DIGITAL COMMUNICATIONS WITH CHAOS. Multiple Access Techniques and Performance Evaluation. Wai M. Tam, Francis C. M. Lau and Chi K.

Transcription

1 DIGITAL COMMUNICATIONS WITH CHAOS Multiple Access Techniques and Performance Evaluation Wai M. Tam, Francis C. M. Lau and Chi K. Tse

2 To our families Tung-Ying, Kin-Pan and Kin-Ho Karen, Valerie and Michelle Belinda and Eugene

3 Preface Since the 1970 s, there has been a great deal of research effort spent on studying chaotic systems and the properties of the chaotic signals generated. Characterized by their wideband, impulse-like autocorrelation and low cross-correlation properties, chaotic signals are considered to be useful spread-spectrum signals for carrying digital information. Spectrum spreading has become one of the most popular modulation techniques for high-speed wireless communications. It makes use of signals of very wide bandwidth to carry information at relatively low data rates, and possesses advantages such as low probability of interception, resistant to jamming, multiple-access capability and mitigation to multipath effect, which are particularly important in a wireless scenario. In addition to enjoying the aforementioned benefits, chaotic signals can be generated using simple circuitries, thus lowering the cost of transceivers. Early study of chaos-based communication systems was focused on a single-user case. In the past few years, more effort has been put on investigating systems with multiple-access capability, which is a key feature of spread-spectrum communication systems. In this book, we aim to present a detailed study of some multiple-access schemes used for chaos-based communications. At the same time, we will evaluate the performance of such systems. In addition, the effectiveness of the multiuser detection techniques, whose primary objective is to reduce interference between users and hence improve performance, will be evaluated in the context of multipleaccess digital communication systems. While this book intends to serve as a reference for the graduate students and researchers who are involved in the study of chaos communications, it also provides useful information on some key features of chaos-based communications for communication engineers and technology developers. Although much theoretical work

4 iv has already been performed on understanding chaos-based communication systems, there are outstanding implementing issues such as robust bit synchronization and channel equalization, which have to be resolved before practical chaos-based communication systems can become fully available. This book begins with an overview of spread-spectrum communication systems and application of chaos to spread-spectrum communications in Chapter 1. An overview of a few basic modulation and demodulation schemes used in chaos-based communication systems is then presented in Chapter 2, along with a brief description of several multiple-access systems. Starting from Chapter 3, we investigate in detail some selected chaos-based digital communication systems with multipleaccess capability. Simulation results of the bit error rates of these systems are presented and compared with analytical ones. The results are also compared with those of some well-known chaos-based communication systems. Assuming that the chaos generators at the transmitter and receiver are synchronized, in Chapter 3, we study the performance of a coherent chaos-based communication system with multiple users. We also present some mathematical techniques which can be used to estimate or to exactly calculate the bit error rates. In Chapter 4, we explore the use of multiuser detection techniques, which aim at reducing the interference between users and improving the overall performance of the multiple-access systems. While robust chaos synchronization is yet to be achieved, noncoherent chaos-based communication systems, which do not require chaos synchronization, are more practical and have been widely studied. Several multiple-access techniques for noncoherent chaos-based systems, together with their operational details, are presented in Chapters 5 to 8. We would like to thank Prof. Géza Kolumbán and Prof. A.J. Lawrance for their invaluable comments and suggestions to our research work. We are also grateful to the colleagues at the Hong Kong Polytechnic University for all the fruitful discussions we have had on the subject of chaos-based communication systems. Further, we are indebted to the University and the Hong Kong Research Grants Council

5 v (CERG Project PolyU5137/02E) for funding our work. We also thank the University for providing us with a splendid environment to perform quality research work. Last but not least, we sincerely thank our families for their enduring support and patience in all these years. Wai M. Tam Francis C. M. Lau Chi K. Tse

6 CONTENTS 1 Introduction Chaos Spread-Spectrum Communication Systems Application of Chaos to Spread-Spectrum Communication Systems Analog Modulation Digital Modulation Direct-Sequence Spread-Spectrum Motivation Book Organization 11 2 Chaos-Based Digital Communication Systems Chaos-Based Digital Modulation and Demodulation Schemes Chaos-Shift-Keying (CSK) Modulation Differential Chaos-Shift-Keying (DCSK) Modulation Frequency-Modulated DCSK (FM-DCSK) Modulation Correlation-Delay-Shift-Keying (CDSK) Modulation Application to the Multiple-Access Systems Two-User DCSK/FM-DCSK System Multiuser FM-DCSK System Based on Walsh Codes Multi-User System Based on Chaotic Frequency Modulation (CFM) 34 vi

7 CONTENTS vii 2.3 Summary 36 3 Multiple-Access Coherent Antipodal Chaos-Shift-Keying Systems Introduction Multiple-Access Antipodal Chaos-Shift-Keying (MA-ACSK) System Analysis of the MA-ACSK System Based on Gaussian Approximation Exact Bit Error Rate Analysis of the MA-ACSK System Results and Discussions Summary 54 Appendix 3: Derivation of the statistical properties for the chaotic sequences generated by the Chebyshev map 55 4 Multiuser Detection Techniques for Multiple-Access Coherent Antipodal Chaos-Shift-Keying Systems Introduction Linear Multiuser Detection Techniques System Description Performance Analysis Results and Discussions Nonlinear Multiuser Detection Techniques Parallel Interference Cancellation (PIC) Detectors Performance Analysis of the PIC Detectors Results and Discussions Summary 98 Appendix 4A: Derivation of means and variances relevant to the analyses of the decorrelating detector and MMSE detector 102

8 viii CONTENTS Appendix 4B: Derivation of means, variances and covariances relevant to the analysis of the decorrelating detector 108 Appendix 4C: Derivation of covariances and mean relevant to the analysis of the MMSE detector 110 Appendix 4D: Calculation of the probability of occurrence of N e (j) (n 1) for the PIC detector Multiple-Access Generalized Correlation Delay-Shift-Keying Systems Review of Correlation-Delay-Shift-Keying (CDSK) Scheme Generalized Correlation-Delay-Shift-Keying (GCDSK) Scheme Transmitter Structure of the GCDSK system Receiver Structure of the GCDSK system Gaussian-Approximated Bit Error Rates Results and Discussions Multiple-Access GCDSK Scheme Transmitter Structure of the MA-GCDSK System Receiver Structure of the MA-GCDSK System Gaussian-Approximated Bit Error Rates Results and Discussions Summary 148 Appendix 5A: Expressions for the variables in the GCDSK system 149 Appendix 5B: Derivation of bit error rates for GCDSK system based on simple Gaussian approximation 152 Appendix 5C: Derivation of bit error rates for CDSK system based on simple Gaussian approximation 159 Appendix 5D: Expressions for the variables in the MA-GCDSK system 160 Appendix 5E: Derivation of bit error rates for MA-GCDSK system 164

9 CONTENTS ix 6 Enhancements of Correlation-Delay-Shift-Keying Scheme Enhanced Correlation-Delay-Shift-Keying System with Method One Transmitter Structure Receiver Structure Gaussian-Approximated Bit Error Rates for ECDSK-M1 System Enhanced Correlation-Delay-Shift-Keying System with Method Two Transmitter Structure Receiver Structure Gaussian-Approximated Bit Error Rates for ECDSK-M2 System Permutation-Based Multiple-Access CDSK Systems Transmitter Structure Receiver Structure Gaussian-Approximated Bit Error Rates Results and Discussions Effect of Gain G Effect of Spreading Factor Comparison of the Simulated and Gaussian-Approximated Bit Error Rates Comparison with PMA-CDSK and PMA-DCSK Systems Summary Multiple-Access Scheme Utilizing Transmitted References And Training Sequences Transmitter Structure Receiver Structures Adaptive Transversal Filter 204

10 x CONTENTS Inverse-and-Average Receiver Results and Discussions Summary Near-Optimum Communication Schemes Near-Optimum Coherent (NOC) and Noncoherent (NON) Systems Single-User System Multiple-User System Near-Optimum Noncoherent System with Transmitted Reference Single-User System Multiple-User System Results and Discussions Effects of the Choice of Transformation Function F ( ) in the NOC System Using Chaotic Maps with Symmetrical Probability Density Function Using Chaotic Maps with Asymmetrical Probability Density Function Effect of the Choice of Spreading Factor Summary 238 Bibliography 249 Index 258