Channel Equalization for Wireless Communications From Concepts to Detailed Mathematics Gregory E Bottom ley ♦IEEE IEEE Press IEEE SEMES ON DIGITAL & MOBILE COMMUNICATION John B Anderson, Series Editor WILEY A JOHN WILEY & SONS, INC., PUBLICATION Copyright © 2011 by the Institute of Electrical and Electronics Engineers, Inc Published by John Wiley & Sons, Inc., Hoboken, New Jersey All rights reserved Published simultaneously in Canada No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning or otherwise, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, (978) 750-8400, fax (978) 750-4470, or on the web at www.copyright.com 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damages For general information on our other products and services please contact our Customer Care Department within the United States at (800) 762-2974, outside the United States at (317) 572-3993 or fax (317) 572-4002 Wiley also publishes its books in a variety of electronic formats Some content that appears in print, however, may not be available in electronic formats For more information about Wiley products, visit our web site at www.wiley.com Library of Congress Cataloging-in-Publication Data is available ISBN 9780470874271 Printed in the United States of America oBook ISBN: 9781118105252 ePDF ISBN: 9781118105283 ePublSBN:9781118105276 MOBI ISBN: 9781118105269 10 To my colleagues at Ericsson CONTENTS IN BRIEF Introduction Matched Filtering 31 Zero-Forcing Decision Feedback Equalization 57 Linear Equalization 69 M M S E and M L Decision Feedback Equalization 99 Maximum Likelihood Sequence Detection 115 Advanced Topics 151 Practical Considerations 173 CONTENTS List of Figures List of Tables Preface Acknowledgments Acronyms Introduction 1.1 1.2 1.3 1.4 1.5 1.6 The Idea More Details 1.2.1 General dispersive and MIMO scenarios 1.2.2 Use of complex numbers The Math 1.3.1 Transmitter 1.3.2 Channel 1.3.3 Receiver More Math 1.4.1 Transmitter 1.4.2 Channel 1.4.3 Receiver An Example 1.5.1 Reference system and channel models The Literature xv xix xxi xxiii xxv 7 11 15 16 16 21 23 24 26 26 X CONTENTS Problems 27 Matched Filtering 31 2.1 2.2 31 33 34 35 35 35 37 38 38 41 42 43 44 44 45 47 49 52 53 53 54 54 55 2.3 2.4 2.5 2.6 The Idea More Details 2.2.1 General dispersive scenario 2.2.2 MIMO scenario The Math 2.3.1 Maximum-likelihood detection 2.3.2 Output SNR and error rate performance 2.3.3 TDM 2.3.4 Maximum SNR 2.3.5 Partial MF 2.3.6 Fractionally spaced MF 2.3.7 Whitened MF 2.3.8 The matched filter bound (MFB) 2.3.9 MF in colored noise 2.3.10 Performance results More Math 2.4.1 Partial MF 2.4.2 The matched filter bound 2.4.3 MF in colored noise 2.4.4 Group matched filtering An Example The Literature Problems Zero-Forcing Decision Feedback Equalization 57 3.1 3.2 3.3 57 59 62 63 63 64 65 66 66 66 3.4 3.5 3.6 The Idea More Details The Math 3.3.1 Performance results More Math 3.4.1 Dispersive scenario and TDM 3.4.2 MIMO/cochannel scenario An Example The Literature Problems Linear Equalization 69 4.1 69 The Idea CONTENTS 4.2 4.3 4.4 4.5 4.6 4.1.1 Minimum mean-square error More Details 4.2.1 Minimum mean-square error solution 4.2.2 Maximum SINR solution 4.2.3 General dispersive scenario 4.2.4 General MIMO scenario The Math 4.3.1 MMSE solution 4.3.2 ML solution 4.3.3 Output SINR 4.3.4 Other design criteria 4.3.5 Fractionally spaced linear equalization 4.3.6 Performance results More Math 4.4.1 ZF solution 4.4.2 MMSE solution 4.4.3 ML solution 4.4.4 Other forms for the CDM case 4.4.5 Other forms for the OFDM case 4.4.6 Simpler models 4.4.7 Block and sub-block forms 4.4.8 Group linear equalization An Example The Literature Problems M M S E and M L Decision Feedback Equalization 5.1 5.2 5.3 5.4 5.5 The Idea More Details The Math 5.3.1 MMSE solution 5.3.2 ML solution 5.3.3 Output SINR 5.3.4 Fractionally spaced DFE 5.3.5 Performance results More Math 5.4.1 MMSE solution 5.4.2 ML solution 5.4.3 Simpler models 5.4.4 Block and sub-block forms 5.4.5 Group decision feedback equalization An Example XI 72 74 74 75 76 79 79 80 82 83 85 85 86 86 87 87 89 89 91 91 92 93 93 94 95 99 99 101 104 104 106 106 106 106 108 108 109 109 109 110 110 XII CONTENTS 5.6 The Literature Problems 110 112 Maximum Likelihood Sequence Detection 115 6.1 6.2 6.3 115 117 120 120 125 130 130 130 131 138 142 142 143 144 145 147 6.4 6.5 6.6 The Idea More Details The Math 6.3.1 The Viterbi algorithm 6.3.2 SISO TDM scenario 6.3.3 Given statistics 6.3.4 Fractionally spaced MLSD 6.3.5 Approximate forms 6.3.6 Performance results More Math 6.4.1 Block form 6.4.2 Sphere decoding 6.4.3 More approximate forms An Example The Literature Problems Advanced Topics 151 7.1 151 151 153 155 156 156 157 160 160 160 166 167 167 167 168 168 168 169 169 7.2 7.3 7.4 7.5 7.6 The Idea 7.1.1 MAP symbol detection 7.1.2 Soft information 7.1.3 Joint demodulation and More Details 7.2.1 MAP symbol detection 7.2.2 Soft information 7.2.3 Joint demodulation and The Math 7.3.1 MAP symbol detection 7.3.2 Soft information 7.3.3 Joint demodulation and More Math An Example The Literature 7.6.1 MAP symbol detection 7.6.2 Soft information 7.6.3 Joint demodulation and Problems decoding decoding decoding decoding CONTENTS XIII Practical Considerations 173 8.1 8.2 173 175 175 176 177 178 179 180 8.3 8.4 8.5 8.6 The Idea More Details 8.2.1 Parameter estimation 8.2.2 Equalizer selection 8.2.3 Radio aspects The Math 8.3.1 Time-invariant channel and training sequence 8.3.2 Time-varying channel and known symbol sequence 8.3.3 Time-varying channel and partially known symbol sequence 8.3.4 Per-survivor processing More practical aspects 8.4.1 Acquisition 8.4.2 Timing 8.4.3 Doppler 8.4.4 Channel Delay Estimation 8.4.5 Pilot symbol and traffic symbol powers 8.4.6 Pilot symbols and multi-antenna transmission An Example The Literature Problems 181 182 182 182 182 183 183 184 184 184 185 185 Appendix A: Simulation Notes A.l Fading channels A.2 Matched filter and matched filter bound A.3 Simulation calibration 189 191 192 192 Appendix B: Notation 193 References 197 Index 217 208 REFERENCES [ManOl] A Mantravadi and V V Veeravalli, "On chip-matched filtering and discrete sufficient statistics for asynchronous band-limited CDMA systems," IEEE Trans Commun., vol 49, pp 1457-1467, Aug 2001 [Mar73] J W Mark and P S Budihardjo, "Performance of jointly optimized prefilter — equalizer receivers," IEEE Trans Commun., vol 21, pp 941-945, Aug 1973 [Mar05] R K Martin and C R Johnson, Jr., "Adaptive equalization: transitioning from single-carrier to multicarrier systems," IEEE Sig Proc Mag., vol 22, no 6, pp 108-122, Nov 2005 [Mas88] T Masamura, "Spread spectrum multiple access system with 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Would she be able to receive his response? PREFACE The working title of this book was Channel Equalization for Everyone Channel equalization for everyone? Well, for