Array Processing Kronecker Product Beamforming
The focus of this book is on array processing and beamforming with Kronecker products. It considers a large family of sensor arrays that allow the steering vector to be decomposed as a Kronecker product of two steering vectors of smaller virtual arrays. I
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Jacob Benesty Israel Cohen Jingdong Chen
Array Processing Kronecker Product Beamforming
Springer Topics in Signal Processing Volume 18
Series editors Jacob Benesty, Montreal, Canada Walter Kellermann, Erlangen, Germany
More information about this series at http://www.springer.com/series/8109
Jacob Benesty Israel Cohen Jingdong Chen •
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Array Processing Kronecker Product Beamforming
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Jacob Benesty INRS-EMT University of Quebec Montreal, QC, Canada
Israel Cohen Department of Electrical Engineering Technion—Israel Institute of Technology Haifa, Israel
Jingdong Chen School of Marine Science and Technology Northwestern Polytechnical University Xi’an, China
ISSN 1866-2609 ISSN 1866-2617 (electronic) Springer Topics in Signal Processing ISBN 978-3-030-15599-5 ISBN 978-3-030-15600-8 (eBook) https://doi.org/10.1007/978-3-030-15600-8 Library of Congress Control Number: 2019934360 © Springer Nature Switzerland AG 2019 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, 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. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland
Abstract
The focus of this book is on array processing and beamforming with Kronecker products. We consider a large family of sensor arrays that enable the decomposition of the steering vector as a Kronecker product of two steering vectors of smaller virtual arrays. Instead of directly designing a global beamformer for the original array, we break it down following the decomposition of the steering vector, and design smaller virtual beamformers separately optimized for each virtual array. This implies smaller matrices to invert, which increases the robustness of the beamformers, and less observations to estimate the statistics when necessary. We explain how to perform beamforming with Kronecker product filters differently from t
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