PATTERN CLASSIFICATION BASED MULTIUSER DETECTORS FOR CDMA COMMUNICATION SYSTEMS CHETAN MAHENDRA (B Eng (Hons.), NUS) A THESIS SUBMITTED FOR THE DEGREE OF MASTER OF ENGINEERING DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING NATIONAL UNIVERSITY OF SINGAPORE 2005 Acknowledgements It is only when I wrote this thesis; I realized how far I have come in the last two years The task was a daunting one, and would have never been completed without the support and encouragement of my family, friends and mentors I would like to thank Dr Sadasivan Puthusserypady, my supervisor, for guiding me with a firm hand and giving me direction whenever I felt lost or discouraged, My parents and my sister for giving me the strength to persevere whenever I felt I could not go any further, for the endless phone conversations and the wonderful times spent in the vacations, My friends in the lab (which had become my second home) – Ajeesh, Luo Huaien, Li Yongfeng, Lim Teck Por – for all the fun times A final note of thanks to my housemates – Navneet, Parth, Ravi and Sachin – for tolerating me when I went nuts and for sticking with me throughout the course i Table of Contents Acknowledgements i Table of Contents ii Summary vii List of Figures ix List of Symbols xi List of Abbreviations xiv Chapter One: Introduction 1.1 Spread Spectrum Communications 1.2 Basic Concepts 1.2.1 Signal-to-Noise Ratio 1.2.2 Processing Gain 1.3 Spread Spectrum System Model 1.4 Code-Division Multiple-Access (CDMA): An Overview 1.4.1 Motivation for CDMA 1.4.2 Basic Synchronous CDMA Model 1.4.3 Basic Asynchronous CDMA Model 1.5 Limitations of Conventional CDMA System ii 1.5.1 Multiple Access Interference (MAI) 1.5.2 Near / Far Effect 10 1.6 Thesis Structure 11 Chapter Two: Multiuser Detection 13 2.1 Introduction 13 2.2 Matched Filter (Conventional) Detector 14 2.3 Decorrelating Detector 17 2.4 Minimum Mean-Squared Error Detector 18 2.5 Optimum Multiuser Detector 20 2.6 Radial Basis Function Detector 20 2.6.1 2.7 RBF as a Multiuser Detector 23 Summary 26 Chapter Three: Receiver Design Through Pattern Classification 27 3.1 Introduction 27 3.2 Signal Detection in Geometric Terms 27 3.2.1 Vector Representation of Signals 28 3.2.2 Gram-Schmidt Procedure 30 iii 3.3 Geometric View of Multiuser Detection 31 3.4 Pattern Classification 33 3.4.1 Linear Classifiers 34 3.4.2 Nonlinear Classifiers 35 3.4.3 Approximate Classifiers 35 3.5 Summary 36 Chapter Four: Support Vector Machines 37 4.1 Introduction 37 4.2 Support Vector Machines 38 4.2.1 Capacity of a Learning Machine 39 4.2.2 Vapnik-Chervonenkis (VC) Dimension 39 4.2.3 Structural Risk Minimization (SRM) 41 4.3 Mathematical Formulation 41 4.3.1 Linear SVMs 41 4.3.2 Lagrangian Method 42 4.3.3 Nonlinear SVMs 43 4.3.4 Solving Quadratic Programming (QP) Problem 45 4.4 Summary 49 iv Chapter Five: Multisurface Method for Multiuser Detection 50 5.1 Introduction 50 5.2 Multisurface Method of Pattern Separation 51 5.2.1 The MSM Algorithm 51 5.2.2 Computational Formulation 58 5.2.2.1 MATLAB® Optimization Toolbox 60 5.2.2.2 Linear Separability 61 5.2.2.3 Alternative Linear Separability 62 5.2.2.4 Complexity Issues 62 5.3 Enhanced Multisurface Method 64 5.3.1 Improving Performance in Distorted Channel 64 5.3.2 Reducing Computational Complexity 67 5.3.2.1 Discriminant Function 68 5.3.2.2 Steepest Descent Learning Method 70 5.4 EMSM Through Example 72 5.5 Summary 74 Chapter Six: Implementation and Results 76 6.1 Introduction 76 6.2 System Description 77 v 6.2.1 Channel Description 77 6.2.2 Preprocessing Stage 78 6.2.3 System Description in Matrix Notation 79 6.2.3.1 Non-dispersive channel 82 6.2.3.2 Dispersive channel 83 6.3 Implementation Details of MSM 85 6.4 Implementation Details of Enhanced MSM 88 6.4.1 Improving Performance in Distorted Channels 89 6.4.2 Improving Computational Complexity 90 6.5 Simulation Results 90 6.5.1 Decision Boundary 91 6.5.2 Illustration of EMSM Through an Example 92 6.5.3 BER Performance 93 6.6 Summary 100 Chapter Seven: Conclusion 102 7.1 Summary 102 7.2 Future Work 105 Publications originating from this work 106 References 107 vi Summary Explosive growth of internet, voice and data communications put an increasing strain on the channel capacity requirements Multi-access communications have emerged as the answer to such demands, offering a more efficient utilization of the available finite resources over the single access methods It is in this capacity that Direct Sequence Code Division Multiple Access (DS-CDMA) has emerged as a preferred method for the next generation wireless systems, and is the topic of a lot of current research including the present work This work deals with the problem of multiuser detection in DS-CDMA systems in a multipath environment; involving demodulation of interfering signals in a demanding channel which is similar to the channels that occur in reality This thesis begins with a brief discussion of the technology behind DS-CDMA, followed by an overview of the existing conventional multiuser detectors The problem of multiuser detection is reformulated as one of pattern recognition, and two multiuser detectors – support vector machine based detector and the enhanced multisurface method based detector – are introduced in detail Simulation results and discussion of the performance of these detectors are then presented The existing multiuser detectors can be divided into two categories (i) low-complexity, poor-performance linear detectors and (ii) high-complexity, good-performance nonlinear detectors In particular, in channels where the orthogonality of the code sequences is destroyed by multipath, detectors with linear complexity perform much worse than the vii nonlinear detectors In this work we propose an Enhanced Multisurface Method (EMSM) for multiuser detection in multipath channels EMSM is an intermediate piece-wise linear detection scheme with a run-time complexity linear in the number of users Its bit error rate (BER) performance is compared with existing linear detectors, namely, a nonlinear radial basis function (RBF) detector trained by a new support vector learning algorithm and Verdu’s optimal detector Simulations in multipath channels indicate that it always outperforms all other linear detectors and performs nearly as well as nonlinear detectors viii List of Figures Figure 1.1: Spread Spectrum communication system model Figure 1.2: Direct-Sequence spreading process Figure 1.3: Digital Communications using spread spectrum modulation Figure 2.1: Matched Filter Receiver 15 Figure 2.2: Basic CDMA channel model with matched filter receiver 15 Figure 2.3: The decorrelator detector for synchronous CDMA 18 Figure 2.4: The MMSE detector for synchronous CDMA 19 Figure 2.5: Basic structure of a RBF network 21 Figure 2.6: The RBF receiver with a MF preprocessor 26 Figure 3.1: A typical equalizer setup for multipath CDMA channels 31 Figure 3.2: Various methods of separation for two-classes 33 Figure 4.1: Relationship between SNR and number of support vectors 49 Figure 5.1: A simple linearly inseparable scenario with two-classes 53 Figure 5.2: Finding a pair of hyperplanes such that only the region in the middle has points of both classes 54 Figure 5.3: Finding another pair of hyperplanes such that only the region in the middle has points of both classes 55 ix Figure 6.10: BER comparison for users in mixed-phase multipath channel Figure 6.11: BER comparison for EMSM in synchronous and asynchronous channels 6.6 Summary As is evident from the results given above, EMSM outperforms the other linear detectors in the presence of severe multipath The main problem is that all the other linear detectors are designed from the perspective of reducing the correlated interference from other users and trying to neutralize the near-far effect caused by the differing transmission powers of the various users However in the cases considered, the number of users is assumed to be quite small and hence the correlated interference is not a serious problem Moreover, since all users are assumed to be transmitting at uniform power, no near-far effect is present However, a strong multipath effect is assumed Since the other linear detectors form their decision boundaries without any consideration for the effect of multipath, their 100 performance is extremely bad in comparison to the MSM RBF, implementing a nearoptimum (optimum for the amount of data available to the receivers) detector, forms a nonlinear boundary instead of the piecewise linear boundary formed by the MSM and hence out-performs MSM 101 Chapter Conclusion Work presented in this thesis focuses primarily on the problem of multiuser detection in the DS-CDMA environment A novel approach based on the multisurface method proposed by Mangasarian and its discriminant function given by Takiyama was presented and analyzed Performance of this scheme was investigated and compared with that of other comparable linear detectors, with the RBF implementation of the optimal multiuser detector serving as the upper bound on achievable performance 7.1 Summary The problem of multiuser detection was first introduced and then a novel solution was proposed in a methodical fashion In the first chapter, a discussion of the basic principles of DS-CDMA communication was undertaken To this end, first the fundamental concepts behind the more general spread spectrum communications were introduced, which was followed by a more specific dealing of the synchronous and asynchronous CDMA It was hoped that this chapter will provide all the necessary basics required to understand the remainder of the thesis even if the reader is not very familiar with the research area 102 In the second chapter, the concept of multiuser detection was introduced and a study of some of the established multiuser detectors was conducted There are a lot of multiuser detectors that have been proposed and it was obviously not feasible to cover all of them The ones discussed in detail are the matched filter (MF), the decorrelating detector (DD), the minimum mean-squared error (MMSE) detector, the optimum multiuser detector (OMD) and the radial basis function (RBF) based implementation of the optimum multiuser detector These were chosen primarily because they are utilized for comparison later in the thesis and hence this chapter should equip the reader with all the necessary knowledge of existing MUDs to tackle the rest of the thesis They are some of the most studied and intuitive detectors and will allow the user to strengthen his understanding of the fundamental concepts of multiuser detection In the third chapter, multiuser detection was presented as a pattern classification problem This involved introducing the relevant concepts of first converting the signals (used more often in the communication theory) into vectors (using the Gram-Schmidt procedure) Once the vector representation of signals is achieved, the vectors can be plotted in the vector space and a geometric view of the problem emerges The geometric way of looking at the problem allows one to apply (modified versions of) algorithms introduced in the pattern recognition literature to achieve multiuser detection It also allows a richer insight into the issue of multiuser detection At the end of this chapter it was hoped that the reader would have a good picture of visualizing the MUD problem as a pattern classification problem 103 In the fourth chapter, the support vector machine (SVM) based multiuser detector was introduced This chapter provides a thorough review of the concepts of structural risk minimization which are at the core of the SVM detector It follows it up with details of implementation of the detector, in particular giving the implementation details of the projection method used to solve the quadratic programming problem This method is different and much simpler than the methods employed by other researchers while implementing SVM detectors, and simulation results confirm that it works just as well as the more computationally expensive methods In the fifth chapter, the Multisurface Method (MSM) was introduced The chapter gives a detailed treatment to the algorithm, dealing with the flowchart and pseudocode for the algorithm, giving a mathematical analysis of the algorithm and providing an introduction to the Optimization toolbox in MATLAB® which was used to implement the algorithm in this work However, this algorithm was provided in the context of general pattern classification and was not entirely appropriate for application in the multiuser detection area Two enhancements to the algorithm were discussed in detail to improve the BER performance in noisy conditions and to improve the computational costs of the algorithm, yielding an enhanced MSM The algorithm and its enhancements were made clearer through examples, and it is hoped that by the end of this chapter the reader would have a good understanding of the MSM and its enhancements – the main thrust of this work In the sixth chapter, the implementation details of the original MSM and later of the enhancements were provided, followed by a discussion of the simulation results This 104 forced first formulating the problem in terms of matrices as MATLAB® deals with everything in terms of matrices only Once the problem was restated in matrices, the implementation of the enhanced MSM was merely a matter of translating each line of the pseudocode into program Some implementation level details that were not explicitly mentioned in the algorithm were identified and dealt with in this chapter Further the chapter involved a discussion of the BER performance of the MSM primarily in noisy dispersive channels, and a comparison with matched filter, decorrelating detector, minimum mean-squared error detector and the radial basis function based optimal multiuser detector was provided As the results demonstrated, MSM outperforms all the other linear detectors and fares well in comparison to the optimal nonlinear detector 7.2 Future Work In this work a novel multiuser detection scheme based on Mangasarian’s multisurface method is investigated in noisy dispersive channels However, due to computational limitations the simulations were restricted to low number of users Also, in this work synchronous communications was assumed and near-far effect was not considered Analysis of the algorithm in a more general setting incorporating the conditions mentioned above serves as a good future research direction Also, the enhancement to improvement in computational costs is as yet mathematically not proven to converge i.e there is no analytical proof for the convergence Deriving such a theoretical proof is also a possible challenge for future work in this direction 105 Publications originating from this work C Mahendra and S Puthusserypady, “Multiuser Receiver for DS-CDMA signals in Multipath Channels: An Enhanced Multisurface Method”, revised version 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(EMSM) based detector, both having their roots in pattern classification Already discussed are the fundamentals of spread spectrum communications and a detailed look at the pros and cons of CDMA which is fast becoming the accepted standard for the next generation of wireless communications Chapter 2 introduces the concept of multiuser detection and provides an overview of some of the multiuser detectors. .. implementations For a detailed analysis of this topic, the interested reader is referred to the many references listed [10-12] 10 1.6 Thesis Structure The primary focus of this thesis is to present pattern classification based multiuser detection techniques for DS -CDMA channels in a multipath environment This thesis presents a fresh look at a recently proposed support vector machine (SVM) based detector,... coincide and this allows a non-fuzzy classification of every point into one of the two classes 56 Figure 5.5: Classification of a pattern x by q pairs of surfaces 57 Figure 5.6: A simple linearly separable scenario for two-classes 65 Figure 5.7: Moving hyperplanes away to improve BER performance in noise 66 Figure 5.8: Example of EMSM’s pattern classification methodology 74 Figure... Conventional CDMA System A discussion and review of some of the salient features of a CDMA system relevant to understanding the development of multiuser detectors are presented below To allow a more macro-level understanding, the treatment avoids mathematical details and highlights the conceptual aspects as much as possible The two primary limitations of the current DS -CDMA systems are the degradation in performance... presented, allowing the pattern classification techniques to be applied Chapter 4 introduces a support vector machine (SVM) based detector The chapter begins with the background of support vector machines, moves on to the application of the ideas 11 to multiuser detection and finally provides the implementation details required to construct such a detector SVMs have been used before for multiuser detection,... overview of some of the multiuser detectors The more established detectors like the matched filter, decorrelating detector, minimum mean-square-error detector, Verdu’s optimal multiuser detector and the radial basis function (RBF) detector were analyzed in some detail Chapter 3 reformulates the problem of multiuser detection in a pattern classification perspective The relevant concepts in both fields... multiple-access (CDMA) scheme was developed mainly to increase capacity The development of the digital cellular systems for increasing capacity came just as the analog cellular systems faced a capacity limitation in 1987 [9] There are three basic multiple-access schemes in digital systems, namely, frequency-division multipleaccess (FDMA), time-division multiple-access (TDMA) and code-division multipleaccess (CDMA) ... treatment of some of the common multiuser detectors The reader familiar with the field may choose to skip this chapter To the unfamiliar reader, this chapter provides all the basic tools required to understand the concept of multiuser detection, and provides an introduction to all the multiuser detectors used in the remainder of the thesis 2.1 Introduction In a conventional CDMA system, all users interfere... However, the main drawback of such an optimal detector is one of complexity This forces us to look at suboptimal approaches for multiuser detection, where a wide range of performance / complexity trade-offs are available Most research is directed at finding an appropriate tradeoff between these two opposing forces of performance and complexity Also, in all the discussions that follow, several simplifying... The entire digital communication process using spread spectrum modulation can be summarized as in Figure 1.3 6 Figure 1.3: Digital Communications using spread spectrum modulation 1.4.2 Basic Synchronous CDMA Model To better understand this multiple access scheme, the basic CDMA U-user channel model is considered It consists of the sum of antipodally modulated synchronous signature waveforms embedded in ... behind DS -CDMA, followed by an overview of the existing conventional multiuser detectors The problem of multiuser detection is reformulated as one of pattern recognition, and two multiuser detectors. .. Multiple-Access (CDMA) : An Overview 1.4.1 Motivation for CDMA 1.4.2 Basic Synchronous CDMA Model 1.4.3 Basic Asynchronous CDMA Model 1.5 Limitations of Conventional CDMA System... presented The existing multiuser detectors can be divided into two categories (i) low-complexity, poor-performance linear detectors and (ii) high-complexity, good-performance nonlinear detectors In particular,