MIMO OFDM Channel Estimation withOptimum Pilot Patterns for Cognitive Radio in

Overlay Spectrum Sharing System

Haval Abdulrahman

April 2009Student Number: 1250795

Thesis Number: IRCTR-A-009-09

Contents

1 Introduction 31.1 Thesis organization . . . . . . . . . . . . . . . . . . . . . . . . . 51.2 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51.3 Novelties of the work . . . . . . . . . . . . . . . . . . . . . . . . 6

2 The Mobile Wireless Channel Model 72.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.2 Wide Sense Stationary Uncorrelated Scattering (WSSUS) channel

model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82.2.1 Power Delay Profile . . . . . . . . . . . . . . . . . . . . 102.2.2 Doppler power spectrum . . . . . . . . . . . . . . . . . . 12

2.3 The MIMO Channel model . . . . . . . . . . . . . . . . . . . . . 132.4 Doppler effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142.5 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . 15

3 MIMO OFDM 173.1 OFDM Modulation and Demodulation . . . . . . . . . . . . . . . 173.2 Generation of an OFDM signal . . . . . . . . . . . . . . . . . . . 253.3 OFDM parameters . . . . . . . . . . . . . . . . . . . . . . . . . 263.4 MIMO model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273.5 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . 30

4 Cognitive Radio 314.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 314.2 Spectrum pooling . . . . . . . . . . . . . . . . . . . . . . . . . . 334.3 Interference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 354.4 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . 35

5 MIMO OFDM Channel Estimation 385.1 Wiener-Hopf equations . . . . . . . . . . . . . . . . . . . . . . . 395.2 2X1D Wiener filtering . . . . . . . . . . . . . . . . . . . . . . . 40

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5.3 Channel Estimation . . . . . . . . . . . . . . . . . . . . . . . . . 415.4 The Pilot Grid/Pattern design and Resulting Pattern . . . .. . . . 445.5 The Hexagonal and Rectangular pilot patterns . . . . . . . . . .. 455.6 Virtual pilot concept . . . . . . . . . . . . . . . . . . . . . . . . 475.7 The pilots pattern and virtual pilot with respect to Licensed User . 495.8 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . 50

6 Simulation Results 536.1 Performance of the Hexagonal, RectangularDf = 4 and Rectan-

gularDf = 2 pilot patterns in the Basic MIMO-OFDM system . . 546.2 Performance of the Hexagonal pattern in the CR system withand

without LU existence . . . . . . . . . . . . . . . . . . . . . . . . 606.3 Analytical validation . . . . . . . . . . . . . . . . . . . . . . . . 65

7 Conclusion and Recommendations 677.1 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 677.2 Recommendations . . . . . . . . . . . . . . . . . . . . . . . . . . 707.3 Personal perspective . . . . . . . . . . . . . . . . . . . . . . . . 71

A The Sliding Window Technique 73

B Filter Design 75

C V-BLAST Architecture 78

D Publications 79Bibliography

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List of Figures

3.1 (a) Serial and (b) Parallel symbol transmission . . . . . . .. . . . 183.2 OFDM spectrum, one subcarrier (left) and five subcarriers (right)

[1] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183.3 Discrete Time OFDM model . . . . . . . . . . . . . . . . . . . . 193.4 Guard Interval . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203.5 OFDM Communication System . . . . . . . . . . . . . . . . . . 203.6 Multicarrier Modulator and Demodulator . . . . . . . . . . . . .213.7 Simplified frequency domain view of OFDM Transmission system 233.8 Time-Frequency Representation of an OFDM symbol and OFDM

frame . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243.9 OFDM Modulator . . . . . . . . . . . . . . . . . . . . . . . . . . 263.10 MIMO setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283.11 MIMO System model (a) Transmitter and (b) Receiver . . . . .. 29

4.1 Basic Cognitive Cycle . . . . . . . . . . . . . . . . . . . . . . . 334.2 Spectrum Pooling concept . . . . . . . . . . . . . . . . . . . . . 354.3 Power density spectrum of four OFDM subcarriers . . . . . . .. 364.4 Power density spectrum of a single OFDM subcarrier [2] . .. . . 374.5 Impact of FFT processing on the power density spectrum ofthe

LU [2] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

5.1 Example of an OFDM frame containing data and pilot symbols[3](redrown) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

5.2 Illustration of two cascaded Wiener filtering in frequency and timedirection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

5.3 Pilot pattern for (a) the first and (b) the second transmitantennas.Black boxes are pilots, X is virtual pilot, 0 is zero and white boxesare data. Adopted from a SISO Hexagonal pattern. . . . . . . . . 47

5.4 Received Hexagonal frame pattern on both of the receive antennas 485.5 Rectangular Pilot pattern withdf = 2 . . . . . . . . . . . . . . . 485.6 Resulting pattern for Rectangular Pilot pattern withdf = 2 . . . . 495.7 Rectangular Pilot pattern withdf = 4 . . . . . . . . . . . . . . . 49

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5.8 Resulting pattern for Rectangular Pilot pattern withdf = 4 . . . . 505.9 Licensed user existence and subcarrier deactivation . .. . . . . . 515.10 Pilot shift due to Licensed user existence . . . . . . . . . . .. . . 52

6.1 MMSE Basic system Individual links Hexagonal, Rectangular dis-tance 4 and Rectangular-Virtual distance 2, normalized Doppler=0.02 54

6.2 MMSE Basic system Averaged links Hexagonal, Rectangular dis-tance 8 and Rectangular-Virtual distance 4, normalized Doppler=0.02 55

6.3 BER Basic system Hexagonal, Rectangular distance 4 and Rectangular-Virtual distance 2 Patterns, normalized Doppler=0.02 . . . .. . . 56

6.4 Concept of Virtual pilot Interpolation . . . . . . . . . . . . . . .. 566.5 MMSE Basic system Hexagonal, Rectangular distance 4 and Rectangular-

Virtual distance 2, normalized Doppler=0.0005 . . . . . . . . . .596.6 BER Basic system Hexagonal, Rectangular distance 4 and Rectangular-

Virtual distance 2 Patterns, normalized Doppler=0.0005 . .. . . . 606.7 MMSE Cognitive Radio+LU, Cognitive Radio without LU, and

Basic system, Hexagonal pattern, normalized Doppler=0.02 .. . . 616.8 BER Cognitive Radio+LU, Cognitive Radio without LU, and Ba-

sic system, Hexagonal pattern, normalized Doppler=0.02 . .. . . 626.9 Reduced power of the subcarriers adjacent to the LU. . . . . .. . 636.10 MMSE Cognitive Radio+LU, Cognitive Radio without LU, and

Basic system, Hexagonal pattern, Reduced Power, normalized Doppler=0.0005 636.11 BER Cognitive Radio+LU, Cognitive Radio without LU, and Ba-

sic system, Hexagonal pattern,Reduced Power, normalized Doppler=0.0005 65

A.1 Sliding Window Technique . . . . . . . . . . . . . . . . . . . . . 73A.2 Filter Window Formate . . . . . . . . . . . . . . . . . . . . . . . 74A.3 Complete Wiener filtering process using Sliding Window onone

OFDM symbol . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

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List of abbreviations

1D - Single dimension2D - Two DimensionsAWGN - Additive White Gaussian NoiseBER - Bit Error RateCIR - Channel Impulse ResponseCR - Cognitive RadioCTF - Channel Transfer FunctionDFT - Discrete Fourier TransformDVB - Digital Video BroadcastingFFT - Fast Fourier TransformICI - Inter Carrier InterferenceIDFT - Inverse Discrete Fourier TransformIFFT - Inverse Fast Fourier TransformISI - Inter Symbol InterferenceLU - Licensed UserMIMO - Multiple Input Multiple OutputMMSE - Minimum Mean Square ErrorMSE - Mean Square ErrorOFDM - Orthogonal Frequency Division MultiplexingPACE - Pilot Aided Channel EstimationQoS - Quality of ServiceRU - Rental UserSISO - Single Input Single OutputUWB - Ultra Wide BandV-BLAST - Vertical Bell Laboratories Layered Space-TimeWSSUS - Wide Sense Stationary Uncorrelated Scattering

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Voorwoord

Dit afstudeerverslag heb ik geschreven in het kader van de opleiding tot elek-trotechnisch ingenieur in de telecommunicatie aan de TUDelft, overeenkomendmet de MSc-graad. Dit verslag is tot stand gekomen na het uitvoeren van een on-derzoeksopdracht binnen het onderzoeksinstituut IRCTR aan de Technische Uni-versiteit Delft. Dit verslag is bestemd voor onderzoekers,vakmensen en geinter-esseerden op het gebied van MIMO OFDM, Cognitieve Radio en schatting vanhet radio kanaal. Gedurende verschillende stadia van dit onderzoek, zijn het con-cept en de verkregen resultaten geevalueerd door veel andere wetenschappers enonderzoekers in het veld. Uit dit verslag zijn twee publicaties voortgekomen, eneen potentiele derde publicatie is zeer wel mogelijk. Ondanks abrupte gezond-heidsproblemen van mij en een heel langzaam herstel daarvanheb ik deze op-dracht met bevredigende resultaten volbracht. Daarom mijndank aan mijn afs-tudeerbegelieder de heer Dr. Homayoun Nikookar voor zijn goede en wijze raadgedurende de hele periode van dit onderzoek en voor zijn constructieve commen-taar tijdens het schrijven van mijn afstudeerverslag . Mijndank gaat ook uit naarmijn mentor Ibrahim Budiarjo voor zijn dagelijkse begeleiding en hulp tijdens hetonderzoek en voor zijn commentaar tijdens het schrijven vanmijn afstudeerver-slag. Verder is mijn dank aan mijn gezin tijdens deze periodeen in het bijzonderediegenen die mij hebben opgevrolijkt. Mijn dank ook aan de vrienden die opvele manieren een bijdrage hebben geleverd en aan iedereen die op welke wijzedan ook een bijdrage heeft geleverd om mijn lasten te verlichten. De winnaar isdiegene die het einddoel bereikt.

Delft, April 2009 Haval Abdulrahman

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Acknowledgment

I would like to thank my supervisor Dr. Homayoun Nikookar forsupervisingme during this research work. This research work has been finished successfullywith his guidance. The discussions with him have enriched meand this thesisvery much. I appreciate his understanding and patience during this research verymuch. I thank also my daily mentor Mr. Ibrahim Budiarjo for thehelp I got fromhim and for the useful discussions with him. The discussionswith him whichwhere sometimes very tough, have extended my knowledge and broaden my wayof thinking. I also thank my predecessor who made the SISO system and all theother engineers who contributed in realizing the SISO system.

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Abstract

The demand for high data rates in wireless communication systems is increasingas well the demand for new (communication) services. Expanding of existing ser-vices or introducing new services needs a portion in the radio spectrum. Meanwhile the radio spectrum is a scarce resource and is regulated by governmentalregulations and policies. Measurements done by the FCC show that the licensedspectrum is not always fully used and hence is not efficientlyutilized. This needfor spectrum resources and the unefficient use of it has lead to the birth of Cog-nitive Radio (CR). CR enables the efficient use of the radio spectrum and makesit possible for new services to operate adjacent to existingLicensed Users (LU)without suppressing their performance. There are several methodologies to realizeCR, one of those methodologies is Orthogonal Frequency Division MultiplexingOFDM. OFDM is one of those methods which is very suited to be used as amodulation and transmission technique in a CR system. OFDM issuited due toits multicarrier property and its robustness in the faded mobile wireless environ-ments. In almost all wireless applications the arrival of the transmitted messagein a good and acceptable quality is an agreement condition. Hence the Bit ErrorRate (BER) is important and must be boosted. Multiple Input Multiple Output(MIMO) has been known as a technique to enhance the transmission quality andcapacity. Learning and understanding capabilities in CR arecrucial to achieve thegoals of efficient spectrum utilization in terms of spectrumresources and energyresources. The wireless channel is central within this context, thus estimatingthe channel is the key to make CR operational, taking in consideration that thetransmission-reception technology is available. In this thesis, we design a MIMOsystem using OFDM modulation technology to transmit and receive two signalsover the mobile wireless channel. We use MIMO concept to enhance system ca-pacity and robustness of the wireless transmission. Due to the influence of thechannel on the transmitted messages and its importance in wireless transmissionto reconstruct the transmitted signals, the channel needs to be known as much aspossible. We gather knowledge about this wireless channel and try to estimate itusing training symbols called pilot symbols. We distributethe pilot symbols ina way were they can estimate the channel. The way those pilotsare organizedand implemented in the data stream is called the pilot pattern. We design threedifferent pilot patterns suitable for implementation in MIMO. Within the pilotpatterns, we implement the novel Virtual Pilot concept, to simplify the filteringprocess and to save energy, because the virtual pilots don’tconsume power. Wetest all three patterns. Based on their performance in estimating the channel, we

chose the best performing one and implement it in a MIMO OFDM based CR sys-tem. The performance of each pattern is measured by means of BER and MeanSquare Error (MSE). We assume that information about the LU is available fromspectrum sensing for the transmitter. Due to the propertiesof the OFDM frame(2D), the estimation is done by using Wiener filtering first infrequency directionfollowed by filtering in time direction. To reduce computation complexity of thefiltering process, we chose the cascaded Wiener filtering as 2x1D filtering insteadof 2D filtering, because the first have a comparable performance compared withthe last and have less computational complexity. Due to the MIMO structure, thereceived signal is the contributions from all transmit antennas. Those differentcontributions from the transmit antennas at the receiver need to be separated. Toseparate the different contributions form each other, we use the layering concept.Vertical Bell Laboratories Layered Space-Time (V-BLAST) is adetection algo-rithm to be used in each receiver to detect and separate the transmitted signals inthe received stream from each other.

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Chapter 1

Introduction

The impressive evolution of mobile wireless networks and the potential of wire-less multimedia communications increases the traffic in thenetwork and the needfor accessible radio spectrum. The number of new wireless applications increasesand some existing applications are expanding. This needs requires regulationsand licenses which is the case now a days. Wireless communication networks areregulated by licensing the radio spectrum. Most of the radiospectrum is alreadylicensed and assigned to different commercial and non commercial users who of-fer different services. Whether the radio spectrum is utilized efficiently is anotherquestion. New wireless services likeLTE, 4G will restrict the spectrum accesseven more and will hardly have any room to access the spectrum. Based on thesefacts, there is a common belief that we are running out of usable radio spectrum.Measurements done by the FCC’s spectrum policy task force to measure the ac-tual usage of the spectrum has shown that at any given time andlocation part ofthe licensed spectrum is idle and hence not occupied. This finding of the FCClet us conclude that the spectrum scarcity and crowdedness result from the inef-ficient use of the spectrum and the spectrum management policy rather than thephysical scarcity of idle spectrum. Several factors like the growing demand fornew communication services, the demand for high data rates which are requiredto cope with the different multimedia communications such as data, video andvoice packets each having different traffic requirements and the underutilizationof the radio spectrum have pushed communication engineers,researchers, eco-nomics and regulation institutes to invent new policies andtechnologies to utilizethe radio spectrum more efficiently and pushes the channel capacity to it’s limits.Beside this there is a large demand for portable, low power andsmall devices.Hence power regulation and consumption is an important issue. Joseph Mitolafrom KTH Sweden had a brilliant idea in 2000 introducing the concept of Adap-tive communication techniques. His concept calledCognitive Radio utilizes thespectrum in an opportunistic manner and makes it possible touse the gaps in the

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spectrum or any free space in the spectrum. Cognitive radio isaware and adap-tive to the radio environment. Cognitive radio provides the capability of usingor sharing the radio spectrum in an opportunistic manner. This technology has amechanism to flexible pooling of the radio spectrum using a set of rules that arecalledformal radio etiquettes. This approach will provide high bandwidth tomobile users via hetrogenious wireless architecture and dynamic spectrum accesstechniques [4].Several techniques have been proposed to be used for the modulation scheme ofcognitive radio. Orthogonal Frequency Division Multiplexing (OFDM) is consid-ered as a very suitable modulation technique for use in cognitive radio becauseof it’s multicarrier characteristics and spectrum efficiency. The orthogonality be-tween the subcarriers of OFDM makes its spectrum more efficient. OFDM hasbeen used and its robustness has been observed in several currently available sys-tems such as IEEE 802.11a, IEEE 802.11g and the European standard for DigitalAudio Broadcasting (DAB) and Digital Video Broadcasting (DVB).In the wireless channel, transmitted signals are received through multipath whichare usually destructively and result in performance degradation (fading). Henceexploiting the spatial diversity of the wireless environment by using Multiple InputMultiple Output (MIMO) expands the system capacity (higherdata throughput)and it combat the faded channel effectively. It has been shown in the literature [5]that the capacity of a single transmit antennas system increases logarithmicallywith the number of receive antennas. Meanwhile, the capacity of a MIMO systemwith equal number of transmitters and receivers increases linearly. Implement-ing MIMO leads to improvement in the data transmission reliability (very lowBER). MIMO is the most effective technique to accomplish reliable communi-cation through the wireless channel where the receiver is provided with indepen-dently faded replicas of the transmitted signal. These advantages are achievablewithout any increase of the transmitted power or expansion of the bandwidth.Several independent signals are transmitted from several antennas. Those signalsare independent. In cognitive radio systems estimating thechannel state informa-tion or the channel transfer function of the radio channel iscrucial to know aboutthe channel and spectrum availability. Using proper techniques to estimate thechannel is very important and spending power on the estimates is an importantissue also especially because most devices are mobile todayand battery supplyis important. This gives us a strong drive to further exploitthe channel estima-tion method that gives the best performance. In OFDM, channel estimation canbe done in several methods. One of these methods is the Pilot Aided Channelestimation (PACE). In this thesis we investigate the PACE. Several pilot patternswhere pilot symbols are embedded in the OFDM stream are investigated for usein OFDM and in particular OFDM based cognitive radio. In OFDMbased cog-

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nitive radio a number of subcarriers has to be deactivated due to the existence ofthe License user. Hence the OFDM frame grid has to be adjustedto cope with thelicensed user occupation of the spectrum. The pilot patternin the region wherethe License user exists is also affected by this adjustment.At the receiver side, the signals received from different transmitters should bedetected and separated properly. Therefore, an efficient and accurate detectionalgorithm must be used at the receiver side. In this thesis weimplement the V-BLAST (Vertical-Bell Laboratories -Layered -Space-Time) algorithm at the re-ceiver. V-BLAST is used at the receiver unit to detect and separate the receivedsignals because of its significant gain [6]. This scheme increases the transmissionrate [5]. In this thesis work, a MIMO OFDM based cognitive radio is designedand tested. Channel estimation is implemented with the aid ofpilots (Pilot AidedChannel Estimation). Virtual pilot concept has been implemented in combinationwith real pilots. Different pilot patterns are tested. System performance is judgedaccording to the less Mean Square Error (MMSE). Based on this performance thebest pilot pattern is chosen and implemented in the cognitive radio system. Wienerfiltering is used to estimate the channel. We consider the 2x1D Wiener filteringas our channel estimation technique. The 2x1D Wiener filtering is much simplerthan the complex 2D Wiener filtering, and their performancesare close to eachother. The above issues are addressed and proper solutions are presented in thisresearch work.

1.1 Thesis organization

This thesis is organized as follows. Chapter two describes the wireless channelmodel used in the simulations. In chapter three, OFDM and MIMO concept arediscussed. Cognitive radio and spectrum pooling are studiedin chapter four. Inchapter five the channel estimation procedure is addressed.Simulation results andanalysis are discussed in chapter six. Finally, conclusions and recommendationsfor future work are given in chapter seven and chapter eight respectively.

1.2 Motivation

The motivations behind this work are as follows:

1. OFDM has been known as a suitable candidate to be used in CR systemsbecause of its flexibility and spectral efficiency, but the estimation in OFDMis a challenging issue.

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2. MIMO has been known as a technique in improving the wireless system per-formance by exploiting the channel spatial diversity, but integrating MIMOwith OFDM is a challenging task because the pilot pattern design becomesmore complex.

3. Enhancing system capacity and estimation performance from previous workon combination of virtual pilot concept and Hexagonal pilotpattern in SISOOFDM by exploring the spatial diversity of the channel by theapplicationof MIMO.

4. Simplifying the filtering process and saving energy by utilize virtual pilotswithin the pilot patterns in the MIMO system.

5. Finding the best performing pilot pattern between several designed pilotpatterns and implementing the best performing pattern in the CR system.

1.3 Novelties of the work

This work has several novelties which can be addressed as follows:

1. Virtual pilot concept utilization in MIMO OFDM pilot pattern. Three MIMOpilot patterns have been observed:

• Two varieties of Rectangular pilot pattern (comb type) with differentspacings in each direction.

• Modified Rectangular pattern to two Hexagonal patterns with the aidof virtual pilots (comb type)

2. Observing the best performing pattern in terms of bit error rate and meansquare error and implementing this pattern in a cognitive radio MIMO sys-tem.

3. Implementing V-BLAST detection algorithm on the estimates for our MIMOin combination with virtual pilot concept in the context of cognitive radio.

4. Implementing of the combination of virtual pilot conceptand the optimumpilot pattern out of the three observed patterns in the CR context.

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Chapter 2

The Mobile Wireless Channel Model

2.1 Introduction

The signal undergoes multipath fading while propagating through the wirelesschannel due to the physical properties of the channel and anyobstructions in theenvironments. The received signal through the multipath fading channel is the su-perposition of many deferent replicas of the signal components received throughreflection, refraction and scattering. There are typicallya large number of suchreplicas with time varying amplitudes and phases. These fluctuations in the signalstrength are difficult to characterize deterministically.The channel can be seenas a random attenuation applied to the signal. Statistical characterization of thechannel gives a suitable solution if the correct assumptions are made. The chan-nel coefficients observed are a complex Gaussian random process. It has a zeromean (Rayleigh fading channel since the absolute value of thechannel gain is aRayleigh random variable) if there is no dominant line of sight component oth-erwise the mean is not zero and the channel is then Rician fading (according tocentral limit theorem). Applying this channel coefficientsto a signal is in factthe time varying channel transfer function. Hence the channel impulse responseCIR is the inverse Fourier transformIFT of the channel transfer functionCTF .The characterization of the complex Gaussian random processesCIR andCTFis done statistically by using the autocorrelation function. The multipath structurecan be be characterized in time domain using the power delay profile (multipathintensity profile) for wireless channels. This model shows the relative powers ofthe received signal through different delays. The extent ofthis function is the mul-tipath spread of the channel. The multipath spread is the time difference betweenthe shortest and longest paths which the signal goes through. The channel cor-relation function and it’s Fourier Transform characterizethe time and frequencyvariations of the fading channel.

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The Doppler power spectrum shows the amount of frequency shift and the spectralbroadening of the received signal. The Doppler spread (BD) is the range of fre-quencies where the Doppler power spectrum is not zero. The inverse ofBD is thecoherence time of the channel(∆t)c where we assume that the channel remainsthe same.

2.2 Wide Sense Stationary Uncorrelated Scattering(WSSUS) channel model

In the previous section we introduced the mobile wireless channel briefly and sawthat it is necessary to characterize or model the channel statistically. Dependingon that we must chose a suitable stochastic channel model. Itis mentioned in theliterature [7] that the uncorrelated dispersiveness in time delay and Doppler shiftsare exhibited by the WSSUS channel model introduced by Bello [8]. Further itwas shown that this model fits into many channels of practicalinterest. In thismodel Linear superposition of uncorrelated scatterers is assumed and wide sensestationarity at least for short periods of time is assumed also. In this thesis wehave observed and considered the discrete time Wide Sense Stationary Uncorre-lated Scattering (WSSUS) as our channel model [7]. This modelis based on theJakes model which uses theTap Delay Line model where the amplitude of alltaps are subject to Rayleigh fading. The Impulse response is [9]:

h(τ, t) =

Np∑

p−1

cp(t)δ(τ − τp) , p = 0, 1, . . . , Np (2.1)

whereNp is the number of taps,cp(t) are the time-dependent complex coeffi-cients for the taps which represent the channel impulse response for each path inthe multipath channel, andτp is the delay of thepth tap. The model assumes sameDoppler spectra for each tap. This model and further assumptions are used tosimplify the correlation function. The mobile radio channel is assumed to be widesense stationary random process. This means that the statistical properties of thechannel remains constant over small periods of time or smallspatial distances. i.e.contributions with different Doppler shifts are uncorrelated and that contributionswith different delays are uncorrelated. For the case ofRayleigh fading channelthe mean power and the Doppler spectrum do not change with time while the in-stantaneous amplitude can change [9]. The channel is given by the time variantchannel impulse responseCIR h(τ, t) which is the ensemble of theNp propaga-tion paths. Taking the fast Fourier transform of theCIR gives the channel transferfunction (CTF ) which is symbolized byH(f, t) .

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In multipath propagation channel the channel impulse responseh(τ, t) is com-posed of a number of scattered impulses received overNp paths [3].

h(τ, t) =

Np∑

p=1

ap expj(2πfD,pt+φp) δ(τ − τp) (2.2)

whereap, fD,p, φp andτp are the amplitude, Doppler frequency, phase and prop-agation delay respectively associated with thepth path. The Doppler frequencyfD,p is given by:

fD,p =υfc

ccos αp (2.3)

whereυ is the velocity of the mobile user,c is the speed of light(3× 108m/sec),fc is the carrier frequency andαp is the angle of incidence of the wave from thepth path. The probability density function(pdf) of the amplitude of the impulseresponse isRayleigh or Rician [7]. Hence using the correlation function will besufficient to characterize the fast fading. Further we assume that the channel haszero mean(Rayleigh fading). Thus due to the randomly time varying nature ofthe channel it is modeled by the autocorrelation function. Hence to characterizethe fast fading of the mobile radio channel we need to describe the correlationfunction of the channel impulse responseh(τ, t). The autocorrelation function ofh(τ, t) is described as:

Rhh(τ1, τ2; ∆t) =1

2E {h(τ1, t)h

∗(τ2, t + ∆t)} (2.4)

where∆t is the observation time,τ is the path delay,E is the expectation takenover the ensamble of possible impulse responses, and∗ denotes the complex con-jugate value. We assumed that the channel is a random processandh(τ1, t) andh(τ2, t) are uncorrelated whenτ1 6= τ2 i.e. the channel response associated withmultipathτ1 is uncorrelated with the response associated with the multipath com-ponent atτ2 since the two components are caused by different scatterers(uncorre-lated scattering channel) , then (2.4) simplifies to:

Rhh(τ1, τ2; ∆t) = ρ(τ1, ∆t)δ(τ1 − τ2) (2.5)

whereρ(τ, ∆t) is the delay cross power spectral density [3].This is the characterization function for the WSSUS mobile radio channel. TheFourier transform ofρ(τ, ∆t) in ∆t gives the scattering function as:

S(τ, fD) =

∫

∞

−∞

ρ(τ, ∆t)e−j2πfD∆td(∆t) (2.6)

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The scattering function (2.6) is a measure of average outputpower of the channelas function of the delayτ and the Doppler frequencyfD. This scattering functionhas a real value and can be used to obtain the delay power density spectrumρ(τ)by integrating (2.6) over the Doppler frequencyfD as:

ρ(τ) =

∫

∞

−∞

S(τ, fD)dfD (2.7)

This delay power density spectrum (2.7) is identical to the delay cross powerspectral densityρ(τ, ∆t) at ∆t = 0. Hence the delay power density spectrumgives the average output power of the channel as a function ofthe delayτ andcan be viewed as a scattering function averaged over all Doppler shifts. Furtherthe channel can be characterized by several other parameters which are explainedbelow.

2.2.1 Power Delay Profile

One important parameter of the channel is the power delay profile Rhh(τ) whichrepresents the average power (also called multipath intensity profile) associatedwith a given multipath delay. In the literature, it has been shown that the expo-nentially decaying power delay profile is a good approximation for most practicalchannels [10]. It is important to know about the channel power delay profile asexact as possible, because it must match the power delay profile used for the fil-ter design (see appendix B) as much as possible. However in oursystem thereis some mismatch between the power delay profile of the channel and the powerdelay profile used for the filter design. This mismatch is explained in our resultsin ch. 6, however minimizing this mismatch requires more research. In this thesis,the exponentially decaying function is used in the channel model. The maximumdelay spread and the Doppler spread correspond to the maximum delay time andfrequency component in the power spectra. The correlation function of the chan-nel RHH(∆f) is derived from the power delay profile via theFFT . It can berepresented when∆t = 0 as:

RHH(∆f) = E {H∗(f)H(f + ∆f)} (2.8)

= FFT {Rhh(τ)}

=po

k + 1

(

k +1

1 + j2π∆fστk1

)

(2.9)

where:k1 = (k + 1)/

√2k + 1 (2.10)

po is the normalized received power which is the sum of the received powers,k isthe Raciank-factor which is the ratio of the dominant path’s power to thepower

10

in the scattered path. In the time domain we can write the autocorrelation functionfor ∆t = 0 as:

Rhh(τ, ∆t) ⇒ Rhh(τ) ≈ Rhh(τ, 0) (2.11)

Meanwhile the average delay spread is:

τ =

∫

∞

0τRhh(τ)dτ

∫

∞

0Rhh(τ)dτ

(2.12)

This is the first moment of the delay power density spectrum [3]. The secondmoment of above equation is known as the RMS-delay spread and is:

στ =

√

∫

∞

0(τ − τ)2Rhh(τ)dτ∫

∞

0Rhh(τ)dτ

(2.13)

This formula represents the effective value of the time dispersion of the transmit-ted signal as resulted from the multipath propagation.In the frequency domain thechannel autocorrelation function of theCTF can be characterized as [3]:

RHH(f1, f2; ∆t) = E {h∗(f1; t1)h(f2; t2} (2.14)

=

∫

∞

−∞

∫

∞

−∞

E {h∗(τ1; t1)h(τ2; t2)} expj2π(f1τ1−f2τ2) dτ1dτ2

=

∫

∞

−∞

∫

∞

−∞

Rhh(τ ; ∆t) expj2π(f1−f2)τ dτ

= Rhh(∆f ; ∆t) (2.15)

where∆f = f1 − f2.For slowly time varying channel, the value ofRhh(∆f ; ∆t) calculated with verysmall observation time is almost similar to the one when∆t = 0.

RHH(∆f ; ∆t) ∼= Rhh(∆f ; 0) = Rhh(∆f) (2.16)

(2.16) is called the frequency correlation function which is the Fourier transformof the power delay profile:

RHH(∆f) =

∫

∞

∞

Rhh(τ) exp−j2π∆fτ dτ (2.17)

The frequency(∆f)c is called theCoherence Bandwidth where the signal prop-agation characteristics are correlated. This bandwidth isproportional to the recip-rocal of the delay spread (2.13):

(∆f)c ≈1

5στ

(2.18)

11

2.2.2 Doppler power spectrum

Another important parameter to characterize the channel isthe Doppler powerspectrum of the channel. To represent the Doppler power spectrum we need tocharacterize the channel in the frequency domain. The autocorrelation functionis:

Rhh(f1, f2; ∆t) = E {h∗(f1; t1)h(f2; t2)} (2.19)

=

∫

∞

−∞

∫

∞

−∞

E {h∗(τ1; t1)h(τ2; t2)} expj2π(f1τ1−f2τ2) dτ1dτ2

=

∫

∞

−∞

∫

∞

−∞

Rhh(τ ; ∆t) expj2π(f1−f2)τ dτ

= Rhh(∆f ; ∆t) (2.20)

where∆f = f1 − f2

When the previous assumption of∆t = 0 is still valid:

Rhh(∆f, ∆t) ≈ Rhh(∆f ; 0) = Rhh(∆f) (2.21)

whereRhh(∆f) is the frequency correlation function which can be written as:

Rhh(∆f) =

∫

∞

−∞

Rhh(τ) exp−j2πfτ dτ (2.22)

Which is the Fourier transform of the power delay profile.Taking the Fourier transform ofRhh(∆f, ∆t) with respect to∆t gives the Dopplereffect:

S(∆f, fD) =

∫

∞

−∞

Rhh(∆f ; ∆t) exp−j2πfD∆t d∆t (2.23)

To characterize the Doppler at a single frequency,∆f is put to zero.

S(0, fD) = S(fD) =

∫

∞

−∞

Rhh(∆t) exp−j2πfd∆t d∆t (2.24)

This function is the Doppler power spectrum of the channel which describesthe power spectral density of the channel as a function of theDoppler. TheCoherence T ime (∆t)c of the channel is the duration over which the channelcharacteristicsCIR can be considered as time invariant. The coherence time isproportional to the reciprocal of the maximum Doppler frequency. The coherencetime can be defined as the time where the time correlation function is above 0.5and is approximated by [3]:

(∆t)c ≈9

16πfDmax

(2.25)

12

2.3 The MIMO Channel model

With the increasing demand for data rate and reliability in Wireless communica-tions and devices, several issues become very important like bandwidth efficiency,quality of service and radio coverage. Because the radio spectrum is almost fullyoccupied, hence time and frequency domains are also fully occupied. The spacedomain can deal with these limitations. Exploring the spatial domain can be donein several manners and is called spatial diversity. In this thesis we explore thespatial diversity by having multiple transmitters and multiple receivers. The chal-lenges we face when we apply MIMO with OFDM are explained in ch. 5 whereimplementing MIMO in OFDM is explored and proper solutions are provided.

When having multiple transmit and receive antennas, the signal (data) is trans-mitted through a number of different independent paths in a multipath fading en-vironment. Hence different replicas of the transmitted signal are received. Duringpropagation through the wireless channel the received signal will undergo differ-ent (independent) channel fades providing spatial diversity. Signals obtained formdifferent diversity channels have to be combined at the receiver to detect the trans-mitted symbol. In a uniform scattering environment, half wavelengthλ

2spacing is

sufficient to obtain independent fading. Without loss of generality, in this thesiswe put our attention to a 2x2 MIMO system. The channel model isbased on thewide sense stationary uncorrelated scattering (WSSUS) model. Each of the chan-nel links uses the WSSUS model. We assume that the channel fading statisticsremain constant over short periods of time or small spatial distances (the channelis aimed constant during at least one OFDM symbol) and the different subchan-nels are uncorrelated. This model has the following channelimpulse responsecir:

hn,k = limn→∞

1√

Np

Np∑

i=1

expj(φi+2πfDiTsk−2πτiFsn) (2.26)

wheren andk are the frequency and time indices of the channel/link,NP is thenumber of multipath components.φi, fDi andτi are the random phase, randomDoppler shift and random delay respectively which characterize each pathi. Ts

andFs are the symbol and carrier spacing respectively.

In 2x2 MIMO system (M=2 transmit antennas,N=2 receive antennas) two spatialstreams (uncorrelated or independent) are transmitted. Due to multipath propa-gation the signal travels along different paths. We assume 4independent links orsubchannels in the MIMO channel.The fading gain along the propagation path between each transmit antenna and areceive antenna isCIRmn. When the fading gains are organized in a matrix, the

13

complex channel matrix will be formed. This matrix is a complex matrix. Usinga linear model the received vector at one of the receivers is:

y = CIRchannel × s + noise (2.27)

whereCIRchannel is theMxN channel matrix,s is the transmitted signal vector(in case of OFDM modulations is a symbol) of size 1xM and thenoise is of size1xN of independent complex Gaussian noise. The noise term at different receiveantennas are independent. The received signal covariance matrix is:

Ryy = CIRchannel × Rss × CIRHchannel (2.28)

whereRss is the received signal covariance matrix andH denotes the Hermitianmatrix (complex conjugate transpose). The channel is characterized not only bythe amplitude statistics of each matrix entry, but also by the correlation betweenthese entries. Equation (2.27) can be expanded further to determine the signals atthe two receive antennas separately as:

y1 = s1 × CIR11 + s2 × CIR21 + n1

y2 = s1 × CIR12 + s2 × CIR22 + n2(2.29)

wherey1 andy2 are the vectors received by receive antennasN1 andN2 respec-tively. s1 and s2 are the transmitted signal vectors from transmit antennasM1

andM2 (all variables are in time domain).CIR11, CIR12, CIR21, CIR22 are thechannel impulse responses of the different subchannels, while n1 andn2 are thenoise vectors of AWGN with zero mean on the two receive antennas. Those twonoise vectors are independent of each other. Taking theFFT of theCIR givesthe frequency domain channel matrixCTF as:

CTF2X2 =

(

CTF11 CTF21

CTF12 CTF22

)

(2.30)

This is valid for one position carrier index and symbol index. Putting (2.29) inmatrix form gives:

(

y1

y2

)

=

(

CIR11 CIR12

CIR21 CIR22

)(

s1

s2

)

+

(

n1

n2

)

(2.31)

2.4 Doppler effect

The Doppler frequency was introduced briefly in sec 2.2. In this section we studyit in more detail. In general case when there is movement of one of the sta-tions/users, the different components of the received signal will have different

14

Doppler shifts. In this thesis we simulate (see ch. 6) two Doppler frequencies.A low one corresponding with pedestrians velocity and a highone correspondingwith vehicular velocity. This Doppler shift will lead to a phase change and can berepresented as:

∆φ =2πυ∆t cos αp

λ(2.32)

where∆φ is the carrier phase change,υ is the velocity of movement (vehicularspeed),∆t time interval,αp is the angle of incidence andλ is the wavelength. TheDoppler phase shift can be represented also as:

φD,p(t) =

∫

t

2πfD,pdt = 2πfD,pt (2.33)

wherefD,p is the Doppler frequency of thepth path. The phase of thepth multi-path component is:

φp(t) = 2πfcτp − 2πfD,pt − φo (2.34)

whereτp is the multipath delay. Then the Doppler frequency can be defined as thephase change due to the movement of the mobile during the infinitesimal interval∆t.

fD = − 1

2π.∆φ

∆t(2.35)

Putting (2.32) in (2.35) gives:

fD =υ

λcos αp = fm cos αp (2.36)

wherefm is the maximum Doppler frequency deviation from the transmitted car-rier frequency due to the mobile movement andαp is the angle of incidence.

fm =υ

λ=

υfc

c(2.37)

wherec is the speed of light. Maximumfm corresponds withαp = 0o and180o.The higher the vehicular speed the higher the Doppler frequency and the faster thetime domainCIR fluctuation (wider Doppler spread) will be.

2.5 Chapter Summary

In this chapter we introduced the mobile wireless channel and its important prop-erties for our research . Further we introduce a statisticalmodel for this channel.Based on our specific case we study the Wide Sense Stationary Uncorrelated Scat-tering channel model to represent our channel. The parameters which characterize

15

this channel model such as the power delay profile and the Doppler power spec-trum are studied. From those parameters, the frequency correlation function andtime correlation functions are derived. Due to relevance ofthe thesis, the channelmodel is expanded to fulfill the MIMO requirements and finallydue to mobilityof the user, the Doppler effect was studied .

16

Chapter 3

MIMO OFDM

3.1 OFDM Modulation and Demodulation

In a single carrier transmission system over frequency selective fading channel,ISI is a common problem. To cope with it sophisticated equalization techniquesand complex signal processing can be used. To prevent or minimizeISI withoutusing relatively complex signal processing we employ multicarrier transmissionin the same frequency band. i.e. if the overall available bandwidth is W . Thisbandwidth is split intoNc frequency sub-bands(W/Nc). Each of those sub-bandsexperiences flat fading. The symbol duration on each multicarrier component is≈ Nc/W which can be made much larger than the multipath spread of thechannelso that the subchannels do not experienceISI. The overall transmission rate isstill W symbols per second [5]. OFDM is such a multicarrier modulation tech-nique. A serial high rate source stream is mapped on to multiple parallel low ratesubstreams. Each substream is modulated on a different subcarrier as depictedin Fig. 3.1. Hence data is transmitted in parallel, i.e. the lower rate streams aresimultaneously (parallel) transmitted over a number of lower rate subcarriers.

The spectrum of OFDM is shown in Fig. 3.2. From the figure we seethat thosesubcarriers are overlapping. Transmitting in parallel increases the symbol dura-tion for the lower rate parallel subcarriers [1]. This reduces the relative amountof dispersion in time caused by multipath delay spread. To save bandwidth in anOFDM signal, the carriers are arranged in a way that the sidebands of the individ-ual carriers overlap as shown in Fig. 3.2 and the signals are still received withoutadjacent carrier interference. To achieve this, the carriers needs to be mathemati-cally orthogonal. The word orthogonal means that the frequencies of the carriersin the system have a precise mathematical relationship. Thus the carriers needto be linearly independent. This linear independence can berealized only if the

17

Serial symbol

duration

Time

Fre

qu

ency

Time

Fre

que

ncy

Parallel symbol duration

(a)

(b)

Figure 3.1: (a) Serial and (b) Parallel symbol transmission

carrier spacing is a multiple of1/Ts, whereTs is the symbol period. The signalobtained from the OFDM demodulator will be integrated over asymbol period torecover the transmitted data. This integration will be zerofor the other subcarriersif the frequencies of those subcarriers (in time domain) have an integer number ofcycles in the symbol periodT .

Figure 3.2: OFDM spectrum, one subcarrier (left) and five subcarriers (right) [1]

OFDM is the most appropriate candidate to be used for the future communicationtechniques such ascognitive radio or smart radio. This is because in OFDM,

18

individual subcarriers can be deactivated (subcarriers are fed with zeros) depend-ing on the availability of the channel. It supports data rates which fulfill the needsof communication today with sufficient robustness of the radio channel. OFDMcan handle multipath propagation efficiently and it is robust against frequency se-lective fading or narrow band interference, because only a certain number of thesubcarriers could be affected. Affected subcarriers can berepaired using errorcorrecting codes. The performance of the OFDM link is determined by the aver-age received power rather than the power of the weakest carrier.

The receiver acts as a bank of demodulators. It converts eachcarrier down toDC. To recover the original data, the resulting signal is integrated over a symbolperiod. The discrete time OFDM model is shown in Fig. 3.3.

IFFT

A/D

Channel

D/A

FFT

Sn Xk S(t)

r(t)YkRn

Figure 3.3: Discrete Time OFDM model

A guard timeTg is built in every OFDM symbol to eliminate intersymbol inter-ference (ISI). The guard time is chosen larger than the expected delay spreador maximum delay of the channelτmax such that multipath components from onesymbol do not interfere with the next symbol, the guard time could consist of ei-ther no signal at all (zero padding). Or the OFDM symbol is cyclically extended(cyclic prefix) in the guard time. In this case the last part of the OFDM symbolis copied and put in front of the symbol. This is explained in Fig. 3.4.

Tg ≥ τmax (3.1)

whereTg is guard interval duration andτmax is maximum delay of the channel.The duration of an OFDM symbol after inserting the guard interval will be:

Ts = Tg + Ts (3.2)

whereTs is the OFDM symbol duration andTs is the OFDM symbol durationinclusive guard interval. To preventISI The discrete lengthLg of the guardinterval (samples) should be:

Lg ≥⌈

τmaxNc

Ts

⌉

(3.3)

19

Symbol 1 Symbol 2Tg

Time

Symbol 1 Symbol 2

CyclicPrefix

Symbol 1 Symbol 2

τmax Time

Figure 3.4: Guard Interval

A block diagram of an OFDM communication system is shown in Fig. 3.5.

Serial/

ParallelIFFT Parallel/

Serial

Insert

Guard

Interval

D/A

Parallel/

SerialFFT Serial/

Parallel

Remove

Guard

Interval A/D

Propagation

Channel

h(τ,t)

+

{Sn} {Xk} X(t)

y(t) n(t){Rn}

{Yk}

Figure 3.5: OFDM Communication System

After inserting the guard interval the sampled sequenceXk (see Fig. 3.5) withcyclic extended guard interval will be:

Xk =1√Nc

Nc∑

n=1

Snej2π(n−1)(k−1)/Nc (3.4)

wherek = 1 − Lg, ..., Nc andSn is the to be transmitted sequence consisting ofNc complex valued source symbols,n = 1, . . . , Nc. The difference in the numberof carrier spacing between two adjacent subcarriers withintheFFT interval mustbe an integer otherwise there is loss of orthogonality and asa result, this willcauseICI. By doing this, Delayed replicas of the OFDM symbol always have aninteger number of cycles within theFFT interval.A more detailed diagram of the multicarrier modulator-demodulator is shown inFig. 3.6. The data sequenceSn wheren = 1, . . . , Nc consisting ofNc complexvalued symbols is transmitted in parallel onNc subcarriers. These symbols areinterpreted as values in the frequency domain. The sequenceSn of rate1/T whereT is the total rate (symbol per second) (all symbols) of the sequence consisting of

20

Serial/

Parallel

Parallel/

Serial

Parallel/

Serial

Channel

Serial/

Parallel

g(t)

g(t)

g(-t)

g(-t)

2 sNj tTe

π

2 sNj tTe

π−

Si

sNc

Yl,i

S(t)

Y(t)

Sn

+ AWGN

Figure 3.6: Multicarrier Modulator and Demodulator

Nc symbols are mapped ontoNc parallel substreams. Hence the source symbol(one symbol) rate per substream reduces to:

1

Ts

=1

Nc.T(3.5)

whereTs (µ sec) is the OFDM symbol duration without guard interval,Nc isthe number of subcarriers andT is the source symbol duration (before OFDMmodulation). To achieve orthogonality between the signalson theNc subcarriers(see Fig. 3.2) assuming rectangular pulse shaping, the spacing of each subcarrierneed to be:

Fs =1

Ts

(3.6)

The mathematical representation of the signals(t) which will propagate throughthe channel is as follows:

s(t) =1√Nc

Nc∑

n=1

Sng(t)ej2πfnt (3.7)

whereSn represents the source symbols,n = 1, ..., Nc, Nc is the number of sub-carriers,g(t) is the pulse shaping filter which maps the digital information to ananalog waveform andfn is the frequency of each subcarrier. The location of theNc subcarrier frequencies are:

fn =n − 1

Ts

(3.8)

21

wheren = 1, ..., Nc andTs is the OFDM symbol duration and is equal toTs =Nc.T whereT is the source symbol duration of the whole sequence. The keyadvantage for implementation purposes of OFDM is the use ofIFFT andFFTas shown in the discrete time model Fig. 3.3 of OFDM. The discrete time OFDMsignal can be represented mathematically as:

Xk =1√Nc

Nc∑

n=1

Snej2π(n−1)(k−1)/Nc (3.9)

wherek = 1, ..., Nc. During one OFDM symbol the channel must not change(time invariant). The fading per subcarrier is then flat fading. hence the OFDMsymbol duration must be smaller than the channel coherence time (∆t)c andthe subcarrier spacing should be smaller than the channel coherence bandwidth(∆f)c.

The output of the channel as can be seen in Fig. 3.5 is the signal y(t). Thissignal result from the convolution of the signalX(t) with theCIR represented byh(τ, t) followed by the addition of noisen(t) (AWGN). This channel output canbe mathematically represented as:

y(t) =

∫ τmax

0

x(t − τ)h(τ, t)dτ + n(t) (3.10)

The signaly(t) will be digitalized after passing through the A/D converter. Theresult will be the discrete sequenceYk wherek = 1 − Lg, ..., Nc. The firstLg

samples of the sequenceYk could haveISI and hence those are removed beforeOFDM demodulation. The remainingISI free partk = 1, ..., Nc of Yk will passthe OFDM demodulation unit whereDFT or FFT is applied. The result of thisDFT is the sequenceRn wheren = 1, ..., Nc in frequency domain which consistsof Nc complex valued symbols and can be represented as:

Rn =1√Nc

Nc∑

k=1

Yke−j2π(n−1)(k−1)/Nc (3.11)

wheren = 1, ..., Nc. Assuming that the fading on each subchannel is flat andthere is noISI, the received symbolRn in frequency domain can be written as:

Rn = HnSn + Nn (3.12)

wheren = 1, ..., Nc. Hn, Sn, andNn are theCTF of the channel, the transmit-ted symbol and the AWGN of thenth subcarrier respectively. Now the OFDM

22

Serial to Parallel Parallel to Serial{Sn} {Rn}

S1

S2

SNc

R1

R2

RNc

H1 N1

H2 N2

HNc NNc

Figure 3.7: Simplified frequency domain view of OFDM Transmission system

transmission system can be simplified as shown in Fig. 3.7. AnOFDM symbolconsists ofNc subcarriers and an OFDM frame consist of a block ofNs subse-quent OFDM symbols as shown in Fig. 3.8.

The frame duration isTfr = NsT′

s, whereNs is the number of OFDM symbolsandT ′

s is the OFDM symbol duration including the guard interval. The sequenceSn, n = 1, ..., Nc of Nc source symbols transmitted in one OFDM symbol has thevectorial representation:

s = (S1, S2, ..., SNc)T (3.13)

The assigned received sequenceRn, n = 1, ..., Nc which is obtained afterDFThas the vectorial form of:

r = (R1, R2, ..., RNc)T (3.14)

From (3.13) and (3.14) the received vector is obtained as:

r = Hs + n (3.15)

whereH is theNcXNc channel matrix which is of Diagonal type in the absenceof ICI.

H =

H1 0 ... 00 H2 ... 0. . . .. . . .. . . .0 0 ... HNc

(3.16)

23

Symbol on

subcarrier n

1

Nc

T’s

Fs=1/Ts

Sub

carie

rs

Sub

carie

rs

OFDM symbolsNs

Nc

1

1

n

OFDM symbol OFDM frame

Tfr=NsT’s

Time

Fre

que

ncy

Figure 3.8: Time-Frequency Representation of an OFDM symboland OFDMframe

The diagonal components ofH are the complex valued flat faded coefficientsHn,n = 1, ..., Nc. The noise (AWGN) vector on theNc subcarriers is:

n = (N1, N2, ..., NNc)T (3.17)

Finally the sequenceXk, k = 1 − Lg, ..., Nc of eq.(3.4) of an OFDM symbolincluding the guard interval at the output of the OFDM modulator which is theIDFT of the input vector (3.13) has the vectorial form:

x = (x1−Lg, x2−Lg, ..., xNc)T (3.18)

The received sequenceYk, k = 1 − Lg, ..., Nc at the input of the OFDM demodu-lator including the guard interval has the following vectorial form:

y = (y1−Lg, y2−Lg

, ..., yNc)T (3.19)

The vectorr in (3.15) is theDFT of the vectory after removing the guard intervalfrom y.

The requirements for the frequency domain implementation are the absence of

24

ISI and ICI, time invariant during one OFDM symbol and flat fading condi-tion per subcarrier. If these requirements are fulfilled, the discreteCTF can berepresented as [3]:

Hn,i = H(nFs, iT′

s) =

Np∑

p=1

apej(2πfD,piT ′

s+φp)e−j2πnFsτp (3.20)

whereap, fD,p , Ts, φpis the amplitude, the Doppler frequency of the OFDMsymbol duration with guard interval, the phase and propagation delay of thepthpath respectively,Fs is the subcarrier spacing. TheCTF is sampled in time atOFDM symbol rate1/T ′

s and in frequency at subcarrier spacingFs. The OFDMsymbol durationT ′

s includes the guard interval duration.

3.2 Generation of an OFDM signal

The subcarriers (certain number) of an OFDM signal are modulated usingPSKor QAM . Those subcarriers are created using inverse Fourier transform IFFT .The OFDM signal can be represented as [1]:

s(t) =

Nc2−1∑

i=−Nc2

di+Nc2

exp(j2π( iTs

)(t−ts)) , ts ≤ t ≤ ts + Ts (3.21)

s(t) = 0 , ts + Ts < t < ts

wheredi are the complexQAM symbols,Nc is the number of subcarriers andTs

is the symbol duration. Each subcarrier has exactly an integer number of cyclesin the intervalTs , and the number of cycles between adjacent subcarriers differsby exactly one (orthogonality between the subcarriers). The orthogonality in (??)could be demonstrated as follows: Each OFDM symbol containssubcarriers thatare nonzero overTs seconds interval. Hence the spectrum of a single symbol is aconvolution of a group of Dirac pulses located at the subcarrier frequencies withthe spectrum of a square pulse that is one forTsec period and zero otherwise. Theamplitude spectrum of the square pulse issinc(πfTs), which has zeros for all fre-quenciesf that are an integer multiple of1/Ts. Other proves of orthogonality andthe demonstration of it could be found in [1]. Each subcarrier can be modulatedfree from the interference of other subcarriers, because ateach subcarrier spec-tra position, all other subcarriers spectra contribution are zero, and because theOFDM receiver calculates the spectra values at those maximums of the individualsubcarriers. See Fig. 3.2 which shows that the spectrum fulfills Nyquist criterion.

25

Serial to

Parallel OFDM

Signal

QAM

data

c s sj N (t-t )/Teπ

c s sj (N -2)(t-t )/Teπ

Figure 3.9: OFDM Modulator

3.3 OFDM parameters

The OFDM system has a number of parameters which have to be taken into con-sideration, such as the number of subcarriers, guard time, symbol duration, sub-carrier spacing, modulation type per subcarrier and the type of error correctingcode. The choice of the different parameters is a trade off between the varioussystem requirements such as available bandwidth, requiredbit rate, tolerable de-lay spread and Doppler values. Some requirements could be conflicting. Forexample to get a good delay spread tolerance, a large number of subcarriers witha small carrier spacing is desirable. The delay spread directly prescribes the guardtime. As a rule the guard time should be about two or four timesthe RMS of thedelay spread. Higher order QAM (64 QAM) is more sensitive to ICI and ISI thanQPSK. While heavier coding reduce the interference sensitivity. The symbol du-ration is also a very important parameter.Ts symbol duration must be much larger(not arbitrary large) than the guard time, to minimize the bitrate loss caused bythe guard time. But large symbol duration means more subcarriers with smallersubcarrier spacing, a larger implementation complexity and more sensitivity tophase noise and frequency offset as well as an increased peak-to-average powerratio. A practical choice is to make the symbol duration at least five times theguard time, which corresponds to 1dB SNR loss because of the guard time. Thenumber of subcarriers is determined by dividing the required bit rate by the bitrate per subcarrier. The bit rate per subcarrier is defined bythe modulation type,coding rate and BER symbol rate.

26

3.4 MIMO model

We employ the MIMO concept in our simulation platform because it has beenproven that MIMO can achieve a major breakthrough in providing reliable wire-less communication links. This reliability is in the context of the channel estima-tion in our case. With the MIMO concept we improve the bitrateand BER of theoverall system. MIMO is capable of this improvement, because of the property ofmultiple transmission multiple reception. This property is a form of spatial diver-sity. This diversity is the most effective technique to accomplish reliable commu-nication over the wireless channel and combating with fading, because it providesthe receiver with multiple copies of the transmitted signal. Those multiple copiesare independently faded. If at least one copy of the transmitted signal is receivedcorrectly, we will have the transmitted signal back. This property improves theBER significantly (low BER) as shown in ch 6. Beside this, MIMO increases thechannel capacity also, which means more throughput. There are different ways toexploit multiple antennas at both sides of the communication channel. To improvethe transmission reliability, the transmit antennas should be used such that trans-mit diversity is achieved. The transmission rate is comparable to the one obtainedin SISO. To improve the transmission rate, independent signals are transmittedfrom the different transmit antennas. i.e. there is no correlation between the trans-mitted signals from the different antennas. In this case thereliability is not muchimproved [5]. The block diagram of the MIMO system for the transmitter side andthe receiver side are shown in Fig. 3.11. The channel is represented as a tappeddelay Line which hasK taps. According to this model the received signal at timet for theMxN MIMO system is given by [5]:

yr(t) =K−1∑

k=0

M∑

i=1

h(k)i,r (t)si(t − k) + nr(t) (3.22)

wheresi(t) is the transmitted signal from antennai at timet, h(k)i,r (t) is the channel

coefficient for thekth path from transmit antennai to receive antennar at timet.nr(t) is the Additive White Gaussian Noise.

For mobile communications, the channel tap coefficients arerandom variables. Incase the wireless channel varies very slowly, the tap coefficients remain constantfor each frame of data. For Rayleigh fading channels, the channel tap coefficientsare modeled as complex Gaussian random variables which havezero mean. Thedifferent channel taps are assumed to be independent. The average channel gainsfor different paths are determined from the power Delay profile of the wirelesschannel. In this work we assume that the channel tap powers decays exponen-tially. Hence we use the exponential power delay profile. If the MIMO-OFDM

27

h11

h12

h21

h22

Tx1

Tx2

Rx1

Rx2

Figure 3.10: MIMO setup

system hasNc subcarriers and the fading coefficients are spatially uncorrelatedand that the fading coefficients remain constant during one OFDM symbol. Thenthe transmitted signal overM antennas can be represented by a matrixXOFDM

with dimensionsNcxM . A symbol transmitted at subcarriern on transmit antennai is xi(n).At the receiver after applyingFFT and removing the cyclic prefix, the resultingsignal at thejth receive antenna for thenth subcarrier will be:

yr(n) =M∑

i=1

xi(n)Hi,r(n) + nr(n) (3.23)

whereHi,r(n) is the channel coefficient from theith transmit to therth receiveantenna for thenth subcarrier and is given by:

Hi,r(n) =K−1∑

k=0

h(k)i,r e−j2πnk/Nc (3.24)

where we can denote the channel coefficients for the(i, r)th links by:

Hi,r = [Hi,r(0) Hi,r(1) . . . Hi,r(Nc − 1)] (3.25)

The vector ofK independent fading coefficients of the different taps can berep-resented by:

Ai,r =[

h(0)i,r h

(1)i,r . . . hK−1

i,r

]

(3.26)

Hence we can see that the equivalent channel coefficients are:

Hi,r = WAi,r (3.27)

28

whereW is theFFT matrix. In (3.27) the fading coefficients for distinct subcar-riers are different but dependent. The maximum rank of the (frequency domain)channel matrix is equal to the number of tapsK, and is usually low. The time

Rx1

Rx2

RxN

GI

removal

GIremoval

GI

removal

Pilots

extraction

for Tx1 ...TxM

Pilots extraction

for Tx1 ...TxM

Pilots

extraction

for Tx1 ...TxM

Channel

Estimation for link

Tx1 ...TxM – Rx1

Channel

Estimation for link

Tx1 ...TxM – Rx2

Channel

Estimation for link Tx1 ...TxM – RxN

V-BLAST

Signal processing

PSK/QAM

Demapping

Tx1

PSK/QAM

Mapping

TxM

Detected

Bits

PSK/

QAM

Mapping

Pilots &

DataMultiplexer

S/P IFFTGI

insertion

Tx1

Pilots

DMUXSource

Bits P/S

Tx2

TxM

(a) Transmitter

(b) Receiver

Figure 3.11: MIMO System model (a) Transmitter and (b) Receiver

domain signals at the receive antennas can be represented as:

y1 = s1 ∗ CIR11 + s2 ∗ CIR21 + n1

y2 = s1 ∗ CIR12 + s2 ∗ CIR22 + n2(3.28)

wherey1 andy2 are the vectors received by receive antennasRX1 andRX2 respec-tively. The transmitted signal vectors by transmit antennasTX1 andTX2 are repre-sented bys1 ands2 where all variables are in time domain.CIR11, CIR12, CIR21

andCIR22 are the channel impulse responses of the different subchannels, whilen1 andn2 are the noise vectors (AWGN) with zero mean on the two receive an-tennas. Those two noise vectors are independent of each other. Putting (3.28) inmatrix form gives:

(

y1

y2

)

=

(

CIR11 CIR12

CIR21 CIR22

)(

s1

s2

)

+

(

n1

n2

)

(3.29)

Taking theFFT of the CIR gives the frequency domain channel matrixCTFas:

CTF2X2 =

(

CTF11 CTF21

CTF12 CTF22

)

(3.30)

29

3.5 Chapter Summary

In this chapter we gave an introduction to parallel transmission in OFDM and itsadvantages regarding spectrum efficiency and interferencerobustness. A concep-tual comparison between serial transmission and parallel transmission was plot-ted. The block diagrams of the OFDM modulator and demodulator and the com-plete OFDM system were introduced. Further to prevent ISI, the guard intervalmeasure and its conditions was studied. An example of the OFDM frame and themathematical representation of the OFDM signals and the channel matrix weredemonstrated. Generation of the OFDM signal and the different OFDM parame-ters were studied. And finally the MIMO channel model was introduced.

30

Chapter 4

Cognitive Radio

4.1 Introduction

The use of the radio spectrum is regulated by governmental rules. Almost allparts of the radio spectrum are licensed today. The FCC published a report in[11] where the spectrum use in the United States is presentedin the aim of betterspectrum utilization. Major findings of this report as mentioned in [12] are”Inmany bands, spectrum access is a more significant problem than physical scarcityof spectrum, in large part due to legacy command-and-control regulation thatlimits the ability of potential spectrum users to obtain such access.”If we wereable to scan portions of the radio spectrum, we would observethat [12]:

1. Some frequency bands in the spectrum are largely unoccupied most of thetime.

2. Some other frequency bands are only partially occupied.

3. The remaining frequency bands are heavily used.

From above observation we see that actually the spectrum is underutilized. Weobserve also that there are free portions of spectrum (spectrum holes). In [12] thespectrum hole is defined as :”A band of frequencies assigned to a primary user,but at a particular time and specific geographic location, the band is not beingutilized by that user”. CR as defined in [12]is an intelligent wireless communica-tion system that is aware of its surrounding environment (i.e. outside world), anduses the methodology of understanding-by-building to learn from the environmentand adapt its internal state to statistical variations in the incoming RF stimuliby making corresponding changes in certain operating parameters (e.g. Transmitpower, Carrier frequency and modulation strategy) in real time, with two primarygoals:

31

• Highly reliable communications whenever and wherever needed.

• Efficient utilization of the radio spectrum.

Cognitive radio (CR) offers the possibility of exploiting the existence of spectrumholes. Those spectrum holes can be used by a secondary user which is termed astherental user[13] when there are spectrum holes which are not occupied by theprimary user (Licensed User (LU)). The rental user is a CR based system sinceit requires the capability to sense the spectrum. A researchon the application ofOFDM based CR including the spectrum sensing platform on a demonstrator plat-form has been performed under the Dutch AAF project [14]. TheCognitive radio(CR) concept was initiated by Joseph Mitola III at KTH Sweden. Cognitive radiowas born due to the scarcity of free radio spectrum portions and hence to sufficethe need of accessible radio spectrum and the need of transmit power control toprevent and minimize any unnecessary interference with other devices. CR is anovel approach for improving the utilization of the radio spectrum. In the contextof cognitive capability we can extract six key words from this definition: aware-ness, intelligence, learning, adaptivity, reliability and efficiency. Implementing allof those capabilities is possible today because of the advances in digital signalprocessing, networking machine learning and computer software and hardware.In principle the CR must be able to [15]:

1. Determine which portions of the spectrum are available and detect the pres-ence of licensed users operating in the licensed band (spectrum sensing).

2. Select the best available channel (spectrum management).

3. Coordinate access to this channel with other users (spectrum sharing).

4. Clear the channel when a licensed user is detected (spectrum mobility).

Above procedures are shown in the basic cognitive cycle in Fig. 4.1. The CR in-teracts with the environments by the cognitive cycle. Such aCR observes the en-vironments continuously, orients itself, create plans, decides and then acts. How-ever the CR have a sleep and prayer periods. A sleep period (theperiod where theradio is not being used) is long, but has sufficient electrical power to process ma-chine learning algorithms without being detracted from itsmain communicationpurpose. During the prayer period, any not resolved machinelearning opportu-nities are resolved. Details about the cognitive cycle and its different periods aredescribed in [13].

32

Spectrum

Decision

Radio Environment

Spectrum Sensing

Spectrum Analysis

RF

StimuliRF

Stimuli

Spectrum Holes

Information

Transmitted

Signal

Channel

capacity

Spectrum Holes

Information

Figure 4.1: Basic Cognitive Cycle

4.2 Spectrum pooling

Spectrum pooling is part of the radio resource management. This managementincludes the assignment of allocated spectrum to communications functions toemploy that spectrum efficiently. The spectrum allocation is regulated by gov-ernmental rules and licenses, where parts or portions of theradio spectrum areauthorized for use of a specific purpose i.e. GSM, Radar, Navigation, . . . etc. Asthe economical value of some services increases due to the advances in the tech-nology, the spectrum needs to be re-allocated from less utilized bands to moreutilized bands. CR offers a technology-based mechanism called spectrum poolingmethod. This method enhances the utilization of the radio spectrum by enablingthe access to a part of the radio spectrum without disturbingthe actual LU. It en-ables the secondary utilization of already licensed frequency bands by a secondaryuser called the rental user [16]. The rental user may temporarily rent the radiospectrum during idle periods of the licensed user as illustrated in Fig 4.2. Beforeusing the free gaps, the spectral activity of the licensed user needs to be analyzed.FFT may be used to analyze the spectral activity. MeanwhileFFT is used inthe OFDM demodulator also. In this thesis we assume that, theinformation fromspectrum sensing about the LU is available at the transmitter side. Hence we knowwhich subband is occupied by the LU. The detection algorithmused for spectrumpooling is based on two major assumptions. The first assumption is that a higherlayer protocol such as medium access control (MAC) must be implemented in therental user. This MAC layer of the rental user must guaranteethe silence of all

33

rental users during the detection period. Hence any remaining spectral power ac-tivities in the air are those emitted by licensed users. The second assumption isthe non line of sight (NLOS) transmission between the transmitting licensed userand the detecting rental user. The reason for this second assumption is because theNLOS is the worst case scenario. This assumption is to ensurethat in a real systemwith a potential line of sight situation, the detection result can only get better thanthe results derived under the assumed worst case scenario. Details about this al-gorithm are described in [17] and [18]. Network infrastructure and mobile deviceintelligences are the important issues to realize this method optimally. Howeverin this thesis we don’t discuses this subject in depth. In order to efficiently fill thespectral gaps unutilized by the licensed user during his ownidle state, the rentaluser needs to be highly flexible with respect to the spectral shape of the transmit-ted signal. This flexibility is absolutely necessary and canbe realized by usingsuitable transmission techniques. As mentioned earlier inthis thesis OFDM is asuited candidate to be used in CR because of its spectral efficiency and flexibilityin notching its spectrum by deactivating its subcarriers individually. The basicidea of spectrum pooling with OFDM is to match the bandwidth of one sub-bandof the licensed user system with an integer multiple of the subcarrier spacing usedin the OFDM rental user. In spectrum pooling system, the mutual interferencebetween the OFDM based rental user and the licensed user could still occur. Dueto the property of OFDM, part of the spectrum form the OFDM based CR rentaluser will be smeared and interfere the LU while part of the spectrum of the LUis vice versa interfering the rental user as depicted in Fig.4.5. This interferencecan be avoided or minimized by deactivating subcarriers adjacent to the licenseduser subbands. This deactivation means sacrificing some of the bandwidth of therental user. In addition to this deactivation, we go one stepfurther, part of thesignal smeared in LU band which is called as sidelobes can be further reduced bydecreasing the power of the symbol on the carriers adjacent to the deactivated car-riers. In our simulations we decrease the power of some pilots which are adjacentto the deactivated pilots gradually to minimize any sidelobe effect as shown inch 6. Another method of sidelobe reduction is by windowing the OFDM symbolstransmitted signal in the time domain which makes the amplitude go smoothly tozero at the symbol boundaries. An example of window is araised cosine window.The domain window is multiplied point by point with the time domain OFDMsignal. Details about window types are given in [2]. In real life we do not knowwhat kind of transmission or modulation a licensed user is using or based on.Some times we know some parameters about the LU, i.e. in TV band, DVB someparameters are available in references. If the LU is not orthogonal to the rentaluser, synchronization is an important issue, however synchronization violates theassumption on spectrum pooling mentioned above. But even if LU and the rental

34

user are not synchronized, spectrum pooling can be implemented. Important issueis low mutual interference. This interference is shown in our simulations in ch 6.

f

OFDM

subcarriers of the Rental User

Subbands allocated

to Licensed Users

Deactivated subcarreirs due

to Licensed user access

Additionally deactivated

subcarriers

Figure 4.2: Spectrum Pooling concept

4.3 Interference

The interference from the rental system to the LU and vice versa is shown in oursimulation results in ch. 6 and is analyzed. But first we explain this interferencemathematically. The interference from the rental user to the LU is caused by thesidelobes of the OFDM used by the rental system as its transmission technique, asexplained in sec 4.2 and Fig 4.4 and Fig 4.3. If the transmitted signals(t) on eachOFDM subcarrier have a rectangular shape. Then the power density spectrum ofthis signal can be represented as [19]:

Φss(f) = a2Ts

(

sin πfTs

πfTs

)2

(4.1)

wherea is the signal amplitude,Ts is the OFDM symbol duration including theguard interval andf is the subcarrier frequency. If we assume that one LU sub-band have a bandwidth∆f which is equal to the reciprocal of the OFDM symboldurationT without guard interval.

∆f =1

T(4.2)

∆f is the subcarrier spacing of the rental user.

4.4 Chapter Summary

In this chapter an introduction about cognitive radio (CR) waspresented to pro-pose a solution for efficient spectrum utilization. The problem of spectrum underutilization was described by introducing FCC findings about the use of the radiospectrum. To understand the proposed solution, definitionsof Cognitive Radio,

35

−6 −5 −4 −3 −2 −1 0 1 2 3 4 5−0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

Interference power due tofirst adjacent subband

OFDM carrierspacing

Figure 4.3: Power density spectrum of four OFDM subcarriers

spectrum holes, the Licensed User and the Rental User were presented. In thecontext of cognitive radio, the spectrum pooling concept was introduced. Andfinally, some consequences like interference causes were discussed.

36

Figure 4.4: Power density spectrum of a single OFDM subcarrier [2]

Figure 4.5: Impact of FFT processing on the power density spectrum of the LU[2]

37

Chapter 5

MIMO OFDM Channel Estimation

We combine the MIMO concept in our OFDM based simulation platform to en-hance the transmission reliability. With the MIMO concept we improve the bitrateand BER of the overall system because of the property of multiple transmissionmultiple reception. This property is called spatial diversity. This property im-proves the BER significantly (low BER) as shown in 6. Beside this, MIMOincreases the channel capacity, which means more throughput and thus increasingthe bitrate. This diversity is the most effective techniqueto accomplish reliablecommunication over the wireless channel and combating withfading, because itprovides the receiver with multiple copies of the transmitted signal. Those multi-ple copies are independently faded when the distance between the two antennas issufficient (at least 0.5λ). Without this spatial diversity we will have only OFDMin the system (SISO), and the performance of the estimation will be limited be-cause we rely om a single link, which if severely faded we willhave a very badestimate. In order to detect and recover the transmitted data optimally, the chan-nel state information needs to be estimated. This information must be known atthe receiver in order to detect and separate the several received data streams fromeach other when there are more than one data stream or from anytraining symbolsused to estimate the channel. There are several methods to estimate the channellike training or pilot symbols channel estimation andBlind channel estimationor combination of both methods [3]. In the first method those pilot symbols areknown symbols and will be multiplexed with the data stream. Pilots are only usedfor channel estimation purpose. Hence in practice there is atrade off between thedensity of the pilots and the estimation quality. An exampleof an OFDM frameis shown in Fig. 5.1. The channel state information is estimated based on utilizingthe initial channel state on pilot position by dividing the received pilots with theknown transmitted pilots. In this thesis we consider the pilot aided channel esti-mation (PACE) method to estimate the MIMO wireless channel. There are threereasons behind our choice in using the PACE method:

38

1. Low complexity degree of this method PACE.

2. The performance of Hexagonal pilot pattern has been used and tested inSISO system (earlier work done in IRCTR [20]).

3. Test the performance of this method within MIMO system andobserve theimprovement compares to SISO.

Pilot insertion is done in two directions namely frequency direction and time di-rection respectively. In this work we use the cascaded 1D Wiener filter. Thiscascade results in 2X1D Wiener filtering (sec 5.2). 2x1D is preferable above 2Dbecause it has less computational complexity and its performance is comparableto 2D [3]. Details about 2D filtering are discussed in [3]. Thepattern in which thepilots are inserted or arranged, within the OFDM frame is called the pilot patternor pilot grid. In this thesis we design different pilot patterns (sec. 5.4) and testtheir performances (ch. 6) in 2X2 MIMO OFDM based system.

0

0

0

Time

Fre

qu

ency 1

1

Ns

Nc

Pilot symbol

Data symbol

Actual estimation position

Auto Correlation

Cross Correlation

Nt

Nf

Figure 5.1: Example of an OFDM frame containing data and pilot symbols[3](redrown)

5.1 Wiener-Hopf equations

The Wiener-Hopf equation can be written as [20]:

E

[

y(n − k)

(

y∗(n) −∞∑

i=0

ω0ix∗(n − i)

)]

= 0, k = 0, 1, 2, . . . (5.1)

whereω0i is theith optimum filter coefficient. After expanding and rearranging(5.1) we get [20]:

∞∑

i=0

ω0iE[x(n − k)]x∗(n − i) = E[x(n − k)y∗(n)], k = 0, 1, 2, . . . (5.2)

39

From (5.2) we can obtain two correlation expressions namely:

1. The autocorrelation function of the filter input in the period i − k which isRxx(i − k) = E[x(n − k)x∗(n − i)].

2. The crosscorrelation function between the filter input and x(n − k) andthe desired outputy(n) in time periodk which is Rxy(k) = Rxx(−k) =E[x(n − k)y∗(n)]

Hence using those two correlation functions, (5.2) can be rewritten as [20]:∞∑

i=0

ω0iRxx(i − k) = Rxy(k), k = 0, 1, 2, . . . (5.3)

This equation is called the Wiener-Hopf equation. In matrixfor it is written as:

Rxxω0 = Rxy (5.4)

The solution of the Wiener-Hopf equation is described as:

ω0 = R−1xxRxy (5.5)

5.2 2X1D Wiener filtering

Important aspects to be considered in implementing this filter for channel estima-tion purposes are given in sec 5.3.In this thesis, first the 2X1D filtering estimates the channelstate information (CSI)first in frequency direction on the pilots contained in the OFDM symbol. Afterthat the estimation of the channel state information is donein time direction. Theresults from the first estimation (in frequency direction) are used as inputs for thesecond estimation. In this way we have a cascade of two estimations. The filteringprocess is illustrated in Fig. 5.2. This filter is linear, hence the order of filteringdoes not influence the estimate. We have examined this part inour simulations. Inthis thesis we consider the wide sense stationary uncorrelated scattering channel(WSSUS) as our channel model. In this model it is assumed that the power de-lay profile and the Doppler power density are statistically independent. Thus theTime-Frequency correlation function can be separated into:

1. Frequency correlation functionRHH(∆f) as in (2.8) and (2.17) which isthe Fourier transform of the power delay profile

2. Time correlation function which is the inverse Fourier transform of theDoppler power density.

Sec. 5.3 gives more mathematical explanation of the 2X1D filtering process mean-while explanation of 2D filtering is given in [3].

40

0

0

0

Time

Fre

qu

ency

Pilot symbol

Data symbol

1

1

Ns

Nc

Second filtering on pilot symbol bearing OFDM symbols

Fir

st filteri

ng o

n

ea

ch s

ubca

rrie

r

Figure 5.2: Illustration of two cascaded Wiener filtering infrequency and timedirection

5.3 Channel Estimation

The channel estimation is applied by the aid of pilots. The pilots are multiplexedwith the transmitted data at the transmitting side and further at the receiver thepilots are separated from the data. The received frequency domain OFDM symbolwithin one OFDM frame will be [3]:

Yn,k = Hn,kSn,k + Nn,k n = 1, ..., Nc k = 1, ..., Ns (5.6)

whereHn,k is theCTF of the channel,Sn,k the transmitted symbol andNn,k isthe AWGN of thenth subcarrier andkth symbol respectively.Nc andNs arethe number of subcarriers and symbols respectively. The mean square error ofthe two cascaded filters working sequentially is calculatedin the following stepswhere superscript[1] refers to values and functions from the first filtering processand[2] refers to values and functions from the second filtering process.

1. The initial channel estimates which are the initialCTFs at pilot positionsare derived by dividing the received pilots by the transmitted pilots [3]

Hn,k =Yn,k

Sn,k

= Hn,k +Nn,k

Sn,k

,∀{

n, k}

∈ p (5.7)

wherep is the set of pilot positions within an OFDM frame.

2. The channel estimates obtained from the first estimation process (first 1Dfiltering) with filter coefficientω[1]

n are [3]:

H[1]n,k = ω[1]T

n hk (5.8)

41

The vectorhk represents the subset of the initial estimatesHn,k (5.7) of

thek-th OFDM symbol used for the estimation ofH[1]n,k. All pilots in one

OFDM symbol undergo this process. The vectorω[1]n represents the filter

coefficients, and is dependent on the frequency indexn only. The MinimumMean Square Error (MMSE) from the first estimation is [3]:

J [1]n = E

{

|Hn,k|2}

− RThhn

ω[1]∗

n − ω[1]Tn R∗

hhn+ ω[1]T

n Rφhhn,k

ω[1]∗n (5.9)

whereRThhn

is the cross-correlation between the pilots and the data.Rφhhn,k

is the autocorrelation between pilot symbols. The superscript T is the matrixtranspose operation and (∗) denotes the complex conjugate.

3. The estimates obtained form the second estimation process (second 1D fil-ter) using filter coefficientsω[2]

k are derived as [3]:

Hn,k = H[2]n,k = ω

[2]Tk h[1]

n (5.10)

The vectorω[2]k represents the second filter coefficients and is dependent

only on the time indexk. The vectorh[1]n represents the subset of the es-

timates which are obtained from the first filtering process. The vectorh[1]n

is used for the second filtering process on then-th subcarrier to estimateH

[2]n,k. All subcarriers undergo this operation. The Mean Square Error of the

overall estimation process (2X1D filtering) is [3]:

Jn,k = J[2]n,k

= E{

|Hn,k|2}

− E{

Hn,kh[1]Hn

}

ω[2]∗k

− ω[2]Tk E

{

h[1]n H∗

n,k

}

+ ω[2]Tk E

{

h[1]n h[1]H

n

}

ω[2]∗k (5.11)

where the superscriptH denotes the Matrix Hermitian operation. The cross-

correlation functionE{

Hn,kH[1]∗n,k

}

in above equation (5.11) is equal to the

discrete time correlation function. This discrete time correlation functioncan be written as [3]:

R[1]hh

−k−k= E

{

Hn,kH[1]∗

n,k

}

(5.12)

The difference between the estimates after the first filtering and the realchannel state is the estimation error. This estimation error can be repre-sented as [3]:

ε[1]n,k = H

[1]n,k − Hn,k (5.13)

42

This error is a zero mean noise process and its variance is represented by[3]:

E{∣

∣

∣ε[1]n,k

∣

∣

∣

}

= J [1]n (5.14)

From (5.12) and (5.14), the autocorrelation function in (5.11) could be writ-ten as [3]:

E{

H[1]n,k′H

[1]∗n,k′′

}

= J [1]n δk′

−k′′ + R[1]hh

−k′−k′′(5.15)

To obtain the mean square error with 2X1D filtering we insert (5.12) and(5.15) in (5.11). In (5.11)J [1]

n can be approximated as1/(γc10 log10(N[1]tap)).

This approximation is a result of the improvement of the SNR after the firstiteration. whereδk′

−k′′ is the Kronecker delta function,γc is the averageSNR per subcarrier at the input of the receiver andNtap is the number offilter taps. In order to reduce the channel estimation computational com-plexity, the sliding window method is used. In sliding window technique asubset of pilots instead of the complete set of pilots is usedin estimating thechannel state. The window size (filter length) is adjustable. There is a tradeoff between computational complexity and performance. Thebigger/longerthe filter length, the better estimation performance we get.At a certain fil-ter length, increasing the length will not give significant improvement anymore.This condition can be observed from our simulation results in ch. 6.

Important aspects regarding the low computational complexity for 2X1D filteringare:

1. The filter coefficientsω should be time invariant because the same filtercoefficient is used for all OFDM symbols.

2. The autocorrelation matrixRφhh should be independent of the actual coordi-

nates(n, k), so thatRφ−1hh can be precomputed and stored.

3. Different sets of the crosscorrelation vectorRhhn,kmay be precomputed and

stored taking in account symmetry in the pilot grid.

4. The optimum number of filter coefficients per estimation isthe number offilter tapsNtap which is equal to the number of pilots per OFDM frameNgrid. The computational complexity can be reduced significantlyby takingonly a subset of filter taps which is less than the number of pilots in theOFDM frame instead of all taps.

43

5.4 The Pilot Grid/Pattern design and Resulting Pat-tern

In this section we show the pilot grids that we designed for the two transmittersin the MIMO OFDM system. There are three different grids which have beenproposed and tested [21]. There performance are presented in ch. 6. In design-ing the pilot grids for MIMO, the pilot grid orthogonality between each transmitantenna should be taken care of. Fulfilling the orthogonality between the frames,the channel state information on each channel/link can be properly estimated. Af-ter propagation through the wireless channel, multiple replicas of the transmittedframes will arrive at the receiver side. Due to MIMO, at each receiver the framesfrom both transmitters will be received. Hence the receivedframe at each receiverwill be the combination of the two transmitted patterns, they will add up together.The resulting frame forms the desired type pilot pattern. Due to the orthogonalityof the pilot grid of each transmit antenna, the receiver can separate the pilots foreach transmit antenna. The pilot distance either in time or frequency direction inboth patterns has to fulfill the sampling theorem [3]. The coherence time and co-herence bandwidth determines the sampling period. The spacing between pilotsin frequency directiondf must be smaller than the channel coherence bandwidthand the pilot spacing in time directiondt must be smaller than the channel co-herence time. The maximum channel delay and the maximum Doppler frequencyof the filter will be the measures of the coherence bandwidth and the coherencetime respectively. The normalized filter bandwidths of the mentioned quantitiesare(τfilter/2)Fs andfDfilterTs respectively. According to the sampling theoremthe distance between pilots in frequency direction is:

df ≤ 1

τfilterFs

(5.16)

and in time direction is:

dt ≤1

2fDfilterTs

(5.17)

whereτfilter is the worst case estimated maximum delay of the channel,Fs is thecarrier spacing,fDfilter is the worst case estimated maximum Doppler frequencyfor the filter, Ts is the OFDM symbol time duration inclusive guard interval. Toguarantee the same sampling rate of the channel in frequencyand time direction,an optimum sampling of the channel transfer function is required. This optimumsampling is achieved by a balanced design. The balanced design is defined as [3]:

fDfilterTsdt ≈1

2τfilterFsdf (5.18)

44

To achieve a reasonable low computation complexity with respect to the filterlength and performance, the choice of approximately two times oversampling isa good choice [3]. We have observed that in our simulations and this choice hasbeen verified in [3]. With two times oversampling, the pilot distance in frequencydirection becomes:

df ≈ 1

2τfilterFs

(5.19)

while in time direction becomes:

dt ≈1

4fDfilterTs

(5.20)

It is obvious thatdf anddt must be integer values, hence (5.19) and (5.20) canonly be fulfilled approximately. We have observed in our simulations that puttingpilots in the edges of the OFDM frame will give better channelestimation. Hencefrom practical point of view it is preferable to design the pilot grid such that thefirst and last OFDM symbol, and the first and last subcarriers in the OFDM framedo contain pilots as shown in Fig. 5.2 [3]. The absence of pilots in the edges causethe channel estimator to predict those pilots on the edges which result in a largerestimation error.So far we have considered only the MSE of the channel estimator. An additionalcriteria for the efficiency of the channel estimation is the overhead and the loss indata rate due to pilot symbols. The overhead due to pilot symbols is the ratio ofthe total number of pilots per frame to the total number of OFDM symbols (pilots+ data + zeros) and it is given by [3]:

Λ =Ngrid

NcNs

(5.21)

whereNgrid is th number of pilots per OFDM frame,Nc is the number of subcar-riers andNs is the number of OFDM symbols. The loss in SNR in dB due to pilotsymbols is given by [3]:

Vpilot = 10 log10

(

1

1 − Λ

)

(5.22)

5.5 The Hexagonal and Rectangular pilot patterns

First we adopt the hexagonal pilot pattern from SISO system [22]. We separatethe hexagonal pattern into two rectangular (comb type) patterns [23]. One rectan-gular pattern is dedicated to one transmit antenna while theother one is dedicatedto the second transmit antenna. This resulting frame forms the desired hexag-onal type pilot pattern. Without loss of generality in this thesis we observed a

45

2x2 MIMO system. The pilot pattern for the first and the second(OFDM mod-ulated) transmitters are depicted in Fig. 5.3. The black boxes denote the pilotpositions, the X boxes are virtual pilot positions which we interpolate or extrapo-late in frequency and time direction according to (5.25) and(5.24) respectively asexplained in sec. 5.6. The boxes signed by 0s are entailed to have pilot orthogonal-ity between the first and the second pilot pattern. The orthogonality is preservedbecause the zeros or nulling are applied to reserve the position for pilots in theother transmitter frame. Data symbols are allocated to the white boxes. The pilotspacing in frequency direction for the patterns of Fig. 5.3 is 4 and the spacing intime direction is 6.

Second we design two new patterns which we call Rectangular pattern. We giveit this name because at the receive side the combined frames have a rectangularpattern. The pattern depicted in Fig. 5.5 have a pilot spacing of df = 2 in fre-quency direction and a spacing ofdt = 3 in time direction. The pilot spacing infrequency direction between real pilots is actually 4, but because we interpolate avirtual pilot in between two pilots (in frequency direction) according to (5.25) insec 5.6, this spacing is reduced to two. The final pilot spacings will bedf = 2 anddt = 3 in frequency and time respectively. Those spacings can alsobe observedin the resulting pattern at the receive side which is depicted in Fig. 5.6.

Now we design the third pilot pattern. We increase the pilot spacing in frequencydirection to 8 (between real pilots) and keep the pilot spacing in time directionthe same as depicted in Fig. 5.7. In this pattern we interpolate in frequency di-rection according to (5.25) twice. By doing this we decrease the pilot spacingin frequency direction todf = 4. The final pilot spacings of this pattern will bedf = 4 anddt = 3 in frequency and time respectively. The resulting pattern at thereceive side is depicted in Fig. 5.8.To calculate the number of pilots in a certain direction (frequency or time) we usethe general formula:

Np = 1 +

(

Nsym − A0

d

)

(5.23)

whereNp is the number of pilots in a one certain direction (frequencyor time),Nsym can be the number of active carriers or the number of OFDM symbols (seeTable 6.1 in ch 6) depending onNp orientation.Nsym is the number of subcarri-ers per OFDM frame if we intend to calculate the number of pilots in frequencydirection. MeanwhileNsym is the number of OFDM symbols per frame if we in-tend to calculate the number of pilots in time direction.A0 is the position of thefirst pilot symbol andd is the spacing between the pilots in that specific direction.We can notice from the pattern in Fig. 5.3 that the position ofthe virtual pilots for

46

X

X

0

X

0

X

0

X

0

X

X

0

0

X

0

X

0

X

X

X

x

0

X

0

X

0

(a) (b)

Figure 5.3: Pilot pattern for (a) the first and (b) the second transmit antennas.Black boxes are pilots, X is virtual pilot, 0 is zero and white boxes are data.Adopted from a SISO Hexagonal pattern.

both transmit antenna frames are the same. This condition reduces the process-ing complexity at the receiver. Virtual pilot concept will be explained in sec. 5.6.The resulting received frame at the receiver for the Hexagonal pattern is shownin Fig. 5.4. Mean while the resulting pattern at the receiverfor the Rectangularpatterns is shown in Fig. 5.6 and Fig. 5.8.

5.6 Virtual pilot concept

The virtual pilots are estimated from two neighboring pilots [24], [22] and [23].This means that virtual pilots in between two real pilots aredetermined by linearinterpolation as in (5.24) and (5.25). This is applied basedon the assumption thatthe channel changes very slowly between pairs of pilots. Thevirtual pilots at theedges of the frame are estimated by simple extrapolation of the most close by pi-lots. The final pattern will resemble as if twice pilot oversampling is applied. Theinterpolation or extrapolation of the virtual pilots is applied at the receiver side,before the MIMO data detection by utilizing V-BLAST. Applying virtual pilotshave several advantages and one minor disadvantage. It gives a better estimate ofthe channel as explained in sec. 5.4. It provides regularityof the pattern in termsof constant distance between deference pilot positions forthe filtering purpose bythe sliding window technique. At last virtual pilot conceptsaves energy, becauseit don’t uses energy. The disadvantage is the accumulation of the error due tointerpolation/extrapolation, and further additional computation are required. Theresulting pattern at the receiver is shown in Fig. 5.4.The interpolation can be expressed as:

Hn,k =1

2

[

Hn,k−1 + Hn,k+1

]

(5.24)

47

Figure 5.4: Received Hexagonal frame pattern on both of the receive antennas

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

(a) Rectangular with df=2 for Tx1 and Tx2

Figure 5.5: Rectangular Pilot pattern withdf = 2

or

Hn,k =1

2

[

Hn−1,k + Hn+1,k

]

(5.25)

whereHn,k−1 andHn,k+1 are the initial estimates of the previous and next pilot

symbols in time direction respectively, whileHn−1,k and Hn+1,k are the initialestimates of the previous and next pilot symbols in frequency direction. The deci-sion directed process applied in SISO system [22] is not included in our system.This is due to the overlapped received signals (addition of the signal from transmitantennas 1 and 2 at the receiver) on the virtual pilot positions that will give a highdecision error. The initial channel estimate on the boxes signed by 0s are derivedonly by linearly interpolating/extrapolating the adjacent pairs of initial estimateson the previously derived initial channel estimates on virtual pilot positions. Thelinear interpolating/extrapolating causes more error than the estimation from realpilots. This is the expense of having a regular comb pilot pattern. This regularityis important to obtain a proper and simple filtering process.The receiver on eachreceive antenna will separate the pilots from the data. The pilots dedicated to thefirst transmit antenna will be separated from the rest of pilots which are dedicatedto the other antenna. In this way the channel states on all links can be estimated.

48

0

0

0

0

0

0

(a) Resulting pattern with df=2

Figure 5.6: Resulting pattern for Rectangular Pilot pattern with df = 2

X

0

X

0

X

X

0

X

0

X

0

X

X

0

X

0

X

0

X

X

0

(b) Rectangular with df=4 for Tx1 and Tx2

Figure 5.7: Rectangular Pilot pattern withdf = 4

5.7 The pilots pattern and virtual pilot with respectto Licensed User

As mentioned in the earlier sections of this thesis, the LU isoccupying someparts of the radio spectrum as depicted in Fig. 5.9. The location of the spectrumband occupied by the LU should be considered in the design of our OFDM basedCognitive Radio. We are not allowed to operate our rental system in this portionof the spectrum because then the LU will be interfered by the rental user. Henceall subcarriers in this portion of the spectrum (the portionoccupied by the LU)must be deactivated as shown in the shaded part of Fig. 5.9 andFig. 5.10. Thisincludes the pilots located in those subcarriers. As a result we will have lesspilots to estimate the channel. Although the LU access reduces the pilot resources,the channel estimation module should be able to estimate thechannel with anacceptable performance. Therefore a pilot should always beavailable on the edgeof each field for the sliding window to slide. In this thesis ifthe position of thepilot is on the edge of the LU band or deactivated carriers, weshift the pilot oneposition, so it will be located on the edge of our band or adjacent to the LU band asdepicted in Fig. 5.10. Another aspect to be considered is that our signal should not

49

X

0

X

0

X

X

0

X

0

X

(b) Resulting pattern with df=4

Figure 5.8: Resulting pattern for Rectangular Pilot pattern with df = 4

interfere or deteriorate the LU by the presence of pilots in the adjacent subcarriersto the LU. In our simulations we assume that the information about spectrumoccupancy (which subband is occupied by the LU) is availablefrom spectrumsensing. This sensing information is known to the transmitter and receiver. i.e.transmitter and receiver know which subcarriers of the OFDMframe must bedeactivated in order not to interfere with the LU. Hence if some pilots are on thesubcarriers which needs to be deactivated, it will result inthe irregularity of thepilot pattern. This irregularity will cause a problem for the filtering process. Theirregularity makes the channel estimation module requiresseveral sets of slidingwindow filters. We solve this irregularity problem by shifting the pilots which layin the occupied subcarrier to an unoccupied subcarrier in a way that the regularityis recovered as depicted in Fig. 5.10. The pilot shifting gives a little loss of datarate, but MIMO could increase the data rate again. By keeping the regularity, theinterpolation or extrapolation (5.24) and (5.25) can be applied easily. It has beenexplained that pilot loss due to carrier deactivation can becompensated by pilotshifting. MSE degradation still occurs, applying virtual pilot concept is intendedto compensate the MSE degradation. The power of the pilots adjacent to the LUcan be adjusted in such a way that the side lobes of the RU to theLU will be small.

5.8 Chapter Summary

This chapter focuses on the channel estimation in the MIMO OFDM based sys-tem. The estimation concept (Pilot Aided Channel Estimation) was studied. Math-ematical modeling of the estimator was given by the finite impulse response filterlike the Wiener filter and its equations. How the filtering is applied in OFDMwas discussed. And how we implemented this filter in our simulations was alsodiscussed. The different designed pilot patterns were defined and plots of thosepatterns were given. Virtual pilot concept and its necessity was introduced. Fi-

50

X

X

0

0

X

0

X

X

X

0

X

(a) (b)

X

X

0

0

X

0

X

X

X

0

X

0

X

0

X

X

x

X

0

X

0

Rental

user

Licensed

user

Rental

user

Deactivated

Rental user

subcarriers

Time

Fre

quen

cy

1

Ns

Nc

Figure 5.9: Licensed user existence and subcarrier deactivation

nally the Licensed User and its effect on the Rental User and vice versa werediscussed.

51

X

X

0

0

X

0

X

X

X

0

X

(a) (b)

X

X

0

0

X

0

X

X

X

0

X

0

X

0

X

X

x

X

0

X

0

Lost pilot due to

subcarrier deactivation

Shifted

pilot

Deactivated subcarriers

due to Licensed user

existence

Rental user

Rental user1

Nc

1 Ns

1

1 Ns

Nc

Time

Fre

quen

cy

Figure 5.10: Pilot shift due to Licensed user existence

52

Chapter 6

Simulation Results

In this chapter we present the simulation results that we obtained from our 2x2MIMO OFDM based radio platform. Since the focus of the thesisis channel es-timation, we use a very fundamental model as mentioned in ch.2. The systemparameters used in the simulations are given in table 6.1. Weimplemented thethree pilot patterns which were designed in sec. 5.5 into thesimulation platform.The performance of those patterns in terms of MSE and BER are presented. Ac-cording to the MSE and BER performances, we chose the pattern which performsthe best to be implemented in our cognitive radio system. In acognitive radiocontext there will be licensed users occupying some parts ofthe band. Therefore,in the rental user side some subcarriers will be deactivated. We have also observeda scheme where the power of the adjacent subcarriers to the LUis decreased. Twokinds of Doppler frequencies have been considered. The two Doppler frequenciescorresponds to fast an slow movements of the mobile. Those two Doppler fre-quencies are normalized to the OFDM symbol duration. Further 3 different sizesof the filter length are used in the simulations. The size means the window size ineach filtering direction or the filter length. We use 4x4, 8x8 and 16x16 (Frequencydirection, Time direction) as the filter lengths. The 2x1D Wiener filtering is ap-plied in the channel estimation unit. The 2x1D Wiener filtering is chosen insteadof the 2D Wiener filter, since the previous one is less complexcompared to thelast one [3], while their performances are close to each other [3].

53

6.1 Performance of the Hexagonal, RectangularDf =

4 and RectangularDf = 2 pilot patterns in theBasic MIMO-OFDM system

First we observe the performance of the hexagonal pattern from Fig. 6.1 whichhas a spacing of 4 in frequency and 6 in time as shown in Fig. 5.3, this spacingwill be decreased to half of it (2 in frequency and 3 in time) after applying thevirtual pilot concept. On the same plot we observe the performance of the tworectangular patterns which have frequency spacings of 2 and4 respectively. Thespacing in time for the rectangular patterns remain the sameas in the hexagonalpattern as shown in Fig. 5.5 and Fig. 5.7 respectively.

0 5 10 15 20 25 30 35 4010

−3

10−2

10−1

100

SNR (dB)

MM

SE

Hexa link11Hexa link21Hexa link12Hexa link22Rect. dist.4 link11Rect. dist.4 link21Rect. dist.4 link12Rect. dist.4 link22Rect−Virt dist.2 link11Rect−Virt dist.2 link21Rect−Virt dist.2 link12Rect−Virt dist.2 link22

Figure 6.1: MMSE Basic system Individual links Hexagonal, Rectangular dis-tance 4 and Rectangular-Virtual distance 2, normalized Doppler=0.02

From Fig. 6.1 we observe 12 curves. Those curves represents the estimation per-formance on each link in the MIMO channel as explained in sec.3.4 and Fig. 3.10.We see from Fig. 6.1 that the hexagonal pattern performs the best because its MSEis the lowest compared with the other two. If we observe specifically on the hexag-onal pattern (the pattern with the smallest MSE), we will findthat the 4 links donot have the same performance. Link 11 and link 12 have a slightly better per-formance than link 21 and link 22. Link 11 and link 12 are estimated from the

54

pattern shown in Fig. 5.3a which is implemented in transmitter 1. This patternhas more real pilots than the other pattern in Fig. 5.3b whichwas implementedin transmitter 2. Hence the difference in performance is dueto the difference inthe number of pilots. Other reason of the estimation performance degradation isthe accumulating error while interpolating/extrapolating the virtual pilots. Thislittle difference in the individual link performance is even less for the rectangularpatterns. Because the rectangular pattern contains more pilots due to its structure.

Because the difference in performance of the individual links is small and to makethe comparison of the different pattern easier, we average the performance of theindividual links, then we obtain for each MIMO channel 1 performance curve asshown in Fig. 6.2 and Fig. 6.3.

0 5 10 15 20 25 30 35 4010

−3

10−2

10−1

100

SNR (dB)

MM

SE

Hexa 4x4FilterHexa 8x8FilterHexa 16x16FilterRect. dist.4, 4x4FilterRect. dist.4, 8x8FilterRect. dist.4, 16x16FilterRect−Virt dist.2, 4x4FilterRect−Virt dist.2, 8x8FilterRect−Virt dist.2, 16x16Filter

Figure 6.2: MMSE Basic system Averaged links Hexagonal, Rectangular distance8 and Rectangular-Virtual distance 4, normalized Doppler=0.02

In Fig. 6.2 we see that the hexagonal pattern outperforms theother two patterns.We run the simulation for 4x4, 8x8 and 16x16 filter lengths. For the different filterlengths we see that at almost 20dB SNR the performance of thispattern convergesand reaches a saturation point. Hence increasing the filter length does not affectthe estimation performance. This is because the effect of the virtual pilot. Dur-ing the interpolation or extrapolation of the virtual pilots, some error occurs. Thiserror accumulates in the estimation process degrading the estimation performance.

55

0 5 10 15 20 25 30 35 4010

−3

10−2

10−1

100

SNR (dB)

BE

R

BER Basic system Hexagonal, Rectangular ditance 4 and Rectangular−Virtual distance 2 Patterns, 0.02Doppler

Hexa 4x4FilterHexa 8x8FilterRect. dist.4, 4x4FilterRect. dist.4, 8x8FilterRect. dist.4, 16x16FilterRect−Virt dist.2, 4x4FilterRect−Virt dist.2, 8x8FilterRect−Virt dist.2, 16x16FilterHexa 16x16Filter

Figure 6.3: BER Basic system Hexagonal, Rectangular distance 4andRectangular-Virtual distance 2 Patterns, normalized Doppler=0.02

The error occurring due to interpolation or extrapolation of the virtual pilots canbe explained by means of Fig. 6.4.

P1 P2V

Figure 6.4: Concept of Virtual pilot Interpolation

In Fig. 6.4,P1 andP2 are two different real pilots in the OFDM grid in a certaindirection which is frequency or time direction.V is the virtual pilot in betweenthose two pilots which is obtained from linear interpolation or linear extrapolation.The estimateH1 on theP1 position is:

H1 = H1 +N1

P1

(6.1)

whereH1 is the initial estimate (received pilot divided by transmitted pilot) andN1 is the noise. From (6.1) we can see that the pilot is noisy, which leads to a

56

deviation error. The same is valid forP2, hence the estimate on theP2 position is:

H2 = H2 +N2

P2

(6.2)

whereH2 is the initial estimate (received pilot divided by transmitted pilot) andN2 is the noise combined with this pilot. From (6.1) and (6.2) weobtain theestimate on the virtual pilot position by averaging those two estimates as:

Hv =H1 + H2

2+

N1 + N2

2P≈ Hv + ∆Hv +

N1 + N2

2P(6.3)

whereHv is the estimate on the virtual pilot position,∆Hv is the deviation in theestimate on the virtual pilot position which is an error occurring due the mismatchresulting from the interpolation or extrapolation. This deviation occurs at eachvirtual pilot position and hence it accumulates to large values at the end of thefiltering process.

This accumulation can be explained by looking at (5.8) and (5.10), the small de-viations∆Hv from each virtual pilot are contained in the vectorh as representedby (6.4). Since the vectorh contains lots of virtual pilots, it contains lots of er-rors also as in (6.4). During the filtering process, the filtercoefficient vectorωis multiplied by the vector of estimatesh as in (5.8) and (5.10) leading to moreerror. Thus, the larger the filter length, the more virtual pilots are included in thefiltering and the more error is included in the estimation.

hV =

H1

V1

H2

V2...

HN

=

H1 + N1

P1

HV1+ ∆HV1

+ N1+N2

2P

...

(6.4)

H[1]n,k = ω[1]T

n hk (6.5)

Hn,k = H[2]n,k = ω

[2]Tk h[1]

n (6.6)

The error accumulation occurs due to the increasing number of virtual pilots in-volved in the estimation process while the filter size is increased. Hence thissaturation of the curves of the hexagonal pattern means alsothat the interpo-lation/extrapolation error propagates further and degrades the estimation perfor-mance.

57

From practical point of view, this means that at 4x4 filter size, this specific pat-tern has already a good performance, hence there is no need toincrease the fil-ter length. Increasing the filter size means adding extra computation complexity.Furthermore it costs memory resources and more computationtime. However,theoretically, increasing the filter size means increasingthe number of filter coef-ficients which consequently requires more pilots in order toestimate one CTF perwindow slide. This will lead to a more accurate estimate of the channel. In otherwords, when more pilots are involved in the estimation process, the correlationvalues will increase in the autocorrelation and crosscorrelation matrices in (5.9)resulting in smaller MSE.

Another factor that influence the MSE is the pilot distance. Increasing the pi-lot distance decreases the correlation between the pilots leading to decreasing thevalue inside the correlation functions. When the value inside the correlation func-tion decreases the MSE increases according to (5.9) and as indicated in appendixB. The rectangular pattern withDf = 2 performs better than the rectangularpattern with distanceDf = 4 because the pilot spacing is made smaller by anadditional interpolation of the virtual pilot as shown in Fig. 5.5. Decreasing thepilot distance makes the pilots more correlated. Accordingto (5.9) this leads tolower MSE. The pattern withDf = 2 is not influenced much by increasing thefilter size, because there are more virtual pilots in this pattern which means moreaccumulating error from the interpolation or extrapolation.

So far we observe that the pilot spacing influences the estimation performance.However the pilot spacing in frequency direction has to do with the maximumdelay of the channel as explained in section 5.4 and eq.(5.16). Hence the pilotspacing in frequency direction must fulfill (5.16). Otherwise, when the channeldelay increases, the filter will not work properly and the Mean Square Error willbe larger and thus the performance of the estimation will be degraded. In otherwords and according to the definition of the coherence bandwidth ,increasing thepilot spacing in frequency direction will decrease the frequency correlation func-tion value.

The BER performance of the patterns are depicted in Fig 6.3. Inthe literature[25] it is mentioned that the MSE is not always a translation of the BER. Thechoice of the modulation scheme influence the BER. A modulationscheme whichhas a small constellation size can still make the right decision of the bits at thedemodulator, even if the MSE is not very low. A modulation scheme which has alarger constellation size is more vulnerable for decision errors.

58

Fig. 6.5 depicts the MSE of the previous pilot patterns on lowDoppler frequency,while Fig. 6.6 shows their BER performance. From Fig. 6.5 and Fig. 6.6 we seethat the performance of all patterns at low Doppler frequency, improves comparedto the same patterns at high Doppler frequency of 82Hz at Fig.6.2 and Fig. 6.3.This is because when we decrease the Doppler frequency (decreasing the vehicu-lar velocity), the channel fluctuation in time decreases which means increasing thechannel coherence time. When the channel coherence time increases, the channelwill vary slowly, which means that the error occurring during the interpolation orextrapolation of the virtual pilots is less, leading to lessdegradation of the estima-tion performance.

The Doppler frequencies are normalized to the OFDM symbol duration with guardinterval. The High Doppler frequency (0,02 normalized) corresponds to:

0, 02

244 . 10−6≈ 82Hz

and the low Doppler frequency corresponds with:

0, 0005

244 . 10−6≈ 2Hz

0 5 10 15 20 25 30 35 4010

−3

10−2

10−1

100

SNR (dB)

MM

SE

Hexa 4x4FilterHexa 8x8FilterHexa 16x16FilterRect. dist.4, 4x4FilterRect. dist.4, 8x8FilterRect. dist.4, 16x16FilterRect−Virt dist.2, 4x4FilterRect−Virt dist.2, 8x8FilterRect−Virt dist.2, 16x16Filter

Figure 6.5: MMSE Basic system Hexagonal, Rectangular distance 4 andRectangular-Virtual distance 2, normalized Doppler=0.0005

59

0 5 10 15 20 25 30 35 4010

−3

10−2

10−1

100

SNR (dB)

BE

R

Hexa 4x4FilterHexa 8x8FilterHexa 16x16FilterRect. dist.4, 4x4FilterRect. dist.4, 8x8FilterRect. dist.4, 16x16FilterRect−Virt dist.2, 4x4FilterRect−Virt dist.2, 8x8FilterRect−Virt dist.2, 16x16Filter

Figure 6.6: BER Basic system Hexagonal, Rectangular distance 4andRectangular-Virtual distance 2 Patterns, normalized Doppler=0.0005

6.2 Performance of the Hexagonal pattern in the CRsystem with and without LU existence

According to the simulation results presented in the previous section, the hexag-onal ⇒ rectangular pattern outperforms the other two patterns. Therefore thispattern is chosen to be implemented in a CR scheme where some carriers willbe deactivated due to the LU access. In this CR system there is alicensed userwho occupies a subband equivalent to 40 subcarriers. Hence we deactivate 40OFDM subcarriers. In addition we deactivate 10 additional OFDM subcarrierson each edge of the deactivated OFDM subband. We do this additional subcarrierdeactivation to insure that we don’t interfere the LU. Two cases are simulated here.

The first one is when the LU is not active but there are deactivated subcarriersof the CR. This case could be seen as the lower bound of the CR scheme, becausethis is the minimum influence which we do to the CR scheme.

The other case is when the LU is active and thus subcarriers ofthe CRmustbe deactivated. The aim of the two cases of deactivation whenthe LU is activeand when the LU is not active is to observe the performance of the CR schemewhen some subcarriers are not available but there is no interference from other

60

systems like the LU, hence this is the lower bound. And when there are subcarri-ers deactivated in addition to LU interference.

The performance of the hexagonal pattern where 60 subcarriers are deactivatedare shown in Fig. 6.7 and Fig. 6.8. From the figures we see that the performanceof the hexagonal pattern is not significantly affected when subcarriers are deacti-vated and theLU is not active. As we deactivate subcarriers, the power assignedto a transmitter is kept the same. Hence the remaining activesubcarriers will havemore power including the pilots in theme. Those pilots with the extra power givesa better estimate of the channel because the degradation of the correlation matri-ces is compensated by the higher SNR as explained in sec 5.3 in(5.11) and (5.15).The trade off is that we lose some throughput because we are not transmitting anydata on the deactivated subcarriers.

When the LU is active, the performance of the hexagonal pattern is degraded(even if no more subcarriers than mentioned above are deactivated). This degra-dation is due to the interference which we suffer from the LU.This performancedegradation depends on the orthogonality of the LU with respect to the CR. In ourcase the LU signal is coming from a different transmission system which is notorthogonal to the CR system.

0 5 10 15 20 25 30 35 4010

−3

10−2

10−1

100

SNR (dB)

MM

SE

Hexa 4x4Filter + LUHexa 8x8Filter + LUHexa 16x16Filter + LUHexa 4x4Filter CR−NO−LUHexa 8x8Filter CR−NO−LUHexa 16x16Filter CR−NO−LUBasic sys. Hexa. 4x4FilterBasic sys. Hexa. 8x8FilterBasic sys. Hexa. 16x16Filter

Figure 6.7: MMSE Cognitive Radio+LU, Cognitive Radio without LU, and Basicsystem, Hexagonal pattern, normalized Doppler=0.02

61

0 5 10 15 20 25 30 35 4010

−3

10−2

10−1

100

SNR (dB)

BE

R

BER Cognitive Radio+LU, Cognitive Radio without LU, & Basic system, Hexagonal pattern, 0.02Doppler

Hexa 4x4Filter + LUHexa 8x8Filter + LUHexa 16x16Filter + LUHexa 4x4Filter CR−NO−LUHexa 8x8Filter CR−NO−LUHexa 16x16Filter CR−NO−LUBasic sys. Hexa. 4x4FilterBasic sys. Hexa. 8x8FilterBasic sys. Hexa. 16x16Filter

Figure 6.8: BER Cognitive Radio+LU, Cognitive Radio without LU, and Basicsystem, Hexagonal pattern, normalized Doppler=0.02

For the same setup mentioned above in this section, we reducethe power of thesubcarriers adjacent to the LU as depicted in Fig. 6.9. This power reduction isdone to insure that the CR system is not interfering the LU system and to decreasethe sidelobes of thesinc function. Because decreasing the power will also de-crease the sidelobes, leading to less interference with theLU. More methods onsidelobe suppression are given in [26]. Hence the pilots included in those subcar-riers have less power than the other pilots. All pilots are used in the estimation, thenormal ones and the ones with less power. The Estimation performance is demon-strated in Fig. 6.10. We see that the estimation performanceis degraded which isobvious. This is because the loss of the correlation in (5.9)is not compensatedby the SNR which is very observable in the MSE. Pilots with less SNR are moredegraded than pilots with more SNR, hence the initial channelestimation error isbigger. This error propagates further to the filtering process leading to a largerMSE.

At last we observe the BER of the LU to see whether we are interfering it ornot. Since it is acceptable, it means that the CR is not influencing the LU much.The major factor which degrades both systems when operatingadjacent to eachother is the orthogonality between them. The orthogonalitybetween the subcarri-ers of the CR with respect to the carriers of the LU is the main issue. Experiments

62

on the orthogonality between both systems and influence of CR on LU in SISOsystem are available in [20].

f

OFDM

subcarriers of the Rental User

Subbands allocated

to Licensed Users

Deactivated subcarreirs due

to Licensed user access

Additionally deactivated

subcarriers

Reduced Power subcarriers

Figure 6.9: Reduced power of the subcarriers adjacent to the LU.

0 5 10 15 20 25 30 35 4010

−3

10−2

10−1

100

SNR (dB)

MM

SE

Hexa 4x4Filter + LUHexa 8x8Filter + LUHexa 16x16Filter + LUHexa 4x4Filter CR−NO−LUHexa 8x8Filter CR−NO−LUHexa 16x16Filter CR−NO−LUBasic sys. Hexa. 4x4FilterBasic sys. Hexa. 8x8FilterBasic sys. Hexa. 16x16FilterHexa 4x4Filter Reduced power+ LU

Figure 6.10: MMSE Cognitive Radio+LU, Cognitive Radio without LU, and Ba-sic system, Hexagonal pattern, Reduced Power, normalized Doppler=0.0005

63

Table 6.1: Simulation ParametersBandwidth 1.28MHzActive Subcarriers 213Subcarrier spacing 5kHzFFT length 256Guard Interval 44µsOFDM symbol duration including cyclic prefix244µsOFDM symbols per frame 46 symbolsPilot symbol modulation BPSKData symbols modulation 4-QAMPilot spacing in frequency df = 4Pilot spacing in time of each transmitter dt = 6Max. Doppler frequency 100MHzMax. delay 12.5µsRMS delay spread 4.3µsNumber of Channel taps 4Number of paths per tap 10Power decrement per tap 1dBTap spacing 4Channel Coding and Interleaver OFF

64

0 5 10 15 20 25 30 35 4010

−3

10−2

10−1

100

SNR (dB)

BE

R

Hex 4x4Filter + LUHex 8x8Filter + LUHex 16x16Filter + LUHex 4x4Filter CR−NO−LUHex 8x8Filter CR−NO−LUHex 16x16Filter CR−NO−LUBasic sys. Hex. 4x4FilterBasic sys. Hex. 8x8FilterBasic sys. Hex. 16x16FilterHex 4x4 Reduced power + LUHex 4x4 Reduced power +LU−BER

Figure 6.11: BER Cognitive Radio+LU, Cognitive Radio without LU,and Basicsystem, Hexagonal pattern,Reduced Power, normalized Doppler=0.0005

6.3 Analytical validation

In this section we show how the results obtained from the simulations could beanalytically validated. The result we show is a real valued because of the choseninterval for the delay power density spectrum of the filter. The vector of transmit-ted data is equal to one. More information about validating results analyticallycan be found in [27] and [28].

The delay power density spectrum for the filter is:

ρfilter(τ) =

1τfilter

|τ | <τfilter

2

0 otherwise

(6.7)

65

The auto correlation functionθn,k can be derived by taking the inverse Fouriertransform of the delay power density spectrum of the filter as:

θn,k =

∫

∞

−∞

ρfilter(τ)ej2πτfiltertdτ (6.8)

=

∫

∞

−∞

1

τfilter

ej2πτfiltertdτ

=1

τfilter

.1

j2πt

[

ej2πτfiltert]

τfilter

2

−τfilter

2

=1

j2πtτfilter

[

ej2πτfilter

2t − e−j2π

τfilter

2t]

=1

πtτfilter

[

sin(2πτfilter

2t)]

=1

πtτfilter

sin(πτfiltert)

=1

π 12,5200

sin(π12, 5

200)

= 0, 01745

Furthermore by choosing the filter parameterfD,filter equal to the maximum ex-pected Doppler frequency of the mobile radio channelfDmax

. The normalizedDoppler power density spectrum used for the filter design is:

SfD,filter(fD) =

12fD,filter

|fD| < fD,filter

0 otherwise

(6.9)

The cross correlation function is derived by taking the inverse Fourier transformof the Doppler power density spectrum as:

φn,k =

∫ fD,filter

−fD,filter

1

2fD,filter

ej2πftdf (6.10)

=1

2fD,filter

.1

j2πt

[

ej2πft]fD,filter

−fD,filter

=1

2fD,filter

.1

j2πt

[

ej2πfD,filtert − e−j2πfD,filtert]

= 0, 0166

According to the MSE equation (5.11) in sec 5.3 the MMSE at this point in fre-quency and time will be equal to 0,048 which is in the order of10−2 and is closeto the simulations results.

66

Chapter 7

Conclusion and Recommendations

7.1 Conclusion

Our objective in this thesis is to solve the radio spectrum scarcity by efficientlyutilizing free or unused portions of the spectrum. We use thewell recommendedOFDM technology to realize a CR system capable of accessing the spectrum with-out interfering the licensed user who have the right to access the spectrum. Thechannel estimation in OFDM is a challenging task. We solve this challenge bydesigning three different pilot pattern to estimate the wireless channel. A wayfor enhancing the spectrum utilization efficiency is by improving the bitrate orBER of the wireless system. It has been shown that the MIMO concept is a goodmeans to do that. But then another challenge faces us. The pilot patterns must beredesigned to be suitable for implementation in MIMO OFDM. We enhance theoverall system performance by implementing the MIMO concept. The channelestimation in MIMO becomes a third challenge. We solve this challenge by mak-ing the designed pilot patterns suitable for MIMO.

In this thesis we designed a 2x2 MIMO OFDM based cognitive radio system. TheWSSUS channel model from SISO has been adopted to design the MIMO chan-nel model used in our simulations. The MIMO channel model hasbeen studied indetails. The most important part of this system which is the channel estimator wasstudied and investigated thoroughly. The channel estimator was investigated us-ing Wiener filtering in cascade. The Wiener filtering was donefirst in frequencydirection followed by filtering in time direction. The filtersize plays a role inthe estimation performance and computational complexity,therefore several fil-ter sizes were simulated. Physical properties of the channel as the power delayprofile and the Doppler power spectrum were reviewed and studied because theyinfluence the pilot spacing in the pilot grid. Physical effects of the mobile like

67

the Doppler and delay spread in different cases have been simulated. The OFDMmodulation technique has been studied and the OFDM parameters has been cho-sen according to our needs for the system. Cognitive radio hasbeen reviewed.Important issues like spectrum pooling and interference inCR were reviewed.A big effort has been made to observe the application of channel estimation ina MIMO OFDM system. Major challenges in applying the pilot aided channelestimation for OFDM in MIMO concept in the context of CR have been solved.Optimum Finite Impulse Response filters, Wiener-Hopf equation, 2x1D Wienerfiltering have been studied to be implemented in the channel estimator part ofthe simulation platform. Important aspects like the low computational complexityhave been studied.

While designing the hexagonal pilot pattern, the emphasis has been put on thevirtual pilot position in time direction as shown in Fig. 5.3where we split thehexagonal pilot pattern into two rectangular patterns in a way that the resultingpatterns for both transmit antennas are orthogonal to each other to make the pat-tern suitable for MIMO. Further while splitting the patterninto two patterns, somereal pilots are sacrificed. Those sacrificed pilots are compensated by virtual pilots.

Virtual pilots are obtained by linear interpolation and linear extrapolation in be-tween two most nearby pilots. The virtual pilots are obtained in frequency direc-tion and in time direction.

Rectangular pilot pattern with different pilot spacing in frequency direction hasbeen designed and implemented in MIMO system. While designing the rectan-gular patterns, the virtual pilots in frequency direction have been emphasized asshown in Fig. 5.5 and Fig. 5.7. Two rectangular patterns havebeen designed. Byjust splitting one rectangular pattern into two we don’t obtain the desired pattern,because some pilots will be lost. The lost pilots are compensated by exploit-ing virtual pilots in frequency direction. In the first rectangular pilot pattern thevirtual pilots are obtained by linearly interpolating or linearly extrapolating twomost nearby pilots only in frequency direction. Virtual pilots in the first rectangu-lar pattern makes the pilot spacing in frequency direction equal to two positionsas shown in Fig. 5.6.

Mean while for the second rectangular pilot pattern, linearinterpolation or linearextrapolation to obtain the virtual pilots is applied in frequency direction twice.First we obtain the virtual pilots from two real pilots and second we obtain a vir-tual pilot from linear interpolation or linear extrapolation between initial channelestimates in real pilot position and initial channel estimates in the most nearby

68

virtual pilot positions. Herewith is the pilot spacing in frequency direction madeequal to four positions as shown in Fig. 5.8.

The MSE and BER are used as measure in judging the performance of each pi-lot pattern. According to that performance the hexagonal pilot pattern has beenimplemented in MIMO OFDM based CR system. Virtual pilot concept has beenreviewed and implemented in all proposed pilot patterns. The advantages anddisadvantages of virtual pilot concept has been discussed through our simulationresults analysis. Performance of the system while a licensed user is occupying asubband of the spectrum and the effect of the licensed user onthe pilot patternhas been studied. Spectrum overlying according to licenseduser activity has beensimulated. The three proposed pilot patterns were implemented in the MIMOsystem and their performances were tested. The decision of the best performingpattern is made by observing the MSE and BER obtained from the simulation re-sults in the case where no LU is active. The hexagonal patternshows the lowestMSE and BER compared to the other two patterns. Hence the hexagonal patternis chosen to be implemented in the CR system.

The main purpose of this thesis is to design a MIMO OFDM based transmit-receive system and find the best performing pilot pattern between the three dif-ferent proposed designed patterns for estimating the MIMO channel for a 2x2MIMO OFDM based cognitive radio system. The hexagonal pattern outperformsthe other two patterns. The hexagonal pattern which was implemented in transmit-ter 1 performs slightly better than the one implemented in transmitter 2 becausemore virtual pilots are utilized in one pattern compared to the other one and thefirst pattern has few more pilots than the second. The performance of this patternconverges at almost 20dB SNR for different filter lengths. Above this SNR valueincreasing the filter size has no influence any more on improving the performance.The longer the filter size is, the more virtual pilots are utilized in the filtering pro-cess, this will result in accumulation of errors. The consequence of this accumu-lation is that the filtering performance will converge to a certain MSE value range.

The pilot spacing influences the estimation performance. The rectangular patternwith Df = 2 performs better than the rectangular pattern withDf = 4 becauseof the smaller pilot spacing of the first pattern. The pilot spacing is related tothe correlation properties of the channel. Decreasing the pilot spacing makes thechannel estimates on the pilot positions more correlated. The rectangular patternwith distanceDf = 2 is not affected by increasing the filter size because thereare lots of virtual pilots in this pattern resulting in a dominating virtual pilot error.The increasing number of virtual pilots in this pattern is related to the twice linear

69

interpolation in frequency direction of the virtual pilot to decrease the pilot spac-ing in frequency direction.

The performance of all patterns is affected by the Doppler frequency. The Dopplerfrequency is related to the vehicular velocity. At lower Doppler frequency, allpatterns performs better than at higher Doppler frequency.At lower Doppler fre-quency the channel coherence time is longer.

The hexagonal pattern is chosen to be implemented in the cognitive radio schemebecause it outperforms the other two patterns. In this scheme some subcarriers aredeactivated due to the LU access. The performance of this pattern is not affectedby this deactivation significantly when the LU is not active,but is degraded whenthe LU is active. This performance degradation is due to the interference from theLU. This interference is caused by the nonorthogonality of the LU with respect tothe CR.

Decreasing the power of the pilots adjacent to the LU, decreases the sidelobesof thesinc function. This sidelobe reduction result in decreasing theinterferenceto the LU, but degrades the performance of the channel estimation. Pilots withhigher SNR are less degraded than pilots with lower SNR. The CR is not affectingthe LU significantly. The LU can still operate with acceptable performance. Majorissue regarding the performance degradation of both systems is the orthogonalitybetween the CR and LU. In case the spectrum pooling is applied,the carriers onthe band occupied by the LU will be deactivated, but part of the CR spectrum onthe LU band will interfere the LU if the CR and LU spectrum are not orthogonalto each other.

7.2 Recommendations

We believe that investigating the following issues is important and will put morelight on the MIMO system and the channel estimation mechanism. If these issuesare implemented, then the system performance could be enhanced especially inthe context of cognitive radio.

1. Enhancing system capacity by expanding to 4x4 MIMO. The hexagonalpattern is very suitable for 4x4 MIMO system. The existing pattern conceptand the pilot spacing in frequency and time directions will remain the same,but the pilots in the additional two patterns will be shiftedby two positionsin frequency direction and three positions in time direction.

2. Concentrating the signal energy at a certain (desired) receiver or direction

70

also called Beam forming. This could be done by exploring the phase of thedifferent signals at the different antennas to form one directional radiationpattern (Beam). Other possibility is Switching the transmitters in cascadeor any way not simultaneously. i.e. not all transmitters aretransmittingin the same time. This will reduce computation complexity atthe receiverand no orthogonality between the transmitted frames is needed any more.This is kind of beam forming. To achieve this signal enhancement, themultiple antenna signals must adds up constructively at thedesired receiveror direction.

3. Channel coding can be applied in deriving the virtual pilots in order to re-duce the decision error which will give a better estimate of the channel.

4. Applications which requires high BER are Critical applications like a banktransaction or monitoring information used to monitor patients or older peo-ple which relay on CR. These kind of data (application) must be transmittedonly on the good subcarriers. Hence channel estimation module shouldgive an indication about which subcarriers are reliable andhence could givea good BER and which subcarriers are less reliable. This is a QoS attributeto support critical applications.

5. In case a critical application is using CR then an End to End QoS is anadditional check for the CR to control wither the QoS attributes are fulfilledor not. Physically this means transmitting a very short message (whichcould be incorporated inside the transmitted data) from thereceive side backto the transmitting side, indicating the quality and validity of the receiveddata. We want to have this check in the physical layer since wethink therewill be no service provider involved in CR, due to the ’free’ concept of CR.

7.3 Personal perspective

Within the context of channel estimation, the author think that the proposed methodwhich was tested by simulations in this thesis is a good method. Because it don’trequires many additional units in the overall radio system.Bust instead it makesuse of existing units of the system. Further this method consumes minimal amountof energy to estimate the radio channel. Those two points areimportant in practicebecause they reduce the cost and by decreasing complexity and energy consump-tion. In addition to this, the system can be easily expanded in the sense of MIMO,to improve the system capacity and performance. We think that our system orbig part of it, can be easily implemented in real hardware systems. Maybe sometranslation is required to match the hardware compatibility, however according to

71

our knowledge there are hardware systems in the market whereour codes couldbe loaded in with minimal translation. Within the context ofcognitive radio, wethink that our method is very suitable to be implemented for general future ap-plications. Because the results it shows are acceptable for estimating the channelwith such low energy cost. In the context of transmitting real data, our system isvery suitable for transmitting real data. We think that BER of10−5 are possibleafter some coding is applied to the real data which needs to betransmitted. Suchresults are suitable for many kinds of applications.

72

Appendix A

The Sliding Window Technique

The sliding window technique is used within the Wiener filtering for the estima-tion. This window slides from the first pilot position to the next pilot positionuntil it arrives at the edge of the OFDM frame as depicted in Fig. A.1. This slid-ing happen in the frequency direction and in the time direction. The format of thefilter window in frequency direction is depicted in Fig. A.2.The filter coefficientω

[1]n in the center withindfreq give the MMSE estimate, hence the best estimate.

while the other coefficients in the edges gives larger errors, hence a larger MSE.The parameterfoffset refers to the position of the coefficientω

[1]n which gives the

smallest MMSE estimate as:

foffset =

dfreq.(

Nf

2− 1)

: Nf even

dfreq.Nf−1

2−⌈

dfreq−1

2

⌉

: Nf odd

(A.1)

One OFDM Symbol

Filter Window Filter Window

Nfsym

Nc

Figure A.1: Sliding Window Technique

The filtering process in frequency direction usesω[1]n form the first (foffset +

dfreq).Nf coefficients of the window at the edge with low subcarrier index, thelast (foffset + dfreq + 1).Nf coefficients at the other edge with the high subcar-rier index and the center coefficients for the rest of the subcarriers as depicted inFig. A.3.

73

foffset

Nfsym = ((Nf - 1) . dfreq) + 1

dfreq foffset + 1

Nf

Figure A.2: Filter Window Formate

One OFDM Symbol

NfsymNc

c

Nfsym

foffset + dfreq

c

dfreq

c

c

foffset + dfreq + 1

Filter Window using the Edges Filter Coefficients

Filter Window using the Center Filter Coefficients

Figure A.3: Complete Wiener filtering process using Sliding Window on oneOFDM symbol

74

Appendix B

Filter Design

The filter is designed by determining the set of filter coefficientsωn,k. The com-plete description of 2D filter design is studied in [3]. In this appendix we will notrepeat the filter design, but we relate our simulation results to the filter design.The Mean Square Error of the overall estimation process for the 2x1D filteringaccording to (5.11) is:

Jn,k = J[2]n,k

= E{

|Hn,k|2}

− E{

Hn,kh[1]Hn

}

ω[2]∗k

− ω[2]Tk E

{

h[1]n H∗

n,k

}

+ ω[2]Tk E

{

h[1]n h[1]H

n

}

ω[2]∗k (B.1)

where the superscriptH denotes the Matrix Hermitian operation.

E{

Hn,kH[1]∗n,k

}

is the crosscorrelation function which is the second term inthe

equationE{

Hn,kh[1]Hn

}

ω[2]∗k . Meanwhile the autocorrelation according to (5.15)

is:E{

H[1]n,k′H

[1]∗n,k′′

}

= J [1]n δk′

−k′′ + R[1]hh

−k′−k′′(B.2)

Increasing the pilot spacing result in decreasing the valueof the correlation func-tions. This will lead to a bigger MSE value. The optimum filterhas to be adaptedto the delay power density spectra (B.3) and the Doppler powerdensity (B.4):

ρ(τ) =

∫

∞

−∞

S(τ, fD)dfD (B.3)

SfD(fD) =

∫

∞

−∞

S(τ, fD)dτ (B.4)

However in practice the delay power density and the Doppler power density ofthe mobile radio channel are not perfectly known at the receiver. Hence the filters

75

of the channel estimator have to be designed according to thefollowing require-ments:

1. A great variety of delay power density spectra whether they are exponen-tially decreasing or not with different delay spreads should be covered.

2. A great variety of Doppler power density spectra such as classical, Gaus-sian, . . . , etc and other power density spectra with different maximum Dopplerfrequencies should be covered.

3. The correlation functionsRhh andRφhh should be real valued functions, to

achieve real valued filter coefficientsωn,k as in 5.5 and thus to reduce com-putational complexity. This corresponds to filtering the quadrature compo-nents ofHn,k by two identical, independent, real valued filters. As a resultthe computational complexity is reduced by a factor of approximately twocompared to the filter with complex valued coefficients.

Hence in our case, we use the rectangular Delay power densityspectrum whichgives constant uniform values for thesinc function, Those constant values resultin real values for the correlation functions and thus reducing the computationalcomplexity. With above requirements, an appropriate solution is to adapt the filtersto uniform power density spectra. Choosing the filter parameterτfilter equal to themaximum expected delay of the mobile radio channelτmax, the normalized delaypower density spectrum used for the filter design is given by [3]:

ρfilter(τ) =

1τfilter

|τ | <τfilter

2

0 otherwise

(B.5)

Furthermore by choosing the filter parameterfD,filter equal to the maximum ex-pected Doppler frequency of the mobile radio channelfDmax

. The normalizedDoppler power density spectrum used for the filter design is [3]:

SfD,filter(fD) =

12fD,filter

|fD| < fD,filter

0 otherwise

(B.6)

With the selection of uniform power density spectra, the discrete frequency corre-lation functions result in:

Rhhn−n′′=

sin(πτfilter(n − n′′)Fs)

πτfilter(n − n′′)Fs

(B.7)

76

and the discrete time correlation function yields:

Rφhhk−k′′

=sin(2πfD,filter(k − k′′)T ′

s)

2πfD,filter(k − k′′)T ′

s

(B.8)

Important aspects with respect to low computational complexity when implement-ing Finite Impulse Response filters for channel estimation are:

1. The filter coefficientsω should be time invariant.

2. The autocorrelation matrixRφhh should be independent of the actual coordi-

nates(n, k), so thatRφ−1hh can be precomputed and stored.

3. Different sets of the crosscorrelation vectorRhhn,kmay be precomputed and

stored taking in account symmetry in the pilot grid.

4. The optimum number of filter coefficients per estimation isthe number offilter tapsNtap which is equal to the number of pilots per OFDM frameNgrid. The computational complexity can be reduced significantlyby takingonly a subset of filter taps which is less than the number of pilots in theOFDM frame instead of all taps.

77

Appendix C

V-BLAST Architecture

Vertical Bell Laboratories Layered Space-Time(V − BLAST ) is a Layered SpaceTime architecture (LST) or as called some times Spatial Multiplexing Scheme.This algorithm is applied at each receiver on the received signal after demodula-tion (FFT) and after the channel state estimates on all linksare available. Thisalgorithm detects the strongest layer in the received signal and then cancels theeffect of this strongest layer from the rest of the received signals. The algorithmproceeds to detect the strongest of the remaining layers in the received signals asexplained briefly below. Details about the algorithm are given in [29] and [30].

1. Determining the optimal order of detection fulfilling thelow of Moore-Penrose pseudo inverse with minimum Euclidian norm. Thus wetake thepseudo inverse of the estimation matrix.

2. The resulting matrix is used as a nulling matrix (row wise which will betransposed) and is used to null out the weakest transmitted signals and ob-tain the strongest transmitted signal.

3. The received signal constellation is sliced to estimate the strongest trans-mitted signal.

4. The strongest transmitted signal is canceled from the received signal vectorto reduce the detection complexity for the remaining transmitted signals.

78

Appendix D

Publications

1. I. Budiarjo, H. Abdulrahman Sulaiman and H. Nikookar’On The Use of Vir-tual Pilots for 2x2 MIMO-VBLAST OFDM Channel Estimation with WienerFilter in Hexagonal Pilot Pattern’, 15th IEEE SCVT, Antwerpen, Belgium,November 2008.

2. I. Budiarjo, H. Abdulrahman Sulaiman and H. Nikookar’Virtual Pilots withHexagonal and Rectangular Pilot Patterns for 2x2 MIMO OFDM ChannelEstimation with Wiener Filter and V-BLAST’, To be submitted to SCVT2010.

79

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