Constrained Linear and Non-Linear Adaptive Equalization Techniques for MIMO-CDMA Systems

Transcription

1 Constrained Linear and Non-Linear Adaptive Equaization Techniques for MIMO-CDMA Systems By Khaid Mahmood ID # P This thesis is submitted in partia fument of the requirements of De Montfort University for the award of Doctor of Phiosophy Emerging Technoogies Research Center (EMTERC) De Montfort University, Leicester December, 2013

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3 Acknowedgments In the name of Aah, The Most Gracious, The Most Mercifu. A praise and gory is for Aah (SubhanahuWa Ta'aaa) who gave me the strength and determination to undertake this work. My utmost gratitude towards De Montfort University for my admittance to this prestigious institute. My heartfet gratitude and appreciation to my adviser, Dr. Shahshi Pau for his support and guidance. His attention and devotion to my research work, with vauabe suggestions, was the impetus that ed to the competion of this work. My co-adviser Professor Raouf Hamzaoui aso provided vauabe feedback which has been incorporated in this research work. I highy appreciate Dr. Moin Uddin's guidance during my research. I woud speciay mention my coeague Syed Asad Afatb, for his support and guidance. Asad's contribution towards this research work wi never be forgotten. Last but not the east, I woud ike to thank my wife Unbereen Sha and my chidren, Duaa, Ahmad, Raania and itte Awad who were very patient with me during my stressfu times. ii

4 Abstract Researchers have shown that by combining mutipe input mutipe output (MIMO) techniques with CDMA then higher gains in capacity, reiabiity and data transmission speed can be attained. But a major drawback of MIMO-CDMA systems is mutipe access interference (MAI) which can reduce the capacity and increase the bit error rate (BER), so statistica anaysis of MAI becomes a very important factor in the performance anaysis of these systems. In this thesis, a detaied anaysis of MAI is performed for binary phase-shift keying (BPSK) signas with random signature sequence in Raeigh fading environment and cosed from expressions for the probabiity density function of MAI and MAI with noise are derived. Further, probabiity of error is derived for the maximum Likeihood receiver. These derivations are veried through simuations and are found to reinforce the theoretica resuts. Since the performance of MIMO suers signicanty from MAI and inter-symbo interference (ISI), equaization is needed to mitigate these eects. It is we known from the theory of constrained optimization that the earning speed of any adaptive tering agorithm can be increased by adding a constraint to it, as in the case of the normaized east mean squared (NLMS) agorithm. Thus, in this work both inear and non-inear decision feedback (DFE) equaizers for MIMO systems with east mean square (LMS) based constrained stochastic gradient agorithm have been designed. More specicay, an LMS agorithm has been deveoped, which was equipped with the knowedge of number of users, spreading sequence (SS) ength, additive noise variance as we as MAI with noise (new constraint) and is named MIMO-CDMA MAI with noise constrained (MNCLMS) agorithm. Convergence and tracking anaysis of the proposed agorithm are carried out in the scenario of interference and noise imited systems, and simuation resuts are presented to comiii

5 pare the performance of MIMO-CDMA MNCLMS agorithm with other adaptive agorithms. iv

6 Contents Contents List of Figures List of Tabes v x xiii 1 Introduction Mutipe Input-Mutipe Output (MIMO) Systems Code Division Mutipe Access (CDMA) MIMO-CDMA Systems Adaptive Equaization Techniques Linear Equaization (LE) Decision Feedback Equaization (DFE) Literature Review Statistica Anaysis of Mutipe access Interference (MAI) in MIMO-CDMA Systems Equaization in Mutipe Input Mutipe Output (MIMO) Systems Drawbacks in Previous Techniques: A motivation for the proposed work Thesis Objective Thesis Organization v

7 1.9 Peer Reviewed Pubished Work and Conference Pubications Statistica Anaysis of mutipe access interference (MAI) and noise in MIMO-CDMA systems Introduction Probabiity Density Function (pdf) of MAI Pus Noise in Fat Fading Environment System Mode Probabiity Density Function (pdf) of Mutipe Access Interference (MAI) Probabiity Density Function (pdf) of Mutipe Access Interference (MAI) and Noise Simuation Resuts Remarks BER Performance of MIMO-CDMA Systems Based on Characterization of Mutipe-Access Interference (MAI) Introduction BER Performance Simuation Resuts Mutipe Input Mutipe Output Decision Feedback Equaization Introduction Decision Feedback Equaization (DFE) Some Aternative Decision feedback equaizer Structures Frequency Shift Decision Feedback Equaizer (FRESH-DFE) FRESH-DFE: A New Structure for Interference Canceation Muti Spit Decision Feedback Equaizers Constrained Adaptive Agorithms Constrained optimization techniques vi

8 4.5.1 Constrained MMSE-DFE Cycic MMSE Limited Feedback ZF-DFE Adaptive Channe Aided DFE Adaptive Conjugate Gradient Decision Feedback Equaizer MBER Space-Time Decision Feedback Equaization Assisted Mutiuser Detection for Mutipe Antenna Aided Space-Division Mutipe Access (SDMA) Systems Fast Techniques for Computing Finite-Length MIMO MMSE Decision Feedback Equaizers Proposed MIMO Receivers Introduction Motivation Agorithm Deveopment MIMO-CDMA MNCLMS Constrained Agorithm for Linear Equaizer (LE) MIMO-CDMA MNCLMS Constrained Agorithm for Decision Feedback Equaizer (DFE) Generaized MIMO MAI and Noise-Constrained LMS Agorithm Computationa Compexity of the Proposed Agorithms Convergence Anaysis, Transient Anaysis and Tracking Anaysis of the MNCLMS Agorithms in The Presence of MAI and Noise Introduction Convergence Anaysis of the MNCLMS Agorithms in the Presence of MAI and Noise Convergence in the Mean for Linear Equaizer (LE) vii

9 6.3.1 Auto-correation Structure of MIMO-CDMA Linear Equaizer (LE) Eigenvaues of Linear Equaizer (LE) Convergence in the Mean for Decision Feedback Equaizer (DFE) Auto-correation Structure of Decision Feedback Equaizer (DFE) Eigenvaues of Decision Feedback Equaizer (DFE) Transient Anaysis of the Proposed Agorithm Error Measures Performance Measures Fundamenta Weighted Energy Reation Time Evoution of the Weighted Variance Constructing the Learning Curves for the Excess Mean Square Error (EMSE) Steady-State Anaysis of the MNCLMS Agorithms Steady State Mean Square Deviation (MSD) Tracking Anaysis of the MNCLMS Agorithms for the Random Wak Channe in the Presence of MAI and Noise Random Wak Mode Fundamenta Energy Reation for the Random Wak Channe Tracking Steady-State EMSE of the MNCLMS Agorithms Simuation Resuts for MIMO-CDMA MNCLMS Agorithm (DFE) Interference Canceation in an AWGN Channe Interference Canceation in Rayeigh Fading Channe Tracking Performance for Random Wak Channe in the Presence of MAI Simuation Resuts For MIMO-CDMA MNCLMS Agorithm(LE) Interference Canceation in an AWGN Channe Interference Canceation in Rayeigh Fading Channe viii

10 7 Dissertation Contribution, Concusion and Recommendation for Future Work Dissertation Contribution and Concusion Recommendations for Future Work Appendix A 109 Appendix B 111 Appendix C 114 References 119 ix

11 List of Figures 1.1 A Bock Diagram of MIMO Systems A bock diagram of CDMA system Bock diagram of MIMO-CDMA system Bock diagram of Linear Transverse Equaizer Bock diagram of Decision Feedback Equaizer Bock Diagram of MIMO-CDMA Transmitter and Receiver pdf of MAI for dierent scenarios of transmit and receive antennas pdf of MAI under various ength of PN sequences pdf of MAI-pus-noise under dierent number of users in the system pdf of MAI-pus-noise for dierent scenarios of transmit and receive antennas Experimenta and anaytica resuts of probabiity of bit error in at Rayeigh fading environment versus SNR Experimenta and anaytica resuts of probabiity of bit error in at Rayeigh fading environment versus number of subscriber Bock diagram of Decision Feedback Equaizer MIMO-DFE at singe antenna Eect of β and γ on MSE earning curves of the MNCLMS agorithm in an AWGN environment with K = 4 at 20 db SNR x

12 6.2 Eect of β and γ on MSE earning curves of the MNCLMS agorithm in an AWGN environment with K = 4 at 10 db SNR MSE behavior for dierent agorithms in an AWGN environment with K = MSE behavior for dierent agorithms in an AWGN environment with K = 4 at 20dB MSE behavior for dierent agorithms in an AWGN environment with K = 4 at 10dB MSE behavior for dierent agorithms in an AWGN environment with K = 20 at 10dB Behavior of time-varying step size of the MNCLMS agorithm for K = 4 at 20 db SNR Behavior of time-varying step size of the MNCLMS agorithm for K = 4 at 10 db SNR Eect of a sudden increase in the number of subscribers from 4 to 10 subscribers MSE behavior for dierent agorithms in an AWGN environment with K = 4 under the unequa transmitted powers scenario at 20 db SNR MSE in at Rayeigh fading, fd = 250Hz, K = 4 at 20dB MSE in at Rayeigh fading, fd = 250Hz, K = 20 at 20dB MSE in at Rayeigh fading, fd = 250Hz, K = 4 at 10dB MSE in at Rayeigh fading, fd = 250Hz, K = 20 at 10dB Tracking performance in a random wak channe with σ q = and SNR of 20 db Tracking performance in a random wak channe with σ q = and SNR of 10 db MSE behavior for dierent agorithms in an AWGN environment with K = 10 at 20dB xi

13 6.18 MSE behavior for dierent agorithms in an AWGN environment with K = 20 at 20dB Behavior of time-varying step size of the MNCLMS agorithm for K = 10 at 20 db SNR Behavior of time-varying step size of the MNCLMS agorithm for K = 25 at 20 db SNR MSE behavior for dierent agorithms in Rayeigh Fading environment with for K = 10 at 10 db SNR MSE behavior for dierent agorithms in Rayeigh Fading environment for K = 20 at 20 db SNR xii

14 List of Tabes 2.1 Kurtosis and variance of MAI in a 4 4 MIMO system with K = Experimenta Kurtosis of MAI-pus-noise under dierent system's capacity Computationa compexity per iteration for dierent agorithms for rea vaued data in terms of the rea mutipications, rea additions and rea divisions Computationa compexity per iteration for dierent agorithms for rea vaued data in terms of the rea mutipications, rea additions and rea divisions Tuning Parameters of MIMO-CDMA MNCLMS agorithm for DFE in the AWGN Environment at 20 db SNR Tuning Parameters of the Proposed MIMO-CDMA MNCLMS Agorithm for DFE in the AWGN Environment at 10 db SNR Eect of N c on the convergence behavior, number of iteration, in the AWGN environment at 20 db Eect of Tuning Parameters of the Adaptive Agorithm in a Random Wak Channe on Anaytica EMSE xiii

15 Nomencature λ n Mean Lagrangian mutipier v n Expected vaue of weight error vector µ m Mean step size ν n Fitered noise which passes through feed forward ter ɛ i Channe attenuation Γ (a, x; b) Generaized incompete Gamma function ˆx n κ Desired response Eigenvaue κ max Maximum eigenvaue κ min Minimum eigenvaue v n Weight error vector w n(opt) Optimum vaue of weight w n Impuse ter response of the decision feedback equaizer w n Weight of the FFF and FBF x n Input process xiv

16 F 1 Inverse Fourier transform Ω Symmetric positive denite weighting matrix ϑ z Average signa to noise ratio Φ P (ω) Characteristic function of U m and is the product of N characteristic functions of independent random variabes U m Φ U m (ω) Characteristic function of the random variabe U m ρ k,j cross-correation between the signature sequences of subscribers j and k for the th symbo σ 2 ɛ Variance of channe attenuation R Auto correation matrix ϑ z Random variabe ξ Steady state EMSE A k Transmitted ampitude of the k th subscriber B n n th MISO feedback ter (FBF) D n Combined input to the DFE E [h mn ] Expexted vaue of channe impuse response e Ω an Weighted a priori error E b Energy per bit e n Error between the output of the decision device and the DFE e Ω pn Weighted a posteriori error erf c Error compement function xv

17 f ( ) e n Genera scaar function of the output estimation error F n n th MISO feed forward ter (FFF) f U m (u) PDF of MAI h mn Enveop of the compex channe for the th symbo H mn (t) Compex impuse response of Rayeigh channe I,k Output of the matched ter I,k Random variabe J ( w n) Cost function to be minimized M M N Q r m (t) Number of receiving antenna Taps of feed froward ter (FFF) Number of transmit antenna Taps of feedback ter (FBF) Observed signa at the mth receiver R yy Auto correation matrix of input to the FFF s,k n (t) Rectanguar signature waveform T b Bit period T c Chip interva T r Trace operator U m MAI at the m th receiver for the th symbo w m,i Desired signa xvi

18 Z m U m + ν m AWGN BER CDMA CF CIR CSI DFE Additive white Gaussian noise Bit error rate Code division muti access Characteristic function Channe impuse response Channe state information Decesion feedback equaizer DS-SSMA Direct sequence spread spectrum muti access DSP EMSE ETP FBF FDMA FFF FIR IGA ISI K KFG Digita signa processor Excess mean square error Equa transmitted powers Feedforward ter Frequency division muti acces Feedforward ter Finite impuse response Improved Gaussian approximation Intersymbo interference Number of subscribers Fast Kaman gain xvii

19 LBER LE MAI MBER MIMO ML MMSE Adaptive east bit error rate Linear equaizer MUtipe access interference Minimum bit error rate Mutipe input-mutipe output Maximum Likeihood Minimum mean suare error MNCLMS Mutipe access interference pus noise constrained LMS MSE MUD Mean squared error Muti user detection NC-VSLMS Noise constrained variabe step size LMS NCLMS Noise constrained LMS NLMF OFDM PBSK PCS pdf PIC RLS SGA Normaized east mean fourth Orthogna frequency division mutipexing Binary phase-shift keying Poycycostationary Probabiity density function Parae interference canceation Recursive east square Standard Gaussian approximation xviii

20 SIC SISO SNR SSMA TDMA UTP Successive interference canceation Singe input-singe output Signa to noise ratio Spread spectrum muti access Time division muti acces Unequa transmitted powers ZF-DFE zero-forcing decesion feedback equaizer ACI BRS CCI Adjacent channe interference Baud rate samper Co-channe interference CP-LMS Compementory pair LMS FSES Fractionay spaced equaizer MS-DFE Muti spit decesion feedback equaizer MSD SCD SER VLMS Mean square deviation Spectra correation density Utra wide band Variabe step size agorithm xix

21 Chapter 1 Introduction There has been a tremendous growth seen in the wireess mobie communication systems since the end of the ast century. Communication systems which were once providing the traditiona service of voice to a imited number of subscribers are now deaing with increasing numbers of subscribers and a shift of demand from just voice to higher data rate services. This ed to an exponentia increase in system capacity and spectra eciency requirements. As bandwidth is imited, this demand in high capacity has to be provided by an ecient use of existing frequency bands and channe conditions. One of the techniques, which can provide the required increase in system capacity and enhanced performance is the use of mutipe antennas at transmitting as we as at receiving end [1]. This is referred to as mutipe-input mutipe-output (MIMO) wireess system. MIMO technique is being used in the third generation and beyond mobie systems [2]. MIMO is an antenna technoogy for wireess communications which utiizes mutipe antennas at the source (transmitter) and the destination (receiver) to enhance the communication system performance by increasing the system capacity and spectra eciency. MIMO conguration can be done in many ways for exampe a 3 3 MIMO conguration consists of 3 signa transmitting antennas (base Station) with three antennas for receiving signa (mobie termina). The antennas at each end 1

22 of the communications system are combined to minimize errors and optimize data speed. The object of modern communication system is to provide higher, reiabe and secure transmission of data to ever increasing number of subscribers demand. Code division mutipe access (CDMA) is one of the communication schemes which aows mutipe subscribers to use a singe radio channe at the same time with itte interference and much higher security. In spite of its numerous advantages, CDMA system suers from MAI probem which arises due to nonzero cross-correation in the spreading codes of dierent subscribers [3]. This can ead to an increased bit error rate (BER). So, statistica anaysis of MAI becomes very important factor in anayzing the performance of this system. Researchers have shown that by combining MIMO techniques with CDMA system higher gains in capacity, reiabiity and data transmission speed can be attained [48]. Such MIMO-CDMA systems have outperformed the SISO-CDMA systems but both are prone to MAI. In most digita data transmission systems the dispersive inear channe exhibits ampitude and phase distortion. As a resut, the received signa is contaminated by ISI. In a system, which transmits a sequence of puse-shaped information symbos, the time domain fu response signaing puses are smeared by the hostie dispersive channe, resuting in ISI. At the receiver, the ineary distorted signa has to be equaized in order to recover the information. The equaizers that are utiized to compensate for the ISI can be cassied according to their structure, the optimizing criterion and the agorithms used to adapt the equaizer coecients. On the basis of their structures, equaizers can be cassied as inear or decision feedback equaizers. The earning speed of an adaptive agorithm can be increased if partia knowedge of the channe is incorporated in the design of an adaptive agorithm. Since MAI is a imiting factor in MIMO-CDMA systems, there is a need for deriving the probabiity 2

23 density functions (pdf) of MAI and noise and then use it as a constraint to deveop an agorithm for MIMO-CDMA systems. 1.1 Mutipe Input-Mutipe Output (MIMO) Systems The need for MIMO systems arrived due to certain performance drawbacks in SISO (singe input, singe output) technoogy used in conventiona wireess communication systems [9]. In SISO, a singe antenna is used at the transmitter, and another singe antenna is used at the receiver. In some cases, this creates certain probems with mutipath eects. When the transmitted signa is obstructed by his, buidings or utiity wires and towers, the wavefront become scattered, and as such can take numerous paths to reach its destination. This ate arriva of scattered portions of the signa creates probems such as fading, cut-out and intermittent reception (picket fencing). Another drawback of SISO can be seen in digita communications systems such as wireess Internet, where the use of this technoogy has created reduction in data speed as we as increased error propagation. The use of two or more antennas, together with the transmission of mutipe signas (one for each antenna) at transmitter and receiver, not ony eiminates the probems created by mutipath wave propagation,but aso can take advantage of this eect and it is achieved by appying an agorithm or a signa processing technique at the receiver to sort out the mutipe signas and produce a signa that has the required transmitted data. MIMO technoogy is nding appication in digita communication because of its certain appications in digita teevision (DTV), wireess oca area networks (WLANs), metropoitan area networks (MANs), and mobie communications. A bock diagram of MIMO system is shown in gure 1.1. The MIMO system shown in the gure 1.1 is made up of N transmitting antennas and M receiving antennas. By utiizing the same channe, every receiving 3

24 Figure 1.1: A Bock Diagram of MIMO Systems antenna is receiving the direct component as we as the indirect components from the transmitters which are intended for the other receivers. For exampe, h 11 represents the direct connection between the transmitter number 1 and the receiver number 1. In this way, a transmission matrix H of N M can be shown to be H = h 11 h h 1n h 21 h h 2n.... (1.1.1) h m1 h m2... h mn If x is considered to be the input vector and y to be the receiving vector, then the output vector y under additive noise ν woud be y = Hx + ν (1.1.2) 4

25 1.2 Code Division Mutipe Access (CDMA) CDMA is one of the communication schemes which aow mutipe subscribers to use a singe radio channe at the same time with itte interference. A bock diagram of CDMA system is shown in gure 1.2. Mutipe-access capabiity in CDMA system is accompished by means of pseudo noise (PN) codes. Every subscriber in this system is aocated a unique code sequence which is being used to encode that subscriber's information signa. At the receiving end, knowing the code sequence of the each subscriber, receiver decodes the received signa and recovers the origina signa. Since bandwidth of the code signa is much arger than the bandwidth of the information signa, the encoding process spreads the spectrum whereas despreading is achieved by correating the received spread signa with a synchronized repica of the spreading code signa. These spreading codes are independent of each other as we as input process. Figure 1.2: A bock diagram of CDMA system Some of the distinguishing features of CDMA systems are ˆ Usage of wide bandwidth: Just ike other spread spectrum techniques, CDMA, aso utiizes wider bandwidth than is normay required. The use of a wider bandwidth resuts in the increased security for signa and immunity to interception or jamming. ˆ Use of spreading codes: Bandwidth is increased by spreading the information signa with the hep of codes and these codes are independent of the 5

26 information signa. ˆ Enhanced eve of security: The spreading code must be known at the receiving end to decode the transmitted signa otherwise, it woud be very dicut if not impossibe to detect the transmitted signa. This feature of CDMA resuts in very high eve of security ˆ Mutipe access: Each subscriber is assigned a unique spreading code and these codes are independent of each other. By using these unique codes together with synchronous reception permits mutipe subscribers to access the same channe simutaneousy. Some of the advantages of CDMA system are ˆ CDMA system has the abiity of using signas which arrive in the receiver having dierent time deays. This is refereed to as mutipath phenomena. Being narrow band systems, frequency-division mutipe access (FDMA) and time division mutipe access (TDMA), are not abe to discriminate between the mutipath signas arriva, and as such need equaization to get rid of the negative eects of mutipath. On the other hand due to its wide bandwidth, CDMA systems use mutipath signas and combine these signas to get a stronger signa at the receiving end. ˆ In FDMA and TDMA schemes, maximum number of subscribers is xed and once that maximum number of subscribers is reached, new subscribers may not be accommodated,where as CDMA system may aow more subscribers with some background noise. ˆ Less timing organization as compared to TDMA, ISI as we as co-channe interference (CCI) are not as severe as is the case in TDMA [10]. ˆ To maintain a required tempora order among symbos, a compicated system organization must be empoyed in TDMA, but such a compicated system is 6

27 not required in CDMA [10]. 1.3 MIMO-CDMA Systems Researchers have shown that by combining MIMO techniques with CDMA system, higher gains in capacity, reiabiity and data transmission speed can be attained [48]. This is reaized by the spatia diversity of mutipe antennas at the transmitting end as we as at the receiving end resuting in added degrees of freedom when compex channe gains between dierent transmitting and receiving antenna pairs are adequatey uncorreated. MIMO-CDMA systems are more robust to MAI as compared to SISO DS-CDMA. In fact MIMO-CDMA is a promising communication scheme aowing faster data speed mutimedia services and web browsing [11]. Combining MIMO and CDMA can further improve the system transmission rate over the traditiona CDMA system [12]. A bock diagram of a typica MIMO-CDMA is given in gure 1.3. Figure 1.3: Bock diagram of MIMO-CDMA system 7

28 1.4 Adaptive Equaization Techniques A signas whie passing through a channe undergo a certain amount of time dispersion since frequency response of that channe does not have constant magnitude and inear phase. Due to this phenomena, tais of adjacent puses interfere with the measurement of current puse (ISI) which can ead to an incorrect decision by the receiver. Equaization techniques are used to avoid this probem. Equaization is the process of adjusting the reative phases of dierent frequencies in order to achieve a constant group deay. The equaizers that are utiized to compensate for the ISI can be cassied according to their structure, the optimizing criterion and the agorithms used to adapt the equaizer coecients. On the basis of their structures, the equaizers can be cassied as inear or non inear (decision feedback) equaizers. Equaizers can aso be distinguished on the basis of the criterion used to optimize their coecients. The optimization is governed by the performance criteria used. For exampe, when appying the mean square error (MSE) criterion, the equaizer is optimized such that the mean squared error between the distorted signa and the actua transmitted signa is minimized. A range of adaptive agorithms can be invoked, in order to provide the equaizer the means of adapting its coecients to the time-varying dispersive channes Linear Equaization (LE) In most digita data transmission systems the dispersive inear channe encountered exhibits ampitude and phase distortion due to which the received signa is aected by ISI. Systems in which a sequence of puse-shaped information symbos are transmitted, the time domain fu response signaing puses are distorted by the hostie dispersive channe which eads to the inter symbo interference. At the receiver, the ineary distorted signa has to be equaized to recover the information. Linear 8

29 equaizers are used to mitigate the eect of ISI by earning the behavior of the channe and inverse its eect. inear equaizer (LE) can be termed as inverse modeing ter in broader sense due to the fact that inear equaizer works as inverse of a channe. Linear equaizers are used in the communication systems, where ISI is not severe [13]. As can be seen in the gure it consists of a feed forward ter which is fed ony with present and future received signa sampes, impying that no atency is inicted. As a resut of this, the feed forward ter eiminates ony the pre-cursor ISI, but not the post-cursor ISI [14]. Figure 1.4: Bock diagram of Linear Transverse Equaizer Decision Feedback Equaization (DFE) The deveopment of the DFE was initiated by the idea of using previous detected symbos to compensate for the ISI in a dispersive channe. DFE oers the potentia for improved performance over the LE whie maintaining comparabe compexity. Reiabe transmission of information at the highest possibe data rates is the desired goa of digita communication system. However one of the most important obstace in achieving this goa of maximum eciency is ISI caused by the communication channe [15]. ISI refers to the eect of neighboring symbos on the current symbo 9

30 and if not mitigated propery it can ead to high BER in the recovery of the transmitted sequence at the receiver.various methods have been deveoped to enhance the performance of the communication systems by reducing the eects of the ISI. Linear equaization is one of the methods empoyed but a major probem with inear equaization is that it doesn't takes in to account the fact that the transmitted sequence has a "nite aphabet" structure. To overcome this drawback of inear equaization, DFE was proposed [15]. DFE uses previous decisions to improve the equaizer performance. Amost a the techniques proposed for equaization make some assumptions about the underying characteristics of the disturbance signas and the structure of the communication channe mode. In many cases where true information about the channe is not avaiabe, agorithms have to be used for the correct estimation of the mode parameters. For exampe, in mobie communications the channe parameters are normay estimated by using the training sequences. The time variations in these parameters aso necessitate the need for tracking them. The errors due to tracking is another point of concern. These concerns bring forward, the question of robustness, that is, whether the sma variations from the true mode, and sma disturbances, can cause arge degradations in the performances of the agorithms using these parameters. Figure 1.5: Bock diagram of Decision Feedback Equaizer Figure 1.5 shows a simpied bock diagram of a DFE where the forward ter and the feedback ter can each be a inear ter, such as transverse ter.the noninear characteristic of the DFE is due to the noninear characteristic of the 10

31 detector which is used to provide input to the feedback ter.the basic idea of a DFE is that if the vaues of the symbos previousy detected are known, then ISI caused by these symbos can be mitigated at the output of the forward ter by subtracting previous symbo vaues with appropriate weighting. The feed forward and feedback tap weights can be adjusted simutaneousy to fu a criterion such as minimizing the MSE. The advantage of a DFE structure is the feedback ter,which is additionay working to remove ISI, operates on noiseess quantized eves resuting in an output which is free of channe noise. 1.5 Literature Review Statistica Anaysis of Mutipe access Interference (MAI) in MIMO-CDMA Systems In spite of its numerous advantages, a major drawback of MIMO-CDMA systems is MAI which can reduce the capacity as we as BER resuting in a degraded communication system, so statistica anaysis of MAI becomes very important factor to anayze the performance of these systems. In CDMA systems, each subscriber is assigned a unique orthogona spreading code. These orthogona codes shoud ideay provide perfect isoation from the other subscribers to maintain error free communication between respective subscribers but in reaity the orthogonaity between these codes is very dicut to preserve due to asynchronism and channe deay spread at the receiving end. Asynchronism and channe deay spread exist on the up ink whie channe deay spread can be seen on the down ink of the channe. Correation receiver cannot perfecty separate the signas for the mutipe subscribers. This phenomena eads to what is caed MAI causing a system performance degradation, which may render the system useess for even moderate subscriber oads with equa power received from each subscriber. Most of the research work has been done on the characterization of SISO-CDMA 11

32 systems and was based on approximate derivations,such as, standard Gaussian approximation (SGA) [16], improved Gaussian approximation (IGA) [17] and simpi- ed IGA (SIGA) [18]. Centra imit theorem was appied in SGA to get an approximate sum of an additive white Gaussian noise process (AWGNP). This method is widey used because of its ease of appication but a major drawback of SGA is that it overestimates the system performance and this probem becomes severe when the number of subscribers is ess [17]. The Standard Hermite poynomia error correction method [19] was empoyed to improve the accuracy of SGA. The conditiona characteristic function of MAI and bounds on the error probabiity were derived for binary direct-sequence spread-spectrum mutipe access (DS/SSMA) systems. This method was named the improved Gaussian approximation (IGA) [20]. In case when the number of subscriber is sma, IGA has outperformed the SGA [17] but the increased computationa compexity is a major imitation of this method. IGA was further simpied and was named simpied IGA (SIGA) [21] Another approach is to perform the BER of a spread spectrum mutipe access (SSMA) system without the knowedge or assumption about MAI. Most of these techniques are basicay an extension of previousy studied ISI. Some of these techniques incude moment space method [22], characteristic function method [23], moments method [24], and the approximate Fourier series method [25]. It has been noted that these techniques are superior to the centra imit theorem based techniques in approximating BER but with higher computationa costs. SNR of Rician fading channes at the correator receiver's output was performed [26]. The BER performance of DS-CDMA system in frequency non seective Rayeigh fading channe for deterministic sequences using SGA approach was evauated by [27], whereas [23] utiized the characteristic function (CF) technique to assess the performance of SSMA scheme in an AWGN environment. The characteristic function (CF) method to evauate the performance of DS-SSMA scheme on mutiptah fading channes with mutipath ISI was appied in [28] but MAI was ignored. An approximate Fourier se- 12

33 ries technique [25,29] was utiized to evauate the BER performance of seective and non seective Rayeigh fading environment. System degradation caused by imperfect chip and phase synchronization were aso assessed in this technique. For a given signa to noise ratio, BER dependency on number of subscribers was anayzed by [30]. A cosed form expression for the characteristic function of MAI for asynchronous operation in Rayeigh fading environment was derived. Conditiona characteristic function of MAI together with bounds on probabiity error rate for DS- SSMA scheme were aso obtained [30]. Average probabiity of error at correation receiver's output for binary as we as quaternary synchronous and asynchronous DS-SSMA schemes which use random signature sequence was derived in [31] Probabiity density function of MAI for synchronous down ink CDMA scheme in an AWGN case was derived and the resuts were then used to derive the conditiona probabiity density function of MAI, inter carrier interference and noise in muti carrier CDMA scheme provided that fading environment was known [32]. A new unied approach to MAI anaysis in fading environmrents was presented [33], assuming that the channe phase is either known or has perfecty been estimated. Random behavior of the channe fading was aso incuded to get the reaistic resuts for the pdf of MAI together with noise. Due to the computationa compexities in the statistica anaysis of MAI in MIMO-CDMA systems, considerabe work is not found in the iterature. So instead of accurate statistica anaysis of MAI, researchers have either used some strong assumptions for exampe, Gaussian assumption for interference in MIMO system [34] or suboptima approaches to detect the subscriber without invoving the need for MAI statistics such as successive interference canceation (SIC) [35] and parae interference canceation (PIC). MAI was anayzed and approximated as Gaussian distribution [36] for fading channe in MIMO case. In contrast to the existing works, an exact characterization of MAI in Rayeigh fading environment is deveoped for MIMO-CDMA systems in this thesis. Consequenty, expicit cosed-form expression 13

34 for both the probabiity density functions (pdfs) of MAI and MAI pus noise is derived for Rayeigh fading channe Equaization in Mutipe Input Mutipe Output (MIMO) Systems Mutipe input mutipe output (MIMO) communication schemes oer the potentia for signicant increases in spectra eciency over their singe-input singe output counterparts by enabing simutaneous transmission of independent data streams. MIMO schemes aso oer the potentia for signicant performance gains in a variety of other metrics. Standard transceiver architectures for these schemes incude inear precoding and equaization, and the combination of inear precoding and DFE, which oers the potentia for improved performance over the inear approach whie maintaining comparabe compexity. Equaization of wireess MIMO frequency-seective channes is a chaenging task mainy due to the fact that the respective MIMO equaizers shoud cope with inter symbo as we as inter stream interference. When the channe is static and has aready been estimated by the receiver, a we estabished soution woud be to appy a muticarrier technique, such as a MIMO orthogona-frequency-division mutipexing (OFDM) system [37]. Even though MIMO OFDM systems oer simpicity in anaysis and receiver design, they sti suer from drawbacks reated to impementation (peak to average power ratio), identiabiity (spectra nus), and sensitivity to carrier synchronization [38]. Another drawback is that uncoded OFDM has no signicant performance gain as the deay spread of the channe increases [39], i.e., uncoded OFDM does not expoit mutipath diversity. On the other hand, singecarrier (SC) moduation is a we-proven technoogy in many existing wireess and wire ine appications and has been extensivey used in practice. Thus, aternative SC approaches for the design of batch MIMO decision feedback equaizers (DFEs) have been proposed [40, 41]. 14

35 However, in MIMO systems with reativey ong bursts and under time varying conditions, the invoved channe impuse responses change within a burst and, as expected, batch MIMO DFEs fai to equaize the channe. On the other hand, if a MIMO OFDM system is empoyed, the frame size shoud be made short and thus cycic prex overhead becomes overwheming [38]. Therefore, to achieve eective channe equaization in such cases, adaptive methods are required. Both a minimum bit error rate (MBER) design [42,43] and the standard minimum mean-square error (MMSE) design [44, 45] and [46] have been invoked for impementing adaptive MIMO DFEs. The respective equaizers are updated either by using gradient Newton methods or by empoying stochastic gradient techniques. The main probems appearing in adaptive MIMO equaization, i.e., the increased ter size and the coored noise caused by inter stream interference, sow down signicanty the performance of stochastic gradient agorithms. On the other hand, the computationa requirements of MIMO RLS agorithms increase signicanty. In some adaptive schemes with convergence properties cose to RLS but of ower computationa cost were proposed in [47]. But sti the computationa compexity is very high compared to the LMS type agorithms. For scenarios in which accurate channe state information (CSI) is avaiabe at both the transmitter and the receiver, there is a we estabished framework that unies the design of inear transceivers under many design criteria [48]. A counterpart for the design of systems with DFE has recenty emerged [4951]. This framework was aso extended to MIMO systems with pre-interference subtraction at the transmitter in [51]. However, in many scenarios, such as frequency division dupex systems, obtaining accurate CSI at the transmitter may require a considerabe amount of feedback to the transmitter. An approach that aows the designer to imit the required amount of the feedback is to quantize the transmitter design. In these imited feedback schemes [52], the receiver uses its CSI to choose the best transmitter design from a code book of avaiabe designs, and then feeds back the 15

36 index of this precoder to the transmitter. This strategy has been considered for beam forming schemes [5356], unitary precoding with inear equaization [57] and unitary precoding for orthogona space time bock codes [58, 59]. For zero-forcing DFE schemes, a imited feedback scheme in which the receiver feeds back the order of interference canceation was proposed in [60, 61]. A imited feedback scheme for systems with a (genera) inear precoder at the transmitter and zero-forcing DFE at the receiver was presented in [51]. From the theory of constrained optimization, it is found that the earning speed of any adaptive tering agorithm can be increased by adding a constraint to it as in the case of the normaized LMS (NLMS) [62] and the normaized east-mean-fourth (NLMF) [63] agorithms. In an LMS-type agorithm that expoits the knowedge of the channe noise variance for identication and tracking of nite impuse response (FIR) channes, caed noise constrained LMS (NCLMS) agorithm, was proposed in [64]. Recenty an LMS based constrained adaptive agorithm was designed for CDMA systems which expoit the knowedge of both MAI and noise variances [65]. The novety of this constraint resides in the fact that the MAI variance was never used as a constraint before. Motivated by this, it is proposed to design both inear and non-inear (DFE) equaizers for MIMO systems using the framework of [65]. 1.6 Drawbacks in Previous Techniques: A motivation for the proposed work There are severa drawbacks in the techniques discussed above which are enumerated as foows: ˆ Athough MIMO OFDM systems oer simpicity in anaysis and receiver design, they sti suer from drawbacks reated to impementation (peak to average power ratio), identiabiity (spectra nus), and sensitivity to carrier synchronization [38]. 16

37 ˆ Uncoded OFDM has no signicant performance gain as the deay spread of the channe increases [38] i.e., uncoded OFDM does not expoit mutipath diversity. ˆ Minimum bit error rate (MBER) DFE [42] can promise a better bit error rate performance but due to its reiance on BER cost function which provides very irreguar surface is highy susceptibe to divergence [66]. ˆ The computationa requirements of MIMO RLS agorithms increase signicanty [47]. ˆ Performance of CSI based DFEs depends on the accurate estimate of channe information [48]. This is probematic due to the time-varying nature of wireess channes. ˆ A major drawback of MIMO-CDMA systems is MAI which can reduce the capacity and increase BER, so statistica anaysis of MAI becomes very important factor in the performance anaysis of these systems. Statistica anaysis of MAI in MIMO-CDMA is quite compicated and most of the researchers have used suboptima approach to detect the subscriber without invoving the need for MAI statistics such as successive interference canceation (SIC) and parae interference canceation (PIC). Lack of research in the characterization of MAI in MIMO-CDMA has provided a motivation to perform a compete statistica anaysis and nd the cosed form soution to the probabiity density functions (pdf's) of MAI and MAI pus noise in Rayeigh channe environment. ˆ If partia knowedge of the channe is avaiabe, it can be used to enhance the system performance. Moreover, CDMA systems suer from MAI and noise, consequenty, there is a dire need to design a mutiuser detector which woud dea with the MAI and noise. In previous research work, MAI has been used as part of interfering noise, and was assumed to be an unstructured 17

38 white Gaussian noise. [33] used MAI and noise to form a new constraint and used it in deveoping an agorithm named MAI pus noise constrained LMS (MNCLMS) agorithm. MNCLMS was shown to have outperformed the other agorithms which were constrained on noise ony but [33]'s work is reated to SISO-CDMA systems. 1.7 Thesis Objective Thus, in the ight of the above discussion it is apparent that there is a need for designing new adaptive equaization techniques which can overcome the above mentioned drawbacks. The earning speed of an adaptive tering agorithm can be increased by adding a constraint to it [62]. Recenty an LMS based constrained adaptive agorithm is designed for CDMA systems based on the knowedge of MAI and noise variances [65]. The novety of this constraint resides in the fact that the MAI variance was never used as a constraint before. Motivated by this, it is proposed to design both inear and non-inear (DFE) equaizers for MIMO systems using the framework of [65]. The objectives of the proposed work are as foows: 1. To design a inear transverse and non-inear equaizer (DFE) for MIMO systems based on constrained optimization technique empoying the framework of [65]. 2. Constraints wi be imposed on both MAI and noise variances. For this, the statistica characterization of MAI and MAI pus noise in MIMO CDMA systems wi be anayzed. 3. Performance anaysis (transient, steady-state, and tracking) of the proposed adaptive agorithms wi be carried out in the scenario of interference and noise imited systems. 4. Extensive simuations wi be presented to corroborate the theoretica ndings. 18

39 1.8 Thesis Organization After the introductory chapter, a comprehensive anaysis of MAI for MIMO synchronous CDMA system using BPSK signa with random signa sequences in fading environments such as Rayeigh is presented in chapter 2 with simuation resuts to support the anaytica resuts. Chapter 3 deas with the investigation of optimum coherent reception in the presence of mutipe access interference and BER is derived for the Rayeigh channe.simuation resuts shown at the end of chapter 3 show the cose agreement to the anaytica ndings. In chapter 4, various types of DFE are discussed. In chapter 5, two types of MIMO receivers have been proposed: One with inear adaptive equaization and the other with MIMO DFE. For both receivers, a new constrained agorithm is proposed. Convergence anaysis, transient anaysis and tracking anaysis of the constrained agorithm are performed in chapter 6. Simuation resuts are presented to vaidate the anaysis. Chapter 7 deas with the concusion, contributions and recommendations for the future work. 1.9 Peer Reviewed Pubished Work and Conference Pubications 1. "Design of MAI constrained decision feedback equaizer for MIMO CDMA system," Mahmood, K.; Moinuddin, M.; Asad, S.M.; Pau, S., Wireess Communications and Signa Processing (WCSP), 2011 Internationa Conference on, vo., no., pp.1,5, 9-11 Nov Statistica Anaysis of Mutipe Access Interference in Rayeigh Fading Environment for MIMO CDMA Systems, Mahmood, K.; Moinuddin, M.; Azzedine Zerguine; Asad, S.M.; Pau,S., submitted to ICASSP SPCOM 19

40 Chapter 2 Statistica Anaysis of mutipe access interference (MAI) and noise in MIMO-CDMA systems 2.1 Introduction In an idea scenario, MIMO-CDMA system oers a great improvement in overa system capacity [67] [68]. But in practice, this achievement is imited due to the presence of MAI. MAI reduces the capacity and increases the BER of the MIMO systems resuting in the degradation of the system. Thus, a compete statistica anaysis of MAI is vita in the design and performance anaysis of these systems. Due to computationa compexities in the statistica anaysis of MAI in MIMO- CDMA systems, there is no substantia research work in the iterature. Thus, either some strong assumptions are used, for exampe, Gaussian assumption for interference in MIMO system [69, 70] or suboptima approaches are empoyed to detect the subscriber without invoving the need for MAI statistics such as successive interference canceation (SIC) [71] and parae interference canceation (PIC) [72]. In contrast to the existing research, an exact characterization of MAI in Rayeigh 20

41 fading environment is deveoped for MIMO-CDMA systems in this thesis. Consequenty, expicit cosed-form expressions for both the probabiity density function (pdfs) of MAI and MAI pus noise is derived for Rayeigh fading channe assuming that the channe phase is either estimated or known at the receiving end. 2.2 Probabiity Density Function (pdf) of MAI Pus Noise in Fat Fading Environment In this section, cosed form expressions for pdf of MAI and MAI pus noise for at fading channe (Rayeigh) has been derived under the assumption that the channe phase is either known or has perfecty been estimated System Mode A bock diagram of a MIMO-CDMA system with N transmit and M receive antennas is considered as shown in gure 2.1. Consider a at-fading channe whose compex impuse response between the nth transmitter and mth receiver for the th symbo is Hmn (t) = h mne jφ δ (t) (2.2.1) where h mn is the enveope and φ n is the phase of the compex channe for the th symbo. Assuming that the receiver is abe to perfecty track the phase of the channe, the detector in the mth receiver observes the signa r m (t) = N K n=1 = k=1 A k b,k n s,k n (t) h mn +ν m (t), m = 1, 2,... M (2.2.2) where K represents the number of users, s,k n (t) is the rectanguar signature waveform with random signature sequence of the k th subscriber dened in the ( 1) T b 21