Linear Estimation and Detection in Krylov Subspaces
This book focuses on the foundations of linear estimation theory which is essential for effective signal processing. In its first part, it gives a comprehensive overview of several key methods like reduced-rank signal processing and Krylov subspace m
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Foundations in Signal Processing, Communications and Networking Series Editors: W. Utschick, H. Boche, R. Mathar Vol.1. Dietl, G. K. E. Linear Estimation and Detection in Krylov Subspaces, 2007 ISBN 978-3-540-68478-7
Guido K. E. Dietl
Linear Estimation and Detection in Krylov Subspaces
With 53 Figures and 11 Tables
Series Editors: Wolfgang Utschick TU Munich Institute for Circuit Theory and Signal Processing Arcisstrasse 21 80290 Munich, Germany
Holger Boche TU Berlin Dept. of Telecommunication Systems Heinrich-Hertz-Chair for Mobile Communications Einsteinufer 25 10587 Berlin, Germany
Rudolf Mathar RWTH Aachen University Institute of Theoretical Information Technology 52056 Aachen, Germany
Author: Guido Dietl Munich, Germany [email protected]
ISSN print edition: 1863-8538 ISBN 978-3-540-68478-7 Springer Berlin Heidelberg New York Library of Congress Control Number: 2007928954 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 for prosecution under the German Copyright Law. Springer is a part of Springer Science+Business Media springer.com c Springer-Verlag Berlin Heidelberg 2007 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. Typesetting: by the author and Integra using Springer LATEX package Cover Design: deblik, Berlin Printed on acid-free paper
SPIN: 11936770
42/3100/Integra
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To Anja
Preface
One major area in the theory of statistical signal processing is reduced-rank estimation where optimal linear estimators are approximated in low-dimensional subspaces, e. g., in order to reduce the noise in overmodeled problems, enhance the performance in case of estimated statistics, and/or save computational complexity in the design of the estimator which requires the solution of linear equation systems. This book provides a comprehensive overview over reduced-rank filters where the main emphasis is put on matrix-valued filters whose design requires the solution of linear systems with multiple right-hand sides. In particular, the multistage matrix Wiener filter, i. e., a reduced-rank Wiener filter based on the multistage decomposition, is derived in its most general form. In numerical mathematics, iterative block Krylov methods are very popular techniques for solving systems of linear equations with multiple right-hand sides, especially if the systems are large and sparse. Besides presenting a detai
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