John G Proakis Masoud Salehi WksM Fifth Edition Digital Communications Digital Communications Fifth Edition John G Proakis Professor Emeritus Northeastern University , Department of Electrical and Computer Engineering, University of California, San Diego Masoud Salehi Department of Electrical and Computer Engineering, Northeastern University H Boston Bangkok Milan Burr Ridge, IL Bogota Montreal Caracas New Delhi McGraw-Hill Higher Education Dubuque, IA New York Kuala Lumpur Santiago Seoul San Francisco St Louis London Madrid Mexico City Singapore Sydney Taipei Toronto Lisbon The McGraw-Hill Companies McGraw-Hill Higher Education DIGITAL COMMUNICATIONS, FIFTH EDITION Published by McGraw-Hill, a business unit of The McGraw-Hill Companies, Americas, New York, NY 10020 Copyright reserved Previous editions in © 2001 and 1995 any form or by any means, or stored of The McGraw-Hill Companies, Inc., 1221 Avenue of the © 2008 by The McGraw-Hill Companies, Inc No part of this publication All rights may be reproduced or distributed in a database or retrieval system, without the prior written consent Inc., including, but not limited to, in any network or other electronic storage or transmission, or broadcast for distance learning Some ancillaries, including electronic and print components, may not be available to customers outside the United States This book is printed on acid-free paper 1234567890 DOC/DOC ISBN 978-0-07-295716-7 MHID 0-07-295716-6 Global Publisher: Raghothaman Srinivasan Executive Editor: Michael Hackett Director of Development: Kristine Tibbetts Developmental Editor: Lorraine K Buczek Executive Marketing Manager: Michael Weitz Senior Project Manager: Kay J Brimeyer Lead Production Supervisor: Sandy Ludovissy Associate Design Coordinator: Brenda A Rolwes Cover Designer: Studio Montage, St Louis, Missouri Compositor: ICC Macmillan Roman Typeface: 10.5/12 Times Printer: R R Donnelley Crawfordsville, IN (USE) Cover Image: Chart located at top left (Figure 8.9-6): ten Brink, S (2001 ) “ Convergence behavior of iteratively decoded parallel concatenated codes,” IEEE Transactions on Communications, vol 49, pp 1727-1737 Library of Congress Cataloging-in-Publication Data Proakis, John G Digital communications p / John G Proakis, Masoud Salehi — 5th ed cm Includes index ISBN 978-0-07-295716-7 Masoud II TK5103.7.P76 2008 621.382— dc22 I Salehi, —ISBN 0-07-295716-6 Title 2007036509 www.mhhe.com (hbk : alk paper) Digital communications DEDICATION To Felia, George, and Elena John G Proakis To Fariba, Omid, Sina, and My Parents Masoud Salehi in BRIEF CONTENTS Preface xvi Chapter Introduction Chapter Deterministic and Chapter Digital Modulation Chapter Optimum Receivers Chapter Carrier and Chapter An Introduction to Information Chapter Linear Block Codes Chapter Trellis Chapter Digital Random Signal Analysis 17 Schemes for 95 AWGN Channels 160 Symbol Synchronization 290 Theory 330 400 and Graph Based Codes 491 Communication Through Band-Limited Channels 597 Chapter 10 Adaptive Equalization 689 Chapter 11 Multichannel and Multicarrier Systems 737 Chapter 12 Spread Spectrum Signals for Digital Communications 762 Chapter 13 Fading Channels I: Chapter 14 Fading Channels II: Chapter 15 Multiple- Antenna Systems 966 Chapter 16 Multiuser Communications 1028 Appendix A Matrices 1085 B Appendix C Error Probability for Multichannel Binary Signals 1090 Characterization and Signaling 830 Capacity and Coding 899 Appendices Appendix Appendix D Error Probabilities for Adaptive Reception of M -Phase Signals 1096 Square Root Factorization 107 References and Bibliography 1109 Index 1142 V CONTENTS Preface Chapter xvi Introduction Elements of a Digital Communication System 1.2 Communication Channels and Their Characteristics 1.3 Mathematical Models for Communication Channels 10 1.4 A 7Historical Perspective in the Development of Digital Chapter 1.1 Communications 12 1.5 Overview of the Book 15 1.6 Bibliographical Notes and References 15 Deterministic and Random Signal Analysis 17 2.2— 2.1 Bandpass and Lowpass Signal Representation 18 2.22.7-7 Bandpass and Lowpass Signals / 2.1-2 Lowpass Equivalent of Bandpass Signals / 1-3 Energy Considerations / 2.1-4 Lowpass Equivalent of a Bandpass System 2.2 2.6Signal Space Representation of Waveforms 28 Vector Space Concepts / 2.2—2 Signal Space Concepts / 2.2-3 Orthogonal Expansions of Signals / 2.3 2.4 Gram- Schmidt Procedure Some Useful Random Variables 2.8- Bounds on Sums 56 Random 2.5 Limit Theorems for 2.6 Complex Random Variables Complex Random Vectors 2.7 Random 40 Tail Probabilities of Variables 63 63 Processes Wide-Sense Stationary 66 Random Processes / 7-2 Random Processes / 7-3 Proper and Random Processes / 7-4 Markov Chains Series Expansion of Random Processes Sampling Theorem for Band-Limited Random Cyclostationary Circular 2.8 74 Processes / 2.8—2 The Karhunen-Loeve Expansion 2.9 vi Bandpass and Lowpass Random Processes 78 Contents vii 2.10 Chapter Bibliographical Notes and References 82 Problems 82 Digital Modulation Schemes 95 3.1 3.2Representation of Digitally Modulated Signals 95 3.2 Memoryless Modulation Methods 97 Pulse Amplitude Modulation (PAM) / 3.2-2 Phase 3.3Modulation / 3.2-3 Quadrature Amplitude Modulation / 3.2-4 Multidimensional Signaling 3.3 3.4 Signaling Schemes with Memory 3.41 Continuous -Phase Frequency-Shift Keying 114 (CPFSK) / 3.3-2 Continuous-Phase Modulation (CPM) Power Spectrum of Digitally Modulated Signals Power Spectral Density of a Digitally Modulated Signal with Memory / 3.4-2 131 Power Spectral Density of Linearly Modulated Signals / 3.4-3 Power Spectral Density of Digitally Modulated Signals with Finite Memory / 3.4-4 Power Spectral Density of Modulation Schemes with a Markov Structure / 3.4-5 Power Spectral Densities of CPFSK and CPM Signals 4.13.5 Chapter Bibliographical Notes and References 148 4.2Problems 148 Optimum Receivers for AWGN Channels 4.1 160 Waveform and Vector Channel Models 160 4.3-1 Optimal Detection for a General Vector Channel 4.2 Waveform and Vector AWGN Channels 167 Optimal Detection for the Vector AWGN Channel / 4.2-2 Implementation of the Optimal Receiver for / 4.2-3 A Union Bound on the Probability of AWGN Channels 4.3 Error of Maximum Likelihood Detection 4.4Optimal Detection and Error Probability for B and-Limited 188 Signaling Optimal Detection and Error Probability for ASK or PAM Signaling Probability for / 4.3-2 Optimal Detection and Error PSK Signaling Error Probability for / 4.3-3 Optimal Detection QAM Signaling and / 4.3-4 Demodulation and Detection 4.4 Optimal Detection and Error Probability for Power-Limited Signaling Optimal Detection and Error Probability for Orthogonal Signaling / 4.4-2 Optimal Detection and Error Probability for Biortho gonal Signaling / 4.4-3 Optimal Detection and Error Probability for Simplex Signaling 203 Contents 4.5 Optimal Detection in Presence of Uncertainty: N oncoherent Detection 210 4.5-1 Noncoherent Detection of Carrier Modulated 7- Signals / 4.5-2 Optimal Noncoherent Detection of FSK Modulated Signals / 4.5-3 Error Probability of Orthogonal Signaling with Noncoherent Detection / 4.5-4 Probability of Error for Envelope Detection of Correlated Binary 4.6- PSK (DPSK) A Comparison of Digital Signaling Methods Signals / 4.5-5 Differential 4.6 4.7 Lattices and Constellations Based on Lattices 4.84 4.8 4.10 4.9 226 Bandwidth and Dimensionality An Introduction to Lattices / 230 7-2 Signal 4.9Constellations from Lattices 4.9Detection of Signaling Schemes with The Memory Maximum Likelihood Sequence Detector Optimum Receiver for CPM Signals Optimum Demodulation and Detection of CPM 242 246 / Performance of CPM Signals / 4.9-3 Suboptimum Demodulation and Detection of CPM Signals Performance Analysis for Wireline and Radio Communication Systems 259 4.10-1 Regenerative Repeaters / 4.10-2 Link Budget Analysis in Radio Communication Systems 4.11 Chapter Bibliographical Notes and References 265 5.2Problems 5.2- 266 Carrier and Symbol Synchronization 290 5.1 Signal Parameter Estimation 5.35.1-1 The Likelihood Function / 5.1-2 Carrier Recovery and 5.3Symbol Synchronization in Signal Demodulation 290 5.2 Carrier Phase Estimation 295 Maximum-Likelihood Carrier Phase Estimation / The Phase-Locked Loop / 5.2-3 Effect of Additive Noise on the Phase Estimate / 5.2-4 Decision-Directed Loops / 5.2-5 Non-Decision-Directed Loops 5.3 Symbol Timing Estimation 315 Maximum-Likelihood Timing Estimation / Non-Decision-Directed Timing Estimation Chapter Symbol Timing 5.4 Joint Estimation of Carrier Phase and 5.5 Performance Characteristics of 5.6 Bibliographical Notes and References 326 Problems 327 ML Estimators An Introduction to Information Theory 6.1 Mathematical Models for Information Sources 321 323 330 331 Contents IX 6.2 6.3 A Logarithmic Measure of Information 332 6.3Lossless Coding of Information Sources 335 The Lossless Source Coding Theorem / 6.3-2 Lossless 6.4Coding Algorithms 6.4 Lossy Data Compression 6.5- Random 6.5 348 Entropy and Mutual Information for Continuous Variables / 6.4-2 The Rate Distortion Function Channel Models and Channel Capacity 354 Channel Models / 6.5-2 Channel Capacity 6.6 Achieving Channel Capacity with Orthogonal Signals 367 6.7 The Channel 369 6.8 The Channel Cutoff Rate Reliability Function 37 6.8-1 Bhattacharyya and Chernov Bounds / 6.8-2 Random Coding 6.9 Bibliographical Notes and References 380 7.1Problems 381 7.2- Chapter 7- Linear Block Codes 7.1 400 401 Basic Definitions The Structure of Finite Fields / 7.1-2 Vector Spaces 7.3General Properties of Linear Block Codes 7.31 7.2 411 Generator and Parity Check Matrices / 7.2-2 Weight and Distance for Linear Block Codes / 7.2-3 The Weight Distribution Polynomial / 7.2-4 Error Probability of Linear 7- Block Codes 7.5- 7.3 Some Specific Linear Repetition 420 Block Codes Codes / 7.3-2 Hamming Codes / Maximum-Length Codes / 7.3-4 Reed-Muller Codes / 7.3-5 Hadamard Codes / 7.3-6 Golay Codes 7.4 7.5 Optimum Soft Decision Decoding of Linear Block Codes 424 Hard Decision Decoding of Linear Block Codes 428 7.71 Error Detection and Error Correction Capability of Block 7.8- Codes / 7.5-2 Block and Bit Error Probability for Hard Decision Decoding 7.6 Comparison of Performance between Hard Decision and 7.7 Bounds on Minimum Distance of Linear Block Codes 436 Soft Decision Decoding Bound Bound / Singleton 7 Plotkin / 7 7-2 7-4 Elias Bound / McEliece-Rodemich-Rumsey-Welch 7.8 440 Hamming Bound / 7-5 (MRRW) Bound / Varshamov -Gilbert Bound Modified Linear Block Codes Shortening and Lengthening / 7.8-2 Puncturing and Extending / 7.8-3 Expurgation and Augmentation 445 , References and Bibliography 1137 Ungerboeck, G (1976) “Fractional Tap-Spacing Equalizer and Consequences for Clock Recovery in Data Modems,” IEEE Trans Commun , vol COM-24, pp 856-864, August Ungerboeck, G (1982) “Channel Coding with Multilevel/Phase Signals,” IEEE Trans Inform Theory vol IT-28, pp 55-67, January Ungerboeck, G 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effective area, 262 a posteriori 162 a priori effective radiated power, L-values, 552 probabilities, 162 factor, Abelian group, 403 cyclic subgroup, 482 Equalizers), 689-731 accelerating convergence of LMS, 700-701 721-731 fractionally-spaced, 702-703 689-702 maximum likelihood sequence estimator, 703-705, 721-725 algorithm, Bemoulh random ARQ (automatic repeat Bessel function 432 state, BEXPERM, ASK, 99 Algorithm BCJR, 541 belief propagation, 570 Automatic gain control (AGC), 294 Automatic repeat request (ARQ), 432 Average energy per bit, 97 Average signal energy, 97 AWGN channel model, EFT, 749-752 Godard, 726-730 Backward recursion, 543 LMS (MSE), 691-693 710-714 RLS (fast), 715 718 square-root, 715 soft-output Viterbi algorithm (SOVA), 532 stochastic gradient, 691-693, 725-730 702 243-246, 510-513 zero-forcing, 690-691 Aliasing, 75 1069-1073 1070 unslotted, 1070 slotted, ALOHA systems, 1069-1073 throughput, 1071-1073 Amplitude distortion, 598 Amplitude-shift keying (ASK), 99 Analytic signal, 21 1142 Bandpass processes, 79 in-phase component, 79 quadrature component, 79 Bandpass signal, 21 Bandwidth efficiency, 226 Bandwidth expansion factor, 428 Bandwidth of a signal, 20 Bandwidth of complex signals, 20 Baseband signal, NRZI, 115 Viterbi, ALOHA protocols, Bandlimited random processes, 75 NRZ, 115 sum-product, 558 tap-leakage, 598-601 lowpass equivalent, 79 (Kalman), 711-714 lattice, Channels), 597-598 Baseline figure of merit, 239 Baudot code, 12 BCH codes, 463 Berlekamp-Massey algorithm, 469 decoding, 467 error location numbers, 468 error locator polynomial, 468 generator polynomial, 464 non-binary, 471 syndrome, 467 730-731 Block error probability, 417 Block interleaver, 476 Boltzmann’s constant, 69 Bounds Chernov, 58, 373, 866-868, 923 950-951 Elias, for binary input channel, 376 Bibliography, 1109 BICM (bit-interleaved coded modulation), 936 Binary antipodal signaling, 101 error probabihty, 174 McEliece-Rodemich-RumseyWelch (MRRW), 443 Plotkin, 442 Singleton, 440 sphere packing, 441 Varshamov-Gilbert, 443 Welch, 801 Binary entropy function, 334 Binary equiprobable signaling error probability, 174 linear precoding for, MMSE, (BEXPERM), 950-951 ZF, 1057 for, 1058-1068 error probabihty for noncoherent lattice reduction, 176 optima] detection, 176 Binary modulation, Binary PSK (BPSK), 102 Binary Symmetric Channel (BSC), 355 Binomial random variable, 41 1058-1062 vector precodmg, 1062-1065 error probability, Biorthogonal signaling, 1065-1068 QR decomposition, 218 Binary orthogonal signaling, 1 208 optimal detection, 207 Bipartite graph, 559 Bit, Bit error probabihty, 164, BSC (binary symmetric channel), 355 Burst error correcting codes, 475-477 Burton codes, 475 Fire codes, 475 Reed-Solomon codes, 471-475 Burst of errors, 475 error probability, Burton codes, 475 Capacity, 13, 360 417 BPSK, 192 PSK, 197 Bit interval, 97 Bit rate, 1055-1058 1057 nonlinear precoding FSK detection, 192 bit error probabihty, Broadcast channels, 1053-1068 Binary expurgated permutation modulation 443 Hamming, 441 BPSK, 102 optimal detection, 173 Binary characterization of, 40 Bias term, 171 10 Band-limited channels (See also recursive least-squares (RLS), RLS RLS RLS line component, 80 Berlekamp-Massey, 469 constant-modulus, 726-730 Levinson-Durbin, 692, 716 LLL, 1067 469 variable, Bhatacharyya parameter, 373 Asymmetric digital subscriber (ADSL), 756 Asymptotic coding gain, 426 Augmented codes, 447 Autocorrelation function, 67 for in-phase component, 80 for quadrature 725-730 modified, 47, 213 for lowpass process, 81 708-710 Affine transformation, 66 Alamouti code, 1007-1011 reduced 996-1021 721-725 with second-order moments, B erlekamp-Massey Antipodal signals, 101 request), algorithms, stochastic gradient algorithms, Belief propagation algorithm, 570 error probability, 189 decision-feedback, 705-706 linear, 262 multiple antenna systems, Adaptive equalization, 689 Adaptive equalizers, (See also blind, 262 illumination efficiency maximum-likelihood backward recursion, 543 forward recursion, 543 SISO decoder, 545 soft output, 544 97 Bit-interleaved coded modulation (BICM), 936 Blind equalization, 721-731 constant modulus algorithm, 726-730 Godard algorithm, 726-730 joint data and channel estimation, 724-725 e-outage, 907 achieved by orthogonal signaling, bandlimited 367 AWGN channel, 365 discrete-time AWGN channel, 365 discrete-time binary-input channel, 362 ergodic, 900 of MIMO channels, 985-986, 990-991 finite-state channels, 903 1 Index of 1143 MIMO channels, 981-991 fading multipath, of multicamer system, 744-745 831-833 of multiple access methods, 1031-1035 outage, 987-990 symmetric channels, 363 Carrier phase estimation, 292-298 Costas loop, 312-313 decision-directed, 303-308 for multi-phase signals, 313-314 ML methods, 296-298, 321-322 nondecision directed, 308-315 phase-locked loop, 298-303 squaring loop, 310-312 Carner recovery, 290-295 833-839 for, 839-843 834 /^-persistent, Catastrophic convolutional underwater acoustic, waveform, 358 844 frequency selective, 844 836, 844 digital signaling over, 872-880 RAKE demodulator for, 871-872 tap weight estimation of, 876-877 tapped delay line model frequency of, 600 offset, Central frequency, 21 memoryless, 355 Central limit theorem (CLT), 63 microwave LOS, models for, ment), 238 Chain rule for entropies, 335 Channel access protocol, 1069 COST 207, Code 1037-1038 597-598 binary symmetric (BSC), 355 1053-1068 360 linear 838-839 time- variant filter, 11-12, 832 MIMO channels, MIMO channels, 966 981-991 slowly fading, 845 839-843 coherence bandwidth, 835 statistical, coherence time, 836 waveform, 358 (R ), 527, 787-791 for fading channels, 957-960 Nakagami continuous-output, 357 discrete-memoryless, 356 358 discrete-time model, 625-628 distortion, 598-601 amplitude, 598 envelope delay, 598-599 frequency offset, 600 impulse noise, 601 600 matrix, Rayleigh fading, 833 Binary signaling over, for, 942-956 for, cutoff rate 899-960 for, 957-960 peak, 641 frequency nonselective, phase jitter, 600 846-849 M-ary orthogonal signaling over, 861-865 squared-error, thermal noise, 645-646 600 Doppler power spectrum, 836 Doppler spread, 836 encoder, code rate, 2, 402 codeword, 2, 372, 401 envelope delay, 598-599 Multiphase signaling over, 859-861 reliability function, state 369 information (CSI), 904, 957-960, 1054 Ricean fading, 833 extended Golay, 424 Fire, 475 fixed weight, 411, asynchronous, 1039-1042 780-784 frequency hopped, 802-804, 813-814 optimum receiver for, 1038-1042 suboptimum detectors for, 1042-1050 decorrelating, 1043-1045 MMSE, 1046-1047 multistage interference cancellation, distance, 1048-1049 function, lengthened, 446 411 low density parity check (LDPC), 569 linear block, maximum distance 440 421 maximum-length shift register, 461 MDS (maximum-distance separable), 440 minimum distance, 414 minimum weight, 414 outer, 479 separable, maximum length, parallel concatenated block, parity product, 477 442 punctured, 446, 6-5 17, 521-523 bit-interleaved, 435 Reed-Muller (RM), 421 Reed-Solomon (RS), 471 trellis, serially concatenated block, rate, Codeword, 936 571-586, 929-935 Codes augmented, 447 bandwidth efficient, 571, 586 bandwidth expansion factor, 428 BCH, 463 bit error probability, 417 block, 401 block error probability, 417 burst error correcting, 475 Burton, 475 classification, 401 481 check matnx, 412 perfect, 434, 1047-1048 416 instantaneous, 340 1042-1043 cancellation, 414 479 successive interference Code 949-953 input-output weight enumeration 63 Coded modulation, 847-849 coding extended, 447 synchronous, 1038-1039 357 coded waveforms expurgated, 447, 950-951 inner, (CDMA), 780-784 single user, 927 412 equivalent, Hamming asymptotic efficiency, 1052 probability transition AWGN, effective distance, Hadamard, 423, 951-953 performance, 1050-1053 600 overspread, 845 phase jitter, 600 927 412 dual, Hamming, 420, 460 division multiple access fading, 841 nonlinear, discrete-input nonlinear, multipath spread, 834 diversity order, Golay, 424, 460 capacity of, 1033-1034 filter, linear, capacity, 13, (central limit theorem), digital cellular, Jakes’ model, 460 Hamming, 460 generator matrix, 412 CLT Hata, 843 160 discrete-time for Rayleigh fading channel, Clairvoyant estimate, 1098 additive Gaussian noise, 10 cutoff rate Channel capacity, 13, 360 Channel coding, 400 Channel L- value, 552 Channel state information (CSI), 904, 957-960, 1054 Characteristic function, 44 Characteristic of a field, 404 Chernov bound, 58, 373, 923 additive noise, 10 for multiuser channels, of cyclic Golay, cyclic binary symmetric, 355 additive noise, 10 broadcast, 5-9 1014-1016 Chernov parameter, 373 X random variable, 45 Circular random vectors, 66 acoustic, band-limited, wireless, wireline, pairwise error probability, 840 discrete memoryless, 356 discrete-time, 358 AWGN, 946-948 430 CRC, 453 cyclic, 447 coset, 866-868 impulse noise, 601 CFM (constellation figure of convolutional, 491-548, 600 frequency nonselective, 836, 869-871 inequality, 3, 69, throughput, 1070 digital signaling over, 416 function, underspread, 845 codes, 509 Cauchy-Schwarz 29-30 thermal noise, finite-state, 903 869-889 1074 1074-1077 conditional weight enumeration constant weight, 949-953 fiber optic, error rate for, 1-persistent, 953-956, 1020-1021 645-646 symmetric, 363 transfer function, nonpersistent, 1074 coding gain, 426, 533 concatenated, 479-480, storage, (CSMA), 1073 1074-1077 squared-error, impulse response, 832 models 837 845 table, correlation functions for, Carrier sense multiple access protocols, scattering function, spread factor, 845 characterization of, quasi-perfect, rate, 480 shortened, 445 shortened cyclic, 452 standard array, 430 syndrome, 430, 467 systematic, 412 442 ternary Golay, turbo, 548 undetected error, 430 uniquely decodable, 339 weight distribution, 41 weight distribution polynomial, 415 1 6 , Index 1144 Codes ( continued) weight enumeration function, 415 word error probability, 417 power density spectrum of, 138-145 representation of, 116-117 rate, 523-525 Continuous-phase modulation weight, 411 Coding (RSCC), 507-508 systematic, 505 effective 243-246 table of generators for MIMO channels, metric computations, 249-251 1001-1021 257-258 performance of, 251-258 suboptimum, 258-259 for Rayleigh fading channel, 942-960 943-944 Equalizers, decision-feedback) maximum 517-520 500 free distance, transfer function, multi-/i, 335-354 661-665, 705-706 sequence estimation, for lossy, diagram, 496 diversity order, 927 distance, 927 1, 335-348 348-354 Decision-feedback equalizer {see soft-decision decoding, state Data compression, lossless, recursive systematic (CPM), 118-123, 243-259 demodulation, 243-258 maximum-likelihood Codeword, 372, 401 D transform, 493 491 rate-compatible punctured, 496 trellis diagram, 496 Viterbi algorithm, 510 tree diagram, Decision region, 163 Decoding, Berlekamp-Massey, 469 Fano algorithm, 525 feedback, 529-531 concatenated, 953-956 full constant-weight codes, linear representation of, Convolutional interleavers, 476 iterative, 128-130 minimum-shift keying (MSK), 123-124 modulation index, 118, 254 multi -h, 118, 257-258 Correlation metric, 173 Meggit, 460 Correlation receiver, 177 partial response, Coset leader, 430 Coset representative, 584 525-528 424 stack algorithm, 528-529 turbo, 552 LDPC, 570 949-953 convolutional codes, 946-948 cutoff rate, 371-380, 516, 957-960 linear block codes, 943-946 space-time codes, 1006-1021 trellis codes, 1016-1019 527, 787-791, response, 118 phase cylinder, phase state, phase trees Huffman, 342-346 in the frequency domain, 942-960 power spectrum 145-148 533 of a lattice, 233 Complementary error function, 44 Complementary gamma function, 911 Complete set of signals, 32 Complex envelope, 22 gain, Complex random processes 18 22 248 Gray, 100 Coding of, trellis of, 20 for Continuous-wave (CW) interference, 772 Convergence almost everywhere Convex pseudocovariance, Complex random Complex random (a.s), CRC (a.e.), vectors, 64 catastrophic, decoding, Complex bandwidth, 20 Concatenated codes, 479-480, 540-541, 953-956, 1020-1021 inner code, 479, 540 outer code, 479, 540 Concave in-phase and quadrature components, 80 CSD 67 maximum Cutoff rate 541-548 Conditional weight enumeration equivalent encoders, 506 416 Constant weight codes, 411, invertible, 508 949-953 Constellation, 34 maximum free distance, 945-946 508 238 Constellation figure of merit (CFM), 238 Constraint length, 96, 49 Continuous-phase frequency-shift keying (CPFSK), 116-118 performance of, 116 (PCCC), 548 performance on channel, 513-516 performance on BSC, 513-516 performance on Rayleigh fading channel, 946-948 punctured, 516-517, 521-523 parallel concatenated AGWN PAM signals, of PSK signals, QAM for intersymbol interference, 623-628 matched filter-type, 178-182 maximum likelihood, 163 maximum-likelihood sequence, 623-628 of binary signals, 219-221 of M-ary orthogonal signals, 216-219, 741-743, 861-865 multichannel, 737-743 Golay, 460 optimum, 212-214 OFDM, 749 Density of a lattice, 236 Hamming, 460 Detector generator polynomial, 448 invertibility conditions, of 188-190 190-195 signals, 196-200 of optimum, 201-203 correlation type, 177-178 of CPM, 243-258 performance, 251-258 decoding, 458 encoding, 455 nonbinary, 499, 504 distance, 185 207-209 noncoherent, 210-224 787-791 513 226-229 of orthogonal signal, 203-207 CRC, 453 hard-decision decoding, of, of biorthogonal signals, Cyclic codes, 447 first-event error probability, figure of merit, companson enumeration function), 416 49 Conjugacy class, 409 Conjugate element, 409 minimum for pulsed interference, 502 (See Carrier coherent CWEF (conditional weight Confluent hypergeometric function, 377-380 957-960 for fading channels, 537-540 first-event error, R ), 371-380, 516, 527 capacity, 525-528 stack algorithm, 528-529 Viterbi, 243-246 distance properties of, function, ( comparison with channel a posteriori, sequential, dual-fc, state information), 904, 957-960, 1054 386 Conditional entropy, 334 function, (cross spectral density), CSI (channel for, phase estimation) of binary signals, 173-177 Crosscorrelation function, 67 Fano algorithm, 525 feedback, 529-531 signals earner recovery codes, 453 Cross-correlation coefficient, 26 constraint length, 491 pseudocovanance matrix, 64 Delay power spectrum, 834 Demodulation, 24 Demodulation and detection, 201 components, 80 532-537 509 concatenated, 540-541 Viterbi algorithm, 243-244, Degrees of freedom, 75 Delay distortion, 598-599 in-phase and quadrature 386 covariance matrix, 64 soft decision, Cross spectral density, 67 63 63 478, 548 sequential, Modulation), 63 functions, applications, variables, 63 processes, 71 modulation index, 1 peak frequency deviation, 17 power spectral density, 138-145 CPM, (See Continuous-Phase Convolutional codes, 491-548 covariance, complex random CPFSK, 116-118, 138-145 120 in distribution, Coset, 430, 483 138-142, of, 249 almost surely Correlative state vector, 248 Covariance representation of, 118-123 state trellis, Correlative state, 248 hard decision, 428 message polynomial, 449 parity check polynomial, 450 shortened, 452 systematic, 453 Cyclic equalization, 694 Cyclic redundancy check (CRC) codes, 453 Cyclic subgroup, 482 Cyclostationary process, of decorrelating, 1043-1045 envelope, 214 970 maximum-likelihood (MLD), 970 MMSE, 970, 1046-1047 inverse channel (ICD), minimum distance, 171 nearest neighbor, 171 973-974 random nonlinear, 70 optimal noncoherent, 212-214 1 Index 1145 single user, 1042-1043 sphere, 973 Effective radiated power, 260-261 Differential encoding, 15 349 Differential entropy, (DPSK), 221 Differentially encoded PSK, 195 Digamma function, 909 Digital communication system model, 1-3 reduced- state, 669-671 443 self-recovering (blind), Encoder 706-708 509 492 455 convolutional, 402, for cyclic codes, average, 97 227 Discrete memoryless source differential, (DMC), 356 Discrete-time AWGN, Discrete-time AWGN channel 358 365 rate, 337 Envelope detection, 214 705Envelope of a signal, 23 Equivalent codes, 412 362 Distance ( see Block codes, capacity, Convolutional codes) 927 enumerator function, 185 Euclidean, 35 Hamming, 414 effective, metric, 173 product, 925 Distortion {see Channel distortion) 352 706equalizers) Extension decision-feedback, 661-665, 706 adaptive, 689-731 examples of performance, 662-665 for MEMO channels, 979-981 of trellis-coded signals, predictive form, 665-667 antenna, 85 binary antipodal signaling, 174 Eye 695-696 equalization, 694 algorithm, 851-859 cyclic Factor Graphs, 558 Channel) DMS {see Discret for MSE, 696-697 MEMO channels, 975-979 945-946 outage capacity, 900, 906, 907, fractionally spaced, Memoryless LMS (MSE) 655-658 algorithm, '691-693 Source) 943-944 FSK, 205 lower bound to, 86 M-ary PSK, 190-194 propagation models FH mean-square error (MSE) PAM, 100 DPSK, 221 minimum MSE, 647-648 error probability, criterion, 223 DSB, 100 Dual code, 412 Dual-k codes, 537-540 Duobinary signal, 610 645-655 SNR for, 104-1 105 1106 message, 164 multichannel binary symbols, 739-741, 1090-1095 e-outage capacity, 907 Early-late gate synchronizer, 318-321 Effective antenna area, 262 Effective distance, 927 noncoherent detection, 216 922, 928 189 maximum (MAP), 291 239 238 Filtered multitone word, 417 (FMT) modulation, 754 union bound, 182 Filters, matched, 178-182 Estimate clairvoyant, 1098 324 324 whitemng, 627 403 Finite fields, consistent, Finite-state channels, efficient, 903-905 Fire codes, 475 First-event error, 502 pilot signal, 1098 Estimate of phase {See Carrier phase estimation) Estimation a posteriority probability 403 403 ground, 404 minimal polynomial of an element, 408 order of an element, 407 primitive element, 407 Galois, constellation, unbiased, 323 671-673 404 finite, baseline, QPSK, 199 659 zero-forcing, 642 iterative equalization/decoding, 404 characteristic, extension, Figure of merit 198 biased, 323 phase-splitting, Spread spectrum signals), Field AWGN channel, 648 passband, 658-659 peak distortion, 641 peak distortion cntenon, 641-645 output spread spectrum signals {see for Rayleigh fading, 859-861, QAM, for, 842-843 Feedback decoding, 529-531 symbol, 164 Double-sideband (DSB) 900, 987-990 for soft-decision decoding, PAM, 899-960 985-987 for hard-decision decoding, pairwise, 184, 372, 418, excess for, ergodic capacity, 900, 905-906, examples of performance, 651-655 time, 851 Fading channels {See also coding RAKE, DMC {see Discret Memoryless 830-844 52 Channels), 830-890 164,417 block, 417 DPSK, 223 bit, orthogonal signaling, 205 928 8, figure, error probability, 65 1-655 851 603 pattern, Fading, polarization, 851 signal space, 552 Extnnsic L- value, 552 signaling, 176 for convergence of MSE 996-997 927 order, 852, 46 404 Extrinsic information, 1100-1103 for Ricean fading, linear, frequency, 850 field, 16QAM, 186, 200 ASK, 189 biorthogonal signaling, 208 668-669 640-649 adaptive, 689-693 baseband, 658-659 Diversity of, Error probability, signaling, 174 708 Distortion-rate function, variable, Extended codes, 447 Extended Golay code, 424 binary orthogonal minimum MSE, 663 350 791-796 792-796 nonlinear, 796 EXIT charts, 555 Exponential random Error floor, 551 Equalizers {See also Adaptive Hamming, 354 interference, binary equiprobable encoders, 506 at transmitter, Excision of narrowband Expurgated codes, 447, 950-951 Error detection, 432 Equivalent convolutional Discrete-time binary-input channel 669-67 44 Error correction, 900 334 349 909 Excess bandwidth, 607 Excess MSE, 696-697 linear, Ergodic capacity, 900, 905-906, 334 joint, Entropy 631-639 985-987 conditional, (DMS), 331 of, reduced-state, chain rule, 335 Discrete-memoryless channel phase, 321-322 performance of, 323-326 Euclidean distance, 35 reduced complexity, Entropy, 333 Dirty paper precoding, 1054 performance 703-705 performance erfc, bit, average, 97 spectrum signals) for, 669-671 per Direct sequence ( See Spread of symbol timing and earner Euler’s constant, channel estimator Energy, 25 Dimensionality theorem, squared-error, 628-631 508 turbo, 549 Encoding {see Block codes; inverse, Digital signaling, 95 capacity, using the Viterbi algorithm, Convolutional codes) Digital modulator, 721-731 of earner phase, 295-315 of signal parameters, 290 of symbol timing, 290 with trellis-coded modulation, catastrophic, Digital modulation, 95 sequence estimation, 623-625, Eigenvector, 29, 1086 Elias bound, Differential phase-shift keying gain, maximum -likelihood Eigenvalue, 29, 1086 maximum-likelihood, 291, 296-298, 321-322 903 capacity, First-event error probability, 513 Fixed weight codes, 411, 949-953 Fixed-length source coding, 339 1 1 Index 1146 Folded spectrum, 644 Forward recursion, 543 Free Euclidian distance, 577 Free-space path loss, Frequency diversity, Frequency range 262 850 Gray coding, 00 Gray labeling, 939 Ground field, 404 Group Abelian, 403 identity element, Irregular Iterative decoding, 478, wireless (radio) channels, Frequency domain coding, 942-960 Frequency hopped (FH) spread spectrum, 802-804 Frequency support, 20 Frequency-shift keying (FSK), 109-110 continuous-phase (CPFSK), 116-118 Hadamard Hard decision decoding, of block codes, 428-436 of convolutional codes, 509-516 Hata model, 843 Hermite parameter, 233 Hermitian matrix, 65, 1085 Hermitian symmetry, 19 Hexagonal noncoherent detection, 215 power density spectrum, 154 Frobenius norm, 982 Fundamental coding gain, 586 Fundamental volume of a lattice, 233 230 Hilbert transform, 22 lattice, Homogeneous Markov chains, 72 Huffman coding, 342-346 fields, 403 minimal polynomial, 464 subfield, 483 Gamma function, 45 complementary, 911 Digamma function, 909 Gamma random variable, 46 Gaussian minimum-shift keying (GMSK), 118 Gaussian noise, 10 Gaussian random process, 10, 68 Gaussian random variable, 41 RAKE demodulator, Generalized 880-882 404 Identity element, iid random variables, 23 of linear block codes, 412 Gilbert- Varsharmov bound, constraint nodes, 561 cycle-free, triangle, 29-30 Information sequence, , 40 Information source discrete memoryless, 331 memoryless, 331 560 558 560 33 variable nodes, Input-output weight enumeration filter, LDPC) equivalent, 22 20 signal, Low probability of intercept, (IOWEF), 416 block, 236 716-721 apenodic equilibrium probabilities, 73 234 Sublattice, 234 Voronoi region, 232 of large numbers (LLN), 63 (low density parity check codes), 568-571 Interleaving, Intersymbol interference, 599-600, 603-604 ergodic, 73 homogeneous, 72 irreducible, 73 penod of state, 73 state, 72 72 72 stationary probabilities, 73 steady-state probabilities, 73 Markov inequality, 57-58 Matched filter, 178-182 state probability vector, frequency domain, 179 Matrix 570 A1 6-All 73 receiver, 178 degree distribution polynomial, uniform, 480^4-81 states, state transition matrix, code density, 569 decoding, 570 476 generalized, 47 M-ary modulation, Markov chains, 71-74 Hermite parameter, 233 hexagonal, 230 kissing number, 232 minimum distance, 232 multidimensional, 234 multiplicity, 232 LDPC 476 415 generator matrix, 231 Law 774 identity, 291 fundamental volume, 233 Interleaver condition number, 1088 eigenvalue, 1086 irregular, eigenvector, 1086 regular, generator, 570 569 Tanner graph, 569 412-413 Hermitian, 65 controlled ( see Partial response Least-squares algorithms, 710-720 Hermitian transpose, 28 609-611 discrete-time model for, 626 Lempel-Ziv algorithm, 346-348 Lengthened codes, 446 Levinson-Durbin algorithm, norm, 1088 signals), equivalent white noise filter 692,716 for, filter, Markov singular values, 1087 skew-Hermitian, 65 Linear equalization {see symmetric, 1085 trace of, 1085 Linear-feedback shift-register, maximum chains, 73 Irreducible polynomial, 405 412-413 Linear block codes, 400-490 Equalizers, linear) 642 orthogonal, 23 parity check, rank, 1085 Likelihood function, 292 (ICD), 970 Inverse Irreducible 560 {see Lowpass Lowpass Mapping by set partitioning, 572 Marcum’s (^-function, 47 co set, 584 Schlafli, Inverse channel detector Tanner, 558 336 Lossy data compression, 335 Low density parity check codes probability), 162-163, recursive least squares, 708, 715 optimum demodulator 623-628 561 546 54 Lossless data compression, 335 variable, MAP (maximum a posteriori 939 Inner product, 26, 28, 30 global function, 561 local functions, a posteriori probability), Mac Williams set portioning, model, 627 factor, 546 maximum Lossless source coding theorem, Inner code, 479 560 cycles, girth, 27 Cauchy-Schwarz, 29-30 Kraft, 340 Markov, 56 gain 552 559 (log Lognormal random Karhunen-Loeve expansion, 76 Kasami sequences, 799 Kissing number of a lattice, 232 Kolmogorov-Wiener filter, Kraft inequality, 340 equivalent, 23 convolutional, bipartite, Log-MAP Kalman (RLS) algorithm, 711-714 Kalman gain vector, 712 density, GMSK, Golay codes, 424, 460 extended, 424 ternary, 442 Gold sequences, 799 Gram-Schmidt procedure, 29 Graphs, 558-568 (log a posteriori probability), processes, 54 Inequality Girth of a graph, 560 118, 127 Log-APP Jointly wide-sense stationary In-phase component, 22 Interference margin, 443 Link budget analysis, 261-265 Link margin, 246 LLN {see law of large numbers) 838-839 Jensen’s inequality, 386 Joint entropy, 334 Jointly Gaussian random variables, 54 Jakes’ model, coding gain, 233 for bandpass systems, function Generator polynomial, 448, 464 Linearly independent signals, 30 Lattice Instantaneous codes, 340 transform domain, 495 553 Gray, 939 Impulse response, of space-time block code, 1006 718 Linear time-varying channel, Labeling 45 Impulse noise, 601 stationary, Generator matrix lattice, forward, 717 residuals, 778-779 Illumination efficiency factor, 262 Galois 10 backward, 718 EXIT charts, 555 codes, 423, 951-953 Hamming bound, 441 Hamming codes, 420, 460 Hamming distance, 414 Hamming distortion, 354 Hermitian transpose of a matrix, 28 205 548-558 Linear prediction, error floor, 551 waterfall region, Frequency division multiple access (FDMA), 1029 capacity of, 103 1-1032 Linear modulation, turbo cliff region, 553 404 wireline channels, error probability, LDPC, 570 Irrelevant information, 166 Linear filter length, channel, 11 798-799 transpose, 28 Max-Log- APP algorithm, 548 Max-Log-MAP algorithm, 548 1 Index 1147 Maximal ratio Maximum ( combiner, 852 a posteriori probability see MAP), singular-value decomposition for, Minimal polynomial, 408 Minimum distance, 414 Maximum free distance codes, 516 Minimum Minimum 517-520 Maximum-length shift register codes, 461,798-799 tables of, likelihood, parameter estimation, 290-291, 321-322 for carrier phase, for joint earner 292-298 and symbol, 321-322 for symbol timing, 315-321 performance of, 323-324 Maximum-likelihood (ML) distance of a constellation, 185 Minimum Minimum weight, 414 Minimum-shift keying (MSK), 123-124 power spectrum 144 ML ( see maximum-likelihood) MLSD, 623-625, Modified duobinary signal, 610 binary, (MLSD), comparison 623-625, Maximum ratio of, 226-229 96 combining, 852 of, QPSK, 193 continuous-phase FSK Multicode MIMO systems, 997-1000 Multidimensional signaling, 8, 83 Multipath intensity profile, 834 equicorrelated (simplex), 112-113, 209-210 frequency-shift keying (FSK), 109-110, 205,215-216 110 M-ary orthogonal, 108-1 204-207,216-219 11, memoryless, 95 multichannel, 737-743 NRZ, 115 1053-1068 1036-1053 random access, 1068-1077 CDMA, for synchronous transmission, 1038-1039 1042-1043 Mutual information, 332 single user detector, Nakagami random variable, 52, 841 Narrowband Narrowband Narrowband interference, 791-796 process, 79 signal, 18-21 Nat, 333 Nearest neighbor detector, 171 Negative spectrum, 20 Noise, Gaussian, 10 white, 90 Noise equivalent bandwidth, 92 Noisy channel coding theorem, 361 Non-central x random 46 Noncoherent combining loss, 741 Noncoherent detection, 210-226 variable, 108 DPSK, 221-223 for thermal, 3, 69 741 Multipath channels, 95 multidimensional, 108-113 Message polynomial, 449 Metnc 737-743 noncoherent combining 741-743 (CPM), 118-123 linear, 752-754 with M-ary orthogonal signals, continuous-phase modulation digital, spectral characteristics, Multichannel communications, with binary signals, 739-741 (CPFSK), 116-118 power spectrum, 138-145 for broadcast channels, for 759 FFT-based system, 749-752 Filtered multitone (FMT), 754 OFDM, 746-742 bit allocation, 754-757 power allocation, 754-757 peak-to-average ratio, 757-759 loss, constraint length, 851-855 McEliece-Rodemich-RumseyWelch (MRRW) bound, 443 MDS (maximum-distance separable) codes, 440 Mean-square error (MSE) entenon, 645-655 Meggit decoder, 460 Memoryless channel, 355 Memoryless modulation, 95 Memoryless source, 33 Mercer’s theorem, 77 Message error probability, 164 PSK, 194 performance of, Modified Bessel function, 47, 213 Modified distance metric, 173 Modulation 123-124, 144 Multicamer communications, 743-759 capacity of, 744-745 channel coding consideration, distance of a lattice, 232 623-625, detection MSK, distance detector, 171 likelihood sequence receiver, 163, Maximum Rumsey-Welch) bound, 443 spread spectrum, 992-996 Maximum-distance separable codes, 440 Maximum MRRW (McEliece-Rodemich- 974-975 error probability for orthogonal signals, 216-218 FSK, 215-216 Multipath spread, 834 Nonlinear distortion, 600 Multiple access methods, Nonlinear modulation, 1029-1031 capacity of, 1031-1035 CDMA, 1033-1034 FDMA, 1031-1032 random accesss, 1068-1077 TDMA, 1032-1033 Multiple antenna systems, 10 Norm of a matrix, 1088 of a signal, 30 of a vector, 28 Normal equations, 716 Normal random variable, 41 NRZ, 115 NRZI, 115 966-1021 NRZI, 115 inverse channel detector, Nyquist entenon, 604-605 correlation, 173 nonlinear, 110 Nyquistrate, 13 distance, 173 OFDM, 746-752 modified distance, 173 offset 970 maximum-likelihood 970 MGF (moment generating function), Microwave LOS 101-103, 191-195 44 channel, MIMO channels, 966 pulse amplitude (PAM, ASK), 98-101, 188-190 capacity of, 982-984, 990-991 985-986 987-990 coding for, 1001-1021 bit-interleaved, 003- 006 space-time codes, 1006-1021 temporal, 1003-1006 slow fading, 968-969, 975-979 ergodic, outage, spread spectrum signals QPSK, phase-shift keying (PSK), for, 992-996 quadrature amplitude (QAM), 103-107, 185-187, 196-200 with memory, 95-96 Modulator, 2, 24 linear, 95 110 space- time codes for, concatenated codes, STBC, 1014 orthogonal STBC, 1011-1013 quasi-orthogonal STBC, 1013 trellis codes, 1016-1019 turbo codes, 1020-1021 232 Multistage interference M-ary, cancellation, 1043-1049 Multiuser communications, 1028 nonlinear, 110 bit 746-752, 844-890 and power allocation, 754-757 degradation due to Doppler spreading, 884-889 1020-1021 differential Multiplicity of a lattice, memoryless, 95 MIMO systems, 966 OFDM, 970 1006-1021 detector, Multiplexing gain, 996-997 binary, digital, minimum MSE detector, FFT implementation, 749-752 889-890 757-759 Offset QPSK (OQPSK), 124-128 On-off keying (OOK), 267, 949 ICI suppression in, peak-to-average ratio, Optimal detection after modulation, 202 binary antipodal signaling, 173 binary orthogonal signaling, 176 biorthogonal signaling, 207 simplex signaling, 209 detectors for, pulse amplitude, 98-101 multiple access, 1029-1034 OQPSK, 124-128 diversity quadrature amplitude, 103-107 multiuser detection, Order of a field element, 407 Orthogonal matrix, 23 Orthogonal signaling, 108 970-974 gam for, 996-997 error rate performance, Moment generating 971-973 973-974 multicode, 997-1000 multiplexing gam for, 996-997 outage probability, 987-988 scrambling sequence for, 997 lattice reduction with memory, 95-96 for, function ( see MGF) Monic polynomial, 405 Moore-Penrose pseudoinverse, 1088 Morse code, 12, 339 1029-1034 random access, 1068-1077 Multiuser detection, 1034 decorrelating detector, 1043-1045 for asynchronous transmission, 1039-1042 achieving channel capacity, 367 error probability, 205 with noncoherent detection, 216-218 Orthogonal signals, 26, 30 1 Index 1148 Orthogonal vectors, 28 Positive spectrum, 20 Orthogonality pnnciple, 646 Power Power mean-square estimation, 646 Orthonormal vectors, 28 basis, 28 signal set, 30 Outage capacity, 900, 907, 913 of MIMO channels, 987-990 Outage of probability, MIMO channels, 987-988 Outer code, efficiency, Pseudocovanance for complex random 226 67 continuous component, 133 CPFSK, 138-145 component, 133 for in-phase component, 80 for lowpass process, 81 for quadrature component, 80 linearly modulated signals, 133 Power spectrum, 67 1014-1016 Chernov bound, 373, 1014-1016 PAM, 98-101 codes, 481 proper, message error sampling theorem, 74 senes expansion, 74 Pulse amplitude modulation {see 412 412 611-612 450 Partial-band interference, 804 Partial response signals, 609-6 duobinary, 610 error probability of, 617-618 modified duobinary, 610 precoding for, 613 Partial-time (pulsed), 784 Path memory truncation, 246 PCCC (parallel concatenated block codes), 481 prediction), Preferred sequences, 799 340 lognormal, 54 196-200 moment Perfect codes, 434, 442 Phase of a signal, 23 Phase jitter, 600 Phase-locked loop (PLL), 298-315 Costas, 312-313 central, 54-56 Product codes, 477 loop damping factor, Product distance, 925 Prolate spheroidal 101-103 1098 Plotkin bound, 442 PN sequences, 463, 796-801 Polynomial 405 minimal, 408 monic, 405 prime, 405 syndrome, 458 (OQPSK), 124 QAM) PSK x , 46 Rayleigh, 48 Ricean, 50 uniform, 41 Random vectors, circular, (QPSK), 102 Rq (channel cutoff rate), 527, 787-791, 957-960 For fading channels, 957-960 Raised cosine spectrum, 607 excess bandwidth, 607 rolloff parameter, 607 RAKE demodulator, 869-882 for binary antipodal signals, 878 874-877 66 circularly symmetric, 97 bit, code, 2, 402 97 signaling, Rate-compatible punctured convolutional codes (RCPCC), 523-525 350 Rate-distortion function, Rate-distortion theorem, 351 878 Rayleigh fading channel, 833, 841, 846-868 orthogonal signals, 879 880-882 Random access, 1068-1077 ALOHA, 1069-1073 carrier sense, 1073-1077 generalized, wave proper, 65 Rate CSI CSI at both sides, 912 at receiver, 909, 957-960 ergodic capacity, 907 for MIMO channels, 985-987 Proper random processes, 71 non outage capacity, 913 Proper random vectors, 65 1074 /^-persistent, 1074-1077 227 autocorrelation function, persistent, 1074 for 1-persistent, (power spectral density), 67 Pseudo-noise (PN) sequences, 796-801 798 generation via shift register, 797 Gold, 799 offered channel slotted traffic, ALOHA, 1070 unslotted, RCC (recursive convolutional 1070 throughput, 1070 codes), RCPCC 1070 Random coding, 362, 375 Random processes, 66-81 MIMO channels, 987-990 Rayleigh random variable, 48 507 (rate-compatible punctured convolutional codes), 523-525 Receiver Kasami, 799 bandlimited, 74-76 correlation, 177 maximal-length, 797 bandpass, 78-81 MAP, 162 peak cross-correlation, 799 preferred, 799 ( see also Spread spectrum cross spectral density, 67 matched 70 discrete-time, 69 Gaussian, 68 ML, signals), 66 Shannon’s lower bound, 353 DPSK signals, for noncoherent detection of matnx of a PSD 120 normal, 41 no CSI, 908 functions, Phase-shift keying (PSK), 44 with collision detection, 1073 natural frequency, 120 non-central probability, 193 for binary orthogonal signals, channel, 357 308-315 generating function, message error for Probability transition square-law type, 310-312 54 complex, 64 decision-directed, 303, non-decision-directed, 45 error probability, 199 binomial, 41 Processing gain, 773-774 313-314 299 Gaussian, 41 Nakagami, 52 Quaternary uniform, 41 308 299 46 gamma, 46 196-200 Quadrature component, 22 Nakagami, 52-53 Rayleigh, 48-50 Rice, 50-52 probability) irreducible, 103-107, 185-187, Probability distributions multivariate Gaussian, see pairwise error Pilot signal, QAM, Quasi-perfect codes, 435 PEP trellis, jointly Gaussian, Primitive element, 407 convolutional codes), 548 Peak distortion criterion, 641-645 Peak frequency deviation, 17 Peak-to-average ratio, 757-759 tree, (2-function, 41 {see BCH codes, 463 44 X 45 exponential, offset chi-square, concatenated binomial, 41 complex, 63 Pnme polynomial, 405 Primitive 40 523-525 Puncturing matnx, 520, 522 Pythagonan relation, 29 Quadrature amplitude modulation Preprocessing, 166 40-57 variables, characteristic function, QPSK, 102 Prediction ( see Linear Prefix condition, Random Bernoulli, error probability, 45-46 noncentral, 46-48 gamma, 46 Gaussian, 41-45 log normal, 54 type, wide-sense stationary, 67 rate performance, 516, 521-523 for spectral shaping, 133-135, Parity check polynomial, (parallel white, 69 iid, 1065-1068 Parity check matrix, PCBC PAM) Pulsed interference, 784 rate compatible, via lattice reduction, codes (PCCC), 548 Parity check bits, probability, 194 vector, Parallel concatenated convolutional power spectral density, 67 power spectrum, 67 differentially encoded, 195 Punctured convolutional codes, 1058-1062 1062-1065 Parallel contatenated block (DPSK), 221 521-523 QR decomposition, 67 power, 68 195 Punctured codes, 446, 516, 1053-1068 dirty paper, 1054 linear, 1055-1058 nonlinear, 1058-1068 184, 372,514, 922, Phase Phase Differential effect for broadcast channels, M-law bit error probability, Precoding Pairwise error probability (PEP), ( PSK, 101-103, 191-195 on error 785-791 Pre-envelope, 21 stationary, narrowband, 79 processes, 71 spectral density, discrete jointly wide-sense cyclostationary, 178-182 623-625 filter, 163, Receiver implementation, 177 Reciprocal polynomial, 450 1 1 1 1149 Index Recursive convolutional codes, quadrature components Recursive least squares (RLS) spectrum, 19 algorithms, 710-721 fast 22 of, codes (RSCC), 507 Reed-Muller codes, 421 Reed-Solomon codes, 441, 446, 471-475 burst error correction, 473 decoding, 473 MDS property, 472 weight enumeration polynomial, 619-623 no intersymbol 604-609 interference, with partial response pulses, 609-611 with raised cosine spectral pulse, 369 binary antipodal, 101 Rice biorthogonal, 111 95 Ricean fading channel, 833, Ricean random variable, 50-52 digital, RS non-retum-to-zero (NRZ), 115 RSCC non-retum-to-zero, inverted convolutional codes) Sampling theorem, 74 Scattering function, 837 SCBC multidimensional, 108 (NRZI), 115 see recursive systematic ( 176 interference margin, on-off, 267 tracking of, 819-822 quasi-orthogonal simplex, 112 turbo, see serially concatenated Signaling interval, 96 Signaling rate, 97 Spatial rate, 1007 Signals Spectral bit rate, 234 Sequential decoding, 525-528 binary coded, Serially concatenated block binary orthogonal, 176-177 codes, 480 572-573, 939 Shannon digitally 1 modulated, 95 cyclostationary, 70-71, 131 lower bound on R(D), 353 second theorem, 361 third theorem, limit, 35 207, 554, 570 Shaping, 586 Shaping gain, 240, 586 Shortened codes, 445 Shortened cyclic codes, 452 Signal (see also Signals) spectral characteristics, 226 131-133, 135-147 Sphere packing, 235 Sphere packing bound, 441 Spread factor, 845 table of, 845 (SSMA), 1031 Spread spectrum signals, analytic, 21 cross correlation of, 67 acquisition of, 816 power density spectrum, 67 for bandwidth, 20 properties of quadrature complex envelope, 22 energy of, envelope 25 of, fading, for quadrature amplitude modulated (QAM), 103-106 23 in-phase component, 22 Signature sequence, 1037 lowpass, 20 Simplex signaling, lowpass equivalent, 22 12-113 optimal detection, 209-210 PAM, multipath, 8, 83 Single-sideband (SSB) narrowband, 18-21 Singleton bound, 440 norm, 30 Singular- value decomposition, phase, 23 left singular vectors, 981, 1087 , Storage channel, Subfield, 483 234 1047-1048 cancellation, Sufficient statistics, 166 Sum-Product algorithm, 558-567 Survivor path, 244, 512 SVD (See Singular-value decomposition) Symbol error probability, 164 Symbol rate, 97 Symbol SNR, 192 Symmetric channel capacity, 363 Synchronization 290-315 effect of noise, 300-303 for multiphase signals, 313-314 with decision-feedback loop, 303-308 with phase-locked loop with squaring loop, 310-312 for, 776-778 765-768 application of, 778-784 coding for, 776-778 demodulation of, 767-768 performance of, 768-773 of spread spectrum signals, with pulse interference, symbol, 290-291,315,321 concatenated codes 784-791 974-975, 981-982, 1087 parameter estimation, 290-326 100 Stationary source, 337 (PLL), 298-303 MIMO systems, 992-996 direct sequence, simplex, 112-113 code division multiple access (CDMA), 779-780, 813-814 components, 79-81 white noise, 69 processes, wide-sense, 67 with Costas loop, 312-315 763-765 bandpass, 21 baseband, 20 random Stationary carrier, Spread spectrum multiple access autocorrelation, 67 bandpass stationary, 78-81 QPSK (SQPSK), 124-128 Standard array, 430 State diagram, 496 Staggered Successive interference Specular component, 841 inner product, 26 M-ary orthogonal, 108-1 multiamplitude, 98 multidimensional, 108-114 multiphase, 101-103 orthogonal, 30 random, 66-8 SSB, 100 Subscriber local loop, 756 by precoding, 134, 611-612 Spectrum of CPFSK and CPM, 138-147 of digital signals, 131-148 of linear modulation, 133-135 Square-root factorization, 715 SQPSK, 124-128 Sublattice, of signals with memory, representation of, 28, 95 theorem, 336 Shannon biorthogonal, 13 763-765 Square-law detection, 216 algorithm, 691-701 Spectral shaping uncoded DS, 775 Spread spectrum system model, Steepest-descent (gradient) correlation function, 835 antipodal, 101 Set partitioning labeling, STBC, 1013 1016-1019 1020-1021 Spaced-frequency, spaced-time Scrambling sequence, 997 synchronization of, 815-822 time-hopped (TH), 814 memoryless (DMS), 332 discrete stationary, 337 encoding, 339-354 discrete memoryless, 339 Huffman, 342-346 Lempel-Ziv, 346-348 Source coding, 1, 339-354 Space-time codes, 1006-1021 concatenated, 1020-1021 differential STBC, 1014 orthogonal STBC, 1011-1013 trellis, with memory, 114 424 discrete orthogonal, 108 774 processing gain, 773-774 Soft decision decoding, block codes) ( Schlafli lattice, first bit, binary, 331 Residuals, 718 codes) Per analog, 330 based on binary codes, 113 codes ( see Reed-Solomon 806-812 Signal space diversity, 928 Signaling with partial-band interference, hybrid combinations, 814-815 Signal constellation, 28 176, 192 block hopping, 803 performance of, 804—806 Skin depth, Source 330-354 Reliable communication, 207, 361 factor, decoder, 545 Skew-Hermitian matrix, 65 607-608 Regenerative repeaters, 260-26 Reliability function, (soft-input-soft-output) per symbol, 192 Signal-to-noise ratio (SNR), References, 1109 SISO SNR, 176 Signal space representation, 34 473 802-804 981, 1087 602 for channels with distortion, for frequency-hopped (FH), singular values, 974, 619-623 for band-limited channel, Recursive systematic convolutional 869-871,997-1000 981, 1087 Signal design, 602-611, RLS, 715 RLS Kalman, 711-714 RLS lattice, 716-721 for multipath channels, right singular vectors, excision of narrowband interference, 791-796 for low-probability of intercept (LPI), 778-779 815-822 with tau-dither loop, 820 with delay-locked loop, 819 sequential search, sliding correlator, 816 Syndrome, 430, 467 polynomial, 458 Systematic block codes, 412 Systematic convolutional codes, Systematic cyclic codes, 453 1 1 1 1150 Index bounds 56-63 Chernov bound, 58-63, 866-868 Transform domain generator Markov bound, Transpose of a matrix, 28 Tail probability 56, 57 Tanner graph 558-561 for low density parity check codes, TATS 569-570 (tactical matrix, 495 Tree diagram, 496 Trellis, 116, transmission 243,496 Undetected 571-589 for, 583 encoders 929-935 577 Telegraphy, 12 for fading channels, Telephone channels, 598-601 Ternary Golay code, 442 free Euclidean distance, Theorem subset decoding, 578 central limit, 63 336 Mercer, 77 noisy channel coding, 361 rate-distortion, 35 Shannon’s second, 361 Shannon’s 35 Wiener-Khinchin, 67 Thermal third, noise, 3, 69 Threshold decoder, 531 Time Time diversity, 85 1030 capacity of, 1032-1033 Timing phase, 315 Toeplitz matrix, 700 Tomlinson-Harashima precoding, 668-669 Transfer function of convolutional codes, 500 745, 902 error, in time, Waveform 430 Unequal error protection, 523 Uniform interleaver, 480-481 Uniform random variable, 41 Union bound, 182-186 Uniquely decodable source coding, 339 Universal source coding, 347 581-582 586-589 Trellis diagram, 496 Triangle inequality, 29-30 Turbo cliff region, 553 Turbo codes, 548-558 Variable-length source coding, 339 turbo coded, Variance, 40 Varshamov-Gilbert bound, 443 Vector space, 28-30, 410-41 Vectors error floor, 551 linearly independent, EXIT norm, 28 charts, 555 for fading channels, 1020-1021 interleaver gain, division multiple access (TDM A), Water-filling interpretation, tables of coding gains for, dimensionality, 227 lossless source coding, 572 set partitioning, Waterfall region, 553 channels, Trellis-coded modulation, system), 813 Underspread fading channels, 899 Underwater acoustic iterative orthonormal, 28 552 multiplicity, algorithm, 548 549 turbo cliff region, 553 553 Turbo TCM, 586-589 Turbo decoding algorithm, 552 Turbo equalization, 671-673 Typical sequences, 336 waterfall region, function), Weight Weight path memory distribution polynomial Weight enumeration function, 415 Weight of a codeword, 41 Welch bound, 801 White processes, 69 Whitened matched filter (WMF), 627 Whitening filter, 167, 627 Wide-sense stationary process, 67 Wiener-Khinchin theorem, 67 Wireless electromagnetic channels, Wireline channels, truncation, 246,513 survivor, 415 distribution, 41 (WEP), 415 Viterbi algorithm, 243-246, 510-513 channels, 358 WEF (weight enumeration orthogonal, 28 decoding, 552 Max-Log-APP 29 912 Word error probability, WSS (side-sense stationary), 67 417 244-245, 512 survivor path, 245, 512 Yule- Walker equations, 716 Voltage-controlled oscillator (VCO), 298 Voronoi region of a lattice point, 232 Z transform, 626 Zero-forcing equalizer, 642 Zero-forcing filter, 642 ... Transactions on Communications, vol 49, pp 1727-1737 Library of Congress Cataloging-in-Publication Data Proakis, John G Digital communications p / John G Proakis, Masoud Salehi — 5th ed cm Includes... Higher Education DIGITAL COMMUNICATIONS, FIFTH EDITION Published by McGraw-Hill, a business unit of The McGraw-Hill Companies, Americas, New York, NY 10020 Copyright reserved Previous editions in.. .Digital Communications Fifth Edition John G Proakis Professor Emeritus Northeastern University , Department of Electrical