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Fundamentals of Signal Enhancement and Array Signal Processing

Fundamentals of Signal Enhancement and Array Signal Processing Jacob Benesty INRS, University of Quebec Montreal, Canada Israel Cohen Technion, Israel Institute of Technology Haifa, Israel Jingdong Chen Northwestern Polytechnical University Xi’an, China

This edition ﬁrst published  ©  John Wiley & Sons Singapore Pte. Ltd All rights reserved. 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 or otherwise, except as permitted by law. Advice on how to obtain permission to reuse material from this title is available at http://www.wiley.com/go/permissions. The right of Jacob Benesty, Israel Cohen, and Jingdong Chen to be identiﬁed as the authors of this work has been asserted in accordance with law. Registered Oﬃces John Wiley & Sons, Inc.,  River Street, Hoboken, NJ , USA John Wiley & Sons Singapore Pte. Ltd,  Fusionopolis Walk, #- Solaris South Tower, Singapore  Editorial Oﬃce The Atrium, Southern Gate, Chichester, West Sussex, PO SQ, UK For details of our global editorial oﬃces, customer services, and more information about Wiley products visit us at www.wiley.com. Wiley also publishes its books in a variety of electronic formats and by print-on-demand. Some content that appears in standard print versions of this book may not be available in other formats. Limit of Liability/Disclaimer of Warranty While the publisher and authors have used their best eﬀorts in preparing this work, they make no representations or warranties with respect to the accuracy or completeness of the contents of this work and speciﬁcally disclaim all warranties, including without limitation any implied warranties of merchantability or ﬁtness for a particular purpose. No warranty may be created or extended by sales representatives, written sales materials or promotional statements for this work. The fact that an organization, website, or product is referred to in this work as a citation and/or potential source of further information does not mean that the publisher and authors endorse the information or services the organization, website, or product may provide or recommendations it may make. This work is sold with the understanding that the publisher is not engaged in rendering professional services. The advice and strategies contained herein may not be suitable for your situation. You should consult with a specialist where appropriate. Further, readers should be aware that websites listed in this work may have changed or disappeared between when this work was written and when it is read. Neither the publisher nor authors shall be liable for any loss of proﬁt or any other commercial damages, including but not limited to special, incidental, consequential, or other damages. Library of Congress Cataloging-in-Publication data applied for Hardback ISBN:  Cover Design by Wiley Cover Image: © naqiewei/Gettyimages Set in /pt Warnock by SPi Global, Pondicherry, India          

v    Contents xi Preface About the Companion Website xiii 1 . .. .. .. .. . . . .   Introduction Signal Enhancement Speech Enhancement and Noise Reduction Underwater Acoustic Signal Enhancement  Signal Enhancement in Radar Systems Signal Enhancement in Ultrasound Systems Approaches to Signal Enhancement Array Signal Processing Organization of the Book  How to Use the Book References     Part I Signal Enhancement      Single-channel Signal Enhancement in the Time Domain Signal Model and Problem Formulation Wiener Method Linear Filtering Performance Measures 2 . . .. .. .. Optimal Filters Spectral Method . Joint Diagonalization and Reformulation of the Problem  .. .. Noise Reduction with Gains  .. .. Determination of the Gains from the Fullmode Output SNR  Performance Measures     Problems References   3 . . Single-Channel Signal Enhancement in the Frequency Domain Signal Model and Problem Formulation Noise Reduction with Gains   

vi Contents . . . .   Performance Measures Optimal Gains Constraint Wiener Gains Implementation with the Short-time Fourier Transform  Problems References         Multichannel Signal Enhancement in the Time Domain Signal Model and Problem Formulation Conventional Method Joint Diagonalization  Linear Filtering Performance Measures 4 . . .. .. .. .. Optimal Filtering Matrices . .. .. .. .. .. Optimal Filters . .. .. Maximization of the Output SNR  .. Minimization of the Output SNR  Spectral Method Temporal Joint Diagonalization and Reformulation of the Problem  Spatial Joint Diagonalization  Spatial Linear Filtering  Performance Measures  Case of a Rank Deﬁcient Noise Correlation Matrix Eigenvalue Decompositions      Problems References      Multichannel Signal Enhancement in the Frequency Domain Signal Model and Problem Formulation  Linear Filtering Performance Measures Input SNR  5 . . . .. .. Output SNR  .. Noise Rejection and Desired Signal Cancellation .. Desired Signal Distortion Index  .. MSE Criterion  . Optimal Filters .. Maximum SNR   .. Wiener .. MVDR   .. Tradeoﬀ LCMV  .. . Generalized Sidelobe Canceller Structure A Signal Subspace Perspective . Joint Diagonalization .. .. Estimation of the Desired Signal      

Contents vii  . Implementation with the STFT  Problems References    6 An Exhaustive Class of Linear Filters . Signal Model and Problem Formulation . Linear Filtering for Signal Enhancement . Performance Measures  . Optimal Filters  .. Wiener .. MVDR   .. Tradeoﬀ LCMV  .. .. Maximum SINR  .. Maximum SIR  .    Filling the Gap Between the Maximum SINR and Wiener Filters Problems References   Part II Array Signal Processing     Fixed Beamforming Signal Model and Problem Formulation Linear Array Model Performance Measures  Spatial Aliasing Fixed Beamformers 7 . . . . . .. Delay and Sum   .. Maximum DF  .. Superdirective .. Robust Superdirective .. Null Steering . .. .. Compromising Between WNG and DF A Signal Subspace Perspective Joint Diagonalization      Problems References      Adaptive Beamforming Signal Model, Problem Formulation, and Array Model Performance Measures Adaptive Beamformers    8 . . .  .. Wiener .. MVDR   .. .. Maximum Array Gain .. LCMV  Tradeoﬀ 

viii Contents SNR Estimation DOA Estimation A Spectral Coherence Perspective . . . .. Deﬁnitions .. Derivation of Optimal Beamformers    Problems References      Differential Beamforming Signal Model, Problem Formulation, and Array Model  Beampatterns Front-to-back Ratios Array Gains Examples of Theoretical Diﬀerential Beamformers First-order Design Principle      9 . . . . . .  .. .. Design Examples .  .. .. Design Examples . Third-order Design  .. .. Design Examples .  .. .. Design Examples   Problems References Principle Second-order Design Principle       Minimum-norm Beamformers Principle  10 . . . . . .    Beampattern Design Beampatterns Revisited Nonrobust Approach Robust Approach Frequency-invariant Beampattern Design Least-squares Method Joint Optimization Problems References       Beamforming in the Time Domain Signal Model and Problem Formulation Broadband Beamforming Performance Measures Fixed Beamformers 11 . . . . .. Delay and Sum   .. Maximum DF .. Distortionless Maximum DF      

Contents ix     Adaptive Beamformers .. Superdirective .. Null Steering .  .. Wiener .. MVDR   .. Tradeoﬀ .. Maximum SNR  .. LCMV  . .. .. Second Order .. General Order .. Hypercardioid .. Supercardioid     Diﬀerential Beamformers First Order  Problems References   Index 

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