Principles of Spread-Spectrum CommunicationSystems

Don Torrieri

Principles ofSpread-SpectrumCommunication Systems

Second Edition

123

Don TorrieriUS Army Research Laboratory

ISBN 978-1-4419-9594-0 e-ISBN 978-1-4419-9595-7DOI 10.1007/978-1-4419-9595-7Springer New York Dordrecht Heidelberg London

Library of Congress Control Number: 2011932168

c� Springer Science+Business Media, LLC 2011All rights reserved. This work may not be translated or copied in whole or in part without the writtenpermission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York,NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use inconnection with any form of information storage and retrieval, electronic adaptation, computer software,or by similar or dissimilar methodology now known or hereafter developed is forbidden.The use in this publication of trade names, trademarks, service marks, and similar terms, even if they arenot identified as such, is not to be taken as an expression of opinion as to whether or not they are subjectto proprietary rights.

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To My Family

Preface

Spread-spectrum communication is a core area within the field of digitalcommunication. Originally used in military networks as countermeasures againstthe threats of jamming and interception, spread-spectrum systems are now widelyused in commercial applications and are part of several wireless and mobilecommunication standards. Although spread-spectrum communication is a stapletopic in textbooks on digital communication, its treatment is usually cursory. Thisbook is designed to provide a more intensive examination of the subject that issuitable for graduate students and practicing engineers with a solid backgroundin the theory of digital communication. As the title indicates, this book stressesprinciples rather than specific current or planned systems, which are described inmany other books. My goal in this book is to provide a concise but lucid explanationof the fundamentals of spread-spectrum systems with an emphasis on theoreticalprinciples. The choice of specific topics to include was tempered by my judgmentof their practical significance and interest to both researchers and system designers.Throughout the book, learning is facilitated by many new or streamlined derivationsof the classical theory. Problems at the end of each chapter are intended to assistreaders in consolidating their knowledge and to provide practice in analyticaltechniques. The listed references are ones that I recommend for further study andas sources of additional references.

A spread-spectrum signal is one with an extra modulation that expands thesignal bandwidth greatly beyond what is required by the underlying coded-datamodulation. Spread-spectrum communication systems are useful for suppressinginterference, making secure communications difficult to detect and process, ac-commodating fading and multipath channels, and providing a multiple-accesscapability. Spread-spectrum signals cause relatively minor interference to othersystems operating in the same spectral band. The most practical and dominantspread-spectrum systems are direct-sequence and frequency hopping systems.

There is no fundamental theoretical barrier to the effectiveness of spread-spectrum communications. That remarkable fact is not immediately apparent sincethe increased bandwidth of a spread-spectrum signal might require a receive filter

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that passes more noise power than necessary to the demodulator. However, whenany signal and white Gaussian noise are applied to a filter matched to the signal, thesampled filter output has a signal-to-noise ratio that depends solely on the energy-to-noise-density ratio. Thus, the bandwidth of the input signal is irrelevant, andspread-spectrum signals have no inherent limitations.

Chapter 1 reviews fundamental results of coding and modulation theory that areessential to a full understanding of spread-spectrum systems. Channel codes, whichare also called error-correction or error-control codes, are vital in fully exploitingthe potential capabilities of spread-spectrum systems. Although direct-sequencesystems can greatly suppress interference, practical systems require channel codesto deal with the residual interference and channel impairments such as fading.Frequency-hopping systems are designed to avoid interference, but the possibilityof hopping into an unfavorable spectral region usually requires a channel code tomaintain adequate performance. In this chapter, coding and modulation theory areused to derive the required receiver computations and the error probabilities of thedecoded information bits. The emphasis is on the types of codes and modulationthat have proved most useful in spread-spectrum systems.

Chapter 2 presents the fundamentals of direct-sequence systems. Direct-sequence modulation entails the direct addition of a high-rate spreading sequencewith a lower-rate data sequence, resulting in a transmitted signal with a relativelywide bandwidth. The removal of the spreading sequence in the receiver causesa contraction of the bandwidth that can be exploited by appropriate filtering toremove a large portion of the interference. This chapter begins with a discussionof spreading sequences and waveforms and then provides a detailed analysis ofhow the direct-sequence receiver suppresses various forms of interference. Severalmethods that supplement the inherent ability of a direct-sequence system to rejectnarrowband interference are explained.

Chapter 3 presents the fundamentals of frequency-hopping systems. Frequencyhopping is the periodic changing of the carrier frequency of a transmitted signal.This time-varying characteristic potentially endows a communication system withgreat strength against interference. Whereas a direct-sequence system relies onspectral spreading, spectral despreading, and filtering to suppress interference. thebasic mechanism of interference suppression in a frequency-hopping system isthat of avoidance. When the avoidance fails, it is only temporary because of theperiodic changing of the carrier frequency. The impact of the interference is furthermitigated by the pervasive use of channel codes, which are more essential forfrequency-hopping than for direct-sequence systems. The basic concepts, spectraland performance aspects, and coding and modulation issues are presented in the firstfive sections of this chapter. The effects of partial-band interference and jammingare examined, and the most important issues in the design of frequency synthesizersare described.

Chapter 4 focuses on synchronization. A spread-spectrum receiver must generatea spreading sequence or frequency-hopping pattern that is synchronized with thereceived sequence or pattern; that is, the corresponding chips or dwell intervals

Preface ix

must precisely or nearly coincide. Any misalignment causes the signal amplitudeat the demodulator output to fall in accordance with the autocorrelation or partialautocorrelation function. Although the use of precision clocks in both the transmitterand the receiver limit the timing uncertainty in the receiver, clock drifts, rangeuncertainty, and the Doppler shift may cause synchronization problems. Codesynchronization, which is either sequence or pattern synchronization, might beobtained from separately transmitted pilot or timing signals. It may be aided orenabled by feedback signals from the receiver to the transmitter. However, toreduce the cost in power and overhead, most spread-spectrum receivers achievecode synchronization by processing the received signal. Both acquisition, whichprovides coarse synchronization, and tracking, which provides fine synchronization,are described in this chapter. The emphasis is on the acquisition system because thissystem is almost always the dominant design issue and most expensive componentof a complete spread-spectrum system.

Chapter 5 provides a general description of the most important aspects offading and the role of diversity methods in counteracting it. Fading is the variationin received signal strength due to a time-varying communications channel. It isprimarily caused by the interaction of multipath components of the transmittedsignal that are generated and altered by changing physical characteristics of thepropagation medium. The principal means of counteracting fading are diversitymethods, which are based on the exploitation of the latent redundancy in two ormore independently fading copies of the same signal. The rake demodulator, whichis of central importance in most direct-sequence systems, is shown to be capable ofexploiting undesired multipath signals rather than simply attempting to reject them.The multicarrier direct-sequence system is shown to be a viable alternative methodof exploiting multipath signals that has practical advantages.

Chapter 6 presents the general characteristics of spreading sequences andfrequency-hopping patterns that are suitable for code-division multiple access(CDMA) systems. Multiple access is the ability of many users to communicatewith each other while sharing a common transmission medium. Wireless multiple-access communications are facilitated if the transmitted signals are orthogonal orseparable in some sense. Signals may be separated in time, frequency, or code.CDMA is realized by using spread-spectrum modulation while transmitting signalsfrom multiple users in the same frequency band at the same time. All signals usethe entire allocated spectrum, but the spreading sequences or frequency-hoppingpatterns differ. CDMA is advantageous for cellular networks because it eliminatesthe need for frequency and time-slot coordination among cells, allows carrier-frequency reuse in adjacent cells, and imposes no sharp upper bound on thenumber of users. Another major CDMA advantage is the ease with which it canbe combined with multibeamed antenna arrays that are either adaptive or have fixedpatterns covering cell sectors. Inactive systems in a network reduce the interferencereceived by an active CDMA system. These general advantages and its resistanceto interference, interception, and frequency-selective fading make spread-spectrumCDMA an attractive choice for many mobile communication networks. The impact

x Preface

of multiple-access interference in spread-spectrum CDMA systems and networksand the role of power control are analyzed. Multiuser detectors, which have greatpotential usefulness but are fraught with practical difficulties, are derived andexplained.

The ability to detect the presence of spread-spectrum signals is often requiredby cognitive radio, ultra-wideband, and military systems. Chapter 7 presents ananalysis of the detection of spread-spectrum signals when the spreading sequenceor the frequency-hopping pattern is unknown and cannot be accurately estimated bythe detector. Thus, the detector cannot mimic the intended receiver, and alternativeprocedures are required. The goal is limited in that only detection is sought,not demodulation or decoding. Nevertheless, detection theory leads to impracticaldevices for the detection of spread-spectrum signals. An alternative procedure is touse a radiometer or energy detector, which relies solely on energy measurementsto determine the presence of unknown signals. The radiometer has applicationsnot only as a detector of spread-spectrum signals, but also as a sensing methodin cognitive radio and ultra-wideband systems.

Chapter 8 examines the role of iterative channel estimation in the design ofadvanced spread-spectrum systems. The estimation of channel parameters, suchas the fading amplitude and the power spectral density of the interference plusnoise, is essential to the effective use of soft-decision decoding. Channel estimationmay be implemented by the transmission of pilot signals that are processed by thereceiver, but pilot signals entail overhead costs, such as the loss of data throughput.Deriving maximum-likelihood channel estimates directly from the received datasymbols is often prohibitively difficult. There is an effective alternative whenturbo or low-density parity-check codes are used. The expectation-maximizationalgorithm provides an iterative approximate solution to the maximum-likelihoodequations and is inherently compatible with iterative demodulation and decoding.Two examples of advanced spread-spectrum systems that apply the expectation-maximization algorithm for channel estimation are described and analyzed in thischapter. These systems provide good illustrations of the calculations required in thedesign of advanced systems.

Three appendices contain mathematical details about bandpass processes, basicprobability distributions, and the convergence of important adaptive algorithms.

The evolution of spread spectrum communication systems and the prominenceof new mathematical methods in their design provided the motivation to undertakethis new edition of the book. This edition is intended to enable readers to understandthe current state-of-the-art in this field. More than twenty percent of the material inthis edition is new, including a chapter on systems with iterative channel estimation,and the remainder of the material has been thoroughly revised.

In writing this book, I have relied heavily on notes and documents prepared andthe perspectives gained during my work at the US Army Research Laboratory. I amthankful to my colleagues Matthew Valenti, Hyuck Kwon, and John Shea for theirtrenchant and excellent reviews of selected chapters of the original manuscript. I amgrateful to my wife, Nancy, who provided me not only with her usual unwaveringsupport but also with extensive editorial assistance.

Contents

1 Channel Codes and Modulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Block Codes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.1.1 Error Probabilities for Hard-Decision Decoding .. . . . . . . . . . . . 71.1.2 Soft-Decision Decoding and Code Metrics for

Pulse Amplitude Modulation.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141.1.3 Code Metrics for Orthogonal Signals . . . . . . . . . . . . . . . . . . . . . . . . . 191.1.4 Metrics and Error Probabilities for Uncoded FSK Symbols. 241.1.5 Performance Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

1.2 Convolutional Codes and Trellis Codes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291.2.1 Chernoff Bound .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 411.2.2 Trellis-Coded Modulation .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

1.3 Interleavers.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 451.4 Classical Concatenated Codes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 471.5 Turbo Codes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

1.5.1 MAP Decoding Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 491.5.2 Turbo Codes with Parallel Concatenated Codes . . . . . . . . . . . . . 531.5.3 Serially Concatenated Turbo Codes . . . . . . . . . . . . . . . . . . . . . . . . . . 59

1.6 Low-Density Parity-Check Codes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 611.6.1 Irregular Repeat-Accumulate Codes . . . . . . . . . . . . . . . . . . . . . . . . . . 64

1.7 Iterative Demodulation and Decoding .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 651.7.1 Bit-Interleaved Coded Modulation.. . . . . . . . . . . . . . . . . . . . . . . . . . . 681.7.2 Simulation Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

2 Direct-Sequence Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 792.1 Definitions and Concepts. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 802.2 Spreading Sequences and Waveforms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

2.2.1 Random Binary Sequence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 832.2.2 Shift-Register Sequences .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 852.2.3 Maximal Sequences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 892.2.4 Autocorrelations and Power Spectrums . . . . . . . . . . . . . . . . . . . . . . 90

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2.2.5 Characteristic Polynomials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 942.2.6 Long Nonlinear Sequences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 982.2.7 Chip Waveforms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

2.3 Systems with BPSK Modulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1022.3.1 Tone Interference at Carrier Frequency .. . . . . . . . . . . . . . . . . . . . . . 1052.3.2 General Tone Interference .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1062.3.3 Gaussian Interference.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

2.4 Quaternary Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1122.4.1 Systems with Channel Codes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117

2.5 Pulsed Interference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1182.6 Despreading with Bandpass Matched Filters . . . . . . . . . . . . . . . . . . . . . . . . . 126

2.6.1 Noncoherent Systems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1322.6.2 Multipath-Resistant Coherent System . . . . . . . . . . . . . . . . . . . . . . . . 135

2.7 Rejection of Narrowband Interference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1402.7.1 Adaptive Filters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1402.7.2 Time-Domain Adaptive Filtering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1442.7.3 Transform-Domain Processing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1472.7.4 Nonlinear Filtering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1492.7.5 Adaptive ACM Filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158

3 Frequency-Hopping Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1593.1 Concepts and Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1593.2 Frequency Hopping with Orthogonal FSK . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163

3.2.1 Soft-Decision Decoding .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1653.2.2 Multitone Jamming .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170

3.3 Frequency Hopping with CPM and DPSK . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1723.4 Hybrid Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1853.5 Codes for Partial-Band Interference .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186

3.5.1 Reed–Solomon Codes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1893.5.2 Trellis-Coded Modulation .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1953.5.3 Turbo and LDPC Codes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197

3.6 Frequency Synthesizers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1993.6.1 Direct Frequency Synthesizer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1993.6.2 Direct Digital Synthesizer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2013.6.3 Indirect Frequency Synthesizers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211

4 Code Synchronization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2134.1 Acquisition of Spreading Sequences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213

4.1.1 Matched-Filter Acquisition. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2174.2 Serial-Search Acquisition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219

4.2.1 Uniform Search with Uniform Distribution . . . . . . . . . . . . . . . . . . 2244.2.2 Consecutive-Count Double-Dwell System . . . . . . . . . . . . . . . . . . . 2254.2.3 Single-Dwell and Matched-Filter Systems . . . . . . . . . . . . . . . . . . . 2264.2.4 Up-Down Double-Dwell System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227

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4.2.5 Penalty Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2294.2.6 Other Search Strategies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2304.2.7 Density Function of the Acquisition Time . . . . . . . . . . . . . . . . . . . 2324.2.8 Alternative Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2334.2.9 Nonconsecutive and Sequential Searches . . . . . . . . . . . . . . . . . . . . 237

4.3 Acquisition Correlator. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2384.4 Code Tracking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2444.5 Frequency-Hopping Patterns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 250

4.5.1 Matched-Filter Acquisition. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2504.5.2 Serial-Search Acquisition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2574.5.3 Tracking System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265

5 Fading and Diversity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2675.1 Path Loss, Shadowing, and Fading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2675.2 Time-Selective Fading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 270

5.2.1 Fading Rate and Fade Duration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2775.2.2 Spatial Diversity and Fading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 278

5.3 Frequency-Selective Fading. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2805.3.1 Channel Impulse Response. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 282

5.4 Diversity for Fading Channels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2845.4.1 Optimal Array. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2855.4.2 Maximal-Ratio Combining .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2895.4.3 Coherent Binary Modulations and Metrics . . . . . . . . . . . . . . . . . . . 2915.4.4 Equal-Gain Combining .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3015.4.5 Selection Diversity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3095.4.6 Transmit Diversity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 315

5.5 Channel Codes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3185.5.1 Bit-Interleaved Coded Modulation.. . . . . . . . . . . . . . . . . . . . . . . . . . . 327

5.6 Rake Demodulator.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3275.7 Diversity and Spread Spectrum .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3355.8 Multicarrier Direct-Sequence Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 339

5.8.1 MC-CDMA System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3415.8.2 DS-CDMA System with Frequency-Domain Equalization .. 356

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 363

6 Code-Division Multiple Access . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3656.1 Spreading Sequences for DS/CDMA .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 366

6.1.1 Synchronous Communications .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3686.1.2 Asynchronous Communications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3716.1.3 Symbol Error Probability. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3766.1.4 Complex-Valued Quaternary Sequences . . . . . . . . . . . . . . . . . . . . . 377

6.2 Systems with Random Spreading Sequences . . . . . . . . . . . . . . . . . . . . . . . . . 3816.2.1 Jensen’s Inequality. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3816.2.2 Direct-Sequence Systems with BPSK . . . . . . . . . . . . . . . . . . . . . . . . 3836.2.3 Quadriphase Direct-Sequence Systems . . . . . . . . . . . . . . . . . . . . . . . 392

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6.3 Cellular Networks and Power Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3966.3.1 Intercell Interference of Uplink . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3996.3.2 Outage Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4036.3.3 Local-Mean Power Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4066.3.4 Bit-Error-Probability Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4106.3.5 Impact of Doppler Spread on Power-Control Accuracy . . . . . 4146.3.6 Downlink Power Control and Outage . . . . . . . . . . . . . . . . . . . . . . . . 419

6.4 Frequency-Hopping Multiple Access . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4206.4.1 Asynchronous FH/CDMA Networks . . . . . . . . . . . . . . . . . . . . . . . . . 4216.4.2 Ad Hoc and Cellular Mobile Networks. . . . . . . . . . . . . . . . . . . . . . . 4236.4.3 Ad Hoc Networks. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4266.4.4 Cellular Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 430

6.5 Multiuser Detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4406.5.1 Optimum Detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4416.5.2 Decorrelating Detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4436.5.3 Minimum-Mean-Square-Error Detector . . . . . . . . . . . . . . . . . . . . . . 4486.5.4 Adaptive Multiuser Detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4526.5.5 Interference Cancellers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4556.5.6 Multiuser Detector for Frequency Hopping . . . . . . . . . . . . . . . . . . 459

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 462

7 Detection of Spread-Spectrum Signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4657.1 Detection of Direct-Sequence Signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4657.2 Radiometer. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 469

7.2.1 Estimation of Noise Power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4777.2.2 Other Implementation Issues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 480

7.3 Detection of Frequency-Hopping Signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4847.4 Channelized Radiometer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 488References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 495

8 Systems with Iterative Channel Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4978.1 Expectation-Maximization Algorithm.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 497

8.1.1 Fixed-Point Iteration .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5028.2 Direct-Sequence Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 504

8.2.1 Encoding, Modulation, and Channel Estimation . . . . . . . . . . . . . 5058.2.2 Iterative Receiver Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5058.2.3 EM Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5078.2.4 Perfect Phase Information at Receiver . . . . . . . . . . . . . . . . . . . . . . . . 5108.2.5 No Phase Information at Receiver . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5128.2.6 Blind-PACE Estimation Trade-Offs . . . . . . . . . . . . . . . . . . . . . . . . . . 5128.2.7 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 512

8.3 Guidance from Information Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5218.4 Robust Frequency-Hopping Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 523

8.4.1 System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5248.4.2 Demodulator Metrics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5258.4.3 Channel Estimators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 528

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8.4.4 Selection of Modulation Index .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5318.4.5 Performance in Partial-Band Interference . . . . . . . . . . . . . . . . . . . . 5348.4.6 Asynchronous Multiple-Access Interference .. . . . . . . . . . . . . . . . 538

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 543

Appendix ASignal Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 545A.1 Bandpass Signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 545A.2 Stationary Stochastic Processes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 547A.3 Direct-Conversion Receiver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 552

Appendix BProbability Distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 555B.1 Chi-Square Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 555B.2 Central Chi-Square Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 557B.3 Rice Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 558B.4 Rayleigh Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 560B.5 Exponentially Distributed Random Variables . . . . . . . . . . . . . . . . . . . . . . . . . 561

Appendix CConvergence of Adaptive Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 563C.1 LMS Algorithm.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 563

C.1.1 Convergence of the Mean . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 563C.1.2 Misadjustment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 565

C.2 Frost Algorithm.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 567C.2.1 Convergence of the Mean . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 567

Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 571