DEPARTMENT OF ELECTRICAL AND INFORMATION ENGINEERING

DEGREE PROGRAMME IN ELECTRICAL ENGINEERING

ULTRA WIDEBAND CHANNEL MODELLING AND COMMUNICATION SYSTEM PERFORMANCE IN OUTDOOR ENVIRONMENT Author _________________________________ Niina Laine Supervisor _________________________________ Jari Iinatti Accepted _______________ Grade _______________

Laine N. (2004) Ultra Wideband Channel Modelling and Communication Sys-tem Performance in Outdoor Environment. Department of Electrical and Informa-tion Engineering, University of Oulu, Oulu, Finland. Master’s Thesis, 92 p.

ABSTRACT This thesis examines the per formance of an ultra wideband (UWB) system at very high and ultra high frequencies (VHF/UHF) (230−390 MHz) in a typical Finnish forest environment. First the UWB propagation channels multipath and path loss proper ties are studied using long (0.5−5.6 km) link distances. The studies are based on frequency response measurements with ver tical polar ized antennas over fixed links. Based on analyses of the measured data, general channel parameters were generated for each link using a tapped delay line structure. A path loss analysis was employed to study UWB signal attenuation in different kinds of environments as a function of the distance.

The generated channel models were used to study the UWB communication systems per formance using link level simulations. The studied system was a sin-gle band UWB system with a single user . Different modulations and multiple access methods were considered, while taking into account both coherent and noncoherent receiver structures. The thesis focuses on systems which are simple and inexpensive to implement. I t was found that the pulse amplitude modula-tion (PAM) gives the best system per formance and on-off keying (OOK) gives the worst. No significant differences were found between the per formances of a direct sequence systems and a time hopping system. According to the generated channel models the par tial-Rake with four fingers was found to be sufficient re-ceiver in the studied environment. I f the selective-Rake or more than four fin-gers are used, the improvement is insignificant.

According to the system simulations and link budget analysis, it was found that when a simply noncoherent receiver is used with a data rate of 16 kbit/s, 10 W of transmission power is needed to reach the required 10-3 bit er ror rate (BER) in all studied links. In this case, the pulse shape modulation (PSM) can be used with a one finger Rake receiver . One watt of transmission power can be used but then the coherent approaches with pulse amplitude modulation and a multi-finger Rake receiver are needed.

Keywords: impulse radio, multipath propagation, path loss, link budget, time hopping, direct sequence.

Laine N. (2004) Ultralaajakaistaisen kanavan mallinnus ja tiedonsiir tojär jestel-män suor ituskyky ulkotilassa. Oulun yliopisto, sähkö- ja tietotekniikan osasto. Diplomityö, 92 s.

TI IVISTELMÄ

Työssä tutkitaan ultralaajakaistaisen (UWB, ultra wideband) jär jestelmän suo-r ituskykyä VHF/UHF-taajuuksilla (230−390 MHz) tyypillisessä suomalaisessa metsämaastossa. Siinä selvitettiin ensin UWB-etenemiskanavan monitieominai-suuksia ja etenemisvaimennuksia 0,5–5,6 km pituisilla linkkiyhteyksillä tehdyis-tä taajuusvastemittauksista käyttäen pystypolar isaatioantenneja. Mittausaineis-ton analyysien pohjalta laskettiin etenemiskanavalle kanavaparametreja sekä luotiin viivelinjamalliin perustuvat kanavamallit jokaiselle linkkivälille. Ete-nemisvaimennusmallinnuksessa selvitettiin UWB-signaalin vaimenemista er ilai-sissa ympär istöissä etäisyyden funktiona.

Luotuja kanavamalleja käytettiin UWB-tiedonsiir tojär jestelmän suor itusky-vyn analysoimiseen linkkitason simuloinneilla. Tutkittu jär jestelmä oli yksikais-tainen UWB-jär jestelmä yhden käyttäjän tapauksessa. Suor ituskykyä tutkittiin er i modulaatio- ja monikäyttömenetelmillä ottaen huomioon sekä koherentit että epäkoherentit vastaanotinrakenteet. Työssä tutkittiin er ityisesti toteutuksel-taan yksinker taisia ja halpoja rakenteita.

Simulointitulokset osoittivat odotetusti pulssin amplitudimodulaation (PAM, pulse amplitude modulation) toimivan parhaiten käytetyistä modulaatiomene-telmistä. Katkoavainnus (OOK, on-off keying) toimi tutkituista huonoiten. Suo-rasekvenssijär jestelmän (DS, direct sequence) ja aikahyppivän jär jestelmän (TH, time hopping) suor ituskyvyt eivät eronneet toisistaan merkittävästi. Kana-vamallien perusteella todettiin, että neljähaarainen osittainen Rake-vastaanotin on r iittävä tutkitussa ympär istössä. Siihen ver rattuna selektiivisellä Rake-vast-aanottimella tai usempaa kuin neljää haaraa käytettäessä ei saavuteta merkit-tävää parannusta.

Simulointituloksien ja linkkibudjettianalyysin perusteella todettiin, että mita-tuilla linkeillä käytettäessä yksinker taista epäkoherenttia vastaanotinta ja 16 kbit/s datanopeutta tarvitaan 10 W:n lähetysteho takaamaan vaadittu bittivir -hetodennäköisyys 10-3 kaikilla linkkiväleillä. Tällöin pulssin aaltomuotomodu-laatiota (PSM, pulse shape modulation) käytettäessä r iittää yksihaarainen Ra-ke-vastaanotin. Alempi 1 W:n lähetysteho on myös r iittävä 16 kbit/s datanopeu-delle, mutta silloin vaaditaan koherentti jär jestelmä, pulssin amplitudimodu-laatio ja useamman haaran Rake-vastaanotin. Avainsanat: impulssiradio, monitie-eteneminen, etenemisvaimennus, linkkibud-jetti, suorahajotus, aikahyppy.

TABLE OF CONTENTS ABSTRACT TIIVISTELMÄ TABLE OF CONTENTS PREFACE LIST OF SYMBOLS AND ABBREVIATIONS 1. INTRODUCTION...............................................................................................10 2. ULTRA WIDEBAND TECHNOLOGY ............................................................12

2.1. General Aspects of UWB Technology ......................................................12 2.1.1. Advantages and Disadvantages......................................................15 2.1.2. Applications...................................................................................17

2.2. UWB Communication System Concepts...................................................17 2.2.1. Binary Modulation Techniques......................................................17 2.2.2. Multiple Access Methods...............................................................20

2.3. Special Benefits of UWB technology in Military Applications................23 3. MULTIPATH RADIO CHANNEL MODELLING...........................................25

3.1. Physical Mechanisms of Multipath Propagation .......................................25 3.2. Fast and Slow Fading.................................................................................26 3.3. Multipath Channel Model ..........................................................................28 3.4. Path Loss Model ........................................................................................31 3.5. Link Budget Analysis in UWB system......................................................32

4. RESULTS OF CHANNEL MEASUREMENTS................................................34 4.1. Measurement Principle and Parameters.....................................................34 4.2. Measurement Environment........................................................................37 4.3. Data Preparation ........................................................................................39 4.4. Channel Characterisation...........................................................................41

4.4.1. Channel Parameters........................................................................41 4.4.2. Path Loss Analysis.........................................................................42 4.4.3. Link Budget Analysis.....................................................................45

4.5. Channel Models.........................................................................................47 4.5.1. Average Power Delay Profiles.......................................................47 4.5.2. Amplitude Fading ..........................................................................49

5. SYSTEM SIMULATIONS.................................................................................51 5.1. Receiver Structure......................................................................................51 5.2. Assumptions and Parameters.....................................................................52 5.3. Simulation Results.....................................................................................54 5.4. Conclusion of the Results..........................................................................62

6. DISCUSSION .....................................................................................................65 7. SUMMARY ........................................................................................................67 8. REFERENCES....................................................................................................69 9. APPENDICES.....................................................................................................73

PREFACE

This thesis project was completed at the Centre for Wireless Communications of the Telecommunication Laboratory at the University of Oulu within two projects, Future Ultra Wideband Radio Systems (FUBS) and Concepts for Ultra Wideband Radio Systems (CUBS). I would like to thank the National Technology Agency of Finland (TEKES), Elektrobit, the Finnish Defence Forces and the Centre for Wireless Com-munication for their financial support.

I would like to express my sincere gratitude to my supervisors, Prof. Jari Iinatti and Prof. Seppo Karhu, and my advisor, Lic. Tech. Matti Hämäläinen for their invaluable help and guidance during all the phases of this thesis project. I owe my thanks to all my colleagues, especially Lassi Hentilä, Raffaello Tesi, Veikko Hovinen and Tommi Jämsä for the numerous and helpful discussions we had during the work. I would also like to thank Matti Nenonen for his contribution to the measurements and the control of the Warfare software.

Finally, I would like to thank my family and friends. I especially wish to express my warmest gratitude to my parents for their support during my studies and to Janne for all his patience and encouragement.

Oulu, May 27, 2004 Niina Laine

L IST OF SYMBOLS AND ABBREVIATIONS

A Amplitude B Bandwidth Bf Fractional bandwidth C Channel capacity

c Velocity of the light, c = m/s103 8⋅ (cp)j j th chip of the pseudorandom code (cw)j j th code word of the pseudorandom code d Distance d1,2 Point’s distance from the transmitter and from the receiver dj Factor depending on chosen data bit

dk kth data bit Eb Average energy of a data bit F Noise figure of the receiver fh Upper −10 dB point in a spectrum fl Lower −10 dB point in a spectrum fMHz Carrier frequency in megahertz GR Receiver antenna gain in dB GT Transmitter antenna gain in dB H (f,t) Transform function Hk(f) Measured channel frequency response h(t,� ) Impulse response j Data bit which will be transmitted [0,1] K Number of pulses used per data bit

k Boltzmann’s constant, W/Hz/K10381.1 23−⋅=k

LdB Path loss Lexc(dB) Excess path loss LF(dB) Free space loss LR Receiver feeder loss in dB LT Transmitter feeder loss in dB lr Number of paths M Link margin in dB m Number of the Fresnel ellipsoid mµ Expected variable of the Gaussian distributed random variable µ

N Thermal noise of receiver NP10dB Number of multipath components within 10 dB related to strongest

component NS Number of accepted sweeps nair Air refractive index, nair =1.0003 n(t) Gaussian noise in the channel P(� ) Power delay profile Pb Average probability of errors

PG Processing gain PG1 Processing gain from pulse repetition PG2 Processing gain from low duty cycle PR Received power in dB PT Transmitted power in dB Ptot Total power p� (t) Probability density function of lognormal distribution random

variable p� (t) Probability density function of Rice distributed random variable

kLdB_local Local path loss of kth sweep over all frequencies

Rb Data rate r(t) Received signal rm Radius of the Fresnel ellipsoid S Signal power S(f) Spectrum of the transmitted signal Snum Number of points per sweep s Dominant signal component of the Rice distribution s(t) Transmitted signal T Temperature of the receiver TA Arrival time of the first path Tb Data bit length Tc Chip length Tf Pulse repetition interval Tp Pulse width TS Length of a single time slot Ts Symbol time t Time tc Coherence time Uj

EGC EGC decision variable for jth data bit Uj

MRC MRC decision variable for jth data bit Uj

SLC+PE SLC+PE decision variable for jth data bit v(t) Gaussian pulse w(t) Generic pulse waveform wtr(t) Transmitted UWB pulse waveform x(t) Modulated information signal Y(f,t) Output of the channel in frequency domain y(t) Output of the channel in time domain

n (t) Amplitude gain of the nth multipath Modulation index (t) Dirac Delta Function dB Ricean K-factor

� Delay resolution

�d Distance resolution

(�

f)c Coherence bandwidth n Phase of the nth multipath Wavelength

� 2 Power of the random part in the Rice distribution �

µ Deviation of the Gaussian distributed random variable µ M Mean excess delay

max Maximum detectable delay n Delay of the nth multipath RMS RMS excess delay tot Maximum excess delay

AET Acoustic to Electrical Transformer AFGU Function Generator AWGN Additive White Gaussian Noise A-Rake All-Rake Receiver a.s.l Above from Sea Level BER Bit Error Rate BPSM Binary Phase Shift Keying Modulation CDF Cumulative Distribution Function CDMA Code Division Multiple Access DFT Discrete Fourier Transform DS Direct Sequence DUT Device Under Test EAT Electrical to Acoustic Transformer EGC Equal Gain Combiner FCC Federal Communications Commission FDMA Frequency Division Multiple Access FIR Finite Impulse Response GPS Global Positioning System GSM Global System for Mobile Communications IDFT Inverse Discrete Fourier Transform ISI Intersymbol Interference KS Kolmogorov-Smirnov Goodness of Fit test LNA Low Noise Amplifier LOS Line-of-Sight LPD Low Probability of Detection LPI Low Probability of Interception MRC Maximum Ratio Combiner NLOS Non-Line-of-Sight OOK On-Off Keying PA Power Amplifier PAM Pulse Amplitude Modulation PAN Personal Area Network PDF Probability Density Function PDP Power Delay Profile PE Power Estimation PPM Pulse Position Modulation PR Pseudorandom PRI Pulse Repetition Interval PSK Phase Shift Keying

PSM Pulse Shape Modulation P-Rake Partial-Rake Receiver RMS Root Mean Square RX Receiver SLC Square-Law Combiner SNR Signal-to-Noise Ratio S-Rake Selective-Rake Receiver TDMA Time Division Multiple Access TH Time Hopping TX Transmitter UHF Ultra High Frequency US Uncorrelated Scattering UMTS Universal Mobile Telecommunications System UWB Ultra Wideband VHF Very High Frequency VNA Vector Network Analyser WLAN Wireless Local Area Network WSS Wide-Sense Stationary

1. INTRODUCTION

Radio frequencies which can be used for wireless communication are already heavily occupied but the need for faster and securer techniques is still growing. These re-quirements have brought out the idea of the old technique of transmitting information without a carrier by using impulses. This so called ultra wideband (UWB) technique uses low power and short impulses, which leads to an extremely large bandwidth with a low power density. This makes its possible to use UWB technology in the al-ready occupied frequencies by sharing the spectrum resources rather than looking for still available new bands.

This impulse radio technique is an old technique. The technique is based on the same idea, which was used in military radars already in 1960 to provide a low prob-ability of interception and detection (LPI/LPD). In the beginning of the 1990’s com-panies became interested in the UWB technique because it makes it possible to de-velop wireless communication systems with very high data rates and low cost [1].

To asses the merit of the UWB technique, the performance studies are needed. In order to study a systems’ performance, the accurate channel models are required. Radio channel modelling takes channel physical properties into account providing system designers with information channel features so that the performance of the system in a real channel can be estimated. If inaccurate channel models are used, the system may not perform as expected, and the realised system’s specification will not be met. Currently published narrowband and wideband channel models do not offer delay resolution high enough for UWB applications. Delay resolution is the delay between the signal components which can be separated. In a narrowband channel model, multipath signals are combined into one signal component, which can be modelled with path loss and envelope’s fading distribution [2]. Multipath propaga-tion is taken into account, but different propagation paths cannot be distinguished. The bandwidth in UWB system is much larger than in wideband systems. Because of the large bandwidth, the delay resolution is also more accurate than in wideband channel models. This means that more multipath components can be detected.

Numerous indoor UWB channel models have been published, e.g., [3–5], but out-door UWB channel models for long link distances have not been presented previ-ously in the open literature. The only UWB channel model based on outdoor meas-urements [6] considers distances less than 20 m. For example, some military applica-tions need predictions of the UWB system performances over the longer distances at the very high (VHF) and ultra high (UHF) frequencies.

The aim of this thesis project is to study the UWB technology’s suitability for long (several kilometres) outdoor distances. In this thesis, an ultra wideband propagation channel will be empirically modelled for outdoor environment using VHF/UHF. The channel modelling will be based on measurements in a rural environment during the late summer 2003. After the channel modelling work, the self-generated models will be used in link level simulations to study the system performance at low data rates. Different kinds of system concepts and receiver algorithms will be studied. One of the goals of the work is to study especially low-complexity structures.

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The thesis consists of all together seven chapters. Chapter 2 briefly presents UWB technology, its advantages and disadvantages. It also gives some applications where UWB technology can be used, focusing especially on military applications. The communication system concepts used in this thesis, are also presented in Chapter 2. Chapter 3 discusses the theory of the multipath radio channel in general. The chapter includes the physical mechanisms of radio wave propagation and fading and also how a radio channel can be modelled. Chapter 4 presents the measurements and channel modelling work based on outdoor measurements done in the Southern Finland. The chapter briefly presents the common channel measurement techniques and then describes in more detail the measurement technique that is used. The meas-urement campaign is described with information on the devices and parameters used. Data processing methodology is described and finally, the results of the channel modelling are presented. A couple of channel models are chosen for the simulation of an UWB communication system. They are evaluated in Chapter 5. The chapter also presents the final results of the system performance analysis with using the self-generated channel models. Different modulation methods and receiver structures are studied. Finally, an overall conclusion is provided in Chapter 6 and the thesis is summarised in Chapter 7.

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2. ULTRA WIDEBAND TECHNOLOGY

This chapter introduces the basics of ultra wideband technology and the main appli-cations that utilise UWB technology. The main communication system concepts, modulation techniques and multiple access methods used in this thesis are also briefly discussed.

2.1. General Aspects of UWB Technology

UWB technology differs from traditional radio transmission systems, which employ a carrier signal modulated with an information signal. Technically, the UWB tech-nique is considered as carrierless baseband transmission. This means that instead of continuous carrier waves, the UWB technique uses a train of very short, low-power pulses. This makes the signal ultra wide in the frequency domain.

An UWB signal is defined as a signal whose bandwidth is greater than 500 MHz, or its fractional bandwidth is more than 20% [7]. Fractional bandwidth can be deter-mined as

lh

lhf 2

ff

ffB

+−

= , (1)

where fh is the upper −10 dB point and

fl is the lower −10 dB point in the spectrum. Correspondingly, a communication system is defined as narrowband if the fractional bandwidth is less than 0.01 and wideband if the fractional bandwidth is from 0.01 to 0.2 [8].

The UWB technique is a spread spectrum technique. However, the wide bandwidth is produced by short pulse duration, not by spreading codes. A direct sequence (DS) or time hopping (TH) spread spectrum technique is used in UWB systems to separate different users from each others by using pseudorandom codes. In Figure 1, the time hopping UWB system concept using three pulses per data bit and in Figure 2 the di-rect sequence UWB system concept are presented. Tb is the data bit length, Tf is the pulse repetition interval (PRI), Tp is the pulse width and Tc is the chip length. In the TH UWB system, the pulse repletion interval is defined by the number of the users multiplied by the length of a single time slot TS within the time hopping frame. In Figure 1 the number of the users in the channel is two. The timeslot is the area in which the pulse is transmitted.

13

Figure 1. Time hopping UWB system concept.

Figure 2. Direct sequence UWB system concept.

In UWB communications systems, one data bit is represented by a long pulse train.

These long sequences of pulses are used to increase the signal-to-noise ratio (SNR) at the receiver [9]. The processing gain from the pulse repetition can be defined as [10]

( )KP 10G1 log10= , (2)

where K is the number of pulses used per data bit. This processing gain is the only one in DS system.

Time hopping UWB systems have very low duty cycle. Duty cycle is the ratio be-tween the pulse width and the pulse repetition interval. In some UWB implementa-tions, the duty cycle is less than 1 % meaning that the average signal level is 1 % of the single pulse level [9]. By using a time hopping multiple access system, the small duty cycle strengthens the processing gain by [10]

��

�

�

��

�

�=

p

f102G log10

T

TP . (3)

Tb

Tf Tp TS

Tb

Spreading code Tc

14

The total processing gain PG in a time hopping UWB system is

PG = PG1 + PG2. (4)

The bit rate can be defined as

bb

1

TR = . (5)

Pulse shape has a crucial influence on UWB system performance. A common UWB pulse waveform is the first derivative of a Gaussian pulse. A Gaussian pulse can be defined as [10]

��

�

�

��

�

�−

= p

6

p3

e6)(

T

t

eT

tAtv

π

, (6)

where t is time and

A is amplitude.

A typical UWB pulse width ranges from 0.2 to 1.5 ns [9]. Figure 3 demonstrates a Gaussian monocycle in the time and frequency domains [10]. A shorter pulse dura-tion leads to a larger bandwidth and a higher nominal centre frequency.

a) b)

Figure 3. Gaussian monocycle a) in the time domain and b) in the frequency domain.

However this so-called Gaussian monocycle does not satisfy the frequency mask

set by the FCC (Federal Communications Commission, USA). The FCC require-ments restrict the radiation power of an UWB system to less than –41.25 dBm/MHz in the frequency band from 3.1 to 10.6 GHz [7]. The regulations of the spectrum mask of UWB signals were made to protect the already existing system against UWB

15

systems. Therefore the radiation power and bandwidth of UWB system were re-stricted. The spectrum requirements can be met by using, for example, higher differ-entiations of the Gaussian pulse such as the fifth or the sixth derivative or higher. The FCC’s radiation mask for an UWB is presented in Figure 4.

Figure 4. FCC’s radiation mask for an UWB system.

An UWB system, which uses modulated baseband impulses for communication, is

called as single band UWB system. According to the FCC mask requirements, any technology that utilizes more than 500 MHz and follows the spectrum and emission limits can be considered as UWB technology [7]. This allocation opens up new pos-sibilities to develop UWB technologies different from impulse radio principle. Mul-tiband UWB technology is one of the new technologies [1]. It is based on the use of multiple frequency bands, each having a bandwidth of more than 500 MHz. This multiband technique makes systems adaptive and scalable. The technique offers a possibility to use a few or many bands at the same time, depending on the required bit rate. Multiband UWB systems are adaptive to different radio regulations, and the level of co-existence with other systems can be increased [11]. In this thesis only single band UWB techniques are discussed.

2.1.1. Advantages and Disadvantages

Advantages An UWB signal has an extremely narrow pulse width in the time domain, which leads to the ultra wide bandwidth. An UWB signal uses low average transmission power. The combination of these three features guarantees that an UWB system does not cause as much interference as narrowband transmission systems. For example the in-band interference caused by UWB signals to GSM (global system for mobile

16

communications), UMTS (universal mobile telecommunications system) and GPS (global positioning system) has been studied in [12]. Also, because of its noiselike nature, it has excellent low probability of interception and low probability of detec-tion properties [9].

UWB systems provide a considered amount of bandwidth. Therefore it makes pos-sible to have more users and higher data rates in the systems. Channel capacity can be defined as [13]

��

���

� +=N

SBC 1log2 , (7)

where

B is bandwidth, S is signal power and N is noise power.

Channel capacity can be increased either by increasing the SNR or the bandwidth. According to (7), channel capacity grows linearly with the bandwidth, but only loga-rithmically with the SNR. UWB systems offer flexibility to develop systems with a large-scale data rate that depends on demand. Systems can be short-range communi-cation systems with a several hundreds Mbit/s data rate or intelligent devices with a much lower data rate [14].

Discrimination of a radio signal is inversely proportional to the bandwidth, and thus highly accurate UWB radars or localisers can be made. For example, accuracy in an UWB localiser can be centimetres, which is much better than GPS, whose accuracy is a few meters [15].

In principle, UWB devices can be implemented more simply than normal radio re-ceivers. A single band UWB transmission system does not need an intermediate fre-quency, which eliminates the need for oscillators, mixers, and other costly hardware [16].

UWB signals might have low centre frequencies, which makes it possible for them to penetrate well through matter. The FCC specified that UWB radars can be used at the frequencies lower than 960 MHz and communications systems can be used in a frequency band between 3.1–10.6 GHz. The FCC mask still offers the possibility to have applications, which have good penetration through matter. These kinds of ap-plications can be used, for example, in rescue and safety applications [7]. Disadvantages There are also some disadvantages in UWB systems. Because of their low transmis-sion power, UWB systems have a limited range. Distances between the transmitter and receiver cannot be extremely long. A longer range can be reached, if the system has a large processing gain. According to (2)–(5), the data rate is inversely propor-tional to the number of pulses per data bit and the frame structure and procession

17

gain is directly proportional to the number of pulses used per data bit. Therefore, as a consequence, the higher the processing gain, the lower the data rate. The UWB sys-tem’s maximum distance varies inversely with the data rate. In [14] it is estimated that with a data rate of 100–500 Mbit/s, the distance can be 1–10 m.

2.1.2. Applications

Many applications are already available, which are using UWB technique. UWB sys-tems can be used in wireless local area networks (WLAN) and in personal area net-works (PAN), offering a high data rate. PAN includes portable devices, like com-puters, personal digital assistants and microphones [1]. Low data rate UWB applica-tions include sensors, positioning applications and LPD tactical networks. UWB technology permits development of these kinds of low-rate applications with posi-tioning information while also providing low power consumption and low manufac-turing cost [14]. UWB technology has many good properties that be used in radar applications [16]. Ground penetrating radars, wall-imaging systems and through wall imaging systems can be developed using UWB technology. UWB technology can also be applied in medicine for devices which are used in a variety of health applica-tions to examine, e.g., the human body or animal body. There will be applications related to vehicles and vehicular radar systems which are able to detect the location and movement of objects near or inside a vehicle [7].

2.2. UWB Communication System Concepts

In UWB communication systems, the choice of the modulation method can have a strong influence on system performance. This chapter introduces the basics of the modulation techniques and spreading concepts used in this thesis.

2.2.1. Binary Modulation Techniques

In UWB communication systems, information is added into the pulse trains by using different kinds of modulation techniques. Four different binary modulation tech-niques are used in this thesis: a) pulse amplitude modulation (PAM), b) on-off key-ing (OOK), c) pulse position modulation (PPM) and d) pulse shape modulation (PSM). Let j denote the data bit to be transmitted, i.e., j [0, 1]. a) Pulse Amplitude Modulation

In binary pulse amplitude modulation two amplitude-reversed pulses are used. The pulses are antipodal, having the same energy and a cross-correlation coefficient of –1 [17]. A PAM modulated waveform x(t) can be presented as [18]

18

)()( tr twdtx j= , (8)

where

)(tr tw is an UWB pulse waveform and

��

==−

=1,1

0,1

j

jd j . (9)

Examples of pulse waveforms using the first derivative of the Gaussian pulse for PAM modulation are presented in Figure 5.

Figure 5. Examples of pulse waveforms for PAM modulation.

b) On-Off Keying In OOK modulation the pulse is transmitted only if bit ”1” is chosen. An OOK modulated waveform can be defined using (8) with jd having as [18]

��

==

=1,1

0,0

j

jd j . (10)

Examples of pulse waveforms for OOK modulation are presented in Figure 6. c) Pulse Position Modulation Pulse position modulation is based on the principle of encoding information with po-sitions of time referred to the nominal pulse position. Thus, when bit “0” is chosen, the pulse will be transmitted in the nominal position. When bit “1” is chosen, the

19

pulse is transmitted an amount after the nominal position. A PPM modulated wave-form can be represented as [18]

)()( tr jdtwtx −= , (11)

where

is the modulation index and dj is as in (10).

Examples of pulse waveforms for PPM modulation are presented in Figure 7.

Figure 6. Examples of pulse waveforms for OOK modulation.

Figure 7. Examples of pulse waveforms used for PPM modulation.

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d) Pulse Shape Modulation Pulse shape modulation is based on the orthogonality property of the pulse wave-forms [19]. Bits “0” and “1” are represented by two orthogonal waveforms wtr

(0) and wtr

(1). The transmitted signal can be defined as

)()()1()( )1(tr

)0(tr twdtwdtx jj +−= , (12)

where dj is as in (10). In Figure 8, the first and the second derivatives of the Gaussian pulse are presented as they could be used in order to implement PSM.

Figure 8. Examples of pulse waveforms for PSM modulation.

2.2.2. Multiple Access Methods

The term “multiple access” means fixed communication resources are shared among numerous users in a co-ordinated manner. This is also called channelisation. In gen-eral, multiple access can be implemented using three different techniques: 1) Fre-quency Division Multiple Access (FDMA), 2) Time Division Multiple Access (TDMA) or 3) Code Division Multiple Access (CDMA). Multiple access in an UWB system is implemented by using the CDMA technique. CDMA technique uses pseu-dorandom codes, which are independent of the information signal. Users each have their own pseudorandom code, which separates the users from each others [17].

In the DS spread spectrum technique, the modulated information signal is multi-plied by a unique pseudorandom code at the modulator. At the receiver, different us-ers are separated by calculating the cross-correlation of the received signal with each possible user code sequence [17].

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Transmission contains redundancy, which is used as an aid against fading and inter-ference. Therefore, the spread spectrum technique affords protection against narrow-band jamming and interference coming from other users. It also protects against noise by spreading the signal to be transmitted and by performing a reverse despread-ing operation on the received signal at the receiver [20].

Two different methods are used for users’ separation in this thesis: a) the direct se-quence spread spectrum technique and b) the time hopping spread spectrum tech-nique. a) Direct Sequence Spread Spectrum Technique In direct sequence spreading, a single information bit is subdivided into a number of spreading chips. Multiple chips retain a chip waveform with an UWB spectrum. The DS UWB system concept was presented in Figure 2.

Direct sequence spreading can be done for PAM, OOK and PSM modulation. PPM is naturally time hopping because of the modulation. Using PPM with DS spreading would create a hybrid TH and DS configuration of the signal. For PAM and OOK modulation, the information signal s(t) for the mth user can be presented as [21]

∞

∞=

−

=

−−=-

1

0

)()(pcbtr

)( ))(()(k

K

j

mk

mj

m dcjTkTtwts , (13)

and for PSM modulation as

∞

−∞=

−

=

−−=k

K

j

mjd

m cjTkTtwts mk

1

0

)(pcb

)( ))(()( )( , (14)

where dk is the kth data bit,

(cp)j is the j th chip of the pseudorandom code and Tb is data length, Tb =KTc=KTf.

Figure 9 shows a single BPAM modulated data bit after DS spreading. The square wave is the random code, which affects the polarity of the single pulses in order to illustrate DS spreading. BPAM modulation is equivalent to binary phase shift keying modulation (BPSK) b) Time Hopping Spread Spectrum Technique In the time hopping spread spectrum technique, the pulse transmission instant is de-fined by a pseudorandom code. UWB transmission is a train of pulses that is divided in frames. Only one pulse is transmitted in each frame. The pseudorandom code de-fines the transmission time inside a frame, called a nominal time moment. Because of

22

the pseudorandom time hopping code, consecutive pulses are transmitted in different timeslots following the frame structure. Each transmitter has a unique time hopping code which allows multiple access. [22] The TH UWB system concept was presented in Figure 1.

Time hopping spreading can be done for PAM, PPM and PSM modulation. For PAM modulation the information signal s(t) for the mth user can be presented as [21]

∞

−∞=

−

=

−−−=k

K

jk

mj

m dTcjTkTtwts1

0c

)(wfbtr

)( ))(()( , (15)

for PPM modulation as

∞

−∞=

−

=

−−−−=k

K

j

mk

mj

m dTcjTkTtwts1

0

)(c

)(wfbtr

)( ))(()( δ , (16)

and for PSM modulation as

∞

−∞=

−

=

−−−=k

K

j

mjd

m TcjTkTtwts mk

1

0c

)(wfb

)( ))(()( )( , (17)

where

(cw)j is the j th code word defined by the pseudorandom (PR) code and Tb is data length, Tb =KTf.

An example of TH spreading is shown in Figure 10. A single PAM modulated data bit is send with TH spreading. In Figure 10, one data bit is sent using five pulses per bit. Both the data bits, “0” and “1” are presented.

Figure 9. PAM modulated data bit with DS spreading.

23

Figure 10. PAM modulated data bit with TH spreading.

2.3. Special Benefits of UWB technology in Military Applications

Communication systems in a military environment have to be secure and robust. Transmission systems have to resist jamming well because it is typically intentional. Jamming is developed on purpose to decrease the enemy’s transmission perform-ance. To make sure the system is secure, transmitted signals also have to be difficult to detect by receivers other than the intended ones.

UWB technology lends itself well to military communication. An UWB signal hav-ing excellent low probability of interception and low probability of detection proper-ties can be used in tactical and strategic communication. Because an UWB signal is noiselike, it has a low probability of being intercepted or detected by another listener. An UWB system has a good protection against jamming. A single band UWB system is in principle simple and cheap to realize. By using an UWB system, positioning resolution is good because of the large bandwidth. UWB systems also have low power consumption [23].

Some existing military applications are described in [24]. Such applications include tactical handheld and network LPI/LPD radios, unmanned aerial and ground vehi-cles, LPI/LPD altimeters, obstacle avoidance radars and precision geolocation sys-tems. The presented tactical handheld radio [24] was designed for full duplex voice and data transmission at rates of to up 128 kbit/s or 115.2 kbit/s. This system does not fulfil the FCC mask because the centre frequency is 1.5 GHz and the bandwidth 400 MHz. The peak transmitted power is 2 W. The units have the range of approxi-mately 1 to 2 km with small antennas and line-of-sight connection. An extension of this was a project called Orion. Orion was a more advanced tactical radio designed for marines use. It operates at 1.3 GHz to 1.7 GHz and its fractional bandwidth is 0.27. The peak power is 0.8 W [25].

24

An UWB radio designed for controlling a small unmanned aerial vehicle is pre-sented in [24]. The robots can receive a video signal of up to 25 Mbit/s. The link uses a bandwidth from 1.3 GHz to 1.7 GHz and peak power is 4 W. Neither does this sys-tem fulfil the requirements of the FCC mask.

One of the presented UWB applications is an UWB tactical ad hoc wireless net-work [24]. It is highly secure and developed for the U.S. Department of Defence. The data rate for voice traffic is 128 kbit/s, and for video traffic, 1.544 Mbit/s. In [25] a more advanced ad hoc UWB network called Drace is presented for tactical communication. It has been tested with 1 km ranges between the nodes.

25

3. MULTIPATH RADIO CHANNEL MODELLING

A radio channel is a channel between a transmitter output and a receiver input. It in-cludes all the antenna and propagation effects. A radio channel is generally time variant, which means channel statistical properties vary over time. A propagation channel which does not include antennas is assumed to be a linear system. It means the channel does not make any new frequency components, restrict the frequency band or cut the signal [17]. So, the propagation channel itself does not modify the signal frequencies, but antennas and the media do affect the transmitted signal wave-form. For example, physical changes in the propagation medium affect the signal’s properties. These changes are taken into account in radio channel modelling. Radio systems can be designed more realistically and their performance can be estimated if the channel information is taken into account.

Usually the signal’s energy usually travels along with several different paths from the transmitter to the receiver. This is called multipath propagation.

3.1. Physical Mechanisms of Multipath Propagation

The most important radio wave propagation phenomena producing multipath propa-gation are scattering, reflection, refraction and diffraction. Absorption reduces the amplitude of propagation waves. The propagation environment determined how much these physical phenomena affect the signal during the propagation.

Signal reflection means the direction of the propagation, the amplitude, the phase and the polarisation of the radio wave change according Snell’s law and the coeffi-cient of reflections. This happens when the signal meets a surface, such as building, a wall and a hill, which has very large dimensions compared to the wavelength [26]. Scattering means the signal scatters in all directions when it meets a rough surface or small particles such as leaves and branches of trees [2]. A signal is diffracted when its direct propagation wave bends around the obstacle causing secondary waves drift-ing behind the obstacle [26]. Diffraction occurs if there are obstacles in the radio path whose dimensions are large in when measured in wavelengths. Also abrupt changes, such as sharp edges like building rooftops or hilltops, cause diffractions [2]. Refrac-tion happens when a radio wave meets an interface between two different materials. The direction of propagation, amplitude, phase and polarisation of the radio wave change when the radio wave propagates through the interface. Refraction can result from such as atmospheric layers or layered or graded materials.

The volume between the transmitter and receiver, which has the strongest effect on a transmitted line-of-sight (LOS) signal, is called a Fresnel ellipsoid. Transmitter and receiver antennas are at the focal points of the Fresnel ellipsoid. Everything inside the first Fresnel ellipsoid causes absorption, diffraction or scattering, affecting the transmitted signal’s phase and amplitude. The radius of the mth Fresnel ellipsoid at each point can be calculated according to [27].

26

21

21

dd

ddmrm +

= , (18)

where is the wavelength, m is the number of the Fresnel’s ellipsoid, d1 is the distance from the transmitter and d2 is the distance from the receiver.

A Fresnel ellipsoid is presented in Figure 11. The measured environments can be analysed by defining the first Fresnel ellipsoid to find obstacles which can affect the transmitted signal. RX is receiver and TX is transmitter.

Figure 11. First Fresnel ellipsoid.

3.2. Fast and Slow Fading

Depending on the propagation environment, each multipath signal component travels a different distance. So, the receiver accepts several copies of the signals, which all have different time delays, amplitudes and phase shifts. At the receiver, various in-coming signals are combined either constructively or destructively, depending mainly on the received signal’s phases. The phase shifts cause power level fluctua-tion in the received signal. This is called fading, which can be subdivided into two types: fast and slow fading.

Fast fading is caused by multipath propagation and is described by unpredictable and rapid changes in signal amplitude and phase. Deep minimum points can be no-ticed at approximately half wavelength intervals. The signal’s power can drop down more than 30 dB from the mean value over a distance of a couple of wavelengths [27]. Time spreading of the signal (or signal dispersion) and time-variation of the channel causes fast fading. Because fast fading is incidental and unpredictable, it can only be treated statistically. In wideband channel models, fast fading is typically modelled using Rice or Rayleigh distributions. In general, published fast fading dis-tribution in an UWB channel differs from Rice and Rayleigh distributions. For ex-ample, in [28] fast fading distribution is lognormal distribution.

The probability density function (PDF) p � of the Rice distributed random variable is [17]

d1 d2

rm

TX RX

27

��

���

�=+

−

20

�22

)(2

22

sxIe

xxp

sx

ξ (19)

where I0 is the modified Bessel function of the first kind and 0th order, s is the dominant signal component and 2 is the power in the random part. Rice distribution is often described in terms of a � value. It can be interpreted as a ratio of the dominant signal power to the power in the multipath components. The parameter � can be defined in dB as [27]

���

����

�=

2

2

10dB 2log10

sκ , (20)

where s2/2 is the power in the constant part.

Slow fading, which is also called shadowing, represents average signal power at-tenuation, or path loss, over large areas in the size of tens of wavelengths. Large ob-stacles, such as buildings and trees, between the mobile transmitter and the receiver, cause slow fading. The variance of slow fading is much smaller than that of fast fad-ing [2]. Fading is typically about 10 dB over 10–100 m distances. Slow fading is mathematically modelled as a log-normal distribution [26]. The PDF p� of lognormal distribution random variables is [29]

��

�

�

��

�

� −−

= �

�

�

ln

2

1

�

�

2

1)(

mx

ex

xpπ

. (21)

where µ is the deviation of the Gaussian distributed random variable

µ = ln and mµ is the expected variable of mµ.

The expected value and variance of are

[ ] 2

� 2�

� +=

meE and (22)

{ } ( )12

�2

�� ��2 −= + eeVar m . (23)

The fast fading and slow fading are illustrated in Figure 12.

28

Figure 12. Fast and slow fading.

The coherence bandwidth (

�f)c of a channel describes the channel’s frequency cor-

relation. For example, if two sinusoidal signals with frequency separation greater than (

�f)c are transmitted through the channel, they are affected differently. There-

fore, when the bandwidth of the transmitted signal is small compared to the channel coherence bandwidth, the channel is said to be flat and it does not distort the trans-mitted signal. But, if the channel’s coherence bandwidth is smaller than signal’s bandwidth, there will be intersymbol interference (ISI) and signal will be distorted severely by the channel [26].

The coherence time tc of the channel is the time over which the channel can be as-sumed to be constant. If the channel is changing too fast, it modulates the transmitted signal and the signal spectrum comes wider. If the symbol time Ts << tc it can be as-sumed that the channel is constant during the symbol, and the distortions can be measured and compensated using channel equalisers. This kind of channel is said to be slow fading from the transmission point of view. If Ts > tc the channel is changing fast. Then the channel is said to be fast fading from the transmission side and the sig-nal will be distorted [26].

3.3. Multipath Channel Model

The characterisation of a linearly time variant multipath radio channel is based on two system functions: impulse response h(t,� ) and transfer function H(f,t). The output of the channel y(t) can be calculated as a convolution between the channel impulse response and the transmitted signal s(t)

29

ττττ dsththtsty �∞

∞−

=⊗= )(),(),()()( . (24)

Multiplying the spectrum of the input signal by the transfer function gives the spec-trum of the output signal [2]

),()(),( tfHfStfY = . (25)

The channel impulse response of a multipath radio channel can be modelled as [27]

−=n

nnn jttth )exp()()(),( φτδατ , (26)

where � n is the nth multipath attenuation,

�(t) is Dirac’s delta function,

�

n is the nth multipath delay and n is the nth phase. The time-variant impulse response is also known as the input delay spread function.

A multipath channel’s impulse response is typically modelled as a linear tapped de-lay line (a finite impulse response (FIR) filter), where the multipath components are modelled as taps with their own gain. The model is based on [30] where Bello has discussed that radio channel is a randomly time variant linear system. The channel can be assumed to be a wide-sense stationary and uncorrelated scattering (WSSUS) channel. Wide-sense stationary (WSS) means the first two moments of the channel correlation function (the mean value and the autocorrelation) are independent of ab-solute time, but they only depend on time difference. Uncorrelated scattering (US) assumes that signals with have different delays are uncorrelated. [30]

A linearly tapped delay line is presented in Figure 13. Complex tap gain � l varies in time by following a statistical distribution. When modelling the channel with a mov-ing link, the Doppler spectrum also has to be modelled. Usually, if the signal in a wideband channel models is a LOS component, the tap factor is Rice distributed, and if the signal is NLOS (Non Line-of-Sight), the tap factor is Rayleigh distributed [2]. Rice and Rayleigh distributions are common in wideband channel models, but the distributions in UWB channel models usually differ from wideband models.

An UWB channel model can also be described as a tapped delay line. If this model is used, the fine delay resolution leads to a need for many taps. The channel model may become too complex, causing the model to take too much time and resources in simulations. Therefore, it may be worthwhile to take several multipath components together as one bin. Then one bin can be modelled as a one tap. If the multipath components are put together, the delay resolution is not as good anymore [31].

30

Figure 13. Tapped delay line.

The radio channel’s power delay profile P(� ) can be defined from the impulse re-

sponse function according to [2]

[ ]2

),()(

2ττ

thEP = . (27)

The channel’s properties can be described using specific parameters based on the

power delay profile (PDP). The parameters are, for example, mean excess delay ( M), RMS (root mean square) delay spread ( RMS) and maximum excess delay ( tot). Figure 14 (modified from [2]) describes the power delay profile and its main parame-ters. TA is the arrival time of the first received multipath component.

Figure 14. Power delay profile.

Mean excess delay describes the power weighted average delay of measured excess

delays and is given by the first moment of the power delay profile [32]. M can be defined as [32]

...

0 1 2 n

OUT

IN

Delay

Power

�

tot

�

RMS

�

M

TA

31

( )

=

=

−=

r

r

l

nn

l

nnAn

th

thT

1

2

1

2

M

),(

),(

τ

τττ , (28)

where �

n is the delay of the nth tap and lr is number of separable paths.

Ptot is the total power of the power delay profile, defined as

=

=rl

nnPP

1tot . (29)

RMS delay spread is the power weighted standard deviation of the excess delays

and is given by the second moment of the impulse response [32]. RMS delay can be defined as [32]

( )

=

=

−−=

r

r

l

nn

l

nnn

RMS

th

thT

1

2

1

2

AM

),(

),(

τ

ττττ . (30)

Maximum excess delay tot, which is also called a multipath spread, is the width of the power delay spectrum. It is the delay between the first and last component. TA can be estimated for the LOS component as

c

dnTA

air= , (31)

where nair is the air refractive index, nair 1.0003 and

c is the velocity of light, c m/s.103 8⋅

3.4. Path Loss Model

Path loss is the ratio of the transmitted power to the received power, which is usually expressed in dB. It is a function of the link distance between the transmitter and the receiver antenna including all the possible loss elements. Path loss models estimate signal attenuation versus link distance. When path loss LdB is calculated properly, the losses and gains in the systems have to be taken into account as [2]

32

RTRRTTdB LLPGGPL −−−++= , (32)

where PT is the transmitted power, GT is the transmitter antenna gain, GR is the receiver antenna gain, PR is the received power, LT is the transmitter feeder loss and LR is the receiver feeder loss. All the variables are in dB. Path loss LdB can be divided into two parts: free space loss LF(dB) and excess loss Lexc(dB) as

exc(dB)F(dB) LLLdB += . (33)

Free space loss in dB for tone frequency can be defined as [2]

MHz1010(dB) F log20log204.32 fdL ++=’ (34)

where d is the distance in kilometres and fMHz is the carrier frequency in megahertz.

Path loss models are used to predict a radio wave’s attenuation in a specific envi-ronment. There are two types of path loss models: analytical models such as free space loss and empirical models based on practical channel measurements. An em-pirical path loss model is, for example, the widely known Okumura-Hata model, which is based on measurements made in and around Tokyo city between 200 MHz and 2 GHz. The measurement results were published as a series of graphs by Oku-mura in year 1968 [33]. Later in 1980 the predictions were expressed in formulae by Hata [2]. UWB path loss is examined, for example, in [34–35], where path loss mod-els are generated for indoor environments.

3.5. Link Budget Analysis in UWB system

The designer of a radio communication system must specify the antennas’ gains, the transmitter power and the SNR requirement to achieve a given level of performance at a desired data rate. In UWB studies, a link budget analysis is important because the FCC mask limits the transmitting power. The achievable minimum bit error rate (BER) of the designed system, has to be estimated using the limited transmitter power. Thus the maximum achievable data rate can be calculated.

The traditional formula for calculating the link budget in dB is [36]

33

MFNRGLGPN

E−−−−+−+= )(log10 b10RdBTT

0

b , (35)

where Eb is the average energy per data bit, N0 is the power spectral density of Gaussian noise, F is the noise figure of the receiver, M is the link margin, N is the thermal noise of the receiver, defined as kTN = , where

k is Boltzmann’s constant, W/Hz/K10381.1 23−⋅=k and T is the physical temperature of the receiver.

The link margin M takes into account the losses coming from for example multipath fading and shadowing.

34

4. RESULTS OF CHANNEL MEASUREMENTS

This chapter presents the measurement principle and the measurement parameters that were used. The measurement environment is described, and the necessary post processing and data preparation process are also briefly discussed. Finally, the gener-ated channel models are introduced.

4.1. Measurement Pr inciple and Parameters

An UWB radio channel can be measured either in the time or in the frequency do-main. In time domain, the radio channel can be measured by transmitting a very short pulse to the channel and observing the multiple received pulses. Another way to do it in the time domain is by using direct sequence spread spectrum technique. Because it gives better coverage than pulse measurement system, this technique is normally used when large areas are measured [37]. When the channel is measured in the time domain, the impulse response of the channel is measured directly. Other advantages are that the probing pulse sequence can be the same as in the final application and the environment does not need to be static [38].

The channel can be measured in the frequency domain by using a frequency sweep technique. A frequency band is swept using a set of narrowband signals and the channel frequency response is recorded with a vector network analyser (VNA). This is equivalent to an S21-parameter measurement set up, where the device under test (DUT) is a radio channel [38]. In the frequency domain sounding system, the VNA measures the frequency response of the channel and the impulse response can be cal-culated by using an inverse discrete Fourier transform (IDFT). The frequency do-main channel sounding system gives the same result as the time domain system, but the limitation in the frequency domain measurement is that the environment has to be static during the recordings. Also, post-processing is needed to get the impulse re-sponse. Because this system uses a network analyser to transmit and receive the probing signal, the measured link distance is limited by the cables.

In this thesis project, the data to be analysed was measured in the frequency domain using the frequency sweeping technique. The measurements were done in an outdoor environment over a long distance (0.5–5.6 km). The measurement system was modi-fied so that the link distance was no longer a limiting factor [39]. The modified fre-quency domain radio channel measurement system is presented in Figure 15.

The basic idea of the modified frequency domain sounding system is to use an ex-ternal sweep signal generator as a transmitter and the vector network analyser as a receiver to calculate the S21 of the channel. A computer with LabViewTM software controls all the measurement procedures. All the adjustments of the devices, timing information and commands go through the LabView TM, which also stores the raw data. The external sweeping signal generator (SMIQ) sends the narrowband probing signal. The VNA and the sweeping signal generator are synchronized to maintain the same frequency. A constant clock reference is used to reach the high frequency sta-bility. In these measurements, an external 10 MHz clock reference based on a TV

35

stripe frequency signal is fed to the transmitter and to receiver. A function generator (AFGU) is used to generate the triggering signal, so the timings of the reference and the sweep signals are the same. Triggering pulse to the VNA is delayed because the probing signal has a propagation delay through the channel. In this system, LV217 radios are used to send the triggering pulses from the receiver to the transmitter. [39]

Figure 15. Modified frequency domain sounding system.

Low noise amplifier (LNA) is used at the receiver to improve the noise figure at the

receiver and to make the probing signal level higher. A power amplifier (PA) is used at the transmitter. In Figure 15 EAT and AET are electrical to acoustic and vice versa transformers, which change the electrical pulses from AFGU to acoustic forms for the radios and the other way around at the transmitter. A 50 termination was used in the VNA TX port to avoid reflections from the unused RF-port. The antennas were vertical polarized Rohde & Schwarz HK014 antennas, which are omni-directional and have a constant phase centre [39]. The antenna patterns are presented in Appen-dix 1 [40]. The used measurement devices are listed in Table 1.

The set-up was measured in an anechoic chamber. This data was used as calibration data to compensate the impact of the measurement devices in the real measurements. The calibration data was saved for post-processing. The frequency response of the calibration data can be found in Appendix 2.

When the modified frequency domain radio channel measurement system is used, the phase information cannot be obtained because the phase difference between the generator signal and the analyser signal is not known. However, in UWB systems phase information is not really dependable information, because if the bandwidth is

EAT

AET

36

really large, the phase is totally different in the lower frequencies than in the higher frequencies of the band.

Table 1. Measurement devices

Device Type

Vector network analyser Agilent 8720ES

Sweeping signal generator SMIQ 06B by Rohde & Schwartz

Function generator AFGU by Rohde & Schwartz

Low noise amplifier Mini-Circuits ZFL-1000LN

Power amplifier Kalmus 710FC

Antennas HK-014 by Rohde & Schwartz

Triggering radios LV217 (military radios) The measured frequency band was from 230 MHz to 390 MHz. According to (1),

the fractional bandwidth is 0.58. The fractional bandwidth satisfies the FCC require-ments for UWB systems. The band was swept using 1601 points and the sweeping time was 4.8 s. This sweeping time is the minimum for both the VNA and the exter-nal sweeping signal generator to step 1601 frequency points when using the external trigger.

The upper bound limit of the detectable delay of the channel max is defined by the number of frequency points per sweep and by the bandwidth B as

B

S 1nummax

−=τ , (36)

where Snum is number of points per sweep. The delay resolution is the delay between the multipath signals which can be sepa-rated. It is

B

1=∆τ . (37)

The path length between the signal components (distance resolution) is

nB

c

n

cd =∆=∆ τ . (38)

All the parameters and their values are presented in Table 2. The presented transmit-ted power is measured from the output of the power amplifier.

37

Table 2. Measurement parameters

4.2. Measurement Environment

Channel measurements were carried out in Riihimäki, Finland during late summer 2003. The measurement environment is slightly hilly and covered by coniferous and deciduous forest and open peatlands. The receiver was located at the same site during the whole measurement campaign. It was installed at the highest point in the garrison to make measurements possible in all directions. The transmitter was moved into nine different sites. For small-scale analysis five independent measurements were carried out at each TX position, when the TX antenna was moved about two metres. To improve the statistical reliability of the measurements, 100 sweeps were recorded at each antenna location. All the antenna positions, including the TXs and RX, were saved as GPS co-ordinates. A map with the measurement sites is presented in Ap-pendix 3.

Examples of the measured link profiles are presented in Figure 16. The rest of the link profiles are presented in Appendix 4. The blue line represents the first Fresnel’s ellipsoid and the straight one is the LOS line. The figures have been drawn using HTZ Warfare software [41], but the link profiles are only suggestive. The software draws the first Fresnel’s ellipsoid so that the ellipsoid’s vertexes are at the antennas’ phase centres, which is not correct. The figures still give a rough idea of how much the obstacles block the measured links. Roads are coloured using pink, water is blue and trees are black and grey.

Parameter Value

Frequency band 230 to 390 MHz

B 160 MHz

Snum 1601

Sweep time 4.8 s

PT 40 dBm = 10 W

Power amplifier gain 40 dB

LT (max) 5 dB

GT, GR 2 dBi (typical)

Polarization of antennas vertical

EIRP (min) 37 dBm = 5 W

max 10 µs �

6.25 ns �

d 1.875m

38

a) Link profile of the measured link TX1

b) Link profile of the measured link TX6

Figure 16. Examples of the link profile of the measured links.

The TX antenna sites are described in Table 3. Antenna height from the ground

level was 4.5 m. The forest density was evaluated using classes 1 to 5, where 1 is open and 5 is the densest. The altitude of measurement areas varies from 94 m to 154 m above mean sea level (a.s.l.). The RX antenna was located 158 m a.s.l., at a site were the forest density was 2. The link distances between the transmitter and the re-ceiver varied from 0.5 km to 5.6 km.

Table 3. Descriptions of TX sites. The scale for forest density is: 1 = open, 5 = dens-est

TX antenna site

L ink distance [km]

Altitude [m a.s.l]

Density of the forest [1–5]

TX1 5.6 154 3

TX2 4.8 112 1

TX3 2.5 109 2

TX4 1.6 104 2

TX5 0.5 130 3

TX6 0.7 125 4

TX7 3.1 94 1

39

4.3. Data Preparation

All the post-processing was done using Matlab 6.5 software. The recorded raw data were converted into a format required by the software. After the transformation an inverse discrete Fourier transform was used to transform the frequency domain data to the time domain, and the delay power spectrum was attained. When the IDFT was done, Hamming windowing was used to get rid of the side lobes. Finally, post proc-essing was done and the power delay spectra were ready to be analysis.

During the data analysis, spurious peaks were found in the frequency responses o the measurement data. The peaks were found in most of the material regardless of the measurement site or time. The spurious peaks were found also found even though probing signals were not sent and only background noise was measured. The meas-ured background noise is presented in Figure 17. As it can be seen, these peaks were much stronger and differed clearly from the average background noise level.

A peak in the frequency domain upraises the noise level in the time domain. There-fore, these peaks severely disturbed the measurement data. The dynamic range (the range between the strongest delay component and the noise level) of the impulse re-sponse became smaller because of the spurious peaks. The effect of the removed peaks on the dynamic range of the each power delay profile was tested separately and is presented in Figure 18. The dynamic range is calculated from the average power from 3–5 µs compared to the power of the strongest delay component.

Figure 17. The measured background noise.

40

Figure 18. Effect of the removed peaks on the dynamics of the impulse responses.

Obviously, the peaks do not belong to the measured radio channel, because they

were 20–30 dB stronger than the average value. The same seven strongest spurious peaks were removed from all the frequency responses. Furthermore, the ten strongest ones were moved from the data of the three measurement sites. All the removed fre-quency components were substituted by the mean value of the ten nearest frequency components. The dynamic ranges of the impulse responses improved after removing the spurious peaks. An example of the original frequency response and its power de-lay profile is presented in Figure 19, where the spurious peaks are still included. The same frequency response and power delay profile are presented in Figure 20, but this time the spurious peaks are removed from the frequency response, which makes the dynamic range of the power delay profile larger. As it can be seen, the beginnings of the power delay profiles are the same and only the noise levels have risen.

a) b)

Figure 19. a) Frequency response and b) power delay profile with spurious peaks.

41

a) b)

Figure 20. a) Frequency response and b) power delay profile without spurious peaks.

At every site the frequency response was measured 500 times (5·100 times). Mal-

functions were noticed in the measurement system, which caused unsuccessful re-cordings of frequency responses from time to time. Because these extremely bad sweeps prejudiced the results of the channel analysis, it was decided to remove from the analysed data. A sweep was taken into account if the dynamic range of the sweep’s impulse response was high enough. Depending on the measurement site, the accepted limit varied from 12 dB to 14 dB. The boundaries were determined sepa-rately for each measurement site. Data from two of the measurement sites were re-jected totally, because most of the sweeps were corrupted.

4.4. Channel Character isation

4.4.1. Channel Parameters

The measured data from all the TX antenna positions were analysed and the main channel parameters were calculated. The average channel parameters including the number of accepted sweeps NS for each measurement site are presented in Table 4. NP10dB is the number of multipath components within 10 dB related to the strongest component. Mean excess delay M and RMS delay RMS spread, which are calculated using (28) and (30) are also shown. TA is the arrival time calculated for the LOS component using (31) Scattering increases the maximum excess delay spread. In the measured links TX2,

TX3, TX4, TX7, the transmitter antenna are located on open peatlands and there are no reflections from the surrounding surface. Therefore, these links have small maximum excess delays. The measurement links TX5 and TX6 had longer tot than the average value compared to the other links. The forest at both sites was quite dense, which explains the long maximum excess delays. These results are compara-ble to the results of [42] where wideband channel measurements were carried out in the frequency band from 20 MHz to 88 MHz in a similar environment. The maxi-mum excess delays that were found there were around 1 µs.

42

Table 4. Channel parameters for each measurement site

TX site NS NP10dB tot [µs] RMS [µs] M [µs] TA[µs]

TX1 331 21 0.9 0.26 0.29 18.67

TX2 442 4 0.7 0.21 0.21 16

TX3 252 4 0.5 0.15 0.16 8.33

TX4 335 4 0.7 0.22 0.25 5.33

TX5 496 3 2.5 0.73 0.85 1.67

TX6 388 3 1.5 0.45 0.57 2.33

TX7 410 7 0.7 0.21 0.21 10.33

4.4.2. Path Loss Analysis

Path loss analysis is an important part of radio channel modelling because accurate predictions are needed to estimate the efficiency and coverage of the system. A diffi-culty in defining UWB path loss is the variation of attenuation with frequency due the large bandwidth. The excess path losses, which can be calculated from (33)–(34), from two of the measured links are presented in Figure 21 and in Figure 22. The ex-cess losses of the other measured links are presented in Appendix 5. The darker line does not include slow fading. Slow fading is included in the lighter line. As it can be seen, path loss is strongly dependent on frequency. In all of the presented path loss results, the path loss analysis is done from the antenna feed point.

As one can notice, the excess path loss of the link TX1 is less than the free space loss. There are some reasonable explanations how it is possible. One of the reasons can be the multipath propagation. In the receiver, the several multipath components can arrive at the same time, which can increase the received power. Other possible reasons are the real antennas’ elevation angles, which differed from the calibration measurement, and therefore the antenna gains had probably been more. The antenna patterns are presented in Appendix 1. In the calibration measurements in an anechoic chamber, the measurement were done with an elevate angle of 0°. In the measure-ment situation, the elevation angle is no longer zero causing more antenna gains than in the calibration situation. The same situation is in all of the measured links. The real antenna gain in the measured situation could have been 5 dB to 10 dB more than in the calibration situation. One issue which can also affect the path loss results is the extraneous radio tranmissions which affect differently to different at measurement sites.

43

Figure 21. Excess path loss of link TX1.

Figure 22. Excess path loss of the link TX3.

Further on in this chapter the path loss analysis is done using the total received

power over the whole measured bandwidth. It was calculated by first defining the local path loss from each sweep at each measurement site. The average local path loss over all the frequencies is calculated as [34]

��

���

�−= =

1601

1

2

10dB_local )(1601

1log10

iik

k fHL , (39)

44

where Hk(fi) is the kth measured channel frequency response. Each measurement sites consists of 252−496 measured sweeps. The average path loss was computed by averaging the corresponding set of local path losses as

��

�

�

��

�

�=

=

NS

k

Lk

NSL

1

1010dB

dB_local

101

log10 . (40)

The calculated path loss points are presented as a function of the link distance in Figure 23.

Typically, a linear regression line could be matched to the set of points, and the slope would describe the path loss dependence on the distance. If the points are drawn to the absolute distance axis, the regression line fits into an exponential func-tion. The computed path loss values are presented in Figure 23. The path loss varies considerably because of the different environments at each measurement site. This makes a comparison of the results irrelevant. It is evident that no regression line can be fitted to the results.

Figure 23. Path loss versus link distance.

The total path loss, mean free space loss and mean excess path loss of each link are

listed in Table 5. Free space loss is the average path loss of the all point frequency. Excess path loss can mostly be explained using the link profiles presented in Figure 16 and in Appendix 4. The longest measured link, TX1=5600 m, is a strongly LOS link because both of transmitter and receiver are situated on top of a hill and so the 1st Fresnel is quite clear. Because the first Fresnel’s ellipsoid is almost empty, the transmitted signal has not been scattered or diffracted very much and thus the re-

45

ceived power is quite high. As a consequence of this, the mean path loss is not more than the free space. In measured links TX2, TX3 and TX4, the transmitter was situ-ated in the middle of open peatlands and they are all on the same line. Link TX2 is a LOS link, which explains the low path loss, although the link distance is the longest of these three. The path loss in link TX4 is high despite the short link distance. This is because the link is greatly obstructed. Links TX5 and TX6 are measured with shorter link distances. Both of the links are strongly obstructed, but link TX5 is a c-learer link than TX6, which is also manifested in the lower path loss. Link TX7 is situated in a different direction and the link is quite clear. Therefore, the received power differs from TX3 even though the measured distances are nearly the same. By using the generated excess path loss and the knowledge of the measured envi-

ronment, different kinds of path loss models can be used to analyse where the excess loss is coming from. The loss from terrain obstructions can be calculated by using knife-edge diffraction models, for example [2].

In order to obtain reliable path loss predictions, additional measurements would be needed.

Table 5. Total path loss, mean free space loss and mean excess path loss of each link

TX site LdB LF(dB) Lexc(dB)

TX1 91.43 97.29 –5.86

TX2 98.75 95.95 2.81

TX3 100.66 90.29 10.39

TX4 101.92 86.41 15.52

TX5 93.07 76.03 16.76

TX6 98.45 79.23 19.22

TX7 96.29 92.15 4.14

4.4.3. Link Budget Analysis

A link budget analysis was done using (35) to find out the capacity which can be reached using the UWB system in the outdoor environment. The generated path loss values of each link were used in the calculations. The examined transmitted powers were 1 mW, 10 mW, 100 mW, 1 W and 10 W. The antenna gains were 1 dB. The physical temperature of the receiver T was estimated as 290 K. The noise figure of the receiver F was defined as 7 dB and the link margin as 7 dB. The examined data rates were 16 kbit/s, 100 kbit/s and 1 Mbit/s.

Because it was not possible to make a consistent path loss model based on the measurements, the link budget analysis were made using the measured path losses from the links. The achieveable Eb/N0 values for each of the links were calculated using different data rates and transmitted powers. Using the generated Eb/N0 values

46

and the simulated performance curves, the achievable BER can be estimated. The achieveables Eb/N0 are listed in the Table 6 using path loss in the centre frequency.

Table 6. Achieveable Eb/N0 values for each measured link with the specific transmit-ted power and data rates

TX site Data rate 1 mW 10 mW 100mW 1W 10W

16 kbit/s -10.5 -0.5 9.5 19.5 29.5

100 kbit/s -18.5 -8.5 1.5 11.5 21.5 TX1

1 Mbit/s -28.5 -18.5 -8.5 1.5 11.5

16 kbit/s -17.8 -35.8 2.2 12.2 22.2

100 kbit/s -25.8 -35.8 -5.8 4.2 14.2 TX2

1 Mbit/s -35.8 -35.8 -15.8 -5.8 4.3

16 kbit/s -19.7 -9.7 0.3 10.3 20.3

100 kbit/s -27.7 -17.7 -7.7 2.3 12.31 TX3

1 Mbit/s -37.7 -27.7 -17.7 -7.7 2.31

16 kbit/s -21.0 -11.0 -1.0 9.0 19.0

100 kbit/s -29.0 -19.0 -9.0 1.1 11.1 TX4

1 Mbit/s -39.0 -29.0 -19.0 -9.0 1.1

16 kbit/s -12.1 -2.1 7.9 17. 9 27.9

100 kbit/s -20.1 -10.1 -0.1 9.9 20.0 TX5

1 Mbit/s -30.1 -20.1 -10.1 -0.1 9.9

16 kbit/s -17.5 -7.5 2.5 12.5 22.5

100 kbit/s -25.5 -15.5 -5.5 4.5 14.5 TX6

1 Mbit/s -35.5 -25.5 -15.5 -5.5 4.5

16 kbit/s -15.4 -5.4 4.6 14.6 24.6

100 kbit/s -23.3 -13.3 -3.3 6.7 16.7 TX7

1 Mbit/s -33.3 -23.3 -13.3 -3.3 6.7

As one can notice, most of the measured links would not work if the transmitted

power is 1 mW, 10 mW and 100 mW. If the transmitted power is 100 mW, the links which are quite clear (TX5 and TX1) might work. In the entire measured link, when using 1 W of transmitted power, an Eb/N0 value of 10 dB can be reached using 16 kbit/s. It seems that a data rate of 100 kbit/s can be transmitted using 1 W of trans-mitted power, if the link distance is small and not strongly obstructed (for example

47

TX5). An Eb/N0 value of 10 dB using a data rate of 100 kbit/s can be reached only if the transmitted power is 10 W. It seems that when using 10 W of transmitting power 1 Mbit/s data rate can also be used in link TX5 which is quite short (0.5 km) and not heavily obstructed. The Eb/N0 values from link TX1 differs from the others because of the transmitter site.

4.5. Channel Models

Channel models were generated separately to each measurement sites. The models based on the average power delay profiles are tapped delay lines. Each model con-sists of the strongest 20–30 taps. The channels were not modelled until the noise level because the delay resolution of UWB channel is huge. Therefore, the models would consist of too many taps for simulation purposes. It would be difficult to make simulations if all the existing taps are modelled.

The section 4.5.1 presents the average power delay profiles for each measurement sites. In section 4.5.2, the amplitude fading analysis is discussed more exact. In Ap-pendix 7 the final channel models are tabulated. In the tables, the taps’ delays com-pared to the first tap, the relative power of each delay compared to the strongest one and -value (20) of the Rice distribution in dB are presented. In TX1 and TX2 cases the amplitude fading is described using the lognormal distribution. Therefore, in channel model tables for TX1 and TX2, the standard deviation of the lognormal dis-tribution is presented.

4.5.1. Average Power Delay Profiles

The link profiles of the measured links are presented in Figure 16 and in Appendix 4. As it was already said, the link profiles are only suggestive. The first Fresnel’s ellip-soid is not drawn correctly and there is a possibility that the tree canopy has been changed between the moment the map was drawn and the moment the measurements were made. However, the link profiles can still be used as an instrument to help un-derstand the PDP of each measurement site.

Examples of the average PDP of each measurement site and the modelled taps are presented in Figures 24–25. The points describe the modelled taps and the continu-ous line is the calculated PDP. The rest are presented in Appendix 6. The number of modelled taps and the maximum dynamic range of each measured link are presented in Table 7.

48

Figure 24. Average PDP and modelled taps for TX1.

Figure 25. Average PDP and modelled taps for TX3.

49

Table 7. Number of modelled taps and maximum dynamic range

TX site Number of modelled

taps

Maximum dynamic range from the

strongest tap [dB]

TX1 28 10.5

TX2 27 15

TX3 26 13

TX4 25 12.5

TX5 24 12

TX6 23 11.5

TX7 26 13

4.5.2. Amplitude Fading

For this amplitude fading analysis, all the recorded data from each measurement site were collected together. Small-scale analyses can be done over a few tens of wave-lengths [27]. This allows incorporating five measured points from one measurement site into one because the transmitter was moved only about 10 meters between the points. Amplitude distribution was selected from the distribution that best fits the ex-perimental data with a 95 % confidence interval using the Kolmogorov-Smirnov goodness-of-fit test (KS). The KS test selects the theoretical distribution which minimises the absolute value of the linear error of the theoretical and measured cu-mulative distribution functions (CDF) [29]. The KS test is described in more detail in Appendix 8.

It was found that an empirical distribution of the path amplitudes best fits to the Rice distribution. The pass rate of the measured data was mostly around 50%. The pass rates for the lognormal and Rice distribution of the each channel models are shown in Table 8. TX1 and TX2 fit the lognormal distribution the best. The PDF for Rice and lognormal distributions are calculated using (19) and (21).

Figure 26 shows an example of the measured data from link TX7, where the PDF and CDF of the data are fitted to the theoretical Rice distribution’s functions.

In the generated channel models introduced in Appendix 7, amplitude fading is modelled as a Ricean distribution in channel models TX3, TX4, TX5, TX6 and TX7. Fading in models TX1 and TX2 is described as a lognormal distribution.

An example of the generated channel model TX3 is represented in Figure 27. The figure also describes the amplitude fading of the channel.

50

Table 8. Pass rates of the Kolmogorov-Smirnov test for each channel model

TX site Pass Rate of the Lognormal (%)

Pass Rate of the Rice (%)

TX1 60.7 % 42.9 %

TX2 44.4 % 25.9 %

TX3 26.9 % 69.2

TX4 20 % 80 %

TX5 16.7 % 45.8 %

TX6 43.5 % 73.9 %

TX7 3.9 % 69.2 %

a) PDF b) CDF

Figure 26. Distribution of the measured signal amplitude’s and Ricean distribution’s.

Figure 27. Channel model TX3.

51

5. SYSTEM SIMULATIONS

This chapter presents the performance analysis related to different types of commu-nication system concepts and receiver structures. System simulations were done us-ing an UWB link level simulator implemented in a Matlab environment. The theoretical background for the receiver structures and assumptions and parameters are presented first. Then the chapter shows the results for the different UWB systems using the generated outdoor UWB channel model.

5.1. Receiver Structure

Multipath components can be utilised by using a Rake receiver which combines energies coming from different propagation paths, assuming that the time of the path arrivals is known. Thus it creates multipath diversity and enhances the SNR. A Rake receiver can be subdivided into different classes: all-Rake (A-Rake), partial-Rake (P-Rake) and selective-Rake (S-Rake) depending on how the receiver captures energy. All-Rake collects all the energy from the channel. Partial-Rake collects the first incoming paths and selective-Rake takes the strongest paths of the channel [36]. In this thesis project the all-Rake receiver was not used due to its complexity.

The receiver used in the studies was a correlation receiver in which the spread re-ceived signal was correlated with a template waveform in order to obtain an estimate of the transmitted bit. A correlation receiver can be either coherent or noncoherent. A coherent receiver takes the phase of the received signal into account and sums the different multipath signals into the same phase. A noncoherent receiver does not ex-ploit the phase of the multipath components. An UWB signal is carrierless and there-fore it does not have a phase in the conventional sense. A coherent UWB receiver must, however, estimate the polarity of the signal because it can be reversed by the channel. There are several different combining techniques which can be used de-pending on the detection type (coherent or noncoherent).

The received signal for a single data bit can be defined as

=

+−=r

1

)()()(l

nnn tntstr τα , (41)

where n(t) is the Gaussian noise in the channel, s(t) is the transmitted signal and � n is the gain of the nth multipath, which can be defined as

nj

nn e�

αα = (42)

where n is the phase of the nth received pulse.

52

Maximum ratio combining (MRC) or equal gain combining (EGC) can be used to coherently combine the signals from different propagation paths. Maximum ratio combining is the optimum form of diversity combining because in a MRC receiver the received power level is estimated for each multipath [43]. The decision variable will follow the form [44]

�=

−=r d

1 0

*MRC )()(l

n

T

jnnj dttwtrU τα , (43)

where wi is the pulse waveform representing data bit j.

EGC is simpler than MRC but it is a suboptimal combining technique [43]. It does

not require knowledge of the channel fading amplitudes, as it uses equal weights instead. The decision variable follows the form [44]

� −==

−dr

01

EGC )()(T

jn

l

n

jj dttwtreU n τθ . (44)

In the noncoherent case, combining can be done using, e.g., an absolute combiner

(AC) or a square-law combiner (SLC). The AC approach sums the absolute values of the outputs of all the correlators before the detector. Correspondingly, the SLC sums the square of the outputs of all the correlators. When a noncoherent absolute combiner or square-law combiner is used, the performance of the system can be improved by using power estimation (PE). PE means the knowledge of the channel power is used to weight the output of each correlator. In this thesis project only SLC with PE was studied (SLC+PE) in the noncoherent approaches. In this case, the decision variable follows the form [44]

2

01

PESLCdr

)()(� −==

+T

jn

l

nnj dttwtrU τα . (45)

5.2. Assumptions and Parameters

The UWB system performances were studied through the bit error rates as a function of the signal-to-noise ratio. The systems in all the simulated cases are single band and single user UWB links without error correction coding. The basic idea of the studied system is that it has to be simple and inexpensive to implement. In the simu-lations, the studied data rates were 100 kbit/s and 1 Mbit/s. The processing gains were calculated using (2) – (4) and are 35 dB and 25 dB, respectively. The pulse was chosen so that its spectrum fits into the measured frequency band. The pulse in the channel was the first derivative of the Gaussian pulse with the exception of PSM

53

modulation where the pulse pair was the first and the second derivative of the Gaus-sian pulse. The pulse width is 3.2 ns. The pulse is presented in Figure 28.

Figure 28. The 1st derivative of the Gaussian pulse with pulse width 3.2 ns and its spectrum.

When using coherent detection, antipodal BPAM modulation is the best choice compared to the others. This is because the average probability of error Pb for binary antipodal signals in an additive white Gaussian noise (AWGN) channel is [17]

��

�

�

��

�

�=

0

bb

2

N

EQP . (46)

Correspondingly, for binary orthogonal signals, which are 3 dB poorer than antipo-dals, the average probability of error is [17]

��

�

�

��

�

�=

0

bb N

EQP . (47)

For OOK modulation, the average probability of error in an AWGN channel is [45]

��

�

�

��

�

�=

0

bb 2N

EQP . (48)

Both multiple access systems, DS and TH, were studied in coherent and noncoherent approaches.

The performances of different types of Rake receivers were compared in the simu-lations. In the coherent approaches, both a MRC and an EGC were studied with a different number of fingers. A SLC+PE was the only studied noncoherent case.

From all of seven generated channel models, two were selected for simulations; TX3 and TX7. The chosen channel models are presented in Figure 25 and in Appen-dix 6. They were chosen because they represent different model types. Model TX3

54

has a strong first component but its other multipath components are highly attenu-ated. Correspondingly, model TX7 has quite strong delayed multipath components coming about 0.07 µs after the first component. The channel is assumed to be con-stant during one data bit but after each bit a new channel is realised. For each Eb/N0

value the simulation was continued until 100 errors were obtained or 100,000 bits were transmitted.

5.3. Simulation Results

Figure 29 shows system performance using different modulation methods and coher-ent approaches with one-finger Rake receiver and Figure 30 shows the same but with a partial Rake with four fingers. The used combining were MRC. The simulations were made in the TX3 channel using a data rate of 1 Mbit/s. Suggestive theoretical results in an AWGN channel are also presented but it should be kept on mind that in an AWGN channel all the energy is in the same, nonfading path. The generated channel models are fading and the total energy is subdivided into several different paths. Therefore, the performance can never be the same as in an AWGN channel.

As expected, the OOK modulation method gives the worst performance and BPAM gives the best. DS-BPAM modulation is about 1 dB better than TH-PPM modulation. In these studies, the pulse waveforms used in DS-PSM modulation produce results that are about 2 dB worse than in TH-PPM modulation. In PSM modulation the pulse waveforms were chosen as 1st and 2nd derivatives because their spectrum fits into the measured bandwidth. If the pulse pair had been chosen differently, the performance of PSM modulation would have been better [46]. Based on Figure 29 and Figure 30, the BPAM modulation was chosen for the coherent approach studies. Eb is the average total energy per bit after the channel, because the energy of the channel is normalised to 1. By comparing the performance differences between the one and four-finger Rakes in Figure 29 and in Figure 30 it can be seen that the benefit is not more than 2 dB when the number of fingers is increased from one to four. As it can be noticed from the structure of the channel models, using more than four-finger Rakes is not expected to give much more improvement.

In Figure 31, the modulation methods are compared using noncoherent approaches with one and four-fingers Rake receivers. Differing from the coherent approaches, TH-PSM modulation outperforms the TH-PPM modulation. TH-PSM is more than 3 dB better than TH-PPM. When using a noncoherent PSM system the benefit is 1 dB when the numbers of Rake fingers is increased from one to four.

55

Figure 29. BERs for UWB systems with different modulation methods and a Rake with one 1 finger at channel TX3.

Figure 30. BERs for UWB systems with different modulation methods and a Rake with four fingers and MRC combining at channel TX3.

.

56

Figure 31. BERs for UWB systems with different modulation methods using nonco-herent approaches at channel TX3.

DS-UWB system Figure 32 shows bit error rate curves in the TX3 channel for a DS-UWB system util-ising BPAM modulation. When using BPAM modulation, only coherent detection can be used. The MRC and EGC combining are compared and the theoretical BER curve for BPAM modulation in AWGN channel is presented in Figure 32. When us-ing a Rake with four fingers the MRC is about 0.5 dB better than EGC.

The difference between these two combining techniques grows according to the number of Rake fingers. Obviously the system’s performance gets better if the num-ber of Rake fingers grows. When the number of fingers was increased from one to two, the system performance increased 1.5 dB in both the MRC and EGC techniques. When the fingers were increased from one to four, performance increased 2.5 dB when using MRC but only 2 dB when the EGC technique was used. As one can no-tice from the measured channel models, there is no need to use more than four finger Rake receivers. The multipath components coming after the first four are much weaker, and therefore they do not provide much more improvement compared to the four-finger Rake.

Figure 33 gives the results for a DS-UWB system using noncoherent SLC+PE de-tection for PSM and OOK modulations in the TX3 channel. PSM modulation outper-forms the OOK modulation. The number of fingers does not have as strong an effect as in the coherent approaches. In PSM modulation, when the number of the fingers is increased from 1 to 2, performance increases about 0.5 dB and when increased from 1 to 4, about 1 dB. It seems that noncoherent combining loss is about 0.5 dB com-pared to coherent combining. When OOK modulation is used with the noncoherent

57

approaches, the combining loss affects right away and therefore increasing the num-ber of fingers worsens performance.

Figure 32. DS-UWB systems, at channel TX3 with MRC and EGC for BPAM.

Figure 33. DS-UWB systems, at channel TX3 with for PSM and OOK.

In order to compare coherent MRC and noncoherent SLC+PE detection PSM

modulation was used. The comparisons between the coherent and noncoherent ap-

58

proaches using DS-PSM are presented in Figure 34. As one can notice with the low number of fingers, coherent detection is about 2 dB better than noncoherent.

Figure 34. Performance of the coherent and noncoherent approaches using PSM.

Figure 35 shows a comparison between performances if a partial-Rake receiver or a

selective-Rake receiver is used. The DS-UWB system is examined using MRC in TX7 channel. As one can notice from Appendix 6, TX7 has strong taps in larger de-lays. The S-Rake uses a stronger tap than the P-Rake as the fourth tap, and therefore the S-Rake with four fingers outperforms the partial one. When a Rake with 10 fin-gers is used, performance increased 1 dB when a selective Rake receiver is used.

Depending on the channel the results that are used can be changed. The comparison between channels TX3 and TX7 is made in Figure 36. As it can be seen, performance varies 1 dB depending on the channel that is used

A comparison between the different data rates is presented in Figure 37 using a DS-UWB system with BPAM modulation. System performance does not change if the data rate is degraded from 1 Mbit/s to 100 kbit/s. Naturally, according to (35) ten times higher data rate also needs ten times more transmitting power to reach the same SNR value. The performances in Figure 37 were examined in the TX3 channel using MRC.

59

Figure 35. DS-UWB systems, at channel TX7 with MRC P-Rake and S-Rake for BPAM.

Figure 36. Performance difference when using channel TX3 or TX7.

60

Figure 37. DS-UWB systems with MRC for BPAM, Rd = 100 kbit/s and 1 Mbit/s.

TH-UWB system The results for both MRC and EGC are presented in Figure 38, for a TH-UWB sys-tem using a partial-Rake. Also in this case, MRC outperforms EGC as was expected. When the number of Rake fingers is increased, performance is better. In this case, performance does not improve substantially if the number of branches is increased from 1 to 2. But when four fingers are used performance increased 2.5 dB in the MRC case and 2 dB in the EGC case compared to the one-finger Rake.

The performance of the noncoherent approaches using a TH-based system using PSM and PPM modulations is shown in Figure 39. PSM modulation outperforms the PPM modulation. When using PSM modulation the number of the fingers does not affect as strongly as in coherent detection. Here performance improves less than 1 dB when the number of fingers is increased from one to four.

Coherent MRC and noncoherent SLC+PE detection using a TH-PSM system are compared in Figure 40. As one can notice, the difference between noncoherent and coherent with the four-finger Rake is more than 2 dB.

The effect of the data rates on TH UWB system performance was studied using BPAM modulation with MRC in the TX3 channel. The performances using 100 kbit/s and 1 Mbit/s are presented in Figure 41, which shows that system performance does not change significantly. The only bigger difference can be found when the two-finger Rake is used. In that case performance is about 1.5 dB better in the 100 kbit/s case than in the 1 Mbit/s case. Of course the higher data rate needs more power than the lower data rates.

61

Figure 38. TH-UWB systems, at channel TX3 with MRC and EGC for BPAM.

Figure 39. TH-UWB systems, at channel TX3 with SLC+PE for PSM.

62

Figure 40. Coherent and noncoherent approaches using TH PSM modulation.

Figure 41. TH-UWB systems, at channel TX3 with MRC for BPAM using data rates of 100 kbit/s and 1 Mbit/s.

5.4. Conclusion of the Results

The system performance studies mainly employed the first derivative of the Gaussian pulse with a pulse width of 3.2 ns. Both coherent and noncoherent approaches were

63

studied using MRC, EGC and SLC+PE combining. A self-generated outdoor channel model was used in all the simulations.

In ranking the analysed modulation schemes, the results of the simulations are as follows: in the coherent approaches the order is BPAM, PPM, PSM and OOK. BPAM is 1 dB better than PPM modulation, 3 dB better than PSM modulation and 4 dB better than OOK modulation. In the noncoherent approaches, the ranking order is PSM, PPM and OOK. In this case PSM is 3 dB better than PPM.

When comparing the DS and TH-based systems, BPAM modulation was used. No significant differences were found when using coherent approaches. The only differ-ence was found when using a two-finger Rake receiver. In that case the DS system outperforms the TH system. In comparing the noncoherent approaches using PSM modulation, the DS-based system performs 1 dB better than the corresponding TH-based system.

When comparing the MRC and EGC techniques in both DS and TH-based systems, no significant difference can be seen. MRC is less than 0.5 dB better than EGC when using a Rake receiver with 1, 2 and 4 fingers.

The coherent and noncoherent approaches where compared using PSM modulation. When the coherent approach is used, the improvement in performance in each branch of combining is about 0.5 dB compared to the noncoherent approaches. For example, when MRC was used, performance increased 2.5 dB when the number of fingers in-creased from one to four. In the noncoherent approaches the same improvement in the DS-based system was only about 1 dB and even less in the TH-based system.

Most of the simulations were done using generated channel TX3. To see the effect of the difference channels, the DS system with BPAM modulation was also simu-lated using channel model TX7. Performance varied more than 1 dB depending on the channel model used. The differences between the partial and selective Rake were also studied using channel TX7. The S-Rake gives about 0.5 dB of improvement when four fingers are used and when 10 fingers are used the S-Rake gives 1 dB bet-ter performance than the partial Rake. This was expected based on the channel model TX7. Because they do not have any strong taps coming with larger delays, the other models probably would not offer any improvement when the S-Rake is used rather than the P-Rake,. Therefore, in order to have a low-complexity receiver structure the partial-Rake receiver is adequate.

The results of the link budget analysis, which was based on (35), were presented in Table 6. According to the analysis and to the system performance simulations, it seems that at least 1 W transmission power is needed to transmit over the measured links, if the required BER value is assumed to be 10-3. When using low data rates (16 kbit/s), 1 W is enough for the entire measured links if coherent approaches with BPAM modulation and a four-finger Rake receiver are used. Measured link TX4 probably still works with the required BER rate of 10-3, but if the link distance is more than 1.6 km and the link is strongly obstructed, then 1 W is not enough. If the links are quite short (

� 0.5 km), then the coherent approaches with BPAM modula-

tion will also work even if only a one-finger Rake receiver is used. If the transmitter power is increased to 10 W, all of the modulation methods are

possible with coherent approaches when the data rate is 16 kbit/s. In this case it is also possible to use noncoherent PSM modulation with one finger. Correspondingly

64

noncoherent OOK modulation with a one-finger Rake receiver can be only used up to a 1.6 km link distance. But, if the link distance is greater and strongly obstructed, then the BER value of 10-3 is not reached. In this case it does not help even if the number of fingers is increased, as it can be seen from Figure 33.

The required BER value can be reached in all the measured links also when the data rate is 100 kbit/s. Then transmitter power should be 10 W and the coherent approach with BPAM modulation and a four-finger Rake should be used. If the Rake receiver has only two fingers, the required BER is not reached if the link distance is more than 1.6 km and the link is strongly obstructed. The data rate can be increased even to 1 Mbit/s if the links are short (

� 0.5 km) and quite clear.

In order to keep the system inexpensive and simple to implement noncoherent ap-proaches should be used. In that case, 10 W of transmission power should be used to transmit with a data rate of 16 kbit/s to reach the required 10-3 BER value. Only when short (

� 0.5 km) and clear links are used, is 1 W of transmission power is

enough. In this kind of links a data rate of 100 kbit/s can also be used with noncoher-ent approaches if 10 W of transmission power is used.

65

6. DISCUSSION

In this thesis project the performance of different single band UWB systems was widely studied using a self-generated outdoor UWB channel model. The thesis pro-ject fills a research gap by giving a comprehensive understanding of the UWB sys-tem’s suitability for long link distances using VHF/UHF frequencies.

During the data analysis two phenomena were found from the data, which both skewed the measured data. Firstly, it was noticed that during the campaign there had been other radio transmissions at the same time in the same area, which were mani-fested as spurious spikes in the frequency responses. These spurious peaks raised the noise level in the impulse responses. Because the spikes did not belong to the chan-nel, there was a clear reason to remove them. Afterwards it was no more possible to find out where the peaks were coming from. Another problem was unsuccessful sweeps, which were noticed inside the data. The bad sweeps probably resulted from synchronisation problems. Since they skewed the general channel parameters and the average impulse responses, they were also removed.

After the post-processing, common channel parameters, like mean excess delay, RMS delay and maximum excess delay, were calculated. The parameters were com-pared to corresponding wideband models due to the lack of corresponding UWB models. After the parameter calculation, tapped delay line models were generated to describe the channel of each link separately. Usually when channel models are gen-erated the aim is generate general channel models based on different terrain classes. This model grouping was not made, because in this case all of the models were very similar and thus the grouping was not strongly needed.

The different terrain types at each measurement site caused problems to the path loss analysis. It was evident that no regression line could be fitted to the results and therefore the path loss analysis was made for each links separately. Despite the lack of a general path loss model, the generated path loss analysis covers well the differ-ent kinds of environments and link distances. The detected path losses were a bit smaller than expected, but reasonable explanations were found. One of the reasons might be the multipath propagation. In the receiver, the several multipath compo-nents can arrive at the same time, which may increase the received power. Another reason was the real antennas’ elevation angles, which differed from the calibration measurement, therefore probably increasing the antenna gains. The extraneous radio tranmissions may also have affected the path loss results, because they affected differently to different measurement sites. Now, when the receiver is on the top of the hill, the extraneous transmissions are stronger than in the transmitter sites. After all, in order to have a consisting path loss model, additional measurements would be needed. The measurement links should be sited on the line in the same kind of envi-ronment in order to compare the results.

The link level simulations were done using different modulation methods. As ex-pected, BPAM modulation outperforms the other modulations when coherent ap-proaches are used. The performance of PSM modulation is strongly related to pulse waveforms used. The waveforms which can be used depend on the spectrum re-

66

quirements. In this thesis, only the 1st and 2nd derivatives of the Gaussian pulse were used. If some other pulse pair, the performance can be changed.

All of the system simulations were made using two of the generated channel mod-els, TX3 and TX7. When the same system performances of these two channels were compared it was found that it can vary about 1 dB when different channel models are used. The results were as expected; system performance was better in channel TX3 than in TX7. This is because the first four taps are stronger in model TX3 than in model TX7. But, in general, all the models are very similar and thus, performance would probably not have varied more even if the other models had been used in the simulations. In almost all of the models only the first few taps are inside 10 dB. Therefore, it can be said that, in general, the partial-Rake receiver with four fingers is a sufficient receiver structure in this kind of environment. The selective-Rake struc-ture with more than four fingers is not going to give any extra improvement.

In the study it was found that when a coherent receiver is used the transmitter power can be 1 W to reach the required BER value in the entire measured links when a data rate of 16 kbit/s is used. In these simulations the coherent approaches had ex-act channel estimates, but in reality the channel estimation is not exact. Therefore, in a real situation the differences between coherent and noncoherent approaches are no longer as great.

In the future the main areas of interest will be to continue the path loss modelling based on new measurements. The new measurements would offer the possibility to increase the reliability of the generated path loss results and expand them to a general UWB outdoor path loss model. If a general path loss model is made, a capacity analysis can also be done. In future studies it would be interesting to study the effect of error correcting codes. Now all the system simulations were done without error correcting coding and it would be useful to study how much improvement error cor-recting coding can give in these kinds of outdoor situations. This study also did not include the impact of interferences and jamming on UWB systems performance in an outdoor environment.

67

7. SUMMARY

The goal of this thesis was to study the suitability of UWB technology for several kilometres long link distance in an outdoor environment. The UWB outdoor channel models have not previously been published in open literature. Therefore, the channel modelling was important since it enabled analysis of system performance using real-istic channel models. The measured frequencies were from 230 MHz to 390 MHz fulfilling the fractional bandwidth specification which the FCC has given for UWB systems. The used measurement system was modified frequency domain sounding system and the used antennas were vertical polarized. The frequency domain measurements were carried out in rural environment, which was slightly hilly and covered with forest and open peatlands. Seven different links with distances varying from 0.5 km to 5.6 km were measured. Based on these measurements, multipath channel models and path loss estimations were generated. The multipath models were needed in link level simulations in order to analyse the performance of different system structures. The path loss estimations were needed for coverage analysis.

The basic of UWB technology was first briefly presented. The advantages, disad-vantages and also some UWB applications, especially military ones, were discussed. The communications system concepts which were used in this thesis were also pre-sented. Then the theory of a multipath radio channel was discussed in general, in-cluding the physical mechanisms of radio wave propagation, fading, and modelling of a radio channel.

The campaign carried out in southern Finland during late summer 2003 was dis-cussed, and the measurement system and the environment were described. The post-processing and data analysis were also presented. Basic channel parameters, such as mean excess delays, RMS delays and total excess delays, were presented and calcu-lated from each of the measured links. The results were found to be similar to the re-sults of wideband channel measurements from a similar environment but the resolu-tion is much better.

For each of the measured links, propagation channel models were generated using a tapped delay line channel model structure. Each of the generated models consists of 20–30 taps. The models include information on the gain, delay and amplitude fading of the tap. The channels were not modelled to the noise level, because the delay reso-lution of an UWB channel is huge and the models would have consisted of too many taps for simulation purposes.

Two of the self-generated channel models were used when the link level simula-tions were done. The simulations were done to study the performance of different single band UWB systems through bit error rate simulations. Different modulation techniques and time hopping and direct sequence concepts were studied. When choosing the studied system structures a prerequisite was that implementation of the system should be inexpensive and simple. The results of the simulations were as fol-lows: when the modulation methods in an outdoor environment are ranked using co-herent approaches the order is BPAM, PPM, PSM and OOK. When a noncoherent approach is used the rank is PSM, PPM and OOK. No significant differences were found between a DS-based system and a TH-based system.

68

According to the link budget analysis and the system performance simulations, it can be said that transmission power of 1 W or greater is needed for transmitting over the measured links.

If coherent approaches can be used, the required BER (10-3) can be reached in all of the measured links with a data rate of 16 kbit/s even if only 1 W of transmission power is used. Then the BPAM modulation with a four-fingers Rake is needed. But, it seems, that if the link distance is more than 1.6 km and strongly obstructed, then the required BER value is not reached.

Noncoherent approaches should be used in order to make the system inexpensive and simple to implement. In that case, 10 W of transmission power is needed to transmit with a data rate of 16 kbit/s in order to reach the required 10-3 BER value. The simplest possible structure would be PSM modulation with a one-finger Rake receiver. PPM modulation would need four fingers. If OOK modulation is desired it was found that with a one-finger Rake receiver it can be only used up to a 1.6 km link distance. But, if the link distance is longer and strongly obstructed, then the BER value of 10-3 is not reached. One watt of transmission power can be only used with noncoherent approaches if the links are short (

� 0.5 km) and clear. In this kind of

link a data rate of 100 kbit/s can also be used with noncoherent approaches if 10 W of transmission power is used.

69

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9. APPENDICES

Appendix 1 Antenna pattern, Rohde & Schwartz HK014 Appendix 2 Frequency responses of the calibration data Appendix 3 Map of measured sites Appendix 4 Link profiles of the measured links Appendix 5 Excess path losses of the measured links Appendix 6 PDF and modelled taps for each measured link Appendix 7 Tabulated channel models Appendix 8 Kolmogorov-Smirnov Goodness-of-Fit Test

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Appendix 1 Antenna pattern, Rohde & Schwartz HK014.

75

Appendix 2 Frequency responses of the calibration data

Frequency response of the calibration data.

Frequency response of the power amplifier.

76

Appendix 3 Map of measurement sites.

The contour lines indicate a 5 m difference in altitude.

1 km

77

Appendix 4 Link profiles of the measured links. TX1 and TX6 link profiles are already presented in Figure 16. TX3

TX2

TX3

TX4

78

TX5

TX7

79

Appendix 5 Excess path losses of the measured links

Excess path loss of the link TX2.

Excess path loss of the link TX4.

80

Excess path loss of the link TX5.

Excess path loss of the link TX6.

81

Excess path loss of the link TX7.

82

Appendix 6 PDP and modelled taps for each measured link The average PDPs and modelled taps for each link are presented.

Average PDP and modelled taps for TX2.

Average PDP and modelled taps for TX4.

83

Average PDP and modelled taps for TX5.

Average PDP and modelled taps for TX6.

84

Average PDP and modelled taps for TX7.

85

Appendix 7 Tabulated channel models Tap gains, delays and parameters describing fading are presented in the tables. Channel model for TX1

Delay [µs] Tap gain

[dB] Amplitude

std

0 0 0.11487 0.00625 -3.0001 0.13955 0.0125 -7.6769 0.28805 0.01875 -6.5709 0.31883 0.025 -6.3988 0.3597

0.03125 -7.1783 0.23637 0.0375 -9.338 0.29018 0.04375 -7.0897 0.13422

0.05 -7.2477 0.172 0.05625 -9.3513 0.26716 0.0625 -9.3235 0.27311 0.06875 -9.4565 0.26978 0.075 -9.7785 0.31196

0.09375 -10.093 0.237 0.13125 -10.245 0.27334 0.1375 -9.4648 0.27656 0.14375 -9.9404 0.22404 0.175 -10.075 0.20255 0.2 -9.5737 0.32236

0.20625 -9.4654 0.31871 0.2125 -10.492 0.30978 0.225 -10.352 0.35993

0.23125 -9.7223 0.38214 0.2375 -9.8899 0.30508 0.24375 -10.283 0.3085 0.25625 -9.9258 0.26917 0.2625 -9.7524 0.21806 0.2875 -10.393 0.34659

86

Channel model for TX2

Delay [µs] Tap gain

[dB] Amplitude

std

0 0 0.18772 0.00625 -3.5327 0.19257 0.0125 -9.3745 0.21843 0.01875 -9.7804 0.17176 0.025 -13.375 0.35957

0.03125 -12.413 0.35673 0.0375 -12.342 0.27285 0.04375 -11.891 0.36252

0.05 -11.615 0.34268 0.05625 -12.506 0.25025 0.0625 -14.226 0.31913 0.06875 -14.608 0.30663 0.08125 -13.883 0.25364 0.0875 -14.223 0.28402

0.1 -14.842 0.29209 0.1125 -13.991 0.32999 0.125 -14.451 0.29178

0.13125 -14.886 0.31967 0.1375 -14.453 0.32745 0.14375 -13.67 0.29232

0.15 -14.997 0.28708 0.15625 -14.701 0.3061 0.1625 -14.375 0.2934 0.20625 -14.596 0.32174 0.24375 -14.659 0.2395 0.275 -14.945 0.27991 0.35 -14.834 0.25673

87

Channel model for TX3

Delay [µs] Tap gain

[dB]

Ricean K –value

[dB] 0 0 17.82

0.00625 -4.5455 17.905 0.0125 -7.415 14.744 0.01875 -7.6001 18.836 0.025 -12.349 7.865 0.0375 -12.235 7.2809 0.04375 -11.884 5.6976 0.06875 -12.749 10.428 0.075 -12.931 7.7647 0.0875 -12.996 8.8238 0.10625 -10.287 13.719 0.11875 -11.243 7.3452 0.125 -10.43 15.552

0.13125 -11.952 8.1247 0.1375 -12.622 9.6005 0.15 -12.028 9.3759

0.15625 -12.855 9.96 0.175 -12.529 11.409

0.19375 -12.066 6.2266 0.2125 -11.852 6.8763 0.21875 -12.769 7.7819

0.25 -11.958 11.865 0.2625 -12.328 9.7931 0.26875 -12.56 10.018

0.4 -12.928 12.455 0.54375 -12.898 10.741

88

Channel model for TX4

Delay [µs] Tap gain

[dB]

Ricean K –value

[dB] 0 0 17.247

0.00625 -4.0514 17.772 0.0125 -11.717 9.6131 0.01875 -8.9811 11.151 0.025 -10.831 8.1096

0.03125 -11.179 9.5079 0.0375 -12.348 8.2075 0.04375 -10.718 10.71

0.05 -9.6615 9.3643 0.05625 -12.142 7.8027

0.1 -11.807 8.4903 0.10625 -12.016 8.9618 0.1125 -11.536 8.5833 0.15625 -12.148 8.4709 0.1625 -11.638 10.587

0.2 -11.829 6.3379 0.24375 -12.126 8.4189

0.25 -11.769 7.4024 0.26875 -11.393 10.38 0.275 -11.817 9.8285

0.30625 -12.276 8.3956 0.3875 -12.21 9.6174 0.39375 -12.35 8.9067 0.41875 -11.959 8.3966

0.55 -12.467 10.267

89

Channel model for TX5

Delay [µs] Tap gain

[dB]

Ricean K –value

[dB] 0 0 17.988

0.00625 -4.2629 16.796 0.0125 -9.6923 7.6488 0.01875 -10.416 7.3086 0.025 -10.684 9.2077

0.03125 -11.762 8.7217 0.0375 -11.535 6.6374 0.04375 -11.379 7.4816

0.05 -11.008 8.2767 0.0625 -11.572 6.8831 0.06875 -11.114 8.59 0.075 -10.594 8.0153

0.08125 -11.807 8.1447 0.1 -11.651 8.0501

0.10625 -11.924 7.6601 0.1125 -11.198 10.3 0.11875 -10.161 9.441 0.125 -11.061 8.3805 0.1375 -11.803 7.7408 0.15 -11.596 6.5579

0.15625 -11.237 6.9042 0.19375 -11.821 9.3136 0.24375 -11.263 9.7435 0.28125 -11.483 10.039

90

Channel model for TX6

Delay [µs] Tap gain

[dB]

Ricean K –value

[dB] 0 0 15.573

0.00625 -4.3747 14.317 0.0125 -8.6734 8.3601 0.01875 -10.223 9.2544 0.03125 -10.561 8.4418 0.0375 -10.421 7.9729 0.04375 -10.092 8.5711 0.05625 -11.216 7.8557 0.06875 -10.63 8.2925 0.075 -10.441 8.0383

0.09375 -10.839 8.3257 0.1 -10.609 8.0285

0.10625 -11.072 8.2882 0.13125 -10.819 8.3743

0.15 -11.116 9.5603 0.1625 -10.881 9.5452 0.175 -11.152 10.721

0.18125 -11.313 9.6134 0.2 -11.298 7.17

0.2125 -10.385 10.125 0.26875 -11.289 8.0667 0.375 -11.365 8.1782

0.51875 -11.168 10.908

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Channel model for TX7

Delay [µs] Tap gain

[dB]

Ricean K –value

[dB] 0 0 14.139

0.00625 -4.2321 14.497 0.0125 -10.57 9.8511 0.01875 -12.257 9.0796 0.025 -10.311 10.172

0.03125 -12.859 8.6902 0.0375 -10.718 11.009 0.04375 -12.45 10.744 0.05625 -11.087 8.1317 0.0625 -11.589 9.363 0.06875 -9.244 11.063 0.075 -10.823 10.163 0.0875 -8.9038 10.597 0.09375 -7.3307 11.625 0.10625 -9.0134 10.397 0.1125 -9.8329 11.298 0.14375 -12.952 10.283 0.15625 -12.786 8.8976 0.1625 -11.868 9.7999 0.18125 -12.047 11.01 0.1875 -12.642 10.432 0.24375 -12.49 10.309 0.29375 -11.795 10.318 0.36875 -12.823 8.6518 0.46875 -12.597 11.431

0.5 -12.662 10.097

92

Appendix 8 Kolmogorov-Smirnov Goodness-of-Fit Test. It is assumed that there are n numbers of components (x1, x2,…xn) from the measured distribution. It is assumed that samples have been ordered in ascending order (X1

� X2

� …

� Xn). Test statistic Z is the maximum deviation Z between the CDF of the

measured distribution Fh(x) and the CDF of the theoretical distribution Fe(x)

)()(max eh xFxFZ −= .

Then the test statistic is compared to the critic value of the test ks1- � (n–1–l), where l is the number of estimated parameters from the material and is the significant level. The measured material can be said to be distributed as a theoretical distribution if

)1(1 lnksZ −−< −α .

The critical values of the Kolmogorov-Smirnov test are listed for example in [29].