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Springer Topics in Signal Processing Volume 1 Series Editors J. Benesty, Montreal, QC, Canada W. Kellermann, Erlangen, Germany

Springer Topics in Signal Processing Edited by J. Benesty and W. Kellermann Vol. 1: Benesty, J.; Chen, J.; Huang, Y. Microphone Array Signal Processing 250 p. 2008 [978-3-540-78611-5]

Jacob Benesty · Jingdong Chen · Yiteng Huang Microphone Array Signal Processing 123

Jacob Benesty INRS-EMT, University of Quebec 800 de la Gauchetiere Ouest Montreal, QC, H5A 1K6 Canada Yiteng Huang WeVoice, Inc. 9 Sylvan Dr. Bridgewater, NJ, 08807 USA Jingdong Chen Bell Labs, Alcatel-Lucent 600 Mountain Ave. Murray Hill, NJ, 07974 USA ISBN 978-3-540-78611-5 e-ISBN 978-3-540-78612-2 DOI 10.1007/978-3-540-78612-2 Springer Topics in Signal Processing ISSN 1866-2609 Library of Congress Control Number: 2008922312 c 2008 Springer-Verlag Berlin Heidelberg This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under the German Copyright Law. The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Coverdesign: WMXDesign GmbH, Heidelberg Printed on acid-free paper 9 8 7 6 5 4 3 2 1 springer.com

Preface In the past few years we have written and edited several books in the area of acoustic and speech signal processing. The reason behind this endeavor is that there were almost no books available in the literature when we ﬁrst started while there was (and still is) a real need to publish manuscripts summarizing the most useful ideas, concepts, results, and state-of-the-art algorithms in this important area of research. According to all the feedback we have received so far, we can say that we were right in doing this. Recently, several other researchers have followed us in this journey and have published interesting books with their own visions and perspectives. The idea of writing a book on Microphone Array Signal Processing comes from discussions we have had with many colleagues and friends. As a con- sequence of these discussions, we came up with the conclusion that, again, there is an urgent need for a monograph that carefully explains the theory and implementation of microphone arrays. While there are many manuscripts on antenna arrays from a narrowband perspective (narrowband signals and narrowband processing), the literature is quite scarce when it comes to sen- sor arrays explained from a truly broadband perspective. Many algorithms for speech applications were simply borrowed from narrowband antenna ar- rays. However, a direct application of narrowband ideas to broadband speech processing may not be necessarily appropriate and can lead to many mis- understandings. Therefore, the main objective of this book is to derive and explain the most fundamental algorithms from a strict broadband (signals and/or processing) viewpoint. Thanks to the approach taken here, new con- cepts come in light that have the great potential of solving several and very diﬃcult problems encountered in acoustic and speech applications. This book is especially written for graduate students and research en- gineers who work on microphone arrays. Our goal is to make the area of microphone array signal processing theory and application available in a com- plete and self-contained text. We attempt to explain the main ideas in a clear and rigorous way so that the reader can have a pretty good idea of the po-

VI Preface tentials, opportunities, challenges, and limitations of microphone array signal processing. We hope that the reader will ﬁnd it useful and inspiring. Finally, we would like to thank Christoph Baumann, Petra Jantzen, and Carmen Wolf from Springer (Germany) for their wonderful help in the prepa- ration and publication of this manuscript. Working with them is always a pleasure and a wonderful experience. Montr´eal, QC/ Murray Hill, NJ/ Bridgewater, NJ Jacob Benesty Jingdong Chen Yiteng Huang

Contents 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 Microphone Array Signal Processing . . . . . . . . . . . . . . . . . . . . . . . 1.2 Organization of the Book . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1 5 7 2 Classical Optimal Filtering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Wiener Filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.3 Frost Filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2.3.1 Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2.3.2 Generalized Sidelobe Canceller Structure . . . . . . . . . . . . . 17 2.3.3 Application to Linear Interpolation . . . . . . . . . . . . . . . . . . 19 2.4 Kalman Filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 2.5 A Viable Alternative to the MSE . . . . . . . . . . . . . . . . . . . . . . . . . . 25 2.5.1 Pearson Correlation Coeﬃcient . . . . . . . . . . . . . . . . . . . . . . 26 2.5.2 Important Relations with the SPCC . . . . . . . . . . . . . . . . . 26 2.5.3 Examples of Optimal Filters Derived from the SPCC . . 29 2.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 3 Conventional Beamforming Techniques . . . . . . . . . . . . . . . . . . . . 39 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 3.2 Problem Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 3.3 Delay-and-Sum Technique . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 3.4 Design of a Fixed Beamformer . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 3.5 Maximum Signal-to-Noise Ratio Filter . . . . . . . . . . . . . . . . . . . . . 49 3.6 Minimum Variance Distortionless Response Filter . . . . . . . . . . . 52 3.7 Approach with a Reference Signal . . . . . . . . . . . . . . . . . . . . . . . . . 54 3.8 Response-Invariant Broadband Beamformers . . . . . . . . . . . . . . . . 55 3.9 Null-Steering Technique . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 3.10 Microphone Array Pattern Function . . . . . . . . . . . . . . . . . . . . . . . 61 3.10.1 First Signal Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 3.10.2 Second Signal Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

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