ABSTRACT. GUNCAVDI, SECIN. Transmitter Diversity and Multiuser Precoding for Rayleigh

Transcription

1 ABSTRACT GUNCAVDI, SECIN Transmitter Diversity and Multiuser Precoding for Rayleigh Fading Code Division Multile Access Channels (Under the direction of Alexandra- Duel-Hallen) Transmitter diversity in the downlin for Code Division Multile Access (CDMA) systems rovides a means to achieve similar erformance gains as for the mobile station (MS) receiver diversity without the comlexity of a MS receiver antenna array Transmitter based methods enable to shift signal rocessing to the transmitter where ower and comutational comlexity are more abundant, thus simlifying receiver units We examine feasibility of several transmitter diversity techniques for the Wideband CDMA (W-CDMA) systems We also investigate an otimal method to combine transmitter diversity and recoding that achieves the gain of maximum ratio combining of all sace and frequency diversity branches Under severe channel conditions (ie multiath), the multile access interference (MAI) becomes the major source of erformance degradation for direct sequence CDMA (DS/CDMA) systems This is because of the loss of orthogonality between the sreading codes used by each user due to the multiath channel effects To overcome this roblem, many receiver based multiuser detection (MUD) techniques have been roosed These techniques demand high comutational comlexity, ower and nowledge of sreading codes of all users As a result, in the downlin of a CDMA system it is not feasible to emloy such methods at the MS Alternatively, transmitter based techniques were roosed to shift comutational comlexity and ower consumtion to the BS, where they can be afforded It

2 was shown that these methods are very effective in removing the MAI Although these methods are owerful, they are high in comlexity since MAI cancellation filters need to be udated continuously as fading coefficients vary We roose a less comlex method with similar erformance imrovements In the roosed method, the functions of multiath combining and MAI cancellation are searated Thus the MAI cancellation matrix does not deend on raidly time-varying fading coefficients Transmitter diversity and multiuser recoding can be combined to further imrove the erformance Multiuser recoding reserves the multiath diversity while removing the MAI Extending multiuser recoding to multile antennas results in sace diversity in addition to multiath diversity Both transmitter diversity and multiuser recoding require the nowledge of the channel state information (CSI) The CSI can be estimated at the receiver and sent to the transmitter via a feedbac channel To enable the studied adative techniques for ractical systems, we emloy the long range rediction (LRP) algorithm, which characterizes the fading channel using the autoregressive (AR) model and comutes the Minimum Mean Squared Error (MMSE) estimate of a future fading coefficient samle based on a number of ast observations Numerical, simulation and theoretical results are resented to show that transmitter diversity and multiuser recoding can be used to remove MAI and achieve frequency and sace diversity through multiath channels and multile antennas

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4 To my family and to all who suorted me ii

5 BIOGRAPHY Secin Guncavdi was born in Istanbul, Turey on November 1, 1975 He graduated from Usudar Science high school in 1993 and moved to Anara He received the Bachelor of Science degree in Electrical and Electronics Engineering from Bilent University, Anara, Turey in June 1997 He started his graduate studies at North Carolina State University, Raleigh NC in Electrical and Comuter Engineering Deartment in Fall 1997, where he was a teaching assistant He became a research assistant in Sring 1998 He was a co-o at Analog Devices Inc, Greensboro, NC during the summer of 1998 and he received his Master of Science degree in Electrical Engineering in Sring 1999 He was enrolled in the PhD rogram in Fall 1999 in the same deartment Since then he has been a research and teaching assistant He was the instructor of ECE 301 in Summer 00 and ECE 331 in Sring 003 in the Deartment of Electrical and Comuter Engineering The author intends to ursue an academic career, focusing on excellence in teaching and research in the area of digital communications iii

6 ACKNOWLEDGEMENTS I would lie to than my advisor, Dr Alexandra Duel-Hallen for her guidance, encouragement and suort through my graduate studies I areciate her hel in suggesting research toics, utting issues in ersective and refining my research I would also lie to than my committee members Dr J Keith Townsend, Dr Brian L Hughes and Dr Hans Hallen for the helful discussions and for serving as my committee Throughout this research, I have received encouragement and hel from many friends Their suort and technical advice heled me become the erson I am and they have a big art in my accomlishments I would lie to than the following individuals for their various hel: Lisa K Miller, Dr Hatice O Oztur, Ozdemir Ain, Dr Mehmet C Oztur, Dr Ayman El-Ezabi and Dr Tugay Eyceoz I am grateful to the Center for Advanced Comuting and Communications and the Deartment of Electrical and Comuter Engineering Deartment at North Carolina State University, National Science Foundation and Analog Devices Inc for their suort of this wor iv

7 TABLE OF CONTENTS LIST OF TABLES viii LIST OF FIGURES ix 1 INTRODUCTION 1 11 Bacground 1 1 Outline of the Thesis 6 FADING MOBILE RADIO CHANNELS 8 1 Fading Channel Characterization 8 Flat Rayleigh Fading Channel 10 3 Jaes Model for Rayleigh Fading Channel 11 4 Taed-Delay-Line Model for Frequency-Selective Fading Channel 14 3 DIRECT SEQUENCE CODE DIVISON MULTIPLE ACCESS SYSTEM Synchronous DS/CDMA System Model 16 3 DS/CDMA Receiver Structures 0 31 The Conventional Detector for AWGN Channels 0 3 The Maximum-Lielihood Detector 1 33 The Decorrelating Detector for AWGN Channels 34 The RAKE Receiver 35 The Multiath Decorrelating Detector 5 36 The RAKE Decorrelating Detector 7 33 Wideband CDMA (W-CDMA) System 9 34 Simulation and Numerical Results 3 v

8 4 LONG RANGE PREDICTION OF RAYLEIGH FADING CHANNELS Linear Mean Squared Error Prediction of the Rayleigh Fading Channels 38 4 Performance Bounds of Long Range Prediction 4 5 TRANSMITTER DIVERSITY TECHNIQUES Time-Switched Transmitter Diversity 46 5 Orthogonal Transmitter Diversity Selective Transmitter Diversity Transmit Antenna Array 5 55 Pre-RAKE Transmitter Precoding Sace-Time Pre-RAKE Transmitter Diversity Method (STPR) Numerical and Simulation Results 61 6 MULTIUSER PRECODING TECHNIQUES Bacground of Multiuser Precoding Multiuser Precoding for AWGN Channels Multiuser Precoding for Flat Rayleigh Fading Channels Multiuser Precoding for Frequency-Selective Channels Multiuser Precoding with the RAKE receiver Multiuser Precoding without the RAKE receiver 79 6 Pre-RAKE Multiuser Precoding for Frequency-Selective Channels Pre-RAKE Multiuser Precoding with CSI Deendent Decorrelation (Pre-RDD) 8 6 Pre-RAKE Multiuser Precoding with CSI Indeendent Decorrelation (Pre- RAKE Multiuser Precoding) 85 vi

9 63 Sace-Time Pre-RAKE Multiuser Precoding for Frequency-Selective Channels (STPR MUP) Numerical and Simulation Results 95 7 CONCLUSIONS AND SUMMARY 104 BIBLIOGRAPHY 108 APPENDIX A Theoretical Bit Error Rate of Selective Transmit Diversity 114 A1 Flat Rayleigh Fading Channels 114 A Frequency-selective Rayleigh Fading Channels 117 vii

10 LIST OF TABLES Table 1 Key characteristics of W-CDMA 31 viii

11 LIST OF FIGURES Figure 1 Figure Tyical signal fading for f dm =100Hz and f dm =400Hz 1 Autocorrelation function of Rayleigh fading for f dm =100Hz and f dm =400Hz 13 Figure 3 Taed delay line model for frequency-selective fading channel 15 Figure 31 Figure 3 Figure 33 Figure 34 Figure 35 Figure 36 CDMA downlin system model with K users 17 CDMA ulin system model with K users 18 RAKE receiver with MRC at the th mobile station 4 Multiath Decorrelating Detector 5 RAKE Decorrelating Detector 7 Bit Error Rate for single antenna single user Single, two and four ath fading channels f dm =00Hz, uncoded, 3 chi sreading Normalized total channel owers 33 Figure 37 Bit Error Rate for single antenna single user Single, two and four ath fading channels f dm =00Hz, coded, 3 chi sreading 34 Figure 38 Bit Error Rate of user 1 for single antenna Two users, two aths f dm =00Hz, uncoded, 16 chi sreading A 1 /A =1 35 Figure 39 Bit Error Rate of user 1 for single antenna Four users, two aths f dm =00Hz, uncoded, 8 chi sreading A 1 /A =1 36 Figure 310 Bit Error Rate of user 1 for single antenna Eight users, four aths f dm =00Hz, uncoded, 3 chi sreading A 1 /A =1 37 ix

12 Figure 41 Theoretical autocorrelation of the Rayleigh fading channel and the memory san of the MMSE rediction for f dm =00 Hz 41 Figure 4 BER of BPSK system with erfect vs MMSE redicted CSI Flat fading, single user, single antenna, uncoded 43 Figure 51 Figure 5 Figure 53 Figure 54 Figure 55 Figure 56 Figure 57 Figure 58 Figure 59 Figure 510 Figure 511 Time Switched Transmit Diversity 46 Orthogonal Transmit Diversity 47 Orthogonal Transmit Diversity vs Maximal Ratio Combining 48 Selective Transmit Diversity 49 Flat fading Selective Transmit Diversity vs Maximal Ratio Combining 50 Frequency-selective STD vs MRC and flat fading STD 51 Bloc diagram of Transmit Adative Array 5 Two antenna four ath Tx AA vs MRC 55 Bloc diagram of Pre-RAKE diversity 57 Bloc diagram of Sace-Time Pre-RAKE diversity combining 60 Simulated erformance and theoretical bounds for long range rediction, f dm =00Hz Uncoded W-CDMA, Tx AA: 4 antennas, flat fading, STPR: antennas, 4 aths 65 Figure 51 Performance of the STD, flat fading channel, transmitter antennas, f dm =00Hz, coded W-CDMA 66 Figure 513 Comarison of STD, Tx AA and Sace-time re-rake, transmitter antennas, 4 aths, f dm =00Hz Coded W-CDMA 67 Figure 514 Comarison of Tx AA and Sace-time re-rake, transmitter antennas, 4 aths, f dm =00Hz Coded W-CDMA 68 x

13 Figure 61 BER of user 1 in AWGN Channel With and Without Precoding 4 Users, uncoded 73 Figure 6 BER of user 1 in flat fading channel with and without recoding 4 users, uncoded 75 Figure 63 Figure 64 Figure 65 Figure 66 Pre-RAKE Multiuser Precoding with CSI Deendent Decorrelation 83 Pre-RAKE Multiuser Precoding with CSI Indeendent Decorrelation 86 Bloc diagram of Sace-Time Pre-RAKE multiuser recoding 91 BER of user 1 in ath 8 users system with 16 chi sreading Perfect CSI A 1 /A =1 100 Figure 67 BER of user 1 in 4 ath 8 users system with 3 chi sreading Perfect CSI A 1 /A,3,4 =1 101 Figure 68 BER of user 1 in antenna, ath,,8 user system Perfect CSI A 1 /A =1 10 Figure 69 BER of user 1 in ath users system with 8 chi sreading A 1 /A =1 Prediction and no rediction for refilter with no RAKE, recoding with RAKE, re-rdd and re-rake multiuser recoding 103 xi

14 Chater 1 Introduction 11 Bacground For the ast decade, the demand for ersonal communications services has been increasing dramatically Wireless systems rovide the most romising means of telecommunications Currently, three channel access schemes are mostly considered: Frequency Division Multile Access (FDMA), Time Division Multile Access (TDMA) and Code Division Multile Access (CDMA) There has been much interest in CDMA techniques as an alternative to both TDMA and FDMA methods in wireless communications systems Among the advantages of CDMA is its ability to combat multiath fading of the radio lin due to the frequency diversity offered by the wideband nature of its signal CDMA offers otential caacity increases over the narrowband techniques This caacity increase is mainly due to the fact that CDMA erformance is interference-limited whereas narrowband systems are bandwidth-limited Increasing customer demand for high-seed services such as the internet, video, multimedia traffic resulted in more research towards new technologies to accommodate these requirements Wideband direct sequence CDMA (W-CDMA) is emerging as the redominant radio access technology for the next-generation (3G) regional and global wireless standard CDMA technology was introduced in the US with the IS-95 standard and this technology has aved the way for ossible future deloyment of a more refined system Since W-CDMA is a relatively new technology, a significant amount of research has been conducted to imrove the roosed W-CDMA systems The roosed W-CDMA system 1

15 offers increased caacity and coverage, variable and high seed data rates, both acet and circuit switched services and multile simultaneous services W-CDMA suorts Adative Antenna Arrays (AAA) by emloying ilot symbols er connection in the downlin The inclusion of the ilot symbols enables accurate estimation of the channels associated with each antenna at the mobiles, hence future channel state information (CSI) rediction via feedbac Transmitter diversity in the downlin using multile transmitter antennas rovides similar erformance gains as for the mobile station (MS) receiver diversity without the comlexity of a second MS receiver antenna Transmitter based methods enable to shift signal rocessing to the transmitter where ower and comutational comlexity are more abundant, thus simlifying receiver units It was shown in [3,9-38] that transmitter diversity at the base station (BS) will increase downlin caacity with only minor imlementation at the mobile terminal imlementation Furthermore, in some cases, the comlexity of the MS can be reduced by eliminating the RAKE receiver but still obtaining the multiath diversity via re-rake filtering [9-31,37] The roosed transmitter diversity techniques include Sace-Time Coding [30], Delay Diversity, Orthogonal Transmit Diversity (OTD), Time-Switched Transmit Diversity (TSTD), Selective Transmit Diversity (STD), Transmit Adative Array (Tx AA) [31-34] and Sace-Time re-rake Transmitter Diversity (STPR) [31,37,48] Some of the transmitter diversity techniques (eg Tx AA, STD) require feedbac of the CSI from the MS We refer to them as adative techniques With the hel of the feedbac, better erformance is achieved than for non-adative methods Adative techniques are classified at closed-loo methods The oen-loo techniques (eg TSTD,

16 OTD) do not require feedbac from the MS For oen-loo techniques, a re-determined algorithm of antenna/coding usage is emloyed For examle, transmission is switched sequentially between N antennas at the rate of R for TSTD Closed-loo techniques achieve better erformance than the oen-loo techniques, because the CSI enables more efficient use of the available ower and sectrum For examle, in the case of the STD, the CSI is used to calculate the ower of the channels associated with each antenna at the instant of transmission Switching to the antenna with the highest channel ower reduces fading and increases the received signal-to-noise ratio (SNR) at the MS Direct sequence CDMA (DS/CDMA) technology is designed to suort simultaneous high data rate users However under severe channel conditions (ie multiath), the multile access interference (MAI) becomes the major source of erformance degradation This is because of the loss of orthogonality between the sreading codes used by each user due to the multiath channel effects To overcome this roblem, many receiver based multiuser detection (MUD) techniques have been roosed [4-13] These techniques demand high comutational comlexity, ower and nowledge of sreading codes of all users As a result, in the downlin of a CDMA system it is not feasible to emloy such methods at the MS Alternatively, transmitter based techniques were roosed to shift comutational comlexity and ower consumtion to the BS, where they can be afforded It was shown that these methods are very effective in removing the MAI [4-46] Although these methods are owerful, they are high in comlexity since MAI cancellation filters need to be udated continuously as fading coefficients vary We roosed in [47] that similar erformance imrovements are ossible with less comlexity In the roosed method, the functions of 3

17 re-rake combining and MAI cancellation are searated Thus the MAI cancellation matrix does not deend on raidly time-varying fading coefficients Transmitter diversity and multiuser recoding can be combined to further imrove erformance Multiuser recoding reserves the multiath diversity while removing the MAI Extending multiuser recoding to multile antennas results in sace diversity in addition to multiath diversity [49] To imlement adative transmission and recoding methods in ractice, the CSI for the ucoming transmission interval must be available at the transmitter The CSI can be estimated the receiver and sent to the transmitter via a feedbac channel Thus, feedbac delay and overhead, rocessing delay and ractical constraints on modulation, coding and/or antenna switching rates have to be taen into account in the erformance analysis of adative transmission methods For very slow fading channels (edestrian or low vehicle seeds), outdated CSI is sufficient for reliable adative transmission However, for faster fading that corresonds to realistic mobile seeds, even small delay will cause significant degradation of erformance since the channel variation increases with the mobile seed As a result, the channel rofile is quite different at the time of transmission when comared to the outdated CSI To enable erformance imrovement using these adative methods, the CSI at the instant of transmission should be reliably redicted, based on the outdated CSI feedbac from the mobile Several adative channel estimation methods have been described in the literature [14-17] However, many of these techniques are better suited for very short range rediction or require very large comutational comlexity Thus, there is a need for adative, low comlexity, long range rediction technique that meets the accuracy requirements for 4

18 realistic mobile radio channels The LRP emloyed to enable the techniques studied in this thesis was develoed and extensively studied in [18-4] This algorithm characterizes the fading channel using the autoregressive (AR) model and comutes the Minimum Mean Squared Error (MMSE) estimate of a future fading coefficient samle based on a number of ast observations The suerior erformance of this algorithm relative to conventional methods is due its low samling rate (on the order of twice the maximum Doler shift and much lower than the data rate) Given a fixed model order, the lower rate results in longer memory san, ermitting rediction further in the future The LRP algorithm is emloyed in this thesis to enable roosed Tx diversity and recoding methods 5

19 1 Outline of the Thesis The goal of this thesis is to investigate and comare the erformance of several transmitter diversity and multiuser detection/recoding methods for Rayleigh fading channels, with the alication of LRP The thesis outline is as follows: Chater describes the multiath fading channels and the fading models Flat and frequency-selective fading channels are introduced Jaes and taed delay line fading models are resented In Chater 3, we introduce the DS/CDMA system and comare between the different multiuser receiver structures We assume the synchronous model and describe the ulin and downlin system with K users and L-ath frequency-selective fading Then the CDMA receiver structures for single and multiuser systems with or without fading are resented The chater is concluded with the ey characteristics of the W-CDMA system Chater 4 describes the LRP algorithm The rinciles of LRP are outlined The alication of LRP to W-CDMA systems is discussed and erformance bounds associated with this algorithm are resented In Chater 5, we analyze different oen-loo and closed-loo transmitter diversity methods for single user systems Previously roosed OTD, TSTD, STD, Tx AA and re- RAKE diversity techniques are investigated We roose a Sace-Time Pre-RAKE (STPR) technique that can achieve the diversity of all sace and frequency diversity branches The simulation and theoretical results are resented to comare the erformance of these methods We emloy the LRP to enable these closed-loo techniques for fast fading channels Actual W-CDMA arameters are used in simulations 6

20 In Chater 6, we describe transmitter based multiuser recoding methods and comare their erformance to receiver based multiuser detection and single user detection First, the bacground and reviously roosed methods are introduced It is shown that these methods can effectively remove the MAI However, they are comlex Next, we roose a similar multiuser recoding method with comlex transmitter but simlified receiver structure We call this CSI deendent decorrelation technique the re-rake Decorrelating Detector (re-rdd) Then we roose a simlified transmitter and receiver structure that can effectively remove MAI with similar erformance gains to other comlex recoding methods We call this method re-rake multiuser recoding Finally, we extend this technique to multile antennas By combining transmitter diversity with re-rake multiuser recoding, the MAI is removed, while multiath and sace-time diversity are reserved Simulation, numerical and theoretical results are resented to evaluate the erformance of these roosed techniques and comare them to reviously investigated methods 7

21 Chater Fading Mobile Radio Channels 1 Fading Channel Characterization Fading is the raid fluctuation of the amlitude of a radio signal over a short eriod of time or travel distance [1,] Fading is caused by interference between two or more versions of the transmitted signal, which arrive at the receiver at slightly different times These waves, called multiath waves, combine at the receiver antenna to give a resultant signal, which can vary widely in amlitude and hase, deending on the distribution of the intensity and relative roagation time of the waves and the bandwidth of the transmitted channel These multiath signals are suerosed either constructively or destructively at the receiver Deending on the relation between the signal arameters (such as bandwidth, symbol eriod etc) and the channel arameters (such as Doler sread), different transmitted signals will undergo different tyes of fading Multiath in the radio channel causes: Raid changes in signal strength over a small travel distance or time interval Random frequency modulation due to varying Doler shifts on different multiath signals and time Time disersion (echoes) caused by multiath roagation delays Due to the relative motion between the mobile station and the base station, each multiath wave exeriences a shift in frequency called the Doler shift given by []: v f n = f c cosθ = f dm cosθ (1) c 8

22 where f c is the carrier frequency, v is the vehicle seed, c is the seed of light, θ is the incident radio wave angle with resect to the motion of the mobile and f dm is the maximum Doler frequency shift The comlex enveloe of the flat fading signal at the receiver is: c( t) = N n= 1 A e n j(πf t+ φ ) n () where N is the number of scatterers, and for the n th scatterer, A n is the amlitude, f n is the Doler frequency shift in (1), and φ is the hase Doler sread B D is a measure of the sectral broadening caused by the time rate of change of the mobile radio channel and is defined as the range of frequencies over which the received Doler sectrum is essentially non-zero If the baseband signal bandwidth is much greater than B D, the effects of Doler sread are negligible at the receiver Then this is a slow fading channel Otherwise, the channel is a fast fading channel The bandwidth of the multiath channel can be quantified by the coherence bandwidth, which is related to the secific multiath structure of the channel The coherence bandwidth is a measure of the maximum frequency difference for which signals are still strongly correlated in amlitude When the bandwidth of the channel is less than the coherence bandwidth, the received signal will undergo flat fading The sectral characteristics of the transmitted signal are reserved at the receiver, however the strength of the received signal changes in time When the bandwidth of the channel is greater than the coherence bandwidth, the received signal will undergo frequency-selective fading The received signal includes multile versions of the transmitted waveform, which are faded and delayed in time Frequency-selective fading is due to time disersion of the transmitted symbols within the channel Thus the channel induces intersymbol interference (ISI) Wideband channels such as W-CDMA usually exerience frequency-selective fading 9

23 Flat Rayleigh Fading Channel There are several robability distributions that can be considered in attemting to model the statistical characteristics of the fading channel When there is a large number of scatterers in the channel that contribute to the signal at the receiver, alication of the central limit theorem leads to a Gaussian rocess model for the channel imulse resonse [1-3] If the rocess is zero mean (no line of sight comonents), then the enveloe of the channel resonse at any time instant has a Rayleigh robability distribution and the hase is uniformly distributed in the interval (0,π) The comlex Gaussian fading coefficients are given by C( t) = C ( t) jc ( t), r + where C r (t) and (t) are real Gaussian rocesses and the enveloe is given by C i i r( t) = C ( t r ) + C (t) If the variance of C r (t) and (t) is σ, then the average channel ower is given by ( ) σ i E C(t) = and E( ) is the exectation oeration The ower sectrum density (PSD) of the random enveloe is given by: C i 1 1 Ψ ( f ) =, f πf d 1 ( f / f ) d f d (3) The robability distribution function (PDF) is given by: ( r) = r σ The PDF of the hase of the rocess is uniform r / σ e r 0 (4) The autocorrelation function R(τ ) of the rocess is [3]: where 1 ( θ ) = θ π (5) π R ( τ ) = σ J o (πf τ ) (6) J o ( ) is the zero order Bessel function of the first ind d 10

24 3 Jaes Model for Rayleigh Fading Channel As described above, while the Rayleigh fading can be modeled as a comlex Gaussian rocess, it can also be aroximated by the sum of a finite number of comlex sinusoids This technique was introduced by William Jae [3] for the simulation of fading mobile radio channels According to this model, the Gaussian rocess can be aroximated by: c( t) = N N n= 1 e j(πfdmt cosαn + φn ) (7) where N is the total number of lane waves arriving at uniformly saced angles α n Jaes model is a stationary model that doesn t tae into account the change in the time varying factors such as the number and location of the scatterers, the vehicle seed and the acceleration etc The model assumes these factors stay constant The shae of the autocorrelation of the generated fading rocess only deends on the number of the scatterers and the maximum Doler shift However, this stationary model is sufficient for alications at which the arameters don t change significantly over short time intervals The number of sinusoids in the set must be large enough, so that the PDF of the resulting enveloe rovides an accurate aroximation to the Rayleigh PDF In this thesis, nine-oscillator Jaes model is used to generate the Rayleigh fading channels in the simulations Tyical signal fading ower and autocorrelation functions are shown in Figures 1 and for maximum Doler shifts of 100Hz and 400Hz Figure 1 is generated using nineoscillator Jaes model and equation (6) is used for Figure As seen in Figure 1, the ower of the fading signal has dee fades and eas As exected, the rate of change of the fading rofile is deendant on the maximum Doler shift Higher Doler shift results in more raid changes 11

25 Figure 1 Tyical signal fading for f dm =100Hz and f dm =400Hz 1

26 Figure Autocorrelation function of Rayleigh fading for f dm =100Hz and f dm =400Hz 13

27 The same conclusion could be drawn from Figure, where higher Doler frequency results in a faster changing autocorrelation function 4 Taed-Delay-Line Model for Frequency Selective Fading Channel For wideband transmissions, the multiath delay is often non-negligible relative to the symbol interval In this case, the received signal consists of several relicas of the same signal delayed with different durations The number of resolvable multiath comonents deends on the bandwidth of the signal comared to the coherence bandwidth of the channel CDMA technology is designed to tae advantage of this multiath channel and diversity is obtained For the comutations and the simulations rovided in this thesis, we assume that each multiath comonent of the channel fades indeendently and arrival delays occur at integer multiles of the chi rate of the CDMA signal Each ath is also assumed to have indeendent identically distributed (iid) Rayleigh fading characteristics A frequency-selective channel can be modeled as a Finite Imulse Resonse (FIR) filter imlemented with the taed delay line (TDL) [1] This TDL model consists of evenly saced ta coefficients, each reresenting one resolved multiath To model the Rayleigh fading in the multiath channel, each ta coefficient has a comlex valued gain with Rayleigh statistics Ta coefficients are assumed to be fading indeendently, since the aths are iid A tyical TDL model is given in Figure 3 We assume that there are L resolvable aths and D reresents a delay of T c (the chi interval) Based on this model, the imulse resonse of the channel is given by: L h( t) = = j 1 0 h δ ( t jt ) (8) j c 14

28 where the imulse resonse of the j th ath is given by h ( t) = h δ ( t) and is the comlex Gaussian fading coefficient corresonding to the j th ath j j h j h o (t) D D h 1 (t) h L-1 (t) Figure 3 Taed delay line model for frequency-selective fading channel 15

29 Chater 3 Direct Sequence Code Division Multile Access System In this chater, we describe the Direct Sequence Code Division Multile Access system (DS/CDMA) and comare between the different multiuser receiver structures 31 Synchronous DS/CDMA System Model The synchronous assumtion is often made to simly the analysis of CDMA detectors In most cases, the conclusions obtained for the synchronous case can be extended to the asynchronous case Throughout this thesis, the CDMA system of interest will be assumed a synchronous DS/CDMA system for both the ulin and the downlin In the downlin, the sreading codes associated with each user are generated to be orthogonal to each other and the transmission is synchronous The ulin signal is often asynchronous in ractice However, in this thesis we use the ulin model rimarily for erformance comarison with the roosed downlin multiuser recoding methods, so the synchronous assumtion is sufficient For the multiath DS/CDMA channel, the delay sread is on the order of several chi intervals, and T c <<T b Thus, ISI and the MAI due to adjacent symbol intervals are negligible As a result, the MAI and self-interference are due only to the effects of the multiath in the current symbol interval In a CDMA system, each user is assigned a unique signature sequence (ie sreading code/waveform) and all users transmit with the same carrier frequency Let s (t) denote the th user s signature waveform We assume that the signature waveforms are normalized and have T b duration T b, ie s ( t) dt = 1 Let b denote the information bit with amlitude A for the th 0 i user over one bit interval T b We consider Biolar Phase Shift Keying (BPSK) modulation, so 16

30 that b є {-1,1} The assband energy of th user s bit is given by E =A / Since the information bit sequence for each user is assumed to be iid equirobable and indeendent of other users, we may consider only one bit interval without loss of generality Assume we have K active users The downlin system model is given in Figure 31 and the ulin system model is given in Figure 3 Additive White Gaussian Noise (AWGN) for the downlin is given by n (t) =1K, with variance N o We assume that n (t) are iid The AWGN for the ulin is given by n(t) with variance N o Base Station Channel Mobile Stations A 1 s 1 (t) n 1 (t) b 1 h 1 (t) Receiver 1 ˆb 1 A s (t) n (t) b A K s K (t) h (t) n K (t) Receiver ˆb b K h K (t) Receiver K bˆk Figure 31 CDMA downlin system model with K users 17

31 Mobile Stations Channel Base Station A 1 s 1 (t) b 1 h 1 (t) 1 ˆb b A s (t) h (t) n(t) Receiver ˆb A K s K (t) b K h K (t) bˆk Figure 3 CDMA ulin system model with K users 18

32 First, consider the downlin system with K active users Then the transmitted signal x(t) at the BS in one bit interval will be: K x( t) = A b s ( t) (31) = 1 Equation (31) can be exressed in vector notation as follows: x ( t) = s T Ab (3) T where A = diag ( ) is the diagonal amlitudes matrix, b = [ b 1 ] is the vector of the data A KxK b K bits of K users, and s = [ s 1 ( t) s K ( t)] T is the vector of signature waveforms Assume the AWGN channel between the BS and each MS Then the received signal at the th MS is given by: r ( t) = x( t) n ( t) (33) + Consider extension of this model to the frequency-selective fading channel If there are L resolvable aths, the imulse resonse of the th user s channel is given by: where L h ( t) = l = 1 0 h δ ( t lt ) (34) l h l is the time varying comlex Gaussian fading coefficient corresonding to the l th ath of the th user The received signal at the th MS is given by: c K L 1 r ( t) Ajb jhls j ( t ltc ) + n = j = 1 l = 0 ( t) (35) Now consider the ulin system with K active users The transmitted signal x (t) at the th MS in one bit interval will be: x ( t) = A b s ( t) (36) Assuming the AWGN channel between the BS and each MS, the received signal at the BS is given by: 19

33 K r( t) = x ( t) + = 1 n( t) (37) If each channel between the BS and MS s is frequency selective with L resolvable multiath comonents as in (34), the received signal at the BS is: r( t) K L 1 = = 1 l = 0 A b h s ( t lt ) l c + n( t) (38) 3 DS/CDMA Receiver Structures 31 The Conventional Detector for AWGN Channels The simlest form of detector is the conventional detector To obtain the decision statistics for the desired user, the received signal is filtered by a matched filter matched to the signature waveform of the desired user and followed by a samler Consider the received signal given in (33) The outut of the filter matched to th user s signature waveform at the th MS, followed by the samler is given by: y = Tb 0 r ( t) s ( t) dt =1K (39) Combining K oututs into a single vector y =[y 1 (t) y (t) y K (t)] T yields: y = RAb + n (310) where R is the crosscorrelation matrix with elements R i,j defined as: Tb R, = s ( t) s ( t) dt, j = 1K (311) i j 0 i j and n Kx1 is a white Gaussian random vector with zero mean and covariance matrix I K N o, denoted by n N( 0, I N ) where 0(K,1) is the vector of K zeros and I K is the KxK identity matrix ~ ( K,1) K o The multile access interference (MAI) arises from the fact that R is not diagonal 0

34 Consider the received signal given in (37) The outut vector of the ban of filters matched to the users signature waveforms at the BS, followed by samlers is given by: y = RAb + n (31) where n ~ N( 0 K,1), RN ( o ) In this case, the filtered noise at the outut of the matched filters is colored since R is not an identity matrix The decision for the th user is given by: b ˆ ( t) = sgn( ) (313) y In vector form, this equation is given by b ˆ = sgn( y) The conventional detector, although simle, erforms oorly when a large number of users are active in the system, since the MAI is treated as additive noise Weaer users also suffer from the near-far roblem, unless ower control is emloyed The near-far roblem arises when mobiles transmit at the same ower but at different distances from the BS Due to different roagation losses, the transmissions can arrive with very different received owers The mobiles near the BS, which have high received signal owers, greatly interfere with the distant mobile, which may not be detected 3 The Maximum-Lielihood Detector The maximum-lielihood receiver gives the lowest achievable Bit Error Rate (BER) by selecting the most liely vector b given the observations, which corresonds to maximizing the lielihood metric [4]: bˆ = T max (y b b K b { 1,1} T RAb) (314) It has been shown in [4] that the comlexity of this detector is exonential in the number of users Therefore, alternative solutions have been roosed that aroach the BER erformance and near-far resistance of this decorrelator with lower comlexity [4-9] 1

35 33 The Decorrelating Detector for AWGN Channels In [4], Luas and Verdu roose a family of linear detectors whose comlexity is also linear in the number of users Assume that the outut of the ban of matched filters is given in (31) The decorrelating detector uses the decision rule: ˆ 1 1 b = sgn( R y) = sgn( Ab + R n) (315) where R -1 is the inverse of the crosscorrelation matrix R As seen in (315), the decorrelator doesn t require the nowledge of user energies, which rovides near-far resistance For the case of unnown user energies, this decorrelator is equivalent to the maximum-lielihood detector [4] The only requirement of the decorrelator is that the signature waveforms are linearly indeendent, so that R is invertible The MAI is eliminated at the exense of increased noise ower The enhanced noise variance for the th user is given by σ =N o (R -1 ), where (R -1 ) is the, th element of the matrix R -1 The robability of error associated with this receiver for user is given by: P Q A = 1 ( R ) N o (316) 1 t / where Q( ) is the error function defined as Q ( x) = e dt π 34 The RAKE Receiver Assume that the users in a CDMA system exerience frequency-selective fading In this case, time delayed versions of the original signal arrive at the receiver A RAKE receiver combines these time delayed signals in order to imrove the signal to noise ratio (SNR) at the receiver The time-shifted versions of the original signal are collected by roviding a searate correlation receiver for each of the multiath signals The RAKE receiver is essentially a x

36 diversity receiver designed secifically for CDMA systems It was shown that diversity techniques can be used to imrove the error erformance of systems exeriencing fading [1] The erformance of the RAKE receiver is based on the design of the sreading sequences Viewed in the time domain, the multiath resistance roerties are due to the fact that the delayed versions of the transmitted signature waveform will have oor correlation with the original signature waveform and will thus aear as another uncorrelated user, which is ignored by the receiver In a multiuser system, the multiath destroys the original orthogonality of the sreading sequences As a result, the erformance of the RAKE receiver is limited by the cross-correlation of the sreading sequences, as well as by the auto-correlation The RAKE receiver utilizes multile correlators that are matched to a secific delayed version of the original signal The oututs of each correlator are weighted by the conjugate of the comlex gain of the corresonding ath Then the resulting signals are summed to achieve the decision metric As a result, the received signal is rocesed in an otimum manner to collect the signal energy from all of the received signal aths The bloc diagram of the RAKE receiver at the th MS is given in Figure 33 We assume that there are K active users with L resolvable aths The received signal is given by equation (35) Assume that that the sreading waveform s (t) of th user has the ideal autocorrelation, that is, E[(s (t)s (t-τ)]=0 when τ 0 Furthermore, assume that there is no MAI (ie Sreading waveforms and their delayed versions have zero cross-correlation) Then the average SNR of the desired signal is given by: SNR = E L 1 l = 0 h N l 0 E (317) 3

37 The BER erformance of this ideal RAKE system is equivalent to the otimal diversity case, ie Maximal Ratio Combining (MRC) with the order of L The robability of error for the th user is given by [1]: L L 1 1 L 1+ l 1 P = (1 µ ) (1 + µ ) (318) l = 0 l Filter Matched to s (t) h * 0(t) r (t) Filter Matched to s (t-t c ) bˆ h * 1(t) Filter Matched to s (t-(l-1)t c ) h * (L-1)(t) Figure 33 RAKE receiver with MRC at the th mobile station where µ = and 1 + is the average SNR er ath, which is assumed to be identical for all aths of all channels 4

38 E = E( hl ) (319) N o As mentioned above, the multiath channel results in the loss of orthogonality between the sreading waveforms and causes self-interference and MAI To overcome this roblem, interference cancellation methods can be emloyed 35 The Multiath Decorrelating Detector This linear multiuser detector (MUD) roosed in [1], consists of a ban of filters matched to delayed versions of the users signature waveforms followed by a linear transformation that decorrelates the multiaths of each user The decorrelated signals for a given user are then whitened and otimally combined s 1 (t) r(t) s 1 (t-(l-1)t c ) s K (t) s K (t-(l-1)t c ) T b 0 ( ) dt Tb + ( L 1) Tc ( L 1) Tc T b 0 ( ) dt ( ) dt Tb + ( L 1) Tc ( L 1) Tc ( ) dt y 1 y L y L+1 y KL R -1 Whitener& Combiner 1 Whitener& Combiner K ˆb 1 bˆk Figure 34 Multiath Decorrelating Detector 5

39 This receiver is subotimal but low-comlexity It alleviates the near-far roblem while reserving the multiath diversity gain Performance loss is due to the zero-forcing nature of the algorithm that increases with the number of aths Refer to Figure 34 for the bloc diagram of this demodulation technique Since the nowledge of all users sreading waveforms is required, this detector is suitable for the ulin The received signal r(t) given in (38) is assed through a ban of KL filters matched to the delayed signature waveforms of the users The oututs are samled at the intervals T b +lt c (l=0,,l-1) and the resulting vector y = [ T y1 y KL ] KLx1 is given by: y = RACb + n (30) where, T b + ltc T T T T T R = [ ( ) ( )] [ ( ) ( )] = 0 1 s t s t t t dt l L 1 K s s 1 K (31) ltc KLxKL T T A = diag[ A1 1( ) A 1( )] C = L T T diag ([ h 1 ( t) hk ( t)]) KLxKL K L (3) (33) T T T b1 1( L) bk ( L) ] KLx1 b = [ 1 (34) n N ( 0, RN ) (35) ~ ( KL,1) o T T where, s ( t ) = [ s ( t) s ( t T ) s ( t ( L 1) T )], h = h h ], 1(n) is a column of n ones, c c [, 0, L 1 0 (m,n) is an mxn matrix of zeros These samles are rocessed by the decorrelator R -1 The resulting vector is T y = ACb + n, where n ~ N ( 0, R N ) We need to otimally combine ( KL,1) o indeendently fading signals in correlated noise The whitening filter for user ( H T ) 1 is obtained through Cholesy decomosition = T H T [ and M[ ] is the, th (LxL) bloc of R - M ] 6

40 1 H 1 Maximal ratio combining is erformed with h The resulting decision metric is h T H 1 ( T ) [ y] ( L( 1) 1: L ) H 1 + conditioned on the fading coefficients is: T The bit error rate of user associated with this decorrelator P h H 1 A h ( M[ ]) h ( e) = Q( ) (36) N Averaging this error robability over the distribution of fading coefficients, we get: o P ( e) = β L 1 j 1 j= 0 1 j + j (37) 1 where j = λ j A / No, λ j are the distinct eigenvalues of the matrix Σ (( M[ ]) ), is the covariance of h (t), and β j = λ /( ) i= 0, i j j λ j λi L 1 36 The RAKE Decorrelating Detector This is a receiver based zero-forcing decorrelating technique roosed in [13] It is based on the general arguments given in [4-5] for a BPSK linear multiuser detector but the received Σ signal is matched to a ban of combined resonses T h ( t) = h s ( t) = 1 K Refer to Figure 35 for the bloc diagram of this technique The matched filter outut vector can be written as: y = RAb + n (38) * h 1 ( t) T b r(t) ( ) h * K t 0 ( ) dt y 1 1 R ˆb 1 T b 0 ( ) dt y K bˆk Figure 35 RAKE Decorrelating Detector 7

41 where, Tb H ( h R ) i, j 1 K * R, = h ( t) h ( t) dt = [, ] h = (39) i j 0 i j R and are defined in the section above and is the i,j th LxL bloc of R h i i j j R[ i, j] KxK T A = diag ([ A 1 A ]) KxK ([ b 1 b K ] ) Kx 1,b =, n N ( 0, RN ) The decorrelator outut is given ~ ( K,1) o by 1 ~ (K, 1) o y = R 1 y = Ab + n, where n N ( 0, R N ) The instantaneous bit error rate of user associated with this decorrelator conditioned on the fading coefficients is: A P h ( e) = Q 1 ( R ) N o (330) To get the unconditional robability of error, (330) should be averaged over the distribution of ( R 1 ), which will be resented with numerical results This robability of error is simly that of the conventional Gaussian channel BPSK detector oerating in a single user 1 environment and whose SNR is scaled by 1 /( R ) This is analogous to the noise enhancement factor of a Gaussian MUD RDD requires the inversion of a KxK matrix, which is deendant on the channel coefficients for each symbol interval MDD requires a KLxKL matrix inversion, but the matrix is not deendant on the channel and the inversion is erformed only once However, there is a comlexity-erformance trade off between the methods Although both methods are zero forcing and subotimal in the maximum lielihood sense and they don t require the nowledge of user energies, RDD rovides the otimum erformance over all linear multiuser detectors for multiath signals of unnown energy, as roved in [5] 8

42 33 Wideband CDMA (W-CDMA) System Wideband DS/CDMA is emerging as the redominant radio access technology for the next-generation regional and global wireless standard CDMA technology was introduced in US with the IS-95 standard and this technology has aved the way for ossible future deloyment of a more refined system The requirements for a future wireless communication system include: High quality service (eg toll quality seech, data services with BER less than 10-6 ) High data rate communication services and asymmetric data transmission Suort for both acet and circuit switched services, such as Internet traffic and video conference New charging mechanism, data volume vs time Higher networ caacity, enhanced sectrum efficiency Suort for numerous and simultaneous connections The roosed W-CDMA system offers: Increased Caacity and Coverage: W-CDMA uses wider channels (5 MHz-15 MHz) Wider bandwidth imroves frequency diversity effects, reduces fading Coherent modulation in the ulin rovides -3 db demodulation gain Due to less fading, ower control accuracy is imroved Fast ower control in both lins combats fading effects and reduces average ower level, increases caacity Field test results show that 5Mhz WCDMA carrier can handle u to 8 times more traffic comared to a narrowband 15Mhz CDMA channel Variable and High Seed Data Rates: 9

43 W-CDMA suorts both low and high bit rates Rates u to 384 bs with full mobility and Mbs in local area suorts different communication requirements from voice to multimedia data Variable data rates are achieved by using variable orthogonal sreading codes and adatation of the transmitted outut ower Both Pacet and Circuit Switched Services: W-CDMA has an otimized acet mode User ays only for the amount of data transmitted Both fast acets for infrequent acets and large or more frequent acets are suorted This is imortant for remote LAN and wireless Internet access High seed circuit switched services for real time alications such as video conferencing are also suorted Multile Simultaneous Services: Each W-CDMA terminal can use several services such as be connected to LAN and receive a voice call Other System Imrovements: W-CDMA suorts Adative Antenna Arrays (AAA) which gives ossibility to use the sectrum more efficiently and increases the caacity W-CDMA uses ilot symbols er connection in downlin that enables AAA Base stations are not required to have GPS synchronization since W-CDMA has an internal system for synchronization W-CDMA suorts Hierarchical Cell Structures by introducing a new hand-off method between CDMA carriers called Mobile Assisted Inter-Frequency Hand-off The mobile stations scan numerous CDMA carriers and enable the deloyment of hot sot micro cells W-CDMA also suorts multiuser detection 30

44 Key Technical Characteristics for UMTS α-concet: Multile-Access Scheme Dulex Scheme Chi Rate Carrier Sacing (4096 Mcs) Frame Length Inter-base Station Synchronization Multi-rate/Variable-date Scheme DS-CDMA FDD/TDD 4096 Mcs (exandable to 819 Mcs and Mcs) Flexible in the range 44-5 Mhz ( Hz carrier raster) 10 ms FDD mode: No accurate synchronization needed TDD mode: Synchronization needed Variable sreading factor and multi-code Channel Coding Scheme Convolution coding (rate 1/-1/3) Otional outer Reed-Solomon coding (rate 4/5) Pacet Access Dual mode (common and dedicated channel) Table 1 Key characteristics of W-CDMA System Descrition: Two hysical channels: Data Channel and Control Channel Convolutional coding only for BER=10-3 (standard) Additional outer Reed-Solomon coding for BER= 10-6 (high quality) Sreading with channelization codes with factors 4 to 56 Downlin scrambling with 10ms Gold code of length

45 Ulin scrambling with VL-Kasami sequences of length 56 for multi-user detection receivers else with 10ms Gold code of length 41-1 QPSK with root-raised cosine ulse shaing filter 34 Simulation and Numerical Results The Wideband CDMA system described in section 33 is used to evaluate the erformance of various receiver structures The sreading codes are created using the orthogonal tree structure Simulation and numerical results are given in Figures For all lots, erfect CSI is assumed MRC gives the otimal erformance with the order of diversity equal to the number of aths Figure 36 and 37 demonstrate the diversity achieved by emloying the RAKE receiver for a single user for two and four aths As the number of aths increase, the BER erformance of the system imroves In Figure 37, coded results are lotted For W-CDMA, half rate, constraint length of nine convolutional coding is used Decoding is erformed using the Viterbi algorithm It is shown that coding imroves the erformance significantly Since the sreading waveforms used with W-CDMA are not ideal, introduction of other users degrade the BER of all users Besides the MAI, the multiath also destroys the selforthogonality of the sreading codes, resulting in ISI The multiuser techniques introduced in section 3 are used to remove the MAI and the results are given in Figures It is observed that these techniques imrove the BER significantly The MAI deends on the number of users, number of aths, sreading factor and the characteristics of the sreading codes More users, more aths and small sreading factor increase the MAI The RAKE receiver does not remove the MAI, so its erformance degrades raidly when MAI increases, as observed in the figures Both RDD and MDD imrove the BER 3

46 erformance by removing the MAI The resulting system aroaches the otimal case of MRC RDD erforms slightly better than MDD As mentioned before, RDD is the otimal decorrelator for the signals of unnown energy and MDD is subotimal Figure 36 Bit Error Rate for single antenna single user Single, two and four ath fading channels f dm =00Hz, uncoded, 3 chi sreading Normalized total channel owers 33

47 Figure 37 Bit Error Rate for single antenna single user Single, two and four ath fading channels f dm =00Hz, coded, 3 chi sreading 34

48 Figure 38 Bit Error Rate of user 1 for single antenna Two users, two aths f dm =00Hz, uncoded, 16 chi sreading A 1 /A =1 35

49 Figure 39 Bit Error Rate of user 1 for single antenna Four users, two aths f dm =00Hz, uncoded, 8 chi sreading A 1 /A =1 36

50 Figure 310 Bit Error Rate of user 1 for single antenna Eight users, four aths f dm =00Hz, uncoded, 3 chi sreading A 1 /A =1 37

51 Chater 4 Long Range Prediction of Rayleigh Fading Channels As mentioned in the introduction, accurate nowledge of the future CSI is very imortant in alication of transmitter diversity and multiuser recoding techniques These methods (excet OTD and TSTD) are closed-loo methods, ie they require feedbac from the receiver (MS) However, because of the time-varying nature of the channel, this feedbac is outdated when it arrives at the transmitter (BS) For very slow fading channels (edestrian or low vehicle seeds), outdated CSI is sufficient for reliable adative system design However, for faster fading that corresonds to realistic mobile seeds, even small delay will cause significant degradation of erformance since channel variation due to large Doler shifts usually results in a different channel at the time of transmission than at the time of channel estimation For W-CDMA channels, channel estimation at the MS is erformed at every slot (065 ms) Simulation results show that when the outdated CSI is used, significant erformance degradation occurs The objective of the LRP is to forecast the future CSI of the time-varying fading channel so that we can imrove the erformance of the diversity and multiuser detection techniques 41 Linear Minimum Mean Squared Error Prediction of the Rayleigh Fading Channels Several adative channel estimation methods have been described in the literature [14-17] However, many of these techniques are better suited for very short range rediction or require very large comutational comlexity Thus, there is a need for adative, low comlexity, long range rediction technique that meets the accuracy requirements for realistic mobile radio channels 38

52 The LRP algorithm that is being emloyed to enable the techniques of interest in this thesis have been extensively studied and develoed in [18-4] This algorithm characterizes the fading channel using the autoregressive (AR) model and comutes the Minimum Mean Squared Error (MMSE) estimate of a future fading coefficient samle based on a number of ast observations Assume we samle the channel at a rate f = 1/, where f, s T s s f dm f dm is the maximum Doler shift The channel is assumed to be comlex Rayleigh fading rocess c(t) as described in Chater Let c = c( it ) s Our aim is to redict cn based on i (AR model order) reviously observed channel samles c n-,c n-+1,,c n-,c n-1 We comute * the (x) autocorrelation matrix R with coefficients R = E c n c ] and (x1) ij [ i n j autocorrelation vector r with coefficients * r i = E[ cncn+ i ] Then the minimum mean square error rediction of cn is : cˆ n = i= 1 d c i n i (41) where d = { d i }, i=1 and d = R 1 r The observation interval can be significantly reduced and matrix inversion can be avioded if adative long range rediction is used [4] The resulting MMSE is given by: 1 i= 0 E[ e( τ ) ] = 1 d r( τ + ) (4) i jt s The suerior erformance of this algorithm relative to conventional methods is due its low samling rate (on the order of twice the maximum Doler shift and much lower than the data rate) Given a fixed model order, the lower rate results in longer memory san, ermitting rediction further in the future The autocorrelation function r( τ ) = E[ c( t) * c( t + τ )] of Rayleigh fading channel is: 39

53 where J o ( ) r ( τ ) = J o (πf τ ) (43) dm is the zero-order Bessel function of the first ind This autocorrelation function has large sidelobes For a given model order and samling rate fs, the memory san is defined as (-1)/f s, which measures the observation interval used for rediction in (41) As the samling rate changes, the ortion of the autocorrelation function catured by the samles r( τ + jt s ) changes When the channel is samled at a high rate, a small ortion of the sidelobes is catured, resulting in high MMSE However when the samling rate is low, the observation samles are saced much further aart and result in a large memory san This ees MMSE small and reliable rediction is achieved for long ranges The lot of the autocorrelation function for f dm =00Hz is given in Figure 41 For a fixed model order, as the samling frequency increases, the memory san decreases For examle, it is observed from the figure that for =50 and f s =16 Hz, the memory san is 3065 ms The range of values of the autocorrelation function samles along this interval is small As τ increases (rediction far ahead), these autocorrelation values become small, and MMSE increases Now consider the case when =50 and f s =16 hz In this case, the memory san is 3065 ms The autocorrelation values used in rediction vary significantly over this interval Due to the large sidelobes of the autocorrelation function, some of these values are large enough to ee the MMSE from getting large and reliable long range rediction can be achieved even when the rediction range is much greater than the coherence time τ o (r(τ o )=1/ ) 40

54 Figure 41 Theoretical autocorrelation of the Rayleigh fading channel and the memory san of the MMSE rediction for f dm =00 Hz For W-CDMA, the samling rate f s is chosen as the slot rate of 16Hz This results in 065 ms delay for calculating the CSI The rediction algorithm described above is used to obtain redicted values of the current and future channel coeffients given the delayed channel samles The transmitter diversity and multiuser recoding methods, which will be discussed in the following chaters, require the CSI In most cases, redicting one ste ahead is not enough (eg STD 400Hz) Prediction algorithm estimates the CSI at the channel samling rate, however for some cases, CSI at the rate of the fading is required (eg Sace- Time re-rake) In those cases, redicting several stes ahead and interolation are necessary 41

55 4 Performance Bounds of Long Range Prediction To analyze the erformance of the LRP algorithm in diversity systems, we aly results of [40,41] as follows The lower bound on the BER of a BPSK system with M iid Rayleigh fading diversity branches, MRC combining and imerfect MMSE channel estimates is: M M 1 1 M 1+ 1 P = (1 ) (1+, = 0 ) est M order µ e µ e (44) where 1 Γ µ e = and Γ is the normalized estimation error variance for each branch, 1+ 1/ defined by: E{ ei } Γ = (45) E{ c } i where e i =c i -ĉ i and ĉ i is the MMSE estimate of the branch weight c i Figure 4 demonstrates the BPSK BER for erfect vs MMSE redicted CSI with single user, single ath Rayleigh fading The Doler shift is 00Hz, =50, 00 samles are used in calculating the autocorrelation function of c n The data rate is 18 bs and the channel samling rate is 16 Hz A delay of 065ms is assumed and three ste rediction is erformed CSI at the data rate is found by low-ass interolation based on these redicted values The estimation error Γ is calculated from the simulation The bound in the figure is found by evaluating equation (44) with this Γ The ey element in using the formulas above is to be able to have a good estimate of the average error figure ie Γ For the simulations of Chater 5, Γ is obtained directly from the rediction of the channel coefficients and averaged over all diversity branches 4

56 Practically the errors for different branches are different because of the finite simulation interval However averaging over all branches gives a good estimate of the rediction error Figure 4 BER of BPSK system with erfect vs MMSE redicted CSI Flat fading, single user, single antenna, uncoded 43

57 Chater 5 Transmitter Diversity Techniques The ulin (from MS to BS) caacity of the CDMA systems can be enhanced by various techniques including multi-antenna (diversity/antenna array) recetion and multiuser detection (MUD) The techniques that increase the downlin (from BS to MS) caacity have not been develoed with the same intensity However, it is understood that the caacity demand imosed by the rojected data services (eg Internet) burdens more heavily the downlin channel Hence, it is imortant to find techniques that imrove the caacity of the downlin channel Bearing in mind the strict comlexity requirements of terminals, and the characteristics of the downlin channel, an alication of advanced detectors with multile receive antennas is not seen as the desired solution to the downlin caacity roblem Transmitter diversity in the downlin using multile transmitter antennas rovides similar erformance gains as for the MS receiver diversity without the comlexity of a second receiver antenna Transmitter based methods enable to shift signal rocessing to the transmitter where ower and comutational comlexity are more abundant, thus simlifying receiver units Different solutions have been roosed suggesting that multile antennas (or transmit diversity) at the BS will increase downlin caacity with only minor increase in terminal imlementation CDMA technology is designed to exloit the multiath characteristics of the channel However, the RAKE receiver is required to achieve multiath diversity gain For the downlin, this requirement increases the comlexity and ower consumtion of the MS Pre-RAKE diversity combining techniques [9-31] were roosed 44

58 to overcome this roblem With this method, RAKE combining is erformed before transmission at the BS so that the MS can emloy a simle matched filter receiver The roosed techniques include Sace-Time Coding [30], Delay Diversity, Orthogonal Transmit Diversity (OTD), Time-Switched Transmit Diversity (TSTD), Selective Transmit Diversity (STD) and Transmit Adative Array (Tx AA) [31-34] We investigate a novel technique called Sace-Time Pre-RAKE Transmitter Diversity (STPR) [37] This method was also indeendently roosed in [31,48] The roosed transmitter diversity methods for W-CDMA can be classified as oenloo or closed-loo techniques Oen-loo techniques do not require feedbac from the MS (eg TSTD, OTD), where closed-loo techniques rely on the feedbac from the MS (eg STD, Tx AA, STPR) Feedbac from the MS is in general used to rovide the BS with information about the fading characteristics of the transmission medium (CSI) The techniques that require the feedbac of CSI are referred to as adative methods With the hel of the feedbac, better erformance is achieved than for non-adative methods For oen-loo techniques, a re-determined algorithm of antenna/coding usage is emloyed For examle, transmission is switched sequentially between N antennas at the rate of R for TSTD Since the BS doesn t use any information about the channel state, time varying channel characteristics are not taen into consideration Closed-loo techniques on the other hand emloy adative algorithms of antenna/coding usage In STD method, for examle, the transmission is switched to the antenna with the highest channel gain The antenna selection is based on the feedbac from the MS As a result, channel characteristics are traced and better erformance than oen-loo techniques is achieved We mainly focus on closed-loo schemes such as the STD, Tx AA and STPR 45

59 In the simulation, numerical and theoretical results given in this chater, we assume that the total transmitted signal energy to noise ratio er bit for the user is given by E / N b o 51 Time-Switched Transmitter Diversity (TSTD) According to the TSTD method, transmission is switched sequentially between different transmit antennas, using one at a time, according to a redetermined switching frequency No channel estimation is required at the transmitter Channel coding, rate matching, interleaving and sreading are done in the same way as in no transmitter diversity case with a single antenna This scheme is shown in Figure 51 Tx Antenna #1 cos w c t FIR Pilot TPC (RI) DTCH data ACCH data Channel Encoder Channel Encoder M U X Rate Matcher Interleaver M U X Odd Even Channelization Orthogonal Code SC m LC I LC I Generator LC Q LC Q Generator Switching Controller FIR FIR sin w c t cos w c t Tx Antenna #N FIR sin w c t Figure 51 Time Switched Transmit Diversity 5 Orthogonal Transmitter Diversity (OTD) In the OTD method, the coded bits of each user are distributed to M antennas Each antenna uses a sreading code that is orthogonal to others The bit ower of the user is equally slit between the antennas, so that the total transmitted ower remains constant The MS collects the information from the transmit antennas by desreading in arallel with M 46

60 dedicated channel codes This multile antenna scheme rovides diversity at the MS The bloc diagram of OTD is given in Figure 5 Sreading s 1 (t) Modulation & Power Scaling User Coded Bits Sreading s (t) Modulation & Power Scaling Sreading s M (t) Modulation & Power Scaling Figure 5 Orthogonal Transmit Diversity Theoretical BER of uncoded OTD with flat fading and two antennas is given in Figure 53 For comarison uroses, flat fading no diversity (single antenna) case and MRC with diversity order of two are also lotted We can conclude from the figure that, the OTD rovides some diversity over the single antenna case, however its erformance is not otimal The otimal case with the diversity of order two is given by -MRC 47

61 Figure 53 Orthogonal Transmit Diversity vs Maximal Ratio Combining 53 Selective Transmit Diversity (STD) According to the STD concet, the dedicated channel of a given user is switched to the designated antenna, as secified by Antenna Selection (AS) message The AS message is signaled in the ulin frame by each MS The roosed concet utilizes a fast feedbac channel from the MS to the BS, where the feedbac channel (AS) determines the best transmit antenna for each MS individually, and the signals to different users are transmitted simultaneously The bloc diagram of STD is given in Figure 54 The feedbac channel can be transmitted by uncturing the ower control bits within the current ulin frame format, rovided that the antenna selection rate is smaller than the rate of ower control channel 48

62 Base Station Ant 1 Pilot RI TPC DATA Encoder Interleaver M U X Sreading & Modulation Switch RF RF Ant M Mobile Station AS Figure 54 Selective Transmit Diversity Alternatively, it can be added to the ulin dedicated channel signal The changes roosed to the BS transmitter are also small In articular, encoding, interleaving and sreading are identical to those used with single-antenna transmission A minor change is roosed for downlin dedicated channel training sequences to further robustify the concet The erformance of this technique matches that of the selection diversity at the receiver STD is a closed-loo technique, since it requires the CSI to mae the antenna selection This CSI is used to calculate the channel ower associated with each antenna and the transmission is switched to the antenna with the highest channel ower The channel corresonding to each antenna is time varying, since the mobile is in motion Due to feedbac delay, the CSI at the instant of antenna selection is outdated Using these outdated CSI values causes BER erformance degradation STD switching frequency determines the rate at which AS signal is fed bac to the BS, hence the switching between the transmit antennas Different switching rates result in different BER erformance of the system The lower bound for the erformance of this technique is achieved when the antenna switching is done for every symbol transmitted The theoretical BER for STD with every symbol switching is given in Aendix A 49

63 As mentioned in Aendix A, transmitting over the channel with the highest SNR results in an increase in the average received SNR at the MS To have a fair comarison among different transmitter diversity techniques, this increase should be taen into account One way to do this is to comare different methods using the received SNR er transmitted bit This results in a shift in the STD curves Figure 55 demonstrates the comarison between the flat Rayleigh fading, uncoded, Everybit STD and MRC for eight diversity cases Perfect CSI is assumed The BER of STD is comuted using equation (A1) and the BER of MRC is given by equation (38) The x-axis is given by the received SNR er bit, as described in (A14) In the figure, L is the number of antennas for STD and M is the order of diversity for MRC Figure 55 Flat fading Selective Transmit Diversity vs Maximal Ratio Combining 50

64 We conclude from the figure that flat fading STD with L antennas erforms similarly to the otimal case of MRC with order of M=L for a modest number of antennas Figure 56 comares multiath, uncoded, Everybit STD with flat fading, uncoded Everybit STD and MRC For the multiath STD, we assume that we have two antennas and the iid channels between the antennas and the MS are frequency selective Rayleigh fading with two aths Perfect CSI is assumed There are four antennas for the flat fading STD and the order of MRC is four The BER of multiath STD is comuted using equation (A30) Figure 56 Frequency-selective STD vs MRC and flat fading STD As seen from Figure 56, the BER erformance of four antennas flat fading STD, two antennas two aths STD and the MRC of order four are almost the same So, the order of 51

65 diversity introduced by STD can be aroximated by the number of antennas for flat fading case and (# of antennas)x(# of ath) for STD with M antennas and L aths 54 Transmit Antenna Array (Tx AA) Tx AA is a closed loo transmitter diversity technique and it requires feedbac from the MS It is assumed that multile transmit antennas are located at the BS and the MS emloys single antenna recetion Tx AA is illustrated in Figure 57 h 1 (t) Tx Base Station Sread Signal w 1 w h (t) h M (t) Rx Mobile Station Comute TxAA Weights w M Figure 57 Bloc diagram of Transmit Adative Array For Tx AA, each antenna transmits coherently with the same coded and sread data but with antenna-secific weighting Each transmitter antenna has a searate ilot signal, which enables the MS to individually estimate the channels used by each antenna The goal of this scheme is to choose these weights alied at the BS such that total ower received by 5

66 the MS is maximized Assuming channels are stationary during one bit interval, we weigh each chi in a bit by the same weight Assume we have a single user and M antennas at the BS with iid flat fading channels between the BS and the MS The imulse resonse of the i th channel is given by h 1( 1 t t) = hδ ( ) Define the row vector of channel fading coefficients and the column vector of weights as: h = h h ] (51) [ 1 h M w1 w w = (5) : w M To ee the total transmitted ower normalized, we need to have the constraint: w H w = 1 (53) H where w is the Hermitian of the vector w Then the received signal at the MS is given by: y( t) = hwx( t) (54) where x(t) is the user s data signal The weight vector is chosen to maximize the received ower under the constraint given in equation (53) Then the Tx AA weights are [35]: P = w H h H hw (55) H h w = (56) H hh Note that, the i th antenna weight for the flat fading case is just the comlex conjugate of the i th channel coefficient, normalized by the total ower of all channels This weighing 53

67 taes lace at the rate of the change of the channel coefficients Then the received signal is given by: H hh y( t) = x( t) (57) H hh For BPSK modulation, the erformance of this technique is equivalent to MRC with the order of M (number of antennas), given in equation (38) Assume we have M antennas with L indeendent aths for each channel between the antennas and the MS The RAKE receiver with L fingers is emloyed at the MS Then the matrix of channel gains is defined as: h h h 11 1 M H = (58) L1 h h h 1 L h h h 1M LM LxM where h ji is the comlex fading coefficient corresonding to the j th ath of the i th antenna Then the weighting vector, which maximizes the total received ower at the MS is the normalized eigenvector matrix H H H [36] vmax, corresonding to the largest eigenvalue, λmax of the MxM The main assumtion that enables Tx AA is the nowledge of the CSI of the downlin channel for each antenna at the time of weighing The CSI is fed bac to the BS from the MS In ractice, due to feedbac delay, the CSI at the instant of antenna weighing is outdated Using these outdated CSI values causes BER erformance degradation It was shown in [37] that although Tx AA with flat fading channels is otimum, Tx AA cannot achieve the otimal erformance in multiath fading due to scalar weighting Moreover, it requires the RAKE receiver at the MS Assume we have two antennas and four 54

68 Rayleigh fading aths for each antenna The simulated BER erformance of this uncoded system is given in Figure 58 We assume that the sreading sequences are ideal For comarison uroses, no diversity flat fading, Tx AA flat fading with eight antennas and MRC of order two, four and eight are also lotted As demonstrated, Tx AA with flat fading achieves the otimal diversity case, given by MRC of order eight Although Tx AA with multiath fading rovides some diversity comared to the MRC of order 4, it is still subotimal Figure 58 Two antenna four ath Tx AA vs MRC 55

69 55 Pre-RAKE Transmitter Precoding As seen in equation (317), when the sreading sequences are ideal, the RAKE receiver collects all the ower available from all aths, ie, it is equivalent to MRC [1] However, this rocessing is done at the MS for the downlin This requires additional signal rocessing and ower consumtion Given the limitations of the mobile stations, it would be more desirable to achieve the same erformance without the need of the RAKE receiver It was shown earlier that re-filtering of the transmitted signal at the BS using an FIR filter could achieve the same erformance by emloying a single ath receiver at the MS [9-31] This transmitter recoding technique is nown as the Pre-RAKE Diversity Combining Assume we have a single user with a single transmit antenna at the BS The channel is frequency-selective Rayleigh fading with L aths The taed delay line channel model is given in Figure 1 The re-rake filter associated with this channel is shown in Figure 59 The re-rake filter is a modeled as a L-taed delay line and the coefficients of the re-transmit filter are the conjugates of the channel coefficients The order of the FIR coefficients is the reverse order of the channel coefficients Pre-filtering the signal before transmission increases the transmit ower To ee the transmitted ower constant, sread inut signal should be scaled The scaling factor is: S f = L 1 1 j = 0 h h * j j = L j= 0 1 h j (59) 56

70 Base Station Pre-RAKE Filter S f User data Sreading s(t) ss(t) h * L-1(t) (t) D D h * L-(t) h * 0(t) Channel n(t) Mobile Station (t) h 0 (t) r(t) Filter Matched to s(t-(l-1)t c ) D D h 1 (t) h L-1 (t) Figure 59 Bloc diagram of Pre-RAKE diversity 57

71 Assume that the user s bit is given by b with amlitude A The bit energy is given by Eb The sread signal is: ss ( t) = Abs( t) (510) Then the transmitted signal in this case is: The received signal is: L 1 1 ( t) = Abh s( t jt ) (511) L 1 j = 0 h j = 0 j * L 1 j c L 1 L 1 1 * r (t) h h s( t ( j + l) T ) + n( t) (51) = L 1 h j= 0 l l = 0 j= 0 j L 1 j c The receiver emloys a single matched filter, matched to s t ( L 1) T ) Assume ( c that the sreading waveform is ideal Then the instantaneous energy of the matched filter outut is given by: E b L 1 j = 0 h j L 1 L 1 j = 0 h j = E b j = 0 h j (513) The average SNR is: SNR PR E ( L 1 j = 0 h j 0 ) E b = (514) N Comaring equation (317) to equation (514), it is observed that re-rake diversity combining is equivalent to RAKE receiver with less receiver comlexity The ey assumtion in alying the method described above is the nowledge of the CSI at the transmitter Filtering taes lace before transmission and we assume that we now 58

72 the channel coefficients of each ath Using inaccurate CSI results in erformance degradation 56 Sace-Time Pre-RAKE Transmitter Diversity Method (STPR) As mentioned above, when Tx AA is used for the multiath fading channels, the resulting system cannot achieve the otimum erformance, ie it cannot achieve the gain of the MRC of all sace and frequency diversity branches [36] This is due to the scalar weights used by the Tx AA We roose a sace-time re-rake method that otimally combines multiath owers associated with all transmitter antennas using re-rake recoding and the aroriate scaling [37] A similar method was indeendently investigated in [31,48], but the analysis in these aers is significantly different The bloc diagram of this technique is given in Figure 510 Assume we have a single user with M antennas at the BS and the channels between the BS and the MS are frequency-selective with L aths The sread signal is given in (510) For antenna m, we filter the sread signal so that the transmitter ulse shae is: 1 L 1 * m( t) = Abh s t jt, 1 ( M L 1 m L j c j = 0 hj = 1 j = 0 ) (515) h mj where is the fading coefficient corresonding to the j th ath of the m th antenna The scaling factor ees the transmitted ower normalized and is included in m (t) The scaling factor is the inverse of the sum of all instantaneous channel owers 1 M L 1 S f = hj (516) = 1 j = 0 The receiver emloys a single filter matched to s(t-(l-1)t c ) Assume that the sreading waveform is ideal The matched filter outut is given by: 59

73 Weights for h 1 (t) h 1 (t) Sreading & Modulation ss(t) S f Weights for h (t) Delay Filter h (t) h M (t) n(t) r(t) Match to s(t-(l-1)t c Weights for hm(t) Delay Filter Weights for m th antenna D D h * m, L-1 h * m, L- h * m,0 Figure 510 Bloc diagram of Sace-Time Pre-RAKE diversity combining 60

74 M L 1 = 1 j = 0 hj Ab + z( t) (517) where z (t) is the filtered noise The SNR is: SNR STPR M L 1 = j = = 1 0 h N o j E b (518) This diversity system is equivalent to MRC with LxM diversity branches The robability of error is given by equation (318) This resulting BER shows that emloying this method, all frequency and sace diversity branches can be combined 57 Simulation and Numerical Results A simulation environment based on the W-CDMA arameters described in Chater 3 was created to evaluate the BER erformance of the closed-loo transmitter diversity schemes described above with GHz carrier frequency, 60 mh vehicle seed, f dm =00 Hz, 4096 Mcs chi rate, and the bit rate of 18 bs [39] Orthogonal codes are obtained using the tree structure, exlained in [39] We assume that there is no estimation error at the MS The results are for a single user where multile access interference is modeled as white Gaussian noise For the coded results, half-rate constraint length 9 convolutional coding is used with generator olynomial arameters 561 and 753 in octal form The minimum distance of the code is 1 The interleaving deth is 10ms The channels associated with different antenna elements are modeled by the Jaes model with 9 oscillators [3] For coded data, MRC, no diversity and Every bit results are obtained by simulation using the refect CSI For the simulations, =50 and the observation interval of 00 samles are used to comute the autocorrelation of c n (41) We utilize multi-ste rediction to redict more than one samle ahead [4] For W-CDMA the samling rate f s is chosen as the slot rate of 16 61

75 Hz [39] This results in at least 065 ms delay for calculating the CSI The rediction algorithm described in Chater 4 is used to obtain redicted values of the current and future channel coeffients in the next slot or bloc of slots, given the delayed channel samles For STD, these coefficients are used to choose the antenna with the largest received ower The number of redicted samles deends on the switching frequency [3,4,38] For Tx AA, they are used to calculate the weights of each antenna Finally, for STPR, they are utilized in filtering the sread signal rior to transmission Both Tx AA and STPR methods require the nowledge of the CSI for every symbol transmitted Since the CSI is fed bac from the MS at 16 Hz, it is necessary to use interolation to obtain the intermediate coefficients of the channel For these methods, the beginning of the current slot and the beginning of the next two slots are redicted using the ast values of the channel Then these and ast values are used to comute the intermediate values for the next slot, so that the CSI at the transmission rate is obtained In Figure 511, erformance of Tx diversity aided by LRP is illustrated for uncoded W-CDMA system For flat fading channel with M=4 antennas, the Tx AA is used The ideal erformance of Tx AA with erfect CSI is that of MRC with 4 branches, and the lower bound on erformance with LRP is given by (44) For the 4-ath multiath channel, STPR is utilized with M= antennas Equation (44) with 8 branches rovides a lower bound on its erformance with LRP For STPR, the deviation from this bound is due to multiath induced self-interference due to non-orthogonality between shifted signature sequences and non-ideal interolation of redicted channel coefficients Simulation results for both Tx AA and STPR without rediction are also included in Figure 511 When rediction is not emloyed, the delayed CSI at the beginning of the revious slot is used during the next slot, and these fixed 6

76 coefficients are used to calculate the weights and re-rake coefficients associated with the Tx AA and the STPR methods It is observed that, for both cases, the erformance with rediction is near otimal, aroximately equivalent to MRC with LxM diversity branches The gain due to accurate channel rediction is aroximately 1 db In Figures , simulation results are resented for coded systems with Tx antennas Figures 51 and 513 comare STD methods for different switching frequencies Results for flat fading channel are resented in Figure 51 It is observed that significant erformance imrovements (1- db) are ossible when rediction is used For low switching frequencies, antenna selection based on averaging redicted channel state information for the duration of the future switching interval is utilized since it results in imroved BER The Tx AA with erfect CSI rovides a lower bound on erformance of STD systems Note that the erformance of STD with higher switching rate aroaches ideal erformance (STD Every bit) and is very close to the erformance of Tx AA with erfect CSI Since STD is much simler to imlement than Tx AA, it reresents a very attractive solution for Tx antenna diversity systems Figure 513 shows the comarison between the STD with RAKE receiver and the STPR methods for a 4-ath channel The gain due to rediction is lower here than in figures (around 05 db) In general, as diversity gain due to multiath and coding increases, the channel becomes less time-variant, resulting in reduced benefit of rediction It is observed that the STPR erforms better than STD for all switching rates The gain is around 1dB gain for 16 Hz switching rate Note that MRC with LxM branches is the lower bound for all methods Due to multiath-induced interference and rediction errors, the STPR system cannot achieve its ideal BER given by the 8-ath MRC 63

77 Figure 514 comares the BER erformance of STPR and Tx AA with the RAKE receiver [36] Comarison of Figures 513 and 514 demonstrates that erformance of Tx AA is similar to that of STD, and that the STPR method significantly imroves uon both Tx AA and STD for multiath fading channels In the figures, the BER is calculated in terms of the received SNR er coded bit This SNR was evaluated theoretically for STD Every bit, no diversity and MRC curves, and comuted from simulations for other methods The comarison in terms of the received SNR er bit allows to comare directly the diversity advantages of various combining methods over different multiath channels It is observed that emloying STPR with LRP achieves near-otimal erformance for a raidly time variant multiath channel with transmission antenna array However, this gain is achieved at the exense of significant comlexity While the feedbac load is high, the RAKE filtering and rediction are erformed at the BS, where this comlexity can be afforded The Tx AA method can reduce feedbac load and feed bac a single comlex weight er antenna, rovided that rediction and the RAKE receiver are erformed at the MS Thus, the comlexity at the MS is higher for Tx AA than for STPR Moreover, Tx AA does not rovide significant erformance gain over STD for a modest number of antennas The comlexity of STD is the lowest since it only requires the feedbac of the antenna selection bits to choose the antenna with the greatest channel ower STD can be easily combined with re-rake, while still retaining lower comlexity than STPR [31] Thus, the methods described in this thesis rovide a variety of erformance/comlexity tradeoffs, with STD being the simlest, but the least ower efficient method, and the STPR technique being more comlex, and achieving near-otimal erformance 64

78 Figure 511 Simulated erformance and theoretical bounds for long range rediction, f dm =00Hz Uncoded W-CDMA, Tx AA: 4 antennas, flat fading, STPR: antennas, 4 aths 65

79 Figure 51 Performance of the STD, flat fading channel, transmitter antennas, f dm =00Hz, coded W-CDMA 66

80 Figure 513 Comarison of STD, Tx AA and Sace-time re-rake, transmitter antennas, 4 aths, f dm =00Hz Coded W-CDMA 67

81 Figure 514 Comarison of Tx AA and Sace-time re-rake, transmitter antennas, 4 aths, f dm =00Hz Coded W-CDMA 68

82 Chater 6 Multiuser Precoding Techniques 61 Multiuser Precoding Bacground The CDMA system is designed to suort simultaneous high data rate users However, the multiath-induced MAI severely degrades the erformance The conventional single user RAKE receiver [1] suffers when the orthogonality of the sreading waveforms are destroyed due to multiath channel The multiuser detection techniques exlained in Chater 3 can be used to effectively cancel MAI, but they demand high comutational comlexity and the nowledge of all users sreading waveform These receiver based techniques are not always feasible in the downlin of the CDMA system, because the ower restrictions of the MS don t ermit high comlexity and all of the sreading waveforms are not available at the MS Multiuser recoding techniques for the downlin shift the MAI suression to the transmitter, where it can be afforded It was shown that these methods are very effective in removing the MAI [4-46] 611 Multiuser Precoding for AWGN Channels As mentioned above, MAI can be removed at the receiver using comlex MUD structures As an alternative, additional filtering can be alied at the transmitter to recode the transmitted data in order to eliminate this interference at every individual receiver Downlin CDMA system is an examle of a system where these techniques can be alied The main oint of linear multiuser recoding schemes is transmitting a linear combination of all active users data instead of just the data The decorrelation rocess 69

83 removes multiuser interference in the received signal for each user Multiuser recoding methods have been reviously roosed for the AWGN, flat and multiath fading channels [4-43,45-46] Transmitter recoding was originally roosed for AWGN channels in [4] Consider the synchronous downlin DS/CDMA model given in Chater 3 The transmitted signal at the BS and the received signal at the th receiver are given by equations (31,33) The transmitted signal x(t) in matrix notation is given in equation (3): x ( t) = s T Ab (61) T where A = diag ( ) is the diagonal amlitudes matrix, b = [ b 1 ] is the vector of the A KxK b K data bits of K users, and s = [ s 1 ( t) s K ( t)] T is the vector of signature waveforms Assume that the receiver at the th MS emloys a filter, matched to the signature waveform of the th user Combining the oututs of these matched filters at K receiver sites, we get the outut vector y y = [ y 1( t) y ( t)] K y = RAb + n T (6) where R is defined in equation (311) and n Kx1 is a white Gaussian random vector with zero mean and covariance matrix I K N o, denoted by n N( 0, I N ) where 0(K,1) is the column ~ ( K,1) K o vector of K zeros and I K is the KxK identity matrix MAI is defined by the R matrix Conventional multiuser techniques use algorithms to maniulate the received signal to minimize the effects of this interference Consider a linear combination technique at the BS, so that the matched filter outut at the MS will be less affected by MAI Suose a linear transformation matrix T will be alied to the transmitted data Then the transmitted signal will be: x ( t) = s T TAb (63) 70

84 where T is a KxK matrix The outut of the matched filters of the receivers is given by: y = RTAb + n (64) We want to choose T such that the mean square error is minimized If we aly the MMSE criterion to the mean-squared error J defined by: J = b y (65) It is shown in [45] that the otimal solution minimizing this error is given by: 1 T = R (66) So that y = b + n As a result multiuser interference is eliminated and the recetion is converted into a single user detection roblem This result is obtained with the trade off caused by transmission energy increase The energy of the transmitted signal is given by: Ε E E E av av av av = E = E = E = tr [ x( t) dt] T T T [ ( s TAb) s TAb) T T T [( Ab) T ( ss dt) T ( E[ T( Ab)( Ab) ]) dt] TAb] (67) using (311), (66) and R 1 = R T Ε Ε av av Then we have = tr K T T ( TA E( bb ) A ) = A R = 1 1, av ( = tr TAA T ) (68) T 1 using E( bb ) = I K, since E( b i b ) = 0, i R, is the th diagonal element of the matrix R [45]: 1 Thus the ratio of transmitted ower with recoding to ower without recoding is 71

85 1 S f E{ Tb 0 = Tb E{ 0 x( t) x( t) dt} dt} K A = 1 = K = 1 R A 1, (69) As a result, to ee the transmitted ower constant relative to the system without recoding case, the transmitted ower should be scaled by S Then the modified transformation matrix will be T using the BPSK robability of error [1] and is given by [45]: 1 = S f R The instantaneous BER of the th can be found f P AWGN = Q S f N A o (610) This robability of error is equivalent to a BPSK system with AWGN, where the amlitude of the bit is scaled by S f Figure 61 resents an examle for this robability of error We assume 4 users with non-ideal sreading sequences Sreading sequences have high crosscorrelation, R1=03, R 13 =04, R 14 =05, R 3 =03, R 4 =04, R 34 =03 The lot shows the BER of user 1 It is observed that the conventional transmitter without recoding results in high MAI, hence high BER Precoding removes the MAI and the resulting erformance of the system aroaches the lower bound, given by the single user curve 7

86 Figure 61 BER of user 1 in AWGN Channel With and Without Precoding 4 Users, uncoded 73

87 61 Multiuser Precoding for Flat Rayleigh Fading Channels Now consider the downlin of a K-user system in a flat Rayleigh fading (frequency non-selective) environment [43] The transmitted signal is given by equation (31) Then the received signal at the th MS will be: r ( t) = h ( t) x( t) n ( t) (611) + where h ( t) = h δ ( t) is the comlex imulse resonse corresonding to the channel between the BS and the th user, h is the comlex Gaussian channel coefficient Then the received signal is given by: where n ~ N ( 0 K,1), I ( K o N ) and T r = C s Ab + n (61) h T C = [ h ( t) ( t)] 1 K Assume that the receiver at the th MS emloys a filter, matched to the signature waveform of the th user Combining the oututs of these matched filters at K receiver sites, we get the outut vector y y = C H CRAb + n (613) where C = diag ( ) h KxK Emloying the recoding matrix T at the transmitter, as in the AWGN channel case, results in the outut vector y: and the otimal solution is again T y = C H CRTAb + n (614) 1 = S f R [43] The resulting outut is: H y = S C CAb + n (615) f The scaling factor S f is the same as the AWGN channel case, given by (69) The instantaneous bit error rate of user associated with this decorrelation conditioned on the fading coefficients is [1]: 74

88 Figure 6 BER of user 1 in flat fading channel with and without recoding 4 users, uncoded 75

89 A ( = (616) P h e) Q( S f h No Averaging over the robability distribution of h, we get [1]: P FlatFading = (617) S f A where = E( h ) is the average SNR N o This robability of error is equivalent to a BPSK system with Rayleigh flat fading, where the amlitude of the bit is scaled by S f Figure 6 resents an examle for this robability of error We assume 4 users with non-ideal sreading sequences Sreading sequences have high crosscorrelation The lot shows the BER of user 1 It is observed that the conventional transmitter without recoding results in high MAI, hence high BER Precoding removes the MAI and the resulting erformance of the system aroaches the lower bound, given by the single user curve 613 Multiuser Precoding for Frequency-Selective Channels Under ideal channel conditions, DS/CDMA is able to sustain many simultaneous high data rate users However, in ractical conditions, CDMA systems face a combination of channel effects and MAI Even if the system is constrained to be synchronous and the sreading waveforms are designed to be orthogonal, the multiath nature of the channel destroys the orthogonality between the received signals As mentioned above, comlex receiver based structures are not ractical for downlin of CDMA Multiuser recoding with a similar aroach to AWGN and flat fading cases can also be alied to frequency-selective 76

90 channels Previously roosed multiuser recoding for multiath channels can be classified as multiuser recoding with the RAKE receiver and without the RAKE receiver 6131 Multiuser Precoding with the RAKE Receiver Consider the downlin of the synchronous CDMA system described in Chater 3 The received signal is given in (35) When the th MS emloys the conventional RAKE receiver to combine the channels arriving with different delays, the outut of the RAKE receiver with MRC can be exressed as: Define: L 1 Tb + ltc * hl l = 0 ltc y = r ( t) s ( t lt ) dt (618) c j ( l) s ( t) s j ( t ltc ) R, = dt, j = 1 K l = 0 L 1 (619) Then the decision variable for the th user can be written as: L 1 K L 1 y b = n= 0 j= 1 l= 0 j A jh * nh lr, j ( l n) + n ~ (60) where, n ~ = L 1 l = 0 h n ( t) s ( t lt ) dt, with zero mean and variance: * l c L 1 L 1 * var( n ~ ) = N h h R ( n l) (61) o n= 0 l = 0 Then using the matrix notations, all RAKE oututs at all K receiver sites can be exressed as: L 1 L 1 n l, H y h ( n ) h( l) R( l n) Ab + n~ (6) = n= 0 l = 0 where h ( l ) = diag( h1 l h Kl ) KxK, n ~ = [ ~ ~ and R( l n) = { R, ( l n)} Further define: T n1 n K ] Kx1 i j KxK 77

91 Rˆ = L 1 L 1 n= 0 l = 0 h H ( n) h( l) R( l n) (63) Then: y = RAb ˆ + n~ (64) As before, we want to insert a filter T at the transmitter, so that J = b y is minimized for y S RTAb ˆ + n~ It is shown in [45] that the otimal solution minimizing this = f error is given by T = Rˆ 1 The ower scaling factor is: S f = K = 1 A K = 1 ˆ A ˆ T 1 ( R RR ), (65) where R is the crosscorrelation matrix of signature waveforms, such that the element in the th row and th column is given by (311) The solution matrix T requires the accurate CSI and the matrix inversion is reeated at the rate the CSI varies The MS is required to have the RAKE receiver, which results in a highly comlex method The robability of error of the th user in the j th bit interval is given by: A S f P =, j Q (66) L 1 L 1 * No hnhlr, ( n l) n= 0 l = 0 78

92 613 Multiuser Precoding Without the RAKE Receiver As an alternative to the multiuser recoding with the RAKE receiver, a new technique that doesn t require RAKE receiver rocessing is roosed in [46] Instead of transmit data filtering, the transmit waveforms are modified The urose of a decorrelating refilter is to filter each transmit signal in such a way as to minimize the MUI and multiath fading at all mobile receivers It is assumed that fixed sreading codes are used for each user and receivers are only allowed to have single matched filters Instead of filtering the data by blocs as done reviously, the roosed technique alies a filter to the signal to be transmitted for each user The multiath comonent resolution available from sread sectrum coding can still be exloited The filtering is done at the chi level and comutation is limited to a single symbol at a time Consider the synchronous CDMA system investigated with K active users and the each channel between the BS and MS s is frequency selective that results in L resolvable multiath comonents Then the received signal at the th receiver is: K r ( t) = Ajbjs j ( t) j ( t) h ( t) + n j = 1 ( t) (67) where (t) is the imulse resonse of the refilter with length N for user j, (t) is the j imulse resonse of the channel between the BS and th user and is convolution The main idea is to design (t) j for each user such that the interfering signals of the other users are orthogonal to the desired user at the outut of the matched filter The aroach taen here is to design the refilters that maximize the SNR at the receiver while simultaneously comletely canceling the MAI at the samling time due to other users transmission in that symbol eriod This method is not a strict error robability minimizing scheme, but rather a h 79

93 zero-forcing simultaneous multiuser interference rejecting and channel re-equalization method Consider the discrete-time equivalent to the matched-filter outut (matched to s (t)) at the receiver of user, for a single symbol transmission The outut is given by: K y [ n] = bl Al sl[ n] l[ n] h [ n] s[ T n] + l = 1 n [ n] n = tt / T s (68) where T is the number of samles er symbol and is discrete-time convolution Assuming samling at chi rate, T is also the sreading factor To simlify, let: Then a [ n] = s [ n] h [ n] s [ T n] i, j = 1 K (69) ij i j j K y [ n] = bl Al l[ n] al[ n] + l = 1 n [ n] (630) The otimization roblem is given by: max( ˆ [ n] a[ n]) n= Tss (631) subject to constraints: ( [ n] a [ n]) = 0 l and s = 1 (63) l n= T ss where T ss is the decision samle and is two-norm These constraints are required for zero-forcing solution and normalized transmit ower The solution is found by solving for two-norm vector ˆ satisfying: a a a [ T ] 1 ss [ T ] : ss [ T ] a a a 1 [ T ss [ T ss : [ T 1] 1] 1] 1 1 [ T K ss K ss 1 ss A : a a a [ T [ T ss ss N + 1] N + 1] ˆ : N + 1] = d (633) 80

94 where d is an all-zero vector excet for a unity entry at osition This equation is solved using the inverse of A, and a solution is guaranteed to exist as long as the length of the refilter N K For normalization, the signal transmitted for user must be scaled by: S f = 1/ s ˆ (634) Then the instantaneous robability of error for user is given by: A P = Q (635) No s ˆ where s is referred as the ower enalty factor This factor is identical to a noise enhancement factor in receiver based decorrelators The solution given in [46] requires the inversion of a KxK matrix for N=K The elements of this matrix include the CSI, so accurate nowledge of the channel characteristics is necessary and recalculation of the inverse matrix is required at the rate of the channel fading Although this method is less comlex than the method [45] described above, it is highly deendent on the channel state information Both of the methods in [45] and [45] erform similar to receiver based multiuser detection schemes In general, these methods are highly deendent on the crosscorrelation and autocorrelation of the signature sequences used but the overall erformances are comarable to RDD and MDD, as resented in the numerical and simulation results 6 Pre-RAKE Multiuser Precoding for Frequency-Selective Channels It was shown in section 55 that the re-rake filtering eliminates the need for the RAKE receiver, while reserving multiath diversity For the multiuser case, we can tae advantage of this feature to design a transmitter structure to cancel MAI rior to transmission and the receiver emloys a single matched filter Deending on where the recoder is laced in the transmitter, we get two different schemes 81

95 61 Pre-RAKE Multiuser Precoding with CSI Deendent Decorrelation (Pre-RDD) This method emloys a decorrelator at the transmitter along with re-rake filtering for each user We call this technique Pre-RDD, because it has very similar structure to receiver based RDD described in section 35 Refer to Figure 63 for the bloc diagram of this method Consider the downlin of the synchronous DS/CDMA system with K active users Each channel between the BS and MS s is frequency selective with L resolvable multiath comonents Then the transmitted signal x(t) at the base station will be: H x ( t) = SC TA' b (636) S f where, T is the KxK recoding matrix and L A = diag ' l = 1 h l 0 KxK A The re-rake weighting matrix is given by: h 0 * 1 * H 0 h : C (637) = : 0 0 : : 0 0 * hk KLxK And h T h, 0 h, L 1] Lx1 = [ is the channel state information vector for the th user S = [ s,, s T T 1 K ] 1 xkl T is the sreading filter and s = [ ( t ( L 1) T ) s ( t)] s c 1 xl The resulting signal after sreading is scaled by S f to ee the total transmitted ower normalized The receiver at the MS of the th user emloys a filter matched to s ( c t ( L 1) T ) The outut vector of matched filter ban, y, can be exressed in matrix notation as: y = S RTA' b + n (638) f 8

96 Tx Rx User 1 Sreading s 1 (t) Pre-RAKE For h 1 S f h 1 h n 1 (t) r 1 (t) n (t) Match to s 1 (t-(l-1)t c y 1 (t) User T Sreading s (t) Pre-RAKE For h x(t) h K r (t) n K (t) Match to s (t-(l-1)t c y (t) User K Sreading s K (t) Pre-RAKE For h K r K (t) Match to s (t-(l-1)t c y K (t) Figure 63 Pre-RAKE Multiuser Precoding with CSI Deendent Decorrelation 83

97 where n ~ N ( 0 K,1), I ( K o N ) and the K x K matrix R is the correlation matrix that can be defined by its elements as: R = i, j = 1 K (639) H i, j ( hi R[ i, j] h j ) KxK where, R[ i, j] is the i,j th LxL bloc of R T b + ltc T T T T R = [ ( ) ( )] [ s t s t 1 K s1 ltc l = 0,, L 1 ( t) s T K ( t)] dt KLxKL (640) For the zero forcing solution, 1 T = R Then The average energy of x(t) is found by: y = S A' b + n f Ε Ε av av = E[ == E[ S x( t) f dt] = E T ( A' b) T T T T T H [ ( S f ( A' b) T CS SC TA' b) T H ( ( CS SC ) dt) TA' b] dt] (641) T H T Using CS SC T = I and T = T, we have: Ε Ε av av = E[ S = tr f T ( A' b) TA' b] = tr T ( E[ S ( A' b) TA' b] ) K T T T ( S f TA' E( bb ) A' ) = tr( S f TA' A' ) = f = 1 Ε R 1, (64) K T where E( bb ) = I K and Εav = Ε = A / Then the scaling factor is given by: = 1 K = 1 S f = K = 1 A K A / = 1 1 L hl l = 0 R 1, (643) 84

98 Note that, for ideal sreading sequences, the scaling factor reduces to re-rake scaling The instantaneous bit error rate of user associated with this recoding, conditioned on the fading coefficients is: P h L 1 S f ( hl ) A l = 0 ( e) = Q N (644) o When we comare this method with the RDD receiver, we see that both methods are structurally the same They have the same decorrelating matrix However, the noise enhancement factor for the th user, given in equation (330) deends only on the (,) th element of the decorrelating matrix For the re-rdd structure, the scaling factor deends on all diagonal elements and all users energies 6 Pre-RAKE Multiuser Precoding with CSI Indeendent Decorrelation (Pre-RAKE Multiuser Precoding) The transmitter recoding techniques investigated in sections 6131, 613 and 61 integrate the nowledge of channel gains into their multiuser re-decorrelators These methods would be difficult to imlement in mobile radio systems where channel arameters are raidly time-variant, since multiuser decorrelating would require the inversion of a matrix at the rate of the channel fading, whose elements involve channel coefficients Also, the technique roosed in section 6131 requires a RAKE receiver at the MS We roose a significantly simler linear transmitter scheme by searating the functions of re-rake filtering and multiuser recoding With this technique, multiuser decorrelating is indeendent of channel fading and the mobile stations emloy single matched filters instead of RAKE receivers 85

99 Pre-RAKE Multiuser Precoding Sreading User 1 Channel Gain Weighing, Scaling Power Scaling User User K Channel Gain Weighing, Scaling Channel Gain Weighing, Scaling Decorrelating Filter G Sreading Filter S x(t) Figure 64 Pre-RAKE Multiuser Precoding with CSI Indeendent Decorrelation 86

100 This method is similar to the re-rdd method, but in this case, we change the order of re-rake filtering and decorrelation Figure 64 resents the bloc diagram of this technique Consider the synchronous downlin DS/CDMA system with K users and L-ath frequency-selective channel for each user First the transmitter alies the re-rake filtering The linear multiuser re-decorrelating filter G rocesses the oututs of these filters and the resulting signal is sread using the sreading filter S Outut of the sreading filter is sent out to all mobile stations The transmitted signal is then given by: H x = SGC A' b (645) S f where A' = S A is the scaled version of the diagonal amlitudes matrix A The re-rake scaling matrix S is given by: H C is the re-rake weighting matrix given by: 1 H 1/ S = diag = ( CC ) (646) L 1 hl l = 0 KxK h 0 * 1 * H = 0 h : C (647) : 0 0 : : 0 0 * hk KLxK where h = T [ h, 0 h, L 1] G is the KLxKL multiuser recoding matrix and outut of the recoder is sread using: S = [ s s s = [ ( t ( L 1) T ) s ( t)] (648) 1 K ] 1xKL s c 1xL The resulting signal after sreading is scaled by S f to ee the total transmitted ower normalized The receiver at the MS of the th user emloys a filter matched 87

101 to s ( c t ( L 1) T ) The outut vector of matched filter ban, y, can be exressed in matrix notation as: y = S CRGC H A' b + n (649) f where n ~ N ( 0 (K, 1, I N ) K o) and the KL x KL matrix R is the correlation matrix that can be { }LxL defined in terms of its sub-matrices R i, {1,, K}, with elements: i, R il, m, = si ( t ( L 1+ l m) Tc ) s ( t ( L 1) Tc ) dt, m, l [0 L 1] (650) For the zero forcing (also MMSE [4]) solution, the decorrelating filter is chosen to be: 1 G = R (651) So that, at the receiver, the outut of matched filter ban of all users (conventional detectors) is: y = S = S = S f f f CRGC H A' b + n H H 1/ CC ( CC ) H ( CC ) 1/ Ab + n Ab + n (65) As seen from equation (65), the decorrelating filter G removes all multiathinduced interference and allows frequency diversity combining at the BS, resulting in simle matched filtering at the mobile Moreover, the decorrelating matrix deends only on the signature sequences and the number of multiath comonents, not on channel gains Thus the matrix inverse does not have to be udated as channel gains vary at the fading rate Pre- RAKE coefficients and scaling factors are udated for each symbol transmitted (assuming channel is constant during one bit interval) The main requirement of this scheme is to be able to imlement the re-rake filter, which requires the nowledge of the CSI 88

102 To be able to normalize the energy to Ε av = K = 1 Ε, we need to calculate the energy of the outut signal The average transmitted energy can be found using a technique similar to section 611 The transmitted signal is given by: In general, for K users and L aths, the energy is: 1 H x( t) = SR C A' b (653) S f Ε Ε Ε av av av = E = E[ = E[ [ x( t) dt] T T T H ( S f ( A' b) CG S SGC A' b) T T T H S f ( A' b) CG ( S S) dt GC dt] ( ) A' b] (654) T T Using (650) and (651), S S G = I and G = G, we have: where E Ε Ε av av T ( bb ) = I K, = E = tr T H T H [ S f ( A' b) CGC A' b] = tr( E[ S f ( A' b) CGC A' b] ) H T T H T ( S ( CGC ) A' E( bb )( A' ) ) = tr( S ( CGC ) A' ( A' ) f A T A '( A' ) = diag L, 1K, and h l 1 l = 0 KxK f ) (655) = Εav = Ε = A K = 1 K = 1 / Then the scaling factor is given by: S f K K A / A / = 1 = 1 = = (656) A / K L 1 = 1 * hlhl l = 0 K H A / H ( CGC ), ( CGC ) L 1, = 1 h l l = 0 Where ( CGC H ), is the th H diagonal element of the KxK matrix CGC 89

103 As seen from the equations, the scaling factor deends on the users owers and channel coefficients This is because the multiuser recoding matrix incororates a combination of the amlitudes and channel coefficients into the outut matrix Intuitively, as the crosscorrelations of the users increase, we need to ut more ower into the system to suress the interference So as the other users ower increase, the scaling factor gets smaller to comensate The comensation is roortional to the contribution of the other users, which is reresented by the R matrix For the th user, the outut of the matched filter at the receiver is given by: L = S f 1 l = 0 l y h A b + n (657) Then the instantaneous robability of error for user is given by: P L = 1 A Q hl S f l = 0 No (658) Note that, for an ideal system, where there is no MAI, this robability of error is equivalent to MRC with L-order of diversity The erformance degradation is introduced with S f, based on the correlation roerties of the sreading codes used 63 Sace-Time Pre-RAKE Multiuser Precoding for Frequency-Selective Channels (STPR MUP) Similar to the method used in section 56, the re-rake multiuser recoding method can be extended to multile antennas to obtain sace gain The urose of STPR MUP is to achieve all available multiath and sace diversity while removing the MAI at the transmitter The bloc diagram of this method is given in Figure 65 90

104 BS MS K Users Data Pre-RAKE Multiuser Precoding Antenna 1 Pre-RAKE Multiuser Precoding Antenna S f S f h 1 1 h 1 h 1 K h M 1 h M n 1 (t) r 1 (t) n (t) r (t) n K (t) Match to s 1 (t-(l-1)t c Match to s (t-(l-1)t c y 1 (t) y (t) Pre-RAKE Multiuser Precoding Antenna M S f h M K r K (t) Match to s (t-(l-1)t c y K (t) Figure 65 Bloc diagram of Sace-Time Pre-RAKE multiuser recoding 91

105 Consider the K user CDMA system, where the BS emloys M transmitter antennas and each channel associated with each antenna is frequency-selective Rayleigh fading with L aths All aths of all channels are assumed indeendent Then each MS receives signals from LxM aths The imulse resonse of the channel between the m th antenna and the th MS is given by: L 1 l = 0 m m h ( t) = h δ ( t lt ) (659) l c where m h l th is the comlex Gaussian channel coefficient corresonding to the l multiath comonent of the channel between the m th antenna and the th user Assume that antenna-secific re-rake filtering and recoding are alied before transmission at each antenna Then the transmitted signal at the m th antenna is given by (ignoring scaling): x ( t) = SG C Ab (660) m m where, G m is the KLxKL recoding matrix for the m th antenna The re-rake weighting matrix for the m th antenna is given by: H m m* h m* H 0 h : C m = (661) : : : 0 m* 0 0 hk KLxK where h m = [ m m T h, 0 h, L 1] Lx1 is the channel state information vector of the m th channel of the th user Assume all of the antennas transmit synchronously Each transmitted signal goes through the corresonding channel and the resulting signals are suerosed at the antenna of 9

106 the th MS The receiver of the th MS emloys a filter matched to s ( c t ( L 1) T ) The outut vector of matched filter ban for all K users can be exressed in matrix notation as: M H y = ( CmRGmCm Ab) + n (66) m= 1 where n ~ N ( 0 K,1), I N ( K o ) and the KL x KL matrix R is the correlation matrix given in equation (650) Note that we can write the outut as a sum, because the sreading codes and user bits/energies are common to all transmitted signals This sum can also be written as a single matrix roduct H y = CRC Ab (663) where, C = KxKLM [ C1 C CM ] (664) R KLMxKLM RG1 0 = : 0 0 RG : 0 : : 0 : : RG M (665) For the zero forcing solution, we should have 1 R = I KL, ie G = G m = R Note that scaling is necessary to ee the transmitted ower normalized As with a single antenna case, scaling is erformed in two stes First stage taes care of the re-rake filtering and the second stage is for the ower increase due to recoding The scaling factors for each antenna should be identical to be able to use suerosition The scaled version of the users bit energies is given by: A ' = S A (666) 93

107 S = diag = 1 K M m= 1 l = 0 1 H 1/ L 1 h m l KxK = ( CC ) (667) The scaling factor due to the recoding is given by: S f = M K = 1 = = M L 1 m 1 1 A K A / h l j = 1 l = 0 j / H ( C GC ) m m, (668) where ( m m, H C GC ) is the th H diagonal element of the KxK matrix C m GC m Then the scaled outut is given by: H 1/ ( CC ) Ab n y = S + (669) For the th user, the outut of the matched filter at the receiver is given by: f M L 1 = S f m= 1 l= 0 m l y h A b + n (670) Then the instantaneous robability of error for user is given by: P Q = S A M L 1 m hl f m= 1 l = 0 No (671) Note that, for M=1, the system reduces to the single antenna re-rake multiuser recoding For ideal sreading sequences, the system reduces to sace-time re-rake transmitter diversity, with MRC diversity of the order LxM 94

108 64 Numerical and Simulations Results BER erformance of Rx based MUD schemes described in section 3 is comared to the erformance of Tx based methods described in sections The models associated with ulin and downlin are different, as described in section II However, all of these methods are zero forcing linear detectors Noise enhancement of Rx MUD through decorrelating is analogous to the transmission ower increase of Tx recoders Both Rx and Tx based methods require the nowledge of signature waveforms all of users but don t require the individual users energies As a result, these methods are more suitable at the BS and given the analogy, we can evaluate the erformance of the Tx recoders comared to the erformance of Rx based decorrelators Numerical analysis is used to evaluate the theoretical BER of the methods described above We assume erfect channel information of all users at the BS and the MS No error control method is emloyed Channels associated with each user and the aths for each channel are indeendent from each other and each fading ath is assumed to have Rayleigh fading statistics Actual orthogonal sreading codes of W-CDMA [39] are used Each method is scaled roerly to ensure equal total transmit owers and fair comarison MRC in the grahs is evaluated analytically based on [1], which rovides the otimal erformance and the lower bound for any given scheme of the same order of diversity because it uses erfect CSI and is not affected by multiath interference The order of diversity for each grah is given by the number of aths times the number of antennas for each user The RAKE receiver and sace-time re-rake transmitter diversity curves in the grahs are found by simulation for the downlin assuming erfect channel estimation at the MS The recoding method with the RAKE receiver described in [45] is labeled as recoding+rake and the 95

109 refilter method described in [46] is labeled as refilters no RAKE The recoding method described in section 61 is labeled as re-rdd It is assumed that MDD and RDD are emloyed at the BS for the ulin, the RAKE receiver, sace-time re-rake transmitter diversity, refilters no RAKE, recoding+rake, re-rdd, re-rake multiuser decorrelator and sace-time re-rake multiuser recoding are emloyed for the downlin Figures resent the numerical results for RDD, MDD, refilters no RAKE, recoding+rake, re-rdd, re-rake multiuser recoding, sace-time re-rake multiuser recoding and simulation results for sace-time re-rake transmitter diversity and RAKE receiver RAKE receiver is emloyed at the MS with the number of fingers equal to the number of aths Oututs of the correlators are otimally combined to generate the decision metric Figure 66 resents the BER of user 1 for the ath 8 users case with 16 chi sreading Number of users and aths results in high MAI as seen from the RAKE receiver erformance This grah shows the effectiveness of MUD For this case, Tx and Rx based MUDs erform similarly, re-rake method being equivalent to recoding+rake, re- RDD, RDD, refilters no RAKE being equivalent to MDD BER of user 1 for the 4 ath 8 users case with 3 chi sreading is given in figure 67 In this case, high number of users and aths results in significant MAI as seen from the RAKE receiver erformance In the revious figures, it was observed that the refilters no RAKE and recoding+rake methods erformed similar to RDD and MDD methods However, in this case a different result is observed The increase in the number of aths results in divergence of the curves with the Tx based methods Although they are still close to each other, recoding+rake erforms better than refilters no RAKE and re-rake 96

110 recoding The erformance of re-rdd is equivalent to recoding+rake BER erformance is imroved by all MUD methods desite different results The lower bound of multiuser detectors is given by RDD The comarison of sace-time re-rake transmitter diversity with sace-time re- RAKE multiuser recoding for antennas, aths and,8 users is given in Figure 68 When no multiuser recoding is alied, the resulting system is equivalent to the STPR system described in section 56, with and 8 users The detection assumes single user, as a result significant MAI and self-interference are observed STPR with multiuser recoding removes this interference, imroving the erformance The otimal diversity is given by MRC of order 4, which is the number of aths times the number of antennas With the alication of the multiuser recoding, the erformance of the system aroaches this bound As observed from the figure, 8 users result in higher interference than users In a more realistic communication environment, the CSI is not nown rior to transmission To evaluate these methods using long range rediction, a simulation environment based on the W-CDMA arameters was created to evaluate the BER erformance of the schemes described above with GHz carrier frequency, 60mh vehicle seed, 4096 Mcs chi rate The data was uncoded For the simulations, we assume 51 bs data rate for sreading factor of 8 Results for -user, -ath are resented in figure 69 Prediction is emloyed for recoding+rake, refilters no RAKE, re-rdd and the re- RAKE multiuser recoding method The RAKE receiver, MDD and RDD assume erfect nowledge We assume a single antenna system, where the frequency-selective Rayleigh fading channels exerienced by the users are modeled by Jaes model We assume erfect ower control, so that both users transmit with the same ower Scaling factor comuted 97

111 from the simulation is used at the BS to ee the transmit ower normalized for all Tx based methods We assume that there is no estimation error at the MS and this erfect channel state information is fed bac to the BS at the end of each slot (16 Hz) The BS receives this information with a 065 ms delay and erforms rediction For comarison uroses, the otimal diversity case (MRC) and the conventional RAKE receiver are also included in the grah The x-axes is based on E /No, which is the SNR for any user Pre-RAKE recoding, re-rdd and refilters no RAKE methods emloy a single matched filter Precoding+RAKE method emloys the RAKE receiver at the MS For this articular system, 8 chi sreading sequence results in significant interference for high SNR For low SNR levels, conventional RAKE receiver erforms close to RDD, however, for high SNR levels, the BER diverges and other methods have better BER than the RAKE receiver The effect of rediction is also observed from the figure We can clearly conclude that these methods are highly deendent on the CSI at the instant of recoding Using delayed CSI results in 1dB loss in BER erformance For any ractical system that requires the CSI at the transmitter, using the delayed CSI results in erformance degradation Emloying the LRP imroves the BER erformance The imrovement deends on the order of diversity achieved by the method used and it is between ½-1 db From the numerical and simulation results, it is observed that Tx based methods erform similarly and they are close to Rx based methods For the Tx methods, the erformance is deendent on the articular code selection and the number of aths All methods reduce the effects of MAI under severe conditions Although the erformances of these methods are similar, the level of comlexity is not the same Precoding+RAKE method 98

112 has the highest comlexity, since it requires the RAKE receiver at the MS and the matrix inversion required for recoding is deendent on the channel conditions This matrix inversion is erformed at the rate of channel variation The refilters no RAKE method and re-rdd are relatively simler, requiring a single matched filter at the MS, however the matrix inversion based on CSI is still necessary The re-rake multiuser recoding method roosed in this thesis is the simlest of all Matrix inversion is not deendent on the CSI and a single matched filter is required at the MS Only additional rocessing is the re-rake filtering and channel rediction Multiuser recoding filter is comuted once; only the re- RAKE filter and scaling are udated to ee trac of the time-varying channel coefficients When the re-rake multiuser recoding method is comared to the Rx based detectors, although the feedbac load is high, the re-rake filtering, multiuser recoding and rediction are erformed at the BS, where this comlexity can be afforded The MS is significantly simlified by not emloying the RAKE receiver and the ower requirement is less, due to better BER erformance 99

113 Figure 66 BER of user 1 in ath 8 users system with 16 chi sreading Perfect CSI A 1 /A =1 100

114 Figure 67 BER of user 1 in 4 ath 8 users system with 3 chi sreading Perfect CSI A 1 /A,3,4 =1 101

115 Figure 68 BER of user 1 in antenna, ath,,8 user system Perfect CSI A 1 /A =1 10

116 Figure 69 BER of user 1 in ath users system with 8 chi sreading A 1 /A =1 Prediction and no rediction for refilter with no RAKE, recoding with RAKE, re-rdd and re-rake multiuser recoding 103