Robust_Adaptive_Beamforming.pdf

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Robust Adaptive Beamforming Edited by Jian Li and Petre Stoica A JOHN WILEY & SONS, INC., PUBLICATION

Robust Adaptive Beamforming

Robust Adaptive Beamforming Edited by Jian Li and Petre Stoica A JOHN WILEY & SONS, INC., PUBLICATION

Copyright # 2006 by John Wiley & Sons, Inc. All rights reserved. Published by John Wiley & Sons, Inc., Hoboken, New Jersey. 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. Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, 201-748-6011, fax 201-748-6008, or online at http://www.wiley.com/go/permission. Limit of Liability/Disclaimer of Warranty: While the publisher and author have used their best efforts in preparing this book, they make no representations or warranties with respect to the accuracy or completeness of the contents of this book and speciﬁcally disclaim any implied warranties of merchantability or ﬁtness for a particular purpose. No warranty may be created or extended by sales representatives or written sales materials. The advice and strategies contained herein may not be suitable for your situation. You should consult with a professional where appropriate. Neither the publisher nor author shall be liable for any loss of proﬁt or any other commercial damages, including but not limited to special, incidental, consequential, or other damages. For general information on our other products and services or for technical support, please contact our Customer Care Department within the U.S. at 877-762-2974, outside the U.S. 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 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: Robust adaptive beamforming/edited by Jian Li and Petre Stoica. p. cm. Includes bibliographical references and index. ISBN-13 978-0-471-67850-2 (cloth) ISBN-10 0-471-67850-3 (cloth) 1. Adaptive antennas. 2. Antenna radiation patterns. I. Li, Jian. II. Stoica, Petre. TK7871.67.A33R63 2005 0 621.382 4--dc22 Printed in the United States of America 10 9 8 7 6 5 4 3 2 1 2004065908

CONTENTS Contributors Preface 1 Robust Minimum Variance Beamforming Robert G. Lorenz and Stephen P. Boyd 1.1 Introduction 1 1.2 A Practical Example 8 1.3 Robust Weight Selection 12 1.4 A Numerical Example 23 1.5 Ellipsoidal Modeling 28 1.6 Uncertainty Ellipsoid Calculus 31 1.7 Beamforming Example with Multiplicative Uncertainties 41 1.8 Summary 44 Appendix: Notation and Glossary 44 References 45 2 Robust Adaptive Beamforming Based on Worst-Case Performance Optimization Alex B. Gershman, Zhi-Quan Luo, and Shahram Shahbazpanahi 2.1 Introduction 49 2.2 Background and Traditional Approaches 51 2.3 Robust Minimum Variance Beamforming Based on Worst-Case Performance Optimization 60 2.4 Numerical Examples 74 2.5 Conclusions 80 Appendix 2.A: Proof of Lemma 1 81 Appendix 2.B: Proof of Lemma 2 81 Appendix 2.C: Proof of Lemma 3 82 Appendix 2.D: Proof of Lemma 4 84 Appendix 2.E: Proof of Lemma 5 85 References 85 ix xi 1 49 v

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