PARALLEL INTERFERENCE CANCELLATION MULTIUSER DETECTORS FOR DS-CDMA COMMUNICATION SYSTEMS. Feng Liu. Presented to the Faculty of the Graduate School of

PARALLEL INTERFERENCE CANCELLATION MULTIUSER DETECTORS FOR DS-CDMA COMMUNICATION SYSTEMS by Feng Liu Presented to the Faculty of the Graduate School of The University of Texas at Arlington in Partial Fulfillment of the Requirements for the Degree of DOCTOR OF PHILOSOPHY THE UNIVERSITY OF TEXAS AT ARLINGTON May 2006

Copyright c by Feng Liu 2006 All Rights Reserved

Dedicated to my mother and father.

ACKNOWLEDGEMENTS I would like to express my sincere gratitude to my thesis advisor, Prof. Vasant K. Prabhu, for his guidance and support throughout my years in UT Arlington. Particularly, Prof. Prabhu endowed me full freedom on selecting research topics and inspired me to consistently pursue with high standard. I would like to thank Prof. William E. Dillon, Prof. Chien-Pai Han, Prof. Qilian Liang, and Prof. Michael T. Manry for being on my thesis committee, and for their precious time and effort in providing valuable suggestions and comments to improve the quality of this thesis. I am also grateful to all my friends and colleagues at the Telecommunication Research Group and UTA: namely Chen Liao, Dongdong Li, Iyad Abdelrazzaqe Al-Falujah, Mahmoud Smadi, Kiran Kuchi, Guy Tshiteya, Cesar Heyaime. Their support has helped me to go through the difficult times and meet the challenges encountered in completing this work. Finally, but not least, I would like to thank my wife, Ke Yang, and all my family members. Without their love and affection, I would not be able to achieve what I have finished. December 7, 2005 iv

ABSTRACT PARALLEL INTERFERENCE CANCELLATION MULTIUSER DETECTORS FOR DS-CDMA COMMUNICATION SYSTEMS Publication No. Feng Liu, Ph.D. The University of Texas at Arlington, 2006 Supervising Professor: Vasant K. Prabhu A non-linear sub-optimal multiuser detector in the form of parallel interference cancellation (PIC) has been studied. The main objective of this thesis is to develop an analytical model for PIC performance analysis and propose new near-optimum approach. Since the exact performance analysis of PIC is difficult to derive due to its nonlinear decision function, previous work tends to adopt computer simulation method or evaluate through Gaussian approximation (GA) method. For PIC detector, the GA method may not apply since there may exist a dominate interference signal. In addition, the central limit theorem is not applicable to model the residual MAI in the case of PIC due to its own structural property. We develop an analytical model to derive the exact BER performance in the case of two users, and extend the method to approximate cases when moderate-to-high SINR can be encountered. We propose a gradient adaptive parallel interference cancellation detector and investigate its performance. The presented PIC detector is equipped with a set of adaptive v

weights which are adjusted through a new proposed gradient adaptive step size-lms (GASS-LMS) algorithm to reduce the cost of wrong interference estimation as existed in the conventional PIC. The initial state is deliberately set based on the function of probability of error to reflect the reliability of the tentative decision from the previous stage. While the most previous work on MUD are restricted to cases where there is no intersymbol interference (ISI), we consider the problem of joint detection of MAI and ISI, which is crucial to enhance the performance of the third and future generation systems with high data rate applications. Simulation results are provided to show that our low complexity joint detector can perform very well, yielding the bit error rate (BER) close to the non-isi single-user error rate. vi

TABLE OF CONTENTS ACKNOWLEDGEMENTS.............................. iv ABSTRACT...................................... v LIST OF FIGURES.................................. ix Chapter 1. INTRODUCTION................................. 1 1.1 Background and Motivation......................... 1 1.2 Outline of Thesis............................... 4 1.3 Contributions................................. 6 2. SYSTEM MODEL AND MULTIUSER DETECTION............. 7 2.1 System Model................................. 7 2.1.1 Synchronous CDMA System..................... 8 2.1.2 Asynchronous CDMA System.................... 11 2.2 Multiuser Detection.............................. 14 2.2.1 Optimum Multiuser Detection.................... 17 2.2.2 Linear Multiuser Detection...................... 20 2.2.3 Nonlinear Multiuser Detection.................... 23 3. PERFORMANCE ANALYSIS OF PIC...................... 30 3.1 Introduction.................................. 30 3.2 Exact BER Analysis of Two Users...................... 31 3.3 Exact BER Analysis of More Than Two Users............... 33 3.4 Approximate Analysis of BER in K-user Scenario............. 34 3.5 Simulation Results.............................. 36 vii

3.6 Conclusion................................... 40 4. ADAPTIVE MULTISTAGE PIC......................... 41 4.1 Introduction.................................. 41 4.2 Frame work of Adaptive PIC......................... 42 4.3 GASS-LMS Algorithm............................ 45 4.4 Optimal Initialization of Weights...................... 47 4.5 In Multipath Fading Channels........................ 49 4.6 Simulation Results.............................. 50 4.7 Conclusion................................... 54 5. JOINT DETECTION OF PIC AND EQUALIZER............... 55 5.1 Introduction: Joint Detection........................ 55 5.2 System Model................................. 59 5.3 Joint Adaptive PIC and Decision Feedback Detection........... 62 5.4 Applying GASS-LMS to Joint Detection.................. 66 5.5 Simulation Results.............................. 68 5.6 Conclusion................................... 69 6. PIC COMBINED WITH ANTENNA ARRAY.................. 73 6.1 Introduction.................................. 73 6.2 Antenna Array Techniques.......................... 75 6.3 Space-time Signal Processing......................... 77 6.4 Space-time Multistage Adaptive PIC.................... 81 6.5 Simulation Results.............................. 83 6.6 Conclusion................................... 85 7. FUTURE WORK.................................. 86 REFERENCES..................................... 87 BIOGRAPHICAL STATEMENT........................... 94 viii

LIST OF FIGURES Figure Page 2.1 K-user synchronous CDMA communication system model......... 8 2.2 Matched filter detector for K-user CDMA system............. 9 2.3 General concept of multiuser detection................... 16 2.4 Classification of multiuser detection..................... 17 2.5 Decorrelating Detector............................ 21 2.6 Minimum Mean-Squared Error Detector................... 22 2.7 A multistage PIC scheme for CDMA.................... 25 2.8 Illustration of parallel interference cancellation in a stage......... 26 2.9 Illustration of Reconstructor......................... 26 2.10 One stage general APIC detector...................... 29 3.1 BER vs. SNR in an AWGN channel..................... 37 3.2 BER vs. SNR with ρ = 3/7.......................... 38 3.3 Performance comparison with conventional matched filters........ 39 3.4 BER vs. SNR with the approximation method............... 40 4.1 One stage of the adaptive multistage PIC detector............. 43 4.2 Adaptive PIC detector in multipath fading channels............ 50 4.3 BER vs. the number of users in an AWGN channel............ 51 4.4 BER vs. the number of users with unbalanced power........... 53 4.5 Performance over a two-path Rayleigh fading channel........... 53 5.1 Asynchronous CDMA over Rayleigh fading channels............ 59 5.2 Contributions from users paths to the received signal........... 70 ix

5.3 Proposed adaptive PIC aided by decision feedback filter.......... 70 5.4 Adaptive multistage PIC detector for one stage............... 71 5.5 BER vs. SNR with / without joint detection................ 71 5.6 BER vs. SNR in an asynchronous 3-ray Rayleigh fading channel..... 72 6.1 Block diagram of antenna arrays....................... 74 6.2 Proposed space-time adaptive PIC...................... 75 6.3 Illustration of incident plane wave...................... 77 6.4 Space-time processing............................. 79 6.5 Improved adaptive multistage PIC detector................. 82 6.6 BER vs. SNR (with 16 active users)..................... 84 6.7 BER vs. the number of users (E b /N 0 = 8dB)................ 85 x

CHAPTER 1 INTRODUCTION 1.1 Background and Motivation The world is in a present stage of transformation to an information epoch. The wealth of nations is measured not merely by the production of agricultural and industrial goods, but also, and more significantly, by the capability of generating, processing, and transferring information, which is the driving force behind the IT (Information and Telecommunication) Industries. Wireless communication is a promising technique that provides people with convenience and much more flexible method to access information. During the past two decades, wireless personal communications started from a concept to a huge market with near 1.527 billion subscribers worldwide. The technology improvement has evolved from the voice transmission originating second-generation (2G) mobile communication systems to the third-generation (3G) systems with much higher data rates and a wide variety of serive types. The 3G mobile communication systems are also expected to offer significantly higher flexibility than that in 2G systems. The direct sequence code division multiple access (DS-CDMA) has been adopted by the 3G wireless communications standard. It has the potential to provide a higher capacity than the time division multiple access (TDMA) and the frequency division multiple access (FDMA) schemes[1][2]. In a CDMA system, new users are allowed to access the system under higher interfernce levels as long as the quality of wireless links is maintained at a certain level. In this way, CDMA systems are more flexible in their capacities. 1

2 In the ideal case, the users in a CDMA system is distinguished by assgning with a signature sequence that is orthogonal to those of other users. Considering cellular mobile systems, mobile units transmit independently so that their signals arrive asynchrnously at the base station. Due to users asynchronicity and hostile wireless channel effects, it is difficult to maintain orthogonality. Actually, there is no known set of code sequences that is completely orthogonal when used in an asynchrnous system. As a result, the interference from other users, which is called the multiple access interference (MAI), can severely degrade the performance of CDMA systems. The MAI in turn is not only due to the non-perfect orthogonality of the signature sequences, but also to the multipath fading channel. The multipath channel causes signal fading and results in significiant power imbalances. Moreover, CDMA systems also suffer from the near/far effect [2]: the signal from a mobile terminal far from the base station is weak and could be destroyed by stronger signals of terminals closer to the base station. The near/far effect is due to both multipath fading and signal power loss as a function of distance from the base station. Many advanced signal processing techniques have been proposed to combat multiple access interference and multipath channel distortion, such as (1) multiuser detecion; (2) antenna arrays and spatial diversity; (3) source and channel coding. This dissertation focuses primarily on the first one, multiuser detection (MUD), while in Chapter 6, the application of combining antenna arrays with multiuser detectors is studied. Multiuser detection can substantially enhance the receiver performance and increase the capacity of CDMA systems by exploit the underlying structure of spreading waveforms of user signals for interference suppression. Instead of treating MAI as noise as in a conventional receiver, MUD makes a joint detection of all the users signals and takes an advantage of investigating the structure of MAI. In 1986, Sergio Verdu proposed his optimum multiuser detector in the sense of minimum bit error rate for CDMA sys-

3 tems [3]. After his milestone work, numerous sub-optimum MUDs have been developed to reduce the computational complexity which increases exponentially with the number of users in the optimum MUD. One group of sub-optimum MUDs are linear multiuser detectors, which perform a linear transformation to the soft outputs of conventional matched filter (MF) bank to obtain a new set of outputs to make the final decisions. They are including the linear decorrelating detectors (DD) [4][5], linear minimum mean squared error (MMSE) detectors [6][7][8][9] and etc. The linear MUDs are well established and intensively studied due to its linear nature and easy of obtaining the analytical results. Another important group of sub-optimum MUDs are nolinear multiuser detectors, or called interference-cancellation-based MUDs, including successive interference cancellation (SIC) detectors [10][11][12], parallel interference cancellation (PIC) detectors [13][14][15][16], decision feedback (DF) detectors [17][18] and etc. The basic principle behind IC detectors is to estimate the interference signals and then remove all or part of the MAI seen by the user of interest before demodulating the user s signal. Among those nonlinear MUDs, PIC detectors are of our special research interest since they have been shown to have close connection to Verdu s optimum detector and also to possess several desirable properties, such as the potential for near optimum performance, very low computational complexity and low decision latency. Note that there exist the linear approaches of PIC which could be considered as efficient methods to implement linear MUDs by approximating matrix inversion using Jacobi iteration [19][20]. In this thesis, term PIC denotes the nolinear approach of parallel interference cancellation unless the linear PIC is explicitly announced. Although PIC as been intensively studied since the original work by Varanasi and Aazhang [13], [14], there still has a big gap between its real performance and that of the optimum MUD. In addition, its theoretical analysis of performance is far from ideal due

4 to the nonlinear hard decision function. The dissertation focuses on the development of advanced processing techniques for multiuser interference cancellation and studies their performance by analysis and computer simulation. The goal of the research is to improve the performance of existing PIC multiuser detection methods, and develop new methods that give high performance (near optimal) with relatively low computational complexity. When the transmitted symbols are channel coded, the outputs of the channel decoders can be used to mitigate the MAI in a way similar to PIC based MUD. Applying the turbo principle [21] [22], which was first used in the decoding of turbo codes [23], to MUD, Wang and Poor [24] proposed turbo MUD, which treats the soft decision feedback from the single-user decoder as a priori information for the MUD and improves the performance iteratively. To reduce the NP-hard complexity of such algorithms, both PIC and SIC can be applied in the same way as in uncoded systems. The information theoretic characterization of CDMA systems via the capacity region is analyzed in [25]. To achieve an arbitrary point in the capacity region, joint MUD and decoding may be required at the receiver, which incurs intolerable computational complexity due to the prohibitively large number of states. Fortunately, a receiver structure having separate MUD and single-user decoders, which is feasible for practical applications, achieves the sum capacity with SIC combined with MMSE MUD (SIC+MMSE) [26]. Therefore, SIC+MMSE is a promising decoding scheme for practical spectrally ecient communication systems. 1.2 Outline of Thesis In Chapter 2 we introduce synchronous and asynchrnous CDMA system models with the notations applied throughout this paper. Several common multiuser detectors are described and studied. Particularly, the frame work of parallel interference cancellation detector is presented. Performance analyses of the related detectors are given.

5 In Chapter 3 we study the performance of PIC detectors by means of bit error rate in CDMA with an AWGN channel. The exact BER is derived for the case of two users and the study reveals that even for two users BER the numerical computation is required and it becomes rather difficult and cumbersome for a handful of users. Therefore, we set up a approximation method to derive the BER of PIC detectors. Instead of modelling the residual MAI as Gaussian random process, we use conditional probability of error to obtain a more accurate model under the assumption that there is only up to one tentative decision error occurs in the previous stage. The simulation results support our method with the excellent match. In Chapter 4 a near-optimum adaptive parallel interference cancellation detector with gradient adaptive step size is proposed. The step size is gradient adaptive to the Euclidean distance between the received signal and its estimate, hence, suppresses the gradient noise and provides a faster convergence rate. The corresponding GASS-LMS algorithm is derived and analyzed. The simulation result shows that the proposed scheme can provide a superior performance over the conventional PIC, the partial PIC and significantly outperforms the original scheme in both AWGN and Rayleigh fading channels. In Chapter 5 the problem of joint detection of multiple access interference and intersymbol interference is considered. We proposed an adaptive PIC with aid of decision feedback filter for its simplicity yet with the excellent performance to approach that of the optimum MAP detector. The optimum adaptive coefficients that are based on the minimum mean square error (MMSE) criteria have been discussed and obtained. Also we modify and extend our algorithm to derive a pratical adaptation implementation based on a gradient adaptive step size to effectively drive the coefficients approaching the optimum values. In Chapter 6 the application of adaptive PIC with antenna array processing technique is studied. Antenna array processing provides significant SIR gain by coherently

6 combining the signal across antenna and can further combat multipath fading through diversity combining. MAI arriving from the directions other than that of the desired user can be significantly suppressed by the spatial filtering, meanwhile, the in-beam MAI is reduced by adaptive PIC. The thesis is summarized in Chapter 7 with a brief introduction to some future research directions. 1.3 Contributions The main contributions are summarized as follows. An accurate model is developed to analyze the BER performance of non-linear parallel interference cancellation detectors. The model can be applied to varieties of PIC detectors. A near-optimum adaptive PIC detector is proposed with low computational complexity O(N K). A fast optimal algorithm with a gradient adaptive step size is derived for the adaptive PIC detector. Extend the adaptive PIC for joint mitigation of MAI and ISI with the aid of decision feedback filters.

CHAPTER 2 SYSTEM MODEL AND MULTIUSER DETECTION This chapter briefly reviews the wireless CDMA communication model and multiuser detection technologies. The system model is described in Section 2.1, which contains synchronous and asynchronous CDMA models. The detection scheme of the conventional receiver is presented therein. Several typical multiuser detectors are summarized in Section 2.2. 2.1 System Model In Direct-Sequence (DS) CDMA systems, the information symbols are directly modulated by the signature sequences (or spreading codes 1 ). The spreading codes used to spread the information data can be in the form of either short or long. In the former case, the period of the signature sequence is equal to the symbol period. Whereas in the latter case, more than one symbol occur in one period of the signature sequence. Both of these codes have their own benefits and drawbacks. For example, when short codes are used, the circuit will be simple, while giving a fixed interference to each other. Therefore, some users suffer from a larger amount of interference than the others. For the long code case, the interference on each user is more random-like, although the complexity will be higher. 1 since the bandwidth of modulated signals are spread through spreading codes 7

2.1.1 Synchronous CDMA System 8 Consider the equivalent model of a synchronous DS-CDMA communication system as shown in Fig. 2.1. Assume there are K users in the system and the binary phase shift keying (BPSK) is applied. d 1 d 2 E b c ) cos( ω t c +θ1) ( 1 1 t E b 2 t c2( ) cos( ω t +θ ) c 2 r(t) M n(t) d K E bk c K (t) cos( ω + θ ) K c t Figure 2.1 K-user synchronous CDMA communication system model. For the kth user, a binary data symbol d k which takes values of {±1} with the symbol duration T b is spread by the binary spreading waveform c k (t) with chip duration T c. c k (t) is the signature waveform of user k, and can be expressed as c k (t) = M 1 m=0 a k(m)p(t mt c ). where a k (m) is the signature sequence and p(t) is the rectangular pulse shaping function, which converts signals from discrete time to continuous time. M is the processing gain given by M = T b /T c. The spread signal is BPSK modulated by a carrier and then transmitted over a wireless channel. The received signal r(t) at the base station can be expressed as

9 r(t) = = K s k (t) + n(t) k=1 K Ebk d k c k (t)cos(ω c t + θ k ) + n(t) (2.1) k=1 where E bk and θ k are the received energy per bit and the carrier phase offset of user k respectively. The carrier frequency is denoted by ω c. The noise n(t) is a complex additive white Gaussian noise with zero mean and two-sided power spectral density of N 0 /2 W/Hz for each real and imaginary components. y 1 ˆd 1 y 2 ˆd 2 y K dˆk Figure 2.2 Matched filter detector for K-user CDMA system.

The conventional receiver used in CDMA systems is a matched filter matched with the signature sequence of the desired user. Assuming that coherent detection is used in the receiver as shown in Fig. 2.2, the output of the matched filter for user k is given by y k = 1 Tb r(t)c k (t)cos(ω c t + θ k )dt T b 0 = E bk d k + = E bk d k + K j=1 j k 1 T b Tb 0 Ebj d j c j (t)cos(ω c t + θ j )c k (t)cos(ω c t + θ k )dt + n k K Ebj d j cosθ jk ρ jk + n k (2.2) j=1 j k where θ jk = θ j θ k. ρ jk,i is defined as the normalized cross correlation coefficient and given by 10 ρ jk = 1 Tb c j (t)c k (t)dt (2.3) T b 0 n k is a complex Gaussian noise component after despreading,the variance of n k is N 0 /2, and can be expressed as n k = 1 Tb n(t)c k (t)dt (2.4) T b 0 In Eqn. (2.2), the first, second and third terms denote the useful information, the MAI and the noise component respectively. We can see, the quality of single user detector strongly depends on the level of multiple access interference, i.e. relative signal strength and the cross-correlation of signature sequences between the active users. as We can group the matched filter outputs into a K-dimensional vector and expressed y = RAd + n (2.5)

where the notations are listed below 11 y = [y 1, y 2,..., y K ] T R i,j = the (i, j) element of R = cosθ ij ρ ij A = diag { Eb1, E b2,..., } E bk d = [d 1, d 2,..., d K ] T n = [n 1, n 2,..., n K ] T where R is a K K dimension symmetric matrix of user signature sequence crosscorrelations. The signature sequences are assumed to be normalized to unit energy such that R kk = 1 for all k = 1, 2,..., K and R kj 1 for all k j. n represent the noise components at the outputs the matched filters and can be demonstrated that E[n] = 0 and E[nn T ] = R. It is instructive to break up R into two matrices: one representing the autocorrelation, the other the cross-correlation. Hence, similar to Eqn. (2.2), the conventional matched filter detector output can be denoted as three terms: y = Ad + QAd + n (2.6) where Q contains off-diagonal elements of R, that is, R = I+Q (I is the identity matrix). The first term is simply the decoupled data weighted by the received amplitudes. The second term represents the MAI interference. 2.1.2 Asynchronous CDMA System To be more accurate, the aforementioned synchronous CDMA system is a symbol synchronous system where the transmitted symbols of all users arrive at the receiver synchronously, i.e. the transmission delay τ k is equal to zero for all k = 1, 2,..., K. Here

when we discuss the asynchronous system, instead of totally without timing control, there still exists the mechanism of synchronization on the chip level, or so called chip 12 synchronous, where chip boundaries of all users are aligned. In a chip synchronous system, τ k is an interger multiple of T c. Consider a chip synchronous CDMA system with K users. The received signal at the base station can be represented as r(t) = K Ebk d k (t τ k )c k (t τ k )cos(ω c (t τ k ) + θ k ) + n(t) (2.7) k=1 without loss of generality, we assume 0 τ k < T for k = 1,..., K. When τ k > τ l, the ith symbol of user l overlaps with the (i 1)th and ith symbols of user k, represented by ρ(i, i 1) lk and ρ(i, i) lk respectively. We define ρ(i, j) lk as the cross-correlation between c k (t) and c l (t) within the intersection interval of the ith symbol of user l and the jth symbol of user k, ρ(i, j) lk = 1 ( t (i + 1/2)Tb τ ) l c l (t τ l )c k (t τ k )rect 2T b T b ( t (j + 1/2)Tb τ ) k rect dt (2.8) T b With (2.8), when i j > 1, ρ(i, j) lk = 0. After coherent detection, the output y l (i) of the matched filter for the ith data symbol of user l is given by which is to be shown as y l (i) = 1 T b (i+1)tb it b r(t)c l (t τ l )cos(ω c (t τ l ) + θ l )dt (2.9)

13 y l (i) = E bl d l (i) + + + K Ebk d k (i)ρ(i, i) lk cos(ω c (τ l τ k ) + (θ k θ l )) k=1 k l K In {τk >τ l } Ebk d k (i 1)ρ(i, i 1) lk cos(ω c (τ l τ k ) + (θ k θ l )) k=1 k l K In {τk <τ l } Ebk d k (i + 1)ρ(i, i + 1) lk cos(ω c (τ l τ k ) + (θ k θ l )) + n k (i) k=1 k l (2.10) where the index function In { } is equal to one when the condition { } is met; otherwise, it is zero. We can represent (2.10) in the form of matrix as y(i) =[R(i, i) + R(i, i 1)z 1 + R(i, i + 1)z]Ad(i) + n(i) =G(i)Ad(i) + n(i) (2.11) where the notations are listed below y(i) = [y 1 (i), y 2 (i),..., y K (i)] T A = diag { Eb1, E b2,..., } E bk d(i) = [d 1 (i), d 2 (i),..., d K (i)] T n(i) = [n 1 (i), n 2 (i),..., n K (i)] T the (l, k)th element of R(i, i), R(i, i 1) and R(i, i + 1) are ρ(i, i) lk cosφ lk, In {τk >τ l }ρ(i, i 1) lk cosφ lk, In {τk <τ l }ρ(i, i + 1) lk cosφ lk,

respectively, where Φ lk = ω c (τ l τ k ) + (θ k θ l ), z 1 and z are the unit delay and advance operators. The K K matrix 14 G(i) = R(i, i) + R(i, i 1)z 1 + R(i, i + 1)z (2.12) is the effective correlation matrix for the ith data symbol in asynchronous system. 2.2 Multiuser Detection The goal of the research is to improve the performance of existing multiuser detection methods, and develop new methods that give high performance (near optimal) with relatively low computational complexity. In a Direct Sequence CDMA system, the signals on all links are transmitted simultaneously (may not be synchronous). The individual signals are separated by using spreading codes, with one or more spreading signals embedded within the desired signal. The spreading codes may not ideally orthogonal to each other. Even in the case of ideal orthogonality, due to the wireless propagation environment, they are only semi-orthogonal, especially in the uplink where the signals originate from disparate geographical locations and propagate through distinct paths. The result is that the desired signal for each user is contaminated not only by the thermal additive noise but also by the signals from other users. This interference from other users, so called Multiple Access Interference (MAI), is an essential limiting factor in the capacity of CDMA systems. In traditional CDMA receivers, MAI is treated as additive noise and detection is based on the assumption that additive noise due to MAI is gaussian [27]. The amount of multiple access interference depends on two factors: signal strength of each individual user, and the cross-correlation properties of the employed spreading codes. Furthermore, The relative signal strengths depend on the transmitted power from each user and their relative distances from the base station in the scenario of uplink.

15 The amount of MAI for the desired user may become so large that it renders a poor performance due to the excessive bit error rate. In most operating scenario, the undesired signal is due to MAI and very little due to thermal noise. This is why in IS-95 cellular communication systems, the call quality often does not correspond closely to the signal quality indicator which measures the signal strength of the desired user including the interference from other users. The multiple access interference becomes high as the number of interfering user increases, in turn, the equivalent noise results in degradation of performance. Even if the number of users is not too large, some user may be received at such high signal levels that a lower power users may be swamped out. This is the near/far effect [2]: users near the receiver are received at higher powers than those far away. The cross-correlation between the signature sequence of the desired user and the signal from a strong interferer can be greater than the correlation with the signal of the desired user. Hence, those far away users suffer a degradation in performance. Even if users are at the same distance to the base station, there can be an effective near/far effect because some users received signals may travel through a deep fading channel. CDMA systems are very sensitive to the near/far effect and a tight power control to the each user s transmitted power has to be employed. A combination of open-loop and fast, closed-loop power control is used to adjust the transmit power of each in-cell user so that the base station receives each user with the same received power [1]. In Direct Sequence CDMA systems, The signal received at the front end of a receiver is the sum of the desired signal, the additive thermal noise and the multiple access interference (MAI). Conventional CDMA receivers demodulate the signal from each user and detect independently while regarding the MAI in the demodulated signal as noise with assumption it has the gaussian possibility density function. This simple treatment limits the capacity of a CDMA system. It is important to note that the MAI

%$ from signals within the cell has a known structure, as compared to the interference from other cells, or unknown MAI [28] where the codes are generally different. 16 y 1! ˆd 1 y 2 "# ˆd 2 & ' y K ( ) dˆk Figure 2.3 General concept of multiuser detection. Multiuser Detection considers all users signal as useful information for each user by joint detection, as indicated in the figure 2.3. It can be proven that while decision metric y k is not sufficient for detecting d k, a group of decision metrics {y 1, y 2,..., y K } are sufficient statistics for joint detecting {d 1, d 2,..., d K } [29]. The conventional matched filter detector is employed as the front-end of multiuser detection scheme sacrifices no information for demodulation [29]. Decoding decision made on processed signals from multiuser detector generate significantly lower bit error rates for individual users. On the other hand, the reduction in MAI allows more active users within a given cell, thus boosting the capacity of the system. Hence, multiuser detection brings lower BERs and a higher number of active users, both of them account for a capacity increase in a CDMA cellular system.

17 Multiuser detection is defined as a class of algorithms or methods in a communication receiver that exploit the considerable structure of the multiuser interference in order to increase the efficiency with which channel resources are employed [29]. Generally speaking, any type of multiuser detector is either optimum or sub-optimum. Under sub-optimum group, there ar two main catalogs: linear and nonlinear (or called interference-cancellation-based) detectors. Figure 2.4 Classification of multiuser detection. 2.2.1 Optimum Multiuser Detection In 1986, Sergio Verdu developed an optimum multiuser detector in the sense of minimum bit error rate for CDMA communication systems [3]. The optimum multiuser detector is based on the Maximum-Likelihood (ML) detection. For analytical simplicity, let us consider the synchronous case here. The baseband received signal at front end can be notated as

18 r(t) = = K s k (t) + n(t) k=1 K Ebk d k (t)c k (t) + n(t) (2.13) k=1 In each bit interval, optimal detector selects the most likely bit sequences d = [d 1, d 2,..., d K ] T such that the criterion is maximum [29]. ( exp 1 Tb 2σ 2 T b 0 [ K r(t) s k (t) ] ) 2 dt k=1 (2.14) In order to maximize Eqn. (2.14), the squared Euclidean distance 1 T b Tb 0 r(t) K k=1 s k(t) 2 dt needs to be minimized. Spread the expression D = 1 Tb K r(t) s k (t) 2 dt T b 0 = 1 Tb r(t) T b k=1 0 k=1 = 1 Tb r(t) 2 dt T b 0 K Ebk d k (t)c k (t) 2 dt 2 Tb r(t) [ K Ebk d k (t)c k (t) ] dt T b 0 k=1 + 1 Tb [ K Ebk d k (t)c k (t) ][ K Ebl d l (t)c l (t) ] dt (2.15) T b 0 k=1 l=1 Discarding the first common term, the minimization problem is equivalent to maximize

19 Ω(d) = 2 Tb r(t) [ K Ebk d k (t)c k (t) ] dt T b =2 0 k=1 1 Tb [ K Ebk d k (t)c k (t) ][ K Ebl d l (t)c l (t) ] dt T b 0 k=1 K Ebk d k y k K k=1 k=1 l=1 l=1 K Ebk E bl d k d l ρ kl =2d T Ay d T Hd (2.16) where y k is the output of matched filter for the kth user, i.e., y k = 1 Tb r(t)c k (t)dt (2.17) T b and we group the output of each matched filter denoted by a column vector 0 y = [y 1, y 2,..., y K ] T (2.18) the received amplitudes contain in a K K matrix A = diag{ E b1, E b2,..., E bk } (2.19) the unnormalized cross-correlation matrix is defined by H = ARA (2.20) where R is the normalized cross-correlation matrix whose element is given by R ij = ρ ij = 1 Tb c i (t)c j (t)dt T b For the maximization of (2.16), the solution can be found by exhaustive search, i.e. compute the criterion function for every possible combination of argument and select the one as optimal solution that maximize the function. The optimum multiuser detector provides the most reliable decision outputs and totally rejects the effect of MAI. 0

20 Hence, its performance is superior to all other multiuser detectors. In spite of its great performance, the computational complexity of the optimum detector is subject to an exponential growth in the number of user since it performs a full search using the Viterbi algorithm. Therefore, when the number of active user K is large, this method with the operational complexity of O(2 K ) turns out to be too complex to implement. As a result, sub-optimum multiuser detectors that are less complex with tolerable sacrifice of performance are of interest. sub-optimum multiuser detectors can be divided into two major catalogs: linear detectors and nonlinear detectors. 2.2.2 Linear Multiuser Detection Linear multiuser detectors apply a linear mapping to the outputs of the matched filters to form a more reliable decision metric. Linear multiuser detectors have the advantage of easy to implement and relatively good performance when the interference is low. Some well-known detectors are Decorrelating Detector (DD) [4][5] and Minimum Mean-Squared Error (MMSE) detector [6][7][8][9]. 2.2.2.1 Decorrelating Detector The decorrelating detector uses the natural strategy of completely removing the effect of the multiple access interfering term. The diagram is shown below in Fig. 2.5. The drawback of this approach is the cost increased noise content in the demodulated signals. Nevertheless, the decorrelating detector provides optimal performance [4]when the amplitudes of user are unknown. The idea behind the DD is to undo the effect of the MAI. This is accomplished by multiplying the received signal by the inverse of the correlation matrix. The final decision metric is made by

21 y 1 ˆd 1 y 2 1 R ˆd 2 y K dˆk Figure 2.5 Decorrelating Detector. ˆd =R 1 y =R 1 RAd + R 1 n =Ad + n (2.21) As can be seen by Eqn. (2.21), in a noiseless environment this approach perfectly recovers the original signals, which the matched filter could not do. The magnitude of the noise enhancement is given by R 1 n. It can be minimized by choosing spreading codes that are near orthogonal to each other. If the codes are perfectly orthogonal then no noise enhancement will take place. However, this is an ideal situation and can not be realized. On the other hand, if the codes become highly correlated with one another the effect of noise enhancement will increase significantly, renders a degradation of performance. Generally, decorrelating detector provides a good performance in many scenarios and serves as a reference to evaluate other multiuser detection schemes.

22 y 1 ˆd 1 y 2 [ ] 2 2 R + σ A 1 ˆd 2 y K dˆk Figure 2.6 Minimum Mean-Squared Error Detector. 2.2.2.2 Minimum Mean-Squared Error Detector The Minimum Mean-Squared Error (MMSE) Detector is an improved linear approach by assuming one has knowledge of strength of each user s received signal. The MMSE works by applying a linear transformation that minimized the mean-squared error between the outputs and the data, i.e., min d f(y) 2 (2.22) where f( ) is the function that maps y to ˆd, and is chosen as to minimize the expected mean-squared error. The function is given by [29] so that the final decision metric is given by ˆd = [R + σ 2 A 2 ] 1 y (2.23) This equation reveals that the MMSE is basically a compromise between the conventional detector and the decorrelating detector. That is, if the signal to noise ration goes to infinity, σ 0, then we can see, [R + σ 2 A 2 ] 1 R 1, which is simply the

decorrelating detector. On the other hand, if the signal to noise ratio goes to zero, 23 σ, then [R + σ 2 A 2 ] 1 will tend to zero. Thus the effect of MMSE (indicated by Eqn. (2.23)) is minimal and the receiver s performance approaches the conventional detector. 2.2.3 Nonlinear Multiuser Detection As the meaning of being named, this kind of detectors apply a nonlinear mapping to the outputs of matched filters to form the final decision metric. They are often referred as interference-cancellation-based or decision-driven-base detectors as well, since they forms tentative decision and then uses these decision to generate an estimate of some or all of the aggregate structured multiple access interference. Then the estimated MAI is subtracted from the received signal to form a new output based on which new decision are made. The idea is nature in that if under the assumption the MAI was estimated perfectly, the output of the detector is composed only of the desired signal and the unstructured additive channel noise. The MAI is removed and the fidelity of the modified received signal is improved, which in turn results in improved bit error rates or increased system capacity. The process of interference cancellation can be done through a number of stage (multistage detectors) or iteratively (iteration detectors). In each stage, it can accomplished successively (Successive Interference Cancellation - SIC) or in parallel (Parallel Interference Cancellation - PIC). In successive interference cancellation approaches [10][11], users are detected one after the other. At the receiver end, users are ranked according to their received power in order to detect the strongest user first, since this user can be detected with the most fidelity. After the demodulation of the strongest user, the second strongest user will be detected on the modified received signal without interfering from the strongest user. The

24 procedure is continued until all users are detected. Although SIC is simple in implementation compared to other type of multiuser detectors, it has several disadvantages and is not of interest of our research. There is delay in linear with the number of users which makes this scheme less efficient for the high-load systems. The detection of all other users depends strongly on the reliability of the correctness of detecting the strong users so that erroneous decision will be propagated through the decision of all other users. When the users are changed, a ranking process is needed to reorder the users according to their receiving powers. The research work in this dissertation focuses on Parallel Interference Cancellation detectors. The first PIC detector for CDMA communication system was proposed Varanasi and Aazhang in [13] and [14] with multistage implementation. The detector was demonstrated to have close relations to Verdu s optimum detector 2 and also to possess several desirable properties including the potential of near optimum performance, low decision delay, and very low computational complexity. 2.2.3.1 Conventional Parallel Interference Cancellation In conventional parallel interference cancellation (CPIC) detectors, parallel processing of multiuser interference simultaneously removes from each user the interference produced by the remaining users accessing the channel [13]. Normally, PIC is performed in a multistage approach as demonstrated in Fig. 2.7. within each stage, the MAI signal is reconstructed based on the tentative decision from the previous stage, and more 2 The optimum detector in the sense of maximum-likelihood (ML) is a one-stage PIC if the data from all interfering user is known a priori [30]. In reality, where such data is unknown, the PIC can be implemented in multiple stages

25 reliable decision statistic is derived after the subtraction of the corresponding estimated MAI signal, as shown in Fig. 2.8. The reconstructor can be implemented as in Fig. 2.9. In this way, each user in the system receives equal treatment insofar as the attempt is made to cancel each user s interference. As compared with the serial processing scheme, since the IC is performed in parallel for all users, the delay required to complete the operation is at most a few bit times. In particular, a multistage approach was suggested in [13], which, in a given stage, estimated a given user s bit under the assumption that the exact knowledge of the other users bits needed to compute the multiuser interference could be replaced by estimates of these bits from the previous stage. r(t) r( t T ) r( t 2T ) r( t ( S 1) T) ˆd 1 (0) (0) ˆd 2 (1) ˆd 1 (1) ˆd 2 ˆd 1 (2) (2) ˆd 2 ˆ ( s) d1 ˆ ( s) d2 (0) dˆk (1) dˆk (2) dˆk ˆ ( s) d K Figure 2.7 A multistage PIC scheme for CDMA. Thus, as discussed afore, the MAI in the sth stage is estimated as Î (s) k = K j=1 j k Ebj ˆd(s 1) j ρ jk (2.24) And then the receiver makes a decision by completely removal of the estimated MAI ˆd (s) k = sgn { Re{y k Î(s) k }} (2.25) As a result, when the estimate from the previous stage become more accurate, the performance of the multistage PIC will be better. However, the CPIC cannot guarantee

26 r( t ( s 1) T ) ˆ ( s 1) d1 ˆ ( s 1) 2 d k 1 k 2 ˆ ( s ) 1 d ˆ ( s ) 2 d ˆ ( s 1) d k k K ˆ ( s) d k Figure 2.8 Illustration of parallel interference cancellation in a stage. ˆ ( s 1) d k E bk sˆ ( s) t k ( ) (t) c k Figure 2.9 Illustration of Reconstructor. the performance improves with more stages. Since the hard decision made in the previous stage may be wrong, such a brute force cancellation can lead to a performance even worse than that without cancellation. As indicated in the [31], if a wrong decision is subtracted, the increased interfering power would be four-fold. 2.2.3.2 Partial Parallel Interference Cancellation In each stage of the iteration, CPIC detectors try to eliminate the interference caused by all the other users. This is not necessarily the best philosophy. Rather, when the interference estimate is poor (as in the early stages of interference cancellation), it

27 is preferable not to cancel the entire amount of estimated multiuser interference. As the IC operation progresses, the estimates of the multiuser interference improve and, thus, in the later stages of the iterative scheme, it becomes desirable to increase the weight of the interference being removed. In [15] a partial cancellation of the MAI by introducing a weight in each stage to determine the amount of cancellation was proposed. The results showed a considerable capacity increase over the CPIC in the AWGN channel. In the proposed partial parallel interference cancellation (PPIC) scheme a compromise is made between cancelling the MAI and reducing the cost caused by an incorrect estimate without the information on the accuracy of the MAI estimation. The motivation behind this approach can also be derived from ML considerations as was done for the total IC approach. The procedure for the multistage interference cancellation is given as follows [15] d (s) k = p (s) (y k Î(s) k ) + (1 p(s) (s 1) ) d k (2.26) where the soft output d (s) k consists of two items: the soft output of CPIC with the weight and the soft output from the previous stage with the complimentary weight. p (s) is the weight for the sth stage cancellation, 0 < p (s) < 1, which is decided by a trial-and-error search. Then, the stage decision is made based on the soft metric ˆd (s) k = sgn { (s) Re{ d k }} (2.27) The weakness for PPIC schemes is falling at that an uniform weight is assigned to all users regenerated signal in each stage, which is not optimal. The philosophy behind it is since the certain knowledge about the MAI to enhance the performance of interference cancellation is only available at the cost of additional complexity, it is desirable to keep this additional complexity as low as possible.

2.2.3.3 Adaptive Parallel Interference Cancellation 28 With a little more deep consideration on the weights in PPIC schemes, it is obvious the weights reflect the reliability of data estimation. Since the reliability of data estimation varies from one user to another and from bit to bit depends on the MAI levels, it is more reasonable for each user to have its own weight per bit interval, rather than on constant weight for all users in each stage throughout the cancellation. In addition, the weights should not necessarily be larger than zero. For instance, when a wrong decision is used to construct the MAI for binary signal, the optimal weight should be 1 as long as the error is detectable. Based on the discussion above, adaptive parallel interference cancellation (APIC) detectors are developed to update the interference cancellation weights adaptively to reflect the reliability and improvement of bit decision. The general structure of APIC is illustrated in Fig. 2.10 where the weights update controlled by some certain algorithms dependent on the criterion adopted. In [7], a recursive least squares (RLS) algorithm is employed to obtain the solution to the criterion: min(n) d n λ n m r(m) ˆr(m) 2 (2.28) m=1 and the tentative decision is updated through iterations as ˆd(n) = Ed + R 1 (n) n λ n m c(m)w(m) (2.29) where the notations are defined as in Section 2.1 system model. Different criterion can be used to develop various APIC detectors. A LMS-based algorithm will be introduced in Chapter 4. m=1

29 (0) ˆd 1 (1) λ 1 ( m) s ˆ ( 1) 1 ( m) r(m) #$ %& (1) ˆd 1 + + (0) ˆd 2 (1) c 1 ( m) λ 2 ( m) s ˆ ( 1) 2 ( m) c ( m 2 ) + e (1) + + ( m)! (1) ˆd 2 (0) dˆk sˆ ) K ( 1 ( m) (1) λ K ( m)!" (1) dˆk + + (m) c K Figure 2.10 One stage general APIC detector.

CHAPTER 3 PERFORMANCE ANALYSIS OF PIC 3.1 Introduction The parallel interference cancellation has been intensively studied since the original work by Varanasi and Aazhang [13], [14], Yoon et al. [32], and Kawabe et al. [33]. In the literature, the majority of the research on the performance analysis of PIC has focus on the linear PIC due to its linear nature and the ability to obtain analytical results [34] [35] [36] [37]. However, the key disadvantage of performance of these linear PIC detectors is that the ultimate performance on any advanced algorithms is limited by the fact that it is linear. It is demonstrated [38] that even the conventional PIC often outperforms the linear MMSE detector in terms of bit error rate in a variety of scenarios. Thus, an improved performance nonlinear PIC potentially offers even greater performance improvements. Although parallel interference cancellation technique is more practical with its low computational complexity, the performance of PIC 1 generally is difficult to analyze due to the nonlinear hard decision function. Some work on the performance of PIC and its modifications such as PPIC also appears in the literature [39] [40]. The analysis is typically based on a Gaussian approximation of the residual multiple access interference [41] [42]. In some scenarios, this assumption fails to hold since there may exist the dominate interference which prohibits the Gaussian approximation from accurately modelling the residual MAI. The other fact can be that the central limit theorem is not suitable to 1 Hereby, we use the term PIC to denote the hard decision nonlinear PIC as introduced in the Chapter 2. we ll use LPIC to stand for linear PIC wherever it is concerned. 30

31 model the residual MAI in the case of parallel interference cancellation due to its own structural property. We investigate the performance of general PIC by analysis. It demonstrates that for the exact computation of bit error rate it is quite cumbersome even for a small number of users and is computationally infeasible for more than a handful of users. Thus, a approximation method is developed to give the much simple expression. We verify the approximate bit error rate with the computer simulation results and find out they have the better match than the Gaussian approximation method. 3.2 Exact BER Analysis of Two Users Let us start the analysis by considering the two users case. We ll adopt the system model and symbol notation introduced in Chapter 2. The initial state, i.e. the output of the matched filters, from Eqn. (2.2), gives y 1 = E 1 d 1 + E 2 d 2 ρ 12 + n 1 y 2 = E 2 d 2 + E 1 d 1 ρ 21 + n 2 (3.1) where we use symbol E k = Eb k = energy per bit, k = 1, 2 for simplicity. n k is the Gaussian noise appeared at the output the matched filter with E[n 2 k ] = σ2. Since the spreading codes are not perfectly orthogonal, the noises n 1 and n 2 are correlated, with the normalized correlation given by E[n 1 n 2 ] E[n 2 1 ]E[n 2 2] = ρ 12 = ρ 12. = ρ (3.2) Let f n1,n 2 (, ) denote the joint pdf of n 1 and n 2. The tentative decision at the initial stage is simply given by ˆd (0) 1 =sgn{y 1 } ˆd (0) 2 =sgn{y 2 } (3.3)