Principles of Spread-Spectrum CommunicationSystems

Don Torrieri

Principles ofSpread-SpectrumCommunication Systems

Third Edition

2123

Don TorrieriUS Army Research LaboratoryAdelphiMarylandUSA

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To my Family

Preface

The continuing vitality of spread-spectrum communication systems and the devel-opment of new mathematical methods for their analysis provided the motivation toundertake this new edition of the book. This edition is intended to enable readersto understand the current state-of-the-art in this field. Almost twenty percent of thematerial in this edition is new, including several new sections, a new chapter on adap-tive arrays and filters, and a new chapter on code-division multiple-access networks.The remainder of the material has been thoroughly revised, and I have removed aconsiderable amount of material that has been superseded by more definitive results.

This book provides a comprehensive and intensive examination of spread-spectrum communication systems that is suitable for graduate students, practicingengineers, and researchers with a solid background in the theory of digital communi-cation. As the title indicates, this book stresses principles rather than specific currentor planned systems, which are described in many less advanced books. The principalgoal of this book is to provide a concise but lucid explanation of the fundamentalsof spread-spectrum systems with an emphasis on theoretical principles and methodsof mathematical analysis that will facilitate future research. The choice of specifictopics to include was tempered by my judgment of their practical significance andinterest to both researchers and system designers. The book contains many improvedderivations of the classical theory and presents the latest research results that bringthe reader to the frontier of the field. The analytical methods and subsystem descrip-tions are applicable to a wide variety of communication systems. Problems at theend of each chapter are intended to assist readers in consolidating their knowledgeand to provide practice in analytical techniques. The listed references are ones thatI recommend for further study and as sources of additional references.

A spread-spectrum signal is one with an extra modulation that expands the signalbandwidth greatly beyond what is required by the underlying coded-data modulation.Spread-spectrum communication systems are useful for suppressing interference andjamming, making secure communications difficult to detect and process, accommo-dating fading and multipath channels, and providing a multiple-access capabilitywithout requiring synchronization across the entire network. The most practicaland dominant spread-spectrum systems are direct-sequence and frequency-hoppingsystems.

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There is no fundamental theoretical barrier to the effectiveness of spread-spectrumcommunications. That remarkable fact is not immediately apparent since the in-creased bandwidth of a spread-spectrum signal might require a receive filter thatpasses more noise power than necessary to the demodulator. However, when anysignal 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 exploiting thepotential capabilities of spread-spectrum systems. Although direct-sequence systemscan greatly suppress interference, practical systems require channel codes to dealwith the residual interference and channel impairments such as fading. Frequency-hopping systems are designed to avoid interference, but the possibility of hopping intoan unfavorable spectral region usually requires a channel code to maintain adequateperformance. In this chapter, coding and modulation theory are used to derive therequired receiver computations and the error probabilities of the decoded informationbits. The emphasis is on the types of codes and modulation that have proved mostuseful in spread-spectrum systems.

Chapter 2 presents the fundamentals of direct-sequence systems. Direct-sequencemodulation entails the direct addition of a high-rate spreading sequence with a lower-rate data sequence, resulting in a transmitted signal with a relatively wide bandwidth.The removal of the spreading sequence in the receiver causes a contraction of thebandwidth that can be exploited by appropriate filtering to remove a large portion ofthe interference. This chapter describes basic spreading sequences and waveformsand provides a detailed analysis of how the direct-sequence receiver suppressesvarious forms of interference.

Chapter 3 presents the fundamentals of frequency-hopping systems. Frequencyhopping is the periodic changing of the carrier frequency of a transmitted sig-nal. This time-varying characteristic potentially endows a communication systemwith great strength against interference. Whereas a direct-sequence system relieson spectral spreading, spectral despreading, and filtering to suppress interference.The basic mechanism of interference suppression in a frequency-hopping systemis that of avoidance. When the avoidance fails, it is only temporary because of theperiodic changing of the carrier frequency. The impact of the interference is fur-ther mitigated 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. The ef-fects of partial-band interference and jamming are examined, and the most importantissues in the design of frequency synthesizers are 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 mustprecisely or nearly coincide. Any misalignment causes the signal amplitude at the

Preface ix

demodulator output to fall in accordance with the autocorrelation or partial autocor-relation function. Although the use of precision clocks in both the transmitter and thereceiver limit the timing uncertainty in the receiver, clock drifts, range uncertainty,and the Doppler shift may cause synchronization problems. Code synchronization,which is either sequence or pattern synchronization, might be obtained from sepa-rately transmitted pilot or timing signals. It may be aided or enabled by feedbacksignals from the receiver to the transmitter. However, to reduce the cost in power andoverhead, most spread-spectrum receivers achieve code synchronization by process-ing the received signal. Both acquisition, which provides coarse synchronization,and tracking, which provides fine synchronization, are described in this chapter. Theemphasis is on the acquisition system because this system is almost always the dom-inant design issue and most expensive component of a complete spread-spectrumsystem.

Adaptive filters and adaptive arrays have numerous applications as componentsof communication systems. Chapter 5 focuses on those adaptive filters and adap-tive arrays that are amenable to exploiting the special spectral characteristics ofspread-spectrum signals to enable interference suppression beyond that inherent inthe despreading or dehopping. Adaptive filters for the rejection of narrowband in-terference or primarily for the rejection of wideband interference are presented.Adaptive arrays for both direct-sequence systems and frequency-hopping systemsare described and shown to potentially provide a very high degree of interferencesuppression.

Chapter 6 provides a general description of the most important aspects of fadingand the role of diversity methods in counteracting it. Fading is the variation inreceived signal strength due to a time-varying communications channel caused bythe interaction of multipath components of the transmitted signal that are generatedand altered by changing physical characteristics of the propagation medium. Theprincipal means of counteracting fading are diversity methods, which are based onthe exploitation of the latent redundancy in two or more independently fading copiesof the same signal. The rake demodulator, which is of central importance in mostdirect-sequence systems, is shown to be capable of exploiting undesired multipathsignals rather than simply attempting to reject them. The multicarrier direct-sequencesystem is shown to be a viable alternative method of exploiting multipath signals.

Multiple access is the ability of many users to communicate with each other whilesharing a common transmission medium. Wireless multiple-access communicationsare facilitated if the transmitted signals are orthogonal or separable in some sense.Signals may be separated in time (time-division multiple access orTDMA), frequency(frequency-division multiple access or FDMA), or code (code-division multiple ac-cess or CDMA). Chapter 7 presents the general characteristics of spreading sequencesand frequency-hopping patterns that are suitable for CDMA systems, which comprisedirect-sequence CDMA (DS-CDMA) and frequency-hopping CDMA (FH-CDMA)systems. The use of spread-spectrum modulation in CDMA allows the simultaneoustransmission of signals from multiple users in the same frequency band. All signalsuse the entire allocated spectrum, but the spreading sequences or frequency-hoppingpatterns differ. Information theory indicates that in an isolated cell, CDMA systems

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achieve the same spectral efficiency as TDMA or FDMA systems only if optimalmultiuser detection is used. However, even with single-user detection, CDMA hasadvantages for mobile communication networks because it eliminates the need forfrequency and time-slot coordination, allows carrier-frequency reuse in adjacentcells, imposes no sharp upper bound on the number of users, and provides resistanceto interference and interception. Multiuser detectors, which have great potentialusefulness but are fraught with practical difficulties, are described and assessed.

The impact of multiple-access interference in mobile ad hoc and cellular net-works with DS-CDMA and FH-CDMA systems is analyzed in Chap. 8. Phenomenaand issues that become prominent in mobile networks using spread spectrum in-clude exclusion zones, guard zones, power control, rate control, network policies,sectorization, and the selection of various spread-spectrum parameters. The outageprobability, which is the fundamental network performance metric, is derived for bothad hoc and cellular networks and both DS-CDMA and FH-CDMA systems. Acqui-sition and synchronization methods that are needed within a cellular DS-CDMAnetwork are addressed.

Chapter 9 examines the role of iterative channel estimation in the design of ad-vanced spread-spectrum systems. The estimation of channel parameters, such as thefading amplitude and the power spectral density of the interference and noise, isessential to the effective use of soft-decision decoding. Channel estimation may beimplemented by the transmission of pilot signals that are processed by the receiver,but pilot signals entail overhead costs, such as the loss of data throughput. Deriv-ing maximum-likelihood channel estimates directly from the received data symbolsis often prohibitively difficult. There is an effective alternative when turbo or low-density parity-check codes are used. The expectation-maximization algorithm, whichis derived and explained, provides an iterative approximate solution to the maximum-likelihood equations and is inherently compatible with iterative demodulation anddecoding. Two examples of advanced spread-spectrum systems that apply iterativechannel estimation, demodulation, and decoding are described and analyzed in thischapter. These systems provide good illustrations of the calculations required in thedesign of advanced systems.

The ability to detect the presence of spread-spectrum signals is often requiredby cognitive radio, ultra-wideband, and military systems. Chapter 10 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 de-modulation or decoding. Nevertheless, detection theory leads to impractical devicesfor the detection of spread-spectrum signals. An alternative procedure is to use aradiometer or energy detector, which relies solely on energy measurements to de-termine the presence of unknown signals. The radiometer has applications not onlyas a detector of spread-spectrum signals, but also as a sensing method in cognitiveradio and ultra-wideband systems.

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Four Appendices contain mathematical details about Gaussian processes and thecentral limit theorem, special functions, signal characteristics, and basic probabilitydistributions.

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 Yingtao Niu 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

Error Probabilities for Hard-Decision Decoders . . . . . . . . . . . . . . . 6Soft-Decision Decoders and Code Metrics for Pulse Amplitude

Modulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12Code Metrics for Orthogonal Signals . . . . . . . . . . . . . . . . . . . . . . . . 20Detection of Uncoded FSK Symbols . . . . . . . . . . . . . . . . . . . . . . . . 24Performance Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

1.2 Convolutional Codes and Trellis Codes . . . . . . . . . . . . . . . . . . . . . . 28Chernoff Bound . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40Trellis-Coded Modulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

1.3 Interleavers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 441.4 Classical Concatenated Codes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 461.5 Turbo Codes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

MAP Decoding Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48Turbo Codes with Parallel Concatenated Codes . . . . . . . . . . . . . . . 52Serially Concatenated Turbo Codes . . . . . . . . . . . . . . . . . . . . . . . . . 59

1.6 Iterative Demodulation and Decoding . . . . . . . . . . . . . . . . . . . . . . . 61Bit-Interleaved Coded Modulation . . . . . . . . . . . . . . . . . . . . . . . . . . 65Simulation Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

1.7 Low-Density Parity-Check Codes . . . . . . . . . . . . . . . . . . . . . . . . . . 69Irregular Repeat-Accumulate Codes . . . . . . . . . . . . . . . . . . . . . . . . . 74LDPC Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

1.8 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

2 Direct-Sequence Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 792.1 Definitions and Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 792.2 Spreading Sequences and Waveforms . . . . . . . . . . . . . . . . . . . . . . . 83

Random Binary Sequence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83Shift-Register Sequences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85Maximal Sequences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89Autocorrelations and Power Spectra . . . . . . . . . . . . . . . . . . . . . . . . . 90

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Characteristic Polynomials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94Long Nonlinear Sequences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98Chip Waveforms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102Partial Correlation of Sequences . . . . . . . . . . . . . . . . . . . . . . . . . . . 102

2.3 Systems with BPSK Modulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103Tone Interference at Carrier Frequency . . . . . . . . . . . . . . . . . . . . . . . 107General Tone Interference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109Gaussian Interference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111

2.4 Quaternary Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114Complex Binary Spreading Sequences . . . . . . . . . . . . . . . . . . . . . . . 120Systems with Channel Codes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122

2.5 Pulsed Interference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1222.6 Noncoherent Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1312.7 Despreading with Bandpass Matched Filters . . . . . . . . . . . . . . . . . . 135

Surface-Acoustic-Wave Filters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138Multipath-Resistant Coherent System . . . . . . . . . . . . . . . . . . . . . . . . 141

2.8 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144

3 Frequency-Hopping Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1473.1 Concepts and Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1473.2 Frequency Hopping with Orthogonal FSK . . . . . . . . . . . . . . . . . . . . 152

Illustrative System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152Multitone Jamming . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158

3.3 Frequency Hopping with CPM and DPSK . . . . . . . . . . . . . . . . . . . . 159FH/CPM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160FH/DPSK . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167

3.4 Power Spectral Density of FH/CPM . . . . . . . . . . . . . . . . . . . . . . . . 1693.5 Digital Demodulation of Dehopped FH/CPFSK . . . . . . . . . . . . . . 1733.6 Codes for Partial-Band Interference . . . . . . . . . . . . . . . . . . . . . . . . . 177

Reed-Solomon Codes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178Trellis-Coded Modulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185Turbo and LDPC Codes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185

3.7 Hybrid Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1873.8 Frequency Synthesizers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189

Direct Frequency Synthesizer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189Direct Digital Synthesizer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191Indirect Frequency Synthesizers . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194

3.9 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200

4 Code Synchronization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2034.1 Acquisition of Spreading Sequences . . . . . . . . . . . . . . . . . . . . . . . . . 203

Matched-Filter Acquisition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207Sequential Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209

4.2 Serial-Search Acquisition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210Uniform Search with Uniform Distribution . . . . . . . . . . . . . . . . . . . 214

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Consecutive-Count Double-Dwell System . . . . . . . . . . . . . . . . . . . 216Single-Dwell and Matched-Filter Systems . . . . . . . . . . . . . . . . . . . . 217Up-Down Double-Dwell System . . . . . . . . . . . . . . . . . . . . . . . . . . . 218Penalty Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220Other Search Strategies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221Density Function of the Acquisition Time . . . . . . . . . . . . . . . . . . . . 223Alternative Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224

4.3 Acquisition Correlator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2284.4 Sequential Acquisition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2354.5 Code Tracking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2374.6 Frequency-Hopping Patterns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242

Matched-Filter Acquisition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242Serial-Search Acquisition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 249Pattern Tracking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 254

4.7 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 256

5 Adaptive Filters and Arrays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2595.1 Real and Complex Gradients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259

Real Gradients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259Complex Gradients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 260

5.2 Adaptive Filters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262Optimal Weight Vector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262Cauchy–Schwarz Inequality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264Method of Steepest Descent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264LMS Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265

5.3 Rejection of Narrowband Interference . . . . . . . . . . . . . . . . . . . . . . . 269Time-Domain Adaptive Filtering . . . . . . . . . . . . . . . . . . . . . . . . . . . . 270Transform-Domain Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273Nonlinear Filtering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 275Adaptive ACM filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 281

5.4 Rejection of Wideband Interference . . . . . . . . . . . . . . . . . . . . . . . . . 283Lagrange Multipliers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283Constrained Minimum-Power Criterion . . . . . . . . . . . . . . . . . . . . . . 284Frost Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 286

5.5 Optimal Array . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2895.6 Adaptive Array for Direct-Sequence Systems . . . . . . . . . . . . . . . . . 293

Derivation of Maximin Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . 293Implementation of Processor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 296Convergence Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 301Simulation of Maximin Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . 303

5.7 Adaptive Array for Frequency-Hopping Systems . . . . . . . . . . . . . . 305Initial and Main Processors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 307Anticipative Adaptive Filters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 310Simulation Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 312

5.8 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 314

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6 Fading and Diversity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3176.1 Path Loss, Shadowing, and Fading . . . . . . . . . . . . . . . . . . . . . . . . . . 3176.2 Time-Selective Fading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 320

Fading Rate and Fade Duration . . . . . . . . . . . . . . . . . . . . . . . . . . . . 327Spatial Diversity and Fading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 328

6.3 Frequency-Selective Fading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 330Channel Impulse Response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 332

6.4 Diversity for Fading Channels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 334Maximal-Ratio Combining . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 334Coherent Demodulation and Metrics . . . . . . . . . . . . . . . . . . . . . . . . 336Equal-Gain Combining . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 346Selection Diversity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 353Transmit Diversity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 358

6.5 Channel Codes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 362Bit-Interleaved Coded Modulation . . . . . . . . . . . . . . . . . . . . . . . . . . 368

6.6 Rake Demodulator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3706.7 Frequency Hopping and Diversity . . . . . . . . . . . . . . . . . . . . . . . . . . . 3786.8 Multicarrier Direct-Sequence Systems . . . . . . . . . . . . . . . . . . . . . . . 379

Multicarrier CDMA System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 383DS-CDMA System with Frequency-Domain Equalization . . . . . . 398

6.9 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 403

7 Code-Division Multiple Access . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4057.1 Implications of Information Theory . . . . . . . . . . . . . . . . . . . . . . . . . 4057.2 Spreading Sequences for DS-CDMA . . . . . . . . . . . . . . . . . . . . . . . . 409

Synchronous Communications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 411Asynchronous Communications . . . . . . . . . . . . . . . . . . . . . . . . . . . . 414Symbol Error Probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 419Complex Quaternary Sequences . . . . . . . . . . . . . . . . . . . . . . . . . . . . 421

7.3 Systems with Random Spreading Sequences . . . . . . . . . . . . . . . . . . 423Jensen’s Inequality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 423Direct-Sequence Systems with BPSK . . . . . . . . . . . . . . . . . . . . . . . . 425Quadriphase Direct-Sequence Systems . . . . . . . . . . . . . . . . . . . . . . . 433

7.4 Frequency-Hopping Patterns for FH-CDMA . . . . . . . . . . . . . . . . . 4377.5 Multiuser Detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 441

Optimum Detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 442Conventional Single-User Detector . . . . . . . . . . . . . . . . . . . . . . . . . . 445Decorrelating Detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 446Minimum-Mean-Square-Error Detector . . . . . . . . . . . . . . . . . . . . . 450Adaptive Multiuser Detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 453Interference Cancelers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 454Multiuser Detector for Frequency Hopping . . . . . . . . . . . . . . . . . . 458

7.6 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 459

Contents xvii

8 Mobile Ad Hoc and Cellular Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . 4618.1 Conditional Outage Probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 461

Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4688.2 DS-CDMA Mobile Ad Hoc Networks . . . . . . . . . . . . . . . . . . . . . . . 470

Guard Zones . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 475Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 478

8.3 DS-CDMA Cellular Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 481Acquisition and Synchronization . . . . . . . . . . . . . . . . . . . . . . . . . . . . 482Power Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 485Adaptive Rate Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 488Spatial Distributions and Network Models . . . . . . . . . . . . . . . . . . . . 488

8.4 DS-CDMA Uplinks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 491Uplink Power Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 493Uplink Rate Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 494Performance Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 497

8.5 DS-CDMA Downlinks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 499Downlink Rate Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 503Downlink Power Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 504Performance Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 504

8.6 FH-CDMA Mobile Ad Hoc Networks . . . . . . . . . . . . . . . . . . . . . . . 507Conditional Outage Probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 509Rate Adaptation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 510Modulation-Constrained Area Spectral Efficiency . . . . . . . . . . . . . 510Optimization Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 511

8.7 FH-CDMA Cellular Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5148.8 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 517

9 Iterative Channel Estimation, Demodulation, and Decoding . . . . . . . . 5199.1 Expectation-Maximization Algorithm. . . . . . . . . . . . . . . . . . . . . . . . 519

Fixed-Point Iteration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5249.2 Direct-Sequence Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 526

Encoding, Modulation, and Channel Estimation . . . . . . . . . . . . . . . 526Iterative Receiver Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 527EM Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 529Perfect Phase Information at Receiver . . . . . . . . . . . . . . . . . . . . . . . 533No Phase Information at Receiver . . . . . . . . . . . . . . . . . . . . . . . . . . . 534Blind-PACE Estimation Tradeoffs . . . . . . . . . . . . . . . . . . . . . . . . . . . 534Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 534

9.3 Guidance from Information Theory . . . . . . . . . . . . . . . . . . . . . . . . . 5429.4 Robust Frequency-Hopping Systems . . . . . . . . . . . . . . . . . . . . . . . . 544

System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 546Demodulator Metrics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 546Channel Estimators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 550

xviii Contents

Selection of Modulation Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 552Partial-Band Interference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 554Asynchronous Multiple-Access Interference . . . . . . . . . . . . . . . . . . 558

9.5 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 562

10 Detection of Spread-Spectrum Signals . . . . . . . . . . . . . . . . . . . . . . . . . . . 56510.1 Detection of Direct-Sequence Signals . . . . . . . . . . . . . . . . . . . . . . . . 56510.2 Radiometer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 569

Rayleigh Fading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 575Estimation of Noise Power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 577Other Implementation Issues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 580

10.3 Detection of Frequency-Hopping Signals . . . . . . . . . . . . . . . . . . . . . 58410.4 Channelized Radiometer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58810.5 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 594

Appendix A: Gaussian Random Variables and Processes . . . . . . . . . . . . . . . 595A.1 General Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 595A.2 Central Limit Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 599

Appendix B: Special Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 605B.1 Gamma Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 605B.2 Beta Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 606B.3 Bessel Functions of the First Kind . . . . . . . . . . . . . . . . . . . . . . . . . . 606B.4 Q-function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 607B.5 Marcum Q-function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 607B.6 Hypergeometric Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 608

Appendix C: Signal Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 609C.1 Bandpass Signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 609C.2 Stationary Stochastic Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 612C.3 Direct-Conversion Downconverter . . . . . . . . . . . . . . . . . . . . . . . . . . 616C.4 Sampling Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 618

Appendix D: Probability Distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 621D.1 Chi-Square Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 621D.2 Central Chi-Square Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . 623D.3 Rice Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 623D.4 Rayleigh Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 625D.5 Exponential and Gamma Distributions . . . . . . . . . . . . . . . . . . . . . . . 626

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 629

Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 635