4, the phase differences ξ are chosen identicalto that of Figure 5.14. The possibility of an amplitude difference D between the two an-tennas enables a large variety of directivity patterns. As shown in Figure 5.18 the ratiobetween the maxima and minima of the directivity pattern can be changed with the con-trolled amplitude difference. When D is chosen very small the directivity pattern of onlyone dipole remains, Figure 5.18 with D = 1/32. This might be beneficial if the qualityof the signals from one of the antennas is very poor.

The two antennas can also be connected to more than one controlled amplifier, phaseshifter and receiver in a similar manner as shown in Figure 5.15 for the equal-gain com-biner. This results in the ability to constitute multiple different directivity patterns at thesame time.

Figure 5.17: Normalised directivity patterns of two parallel dipoles connectedas shown in Figure 5.16 with an antenna separation ra of λ/2,combined with a fixed amplitude difference D = 0.4 but differentphases ξ : 0, π/3, 2π/3, π , 4π/3, 5π/3.

5.4. Performance and comparison of diversity combining techniques 111

Figure 5.18: Normalised directivity patterns of two parallel dipoles connectedas shown in Figure 5.16 with an antenna separation ra of λ/2,combined with a fixed phase difference ξ = π/3 but different am-plitudes D: 1, 1/2, 1/4, 1/8, 1/16, 1/32.

5.4 Performance and comparison of diversity combiningtechniques

In the previous sections different combining techniques have been introduced. With thechoice of space diversity as the most favourable diversity implementation (Section 5.2.7)the diversity receiver can be completed by choosing a combining technique. In order tocompare receivers with different combining techniques a measure of their performance isneeded. In this work the performance of a diversity system is expressed in diversity gainand array gain. The considered combining implementations in this section are all basedon space diversity with two antennas at a separation of half a wavelength.

The combining techniques generate an output signal Vout which is a based on thesignals received by two antennas Vr,1 and Vr,2. The performance of the combining tech-niques in this section are based on the normalised Signal-to-Noise Ratio (SNR). The nor-malisation value is the mean SNR of a signal of a single antenna. The mean SNRs ofboth antennas at a large (in terms of wavelengths) distance from the basestation are equaldue to the small distance between the receive antennas (half a wavelength). In this casethe noise power of a single antenna is not relevant, but the improvement in SNR dueto diversity combining is important. This effect has already been taken into account inthe description of the combining algorithms (Section 5.3 and Equations 5.1, 5.2, 5.7 and5.15).

Some results in this and the following sections of this chapter are based on mea-surements inside an office, which can be considered to be a typical DECT propagationenvironment. The measurement set-up is described in Chapter 4. The measurement band-


width has been 25 MHz divided into 1601 frequency points. The antennas at the receiveand transmit side have been half-wavelength dipole antennas. At one side two dipoleantennas, parallel to each other and separated by half a wavelength, have been used toanalyse the diversity combining techniques. These two antennas are connected to theswitch of the measurement set-up shown in Figure 4.1. The measurement plane has beenchosen such that the direct path between the transmit and receive antennas was obstructedfor a about half the number of observation points. This means that both line-of-sight andnon line-of-sight data is included in the results. The results presented in the sections arerepresentative for diversity systems in indoor environments. This has been verified bycomparing the presented results with the results of other measurements.

5.4.1 Measures of performance

In this section the performance of a (diversity) receiver in a multi-path environment isrelated to the Cumulative Distribution Function (CDF), the diversity gain gdiv and thearray gain grr . The CDF for a specified Probability Density Function (PDF) of the SNRγ is defined as follows:

CDF(µ) =∫ µ

−∞PDF(γ )dγ. (5.17)

Figure 5.19 shows the measured CDF of the normalised SNR of a single antenna anddifferent combining techniques normalised to the SNR of a single antenna. The CDFsare based on the time domain amplitudes, that have been obtained with the procedure ofChapter 4. The figure shows that diversity combining result in a SNR distribution that hasa smaller probability of lower SNR values at a specified normalised SNR value.

The probability that the normalised SNR values are lower than a fixed value, µ inEquation 5.17, is called outage. The performance of diversity systems is normally spec-ified for an outage of 1% or 0.1%, e.g. [Green and Jensen, 2000]. A communicationsystem is designed for a specified outage value. In this way the outage is the measureof the reliability of the system. It will be shown that by applying diversity the requiredoutage value can be obtained with a smaller normalised SNR. This improvement can beused to improve a communication system on different points, like reliability, covered area,transmitted power and number of bits per symbol. In this work the diversity gain gdiv isdefined as the improvement of the SNR for an outage of 1%. In figure 5.19 the diver-sity gain for maximum-ratio combining is shown as an example. The diversity gain is afunction of the desired outage as can be seen in the figure: lower outage values result in ahigher diversity gain. By using the diversity gain, different types of diversity combiningtechniques can be compared in a quantitative manner.

Towards lower SNR values the CDF curves in Figure 5.19 become discretised due tothe lower number of measured SNR values in those intervals. This effect will be presentin all CDF curves. At an outage of 1% enough data points, about 25 in Figure 5.19,contribute to allow the calculation of the diversity gain with a reasonable accuracy. Forlower outage values less data points will contribute and the accuracy will decrease.


−40 −30 −20 −10 0 10 200.1

1

10

100

Normalised SNR (dB)

Out

age

(%)

no div sw se

eg =

mr

9.6 dB

Figure 5.19: Measured CDFs of the normalised SNR, ’no div’ = no diversity orsingle antenna, ’sw’ = switched, ’se’ = selective, ’eg’ = equal-gainand ’mr’ = maximum-ratio. The bandwidth B30 is 0 Hz (singlefrequency). The diversity gain for maximum-ratio combining at anoutage of 1% is shown.

The array gain grr is defined as the improvement of the normalised mean SNR at theoutput of the combining circuit, relative to that of a single antenna, averaged over manylocations:

grr = ErSout ErSn,1ErS1 ErSn,out , (5.18)

where Er means the ensemble average over an area, S1 and Sout are the time-averagedreceived signal powers of antenna 1 and the output of the combining circuit, respectively,and Sn,1 and Sn,out are the associated received noise powers. For a two-antenna system thearray gain has a maximum of 3 dB. In this case the output of the two antennas is optimallycombined. Maximum-ratio combining is such an optimal combining technique. The arraygain is often associated with the gain obtained by a phased antenna array that has thecapability of steering its main beam towards a desired direction. The array gain, however,can best be interpreted as the mean improvement of the link budget [Andersen, 2000].


The array gain presented in this work should also be interpreted in this way. The arraygain is an important parameter in those situations in which the coverage is dominated bylow mean power levels caused by large-scale fading or by shielding by objects. Thesesituations can occur at the boundaries of the area that must be covered by a basestation.The diversity gain is important in a multi-path fading environment with sufficiently highmean received power levels, but with a lot of destructive interference.

When a Rayleigh distribution of the received signals is assumed, the array gains of thedifferent combining techniques can be calculated as a function of the number of diversitybranches, also called diversity order, M [Jakes, 1994]:

grr,se =M∑

n=1

1

n, (5.19)

grr,eg = 1+ (M − 1)π

4, (5.20)

grr,mr = M, (5.21)

where se, eg and mr denote selective, equal-gain and maximum-ratio combining, respec-tively. Table 5.2 shows the array gains for two antennas and several values of M . Thistable shows that the array gains slowly (in a logarithmic way) increase as the diversityorder is increased. The array gains of equal-gain combining is close to that of maximum-ratio combining. The array gain of selective combining is much lower than the othertwo.

M 1 2 3 4 10

grr,se (dB) 0 1.76 2.63 3.19 4.67

grr,eg (dB) 0 2.52 4.10 5.26 9.07

grr,mr (dB) 0 3.01 4.77 6.02 10

Table 5.2: Array gain of diversity combiners as a function of diversity orderM from Equations 5.19, 5.20 and 5.21.

The array gain of switched combining grr,sw is a function of the normalised SNR.This is shown in Figure 5.20. The shape of the curve depends on the threshold level andhysteresis time [Jakes, 1994]. The curve of the figure is obtained by using a hystere-sis time of about 0.25 s and the speed of movement of the portable device ν is chosento be 5 km/h. Towards smaller normalised SNRs the same numerical artefacts occur asalready explained for the CDF of Figure 5.19. If the hysteresis is set to zero the perfor-mance of switched combining is equal to that of selective combining. The performanceof the switched combiner depends on many implementation and communication systemparameters [Jakes, 1994]. The switched combiner that switches between antennas will beomitted in the remainder of this work. Switching will be considered in combination withan equal-gain combining technique with a discrete phase shifter (Section 5.5). In this casethe switching is done between combinations of the antennas.


−40 −30 −20 −10 0 10 20−0.5

0

0.5

1

1.5

Normalised SNR (dB)

Arr

ay g

ain

(dB

)

Figure 5.20: Array gain of switched combining as a function of normalised SNR.The bandwidth B30 is 0 Hz (single frequency).

5.4.2 Diversity combining performance as a function of bandwidth

In most textbooks and papers combining techniques are analysed for a bandwidth of 0 Hz[Jakes, 1994], [Proakis, 2000], [Lee, 1993]. As already shown in the simulations ofSection 3.8, a single frequency signal is equivalent to a infinite time duration. This resultsin a standing-wave pattern with a large difference between maximum values (constructiveinterference) and minimum values (destructive interference). The other extreme is usedin channel characterisation and ray-tracing methods, in which the signals have very largebandwidths (Sections 2.8 and 3.5.1). A large bandwidth is equivalent to a very short timeduration. As will be shown in this section the performance of diversity implementationsis a function of the considered bandwidth.

Figure 5.19 shows the measured CDF for a bandwidth of 0 Hz. The results are ob-tained from a single frequency point within the measurement bandwidth. The signalsof each frequency point, however, are measured within 3700 Hz, which is the defaultintermediate-frequency bandwidth of the network analyser. This bandwidth is very smallcompared to the carrier frequencies (in the order of 2 GHz). As a consequence the mea-surement results can be considered to have a zero bandwidth: B30 = 0 Hz. Figures5.21 shows the CDFs for a bandwidth of 25 MHz and 1.5 MHz, respectively. The CDFsare based on the time domain amplitudes, that have been obtained with the procedure ofChapter 4. The bandwidths are the -30 dB or system bandwidths as defined by Equation2.14. The bandwidth is varied by varying the width of the Gaussian window (Section 4.6).The bandwidth of 1.5 MHz has been chosen, because it equals the -30 dB bandwidth ofDECT (Figure 2.1). The curves of the three different bandwidths show large differences.


−40 −30 −20 −10 0 10 200.1

1

10

100

Normalised SNR (dB)

Out

age

(%)

no div se

eg =

mr

B30

= 1.5 MHz

−40 −30 −20 −10 0 10 200.1

1

10

100

Normalised SNR (dB)

Out

age

(%)

no div se

eg =

mr

B30

= 25 MHz

Figure 5.21: Measured CDFs of different combining techniques for the specifiedbandwidth B30, ’no div’ = no diversity or single antenna, ’se’ =selective, ’eg’ = equal-gain and ’mr’ = maximum-ratio.

Figure 5.22 gives the diversity gains for an outage of 1% and the array gains of thecombining techniques as a function of bandwidth. This figure shows that the measuredarray gain for B30 = 0 Hz is close to the gain for the single frequency Rayleigh fadingsignals given in Table 5.2 for M = 2. The diversity gains of all combining techniquesdecrease as a function of increasing bandwidth. In this experiment bandwidths larger than25 MHz were not possible due to the interference from communication systems and otherequipment.

An FDTD simulation (the same as described in Section 3.6) is used to analyse theeffect of increasing the bandwidth to higher values. The results are shown in Figure 5.23.The simulated gains are higher than those of the measurements (Figure 5.22), but the be-haviour as a function of bandwidth and combining technique are similar. The differencesin the gain values are caused by the difference in statistics between the measured and sim-ulated signals. The statistics may depend on many factors: distance between receiver andtransmitters, line-of-sight (LOS) or non LOS situation, attenuation of walls, maximumdynamic range of signals, etc.


100

101

102

0

3

6

9

12

Frequency (MHz)

Div

ersi

ty g

ain

(dB

) Diversity gain

Array gain

selective equal−gain maximum−ratio

Figure 5.22: Measured diversity gains, solid lines, and array gains, dashedlines, at an outage of 1% of diversity combiners as a function of-30 dB bandwidth for the values indicated by the markers.

100

101

102

103

104

0

3

6

9

12

Frequency (MHz)

Div

ersi

ty g

ain

(dB

)

Diversity gain

Array gain

selective equal−gain maximum−ratio

Figure 5.23: Simulated diversity gains, solid lines, and array gains, dashedlines, at an outage of 1% of diversity combiners as a function of-30 dB bandwidth for the values indicated by the markers.


For large bandwidths the array gain of equal-gain combining increases to 3 dB whilethat of selective combining decreases to 0 dB. The decreasing diversity gains can be ex-plained from the fact that for increasing bandwidths the pulse duration decreases. As aresult for a very large bandwidth, like about 1 GHz in Figure 5.23, the overlap of thepulses becomes insignificant. In this case there is not a significant effect of constructiveor destructive interference between replicas of a single transmitted pulse. If a continuousstream of pulses is sent with very small time delays, then there will be large amount ofISI . The reflections of a previously transmitted symbol will interfere with pulses that aretransmitted at later time instances. This interference will also result in envelope fadingcomparable to that of narrowband systems. In order to avoid large amount of ISI mostcommunication systems are designed such that the symbol duration is 10 times the ex-pected mean delay spread. For larger delay spread values, these systems quite often needan equaliser to reduce the ISI (Section 5.8).

The diversity and array gain results for large bandwidths can also be derived from thediversity equations. The mean received powers from the two antennas, Sr,1 and Sr,2 arealmost identical in the time domain, because the distance between the receive antennas(half a wavelength) is much smaller than the distance between the transmit antenna andthe receive antennas (a few metres). The places of the fades within the frequency band ofboth signals differ, because the two antennas have different positions within the propaga-tion environment. Due to the large bandwidth, however, many fades within the frequencybandwidth of each signal exist (the bandwidth is much larger than the coherence band-width). As a result both time domain signals have almost identical amplitudes. The meanmagnitude of the received voltages, |Vr,1| and |Vr,2| will also be almost identical in thetime domain. Using this in Equations 5.2, 5.7 and 5.15, results in a diversity gain of 0 dBfor selective combining and 3 dB for equal-gain and maximum-ratio combining. Thesevalues correspond to the simulated values shown in Figure 5.23 for B30 = 1.18 GHz. Thecorresponding CDFs are shown in Figure 5.24. In order to make use of the power in thereceived signals of both antennas an equaliser instead of a diversity implementation canbe used (Section 5.8).

Some communication systems with very large bandwidths (ultra wideband systems)use pulse-position modulation with a large delay time, compared to the delay spread,between the pulses. The reflections of a single pulse will arrive between two consecu-tively transmitted pulses. These systems do not suffer from envelope fading due to theabsence of interference from reflected signals. The expected improvement of a diversityimplementation on the received signal strength is therefore only 3 dB.

The diversity gain for a single carrier system can also be calculated based on thecorrelation between the signals of the antennas [Mattheijssen, 2001]. For example, byassuming independent Rayleigh fading signals the diversity gain of equal-gain combiningbecomes 10.2 dB and that of maximum-ratio combining becomes 11.7 dB. These valuesare close to the simulated values, 10.6 dB and 11.1 dB , respectively, shown in Figure 5.23for B30 = 0 Hz. The small difference is caused by the difference in statistics between thesimulated and the assumed independent Rayleigh fading signals.

In this section only the array and diversity gain of a diversity implementation is con-sidered. However, diversity will also help to reduce the effects of delay spread or phasevariations on the BER.


−4 −2 0 2 4 60.1

1

10

100

Normalised SNR (dB)

Out

age

(%)

no divse

egmr

Figure 5.24: Simulated CDFs of three different combining techniques, B30 =1.183 GHz, ’no div’ = no diversity or single antenna, ’se’ = se-lective, ’eg’ = equal-gain and ’mr’ = maximum-ratio. Note theenlarged horizontal scale compared to previous CDF curves.

5.4.3 Selection of combining technique

Figures 5.22 and 5.23 show that combining the output of two antennas instead of selectingonly one of them results in a higher array gain. Moreover, the diversity performance ofthe selective combining technique is lower than that of the other two techniques. In animplementation of an equal-gain or maximum-ratio combiner the signals of two or moreantennas are combined. This results in antenna directivity patterns that are non-uniform,for example, see Figure 5.14. As a result, the equal-gain and the maximum-ratio combinercan suppress an interfering signal or wave by steering the minimum of the directivity pat-tern in its direction. The interference can be a reflected signal from the desired transmitter(multi-path) or from a different transmitter. In section 5.9.2 a quality signal will be intro-duced to control an equal-gain or maximum-ratio combiner such that an interfering sourcecan be suppressed. In general, it is better to combine the signals of uniform antennas toobtain non-uniform directivity patterns before a switched or selective combiner is used[Mattheijssen, 2000]. In this thesis, switching will be considered in combination with anequal-gain combining technique with a discrete phase shifter (Section 5.5). In this casethe switching is done between combinations of the antennas.

The diversity and array gain of an equal-gain combiner is very close tot that of amaximum-ratio combiner. The circuit implementation of the equal-gain combiner, how-ever, is less complex than that of the maximum-ratio combiner. One of the reasons is thatfor a maximum-ratio combiner the phase as well as the amplitude of the received signalneeds to be controlled. This means that twice as many control circuits are needed than foran equal-gain combiner.

The equal-gain combiner is therefore chosen as the most favourable combining tech-nique for this work. The following two sections will concentrate on implementation issuesof the equal-gain combiner. For the DECT channel bandwidth of 1.5 MHz, the diversitygain is about 9.5 dB and the array gain is about 2.6 dB.


5.5 Equal-gain combiner with discrete phase shifter

In Section 5.4 the equal-gain combiner has been chosen as the most favourable for im-plementation in the handset. The diversity and array gain values listed for this techniqueare based on a ’perfect’ combiner. This combiner is capable of adding the two receivedsignals with any desired phase-shift value. Therefore, it consists of a continuous phaseshifter and an adder (Figure 5.15). In practice, however, such a phase shifter is difficult tomake. Easier implementations are based on a discrete phase shifter. Such a phase shifterhas a limited number of discrete phase-shift values. In this section the performance ofan equal-gain combiner with a discrete phase shifter with a few well chosen phase-shiftvalues is compared to one with a continuous phase shifter.

A suitable set of discrete phase-shift values can be chosen based on the differencebetween the propagation delay of the signals received by the two antennas. As explainedin Section 5.3.3 and shown in Figure 5.11 the equal-gain combiner is based on a controlledtime delay, which can be substituted by an controlled phase shifter for narrowband signals(Equation 5.10). Figure 5.25 shows the propagation delay calculated with the FDTDmethod for the configuration described in Figure 3.13. The propagation delay is definedas the (arrival) time of the maximum of the power delay profile.

0

20

40

60

80

100

120

140

0 4 8 12 16 20 24 28 320

4

8

12

16

20

24

28

32

x−position (m)

y−po

sitio

n (m

)

Propagation delay (ns)

Figure 5.25: Propagation delay in ns calculated with FDTD for the configura-tion shown in Figure 3.13.

5.5. Equal-gain combiner with discrete phase shifter 121

Figure 5.26 shows the histograms of the difference in propagation delay between twoantennas at a separation of half a wavelength expressed in degrees. The values in de-grees are obtained by relating the propagation delay difference to a period of the carrierfrequency. The antennas are located in the room left to the room with the source shownin Figure 5.25 and 3.13. The histograms have a discrete time axis corresponding to thediscrete time steps of the FDTD simulation. The figure shows that the propagation delaydifference is not uniformly distributed if the antennas are oriented parallel to the x- ory- axis (top figures). Normally the antennas will have an arbitrary orientation inside theroom. The bottom left figure of Figure 5.26 shows the propagation delay distribution forarbitrary orientations. This means that the antennas have been positioned with differentorientations and at different locations in the room. Due to the separation of half a wave-length between the antennas, almost all propagation delay values fall within the intervalfrom −180 to 180. This interval is shown in the bottom right part of Figure 5.26. Thepropagation delay distribution within this interval is close to uniform.

−200 −100 0 100 2000

2500

5000

7500

10000

Delay difference (degrees)

Cou

nt

−180° 180°

−400 −200 0 200 4000

2500

5000

7500

10000


Cou

nt

−400 −200 0 200 4000

1000

2000

3000


Cou

nt

−400 −200 0 200 4000

1000

2000

3000

4000


Cou

nt

Figure 5.26: Propagation-delay difference as a function of the number of obser-vations (Count) between the signals of two antennas at a separa-tion of half a wavelength. Top left: the antennas are parallel tothe x-axis, top right: the antennas are parallel to the y-axis, bot-tom left: the antennas have arbitrary orientations, bottom right:enlargement of figure at the bottom left.


Based on the results for the propagation delay distribution, the phase-shift values ofa discrete phase shifter are also chosen to be equally spaced. An advantage of this isthat such a phase shifter is easy to implement in a large class of receivers. This is elabo-rated in Section 6.3.2. Figure 5.27 shows the measured CDFs of an equal-gain combinerwith a continuous phase shifter versus one with a discrete phase shifter with 2, 4 and 8phase-shift values. The measurement conditions are described in Section 5.4. Table 5.3gives the diversity gain and array gain of the different implementations. The table showsthat only two phase-shift values are enough to obtain a performance close to that of animplementation with a continuous phase shifter.

−30 −20 −10 0 100.1

1

10

100

Normalised SNR (dB)

Out

age

(%) no div 2,4,8

Figure 5.27: Measured CDFs of the normalised SNR of discrete equal-gain com-bining techniques for 2, 4 and 8 phase-shift values, ’no div’ = nodiversity and B30 = 1.5 MHz.

Figure 5.28 shows a schematic representation of such a simple equal-gain combiner.In this implementation switched instead of selective combining of the two antenna com-binations is used. The performance of such a prototype depends also on the parametersof the switched combiner. The advantage of switching between the antenna combinationsinstead of switching between the antennas is the obtained array gain and the possibility ofsuppressing interference or reducing delay spread by directive antenna patterns.

5.6. Equal-gain combining and body effects 123

Phase-shift values gdiv,eg (dB) grr,eg (dB)

(0,180) 8.0 2.1

(−90,0,90,180) 8.7 2.4

(0,90,180,...,270) 8.8 2.5

Continuous 9.0 2.5

Table 5.3: Measured diversity and array gain at an outage of 1% of spacediversity with equal-gain combiner with different phase shiftersforB30 = 1.5 MHz. The results for the continuous phase shifterare taken from Figure 5.22.

RX

+

+180180

sq

data

Figure 5.28: Two-phase equal-gain combiner, solid lines represent signal lines,dashed lines represent control lines, sq is the signal of the qualityindicator. Building blocks from left to right: antennas, 180 phaseshifter, summing circuits +, controlled switch and receiver RX.

5.6 Equal-gain combining and body effects

In the previous sections equal-gain combining with space diversity is chosen as the mostfavourable technique. As explained in Section 5.3.3, this technique results in antennadirectivity patterns that change as a function of the phase difference between the two an-tennas. This property can be used in the transmit state of a handset to direct the transmittedpower away from the human head [Dolmans, 1997b].


Table 5.4 shows the reduction of the Specific Absorption Rate (SAR) as a function ofthe phase difference between the two half wavelength dipole antennas with a separationof half a wavelength at a frequency of 900 MHz. The configuration is depicted in Figure5.29. The SAR is a measure of the power absorbed in the human body expressed in W/kg.The results are obtained from simulations with a 3-dimensional FDTD method. The headhas been modelled as a single material with a relative permittivity of 50.5 and an electricconductivity of 1.2 S/m. The distance between human head and the nearest dipole is 4 cm.

Phase difference 0 45 90 135 180 225 270 315

SAR (dB) 0.0 -0.7 -2.7 -5.9 -9.8 -4.6 -1.9 -0.4

Table 5.4: SAR levels as a function of phase difference between the two trans-mitted signals normalised to the value of a beam directed towardshead (0) [Dolmans, 1997b].

head

21

Figure 5.29: Top view of the position of the dual-antenna system relative to thehuman head. The numbers 1 and 2 denote the two antennas.

The SAR in Table 5.4 is normalised to the value of a beam directed towards the head(0). As can be seen from the table the SAR can be reduced by about 10 dB for a phasedifference of 180. This means that in that case 10 times less power is absorbed in thehuman head. The SAR values as a function of the phase-shift value are not distributedequally around the minimum SAR level due to the asymmetric position of the antennasystem (Figure 5.29).

In literature many calculations of the power absorbed in the head can be found [Iskan-der, 2000],[Schiavoni, 2000],[Green and Jensen, 2000] most values are close to 50% ofthe transmitted power. The resulting SAR values of single antenna handsets are withinthe safety limits imposed by the official organisations for all current products. A reduc-tion with 10 dB of this value, however, is relevant not only in view of the discussionson the effects of the absorbed power on the human health, but also for the link budget.In a multi-path environment the transmitted power can be reduced by about 3 dB due to

5.7. Adaptation speed 125

the reduced power absorption by using an optimal phase difference in the combiner. Thissaves the batteries of the handset.

The SAR reduction is an advantage of space diversity with equal-gain or maximum-ratio combining compared to the other combining techniques, when used in the transmitstate. This advantage can be exploited in a consumer product by implementing an al-gorithm that either optimises the BER or that minimises the SAR. The choice betweenboth could be made by the user. This idea has been patented by Philips [Leyten, 2000].If the user chooses for minimising the SAR, then some of the phase-shift values of theequal-gain combiner will not be used. If the user chooses for the best performance, thenthe diversity algorithm is allowed to use all possible phase-shift values. In this case thediversity gain can be expected to be equal to that of free space, although the antennas areclose to the human head [Green and Jensen, 2000]. Due to absorption of the energy in thehuman body, however, the array gain will be lower.

5.7 Adaptation speed

Depending on the type of system the implementation of diversity algorithm should be fastenough to track the variations of the received signals [Dolmans, 1997a], [Dolmans andLeyten, 1999b]. This is shown in Figure 5.30, in which two-phase equal-gain combinerswith zero, 25 ms, 50 ms and 100 ms response time (or adaptation time) are compared to asingle antenna receiver. The curves are obtained from measured data. The measurementconditions are described in Section 5.4. The curve of the figure is obtained by assumingthe speed of movement of the portable device ν to be 5 km/h. The diversity gain and arraygain are given in Table 5.5.

Response time (ms) gdiv,eg (dB) grr,eg (dB)

0 8.0 2.1

25 8.0 2.1

50 7.1 2.1

100 2.7 1.9

Table 5.5: Measured diversity and array gain at an outage of 1% of a two-phase equal-gain combiner with different response times, ν =5 km/h and B30 = 1.5 MHz. The values for a zero response timeare from Table 5.3.

The diversity and array gain decrease when the response time increases. If the re-sponse time would remain constant, but the speed of movement would increase, a similareffect would be observed. A total response time of less than 50 ms seems acceptablefor a practical implementation for a handset and does not result in a large performancedegradation (Table 5.5). If an equal-gain combiner with more than two phase-shift valuesis used, the total response time should remain the same. The amount of time available,


−30 −20 −10 0 100.1

1

10

100

Normalised SNR (dB)

Out

age

(%) no div

100 ms 50 ms, 25 ms

Figure 5.30: Measured CDFs of the normalised SNR of a two-phase equal-gaincombiner with different response times (specified in the figure), ’nodiv’ = no diversity, ν = 5 km/h and B30 = 1.5 MHz.

however, to assess the quality of each phase is reduced.

5.8 Diversity and equalisers

Diversity is a means of improving the signal quality of a portable receiver in a multi-pathenvironment. In addition to diversity there are other ways of improving the reliability ofa communication link. The most important alternatives are channel coding and equalisa-tion. It is beyond the scope of this study to treat these alternatives in detail. It is important,however, to note the contribution to the system performance of diversity and equalisation.Figure 5.31 shows a receiver with diversity and with an equaliser. In current designs theequaliser is implemented in the digital domain.

An adaptive equaliser is an adaptive filter with controlled weighting coefficients thatare updated as a function of time. Figure 5.32 shows an implementation of an adaptivelinear equaliser (transversal filter). The transfer function of the equaliser of Figure 5.32is:

Vout(t) =N∑

n=−N

Cn(t)Vin(t − (n + N)td ), (5.22)

where Vout(t) is the output signal, Vin(t) is the input signal, C−N ...CN are complexweighting functions and td is a fixed time delay.

5.8. Diversity and equalisers 127

eq

sq,1

RXdiv

sq,2

data

Figure 5.31: Receiver with diversity and equaliser, solid lines represent signallines, dashed lines represent control lines, sq,1 is the control signalfor the adaptive diversity circuits, sq,2 is the control signal for theadaptive equalisation circuits. Building blocks from left to right:antennas, diversity circuits ’div’, receiver ’RX’, equaliser ’eq’ andbit slicer.

++ + +

Vin

sq,−N

C−N C2−N

td

µC

C1−N

td

sq,1−N sq,2−N sq,N−1

td

sq,N

Vout

sq

CN

td

CN−1

Figure 5.32: Equaliser, solid lines represent signal lines, dashed lines representcontrol lines, sq,−N . . . sq,N are control signals for the complexweighting functions, sq is the control signal for the micro controller.Building blocks: micro controllerµC , complex weighting functionsC−N . . .CN , fixed time delays td and summing circuits +.

The WSSUS radio channel (Section 2.3.2) is a slowly varying, Tb < tc, frequencyselective, B > Bc, radio channel. It can be modelled as the transversal filter shown inFigure 5.32 [Proakis, 2000] (compare Equation 5.22 with Equation 2.6). In this casethe complex weights C−N through CN are updated to represent the slowly time-varyingnature of the radio channel. As a consequence the adaptive linear equaliser is capable ofinverting the impulse response of the radio channel such that the received signals becomeidentical to the transmitted signals. An optimal implementation of this, including thedemodulator, is called a RAKE receiver [Proakis, 2000]. The RAKE receiver works withthe signal of only one antenna. Diversity is based on combining the signal of two or moreantennas.


Equalisers and diversity implementations are therefore both capable of counteractingmulti-path effects. In modern receivers they are considered both as solutions to improvereception. The operation of a diversity circuit results in an output signal that has a differentbehaviour than that of a single antenna. This must be taken into account during the designof the equaliser. The following observations can be made for diversity implementationsand equalisers:

• The basic form of the equations is the same. An equaliser adds the input signalto a weighted and time delayed version of the input signal. The maximum-ratiocombining technique adds the output signal of one antenna to a weighted outputsignal of a (in this case identical) translated antenna.

• Maximum-ratio or equal-gain combining constitutes a spatial domain filter that re-sults in an improved signal-to-noise-plus-interference ratio. Equalisation consti-tutes a frequency or time domain filter resulting in an improved inter-symbol inter-ference.

• The typical time delays or phase-shift values of diversity receivers are within aperiod of the carrier frequency or within 0, 360, respectively. As a consequencediversity only works for a limited part of the received signals. Often an equaliser isdesigned for time delays that are larger than a period of the carrier frequency.

• Diversity implementations react faster to received signal variations than equalisers.An equaliser reacts slower due to the delays, but takes the history of the previousbits into account.

• Both diversity and equalisation reduce the delay spread but not to the same extent.An equaliser can do this in a better way.

The conclusions also hold for an equal-gain combiner, which can be seen as a maximum-ratio combiner with a fixed value of the modulus of the complex weighting factor.

The focus of this work is on diversity systems. It should be noted however that somemobile systems, like GSM, also use equalisers to improve the quality of the receivedsignals. The addition of a diversity circuit might even further improve the quality of thesesystems. Diversity results in signals with a larger mean signal-to-noise ratio, which caneven improve the performance of an equaliser. For systems without an equaliser, likeDECT, diversity can give a big improvement without adding a lot of circuitry and withouthigh costs. If diversity and equalisation are implemented, then care should be taken thatperformance of one of them is not influenced by the the operation of the other.

5.9. Quality indicators 129

5.9 Quality indicators

Most quality signals are based on optimising the received signal strength or Signal-to-Noise-plus-Interference Ratio (SNIR) . A communication system, however, can be delay-spread limited. In this case, increasing the power will not result in a better probabilityof error because ISI will still exist. These are the so called irreducible errors (Section2.11.1). With the measurement set-up presented in Chapter 4, an estimate of the reductionof the delay spread when using diversity can be made [Dolmans and Leyten, 1999a]. Forthis purpose, two criteria when combining the two antenna signals will be considered inSection 5.9.1:

1. Select a phase-shift value by maximising the received signal strength.

2. Select a phase-shift value by minimising the delay spread.

For these two criteria the effect on the diversity and array gain as well as the delay spreadwill be considered. In Section 5.9.2 a quality signal to steer the adaptive diversity circuitsis introduced. This quality signal is a measure of the signal-to-noise-plus-interferenceratio. This signal is obtained from an out-of-band noise detector. The results in thissection are obtained from measured data. The measurement conditions are described inSection 5.4.

5.9.1 Quality signal and diversity performance

The diversity and array gain for maximum-signal-strength combining and minimum-delay-spread combining as a function of the number of phase-shift values are given inTable 5.6. The mean delay spread and its improvement compared to a single antenna aregiven in Table 5.7. The delay spread τδ is calculated with Equation 2.44 the mean delayspread Erτδ is the delay spread averaged over all observation points. The percentageimprovement in delay spread is defined as:

percentage improvement= Erτδ − Er τδ,egErτδ · 100 %, (5.23)

in which τδ is the delay spread of a single antenna and τδ,eg is the delay spread afterequal-gain combining. Figure 5.33 illustrates the previous observations in another way.It shows the delay spread plotted versus the normalised SNR for a single antenna, forminimum-delay-spread combining and for maximum-signal-strength combining.

As expected, the results based on measurements show that minimum-delay-spreadcombining performs better on minimising delay spread than the maximum-signal-strengthcombining. The performance for diversity gain is about 2 dB lower and the array gainvanishes. Although maximum-signal-strength combining reduces the mean delay spreadaccording to Table 5.7, the delay spread distribution has become worse for lower delay-spread values compared to minimum-delay-spread combining (Figure 5.33). For higherdelay spread values, above 20 ns, maximum-signal-strength combining improves the de-lay spread distribution. The delay spread in this region can determine the performance ofa narrowband system if a low BER, much smaller than 10−3, must be achieved (Section2.11.1).


maximum-signal-strength minimum-delay-spread

Phase-shift values gdiv,eg (dB) grr,eg (dB) gdiv,eg (dB) grr,eg (dB)

(0,180) 8.0 2.1 5.4 1.1

(−90,0,90,180) 8.7 2.4 6.3 0.8

(0,90,180,...,270) 8.8 2.5 5.0 -0.3

Table 5.6: Measured diversity and array gain at an outage of 1% of a discreteequal-gain combiner with 2, 4 and 8 phase-shift values for B30 =1.5 MHz. Two criteria are considered: maximum-signal-strengthcombining and minimum-delay-spread-combining. The results forthe maximum-signal-strength combining are taken from Table 5.3.

maximum-signal-strength minimum-delay-spread

Phase-shift values Er τδ (ns) improv. (%) Erτδ (ns) improv. (%)

single antenna 26 0 26 0

(0,180) 24 9.0 21 18

(−90,0,90,180) 24 8.4 20 24

(0,90,180,...,270) 23 10 18 31

Table 5.7: Measured delay spread of a discrete equal-gain combiner with 2, 4and 8 phase-shift values for B30 = 1.5 MHz and the percentage ofimprovement with respect to the delay spread of a single antenna(improv.). Two criteria are considered: maximum-signal-strengthcombining and minimum-delay-spread combining.

The strongest signals of the PDPs from both antennas are added without a phase dif-ference by using the maximum-signal-strength combining criterion. The rest of the twoPDPs are also added but the phase difference is undefined. The result is a new PDP witha stronger desired signal relative to the other signals. This PDP has a lower delay spreadvalue and an larger SNR. This explains the relative good delay-spread performance of themaximum-signal-strength combining.

The delay spread is effectively reduced by a dual-antenna system. Even with a simpledetection technique, based on the maximum-signal-strength, the delay-spread is signifi-cantly reduced [Dolmans and Leyten, 1999a]. The performance of this technique and theease of implementation are the reason that it has been chosen as the optimal for handsets.For a full implementation of minimum-delay-spread criterion an estimate of the receiveddelay spread should be made which might be more difficult to realise.


−30 −15 0 150

15

30

45

60

Normalised SNR (dB)

Del

ay s

prea

d τ δ (ns

)

−30 −15 0 150

15

30

45

60

Normalised SNR (dB)

Del

ay s

prea

d τ δ (ns

)

−30 −15 0 150

15

30

45

60

Normalised SNR (dB)

Del

ay s

prea

d τ δ (ns

)

Figure 5.33: Scatter-plots of the measured delay spread values versus the nor-malised SNR for a single antenna, top figure, for minimum-delay-spread combining, bottom left, and for maximum-signal-strengthcombining, bottom right.

5.9.2 Out-of-band noise detection

Most adaptive antenna diversity implementations use the Received Signal-Strength In-dicator (RSSI) as the quality signal to steer the adaptive circuits. This RSSI is alreadypresent in the receiver to steer the Automatic Gain Control (AGC) circuits. The RSSIcannot discriminate between desired signals (data, speech) and interfering signals. Theinterfering signals can come from neighbouring telecommunication systems that operatein the same frequency band (co-channel interference) or from any other type of electronicequipment (microwave oven, computer, etc.). The received thermal noise power of mostcommunication systems has a fixed level. Changes of the RSSI level can therefore be in-terpreted as changes of the received signal power. Therefore, in the absence of interferers,the RSSI is a measure for the SNR.

Here a different technique is proposed for obtaining a quality signal sq , which is ameasure of the Signal-to-Noise-plus-Interference Ratio (SNIR) [Dolmans and Leyten,1997], [Dolmans and Leyten, 1999b]. The technique, called out-of-band noise detection,is based on measuring the noise power in a frequency band just above the signal band.


This is implemented by a band-pass filter, a power detector and a low-pass filter (integra-tor) placed behind the frequency demodulator. The out-of-band noise detector is shownin Figure 5.34.

noise

FV sq

frequency

ampl

itude

FE

filter curve

out-of-band noisedata

Figure 5.34: Out-of-band noise detection. Top figure shows the building blocks;antenna, radio front-end FE, frequency demodulator ’F/V’, band-pass filter, power detector and integrator. Bottom figure shows thebaseband frequency signal spectrum after demodulation; ’data’ in-dicates the baseband data frequency spectrum, ’noise’ gives thenoise frequency spectrum and ’filter curve’ is the filter transferfunction of the band-pass filter of the detector.

The frequency demodulator has a large gain, but a fixed voltage swing at its output.This results in clipped (square-wave) signals or bits (zeros and ones) at the output. Theinput noise power has a uniform frequency distribution and has a fixed (thermal) level.At the output the noise power increases as a function of frequency, because a frequencydemodulator acts as a differentiator. The data and noise frequency spectrum at the outputof the demodulator are also shown in Fig. 5.34. Two situations, which give rise to anincreased out-of-band noise power, can be distinguished:

1. The input signal power decreases. Due to the very large gain of the demodulatorthe output signals are still clipped but the SNR has decreased, which results in anincreased out-of-band noise power.

2. An interferer is present in the receive bandwidth. The sum of the desired and in-terfering signal has more zero-crossings per second than that of the desired signalalone. The frequency demodulator translates this into out-of-band high frequencycomponents (FM-clicks) which add to the out-of-band noise power.

These two situations will be illustrated with measurements further down. The quality


signal obtained with the out-of-band noise detection is therefore a measure of the SNIR.This technique only works for systems that use frequency or phase modulation. The typeof frequency discriminator considered here will destroy any amplitude information. Theout-of-band noise detector can also be found in state-of-the-art diversity receivers forautomotive applications [Philips Semiconductors, 1992].

Figure 5.35 shows the measured spectrum at the output of the frequency demodulatorfor four situations: a high SNIR, a low SNR, a low signal-to-interference ratio and a lowSNIR. In the figures the filter characteristic of a simulated ideal filter from 6.5 to 7.5 kHzis also drawn. The voltage at the output of the detector Vdet is specified above each figure.

3 4 5 6 7 8−100

−80

−60

−40

−20

Frequency (kHz)

Pow

er (

dBm

) 1.17 mV

3 4 5 6 7 8−100

−80

−60

−40

−20

Frequency (kHz)

Pow

er (

dBm

) 37.6 mV

3 4 5 6 7 8−100

−80

−60

−40

−20

Frequency (kHz)

Pow

er (

dBm

) 10.4 mV

3 4 5 6 7 8−100

−80

−60

−40

−20

Frequency (kHz)

Pow

er (

dBm

) 13.9 mV

Figure 5.35: Measured spectrum at the output of a frequency demodulator for asingle carrier signal at 5 kHz, top left: high SNIR, top right: lowSNR, bottom left: low signal-to-interference ratio and bottom right:low SNIR. The grey area indicates the position of the filter, abovethis area the voltage of a simulated out-of-band noise detector isspecified.

The figure shows that for all cases the amplitude of the 5 kHz signal remains almostconstant. This is caused by the limiter that is part of the frequency detector. When theinput signal drops, the noise floor rises and the output voltage of the noise detector in-creases. This is shown in the top right subfigure of Figure 5.35. A similar effect can beobserved if an interferer is present. This is shown in the bottom left subfigure for a signal-


to-interference ratio of 10 dB. Finally, if the signal strength is low and if an interferer ispresent, both effects result in an increase of the noise floor. This is shown in the bottomright subfigure.

5.10 Conclusions

In this Chapter, diversity systems with multiple antennas are considered. An overview ofseveral diversity implementations is given in Section 5.2. The angle diversity implemen-tation with adaptive beam steering is chosen as the most favourable diversity form.

In section 5.3 different combining techniques: switched, selective, equal-gain andmaximum-ratio combining are introduced. These techniques are compared based on theirdiversity and array gain for a two-antenna space diversity implementation (Section 5.4).The diversity gain of equal-gain and maximum-ratio combining decreases as a functionof the bandwidth from about 10 dB to 3 dB. An explanation of this effect is given. Thediversity and array gain of an equal-gain combiner, are very close tot that of a maximum-ratio combiner. The circuit implementation of the equal-gain combiner is less complexthan that of the maximum-ratio combiner. The equal-gain combiner is therefore chosenas the most favourable combining technique for this work. For the DECT channel band-width of 1.5 MHz, the diversity gain of the equal-gain combiner is about 9.5 dB and thearray gain is about 2.6 dB. An additional advantage of an equal-gain or maximum-ratiocombiner is their ability to suppress interference or reduce delay spread by steering thedirective antenna patterns (Section 5.4.3 and 5.9.2).

In practice a continuous phase shifter is difficult to make. Easier implementationsare based on a discrete phase shifter. In Section 5.5 the performance of an equal-gaincombiner with a discrete phase shifter with a few well chosen phase-shift values is com-pared to one with a continuous phase shifter. It is shows that only two phase-shift valuesare enough to obtain a performance close to that of an implementation with a continuousphase shifter Table (5.3). The diversity and array gain of a continuous phase shifter are9 dB and 2.6 dB, respectively, those of a two-step discrete phase shifter are 8 dB and2.1 dB, respectively.

An equal-gain combiner can also be used during transmission. In this case the com-biner can direct the transmitted power away from the human head. The power absorbedin the human head can be reduced in this way by about 10 dB (Section 5.6). In a multi-path environment the transmitted power can be reduced by about 3 dB due to the reducedpower absorption by using an optimum phase difference in the combiner. This saves thebatteries of the handset.

In section 5.7 two-phase equal-gain combiners with different response times are com-pared to a single antenna receiver. In this comparison the speed of movement of theportable device is 5 km/h. A total response time of less than 50 ms seems acceptable for apractical implementation for a handset and does not result in a large performance degra-dation. The diversity gain drops from 8.0 dB for zero response time to 7.1 dB for 50 msresponse time (Table 5.5), the array gain remains 2.1 dB for both response-time values.

Equalisers and diversity implementations are both applied to improve the quality ofthe received signals such that the bit-error rate is reduced. Some aspects of these two


techniques are given in Section 5.8.Two criteria when combining the two antenna signals are considered in Section 5.9.1:

maximum-signal-strength combining and minimum delay-spread combining. For thesetwo criteria the effect on the diversity and array gain as well as the delay spread areanalysed. The delay spread is effectively reduced by a dual-antenna system with themaximum-signal-strength combining criterion. The performance of this criterion and theease of implementation are the reason that it has been chosen as the optimal for handsets.

In Section 5.9.2 a quality signal to control the adaptive diversity circuits is introduced.This quality signal is a measure of the signal-to-noise-plus-interference ratio. This signalis obtained from an out-of-band noise detector.

The conclusions of the sections 5.2.7, 5.4.3, 5.5 and 5.9 lead to a diversity implemen-tation of low complexity and high performance. It has the following features:

• Type of diversity implementation: space.

• Type of combining technique: equal-gain.

• Type of phase shifter: continuous or discrete with equally spaced phase-shift values.

• Type of quality signal: obtained from an out-of-band noise detector.

The new features of the proposed system are patented by Philips [Baltus, 1999], [Baltus,1998]. Within the project the proposed system is referred to as an angle-scanning diversitysystem [Dolmans and Leyten, 1997], [Dolmans and Leyten, 1999b]. Its implementationis described in the next chapter.

Chapter 6

Practical diversityimplementations

6.1 Introduction

In the previous chapter a choice for a diversity implementation for a handset has beenmade based on simulations and measurement, namely angle scanning diversity. Thisis an equal-gain combiner with space diversity and an out-of-band noise detector. Inthis chapter the hardware implementation and the evaluation of the prototype will bediscussed. The block diagram of the prototype is shown in Figure 6.1 [Dolmans andLeyten, 1997], [Dolmans and Leyten, 1999b]. The basis is a dual equal-gain combiner,which has also been shown in Figure 5.15 of Section 5.3.3. The numbers inside theindividual building blocks of Figure 6.1 refer to the sections of this chapter. Some ofthe building blocks have the same symbol, like FE and ξ , this is done to emphasise thatthese are identical circuits. Their operation, however, is completely independent fromeach other.

The signals of the antennas are processed in the front-end FE, described in Section 6.2.The receiver architecture chosen for the prototype is a zero Intermediate Frequency (zero-IF) architecture. In such a receiver the antenna signal is amplified and then converted toa zero IF by mixing the signal with its carrier frequency. As a consequence the twophase shifters, denoted by ξ in Figure 6.1, must also work at a zero IF. Two types ofphase shifters are considered in Section 6.3: a continuous phase shifter and a discretephase shifter. The discrete phase shifter has been chosen because of its relatively simpleimplementation. The discrete phase shifter generates 8 phase-shifted versions of the inputsignal. One of these outputs is selected by means of the selection circuit sel in Figure 6.1(Section 6.4). The selection circuit is controlled by the microcontrollerµC.

A phase-shifted version of the signal of one front-end is combined with the originalsignal of the other front-end in the combiner, indicated with +. The combiner has twomodes: combining of the two input signals or routing one input signal directly to theoutput (Section 6.5). The first mode is used during normal operation. The second mode

137

138 Chapter 6. Practical diversity implementations

FE

6.2+ BB

6.6det

6.5

µC6.7

6.5 6.2BB+

6.6det

DECT

ξ sel

ξ sel

6.3 6.4

6.3 6.4

FE6.2

6.2

Figure 6.1: Block diagram of angle scanning diversity prototype. Solid linesrepresent signal lines, dashed lines represent control lines. Thenumbers inside the individual building blocks refer to the sectionsof this chapter.

is for testing and adjusting the two receiver chains. The combined signals are then routedto the baseband receiver BB, that retrieves the data (Section 6.2). The data of one ofthe baseband receivers can be switched by the microcontroller to the remaining part of aDECT receiver. This part takes care of the DECT protocol including error correction anddecompression of the audio signal.

The quality of the received signal is determined by the out-of-band noise detector detdescribed in Section 6.6. The resulting quality signal is converted to a digital signal by themicrocontroller µC (Section 6.7). The microcontroller steers the adaptive receiver basedon the quality signals of both receiver chains, such that a maximum reception quality isobtained.

In the following section each building block is described. Not all the circuit detailsare specified, only those relevant for the correct operation. The focus will partly be on thealignment of both receiver chains by taking care of offset compensation and gain adjust-ments. If a misalignment exists between the two receiver chains, the diversity algorithmwill not work in an optimal way. For all the circuits, symbol representations showing therelevant in- and outputs will be given. Using these symbols the full circuit implementa-tion of the prototype is given in Section 6.8. In this section the operation of the prototypeis explained in more detail. This chapter ends with the performance evaluation of thediversity prototype (Section 6.9) and the conclusion (Section 6.10).

6.2. DECT zero-IF transceiver 139

The references for all relevant circuit blocks, ICs and components will not be giveneach time a component is introduced. A list of references is given below:

• full description of DECT demo board: [Philips Semiconductors, 1995c],

• zero-IF front-end receiver UAA2078M: [Philips Semiconductors, 1995d],

• zero-IF baseband receiver UAA2079M: [Philips Semiconductors, 1995e],

• operational amplifier (opamp) AD847: [Analog Devices, Inc., 1997],

• 8-channel analogue (de-) multiplexer HCT4051: [Philips Semiconductors, 1990a],[Philips Semiconductors, 1995a],

• Schottky barrier diode BAT83: [Philips Semiconductors, 1996],

• 8-bit microcontroller family MC68HC11, including the applied MC68HC11A1:[Motorola, 1996],

• TTL/CMOS levels (0 V, +5 V) to RS-232 computer levels (-10 V, +10 V) converterICL232CPE: [Intersil, 1999],

• triple 2-channel analogue (de-) multiplexer HCT4053: [Philips Semiconductors,1990b], [Philips Semiconductors, 1995b].

6.2 DECT zero-IF transceiver

The diversity prototype is based on a DECT zero-IF transceiver demo board. Zero-IFstands for zero Intermediate Frequency. A zero-IF receiver converts the received highfrequency signals in one step to an intermediate frequency of 0 Hz. This is achievedby multiplying the received signal with its carrier frequency. Such a receiver is alsocalled a direct conversion receiver. This type of receiver has been chosen for the diversityprototype because some of the signal processing is very easily done at a zero-IF (or low-IF for other receiver architectures). This is especially true for the phase shifter, which isdescribed in Section 6.3.

The transceiver on the demo-board consists of a separate receive and transmit part.The receive part is build around two ICs: the UAA2078M zero-IF front-end receiver andthe UAA2079M zero-IF baseband receiver. A 1.9 GHz Voltage Controlled Oscillator(VCO) controlled by a Phase Lock Loop (PLL) synthesiser provides the local oscillatorsignal to the front-end. In the transmit part the same combination of VCO and PLLsynthesiser is used to generate the modulated carrier by means of direct modulation. Thissignal is subsequently amplified by the power amplifier and fed to the antenna. Thecontrol of the different ICs is done by digital baseband ICs mounted on a separate board.The transmit and receive part are completely separate. The antenna is switched betweenthose. Figure 6.2 shows a block diagram of the receive chain.


0

90

UAA2078Mfront-endreceiver

UAA2079Mbasebandreceiver

Vre f

AGC-FE

AGC-BB

transmitter

LO

FV

MON

DATA

I Q

Figure 6.2: DECT zero intermediate frequency receiver.

The signal is received by the antenna and then filtered to protect the receiver againststrong signals outside the DECT frequency band. The DECT system uses GFSK as amodulation form (Section 2.2).

6.2. DECT zero-IF transceiver 141

Under ideal conditions, the received voltage at the antenna terminals V ra can be written

as a phase-modulated carrier:

V ra = A cos(2π f0t + ψ(t)), (6.1)

where A is the amplitude, f0 is the carrier frequency and ψ(t) is the phase modulation.This expression is identical to that given in Equation 2.16. The received noise is omittedthroughout the expressions in this chapter. The phase modulation of a GFSK system is acomplex signal that results in a spectrally efficient system. It is a function of time, becauseits value changes depending on the transmitted symbol.

The automatic gain control, AGC-FE in Figure 6.2, reduces the dynamic range of thereceived signal, whereafter the signal is fed to an IQ mixer. The IQ mixer generates thezero-IF in-phase I and quadrature Q signals by multiplying the received signal with thecarrier frequency LO and a 90 phase-shifted version of the carrier frequency. The I andQ signals are defined in Equations 2.18 and 2.19, respectively. The two signals still havean varying amplitude depending on the received signal strength. The conversion to thezero-IF does not effect the phase of the signals. The mixer outputs of the UAA2078Msupply the I and Q signals to the baseband receiver UAA2079M shown in Figure 6.2.After the low-pass channel filtering, the dynamic range of the signals is further reducedby another AGC called AGC-BB. Subsequently, the I and Q signals are converted tobaseband signals by means of the frequency discriminator F/V. Finally, the basebandsignals are converted to digital signals by the bit slicer. The output of the frequencydiscriminator, labelled MON is available at a special monitoring pin of the UAA2079M.It can be obtained by putting the IC in one of its test modes. This signal is needed forthe out-of-band noise detection method described in Section 5.9 and illustrated in Figure5.34. A reference voltage Vre f from the UAA2078M is connected to the UAA2079M(Figure 6.2). This voltage defines the DC output level of the I and Q channel outputs.The reference voltage ensures that the DC offsets between the front-end and the basebandreceiver do not affect performance.

The symbolic representation of both ICs is shown in Figure 6.3. The ICs are repre-sented by symbols showing only the relevant in- and outputs.

Vre f

Q

UAA2079M

I

AGCLO

ANT

UAA2078Mfront-end

I

Vre f

Q DATA

AGC MON

baseband

Figure 6.3: Symbolic representation of the UAA2078M and UAA2079M, show-ing only relevant in- and outputs.


6.3 IQ phase shifter at zero-IF

In order to implement an equal-gain combiner, a phase shifter is needed in the signalpath before combining the received signals (Section 5.3.3 and Figure 5.15). Up to nowthe phase shifter has been put in the RF signal part directly behind the antenna. Thesame phase-shift value, however, can also be obtained by putting a phase shifter at anintermediate frequency inside the receiver. In the case of the zero-IF receiver the phaseshifter is placed between the UAA2078M and the UAA2079M in Figure 6.2. Putting thephase shifter at the IF has several advantages:

• It is easier to make a good, low-loss and low-distortion phase shifter at the IF.

• At the RF any of the imperfections of the phase shifter can cause a larger distur-bance of the relatively weak signals. At the IF the signals have been amplified andprocessed so that they are less susceptible to imperfections of the signal processingcircuits.

• Phase shifters at the IF can be easily integrated with the rest of the baseband pro-cessing circuits into one IC.

• It is expected that the power dissipation of an IF phase shifter is lower than an RFphase shifter.

• A phase shifter at the IF can be made more accurate and stable.

Because of these advantages the phase shifter has been implemented at the IF.For this work two possible implementations have been analysed:

1. a continuous phase shifter based on voltage controlled amplifiers (VCAs),

2. a discrete phase shifter based on interpolation of the I and Q signals.

In Sections 6.3.1 and 6.3.2 the two possibilities are described. The discrete phase shifteris implemented in the diversity prototype. Therefore, it is described in more detail thanthe continuous phase shifter.

6.3.1 Continuous phase shifter

Figure 6.4 shows the diagram of the continuous phase shifter. The operation principle isbased on multiplication of the original I and Q signals with real variables α and β andthen summing them to obtain the phase-shifted versions I ′ and Q′:

I ′ = α I + β Q,

Q′ = −β I + α Q.(6.2)

Figure 6.5 shows a vector diagram of the principle. The phase-shift value ξ also specifiedin Figure 6.5 follows from:

ξ = arctanβ

α. (6.3)

6.3. IQ phase shifter at zero-IF 143

+ +

−1

Q

I ′ Q′

α

β

I

Figure 6.4: Continuous phase shifter made from four voltage controlled am-plifiers, an inverter and two summing circuits. I and Q are theoriginal received signals, I ′ and Q′ are the phase-shifted versionsand α and β are two real numbers with which the I and Q aremultiplied.

Q′

Q

αQ

βQ

I ′

ξ

ξ

−β I α I I

Figure 6.5: Vector equivalent of the continuous phase shifter shown in Figure6.4.

The operation of the continuous phase shifter has been simulated with a circuit simu-lator. A few measurements to verify the simulations have been done on a single VCA. Theconclusions of the experiments in combination with the application of the phase shifter atthe IF are:


• The considered simple VCAs based on a mixer are highly non-linear as a functionof the control voltage. The control signals to obtain the correct multiplication fac-tors α and β should therefore also be non-linear to obtain a linear phase shifter.Due to this non-linearity care should be taken to maintain a good resolution for thecomplete tuning range.

• The phase shifter changes the DC level of the I and Q signals. This is not allowedfor the correct operation of the UAA2079M (Section 6.2).

• The best way of implementing the multiplication factors α and β is with a Digital-to-Analogue Converter (DAC) and microcontroller.

For all the items mentioned, circuit solutions have been found that result in a suitablephase shifter. This circuit is rather complex in terms of transistors, matching and ad-justments. A discrete phase shifter has a performance close to that of a continuous one(Section 5.5) and its implementation is expected to be less complex. A discrete phaseshifter is considered in the next section.

6.3.2 Discrete phase shifter

Figure 6.6 shows the circuit diagram of a discrete phase shifter [Dolmans and Leyten,1999b]. It is based on the original I and Q signals, their inverted or 180 phase-shiftedversions I and Q and a resistive interpolator. These inverted signals can easily be madeby an inverting buffer, this will be explained later in this section. The specific numberingof the phase-shifted signals, ξ1 to ξ7, will become logical further on in this section.

ξ5

Q

I

Q

I

ξ1

ξ3

ξ7

Figure 6.6: Discrete phase shifter made by resistive interpolation using 8 re-sistors. I and Q are the original received signals, ξ1, ξ3, ξ5 and ξ7are the phase-shifted versions obtained by interpolation and I andQ are inverted or 180 phase-shifted versions.

6.3. IQ phase shifter at zero-IF 145

As an example, ξ1, the phase-shifted version of either I or Q, (Equations 2.18 and2.19), respectively, is:

ξ1 = 1

2cos(ψ)+ 1

2sin(ψ) = 1

2

√2 sin

(ψ + π

4

), (6.4)

where ψ is the phase modulation of the received signal defined in Equation 6.1. The am-plitude of the I and Q signals have been normalised to 1. Hereafter, only the normalisedversions will be used. All equations scale linearly with the amplitude, as a result, specify-ing the amplitude in every equation and figure is not necessary. Figure 6.7 shows a vectorequivalent of ξ1 for the discrete phase shifter. By comparing the derived expression withEquations 2.18 and 2.19 it can be concluded that ξ1 is a 45 phase-shifted version of I ora 315 phase-shifted version of Q. The phase-shifted versions ξ3, ξ5 and ξ7 can be inter-preted in the same way. By choosing, for example, ξ1 as I ′ and ξ3 as Q′, a phase-shiftvalue of 45 for the I and Q vector diagram is achieved.

12

√2

I

Q

ξ1

Figure 6.7: Vector equivalent of the discrete phase shifter shown in Figure 6.6.

The amplitude of the phase-shifted signals, however, is 1/√

2 smaller than that of Iand Q (Figure 6.7). In the diversity receiver a choice between the original signals andtheir phase-shifted versions will be made. The amplitude of all signals should thereforebe equal. The circuit solution is shown in Figure 6.8. The amplitude of the original I andQ signal is lowered by resistive dividers. This results in four signals: ξ0, ξ2, ξ4 and ξ6.The current i through the resistors resistors R2 and R3 is:

i = 2

2R2 + R3. (6.5)

The voltage V at, for example, ξ0 is:

V = 1− 2R2

2R2 + R3= R3

2R2 + R3. (6.6)


By imposing the voltage V to be 1/√

2, the relation between R2 and R3 becomes:

R3 = (2√

2+ 2)R2 = 4.83 R2. (6.7)

With this relation the amplitudes of ξ0 through ξ7 become equal. The resistors R1 and R2are chosen to be 1 k. This value results in signal levels that do not suffer much fromthe parasitic capacitance and inductance caused by the tracks of the Printed Circuit Board(PCB) and of the resistors themselves. The resistor R3 becomes 4.83 k with Equation6.7.

R3

R1

R1

R1R1

R1

R1

R1 R1

I

Q

I

QR3R2 R2

ξ0

ξ7 ξ1

ξ5 ξ3

ξ4

ξ6

ξ2

R2

R2

Figure 6.8: Equal-amplitude discrete phase shifter made by resistive interpola-tion. I and Q are the original received signals, ξ0 through ξ7 arethe phase-shifted versions obtained by interpolation and I and Qare inverted or 180 phase-shifted versions.

Figure 6.9 shows the circuit diagram of the discrete phase shifter, that is realised inhardware. Four input buffers based on the AD847 are added to the resistive interpola-tor. The inverted signals I and Q are made by inverting buffers. These buffers invertthe original signal, but maintain the required DC-level by using Vre f (Section 6.2). Inthe design and implementation care has been taken to minimise the input offset-current.Because of its simplicity the discrete phase shifter has been chosen for implementation inthe prototype.

6.4. Selection circuit 147

+

-AD847

+

-AD847

+

-AD847

+

-AD847

Q

ξ0

ξ7 ξ1

ξ5 ξ3

ξ4

ξ6

ξ2

I

I

Vre f

Q

10 k

5 k

1 k4.83 k

10 k

5 k

10 k10 k

1 k1 k

1 k

1 k

1 k 1 k

1 k

1 k

1 k

4.83 k 1 k1 k

I

Q

Figure 6.9: Circuit diagram of the discrete phase shifter of Figure 6.8 includingbuffers.

6.4 Selection circuit

In the previous section eight different signals, ξ0 through ξ7, are obtained from the originalI and Q signals with the discrete phase shifter. By using a control signal a combinationof these signal must be selected such that a phase-shifted version of the I and Q signalsis obtained. Figure 6.10 shows the circuit diagram of the selection circuit.


+

-AD847

+

-AD847

+

-AD847

+

-AD847

S0ξ0

ξ2

ξ1

ξ3

ξ4

ξ5

ξ7

ξ6

74HCT4051

74HCT4051

I ′

Q′

Y0

Y1

Y2

Y3

Y4

Y5

Y6

Y7

S0

S1

S2

Z

EGND

Y0

Y1

Y2

Y3

Y4

Y5

Y6

Y7

S0

S1

S2

Z

EGND

ξ2

ξ0

S1

S2

Figure 6.10: Circuit diagram of selection circuit.

The selection of one of the 8 phase-shift values is done by an analogue multiplexer.This device routes one of the 8 phases at its inputs Y0 through Y7 depending on the valuesof the digital select signals, S0, S1 and S2 to the output Z. The device is always enabled byconnecting E to ground. The 8 signals are connected to the inputs of the two multiplexerssuch that the phase-shift value of the I signal is equal to that of the Q signal. In this way aphase-shifted version, I ′ and Q′, is obtained. The outputs of the multiplexers are buffered.Two additional buffers are used for the ξ0 and ξ2 signals. These signals are the originalI and Q signals with a lower amplitude (Section 6.3.2). They will be combined withthe phase-shifted versions of the I and Q signals of the second receiver in the diversityprototype.

The analogue multiplexers, two times 74HCT4051, have a low and reasonable ac-curate on-resistance. This is beneficial in the application of Figure 6.10, in which thematching of the signals can be influenced by a varying on-resistance. For monitoring pur-poses a LED array showing the selected phase has also been implemented on the diversityprototype. The selection circuit including the discrete phase shifter will be represented bythe symbol shown in Figure 6.11.

6.5. Combiner 149

S0

S1

S2

I ′

Q′

phase-shifter

QI

ξ2

ξ0

Vre f

Figure 6.11: Symbol representation of discrete phase shifter and selection cir-cuit.

6.5 Combiner

For an equal-gain combiner the signals of two antennas or receivers should be added. Theoutput of the UAA2078M and that of the phase shifter behave like voltage sources. Theinput of the UAA2079M is a current input. This means that the signals can be addedby using resistors. Figure 6.12 shows the implementation for the prototype. The phase-shifted signals I ′ and Q′ of one receiver are added to the non phase-shifted signals ξ0 andξ2 of the other receiver. The combined signals are then passed through a variable resistorto compensate for a gain unbalance that occurred during tests. This results in the outputsignals Ic and Qc.

combiner

2Z

2Y1

3.4 k1Z

1Y1

1S

2SQ′

ξ0

I ′Ic

Qc

3.4 k

3.4 k

3.4 kξ2

1Y0

2Y0

5 k

5 kS

I ′

ξ0

Q′

ξ2S

Qc

Ic

74HCT4053

74HCT4053

Figure 6.12: Circuit diagram of the combiner, left part, and its symbol represen-tation, right part.


Figure 6.12 also shows two switches. With these switches the combiner can be turnedoff so that the received signal are directly routed two the baseband receiver. This is doneto compare the performance of the diversity receiver to a standard receiver and to be ableto check the behaviour of a single receiver. The two switches switch to ground to preventcross-talk. The symbol representation of the combiner is also shown in Figure 6.12.

6.6 Out-of-band noise detector

The diversity prototype needs a quality signal to steer the selection circuit of Section 6.4.This quality signal comes from the out-of-band noise detector (Section 5.9). Figure 5.34shows the block diagram of the detector. The basic blocks are a band-pass filter, a rectifierand an integrator (low-pass filter). The input of the detector comes from the frequencydiscriminator. This is the MON output of the UAA2078M, shown in Figure 6.2.

Figure 6.13 shows the hardware implementation of the band-pass filter. It consists offour Sallen and Key filter stages [Sallen and Key, 1955]. The first two operational ampli-fiers (opamps) form a high-pass filter with a 3 dB cut-off frequency of about 1.3 MHz.The following two opamps form a low-pass filter with a 3 dB cut-off frequency of about3.1 MHz. As a result the whole circuits forms a band-pass filter. The filter characteris-tic is given in Figure 6.14. The DC-level of the signals within the filters is determinedby Voff (Figure 6.13), which is chosen for an optimal peak-to-peak voltage swing. Theimplementation of the required band-pass filter can also be done with less componentsand with a better performance in terms of noise and linearity by using a different circuittopology. However, the performance of the described Sallen and Key filter is sufficientand another design has not been considered.

6.6. Out-of-band noise detector 151

-

+AD847

-

+AD847

-

+AD847

-

+AD847 filter out

1 k

1.2 k 2.8 k

410

100 pF 100 pF 100 pF100 pF

MON

Voff

2.2 k 2.2 k 2.2 k 2.2 k

33 pF

27 pF

56 pF

10 pF

Figure 6.13: Circuit diagram of Sallen and Key band-pass filter.

0.1 1 10 100−40

−30

−20

−10

0

Frequency (MHz)

Nor

mal

ised

tran

sfer

(dB

)

Figure 6.14: Filter characteristic of the filter shown in Figure 6.13.


Next, the filtered signal is fed to the rectifier and integrator. The hardware implemen-tation of the rectifier and integrator is shown in Figure 6.15. It is based on a full-waverectifier built with an opamp and two Schottky barrier diodes. These diodes have beenchosen because of their low forward voltage. The integrator is is made with the resistorand capacitor at the output of the rectifier. This integrator determines for a large partthe response time of the diversity prototype. Its RC-time constant is 0.7 ms, for eightphase-shift values the total response time is 5.7 ms. This response time is well below therequired value of 50 ms derived in Section 5.7. Finally, Figure 6.16 shows the symbolrepresentation of the complete out-of-band noise detector.

The complete diversity circuit will include only one detector that is used to monitorall signals. This prevents mismatch problems that can occur by using multiple detectors.After the measurement of the output voltage of the detector the integrator should be resetbefore a new measurement can be made (integrate and dump algorithm). This can be doneby a switch that connects the output to ground before a new measurement is done.

-

+AD847

-

+AD847

filter outC

1 k

1 k

1 k

100 k 100 k

68 k

22 k

33 nF

BAT83

BAT83

39 k

Voff

Figure 6.15: Circuit diagram of the full-wave rectifier and integrator.

C

quality detector

MON

Figure 6.16: Symbol representation of the out-of-band noise detector.

6.7. Controller 153

6.7 Controller

In Figure 6.17 a 8-bit microcontroller is shown, which is used to implement the algorithmand to steer all the circuitry. The microcontroller has many in- and output ports including8 channel 8-bit Analogue-to-Digital Converters (ADCs). Not all of the available portsare used in the diversity prototype. The diversity algorithm is implemented in its internalmemory: 256 bytes of RAM, 512 bytes of EEPROM. The algorithm is programmed intothe EEPROM by means of a personal computer and a RS232/TTL level converter. Infigure 6.17 the relevant in- and output ports are shown. Their function will become clearin the next section, in which the full circuit implementation will be introduced.

C

C-selRX-sel

RX 1

LOCK

controller

RX 0S00

S01

S02

SYNCS12

S11

S10

MC68HC11A1

S

PB0PB1PB2PB3

PB4

PB5PB6PB7PA6

PA3PA4PD5PA7PE1

S02

S01

S10

S11

S12

S

S00 RX 0RX 1RX-selC-selLOCKSYNCC

RxD TxD

personal computer

ICL232CPE

RS-232

TTL/HCMOS

T1OUTR1IN

R1OUT T1IN

Figure 6.17: Circuit diagram of microcontroller with PC interface, left part,and its symbolic representation, right part. The labels inside theMC68HC11A1 refer to its in- and output ports.

6.8 Full circuit implementation

In Figure 6.18 the full circuit implementation of the angle scanning diversity prototype isshown. In the figure the previously introduced symbols of the building blocks are used.The full circuit implementation is equivalent to that shown in Figure 6.1.


Z

Z

RSSI

I ′

ξ0

Q′

ξ2S

Qc

Ic

combiner

I

Vre f

Q DATA

AGC RSSI

basebandUAA2079M

QI

ξ2

ξ0

Vre f

phase-shifter

S0

S1

S2

I ′

Q′

I ′

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Q′

ξ2S

Qc

Ic

combiner

I

Vre f

Q DATA

AGC

basebandUAA2079M

QI

ξ2

ξ0

Vre f

phase-shifter

S0

S1

S2

I ′

Q′

Y1

SY0

Y0

Y1

Z

Y1

SY0

Z

Y1

SY0

DECT

DATARX-enTX-en

RSSI

C

C-selRX-sel

1 k

330

330

RX 1

Vre f

QI

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UAA2078Mfront-end

1 k

LO

AGC

1

2

3

4

Vre f

QI

LO

ANT

UAA2078Mfront-end

AGC

S

LOCK

controller

AGC

RX 0S00

S01

S02

SYNCS12

S11

S10

S

Figure 6.18: Implementation of the angle scanning diversity prototype, solidlines represent signal lines, dashed lines represent control lines.

6.8. Full circuit implementation 155

There is, however, one difference: instead of using the out-of-band noise detector theReceived Signal-Strength Indicator RSSI is used as the quality signal. The reason forthis is the problem with the bandwidth of the output of the UAA2079M. The prototypehas been built with the most advanced ICs and architecture available within Philips. Thismeant that there were still some problems with the test ICs used in the prototype. Anotherproblem also occurred. It seemed that not a full frequency discriminator had been imple-mented. The normalisation of the output to the amplitude of the input signals had notbeen implemented for stability reasons. Especially the normalisation would have resultedin the out-of-band-noise that should have been detected. The RSSI signal is a measure ofthe signal-to-noise ratio and not of the signal-to-noise-plus-distortion ratio as explainedin Section 5.9. As a consequence, the performance of the demonstrator in the presence ofinterfering sources could not be measured.

In the symbol representations of the UAA2079M, shown Figure 6.18, the MON outputis replace with the RSSI output. The quality detector is omitted. The RSSI signals are fedto the analogue-to-digital converters of the controller. Apart from the problem of notbeing able to use the designed detector, the prototype functioned as designed.

Figure 6.18 also shows four numbered switches. The function of the switches willbe explained later on. Two LEDs are connected to the controller. These LEDs indicatewhich of the two receiver chains is active. Finally a building block DECT is shown. Thisbuilding block represents the rest of a full DECT receiver. It takes care of the protocol, theconversion of bits to speech and it also contains the transmitter. The AGC signals of thefront-end and and the baseband receivers and the LO signals of the front-end are connectedto this DECT block. Next an explanation of the implementation of the prototype is given:

• The signals received by the antennas are converted by the two front-ends to I andQ signals at an IF of 0 Hertz.

• The complex signal (I , Q) is phase shifted and buffered in the phase shifters. Eachphase shifter generates the phase-shifted components I ′ and Q′ but also non phase-shifted versions, ξ0 and ξ2, with the same amplitudes as those of the phase-shiftedcomponents. The phase-shift value is selected by the digital inputs S0, S1 and S2.

• In the two combiners the phase-shifted version of one front-end is combined withthe non phase-shifted version of the other front-end.

• The combined signal are fed to the baseband receivers, in which they are convertedto baseband data.

• The controller selects one of the outputs of the baseband receiver with the switchlabelled ’4’. At the same time the RSSI signal of this receiver is switched to theDECT block with the switch labelled ’1’. This signal is needed for the correctoperation of the DECT block.

• The controller selects the phase-shift value of the two phase shifters with its outputsS00 through S12.


• The output S of the controller is used to turn the combiners on or off. If they areswitched off, they route the signal of the front-end to the baseband without a phaseshift. This mode is used for alignment and test purposes.

• The TX-en (transmitter enable) signal of the DECT block is used by the controllerto detect if the complete transceiver is locked on the basestation. The controllerwaits until this signal is present, before it continuous with its algorithm.

• The RX-en (receiver enable) signal of the DECT block is used for the timing ofthe measurement of the RSSI signal. The value of the RSSI signal is correct duringonly a small time period of a time-slot. The RX-en is used to make sure that ameasurement only takes place in this time slot. This signal is used as a gatingsignal to steer switch labelled ’2’.

• Switch labelled ’3’ routes the RSSI signal of one of the two baseband parts to thecontroller. By means of this switch the two RSSI signals can be compared and thebest receiver can be selected.

The algorithm inside the controller works as follows :

1. Select a receiver as the active receiver and also select a phase-shift value.

2. Wait for lock (TX-en signal). If no lock is obtained, change phase-shift value andrepeat procedure.

3. Store the value of the quality signal of the active receiver.

4. Select the quality signal of the other, scanning, receiver and select a phase-shiftvalue.

5. Compare the quality of the scanning receiver with the previously stored value of theactive receiver. If this value is higher, then make the scanning receiver the activereceiver and make the other the scanning receiver. Repeat the procedure from item3. If the value is lower then select the next phase-shift value of the scanning receiverand repeat the procedure.

In this way the receiver selects the best combination of the two antennas without inter-rupting the data stream.

Figure 6.19 shows the angle scanning diversity prototype. In this figure the differentbuilding blocks are identified. In this figure so-called ’flat-cables’ can be seen that areused to connect the different parts. The critical signals, especially all I and Q signals, areseparated within a flat-cable by ground wires to prevent cross-talk.

6.8. Full circuit implementation 157

DECT controller

noise detector

phase shifters, selectors, combinerszero-if transceiver

controllerout-of-band

Figure 6.19: Block diagram of the angle-scanning diversity prototype.


6.9 Performance evaluation

The angle scanning diversity prototype is evaluated with the xy-table of the measure-ment set-up of Section 4.2 [Dolmans and Leyten, 1997], [Dolmans and Leyten, 1999b].The evaluation set-up is shown in Figure 6.20. The figure shows the xy- table and its con-troller, the antennas mounted on the xy-table, the diversity prototype, a personal computerand two operators.

Figure 6.20: Evaluation of the angle scanning diversity prototype.

The controller of the prototype steers all relevant information, like the received signalstrength for each step of the phase shifter, to a Personal Computer (PC). The PC storesall the data, whereafter it is analysed with MatLab [The MathWorks Inc., 1999]. Figure

6.9. Performance evaluation 159

6.21 shows the normalised received signal strength of a single antenna and of the opti-mally combined antennas of a typical measurement. The total number of observed signalstrengths (counts) is almost the same for both situations.

−60 −45 −30 −15 0 150

100

200

300

Cou

nt

Normalised amplitude (dB)−60 −45 −30 −15 0 150

100

200

300

Cou

nt

Normalised amplitude (dB)

Figure 6.21: Histogram of the normalised received signal strength of a typicalmeasurement. Left side: signal of a single antenna, right side:optimally combined signals of two antennas.

Measurements have been done in an office environment. During the measurementspeople were moving in the neighbourhood of the antennas to obtain realistic results.Sometimes, the direct path between the basestation and diversity antennas was blockeddue to moving people or due placement of the antennas behind walls and objects. Theantennas are two dipole antennas separated by half a wavelength. The array gain and thediversity gain (Section 5.4) are shown in Table 6.1 together with values based on mea-surements of the received signals from two dipole antennas (Section 5.5).

Diversity gain (dB) Array gain (dB)

Prototype, 8 phase-shift values 6.8 2.8

Simulated, 8 phase-shift values 8.8 2.5

Simulated, continuous 9.0 2.6

Table 6.1: Diversity and array gain of the angle scanning diversity proto-type and the associated simulated values. The simulated valuesare copied from Table 5.3.

The following conclusion can be drawn from this table. The diversity gain of theprototype is 2 dB lower than the simulated value. Its array gain is 0.3 dB higher than thesimulated value; it is closer to the value of a continuous phase shifter. Possible causes forthe differences are: the propagation environment during the measurements was differentfrom the simulated environment and the implementation of the diversity algorithm causes


some performance loss (so-called ’implementation loss’) for the diversity gain. Moreover,The performance of a real receiver depends on more parameters than the received signalstrength and delay spread that have been considered in the design of the prototype. A morein-depth study to resolve the difference between the predicted and measured diversity gainis beyond the scope of this work.

The diversity prototype is programmable, so also the effect of varying the numberof phase steps could be analysed. The result is shown in Table 6.2 together with thesimulated values (Section 5.5). The trend in diversity gain of the prototype as a functionof reducing the number of phase steps follows that of the simulated values. About 1 dB islost by going from 8 to 2 phase steps.

Prototype Simulated values

Phase-shift values gdiv (dB) grr (dB) gdiv (dB) grr (dB)

2 5.8 2.8 8.0 2.1

4 6.5 2.8 8.7 2.4

8 6.8 2.8 8.8 2.5

Table 6.2: Diversity gain gdiv and array gain grr of the angle scanning diver-sity prototype and the associated simulated values. The simulatedvalues are copied from Table 5.3.

6.10 Conclusions

This chapter describes the circuit implementation of the angle scanning diversity algo-rithm. This took about one year of work. The prototype itself functioned as expectedfrom simulations. Its performance is somewhat less than predicted by simulations. Amore in-depth study to resolve the difference between the predicted and measured diver-sity gain is beyond the scope of this work. The obtained diversity gain, however, has beenmore than convincing to demonstrate the value of diversity receivers (Chapter 7).

During the construction special care has been taken to prevent cross- talk and to im-prove the matching of all circuits. Most of the circuit solutions to achieve these goalshave only been implemented after the occurrence of some problems. They proved to beessential for a correct operation of the angle scanning diversity prototype. The most im-portant circuit considerations, that have been implemented, are described in this chapter.Especially the test mode of the combiner (no combining but directly routing the signals)helped to check the matching between the two receiver chains including all the diversitycircuits.

The prototype showed a good performance, about 7 dB diversity gain, with a rela-tive low circuit complexity. The performance improvement is so much that even moresimple implementations, like shown in Figure 5.28, can be considered. The performanceimprovement will then still be significant. The prototype had been designed such that it


can be implemented into a single integrated circuit. This has also been done, which isshown in Figure 6.22. This implementation has been tested on the board and was fullyfunctional.

Figure 6.22: Integrated circuit implementation of the angle scanning diversityprototype.

6.10.1 Current handheld diversity implementation

The state-of-the-art prototype of this chapter showed the value of diversity inside a hand-set [Dolmans and Leyten, 1999b]. As already mentioned in the introduction (Section 1.1)Philips has made a DECT handset with diversity implemented. This diversity method isa ‘select and stay’ method. During the preamble of a DECT time-slot the best antenna ischosen. During the remainder of the time-slot no switching will take place. The signalsof the antennas are not combined.

This DECT handset is the first diversity product on the consumer market. The di-versity implementation inside this handset is not very advanced. It can be improved byimplementing the ideas and principles of the prototype described in this chapter.

Chapter 7

Conclusions

The main results of this Ph.D. thesis are summarised in Section 7.1. Many aspects ofantenna-diversity transceivers are presented. The focus has been on a procedure to designthese transceivers. In some cases the issues and results that have been obtained by definingand verifying this procedure could not be investigated. The most relevant that could bestudied in more detail are listed in Section 7.2

The market for cordless and mobile communication is expanding very fast. The re-search and development efforts are increasing everywhere. This thesis is one of the resultsof an research programme that is still being continued. In Section 7.3 a small overview ofsome recent developments within and outside of Philips are given.

7.1 Results obtained

The goal of the Ph.D. project was to define and verify a procedure to design adaptivediversity implementations for portable consumer products (Section 1.2). This procedurefocuses on an optimal design with respect to circuit complexity, power dissipation, size,cost and other relevant issues. The procedure enforces a systematic approach towardsdesigning and testing diversity implementations. To verify the procedure, it has beenapplied to design a state-of-the-art antenna-diversity receiver (Chapter 5). This receiverhas been built and tested (Chapter 6). The performance of the receiver is close to thatpredicted by simulations.

Section 7.1.1 gives the results that have been obtained during the selection of the toolsfor the procedure. This covers the first part of this thesis. The remainder of this thesis isabout the design and test of a state-of-the diversity receiver for consumer products. Theresults are presented in Section 7.1.2.

7.1.1 Selection of tools

The procedure consists of two main parts: a simulation tool (Chapter 3) and a measure-ment set-up (Chapter 4). The requirements for these parts are obtained by studying the

163

164 Chapter 7. Conclusions

characteristics of the radio channel in Chapter 2. Two parameters derived from the PowerDelay Profile (PDP) are used in the design of the diversity receiver: the Signal-to-NoiseRatio (SNR) and the mean delay spread. With respect to obtaining the mean delay spreadtwo important results have been obtained:

• The mean delay spread is a wideband radio-channel parameter. In Section 2.9 itshown that its value can be obtained from narrowband measurements or simula-tions. In this way simulations and measurements can efficiently be done with areduced bandwidth. Moreover, the behaviour and performance of realistic, in mostcases narrowband, communication systems are better predicted with narrowbandsimulation or measurement results than with wideband results.

• The definition of the mean delay spread involves the averaging of the local PDPsover a small area. In Section 2.10.3 it is demonstrated that the wideband delayspread can also be obtained from averaging the local narrowband delay-spread val-ues. This is convenient for measurement set-ups and simulation tools, because thelocal delay spread can be computed for every observation point and then stored asa single number. The alternative would be to store a certain amount of PDPs andthen to compute the mean delay spread by averaging these PDPs. This would resultin more CPU time usage and higher memory requirements.

In Chapter 3 several methods for radio channel modelling are introduced. Two typesof methods are suitable for the procedure: ray-tracing and FDTD. An implementation of a2-dimensional FDTD method is compared to an implementation of a 2-dimensional ray-tracing method (Section 3.8). Both models are capable of predicting small-scale fadingeffects. The implementation of the available ray-tracing method, however, is less precisethan the FDTD implementation. The results obtained by an FDTD method can containspurious signals caused by switching on the source. In Section 3.6.2 this effect is stud-ied and it is shown that by using a source ramp-up the generation of spurious signals isavoided. Finally, an efficient way of implementing the calculation of the delay-spreadvalues is given in Section 3.6.4.

As a part of the procedure, a measurement set-up has been devised to be able to verifythe predictions of the computer tools, to obtain relevant information to design diversitysystems and to test hardware prototypes in a quantitative way (Chapter 4). The main partsof the measurement set-up are an xy-table or scanner with controller, a network analyser,a pre-amplifier, a personal computer (PC), switch, cables and antennas (Figure 4.1). Insection 4.4 a procedure to obtain the PDP based on the frequency domain measurementsis introduced. The accuracy of the measurement results is about 1 dB (Section 4.5). Thestatistical errors that remain after calibration of the network analyser result in a noise floorat about -60 dB from the maximum of the PDP.

7.1.2 Designing and building the diversity receiver

With the FDTD method and the measurement set-up different diversity systems for anhandset are analysed. The suitability of different diversity methods with respect to im-plementation in a handset is summarised (Section 5.2.7). Space diversity based on twodipole antennas separated by half a wavelength is chosen in this work.

7.1. Results obtained 165

The performance of different diversity-combining methods is analysed with the Cu-mulative Distribution Function (CDF), array gain and diversity gain (Section 5.4). Equal-gain combining is chosen as the most suitable method for implementation into an handset.Compared to maximum-ratio combining, which is the optimal combining method, its per-formance is comparable (Figure 5.22), but its circuit implementation is less complex. InSection 5.4.2 the effects of system bandwidth on the performance of the different combin-ing methods is analysed with measurements and simulations. In Section 5.5) it is shownthat the performance of an equal-gain combiner remains close to ideal if the phase shifteris discretised into a small number of phase-shift values. Only two phase shift values resultin a diversity of 8 dB which is one dB less than that of a continuous phase shifter (Table5.3).

The diversity receiver can be used to maximise the received signal strength or to min-imise the delay spread. The maximum-signal-strength combining method is easier toimplement than the minimum-delay-spread combining. The performance of a maximum-signal-strength combining criterion is compared to that of a minimum-delay-spread com-bining criterion (Section 5.9.1). The results show that maximum-signal-strength combin-ing also reduces the mean delay spread significantly (up to 10 %). Minimal-delay-spreadcombining does not result in an array gain and results in a lower diversity gain. The detec-tion of the received signal strength is done by an out-of-band noise detection method. Thismethod not only maximises the received signal strength but also the signal-to-interferenceratio (Section 5.9.2).

The results of the comparisons and analyses resulted in the angle scanning diversityreceiver, which is based on space diversity, equal-gain combining with a discrete phaseshifter and out-of-band noise detection (Chapter 6). The proposed system has been built.The out-of-band noise detection could not be implemented and has been replaced byreceived signal strength detection. The implementation is tested and works satisfactory.The diversity gain is 6.8 dB and the array gain 2.8 dB (Section 6.9). The correspondingsimulated diversity and array gain are 8.8 dB and 2.5 dB, respectively (Table 5.3). Thesimulated performance differs from the measured performance for three reasons:

1. the simulated propagation environment is different from the real one,

2. the hardware implementation can only approach the behaviour of the proposed an-gle scanning diversity system,

3. the performance of a real receiver depends on more parameters than the consideredreceived signal strength and delay spread.

The necessary hardware is of low complexity and suitable for integration into an Inte-grated Circuit (IC). This is achieved by using a zero Intermediate Frequency (zero-IF)receiver architecture (Section 6.3) and by implementing the phase shifter at the zero-IF(Section 6.2).

The performance improvement of the diversity receiver compared to receivers with-out diversity cannot easily and inexpensively be obtained by other means. Antenna di-versity will therefore be in important principle that will be encountered in many wirelessconsumer products, like cordless phones, Wireless Local Area Networks (WLANs) andmobile phones.


7.2 Recommendations for further research

Today, many papers are being published on the transformation of the multi-antenna con-cept to combat multi-path fading into the Space-Time coding concept, that exploit themulti-path effects to increase channel capacity [Foschini, 1996]. This Space-Time codingstrives for a joint optimisation of advanced signal processing and coding techniques incombination with the diversity and receiver circuits. At this moment it is not clear forwhich type of communication system or product this technique is most suitable or whenit will appear in commercial products. A possible research project is to extend the simu-lation tools and measurement set-up such that they can be used for analysing Space-Timesystems [Leyten and Dolmans, 2000a]. In this way a quantitative comparison betweenthese new systems and the classical diversity systems is possible.

A more advanced measurement set-up than that introduced in Chapter 4 could bedevised based on an arbitrary waveform generator. In this way the modulated high-frequency signals can be generated with the arbitrary waveform generator, transmittedacross the radio channel and subsequently received with an analogue to digital convertoror sampling scope. With such a set-up the propagation effects on the transmitted signalscan be analysed in detail. For example, the performance of different type of modulationmethods, like Orthogonal Frequency Division Multiplexing (OFDM) or Quadrature Am-plitude Modulation (QAM) can be studied. By using deep-memory sampling scopes, thereceived data can be stored on a computer, such that the performance of different imple-mentations of signal processing methods, like diversity and equalising, can be analysed[Leyten and Dolmans, 2000a].

The diversity prototype uses a received signal-strength indicator as a quality signalfor the adaptive circuits. The out-of-band noise detection method, described in this thesis,could not be implemented (Section 6.8). If this method is implemented then the expectedbehaviour and performance of this method in the presence of interfering systems could beanalysed.

The analysis of diversity systems is based on only two parameters: received signalstrength and delay spread (Section 5.4). The real behaviour of a transceiver depends onmany more parameters. A behavioural model of the transceiver in combination with achannel model based on simulations or measurements will result in a much better predic-tion of the performance.

In some modern digital communication transceivers both an equaliser as well as adiversity method is implemented (Section 5.8). This means that there are two adaptivesystems that should work together. The analysis and design of such a complex transceiversuch that its performance is optimal is a relevant research topic.

In this Ph.D. thesis the Finite Difference Time Domain (FDTD) method is appliedto simulate the effect of the radio channel on a transmitted pulse. In this simulation thecarrier frequency is present. This carrier frequency should be sampled with a sufficientnumber of points according to the Courant criterion (Section 3.6). This requires a veryhigh time resolution. The analysis of the received signal, however, is based on its envelopeor lowpass representation. Recently, FDTD methods have been published that are basedon such a lowpass representation. With these methods the envelope should be sampledwith a sufficient number of points. This results in a required time resolution that is much

7.3. Recent developments 167

lower than the FDTD implementation of this work. The number of time steps can alsosignificantly be reduced such that the computer simulations require less CPU time. Theimplementation of a lowpass equivalent of the FDTD method is therefore an interestingresearch topic.

The computer simulations are based on a 2D implementation of the FDTD method.A detailed analysis of the differences between a 3D and a 2D implementation includingthe effects of the uncertainties in the location and dielectric properties of the modelledobjects should be done (Section 3.7). For this analysis the measurement set-up, placed ina well defined propagation environment, could be used for benchmarking.

The probability that delay spread is below a certain threshold can be used to definea delay-spread gain in similar way as the diversity gain defined in Section 5.4.1. Theinterpretation of this quantity, however, should be further analysed.

The accuracy of the PDP is estimated to be about 1 dB (Section 4.5). This accu-racy is determined for large part by the time resolution of the power delay profile (PDP).The accuracy can be analysed in more detail by performing measurements with largerbandwidths. The effect of the time resolution of the PDP on the performance analysis ofnarrowband communication systems with realistic pulse durations could also be furtheranalysed. In many cases, the pulse duration is much larger than the time resolution ofthe measured PDP. As a result, the shape of the response obtained by transmitting a pulsethrough the radio channel will be determined for a large part by the pulse itself. Improvingthe resolution of the PDP might not be needed in this case.

For the derivation of the relation between the narrowband and wideband delay spreadmeasurement results are used. The processing of these results supports two importantassumptions of the indoor radio channel: the phase distribution can be assumed to be uni-form in a small area and the amplitude of the contributing pulses can be assumed constantin the same area (Section 2.9). These assumptions are quite often used in publicationsin which these are derived from a reasoning based on physical grounds. In this work,quantitative results are obtained that support this reasoning. Moreover, a beginning hasbeen made to analyse the size of the circular area for which the phase distribution can beconsidered uniform. However, more research is needed to explain the behaviour of thedelay spread as a function of this radius.

7.3 Recent developments

Two activities have been started as an extension of the work reported in this Ph.D. thesis[Leyten and Dolmans, 2000a]:

• The measurement set-up in combination with an high resolution algorithm, (MU-SIC) has been used to obtain the Angle-Of-Arrival (AOA) of the incoming waves[Mattheijssen, 2000]. AOA information is used, for example, to further optimiseradiation patterns of antenna systems [Mattheijssen, 2001].

• The measured Power Delay Profiles (PDPs) have been processed such that equiva-lent tapped-delay-line models were obtained for different propagation environments[Siemons, 2000]. These models have been implemented into a system simulator


such that different types of modulation schemes in combination with different sig-nal processing and coding methods can effectively be analysed.

In 1992 at the start of this work, antenna diversity was only considered for largetransceivers, like basestations. Nowadays, antenna diversity on a mobile or portable ter-minal is considered to be one of the key solutions to provide reliable high-speed com-munication. In 2000, for example, the Universal Mobile Telecommunications System(UMTS) standard includes multiple antennas for the handset [ETSI, 2000]. Diversity isalso part of many wireless local-area networks and is expected to be included in productsfor new standards, like Hiperlan.

In this work the focus is on the implementation of diversity inside a DECT handset. Itcan be expected that future communication systems will operate at higher frequencies, e.g.Hiperlan in the 5 GHz frequency band. The antennas for such systems will be smaller dueto the reduced wavelength. As a result a larger antenna (compared to the wavelength), forexample, multiple patch antenna, can be used without increasing the volume occupied.These antennas can also result in an improvement of the array gain, diversity gain anddelay spread [Leyten and Dolmans, 2000b], [Leyten and Dolmans, 2000a].

Two recent press releases show that also other research groups and start-up companiespromote the advantages of having two antennas with a smart combining network [RadioResearch Laboratory, 2001], [Antenova, 2001]. The claimed advantages are a reductionof the Specific Absorption Rate (SAR) by more than 30 percent, an improvement of voicequality by more than 25 percent, a ’talk- time’ increase of around a factor of three and anincreased capacity of a network without having to reduce cell size. The implementationsare built around a directional antenna, which operates electronically and has no movingparts. The signal processing circuits determine the most effective channel and fires thesignal in the right direction, thereafter, the antenna sweeps its surroundings to confirm thatit is still locked onto the best channel. The angle scanning diversity prototype describedin Chapter 6 has been developed to obtain similar performance improvements, which arelisted in Section 1.3.

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Samenvatting

Antenne-diversity implementaties bestaan uit twee of meer antennes en een schakelingom de signalen van de antennes optimaal te combineren. De kwaliteit van een antenne-diversity transceiver is beter dan een standaard transceiver met een enkele antenne. Dezeverbetering kan niet gemakkelijk en niet goedkoop met andere technieken behaald wor-den. Antenna-diversity is daarom een belangrijk principe, dat veel toegepast kan wordenin draadloze consumentenproducten, zoals mobiele telefoons en draadloze netwerken.

Dit proefschrift beschrijft een procedure voor het ontwerpen van antenna-diversitytransceivers voor draadloze consumentenproducten. Het volgen van deze procedure leidttot een zo goed mogelijke antenna-diversity implementatie met betrekking tot de com-plexiteit van de totale schakeling, het vermogensgebruik, de grootte, de kosten en andererelevante aspecten. De eerste stap is de analyse van antenna-diversity principes met si-mulaties betrekking tot efficientie, afmetingen en stralingspatroon. De volgende stap ishet bepalen van eigenschappen, zoals signal-ruis verhouding en bit-fouten kans, voor eenmulti-pad omgeving. Tenslotte, wordt een prototype gebouwd en worden er veldtestenuitgevoerd om de kwaliteit te bepalen.

Voor de procedure is een simulatieprogramma geselecteerd en een meetopstelling sa-mengesteld. Het simulatieprogramma is gebaseerd op de Finite Difference Time Domain(FDTD) methode. Met de meetopstelling wordt de frequentieresponsie van het radioka-naal met inbegrip van de antenne karakteristieken verkregen. Bovendien kunnen antenna-diversity transceivers opgenomen worden in de meetopstelling om de kwaliteit te beoor-delen en ze op een quantitatieve manier met elkaar te vergelijken.

Signalen worden uitgesmeerd in de tijd als ze zich voortplanten door het radiokanaal.Een afschatting van deze uitsmering wordt normaal gesproken met behulp van breedban-dige metingen of simulaties verkregen. In dit proefschrift wordt een methode beschrevenom deze afschatting te verkrijgen met behulp van smalbandige metingen of simulaties.De op deze manier verkregen uitsmering is een meer realistische maat voor de kwaliteitvan een antenna-diversity transceiver. De methode is toegepast om de relatie tussen debandbreedte van de uitgezonden signalen en de kwaliteit van antenna-diversity techniekente analyseren. Deze analyse laat zien dat de kwaliteit van alle technieken afneemt als debandbreedte toeneemt.

177

178

Met de beschreven procedure is een antenna-diversity transceiver ontworpen volgensde laatste stand der techniek voor implementatie in een draagbaar consumentenproduct.Deze antenna-diversity transceiver is gebouwd en getest. Het bestaat uit een twee-antennespace-diversity techniek met een discrete equal-gain schakeling die de signalen combi-neert in het basisband gedeelte. De signaal-ruis verhouding is met een factor vijf verbeterdten opzichte van een standaard ontvanger met een enkele antenne.

Acknowledgments

This Ph.D. thesis could not have been completed without the moral support and valu-able contributions of various people. In particular, I would like to express my gratitudeto the following people. Dieter Kasperkovitz and Peter Baltus for the motivating dis-cussions and their valuable input to my project proposals. Guido Dolmans for the manydiscussions that I had with him and for his valuable contributions as an expert. My othercolleagues within Philips, especially, those of the Integrated Transceivers group of thePhilips Research Laboratories Eindhoven and those of the Philips Research LaboratoriesRedhill and Aachen for their contributions and for their enjoyable company. The students,Bart van Leersum, William van Beek, Arthur van de Kerkhof, Jasper Siemons and PaulMahttheijssen for their contributions to this thesis and for their enthusiasm and dedication.

A part of the research project has been carried out as a co-operation with the Electro-magnetics Group of the Eindhoven University of Technology (TU/e). I am very grateful tothe late dr. M. Jeuken, the project leader at the TU/e, for his contributions and dedicationto the project.

I would like to thank my first promotor prof.dr. Gert Brussaard and my copromotordr. Matti Herben for their faith in me, when I asked them to supervise my Ph.D. workand during those occasions that I was not able to keep to the time schedule. I would alsolike to thank them together with my second promotor prof.dr. Wim van Bokhoven andthe other members of the kernel committee, prof.dr. Anton Tijhuis and prof.dr. RamjeePrasad for reviewing my Ph.D. thesis and giving me their comments to improve it.

I am indebted to the management of Philips Research for supporting the completionof this thesis in many ways.

My enthusiasm to start something without thinking of the consequences is one of thereasons for starting my Ph.D. work. I would like to thank my family for their moralsupport. Above all, I thank my girlfriend Yvonne for her implicit support and for havingto deal with the consequences of my enthusiasm.

179

Biography

Lukas Leijten was born in Woudenberg, the Netherlands, on October 28, 1966. In 1985he successfully completed his studies at the municipal grammar school Johan van Old-enbarnevelt in Amersfoort. In the same year he started studying electrical engineeringat the Eindhoven University of Technology (TU/e). During his study at the TU/e he hasbeen president of the Eindhoven Student Radio Amateur Club (ESRAC) for one year. Heobtained his Master of Science degree in 1989 with his thesis on the reflection of elec-tromagnetic plane waves by absorbers of an anechoic room. The work for this thesishas been carried out at the EMC cluster of the Philips Research Laboratories Eindhoven(PRLE). In 1989 he also obtained his radio-amateur licence with call sign PA3FQD. From1989 to 1991 he followed a post-graduate program at the Stan Ackermans Institute of theTU/e. He received the Master of Technological Design degree with his thesis on wavepropagation between satellites and groundstations. This work has been carried out inco-operation with the University of Bradford for the European Space Agency as the con-tractor. He started working in the Integrated Transceivers group of the IC-Design divisionof the PRLE in 1991. His activities include characterisation and modelling of the radio-channel, of microwave circuits, and of passive components. In the period from 1994 to1996 he has been involved in several initiatives to improve the quality of work at thePRLE. From 1998 to 1999 he has been detached to the Philips Research LaboratoriesAachen. In this period he has contributed to the research on high-frequency passive com-ponents for cordless and mobile products. From 1998 to 2001 he has worked on this Ph.D.thesis based on the various research projects in which he has participated.

181

Levensbeschrijving

Lukas Leijten werd geboren in Woudenberg, op 28 oktober 1966. In 1985 behaalde hijzijn diploma aan het stedelijk gymnasium Johan van Oldenbarnevelt te Amersfoort. Indatzelfde jaar begon hij zijn studie elektrotechniek aan de Technische Universiteit Eind-hoven (TU/e). Tijdens zijn studie aan de TU/e is hij een jaar voorzitter van de EindhovenseStudenten Radio Amateur Club (ESRAC) geweest. In 1989 verkreeg hij het ingenieurs-diploma met zijn afstudeerwerk over de reflectie van elektromagnetische vlakke golventegen de absorbers van een anechoische ruimte. Hij voerde zijn afstudeerwerk uit in hetEMC-cluster van het Philips Natuurkundig Laboratorium (Nat.Lab.) in Eindhoven. In1989 behaalde hij ook zijn radioamateur licentie met als roepnaam PA3FQD. Van 1989tot 1991 volgde hij de tweede-fase opleiding aan het Stan Ackermans Instituut van deTU/e. Hij behaalde zijn ontwerpersdiploma met een onderzoek naar de golfvoortplantingtussen satellieten en grondstations. Dit werk werd uitgevoerd in samenwerking met deUniversiteit van Bradford onder een contract voor de Europese Ruimtevaart Organisatie.Sinds 1991 werkt hij in de groep Integrated Transceivers van de sector IC-Design vanhet Nat.Lab. Zijn werk omvat karakterisering en modellering van het radiokanaal, vanmicrogolf circuits en van passieve componenten. In de periode van 1994 tot 1996 washij betrokken bij diverse initiatieven om de kwaliteit van het werk op het Nat.Lab. te ver-beteren. Van 1998 tot 1999 was hij gedetacheerd bij Philips Research in Aken. In dezeperiode heeft hij bijgedragen aan het onderzoek naar hoogfrequent passieve componentenvoor draadloze en mobiele producten. In de periode van 1998 tot 2001 werkte hij aan ditproefschrift dat gebaseerd is op de verschillende onderzoeksprojecten waaraan hij heeftdeelgenomen.

183

Index

A

aliasingFourier transformation . . . . . . . . 85

angle diversity . . . . . . . . . . . . . . . . . . . . 97angle of incidence . . . . . . . . . . . . . . . 102angle-scanning diversity . . . . . 135, 137

full circuit . . . . . . . . . . . . . . . . . . 153antenna . . . . . . . . . . . . . . . . . . . . . . . . . . 16

characteristics . . . . . . . . . . . . . . . .82current distribution . . . . . . . . . . . 16dipole . . . . . . . . . . . . . . . . . . . . . . 107directional . . . . . . . . . . . . . . . . . . . 97directivity . . . . . . . . . . . . . . . . . . . 47efficiency . . . . . . . . . . . . . . . . . . . . 47far-field . . . . . . . . . . . . . . . . . . . . . 47gain . . . . . . . . . . . . . . . . . . . . . . . . . 47impedance . . . . . . . . . . . . . . . 17, 82incident field . . . . . . . . . . . . . . . . . 16match . . . . . . . . . . . . . . . . . . . . . . . 82mismatch . . . . . . . . . . . . . . . . 82, 83portable product . . . . . . . . . . . . . . 42received voltage . . . . . . . . . . . . . . 16reflection coefficient . . . . . . . . . . 82Thevenin representation . . . . . . .17

array gain . . . . . . . . . . . . . . . . . . . . . . . 113bandwidth . . . . . . . . . . . . . . . . . . 115combining techniques . . . . . . . 114phased array . . . . . . . . . . . . . . . . 113

attenuation factor . . . . . . . . . . . . . . . . . 16averaged delay spread . . . . . . . . . . . . . 34

averaging area . . . . . . . . . . . . . . . 35

B

band-limited signals

Fourier transformation . . . . . . . . 86behavioural model of receiver . . . . . . 37BER . . . . . . . . . . . . . . . . see bit-error rateBerenger’s Perfectly Matched Layer 53bit

duration . . . . . . . . . . . . . . . . . . . . . 11rate . . . . . . . . . . . . . . . . . . . . . . . . . 11

bit-error ratechannel parameter . . . . . . . . . . . . 37delay spread . . . . . . . . . . 24, 37, 38envelope fading . . . . . . . . . . . 37, 38irreducible errors . . . . . . . . . . . . . 39local quantities . . . . . . . . . . . . . . . 36phase variations . . . . . . . . . . . . . . 38random FM . . . . . . . . . . . . . . . . . . 38signal-to-noise ratio . . . . . . . 38, 39thermal noise . . . . . . . . . . . . . . . . 38

C

CDF . . . . . . see cumulative distributionfunction

CDMA . . . . . . . . . . . . . . . . . . . . . . . . . . 95channel

flat . . . . . . . . . . . . . . . . . . . . . . . . . . 13modelling methods . . . . . . . . . . . 45

channel characterisation . . . see channelmeasurement

channel impulse response . . . . . . 16, 72channel measurement

narrowband . . . . . . . . . . . . . . 26, 30wideband . . . . . . . . . . . . . . . . . . . . 26

characterisation . . . . . see measurementcoherence

time . . . . . . . . . . . . . . . . . . . . . . . . .79coherence bandwidth . . . . . . . . . . . . . . 13

185

186 Index

frequency diversity . . . . . . . . . . . 95coherence time . . . . . . . . . . . . . . . . 14, 43

frequency diversity . . . . . . . . . . . 98complex envelope . . . . . . . . . . . . . . . . .21Courant criterion . . . . . . . . . . . . . . 54, 65cumulative distribution function . . . 112

outage . . . . . . . . . . . . . . . . . . . . . 112signal-to-noise ratio . . . . . . . . . 112

D

DECT . . . . . . . . . . . . . . . . . . . . . . . . . . . 10carrier frequencies . . . . . . . . . . . .11channel classification . . . . . . . . . 16diversity implementation . . . . . 161frequency diversity . . . . . . . . . . . 95Kala . . . . . . . . . . . . . . . . . . . . . . . 161power delay profile duration . . . 33power spectral density . . . . . 11, 19system characteristics . . . . . . . . . 12zero-IF receiver . . . . . . . . . . . . . 139

DECT Installation Assistant . . . . 51, 67delay spread . . . . . . . . . . . . . . . 13, 22, 23

accuracy . . . . . . . . . . . . . . . . . . . . .65angle diversity . . . . . . . . . . . . . . . 97averaged . . . . . . . . . . . . . . . . . . . . 34averaging area . . . . . . . . . . . . 30, 35based on envelope . . . . . . . . . . . . 33based on received signal . . . . . . 33bit-error rate . . . . . . . . . . . . . . . . . 38diversity combining . . . . . . . . . 129Gms source . . . . . . . . . . . . . . . . . . 28implementation . . . . . . . . . . . 53, 64local . . . . . . . . . . . . . . . . . 23, 34, 63mean . . . . . . . . . . . . . . . . . . . . . . . .24modulated signal . . . . . . . . . . . . . 65narrowband . . . . . . . . . . . . . . 28, 34overview . . . . . . . . . . . . . . . . . . . . 41practical calculation . . . . . . . . . . 32pulse delay spread . . . . . . . . . . . . 34pulse-position modulation . . . .118rms . . . . . . . . . . . . . . . . . . . . . . . . . 24wideband . . . . . . . . . . . . . 26, 28, 34

diffraction . . . . . . . . . . . . . . . . . . . . . . . .50ray tracing . . . . . . . . . . . . . . . . . . . 51

dipole antenna . . . . . . . . . . . . . . . . . . . 107direct conversion receiver . . . . . . . . .139discrete Fourier transformation . . . . . 84dispersion

frequency . . . . . . . . . . . . . . . . . . . 15time . . . . . . . . . . . . . . . . . . . . . . . . .14

diversityadaptive . . . . . . . . . . . . . . . . . . . . . 93algorithm . . . . . . . . . . . . . . . . . . .156angle . . . . . . . . . . . . . . . . . . . . . . . .97angle scanning . . . . . . . . . 135, 137antenna . . . . . . . . . . . . . . . . . . . . 159array gain . . . . . . . . . . . . . . . . . . 113combiner circuit . . . . . . . . . . . . 149controller . . . . . . . . . . . . . . 153, 156diversity gain . . . . . . . . . . . . . . . 112equaliser . . . . . . . . . . . . . . . . . . . 126field-component . . . . . . . . . . . . . . 96frequency . . . . . . . . . . . . . . . . . . . 95full circuit implementation . . . 153IC implementation . . . . . . . . . . 161implementation comparisons . . 98performance . . . . . . . . . . . . . . . . 158polarisation . . . . . . . . . . . . . . . . . . 96principle . . . . . . . . . . . . . . . . . 93, 94quality signal . . . . . . . . . . . . . . . . 99selection circuit . . . . . . . . . . . . . 147space . . . . . . . . . . . . . . . . . . . . . . . .94spatial filter . . . . . . . . . . . . . . . . . 103time . . . . . . . . . . . . . . . . . . . . . . . . .98

diversity combining . . . . . . . . . . . . . . 100adaptation speed . . . . . . . . . . . . 125array gain . . . . . . . . . . . . . . . . . . 114bandwidth . . . . . . . . . . . . . . . . . . 115circuit . . . . . . . . . . . . . . . . . . . . . .149comparison . . . . . . . . . . . . . . . . . 119directivity pattern . . . . . . . 106, 110dual equal-gain . . . . . . . . . 107, 137equal-gain . . . . . . . . . . . . . . . . . . 105hybrid form . . . . . . . . . . . . . . . . .102hysteresis . . . . . . . . . . . . . . 101, 102maximum-ratio . . . . . . . . . . . . . 109maximum-signal-strength . . . . 129minimum-delay-spread . . . . . . 129outage . . . . . . . . . . . . . . . . . . . . . 112

Index 187

output signal . . . . . . . . . . . . . . . .100performance . . . . . . . . . . . . . . . . 112preamble . . . . . . . . . . . . . . . . . . . 102response time . . . . . . . . . . . . . . . 125select and stay . . . . . . . . . . . . . . 102selection circuit . . . . . . . . . . . . . 147selective . . . . . . . . . . . . . . . . . . . .101spatial filter . . . . . . . . . . . . . . . . . 103specific absorption rate . . . . . . 124switched . . . . . . . . . . . . . . . . . . . 100switching loss . . . . . . . . . . . . . . 101threshold . . . . . . . . . . . . . . . . . . . 100

diversity gain . . . . . . . . . . . . . . . . . . . .112bandwidth . . . . . . . . . . . . . . . . . . 115

diversity prototypealignment . . . . . . . . . . . . . . . . . . 138block diagram . . . . . . . . . . . . . . 137performance . . . . . . . . . . . . . . . . 158

Dopplerfrequency . . . . . . . . . . . . . . . . . . . 14spread . . . . . . . . . . . . . . . . . . . . . . .14

dynamic range . . . . . . . . . . . . . . . . 59, 61

E

envelope . . . . . . . . . . . . . . . . . . . . . . . . . 21equal-gain

dual . . . . . . . . . . . . . . . . . . . . . . . .107phase shifter . . . . . . . . . . . 105, 142

equal-gain combining . . . . . . . . . . . . 105adaptation speed . . . . . . . . . . . . 125array gain . . . . . . . . . . . . . . . . . . 114bandwidth . . . . . . . . . . . . . . . . . . 115continuous phase shifter . . . . . 120directivity pattern . . . . . . . . . . . 106discrete phase shifter . . . . . . . . 120maximum-signal-strength . . . . 129minimum-delay-spread . . . . . . 129performance . . . . . . . . . . . . . . . . 122response time . . . . . . . . . . . . . . . 125specific absorption rate . . . . . . 124two-phase . . . . . . . . . . . . . .123, 125

equaliser . . . . . . . . . . . . . . . . . . . . . . . . 126diversity . . . . . . . . . . . . . . . . . . . .126RAKE receiver . . . . . . . . . . . . . 127

equivalent lowpass signal . . . . . . . . . . 21equivalent noise bandwidth . . . . . . . . 12

F

fading . . . . . . . . . . . . . . . . . . . . . . . . . . . 12classification . . . . . . . . . . . . . 13, 15diversity . . . . . . . . . . . . . . . . . . . . . 93fast . . . . . . . . . . . . . . . . . . . . . . . . . 15flat . . . . . . . . . . . . . . . . . . . . . . . . . .14frequency-non-selective . . . . . . . 14frequency-selective . . . . . . . . . . . 14large-scale fading . . . . . . . . . . . . 12slow . . . . . . . . . . . . . . . . . . . . . . . . 14small-scale . . . . . . . . . . . . . . . . . . 12

far-field . . . . . . . . . . . . . . . . . . . . . . . . . . 47fast fading . . . . . . . . . . . . . . . . . . . . . . . 15FDTD see finite difference time domainfield-component diversity . . . . . . . . . . 96finite difference time domain . . . . . . . 53

accuracy . . . . . . . . . . . . . . . . . . . . .65cell size . . . . . . . . . . . . . . . . . . . . . 54Courant criterion . . . . . . . . . .54, 65delay spread . . . . . . . . . . . . . . 33, 64dynamic range . . . . . . . . . . . . 59, 61Gaussian modulated sine source 61higher-order scheme . . . . . . . . . . 53power delay profile . . . . . . . . . . . 32propagation model . . . . . . . . . . . 67resonances . . . . . . . . . . . . . . . . . . .57source ramp-up . . . . . . . . . . . . . . 54spurious . . . . . . . . . . . . . . . . . 55, 61time step size . . . . . . . . . . . . . . . . 54two-dimensional . . . . . . . . . . . . . 66

flat fading . . . . . . . . . . . . . . . . . . . . . . . . 14Fourier transformation . . . . . . . . . . . . 18

aliasing . . . . . . . . . . . . . . . . . . . . . 85band-limited signals . . . . . . . . . . 86discrete . . . . . . . . . . . . . . . . . . . . . 84discrete inverse . . . . . . . . . . . . . . 84inverse . . . . . . . . . . . . . . . . . . . . . . 84reciprocity relation inverse . . . . 84spectral leakage . . . . . . . . . . . . . . 86windowing . . . . . . . . . . . . . . . . . . 86

frame . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

188 Index

frequency demodulator . . . . . . . . . . . 132output spectrum . . . . . . . . . . . . . 133

frequency discriminator . . . . . . 141, 155frequency dispersion . . . . . . . . . . . . . . 15frequency diversity . . . . . . . . . . . . . . . .95

DECT . . . . . . . . . . . . . . . . . . . . . . . 95GSM . . . . . . . . . . . . . . . . . . . . . . . . 95

frequency transfer function . . . . . . . . 82measurement . . . . . . . . . . . . . . . . 81

frequency-non-selective fading . . . . . 14frequency-selective fading . . . . . . . . . 14Friis transmission formula . . . . . . . . . 46

G

Gaussian modulated sine source . . . seeGms source

Gaussian pulse . . . . . . . . . . . . . . . . . . . 18Fourier transformation . . . . . . . . 18

Gaussian window . . . . . . . . . . . . . .88, 89GFSK . . . . . . . . . . . . . . . . . . . 11, 17, 140Gms source . . . . . . . . . . . . . . . . . . . . . . 18

causality . . . . . . . . . . . . . . . . . . . . 19delay spread . . . . . . . . . . . . . . . . . 28equivalent lowpass voltage . . . . 22finite difference time domain . . 61Fourier transform . . . . . . . . . . . . 20Fourier transformation . . . . . . . . 19mean PDP . . . . . . . . . . . . . . . . . . . 27power delay profile . . . . . . . . . . . 22power spectral density . . . . . . . . 20pulse delay spread . . . . . . . . . . . . 28time discretised . . . . . . . . . . . . . . 61

GMSK . . . . . . . . . . . . . . . . . . . . . . . 11, 17Green’s function . . . . . . . . . . . . . . . . . . 49GSM . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

frequency diversity . . . . . . . . . . . 95

H

harmonic propagation model . . . . . . . 49

I

impulse response

complex lowpass equivalent . . . 21mean PDP . . . . . . . . . . . . . . . . . . . 25measurement . . . . . . . . . . . . . . . . 83

in-phase component . . . . . . . . . . 20, 141inter-symbol interference . . . . . . . . . . 22

bandwidth . . . . . . . . . . . . . . . . . . 118irreducible errors . . . . . . . . . . . . 129

irreducible errors . . . . . . . . . . . . . 39, 129ISI . . . . . . see inter-symbol interference

L

large-scale fading . . . . . . . . . . . . . . . . . 12local delay spread . . . . . . . . . . . . . 23, 34local power delay profile . . . . . . . . . . 21loss factor . . . . . . . . . . . . . . . . . . . . 47, 67lowpass signal . . . . . . . . . . . . . . . . . . . . 21

equivalent . . . . . . . . . . . . . . . . . . . 21

M

maximum-ratio combining . . . . . . . .109array gain . . . . . . . . . . . . . . . . . . 114bandwidth . . . . . . . . . . . . . . . . . . 115directivity pattern . . . . . . . . . . . 110

mean delay spread . . . . . . . . . . . . . . . . 24mean narrowband delay spread . . . . . 28mean power delay profile . . . . . . . . . . 21

averaging area . . . . . . . . . . . . . . . 30Gms . . . . . . . . . . . . . . . . . . . . . . . . 27impulse response . . . . . . . . . . . . . 25

measurementaccuracy . . . . . . . . . . . . . . . . . . . . .89characteristics . . . . . . . . . . . . . . . .81coherence time . . . . . . . . . . . 43, 79diversity prototype . . . . . . . . . . 158frequency transfer function . . . . 81impulse response . . . . . . . . . . . . . 83power delay profile . . . . . . . . . . . 83procedure . . . . . . . . . . . . . . . . . . . 91set-up . . . . . . . . . . . . . . . 79, 80, 158speed . . . . . . . . . . . . . . . . . . . . . . . 43system bandwidth . . . . . . . . . . . . 91time . . . . . . . . . . . . . . . . . . . . . . . . .79

measurement set-up

Index 189

requirements . . . . . . . . . . . . . 42, 43multi-path

channel . . . . . . . . . . . . . . . . . . . . . 12environment . . . . . . . . . . . . . . . . . 12

N

narrowband delay spread . . . . . . . . . . 34network analyser . . . . . . . . . . . . . . . . . .27

aliasing . . . . . . . . . . . . . . . . . . . . . 85calibration . . . . . . . . . . . . . . . . . . . 81sweep time . . . . . . . . . . . . . . . . . . 79windowing . . . . . . . . . . . . . . . . . . 86

noisebit-error rate . . . . . . . . . . . . . . . . . 38equivalent bandwidth . . . . . . . . . 12figure . . . . . . . . . . . . . . . . . . . . . . . 38thermal . . . . . . . . . . . . . . . . . . . . . . 38

O

OFDM . . . . . . . . . . . . . . . . . . . . . . . . . . .95out-of-band noise detection . . 131, 141out-of-band noise detector . . . . . . . . 155

circuit . . . . . . . . . . . . . . . . . . . . . .150outage . . . . . . . . . . . . . . . . . . . . . . . . . . 112

P

path-loss model . . . . . . . . . . . . . . . . . . . 46fading . . . . . . . . . . . . . . . . . . . . . . . 46partitioned . . . . . . . . . . . . . . . . . . . 48transmission loss . . . . . . . . . . . . . 48

PDP . . . . . . . . . . see power delay profilephase shifter

circuit of continuous . . . . . . . . .142circuit of discrete . . . . . . . . . . . .144continuous . . . . . . . . . . . . . 120, 142discrete . . . . . . . . . . . . . . . . 120, 142diversity . . . . . . . . . . . . . . . . . . . .105equal-gain . . . . . . . . . . . . . . . . . . 142equal-gain combiner . . . . . . . . . 105zero-IF . . . . . . . . . . . . . . . . . . . . . 142

phase-shifterequal-amplitude discrete . . . . . 146

phased array . . . . . . . . . . . . . . . . . . . . 102directivity pattern . . . . . . . . . . . 103gain . . . . . . . . . . . . . . . . . . . . . . . .113

PHS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10PML . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53polarisation diversity . . . . . . . . . . . . . . 96

slanted . . . . . . . . . . . . . . . . . . . . . . 96power

time-averaged . . . . . . . . . . . . . . . .21power delay profile . . . . . . . . . . . . . . . 21

averaging area . . . . . . . . . . . . . . . 30duration . . . . . . . . . . . . . . 32, 42, 85local . . . . . . . . . . . . . . . . . . . . . 21, 29mean . . . . . . . . . . . . . . . . . . . . 21, 29measurement . . . . . . . . . . . . . . . . 83noise . . . . . . . . . . . . . . . . . . . . . . . . 32

power spectral density . . . . . . . . . . . . . 11probability density function . . . . . . . 112propagation delay . . . . . 16, 19, 24, 120

distribution . . . . . . . . . . . . . . . . . 121power delay profile . . . . . . . . . . . 88windowing . . . . . . . . . . . . . . . . . . 88

propagation modelaccuracy . . . . . . . . . . . . . . . . . . . . .67analytical . . . . . . . . . . . . . . . . . . . . 49comparison . . . . . . . . . . . . . . . . . . 77deterministic . . . . . . . . . . . . . . . . . 48FDTD . . . . . . . . . . . . . . . . . . . 53, 67harmonic . . . . . . . . . . . . . . . . . . . . 49inverse exponent-law . . . . . . . . . 47partitioned . . . . . . . . . . . . . . . . . . . 48path-loss . . . . . . . . . . . . . . . . . . . . 46radio transmission equation . . . 46ray-tracing . . . . . . . . . . . . . . . 50, 67statistical . . . . . . . . . . . . . . . . . . . . 48three-dimensional . . . . . . . . . . . . 66two-dimensional . . . . . . . . . . . . . 66

PSD . . . . . . . see power spectral densitypulse

decay . . . . . . . . . . . . . . . . . . . . . . . 18Gaussian . . . . . . . . . . . . . . . . . . . . 18

pulse decay . . . . . . . . . . . . . . . . . . . . . . 71-30 dB bandwidth . . . . . . . . . . . . 20-30 dB duration . . . . . . . . . . . . . . 20causality . . . . . . . . . . . . . . . . . . . . 88

190 Index

pulse delay spread . . . . . . . . . . . . 28windowing . . . . . . . . . . . . . . . . . . 87

pulse delay spread . . . . . . . . . . . . . 28, 29delay spread . . . . . . . . . . . . . . . . . 34Gms source . . . . . . . . . . . . . . . . . . 28rectangular wave source . . . . . . .28triangular wave source . . . . . . . . 28

pulse-position modulation . . . . . . . . 118

Q

quadrature component . . . . . . . . 20, 141quality signal . . . . . . . . . . . . . . . . . . . . . 99

R

radio channel . . . . . . . . . . . . .see channelradio transmission equation . . . . . . . . 46RAKE receiver . . . . . . . . . . . . . . . . . . 127ray-tracing

algorithm . . . . . . . . . . . . . . . . . . . . 51DECT Installation Assistant . . . 51delay spread . . . . . . . . . . . . . . . . . 53diffraction . . . . . . . . . . . . . . . . . . . 51propagation model . . . . . . . . 50, 67

Rayleigh fading . . . . . . . . . . . . . . . . . . .48received antenna voltage . . . . . . . . . . .16received signal-strength indicator . 131,

155reciprocity relation of Fourier transfor-

mation . . . . . . . . . . . . . . . . . . 84reflection coefficient . . . . . . . . . . . . . . 82Ricean fading . . . . . . . . . . . . . . . . . . . . 48rms delay spread . . . . . . . . . . . . . . . . . . 24

S

SAW filter . . . . . . . . . . . . . . . . . . . . . . . 12selective combining . . . . . . . . . . . . . . 101

array gain . . . . . . . . . . . . . . . . . . 114bandwidth . . . . . . . . . . . . . . . . . . 115hybrid form . . . . . . . . . . . . . . . . .102hysteresis . . . . . . . . . . . . . . . . . . 102preamble . . . . . . . . . . . . . . . . . . . 102

signal-to-noise ratio

bit-error rate . . . . . . . . . . . . . .38, 39cumulative distribution . . . . . . 112normalised . . . . . . . . . . . . . . . . . 111

signal-to-noise-plus-interference . . 129,131

simulationrequirements . . . . . . . . . . . . . 42, 43

slow fading . . . . . . . . . . . . . . . . . . . . . . .14small-scale fading . . . . . . . . . . . . . . . . .12

classification . . . . . . . . . . . . . 13, 15SNIR . . . . . . . . see signal-to-noise-plus-

interferenceSNR . . . . . . . . . see signal-to-noise ratiosource ramp-up . . . . . . . . . . . . . . . . . . . 54

cosine shape . . . . . . . . . . . . . . . . . 55space diversity . . . . . . . . . . . . . . . . . . . .94spatial filter . . . . . . . . . . . . . . . . . . . . . 103spatial resolution . . . . . . . . . . . . . . . . . .42specific absorption rate . . . . . . . . . . . 124spectral leakage . . . . . . . . . . . . . . . . . . .86spectrogram . . . . . . . . . . . . . . . . . . . . . . 57spurious . . . . . . . . . . . . . . . . . . .54, 55, 61statistical propagation model . . . . . . . 48

Rayleigh fading . . . . . . . . . . . . . . 48Ricean fading . . . . . . . . . . . . . . . . 48

switched combining . . . . . . . . . . . . . .100array gain . . . . . . . . . . . . . . . . . . 114hysteresis . . . . . . . . . . . . . . 101, 114switching loss . . . . . . . . . . . . . . 101threshold . . . . . . . . . . . . . . . . . . . 100

T

TDMA . . . . . . . . . . . . . . . . . . . . . . . . . . 98Thevenin representation of antenna . 17thermal noise . . . . . . . . . . . . . . . . . . . . . 38

bit-error rate . . . . . . . . . . . . . . . . . 38three-dimensional model . . . . . . . . . . 66time delay

diversity . . . . . . . . . . . . . . . . . . . .104time dispersion . . . . . . . . . . . . . . . . . . . 14time diversity . . . . . . . . . . . . . . . . . . . . .98time resolution . . . . . . . . . . . . . . . . . . . 42time slot . . . . . . . . . . . . . . . . . . . . . . . . . 12time-averaged power . . . . . . . . . . . . . . 21

Index 191

transmission loss . . . . . . . . . . . . . . . . . .48transmission-loss model . . see path-loss

modeltransversal filter . . . . . . . . . . . . . . . . . 127two-dimensional model . . . . . . . . . . . . 66

W

wideband delay spread . . . . . . . . . 26, 34averaging area . . . . . . . . . . . . . . . 30

windowingcausality . . . . . . . . . . . . . . . . . . . . 88constructed . . . . . . . . . . . . . . . . . . 87Fourier transformation . . . . . . . . 86Gaussian . . . . . . . . . . . . . . . . . 87, 89overview . . . . . . . . . . . . . . . . . . . . 87process loss . . . . . . . . . . . . . . . . . . 86rectangular . . . . . . . . . . . . . . . . . . 86sidelobe level . . . . . . . . . . . . . . . . 86spectral leakage . . . . . . . . . . . . . . 86

WSSUS channel . . . . . . . . . . . . . . . . . . 15equaliser . . . . . . . . . . . . . . . . . . . 127transversal filter . . . . . . . . . . . . . 127

Y

Yee cell . . . . . . . . . . . . . . . . . . . . . . . . . . 53

Z

zero-IF . . . . . . . . . . . . . . . . . . . . . . . . . 139

design of antenna-diversity transceivers for wireless ...is therefore an important principle that...

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