Digital communications john g proakis, masoud salehi 5th edition

www.elsolucionario.org Proakis-27466 pro57166˙fm September 26, 2007 12:35 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 www.elsolucionario.org Proakis-27466 pro57166˙fm September 26, 2007 12:35 DIGITAL COMMUNICATIONS, FIFTH EDITION Published by McGraw-Hill, a business unit of The McGraw-Hill Companies, Inc., 1221 Avenue of the Americas, New York, NY 10020 Copyright © 2008 by The McGraw-Hill Companies, Inc All rights reserved Previous editions © 2001 and 1995 No part of this publication may be reproduced or distributed in any form or by any means, or stored in a database or retrieval system, without the prior written consent of The McGraw-Hill Companies, 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 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 Typeface: 10.5/12 Times Roman 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 / John G Proakis, Masoud Salehi.—5th ed p cm Includes index ISBN 978–0–07–295716–7—ISBN 0–07–295716–6 (hbk : alk paper) Digital communications I Salehi, Masoud II Title TK5103.7.P76 2008 621.382—dc22 2007036509 www.mhhe.com www.elsolucionario.org Proakis-27466 pro57166˙fm September 26, 2007 12:35 D E D I C A T I O N To Felia, George, and Elena John G Proakis To Fariba, Omid, Sina, and My Parents Masoud Salehi www.elsolucionario.org iii Proakis-27466 pro57166˙fm September 26, 2007 12:35 www.elsolucionario.org Proakis-27466 pro57166˙fm September 26, 2007 12:35 B R I E F Preface Chapter Chapter Chapter Chapter Chapter Chapter Chapter Chapter Chapter Chapter 10 Chapter 11 Chapter 12 Chapter 13 Chapter 14 Chapter 15 Chapter 16 C O N T E N T S xvi Introduction Deterministic and Random Signal Analysis Digital Modulation Schemes Optimum Receivers for AWGN Channels Carrier and Symbol Synchronization An Introduction to Information Theory Linear Block Codes Trellis and Graph Based Codes Digital Communication Through Band-Limited Channels Adaptive Equalization Multichannel and Multicarrier Systems Spread Spectrum Signals for Digital Communications Fading Channels I: Characterization and Signaling Fading Channels II: Capacity and Coding Multiple-Antenna Systems Multiuser Communications Appendices Appendix A Matrices Appendix B Error Probability for Multichannel Binary Signals Appendix C Error Probabilities for Adaptive Reception of M-Phase Signals Appendix D Square Root Factorization References and Bibliography Index 17 95 160 290 330 400 491 597 689 737 762 830 899 966 1028 1085 1090 1096 1107 1109 1142 www.elsolucionario.org v Proakis-27466 pro57166˙fm September 26, 2007 12:35 C O N T E N T S Preface xvi Chapter Introduction 1.1 1.2 1.3 1.4 1.5 1.6 Elements of a Digital Communication System Communication Channels and Their Characteristics Mathematical Models for Communication Channels A Historical Perspective in the Development of Digital Communications Overview of the Book Bibliographical Notes and References Chapter Deterministic and Random Signal Analysis 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 vi Bandpass and Lowpass Signal Representation 2.1–1 Bandpass and Lowpass Signals / 2.1–2 Lowpass Equivalent of Bandpass Signals / 2.1–3 Energy Considerations / 2.1–4 Lowpass Equivalent of a Bandpass System Signal Space Representation of Waveforms 2.2–1 Vector Space Concepts / 2.2–2 Signal Space Concepts / 2.2–3 Orthogonal Expansions of Signals / 2.2–4 Gram-Schmidt Procedure Some Useful Random Variables Bounds on Tail Probabilities Limit Theorems for Sums of Random Variables Complex Random Variables 2.6–1 Complex Random Vectors Random Processes 2.7–1 Wide-Sense Stationary Random Processes / 2.7–2 Cyclostationary Random Processes / 2.7–3 Proper and Circular Random Processes / 2.7–4 Markov Chains Series Expansion of Random Processes 2.8–1 Sampling Theorem for Band-Limited Random Processes / 2.8–2 The Karhunen-Lo`eve Expansion Bandpass and Lowpass Random Processes www.elsolucionario.org 1 10 12 15 15 17 18 28 40 56 63 63 66 74 78 Proakis-27466 pro57166˙fm September 26, 2007 12:35 Contents vii 2.10 Bibliographical Notes and References Problems Chapter Digital Modulation Schemes 3.1 3.2 3.3 3.4 3.5 Representation of Digitally Modulated Signals Memoryless Modulation Methods 3.2–1 Pulse Amplitude Modulation (PAM) / 3.2–2 Phase Modulation / 3.2–3 Quadrature Amplitude Modulation / 3.2–4 Multidimensional Signaling Signaling Schemes with Memory 3.3–1 Continuous-Phase Frequency-Shift Keying (CPFSK) / 3.3–2 Continuous-Phase Modulation (CPM) Power Spectrum of Digitally Modulated Signals 3.4–1 Power Spectral Density of a Digitally Modulated Signal with Memory / 3.4–2 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 Bibliographical Notes and References Problems Chapter Optimum Receivers for AWGN Channels 4.1 4.2 4.3 4.4 Waveform and Vector Channel Models 4.1–1 Optimal Detection for a General Vector Channel Waveform and Vector AWGN Channels 4.2–1 Optimal Detection for the Vector AWGN Channel / 4.2–2 Implementation of the Optimal Receiver for AWGN Channels / 4.2–3 A Union Bound on the Probability of Error of Maximum Likelihood Detection Optimal Detection and Error Probability for Band-Limited Signaling 4.3–1 Optimal Detection and Error Probability for ASK or PAM Signaling / 4.3–2 Optimal Detection and Error Probability for PSK Signaling / 4.3–3 Optimal Detection and Error Probability for QAM Signaling / 4.3–4 Demodulation and Detection Optimal Detection and Error Probability for Power-Limited Signaling 4.4–1 Optimal Detection and Error Probability for Orthogonal Signaling / 4.4–2 Optimal Detection and Error Probability for Biorthogonal Signaling / 4.4–3 Optimal Detection and Error Probability for Simplex Signaling www.elsolucionario.org 82 82 95 95 97 114 131 148 148 160 160 167 188 203 Proakis-27466 pro57166˙fm September 26, 2007 12:35 viii Contents 4.5 Optimal Detection in Presence of Uncertainty: Noncoherent Detection 4.5–1 Noncoherent Detection of Carrier Modulated 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 Signals / 4.5–5 Differential PSK (DPSK) 4.6 A Comparison of Digital Signaling Methods 4.6–1 Bandwidth and Dimensionality 4.7 Lattices and Constellations Based on Lattices 4.7–1 An Introduction to Lattices / 4.7–2 Signal Constellations from Lattices 4.8 Detection of Signaling Schemes with Memory 4.8–1 The Maximum Likelihood Sequence Detector 4.9 Optimum Receiver for CPM Signals 4.9–1 Optimum Demodulation and Detection of CPM / 4.9–2 Performance of CPM Signals / 4.9–3 Suboptimum Demodulation and Detection of CPM Signals 4.10 Performance Analysis for Wireline and Radio Communication Systems 4.10–1 Regenerative Repeaters / 4.10–2 Link Budget Analysis in Radio Communication Systems 4.11 Bibliographical Notes and References Problems Chapter Carrier and Symbol Synchronization 5.1 5.2 5.3 5.4 5.5 5.6 Signal Parameter Estimation 5.1–1 The Likelihood Function / 5.1–2 Carrier Recovery and Symbol Synchronization in Signal Demodulation Carrier Phase Estimation 5.2–1 Maximum-Likelihood Carrier Phase Estimation / 5.2–2 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 Symbol Timing Estimation 5.3–1 Maximum-Likelihood Timing Estimation / 5.3–2 Non-Decision-Directed Timing Estimation Joint Estimation of Carrier Phase and Symbol Timing Performance Characteristics of ML Estimators Bibliographical Notes and References Problems Chapter An Introduction to Information Theory 6.1 Mathematical Models for Information Sources www.elsolucionario.org 210 226 230 242 246 259 265 266 290 290 295 315 321 323 326 327 330 331 Proakis-27466 pro57166˙fm September 26, 2007 12:35 Contents ix 6.2 6.3 6.4 6.5 6.6 6.7 6.8 6.9 A Logarithmic Measure of Information Lossless Coding of Information Sources 6.3–1 The Lossless Source Coding Theorem / 6.3–2 Lossless Coding Algorithms Lossy Data Compression 6.4–1 Entropy and Mutual Information for Continuous Random Variables / 6.4–2 The Rate Distortion Function Channel Models and Channel Capacity 6.5–1 Channel Models / 6.5–2 Channel Capacity Achieving Channel Capacity with Orthogonal Signals The Channel Reliability Function The Channel Cutoff Rate 6.8–1 Bhattacharyya and Chernov Bounds / 6.8–2 Random Coding Bibliographical Notes and References Problems Chapter Linear Block Codes 7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8 Basic Definitions 7.1–1 The Structure of Finite Fields / 7.1–2 Vector Spaces General Properties of Linear Block Codes 7.2–1 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 Block Codes Some Specific Linear Block Codes 7.3–1 Repetition Codes / 7.3–2 Hamming Codes / 7.3–3 Maximum-Length Codes / 7.3–4 Reed-Muller Codes / 7.3–5 Hadamard Codes / 7.3–6 Golay Codes Optimum Soft Decision Decoding of Linear Block Codes Hard Decision Decoding of Linear Block Codes 7.5–1 Error Detection and Error Correction Capability of Block Codes / 7.5–2 Block and Bit Error Probability for Hard Decision Decoding Comparison of Performance between Hard Decision and Soft Decision Decoding Bounds on Minimum Distance of Linear Block Codes 7.7–1 Singleton Bound / 7.7–2 Hamming Bound / 7.7–3 Plotkin Bound / 7.7–4 Elias Bound / 7.7–5 McEliece-Rodemich-Rumsey-Welch (MRRW) Bound / 7.7–6 Varshamov-Gilbert Bound Modified Linear Block Codes 7.8–1 Shortening and Lengthening / 7.8–2 Puncturing and Extending / 7.8–3 Expurgation and Augmentation www.elsolucionario.org 332 335 348 354 367 369 371 380 381 400 401 411 420 424 428 436 440 445 Proakis-27466 book September 26, 2007 23:27 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 (1987) “Trellis-Coded Modulation with Redundant Signal Sets, Parts I and II,” IEEE Commun Mag., vol 25, pp 5–21, February Ungerboeck, G., and Csajka, I (1976) “On Improving Data-Link Performance by Increasing the Channel Alphabet and Introducing Sequence Coding,” 1976 Int Conf Inform Theory, Ronneby, Sweden, June Vaidyanathan, P P (1993) Multirate Systems and Filter Banks, Prentice-Hall, Englewood Cliffs, NJ Van Etten, W (1975) “An Optimum Linear Receiver for Multiple Channel Digital Transmission Systems,” IEEE Trans Commun., vol COM-23, pp 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January Zhang, X., and Brady, D (1993) “Soft-Decision Multistage Detection of Asynchronous AWGN Channels,” Proc 31st Allerton Conf on Commun., Contr., Comp Allerton, IL, October Zhou, K., and Proakis, J G (1988) “Coded Reduced-Bandwidth QAM with Decision-Feedback Equalization,” Conf Rec IEEE Int Conf Commun., Philadelphia, PA, pp 12.6.1–12.6.5, June Zhou, K., Proakis, J G., and Ling, F (1990) “Decision-Feedback Equalization of TimeDispersive Channels with Coded Modulation,” IEEE Trans Commun., vol COM-38, pp 18–24 January Zhu, X., and Murch, R D (2002) “Performance Analysis of Maximum Likelihood Detection in a MIMO Antenna System,” IEEE Trans Commun., vol 50, pp 187–191, February Zigangirov, K S (1966) “Some Sequential Decoding Procedures,” Probl Peredach Inform., vol 2, pp 13–25 Ziv, J (1985) “Universal Quantization,” IEEE Trans Inform Theory, vol 31, pp 344–347 Ziv, J., and Lempel, A (1977) “A Universal Algorithm for Sequential Data Compression,” IEEE Trans Inform Theory, vol IT-23, pp 337–343 Ziv, J., and Lempel, A (1978) “Compression of Individual Sequences via Variable-Rate Coding,” IEEE Trans Inform Theory, vol IT-24, pp 530–536 Zvonar, Z., and Brady, D (1995) “Differentially Coherent Multiuser Detection in Asynchronous CDMA Flat Rayleigh Fading Channels,” IEEE Trans Commun., vol COM-43, pp 1252–1255, February/March/April www.elsolucionario.org Proakis-27466 pro57166˙ind October 2, 2007 0:57 I N D E X a posteriori L-values, 545 probabilities, 162 a priori L-values, 552 probabilities, 162 Abelian group, 403 cyclic subgroup, 482 Adaptive equalization, 689 Adaptive equalizers, (See also Equalizers), 689–731 accelerating convergence of LMS, 700–701 blind, 721–731 decision-feedback, 705–706 fractionally-spaced, 702–703 linear, 689–702 maximum likelihood sequence estimator, 703–705, 721–725 reduced state, 708–710 Affine transformation, 66 Alamouti code, 1007–1011 Algorithm BCJR, 541 belief propagation, 570 Berlekamp-Massey, 469 constant-modulus, 726-730 FFT, 749–752 Godard, 726–730 Levinson-Durbin, 692, 716 LLL, 1067 LMS (MSE), 691–693 recursive least-squares (RLS), 710–714 RLS (fast), 715 RLS (Kalman), 711–714 RLS lattice, 718 RLS square-root, 715 soft-output Viterbi algorithm (SOVA), 532 stochastic gradient, 691–693, 725–730 sum-product, 558 tap-leakage, 702 Viterbi, 243–246, 510–513 zero-forcing, 690–691 Aliasing, 75 ALOHA protocols, 1069–1073 slotted, 1070 unslotted, 1070 ALOHA systems, 1069–1073 throughput, 1071–1073 Amplitude distortion, 598 Amplitude-shift keying (ASK), 99 Analytic signal, 21 1142 Antenna beamwidth, 263 effective area, 262 effective radiated power, 262 illumination efficiency factor, 262 multiple antenna systems, 996–1021 Antipodal signals, 101 ARQ (automatic repeat request), 432 ASK, 99 error probability, 189 Asymmetric digital subscriber line (ADSL), 756 Asymptotic coding gain, 426 Augmented codes, 447 Autocorrelation function, 67 for in-phase component, 80 for lowpass process, 81 for quadrature component, 80 Automatic gain control (AGC), 294 Automatic repeat request (ARQ), 432 Average energy per bit, 97 Average signal energy, 97 AWGN channel model, 10 Backward recursion, 543 Band-limited channels (See also Channels), 597–598 characterization of, 598–601 Bandlimited random processes, 75 Bandpass processes, 79 in-phase component, 79 lowpass equivalent, 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, NRZ, 115 NRZI, 115 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 BCJR algorithm, 541 backward recursion, 543 forward recursion, 543 SISO decoder, 545 soft output, 544 Belief propagation algorithm, 570 Berlekamp-Massey algorithm, 469 Bernoulli random variable, 40 Bessel function modified, 47, 213 BEXPERM, 950–951 Bhatacharyya parameter, 373 for binary input channel, 376 Bias term, 171 Bibliography, 1109 BICM (bit-interleaved coded modulation), 936 Binary antipodal signaling, 101 error probability, 174 optimal detection, 173 Binary entropy function, 334 Binary equiprobable signaling error probability, 174 Binary expurgated permutation modulation (BEXPERM), 950–951 Binary FSK error probability for noncoherent detection, 218 Binary orthogonal signaling, error probability, 176 optimal detection, 176 Binary modulation, Binary PSK (BPSK), 102 Binary Symmetric Channel (BSC), 355 Binomial random variable, 41 Biorthogonal signaling, 111 error probability, 208 optimal detection, 207 Bipartite graph, 559 Bit, Bit error probability, 164, 417 BPSK, 192 PSK, 197 Bit interval, 97 Bit rate, 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 www.elsolucionario.org maximum-likelihood algorithms, 721–725 stochastic gradient algorithms, 725–730 with second-order moments, 730–731 Block error probability, 417 Block interleaver, 476 Boltzmann’s constant, 69 Bounds Chernov, 58, 373, 866–868, 923 Elias, 443 Hamming, 441 McEliece-Rodemich-RumseyWelch (MRRW), 443 Plotkin, 442 Singleton, 440 sphere packing, 441 Varshamov-Gilbert, 443 Welch, 801 BPSK, 102 bit error probability, 192 Broadcast channels, 1053–1068 linear precoding for, 1055–1058 MMSE, 1057 ZF, 1057 nonlinear precoding for, 1058–1068 lattice reduction, 1065–1068 QR decomposition, 1058–1062 vector precoding, 1062–1065 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 Burton codes, 475 Capacity, 13, 360 ε-outage, 907 achieved by orthogonal signaling, 367 bandlimited 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 Proakis-27466 pro57166˙ind October 2, 2007 0:57 Index of MIMO channels, 981–991 of multicarrier system, 744–745 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 Carrier recovery, 290–295 Carrier sense multiple access (CSMA), 1073 protocols, 1074–1077 nonpersistent, 1074 1-persistent, 1074 p-persistent, 1074–1077 Catastrophic convolutional codes, 509 Cauchy-Schwarz inequality, 29–30 Central frequency, 21 Central limit theorem (CLT), 63 CFM (constellation figure of merit), 238 Chain rule for entropies, 335 Channel access protocol, 1069 acoustic, additive noise, 10 additive Gaussian noise, 10 AWGN, 160 band-limited, 597–598 binary symmetric (BSC), 355 broadcast, 1053–1068 capacity, 13, 360 of MIMO channels, 981–991 coherence bandwidth, 835 coherence time, 836 cutoff rate (R0 ), 527, 787–791 for fading channels, 957–960 discrete-input continuous-output, 357 discrete-memoryless, 356 discrete-time AWGN, 358 discrete-time model, 625–628 distortion, 598–601 amplitude, 598 envelope delay, 598–599 frequency offset, 600 impulse noise, 601 nonlinear, 600 peak, 641 phase jitter, 600 squared-error, 645–646 thermal noise, 600 Doppler power spectrum, 836 Doppler spread, 836 encoder, code rate, 2, 402 codeword, 2, 372, 401 envelope delay, 598–599 1143 fading multipath, characterization of, 831–833 correlation functions for, 833–839 impulse response, 832 models for, 839–843 transfer function, 834 fiber optic, finite-state, 903 frequency nonselective, 836, 844 digital signaling over, 844 frequency selective, 836, 844 digital signaling over, 869–889 error rate for, 872–880 RAKE demodulator for, 871–872 tap weight estimation of, 876–877 tapped delay line model of, 869–871 frequency offset, 600 impulse noise, 601 memoryless, 355 microwave LOS, models for, additive noise, 10 binary symmetric, 355 COST 207, 840 discrete memoryless, 356 discrete-time, 358 for multiuser channels, 1037–1038 Hata, 843 Jakes’ model, 838–839 linear filter, 11 linear, time-variant filter, 11–12, 832 MIMO channels, 966 slowly fading, 845 statistical, 839–843 waveform, 358 multipath spread, 834 Nakagami fading, 841 nonlinear, 600 overspread, 845 phase jitter, 600 probability transition matrix, 357 Rayleigh fading, 833 Binary signaling over, 847–849 coded waveforms for, 942–956 coding for, 899–960 cutoff rate for, 957–960 frequency nonselective, 846–849 M-ary orthogonal signaling over, 861–865 Multiphase signaling over, 859–861 reliability function, 369 state information (CSI), 904, 957–960, 1054 Ricean fading, 833 scattering function, 837 spread factor, 845 table, 845 squared-error, 645–646 storage, symmetric, 363 thermal noise, 3, 69, 600 throughput, 1070 underspread, 845 underwater acoustic, waveform, 358 wireless, 5–9 wireline, 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 for Rayleigh fading channel, 866–868 pairwise error probability, 1014–1016 Chernov parameter, 373 χ random variable, 45 Circular random vectors, 66 Clairvoyant estimate, 1098 CLT (central limit theorem), 63 Code division multiple access (CDMA), 780–784 asymptotic efficiency, 1052 asynchronous, 1039–1042 capacity of, 1033–1034 digital cellular, 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, 1048–1049 performance, 1050–1053 single user, 1042–1043 successive interference cancellation, 1047–1048 synchronous, 1038–1039 Code rate, Codeword, Coded modulation, bit-interleaved, 936 trellis, 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 www.elsolucionario.org coding gain, 426, 533 concatenated, 479–480, 953–956, 1020–1021 conditional weight enumeration function, 416 constant weight, 949–953 convolutional, 491–548, 946–948 coset, 430 CRC, 453 cyclic, 447 cyclic Golay, 460 cyclic Hamming, 460 diversity order, 927 dual, 412 effective distance, 927 equivalent, 412 expurgated, 447, 950–951 extended, 447 extended Golay, 424 Fire, 475 fixed weight, 411, 949–953 generator matrix, 412 Golay, 424, 460 Hadamard, 423, 951–953 Hamming, 420, 460 Hamming distance, 414 inner, 479 input-output weight enumeration function, 416 instantaneous, 340 lengthened, 446 linear block, 411 low density parity check (LDPC), 569 maximum distance separable, 440 maximum length, 421 maximum-length shift register, 461 MDS (maximum-distance separable), 440 minimum distance, 414 minimum weight, 414 outer, 479 parallel concatenated block, 481 parity check matrix, 412 perfect, 434, 442 product, 477 punctured, 446, 516–517, 521–523 quasi-perfect, 435 rate, Reed-Muller (RM), 421 Reed-Solomon (RS), 471 serially concatenated block, 480 shortened, 445 shortened cyclic, 452 standard array, 430 syndrome, 430, 467 systematic, 412 ternary Golay, 442 turbo, 548 undetected error, 430 uniquely decodable, 339 weight distribution, 411 weight distribution polynomial, 415 Proakis-27466 pro57166˙ind October 2, 2007 0:57 1144 Codes (continued) weight enumeration function, 415 word error probability, 417 Codeword, 372, 401 weight, 411 Coding diversity order, 927 effective distance, 927 for MIMO channels, 1001–1021 for Rayleigh fading channel, 942–960 concatenated, 953–956 constant-weight codes, 949–953 convolutional codes, 946–948 cutoff rate, 371–380, 516, 527, 787–791, 957–960 linear block codes, 943–946 space-time codes, 1006–1021 trellis codes, 1016–1019 Gray, 100 Huffman, 342–346 in the frequency domain, 942–960 Coding gain, 533 of a lattice, 233 Complementary error function, 44 Complementary gamma function, 911 Complete set of signals, 32 Complex envelope, 22 Complex random processes covariance, 71 pseudocovariance, 71 Complex random variables, 63 Complex random vectors, 64 covariance matrix, 64 pseudocovariance matrix, 64 Complex signals bandwidth, 20 Concatenated codes, 479–480, 540–541, 953–956, 1020–1021 inner code, 479, 540 outer code, 479, 540 Concave function, 386 Conditional entropy, 334 Conditional weight enumeration function, 416 Confluent hypergeometric function, 49 Conjugacy class, 409 Conjugate element, 409 Constant weight codes, 411, 949–953 Constellation, 34 figure of merit, 238 minimum distance, 185 Constellation figure of merit (CFM), 238 Constraint length, 96, 491 Continuous-phase frequency-shift keying (CPFSK), 116–118 performance of, 116 Index power density spectrum of, 138–145 representation of, 116–117 Continuous-phase modulation (CPM), 118–123, 243–259 demodulation, 243–258 maximum-likelihood sequence estimation, 243–246 metric computations, 249–251 multi-h, 257–258 performance of, 251–258 suboptimum, 258–259 full response, 118 linear representation of, 128–130 minimum-shift keying (MSK), 123–124 modulation index, 118, 254 multi-h, 118, 257–258 partial response, 118 phase cylinder, 122 phase state, 248 phase trees of, 120 power spectrum of, 138–142, 145–148 representation of, 118–123 state trellis, 249 trellis of, 120 Continuous-wave (CW) interference, 772 Convergence almost everywhere (a.e.), 63 almost surely (a.s), 63 in distribution, 63 Convex functions, 386 Convolutional codes, 491–548 applications, 532–537 catastrophic, 509 constraint length, 491 concatenated, 540–541 decoding, Fano algorithm, 525 feedback, 529–531 maximum a posteriori, 541–548 sequential, 525–528 stack algorithm, 528–529 Viterbi, 243–246 distance properties of, 516 dual-k, 537–540 equivalent encoders, 506 first-event error, 502 first-event error probability, 513 hard-decision decoding, 945–946 invertibility conditions, 508 invertible, 508 maximum free distance, 516 nonbinary, 499, 504 parallel concatenated (PCCC), 548 performance on AGWN channel, 513–516 performance on BSC, 513–516 performance on Rayleigh fading channel, 946–948 punctured, 516–517, 521–523 rate, 491 rate-compatible punctured, 523–525 recursive systematic (RSCC), 507–508 soft-decision decoding, 943–944 state diagram, 496 systematic, 505 table of generators for maximum free distance, 517–520 transfer function, 500 tree diagram, 496 trellis diagram, 496 Viterbi algorithm, 510 Convolutional interleavers, 476 Correlation metric, 173 Correlation receiver, 177 Correlative state, 248 Correlative state vector, 248 Coset, 430, 483 Coset leader, 430 Coset representative, 584 Covariance for complex random processes, 71 CPFSK, 116–118, 138–145 modulation index, 118 peak frequency deviation, 117 power spectral density, 138–145 CPM, (See Continuous-Phase Modulation), CRC codes, 453 Cross spectral density, 67 in-phase and quadrature components, 80 Cross-correlation coefficient, 26 Crosscorrelation function, 67 in-phase and quadrature components, 80 CSD (cross spectral density), 67 CSI (channel state information), 904, 957–960, 1054 Cutoff rate (R0 ), 371–380, 516, 527 comparison with channel capacity, 377–380 for fading channels, 957–960 for pulsed interference, 787–791 CWEF (conditional weight enumeration function), 416 Cyclic codes, 447 CRC, 453 decoding, 458 encoding, 455 generator polynomial, 448 Golay, 460 Hamming, 460 message polynomial, 449 parity check polynomial, 450 shortened, 452 systematic, 453 Cyclic equalization, 694 Cyclic redundancy check (CRC) codes, 453 Cyclic subgroup, 482 Cyclostationary random process, 70 www.elsolucionario.org D transform, 493 Data compression, 1, 335–354 lossless, 335–348 lossy, 348–354 Decision-feedback equalizer (see Equalizers, decision-feedback), 661–665, 705–706 Decision region, 163 Decoding, Berlekamp-Massey, 469 Fano algorithm, 525 feedback, 529–531 hard decision, 428 iterative, 478, 548 Meggit, 460 sequential, 525–528 soft decision, 424 stack algorithm, 528–529 turbo, 552 LDPC, 570 Viterbi algorithm, 243–244, Degrees of freedom, 75 Delay distortion, 598–599 Delay power spectrum, 834 Demodulation, 24 Demodulation and detection, 201 carrier recovery for, (See Carrier phase estimation) coherent comparison of, 226–229 of binary signals, 173–177 of biorthogonal signals, 207–209 of orthogonal signal, 203–207 of PAM signals, 188–190 of PSK signals, 190–195 of QAM signals, 196–200 optimum, 201–203 correlation type, 177–178 of CPM, 243–258 performance, 251–258 for intersymbol interference, 623–628 matched filter-type, 178–182 maximum likelihood, 163 maximum-likelihood sequence, 623–628 noncoherent, 210–224 of binary signals, 219–221 of M-ary orthogonal signals, 216–219, 741–743, 861–865 multichannel,737–743 optimum, 212–214 of OFDM, 749 Density of a lattice, 236 Detector decorrelating, 1043–1045 envelope, 214 inverse channel (ICD), 970 maximum-likelihood (MLD), 970 MMSE, 970, 1046–1047 minimum distance, 171 nearest neighbor, 171 nonlinear, 973–974 optimal noncoherent, 212–214 Proakis-27466 pro57166˙ind October 2, 2007 0:57 Index single user, 1042–1043 sphere, 973 Differential encoding, 115 Differential entropy, 349 Differential phase-shift keying (DPSK), 221 Differentially encoded PSK, 195 Digamma function, 909 Digital communication system model, 1–3 Digital modulation, 95 Digital modulator, Digital signaling, 95 Dimensionality theorem, 227 Direct sequence (See Spread spectrum signals) Dirty paper precoding, 1054 Discrete memoryless source (DMS), 331 Discrete-memoryless channel (DMC), 356 Discrete-time AWGN, 358 Discrete-time AWGN channel capacity, 365 Discrete-time binary-input channel capacity, 362 Distance (see Block codes; Convolutional codes) effective, 927 enumerator function, 185 Euclidean, 35 Hamming, 414 metric, 173 product, 925 Distortion (see Channel distortion) Hamming, 354 squared-error, 350 Distortion-rate function, 352 Diversity antenna, 851 frequency, 850 gain, 996–997 order, 852, 927 performance of, 851–859 polarization, 851 RAKE, 851 signal space, 928 time, 851 DMC (see Discret Memoryless Channel) DMS (see Discret Memoryless Source) Double-sideband (DSB) PAM, 100 DPSK, 221 error probability, 223 DSB, 100 Dual code, 412 Dual-k codes, 537–540 Duobinary signal, 610 ε-outage capacity, 907 Early-late gate synchronizer, 318–321 Effective antenna area, 262 Effective distance, 927 1145 Effective radiated power, 260–261 Eigenvalue, 29, 1086 Eigenvector, 29, 1086 Elias bound, 443 Encoder catastrophic, 509 convolutional, 402, 492 for cyclic codes, 455 inverse, 508 turbo, 549 Encoding (see Block codes; Convolutional codes) Energy, 25 average, 97 per bit, average, 97 Entropy, 333 chain rule, 335 conditional, 334 differential, 349 joint, 334 Entropy rate, 337 Envelope detection, 214 Envelope of a signal, 23 Equivalent codes, 412 Equivalent convolutional encoders, 506 Equalizers (See also Adaptive equalizers) at transmitter, 668–669 decision-feedback, 661–665, 705–706 adaptive, 689–731 examples of performance, 662–665 for MIMO channels, 979–981 of trellis-coded signals, 706–708 minimum MSE, 663 predictive form, 665–667 linear, 640–649 adaptive, 689–693 baseband, 658–659 convergence of MSE algorithm, 695–696 cyclic equalization, 694 error probability, 651–655 examples of performance, 651–655 excess MSE, 696–697 for MIMO channels, 975–979 fractionally spaced, 655–658 LMS (MSE) algorithm, 691–693 mean-square error (MSE) criterion, 645–655 minimum MSE, 647–648 output SNR for, 648 passband, 658–659 peak distortion, 641 peak distortion criterion, 641–645 phase-splitting, 659 zero-forcing, 642 iterative equalization/decoding, 671–673 maximum a posteriority probability (MAP), 291 maximum –likelihood sequence estimation, 623–625, reduced-state, 669–671 self-recovering (blind), 721–731 with trellis-coded modulation, 706–708 using the Viterbi algorithm, 628–631 channel estimator for, 703–705 performance of, 631–639 reduced complexity, 669–671 reduced-state, 669–671 erfc, 44 Ergodic capacity, 900, 905–906, 985–987 Error correction, 900 Error detection, 432 Error floor, 551 Error probability, 16QAM, 186, 200 ASK, 189 binary antipodal signaling, 174 binary equiprobable signaling, 174 binary orthogonal signaling, 176 biorthogonal signaling, 208 bit, 164, 417 block, 417 DPSK, 223 for hard-decision decoding, 945–946 for soft-decision decoding, 943–944 FSK, 205 lower bound to, 186 M-ary PSK, 190–194 for Rayleigh fading, 859–861, 1100–1103 for Ricean fading, 1104–1105 for AWGN channel, 1106 message, 164 multichannel binary symbols, 739–741, 1090–1095 orthogonal signaling, 205 noncoherent detection, 216 pairwise, 184, 372, 418, 922, 928 PAM, 189 QAM, 198 QPSK, 199 symbol, 164 union bound, 182 word, 417 Estimate biased, 323 clairvoyant, 1098 consistent, 324 efficient, 324 pilot signal, 1098 unbiased, 323 Estimate of phase (See Carrier phase estimation) Estimation maximum-likelihood, 291, 296–298, 321–322 www.elsolucionario.org of carrier phase, 295–315 of signal parameters, 290 of symbol timing, 290 of symbol timing and carrier phase, 321–322 performance of, 323–326 Euclidean distance, 35 Euler’s constant, 909 Excess bandwidth, 607 Excess MSE, 696–697 Excision of narrowband interference, 791–796 linear, 792–796 nonlinear, 796 EXIT charts, 555 Exponential random variable, 46 Expurgated codes, 447, 950–951 Extended codes, 447 Extended Golay code, 424 Extension field, 404 Extrinsic information, 552 Extrinsic L-value, 552 Eye pattern, 603 Factor Graphs, 558 Fading, 8, 830–844 figure, 52 Fading channels (See also Channels), 830–890 coding for, 899–960 ergodic capacity, 900, 905–906, 985–987 outage capacity, 900, 906, 907, 900, 987–990 propagation models for, 842–843 Feedback decoding, 529–531 FH spread spectrum signals (see Spread spectrum signals), Field characteristic, 404 extension, 404 finite, 403 Galois, 403 ground, 404 minimal polynomial of an element, 408 order of an element, 407 primitive element, 407 Figure of merit baseline, 239 constellation, 238 Filtered multitone (FMT) modulation, 754 Filters, matched, 178–182 whitening, 627 Finite fields, 403 Finite-state channels, 903 capacity, 903–905 Fire codes, 475 First-event error, 502 First-event error probability, 513 Fixed weight codes, 411, 949–953 Fixed-length source coding, 339 Proakis-27466 pro57166˙ind October 2, 2007 0:57 1146 Folded spectrum, 644 Forward recursion, 543 Free Euclidian distance, 577 Free-space path loss, 262 Frequency diversity, 850 Frequency range wireline channels, wireless (radio) channels, Frequency division multiple access (FDMA), 1029 capacity of,1031–1032 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 error probability, 205 noncoherent detection, 215 power density spectrum, 154 Frobenius norm, 982 Fundamental coding gain, 586 Fundamental volume of a lattice, 233 Galois 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 Generalized RAKE demodulator, 880–882 Generator matrix lattice, 231 of linear block codes, 412 of space-time block code, 1006 transform domain, 495 Generator polynomial, 448, 464 Gilbert-Varsharmov bound, 443 Girth of a graph, 560 GMSK, 118, 127 Golay codes, 424, 460 extended, 424 ternary, 442 Gold sequences, 799 Gram-Schmidt procedure, 29 Graphs, 558–568 bipartite, 559 constraint nodes, 561 cycle-free, 560 cycles, 560 factor, 558 girth, 560 global function, 561 local functions, 561 Tanner, 558 variable nodes, 560 Index Gray coding, 100 Gray labeling, 939 Ground field, 404 Group Abelian, 403 identity element, 404 Hadamard codes, 423, 951–953 Hamming bound, 441 Hamming codes, 420, 460 Hamming distance, 414 Hamming distortion, 354 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 Hermitian transpose of a matrix, 28 Hexagonal lattice, 230 Hilbert transform, 22 Homogeneous Markov chains, 72 Huffman coding, 342–346 Identity element, 404 iid random variables, 45 Illumination efficiency factor, 262 Impulse noise, 601 Impulse response, for bandpass systems, 27 In-phase component, 22 Inequality Cauchy-Schwarz, 29–30 Kraft, 340 Markov, 56 triangle, 29–30 Information sequence, 1, 401 Information source discrete memoryless, 331 memoryless, 331 stationary, 331 Inner code, 479 Inner product, 26, 28, 30 Input-output weight enumeration function (IOWEF), 416 Instantaneous codes, 340 Interference margin, 774 Interleaver block, 476 convolutional, 476 gain 552 uniform, 480–481 Interleaving, 476–477 Intersymbol interference, 599–600, 603–604 controlled (see Partial response signals), 609–611 discrete-time model for, 626 equivalent white noise filter model, 627 optimum demodulator for, 623–628 Inverse channel detector (ICD), 970 Inverse filter, 642 Irreducible Markov chains, 73 Irreducible polynomial, 405 Irregular LDPC, 570 Irrelevant information, 166 Iterative decoding, 478, 548–558 error floor, 551 EXIT charts, 555 turbo cliff region, 553 waterfall region, 553 Jakes’ model, 838–839 Jensen’s inequality, 386 Joint entropy, 334 Jointly Gaussian random variables, 54 Jointly wide-sense stationary processes, 54 Kalman (RLS) algorithm, 711–714 Kalman gain vector, 712 Karhunen-Loève expansion, 76 Kasami sequences, 799 Kissing number of a lattice, 232 Kolmogorov-Wiener filter, 13 Kraft inequality, 340 Labeling Gray, 939 set portioning, 939 Lattice coding gain, 233 coset, 584 density, 236 equivalent, 231 filter, 716–721 fundamental volume, 233 generator matrix, 231 Hermite parameter, 233 hexagonal, 230 kissing number, 232 minimum distance, 232 multidimensional, 234 multiplicity, 232 recursive least squares, 708, 715 Schläfli, 234 Sublattice, 234 Voronoi region, 232 Law of large numbers (LLN), 63 LDPC (low density parity check codes), 568–571 code density, 569 decoding, 570 degree distribution polynomial, 570 irregular, 570 regular, 569 Tanner graph, 569 Least-squares algorithms, 710–720 Lempel-Ziv algorithm, 346–348 Lengthened codes, 446 Levinson-Durbin algorithm, 692, 716 Likelihood function, 292 Linear block codes, 400–490 Linear equalization (see Equalizers, linear) Linear-feedback shift-register, maximum length, 798–799 Linear filter channel, 11 www.elsolucionario.org Linear modulation, 110 Linear prediction, 716 backward, 718 forward, 717 residuals, 718 Linear time-varying channel, 11 Linearly independent signals, 30 Link budget analysis, 261–265 Link margin, 246 LLN (see law of large numbers) Log-APP (log a posteriori probability), 546 Log-MAP (log maximum a posteriori probability), 546 Lognormal random variable, 54 Lossless data compression, 335 Lossless source coding theorem, 336 Lossy data compression, 335 Low density parity check codes (see LDPC) Lowpass equivalent, 22 Lowpass signal, 20 Low probability of intercept, 778–779 MacWilliams identity, 415 MAP (maximum a posteriori probability), 162–163, 291 Mapping by set partitioning, 572 Marcum’s Q-function, 47 generalized, 47 M-ary modulation, Markov chains, 71–74 aperiodic states, 73 equilibrium probabilities, 73 ergodic, 73 homogeneous, 72 irreducible, 73 period of state, 73 state, 72 state probability vector, 72 state transition matrix, 72 stationary probabilities, 73 steady-state probabilities, 73 Markov inequality, 57–58 Matched filter, 178–182 frequency domain, 179 receiver, 178 Matrix condition number, 1088 eigenvalue, 1086 eigenvector, 1086 generator, 412–413 Hermitian, 65 Hermitian transpose, 28 norm, 1088 orthogonal, 231 parity check, 412–413 rank, 1085 singular values, 1087 skew-Hermitian, 65 symmetric, 1085 trace of, 1085 transpose, 28 Max-Log-APP algorithm, 548 Max-Log-MAP algorithm, 548 Proakis-27466 pro57166˙ind October 2, 2007 0:57 Index Maximal ratio combiner, 852 Maximum a posteriori probability (see MAP), Maximum-distance separable codes, 440 Maximum free distance codes, 516 tables of, 517–520 Maximum-length shift register codes, 461, 798–799 Maximum likelihood, parameter estimation, 290–291, 321–322 for carrier phase, 292–298 for joint carrier and symbol, 321–322 for symbol timing, 315–321 performance of, 323–324 Maximum-likelihood (ML) receiver, 163, 623–625, Maximum likelihood sequence detection (MLSD), 623–625, Maximum ratio combining, 852 performance of, 851–855 McEliece-Rodemich-RumseyWelch (MRRW) bound, 443 MDS (maximum-distance separable) codes, 440 Mean-square error (MSE) criterion, 645–655 Meggit decoder, 460 Memoryless channel, 355 Memoryless modulation, 95 Memoryless source, 331 Mercer’s theorem, 77 Message error probability, 164 PSK, 194 QPSK, 193 Message polynomial, 449 Metric correlation, 173 distance, 173 modified distance, 173 MGF (moment generating function), 44 Microwave LOS channel, MIMO channels, 966 capacity of, 982–984, 990–991 ergodic, 985–986 outage, 987–990 coding for, 1001–1021 bit-interleaved, 1003–1006 space-time codes, 1006–1021 temporal, 1003–1006 slow fading, 968–969, 975–979 spread spectrum signals for, 992–996 MIMO systems, 966 detectors for, 970–974 diversity gain for, 996–997 error rate performance, 971–973 lattice reduction for, 973–974 multicode, 997–1000 multiplexing gain for, 996–997 outage probability, 987–988 scrambling sequence for, 997 1147 singular-value decomposition for, 974–975 spread spectrum, 992–996 Minimal polynomial, 408 Minimum distance, 414 Minimum distance detector, 171 Minimum distance of a constellation, 185 Minimum distance of a lattice, 232 Minimum weight, 414 Minimum-shift keying (MSK), 123–124 power spectrum of, 144 ML (see maximum-likelihood) MLSD, 623–625, Modified Bessel function, 47, 213 Modified distance metric, 173 Modified duobinary signal, 610 Modulation binary, comparison of, 226–229 constraint length, 96 continuous-phase FSK (CPFSK), 116–118 power spectrum, 138–145 continuous-phase modulation (CPM), 118–123 digital, 95 DPSK, 221–223 equicorrelated (simplex), 112–113, 209–210 frequency-shift keying (FSK), 109–110, 205, 215–216 linear, 110 M-ary orthogonal, 108–111, 204–207, 216–219 memoryless, 95 multichannel, 737–743 multidimensional, 108–113 NRZ, 115 NRZI, 115 nonlinear, 110 OFDM, 746–752 offset QPSK, phase-shift keying (PSK), 101–103, 191–195 pulse amplitude (PAM, ASK), 98–101, 188–190 quadrature amplitude (QAM), 103–107, 185–187, 196–200 with memory, 95–96 Modulator, 2, 24 binary, digital, 95 linear, 110 M-ary, memoryless, 95 nonlinear, 110 pulse amplitude, 98–101 quadrature amplitude, 103–107 with memory, 95–96 Moment generating function (see MGF) Monic polynomial, 405 Moore-Penrose pseudoinverse, 1088 Morse code, 12, 339 MRRW (McEliece-RodemichRumsey-Welch) bound, 443 MSK, 123–124, 144 Multicarrier communications, 743–759 capacity of, 744–745 channel coding consideration, 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 spectral characteristics, 752–754 Multichannel communications, 737–743 noncoherent combining loss, 741 with binary signals, 739–741 with M-ary orthogonal signals, 741–743 Multicode MIMO systems, 997–1000 Multidimensional signaling, 108 Multipath channels, 8, 831 Multipath intensity profile, 834 Multipath spread, 834 Multiple access methods, 1029–1031 capacity of, 1031–1035 CDMA, 1033–1034 FDMA, 1031–1032 random accesss, 1068–1077 TDMA, 1032–1033 Multiple antenna systems, 966–1021 inverse channel detector, 970 maximum-likelihood detector, 970 minimum MSE detector, 970 space-time codes for, 1006–1021 concatenated codes, 1020–1021 differential STBC, 1014 orthogonal STBC, 1011–1013 quasi-orthogonal STBC, 1013 trellis codes, 1016–1019 turbo codes, 1020–1021 Multiplexing gain, 996–997 Multiplicity of a lattice, 232 Multistage interference cancellation, 1043–1049 Multiuser communications, 1028 multiple access, 1029–1034 multiuser detection, 1029–1034 random access, 1068–1077 Multiuser detection, 1034 decorrelating detector, 1043–1045 for asynchronous transmission, 1039–1042 www.elsolucionario.org for broadcast channels, 1053–1068 for CDMA, 1036–1053 for random access, 1068–1077 for synchronous transmission, 1038–1039 single user detector, 1042–1043 Mutual information, 332 Nakagami random variable, 52, 841 Narrowband interference, 791–796 Narrowband process, 79 Narrowband signal, 18–21 Nat, 333 Nearest neighbor detector, 171 Negative spectrum, 20 Noise, Gaussian, 10 thermal, 3, 69 white, 90 Noise equivalent bandwidth, 92 Noisy channel coding theorem, 361 Non-central χ random variable, 46 Noncoherent combining loss, 741 Noncoherent detection, 210–226 error probability for orthogonal signals, 216–218 FSK, 215–216 Nonlinear distortion, 600 Nonlinear modulation, 110 Norm of a matrix, 1088 of a signal, 30 of a vector, 28 Normal equations, 716 Normal random variable, 41 NRZ, 115 NRZI, 115 Nyquist criterion, 604–605 Nyquist rate, 13 OFDM, 746–752, 844–890 bit and power allocation, 754–757 degradation due to Doppler spreading, 884–889 FFT implementation, 749–752 ICI suppression in, 889–890 peak-to-average ratio, 757–759 Offset QPSK (OQPSK), 124–128 On-off keying (OOK), 267, 949 Optimal detection after modulation, 202 binary antipodal signaling, 173 binary orthogonal signaling, 176 biorthogonal signaling, 207 simplex signaling, 209 OQPSK, 124–128 Order of a field element, 407 Orthogonal matrix, 231 Orthogonal signaling, 108 achieving channel capacity, 367 error probability, 205 with noncoherent detection, 216–218 Orthogonal signals, 26, 30 Proakis-27466 pro57166˙ind October 2, 2007 0:57 1148 Orthogonal vectors, 28 Orthogonality principle, 646 mean-square estimation, 646 Orthonormal vectors, 28 basis, 28 signal set, 30 Outage capacity, 900, 907, 913 of MIMO channels, 987–990 Outage probability, of MIMO channels, 987–988 Outer code, Pairwise error probability (PEP), 184, 372, 514, 922, 1014–1016 Chernov bound, 373, 1014–1016 PAM, 98–101 Parallel contatenated block codes, 481 Parallel concatenated convolutional codes (PCCC), 548 Parity check bits, 412 Parity check matrix, 412 Parity check polynomial, 450 Partial-band interference, 804 Partial response signals, 609–611 duobinary, 610 error probability of, 617–618 modified duobinary, 610 precoding for, 613 Partial-time (pulsed), 784 Path memory truncation, 246 PCBC (parallel concatenated block codes), 481 PCCC (parallel concatenated convolutional codes), 548 Peak distortion criterion, 641–645 Peak frequency deviation, 117 Peak-to-average ratio, 757–759 PEP (see pairwise error probability) Perfect codes, 434, 442 Phase of a signal, 23 Phase jitter, 600 Phase-locked loop (PLL), 298–315 Costas, 312–313 decision-directed, 303, 308 loop damping factor, 299 M-law type, 313–314 natural frequency, 299 non-decision-directed, 308–315 square-law type, 310–312 Phase tree, 120 Phase trellis, 120 Phase-shift keying (PSK), 101–103 Pilot signal, 1098 Plotkin bound, 442 PN sequences, 463, 796–801 Polynomial irreducible, 405 minimal, 408 monic, 405 prime, 405 syndrome, 458 Index Positive spectrum, 20 Power efficiency, 226 Power spectral density, 67 continuous component, 133 CPFSK, 138–145 discrete component, 133 for in-phase component, 80 for lowpass process, 81 for quadrature component, 80 linearly modulated signals, 133 Power spectrum, 67 Pre-envelope, 21 Precoding for broadcast channels, 1053–1068 dirty paper, 1054 linear, 1055–1058 nonlinear, 1058–1068 QR decomposition, 1058–1062 vector, 1062–1065 via lattice reduction, 1065–1068 for spectral shaping, 133–135, 611–612 Prediction (see Linear prediction), Preferred sequences, 799 Prefix condition, 340 Preprocessing, 166 Prime polynomial, 405 Primitive BCH codes, 463 Primitive element, 407 Probability distributions binomial, 41 chi-square, central, 45–46 noncentral, 46–48 gamma, 46 Gaussian, 41–45 log normal, 54 multivariate Gaussian, 54–56 Nakagami, 52–53 Rayleigh, 48–50 Rice, 50–52 uniform, 41 Processing gain, 773–774 Probability transition matrix of a channel, 357 Product codes, 477 Product distance, 925 Prolate spheroidal wave functions, 227 Proper random processes, 71 Proper random vectors, 65 PSD (power spectral density), 67 Pseudo-noise (PN) sequences, 796–801 autocorrelation function, 798 generation via shift register, 797 Gold, 799 Kasami, 799 maximal-length, 797 peak cross-correlation, 799 preferred, 799 (see also Spread spectrum signals), Pseudocovariance for complex random processes, 71 PSK, 101–103, 191–195 bit error probability, 195 Differential (DPSK), 221 differentially encoded, 195 message error probability, 194 Pulse amplitude modulation (see PAM) Pulsed interference, 784 effect on error rate performance, 785–791 Punctured codes, 446, 516, 521–523 Punctured convolutional codes, 516, 521–523 rate compatible, 523–525 Puncturing matrix, 520, 522 Pythagorian relation, 29 Q-function, 41 QAM, 103–107, 185–187, 196–200 error probability, 196–200 QPSK, 102 error probability, 199 message error probability, 193 offset (OQPSK), 124 Quadrature amplitude modulation (see QAM) Quadrature component, 22 Quasi-perfect codes, 435 Quaternary PSK (QPSK), 102 R0 (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 for binary orthogonal signals, 874–877 for DPSK signals, 878 for noncoherent detection of orthogonal signals, 879 generalized, 880–882 Random access,1068–1077 ALOHA, 1069–1073 carrier sense, 1073–1077 with collision detection, 1073 non persistent, 1074 l-persistent, 1074 p-persistent, 1074–1077 offered channel traffic, 1070 slotted ALOHA, 1070 throughput, 1070 unslotted, 1070 Random coding, 362, 375 Random processes, 66–81 bandlimited, 74–76 bandpass, 78–81 cross spectral density, 67 cyclostationary, 70 discrete-time, 69 Gaussian, 68 www.elsolucionario.org jointly wide-sense stationary, 67 narrowband, 79 power, 68 power spectral density, 67 power spectrum, 67 proper, 71 sampling theorem, 74 series expansion, 74 white, 69 wide-sense stationary, 67 Random variables, 40–57 Bernoulli, 40 binomial, 41 characteristic function, 44 χ , 45 complex, 63 exponential, 46 gamma, 46 Gaussian, 41 iid, 45 jointly Gaussian, 54 lognormal, 54 moment generating function, 44 Nakagami, 52 non-central χ , 46 normal, 41 Rayleigh, 48 Ricean, 50 uniform, 41 Random vectors, circular, 66 circularly symmetric, 66 complex, 64 proper, 65 Rate bit, 97 code, 2, 402 signaling, 97 Rate-compatible punctured convolutional codes (RCPCC), 523–525 Rate-distortion function, 350 Shannon’s lower bound, 353 Rate-distortion theorem, 351 Rayleigh fading channel, 833, 841, 846–868 CSI at both sides, 912 CSI at receiver, 909, 957–960 ergodic capacity, 907 for MIMO channels, 985–987 no CSI, 908 outage capacity, 913 for MIMO channels, 987–990 Rayleigh random variable, 48 RCC (recursive convolutional codes), 507 RCPCC (rate-compatible punctured convolutional codes), 523–525 Receiver correlation, 177 MAP, 162 matched filter, 178–182 ML, 163, 623–625 Receiver implementation, 177 Reciprocal polynomial, 450 Proakis-27466 pro57166˙ind October 2, 2007 0:57 Index Recursive convolutional codes, Recursive least squares (RLS) algorithms, 710–721 fast RLS, 715 RLS Kalman, 711–714 RLS lattice, 716–721 Recursive systematic convolutional 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, 473 References, 1109 Regenerative repeaters, 260–261 Reliability function, 369 Reliable communication, 207, 361 Residuals, 718 Rice factor, 51 Ricean fading channel, 833, Ricean random variable, 50–52 RS codes (see Reed-Solomon codes) RSCC (see recursive systematic convolutional codes) Sampling theorem, 74 Scattering function, 837 SCBC (see serially concatenated block codes) Schläfli lattice, 234 Scrambling sequence, 997 Sequential decoding, 525–528 Serially concatenated block codes, 480 Set partitioning labeling, 572–573, 939 Shannon first theorem, 336 lower bound on R(D), 353 second theorem, 361 third theorem, 351 Shannon limit, 207, 554, 570 Shaping, 586 Shaping gain, 240, 586 Shortened codes, 445 Shortened cyclic codes, 452 Signal (see also Signals) analytic, 21 bandpass, 21 bandwidth, 20 baseband, 20 complex envelope, 22 energy of, 25 envelope of, 23 fading, in-phase component, 22 lowpass, 20 lowpass equivalent, 22 multipath, 8, 831 narrowband, 18–21 norm, 30 parameter estimation, 290–326 phase, 23 1149 quadrature components of, 22 spectrum, 19 Signal design, 602–611, 619–623 for band-limited channel, 602 for channels with distortion, 619–623 for no intersymbol interference, 604–609 with partial response pulses, 609–611 with raised cosine spectral pulse, 607–608 Signal constellation, 28 Signal space diversity, 928 Signal space representation, 34 Signal-to-noise ratio (SNR), 176, 192 Signaling based on binary codes, 113 binary antipodal, 101 biorthogonal, 111 digital, 95 multidimensional, 108 non-return-to-zero (NRZ), 115 non-return-to-zero, inverted (NRZI), 115 on-off, 267 orthogonal, 108 simplex, 112 with memory, 114 Signaling interval, 96 Signaling rate, 97 Signals antipodal, 101 binary coded, 113 binary orthogonal, 176–177 biorthogonal, 111 digitally modulated, 95 cyclostationary, 70–71, 131 representation of, 28, 95 spectral characteristics, 131 inner product, 26 M-ary orthogonal, 108–111 multiamplitude, 98 multidimensional, 108–114 multiphase, 101–103 orthogonal, 30 random, 66–81 autocorrelation, 67 bandpass stationary, 78–81 cross correlation of, 67 power density spectrum, 67 properties of quadrature components, 79–81 white noise, 69 quadrature amplitude modulated (QAM), 103–106 simplex, 112–113 Signature sequence, 1037 Simplex signaling, 112–113 optimal detection, 209–210 Single-sideband (SSB) PAM, 100 Singleton bound, 440 Singular-value decomposition, 974–975, 981–982, 1087 left singular vectors, 981, 1087 right singular vectors, 981, 1087 singular values, 974, 981, 1087 SISO (soft-input-soft-output) decoder, 545 Skew-Hermitian matrix, 65 Skin depth, SNR, 176 Per bit, 176 per symbol, 192 Soft decision decoding, 424 Source 330–354 analog, 330 binary, 331 discrete 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 quasi-orthogonal STBC, 1013 trellis, 1016–1019 turbo, 1020–1021 Spaced-frequency, spaced-time correlation function, 835 Spatial rate, 1007 Spectral bit rate, 226 Spectral shaping by precoding, 134, 611–612 Spectrum of CPFSK and CPM, 138–147 of digital signals, 131–148 of linear modulation, 133–135 of signals with memory, 131–133, 135–147 Specular component, 841 Sphere packing, 235 Sphere packing bound, 441 Spread factor, 845 table of, 845 Spread spectrum multiple access (SSMA), 1031 Spread spectrum signals, 763–765 acquisition of, 816 for code division multiple access (CDMA), 779–780, 813–814 for MIMO systems, 992–996 concatenated codes for, 776–778 direct sequence, 765–768 application of, 778–784 coding for, 776–778 demodulation of, 767–768 performance of, 768–773 with pulse interference, 784–791 excision of narrowband interference, 791–796 for low-probability of intercept (LPI), 778–779 www.elsolucionario.org for multipath channels, 869–871, 997–1000 frequency-hopped (FH), 802–804 block hopping, 803 performance of, 804–806 with partial-band interference, 806–812 hybrid combinations, 814–815 interference margin, 774 processing gain, 773–774 synchronization of, 815–822 time-hopped (TH), 814 tracking of, 819–822 uncoded DS, 775 Spread spectrum system model, 763–765 Square-law detection, 216 Square-root factorization, 715 SQPSK, 124–128 SSB, 100 Staggered QPSK (SQPSK), 124–128 Standard array, 430 State diagram, 496 Stationary random processes, wide-sense, 67 Stationary source, 337 Steepest-descent (gradient) algorithm, 691–701 Storage channel, Subfield, 483 Sublattice, 234 Subscriber local loop, 756 Successive interference cancellation, 1047–1048 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 carrier, 290–315 effect of noise, 300–303 for multiphase signals, 313–314 with Costas loop, 312–315 with decision-feedback loop, 303–308 with phase-locked loop (PLL), 298–303 with squaring loop, 310–312 of spread spectrum signals, 815–822 with tau-dither loop, 820 with delay-locked loop, 819 sequential search, 818 sliding correlator, 816 symbol, 290–291, 315, 321 Syndrome, 430, 467 polynomial, 458 Systematic block codes, 412 Systematic convolutional codes, Systematic cyclic codes, 453 Proakis-27466 pro57166˙ind October 2, 2007 0:57 1150 Tail probability bounds 56–63 Chernov bound, 58–63, 866–868 Markov bound, 56, 57 Tanner graph 558–561 for low density parity check codes, 569–570 TATS (tactical transmission system), 813 Telegraphy, 12 Telephone channels, 598–601 Ternary Golay code, 442 Theorem central limit, 63 dimensionality, 227 lossless source coding, 336 Mercer, 77 noisy channel coding, 361 rate-distortion, 351 Shannon’s second, 361 Shannon’s third, 351 Wiener-Khinchin, 67 Thermal noise, 3, 69 Threshold decoder, 531 Time diversity, 851 Time division multiple access (TDMA), 1030 capacity of, 1032–1033 Timing phase, 315 Toeplitz matrix, 700 Tomlinson-Harashima precoding, 668–669 Transfer function of convolutional codes, 500 Index Transform domain generator matrix, 495 Transpose of a matrix, 28 Tree diagram, 496 Trellis, 116, 243, 496 Trellis-coded modulation, 571–589 encoders for, 583 for fading channels, 929–935 free Euclidean distance, 577 set partitioning, 572 subset decoding, 578 tables of coding gains for, 581–582 turbo coded, 586–589 Trellis diagram, 496 Triangle inequality, 29–30 Turbo cliff region, 553 Turbo codes, 548–558 error floor, 551 EXIT charts, 555 for fading channels, 1020–1021 interleaver gain, 552 iterative decoding, 552 Max-Log-APP algorithm, 548 multiplicity, 549 turbo cliff region, 553 waterfall region, 553 Turbo TCM, 586–589 Turbo decoding algorithm, 552 Turbo equalization, 671–673 Typical sequences, 336 Underspread fading channels, 899 Underwater acoustic channels, Undetected error, 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 Variable-length source coding, 339 Variance, 40 Varshamov-Gilbert bound, 443 Vector space, 28–30, 410–411 Vectors linearly independent, 29 norm, 28 orthogonal, 28 orthonormal, 28 Viterbi algorithm, 243–246, 510–513 path memory truncation, 246, 513 survivor, 244–245, 512 survivor path, 245, 512 Voltage-controlled oscillator (VCO), 298 Voronoi region of a lattice point, 232 www.elsolucionario.org Waterfall region, 553 Water-filling interpretation, 745, 902 in time, 912 Waveform channels, 358 WEF (weight enumeration function), 415 Weight distribution, 411 Weight distribution polynomial (WEP), 415 Weight enumeration function, 415 Weight of a codeword, 411 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, Word error probability, 417 WSS (side-sense stationary), 67 Yule-Walker equations, 716 Z transform, 626 Zero-forcing equalizer, 642 Zero-forcing filter, 642 www.elsolucionario.org ... Cataloging-in-Publication Data Proakis, John G Digital communications / John G Proakis, Masoud Salehi. ? ?5th ed p cm Includes index ISBN 978–0–07–295716–7—ISBN 0–07–295716–6 (hbk : alk paper) Digital communications. .. 12:35 P R E F A C E It is a pleasure to welcome Professor Masoud Salehi as a coauthor to the fifth edition of Digital Communications This new edition has undergone a major revision and reorganization...Proakis-27466 pro57166˙fm September 26, 2007 12:35 Digital Communications Fifth Edition John G Proakis Professor Emeritus, Northeastern University