UNITED STATES PATENT AND TRADEMARK OFFICE
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`
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`BEFORE THE PATENT TRIAL AND APPEAL BOARD
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`Google LLC,
`
`Petitioner
`
`v.
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`Vocalife LLC,
`
`Patent Owner
`
`
`
`
`Case No. IPR2022-00005
`
`U.S. Patent No. RE48,371
`____________________________________________
`
`
`Declaration of Shauna L. Wiest Regarding Van Trees
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`Page 1 of 52
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`GOOGLE EXHIBIT 1020
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`I.
`
`Introduction
`1.
`I have prepared this Declaration in connection with the Petition for
`
`Declaration of Shauna L. Wiest
`
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`Inter Partes Review of U.S. Patent No. RE48,371, which I understand will be
`
`filed concurrently with this Declaration.
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`2.
`
`I am currently a contract research analyst with the Research &
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`Information Services team at Finnegan, Henderson, Farabow, Garrett &
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`Dunner, LLP, located at 901 New York Avenue, NW, Washington, DC 20001-
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`4413.
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`3.
`
`I am over eighteen years of age, and I am competent to make this
`
`Declaration. I make this Declaration based on my own personal knowledge,
`
`and my knowledge of library science practices.
`
`4.
`
`I earned a Master of Science in Library Science from the
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`University of North Carolina at Chapel Hill in 1999, and a Bachelor of Arts in
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`Political Science from the University of California at San Diego in 1985. I
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`have worked as a librarian for over twenty years. I have been employed in the
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`Research & Information Services Department at Finnegan Henderson since
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`2021. Before that, from 2000-2015, I was employed as a Law Librarian at
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`Stoel Rives LLP. And from 2015-2016, I was employed as a Competitive
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`Intelligence Specialist for Nossaman LLP.
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`2
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`II.
`
`Declaration of Shauna L. Wiest
`
`
`Standard Library Practice for Receiving, Cataloging, and Shelving
`Materials
`I have knowledge of and experience with standard library practices
`5.
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`regarding the receipt, cataloging, and shelving of materials. I have knowledge of
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`and experience with the Machine-Readable Cataloging (MARC) system, an
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`industry-wide standard that libraries use to catalog materials.
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`6.
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`Based on standard library practice, when a library receives an item, it
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`stamps the item with the library name and often with a date within a few days or
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`weeks of receipt. The library will then catalog the item within a few days or weeks
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`of receiving it.
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`7.
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`By the mid-1970s, standard library practice involved cataloging
`
`items using the MARC system. The MARC system was developed during the
`
`1960s to standardize bibliographic records so they could be read by computers and
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`shared among libraries. By the mid-1970s, MARC had become the international
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`standard for bibliographic data. And it is still used today.
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`8.
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`After an item is cataloged, the public may access the item by
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`searching the catalog and requesting the item from the library. Standard library
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`practice is to shelve an item within a few days or weeks of cataloging it.
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`9.
`
`Given the matter of a few days or weeks between receiving an
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`item and cataloging it, and the matter of a few days or weeks between
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`
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`3
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`cataloging an item and shelving it, the total time between receiving an item and
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`Declaration of Shauna L. Wiest
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`shelving it is usually a matter of a couple of weeks or months.
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`III. MARC Records
`10. Many libraries provide public access to their MARC records via the
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`Internet and/or their electronic cataloging system at the library. In a MARC record,
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`each field provides information about the cataloged item. MARC uses a simple
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`three-digit numeric code (from 001-999) to identify each field in the record. For
`
`example, field 245 identifies the title information of the work (which includes the
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`title, other title information, and the statement of responsibility). Field 250
`
`identities the edition of the work. Field 260 identifies the publication information
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`of the work. Field 264 identifies the Production, Publication, Distribution,
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`Manufacture, and Copyright Notice information for the work. Field 020 identifies
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`the International Standard Book Number (ISBN) for the work. Field 008 provides
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`the date that the item was cataloged (Date entered on file). The first six characters
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`of field 008 are always in the “YYMMDD” format. Finally, MARC fields 500-
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`59X provide general bibliographic notes about a work.
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`IV. Library and MARC Records for Van Trees Part IV
`11. Appendix A to this declaration is a true and correct copy of the
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`Frontmatter and Index (Pages: i-xxiv), title and cover page of the book by Van
`
`Trees, Harry L., “Optimum Array Processing: Part IV of Detection, Estimation,
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`and Modulation Theory” (“Van Trees”), published by John Wiley & Sons, Inc.
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`
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`4
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`in 2002. The ISBN number for the print work is ISBN: 0-471-09390-4
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`Declaration of Shauna L. Wiest
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`(Hardback). I understand that excerpts of Van Trees have been submitted as
`
`Exhibit 1010 in this proceeding.
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`12. Appendix B to this declaration includes a true and accurate copy of
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`the MARC record from the Washington Research Library Consortium
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`(“WRLC”) for its copy of Van Trees, downloaded from https://wrlc-
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`amu.primo.exlibrisgroup.com/discovery/sourceRecord?vid=01WRLC_AMU:prod
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`&docId=alma9911024289504101&recordOwner=01WRLC_NETWORK on
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`August 23, 2021.
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`13.
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`In this WRLC MARC record, the Title Statement field 245
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`denotes the title and statement of responsibility for the work as “Optimum
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`array processing” by Harry L. Van Trees. (App’x B at 1.) Field 264 denotes
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`the publisher, location, and copyright date of the work. (App’x B at 1.) Field
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`300 denotes the complete physical description of this work. (App’x B at 1.)
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`Field 500 denotes that the work is “Pt. 4 of Detection, estimation and modulation
`
`theory.” (App’x B at 1.)
`
`14.
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`In this WRLC MARC record, Field 008 lists the first six
`
`characters “020410s2002” in typical “YYMMDD” format, indicating that Van
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`Trees was cataloged by the Washington Research Library Consortium on April
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`10, 2002. Based on standard library practices, Van Trees would have been shelved
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`and made available to the public a few days or weeks after April 10, 2002.
`5
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`Standard library practices for cataloging also include making records searchable to
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`Declaration of Shauna L. Wiest
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`the public via print and/or online library catalogs.
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`15. Appendix C to this declaration is a true and accurate copy of the
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`MARC record downloaded from the Library of Congress for its copy of Van
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`Trees at https://lccn.loc.gov/2002276850/marcxml on August 23, 2021. In this
`
`Library of Congress MARC record, Field 008 lists the date as
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`“020308m20019999nyua b 001 0 eng,” which includes the up to forty character
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`positions numbered from 00 to 39 often found within MARC Field 008 to better
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`define an item. This record indicates that Van Trees was cataloged by the Library
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`of Congress on March 8, 2002, with an indicator of “m” referring to a multi-
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`volume item with the first volume of the series published in 2001 and the last
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`volume not yet dated (“9999”). Field 008 for this record further indicates the item
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`was published in New York City (“nyu”), has illustrations (“a”), is non-fiction
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`(“0”) and is an English language publication (“eng”). (App’x C at 1.) Based on
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`standard library practices, Van Trees would have been shelved and made available
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`to the public a few days or weeks after March 8, 2002. Additionally, Library of
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`Congress MARC field tag 955 denotes “local function identifying information,”
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`including subfield code “c” which indicates that Van Trees was added to the main
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`record as “pt. 4” on 7-26-2002. (App’x C at 1.) Finally, Library of Congress
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`MARC Field 505 subfield code “a” lists the parts comprising the main title,
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`including “pt. 4. Optimum array processing.” (App’x C at 2.).
`6
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`16.
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`The United States Copyright Office, a part of the Library of
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`Declaration of Shauna L. Wiest
`
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`Congress, is the official U.S. government body that maintains records of copyright
`
`registration in the United States including a Copyright Catalog. These records are
`
`publicly accessible and are routinely used by copyright title searchers who are
`
`attempting to clear a chain of title for copyrighted works.
`
`17.
`
`Appendix D to this declaration is a true and accurate copy of the
`
`U.S. Copyright Office record for its copy of Van Trees, downloaded from
`
`https://cocatalog.loc.gov/cgi-
`
`bin/Pwebrecon.cgi?Search_Arg=optimum+array+processing&Search_Code=T
`
`ALL&PID=BBQ9pyuaH2NTAKnxXoKNlNyXd&SEQ=20210824182925&C
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`NT=25&HIST=1 on August 24, 2021.
`
`18.
`
`Appendix D indicates a title of “Optimum array processing : pt. 4 of
`
`detection, estimation, and modulation theory / Harry L. VanTrees” which is the
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`same title as found in Van Trees. The date of publication field in Appendix D is
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`listed as March 21, 2002. The “Variant title” for this record is listed as “Optimum
`
`array processing : pt. 4 of detection, estimation, and modulation theory.” (App’x D
`
`at 1.)
`
`19. WorldCat is the world’s largest network of library content and
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`services with 517,963,343 bibliographic records from over 72,000 libraries as of
`
`July 2021. (Source: https://www.oclc.org/en/worldcat/inside-worldcat.html). An
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`Online Computer Library Center (“OCLC”) number is a unique control number
`7
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`given to all bibliographic records in the WorldCat catalog. A search of the
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`Declaration of Shauna L. Wiest
`
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`WorldCat catalog for “Optimum Array Processing: Part IV of Detection,
`
`Estimation, and Modulation Theory” indicates that six editions of this title are held
`
`at 10 libraries around the world (OCLC Control Number 639211194). (App’x E at
`
`1-2, and available at http://www.worldcat.org/oclc/639211194),
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`V. Conclusion
`20.
`In signing this Declaration, I understand it will be filed as
`
`evidence in a contested case before the Patent Trial and Appeal Board of the
`
`United States Patent and Trademark Office. I understand I may be subject to
`
`cross-examination in this case and that cross-examination will take place
`
`within the United States. If cross-examination is required of me, I will appear
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`for cross-examination within the United States during the time allotted for
`
`cross-examination.
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`8
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`Declaration of Shauna L. Wiest
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`21.
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`I declare that all statements made herein of my knowledge are true,
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`that all statements made on information and belief are believed to be true, and that
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`these statements were made with the knowledge that willful false statements and
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`the like so made are punishable by fine or imprisonment, or both, under Section
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`1001 of Title 18 of the United States Code.
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`Executed on October 7, 2021, in Washington, DC.
`
`Shauna L. Wiest
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`9
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`Page 9 of 52
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`

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`APPENDIX A
`APPENDIX A
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`Page 10 of 52
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`Optimum Array Processing: Part IV of Detection, Estimation, and Modulation Theory
`Harry L. Van Trees
`Copyright © 2002 John Wiley & Sons, Inc.
`ISBNs: 0-471-09390-4 (Hardback); 0-471-22110-4 (Electronic)
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`Page 11 of 52
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`Optimum Array Processing
`Part IV of Detection, Estimation,
`and Modulation Theory
`
`HarryL. Van Trees
`
`Af)WILEY.
`
`INTERSCIENCE
`
`A JOHN WILEY & SONS, INC., PUBLICATION
`
`Page 12 of 52
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`Page 12 of 52
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`Designations used by companies to distinguish their products are often
`claimed as trademarks. In all instances where John Wiley & Sons, Inc., is
`aware of a claim, the product names appear in initial capital or ALL
`CAPITAL LETTERS. Readers, however, should contact the appropriate
`companies for more complete information regarding trademarks and
`registration.
`
`Copyright © 2002 by John Wiley & Sons, Inc. 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 or mechanical,
`including uploading, downloading, printing, decompiling, recording or
`otherwise, except as permitted under Sections 107 or 108 of the 1976
`United States Copyright Act, without the prior written permission of the
`Publisher. Requests to the Publisher for permission should be addressed to
`the Permissions Department, John Wiley & Sons, Inc., 605 Third Avenue,
`New York, NY 10158-0012, (212) 850-6011, fax (212) 850-6008,
`E-Mail: PERMREQ@WILEY.COM.
`
`This publication is designed to provide accurate and authoritative
`information in regard to the subject matter covered. It is sold with the
`understanding that the publisher is not engaged in rendering professional
`services. If professional advice or other expert assistance is required, the
`services of a competent professional person should be sought.
`
`ISBN 0-471-22110-4
`
`This title is also available in print as ISBN 0-471-09390-4.
`
`For more information about Wiley products, visit our web site at
`www.Wiley.com.
`
`Page 13 of 52
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`

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`To Diane
`
`For her continuing support and
`encouragement during the many years
`that this book was discussed, researched,
`andfinally written. More importantly,
`for her loyalty, love, and
`understanding during a sequence of
`challenging periods,
`
`and to
`
`Professor Wilbur Davenport, whose
`book introduced me to random
`processes and who was a mentor, friend,
`and supporter during my career at
`Massachusetts Institute of
`Technology.
`
`Page 14 of 52
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`Contents
`
`Preface
`
`xix
`
`1
`
`1
`Introduction
`1.1 Array Processing .. 6.6ee 2
`1.2 Applications.2... 6
`1.2.1 Radar... .. ee 6
`1.2.2 Radio Astronomy... .... 2... 00. ee eee ee
`7
`1.2.3 Sonar... 2 ee 8
`1.2.4 Communications .... 0... 00.0. ee eee eee
`9
`1.2.5 Direction Finding. ........... 000.05 ee ee
`10
`1.2.6
`Seismology 2... 2. ee ee 10
`1.2.7 Tomography .... 0... 00.0 ee eee ee ee ll
`1.2.8 Array Processing Literature... ....--...005.
`12
`1.3 Organization of the Book .. 1... 1. ee ee ee es
`12
`1.4
`Interactive Study .. 2... ee 14
`
`17
`2 Arrays and Spatial Filters
`2.1
`Introduction...2... 17
`2.2 Frequency-wavenumber Response and Beam Patterns..... 23
`2.3 Uniform Linear Arrays... 6. ee ee 37
`2.4 Uniformly Weighted Linear Arrays ......--.--. 0: 42
`2.4.1 Beam Pattern Parameters ..........-.--4. 46
`2.5 Array Steering ©... ee es 51
`2.6 Array Performance Measures ....-. +22) ee eee 59
`2.6.1 Directivity
`... 2.2... . 5.2.0.0 500222 eee 60
`2.6.2 Array Gain vs. Spatially White Noise (Ay) ......- 63
`2.6.3
`Sensitivity and the Tolerance Factor .......... 66
`2.64
`Summary ......... 0-052 5 22 ee ee eee 70
`2.7 Linear Apertures 2...2 ee 71
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`vii
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`viti
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`Contents
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`Frequency-wavenumber Response. ........... 71
`2.7.1
`2.7.2 Aperture Sampling.........ee 74
`2.8 Non-isotropic Element Patterns
`.............0.. 75
`2.9 Summary .......... 020000200 0b ee eee 78
`° 2.10 Problems 2... 0... ee 79
`
`3
`
`90
`Synthesis of Linear Arrays and Apertures
`95
`3.1 Spectral Weighting ................2.22-2205.
`3.2 Array Polynomials and the z-Transform ............ 109
`3.2.1 z-Transform....... ee ee 109
`3.2.2 Real Array Weights ............0. 0000 110
`3.2.3 Properties of the Beam Pattern Near a Zero...... 114
`3.3 Pattern Sampling in Wavenumber Space ............ 118
`3.3.1 Continuous Aperture... .... 2.0.2... eee 118
`3.3.2 Linear Arrays... 2... ee ee 120
`3.3.3 Discrete Fourier Transform ...........000.% 122
`Soc, NOMS «seat etme ew ew ea we 126
`3.3.5
`Summary ..........-...2. 000002000004 128
`3.4 Minimum Beamwidth for Specified Sidelobe Level... .... 128
`3.4.1
`Introduction
`.............2..02.-2+0224- 128
`3.4.2.
`Dolph-Chebychev Arrays .............00- 130
`34.3
`‘Taylor Distribution. 2.6.66 sei ea te tea nw s 143
`3.4.4 Villeneuve 7 Distribution ................ 147
`3.5 Least Squares Error Pattern Synthesis ............. 149
`3.6 Minimax Design .........-0-. 0.000 eee eee ee 156
`3.6.1 Alternation Theorem.......re 159
`3.6.2
`Parks-McClellan-Rabiner Algorithm .......... 160
`3.6.3
`Summary .... 2... 2... . 00202 ee ee eee 163
`3.7 Null Steering .. 2... ee 165
`3.7.1 Null Constraints .......... 0... 000008. 165
`3.7.2 Least Squares Error Pattern Synthesis with Nulls.
`.
`. 166
`3.8 Asymmetric Beams... 2... ee 173
`3.9 Spatially Non-uniform Linear Arrays... .........04. 178
`3.9.1
`Introduction ........... 0.2.2.0 00 000008 178
`3.9.2 Minimum Redundancy Arrays ............. 179
`3.9.3 Beam Pattern Design Algorithm ............ 183
`3.10 Beamspace Processing ...... 2.2.02 002.2 eee eee 192
`3.10.1 Full-dimension Beamspace................ 192
`3.10.2 Reduced-dimension Beamspace ........-..... 193
`3.10.3 Multiple Beam Antennas ............. 08. 200
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`Contents
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`1x
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`3.10.4 Summary ... 2... ee 200
`3.11 Broadband Arrays
`. 2... ee 200
`3:12 Summary «iwi kes et ew ew me ee 204
`3.138 Problems
`. 0... 0. eee ee ee ee ee ee 207
`
`231
`4 Planar Arrays and Apertures
`4.1 Rectangular Arrays... 1... ee 233
`4.1.1 Uniform Rectangular Arrays ..........004. 233
`4.1.2 Array Manifold Vector. .........525--045% 249
`4.1.3
`Separable Spectral Weightings ............. 251
`4.1.4 2-Dz-Transforms...................04. 251
`4.1.5 Least Squares Synthesis .............004. 253
`4.1.6 Circularly Symmetric Weighting and Windows .... 259
`4.1.7 Wavenumber Sampling and 2-D DFT ......... 260
`4.1.8 Transformations from One Dimension to Two Dimen-
`SIONS... se AEM EG HEE me wes 264
`4.1.9 Null Steering .. 6.65 sums wine ews wees 269
`4.1.10 Related Topics .. 2... 0.
`. ee ee 272
`4.2 Circular Arrays...1. 274
`4.2.1 Continuous Circular Arrays (Ring Apertures) ..... 275
`4.2.2 Circular Arrays... 2... .. 2. 2.2-00 00000004 280
`4.2.3
`Phase Mode Excitation Beamformers.......... 284
`4.3 Circular Apertures... 2.2. eee 289
`4.3.1
`Separable Weightings .............2000- 290
`4.3.2 Taylor Synthesis for Circular Apertures ........ 294
`4.3.3
`Sampling the Continuous Distribution ......... 298
`4.3.4 Difference Beams ........... 0.00040 eee 299
`43.5
`Summary 2.4: 6526 eeu ts peewee ws wwe ms 304
`4.4 Hexagonal Arrays... 6
`6 1 ee ee eee 305
`4.4.1
`Introduction
`.. 2... 0... ee ee ee ee 305
`4.4.2 Beam Pattern Design ..........0.02-00-- 307
`4.4.3 Hexagonal Grid to Rectangular Grid Transformation . 314
`AAA Summary... .. 2.626 se eee ee Ew ee 316
`4.5 Nonplanar Arrays... 10. 316
`4.5.1 Cylindrical Arrays
`. 2... 2 ee ee ee ee es 317
`4.5.2
`Spherical Arrays ... 1... ee eee ee ee 320
`4.6 Summary i.ss6 1 ees eee es eee Ee 321
`4.7 Problems ....... 02000 ee 322
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`oe
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`Contents
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`332
`—
`5 Characterization of Space-time Processes
`5.1
`Introduction... .. 2... 0... 0.000.002.0000 00048 332
`5.2 Snapshot Models .................2..22.0004 333
`5.2.1
`Frequency-domain Snapshot Models .......... 334
`5.2.2 Narrowband Time-domain Snapshot Models. .... . 349
`6.2.3
`Summary .. 1... ... ee ee 352
`5.3 Space-time Random Processes...
`. 1... ee ee 303
`5.3.1
`Second-moment Characterization ............ 353
`5.3.2 Gaussian Space-time Processes ............. 359
`5.3.3
`Plane Waves Propagating in Three Dimensions .. .
`. 361
`5.3.4
`1-D and 2-D Projections. ................ 365
`5.4 Arraysand Apertures ............ 0000000 ee 369
`BAL
`ATPAYS «i es awe ww tw Em EE wm Ew Om 369
`5.4.2 Apertures... . ee 374
`5.5 Orthogonal Expansions
`...........-...2...2004 3795
`5.0.1
`Plane-wave Signals... . 2... 2.0.0... eee 377
`5.5.2
`Spatially Spread Signals... ..........004. 385
`5.5.3
` Frequency-spread Signals ............008. 390
`5.0.4 Closely Spaced Signals..............000. 393
`5.5.5 Beamspace Processors .........0.. 0020085 393
`5.5.6
`Subspaces for Spatially Spread Signals ......... 394
`5.6 Parametric Wavenumber Models ..............--. 394
`5.6.1 Rational Transfer Function Models ........... 395
`5.6.2 Model Relationships ... 2... 0.0.02... 24 a 407
`5.6.3 Observation Noise ........ pote 408
`5.6.4 Summary... 2... 2 ee ees 414
`5.7 Summary ..1... 414
`5.8 Problems ... 1... ..ee 415
`
`428
`6 Optimum Waveform Estimation
`6.1
`Introduction...0... 428
`6.2 Optimum Beamformers ... 6... ee eee eee es 439
`6.2.1 Minimum Variance Distortionless Response (MVDR)
`Beamformers ... 2.2.00. ee es 440
`6.2.2 Minimum Mean-Square Error (MMSE) Estimators .
`. 446
`6.2.3 Maximum Signal-to-Noise Ratio (SNR) ........ 449
`6.2.4 Minimum PowerDistortionless Response (MPDR) Beam-
`formers .....68 ¢@ EO Rw EHH Tw ew ew 451
`Summary ......00.885 5+ Rene tee wee 452
`6.2.5
`6.3. Discrete Interference .. 1... 1. ee 452
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`Contents
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`Lt
`
`6.4
`
`6.5
`
`6.6
`
`6.7
`
`Single Plane-wave Interfering Signal .......... 453
`6.3.1
`6.3.2 Multiple Plane-wave Interferers............. 465
`6.3.3
`Summary: Discrete Interference. ............ 471
`Spatially Spread Interference ............. 2.0005 473
`6.4.1
`Physical Noise Models ..........-....04005 473
`6.4.2 ARMA Models ..............0 5000004 A474
`Multiple Plane-wave Signals... 2... ee ee 477
`6.5.1 MVDR Beamformer ................... A77
`6.5.2 MMSE Processors .........2. 0.0002 eee 485
`Mismatched MVDR and MPDRBeamformers......... 488
`6.6.1
`Introduction ........0..0...2 0200200004 488
`6.6.2 DOA Mismatch... «ise wi ee aw i wwe ws we 490
`6.6.3 Array Perturbations .......... 0.0.00 0004 501
`6.6.4 Diagonal Loading. ............. 000000, 505
`6.6.5
`Summary ...........02. 2000000000. 510
`LCMV and LCMP Beamformers .........-..-..-.-.- 513
`6.7.1 Typical Constraints ...............2.0-. 514
`6.7.2. Optimum LCMV and LCMP Beamformers ...... 526
`6.7.3 Generalized Sidelobe Cancellers............0. 528
`6.7.4
`Performance of LCMV and LCMP Beamformers
`.
`.
`. 532
`6.7.5 Quiescent Pattern (QP) Constraints .......... 547
`6.7.6 Covariance Augmentation .............0-. 504
`6.7.7
`Summary ...... 555
`Eigenvector Beamformers
`.. 1... 00. eee eee eee 596
`6.8.1
`Principal-component (PC) Beamformers........ 560
`6.8.2 Cross-spectral Eigenspace Beamformers ........ 567
`6.8.3. Dominant-mode Rejection Beamformers........ 569
`6.8.4
`Summary ........ 0000 eee ee ee 573
`Beamspace Beamformers..........0 00. eee eee 575
`6.9.1 BeamspaceMPDR.............. 0.008. 576
`6.9.2 Beamspace LCMP ............0 0000004 583
`6.9.3
`Summary: Beamspace Optimum Processors ...... 585
`Quadratically Constrained Beamformers ............ 585
`Soft-constraint Beamformers ..........005 50006 593
`6.11
`Beamforming for Correlated Signal and Interferences..... 599
`6.12
`6.12.1 Introduction 2.2... ee es 599
`6.12.2 MPDR Beamformer: Correlated Signals and Interference600
`6.12.3 MMSE Beamformer: Correlated Signals and Interference603
`6.12.4 Spatial Smoothing and Forward—Backward Averaging
`605
`6.12.5 Summary .. 1... ee 620
`
`6.8
`
`6.9
`
`6.10
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`6.13 Broadband Beamformers...........-........4. 621
`6.13.1 Introduction .......... 0.002.000.0200, 621
`6.13.2 DFT Beamformers .................00564 627
`6.13.3 Finite impulse response (FIR) Beamformers..... . 647
`6.13.4 Summary: Broadband Processing. ........... 664
`6.14 Summary ..2... 666
`6.15 Problems 2... 2... ee 669
`
`710
`7 Adaptive Beamformers
`7.1
`Introduction... 0... ee 710
`7.2 Estimation of Spatial Spectral Matrices 2... ......0.. 712
`7.2.1
`Sample Spectral Matrices ..............02. 714
`7.2.2 Asymptotic Behavior. ...............24.- 717
`7.2.3
`Forward-Backward Averaging. ...........-.- 718
`7.2.4 Structured Spectral Matrix Estimation. ........ 726
`7.2.5
`Parametric Spatial Spectral Matrix Estimation .... 726
`7.2.6
`Singular Value Decomposition. ............. 727
`7.2.7
`Summary .. 2... ee 727
`7.3 Sample Matrix Inversion (SMI) ..............0-.% 728
`7.3.1
`SINRgm;i Behavior: MVDR and MPDR........ 731
`7.3.2 LCMV and LCMP Beamformers ............ 739
`7.3.3
`Fixed Diagonal Loading ..............04. 739
`7.3.4 Toeplitz Estimators ........... 0550 eae 751
`7.3.55
`Summary ..........0.-0 5505225 eee eee 751
`7.4 Recursive Least Squares (RLS) ........ 0200+ eee 752
`7.4.1 Least Squares Formulation .............6. 752
`7.4.2 Recursive Implementation ................ 756
`7.4.3 Recursive Implementation of LSE Beamformer ... . 763
`7.4.4 Generalized Sidelobe Canceller ............. 766
`7.4.5
` Quadratically Constrained RLS............. 768
`7.4.6 Conjugate Symmetric Beamformers .......... 773
`7.4.7
`Summary .. 1... 777
`7.5 Efficient Recursive Implementation Algorithms ........ 778
`7.5.1
`Introduction ..........0 2.2002 eee es 778
`7.5.2 QR Decomposition (QRD)
`........--2-0-55 779
`7.6 Gradient Algorithms ... 2.0.0.0... 0.000052 eee 789
`7.6.1
`Introduction 2... ee ee 789
`7.6.2
`Steepest Descent: MMSE Beamformers ........ 791
`7.6.3
`Steepest Decent: LCMP Beamformer ......... 799
`
`7.6.4 Summary .... 2....ee ee ee 805
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`7.7 LMS Algorithms .................2.2.22005. 805
`7.7.1 Derivation of the LMS Algorithms ........... 806
`7.7.2
`Performance of the LMS Algorithms .......... 813
`7.7.8.
`LMS Algorithm Behavior ................ 817
`7.74 Quadratic Constraints ............. 00006 822
`7.7.5
`Summary: LMS algorithms ............... 826
`7.8 Detection of Signal Subspace Dimension ............ 827
`7.8.1 Detection Algorithms .................. 828
`7.8.2 Eigenvector Detection Tests. .............. 841
`7.9 Eigenspace and DMR Beamformers............... 845
`7.9.1
`Performance of SMI Eigenspace Beamformers .... . 846
`7.9.2 Eigenspace and DMR Beamformers: Detection of Sub-
`space Dimension ............-. 00%) ee eee 850
`Subspace tracking ............0. 00000. 860
`7.9.3
`Summary .........0.. 0000 eee ee eee 863
`7.9.4
`7.10 Beamspace Beamformers...........-....2-2-4. 864
`7.10.1 BeamspaceSMI..............0. 2.000004 865
`7.10.2 Beamspace RLS ..................00.. 869
`7.10.3 Beamspace LMS .............. 00000048 872
`7.10.4 Summary: Adaptive Beamspace Processing ...... 873
`7.11 Broadband Beamformers............. 00000005 874
`7.11.1 SMI Implementation ...............000. 875
`7.11.2 LMS Implementation. .................. 878
`7.11.3 GSC: Multichannel Lattice Filters ........... 884
`Cilla SUMMERS «we wt ew te ee 885
`7.12 Summary... 2... cc aw EH 885
`7.13 Problems ........0. 00000 ee ee 887
`
`917
`8 Parameter Estimation I: Maximum Likelihood
`8.1
`Introduction... 2...2. 917
`8.2. Maximum Likelihood and Maximumaposteriori Estimators . 920
`8.2.1 Maximum Likelihood (ML) Estimator ......... 922
`8.2.2 Maximum a posteriori (MAP) Estimator ....... 924
`8.2.3 Cramér-Rao Bounds ... 1... 0.0 ee eee 925
`8.3 Parameter Estimation Model ..............0.4. 933
`8.3.1 Multiple Plane Waves .........-.-.22000- 933
`8.3.2 Model Perturbations ............. 020050, 936
`8.3.3
`Parametric Spatially Spread Signals .......... 938
`8.3.4
`Summary ......... 2.0. eee ee ee 938
`8.4 Cramér-Rao Bounds ..........-.-. 0.000850 0 | 938
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`8.5
`
`8.6
`
`8.7
`
`8.8
`8.9
`
`8.10
`
`8.4.1 Gaussian Model: Unknown Signal Spectrum. .... . 939
`8.4.2 Gaussian Model: Uncorrelated Signals with Unknown
`Power «i: ee tee eww EE ew ee ww ES 958
`8.4.3 Gaussian Model: Known Signal Spectrum ....... 967
`8.4.4 Nonrandom (Conditional) Signal Model ........ 971
`8.4.5 Known Signal Waveforms ................ 978
`8.4.6
`Summary ........ eee 980
`Maximum Likelihood Estimation ................ 984
`8.5.1 Maximum Likelihood Estimation ............ 984
`8.5.2 Conditional Maximum Likelihood Estimators ..... 1004
`8.5.3 Weighted Subspace Fitting ............0... 1009
`8.5.4 Asymptotic Performance...............2.. 1014
`8.5.5 Wideband Signals ........ 0.0.00 e eevee 1015
`8.5.6
`Summary ......... 0.00. ee eee ee ee 1018
`Computational Algorithms ....... 0... 000024 1018
`8.6.1 Optimization Techniques ...........0026. 1018
`8.6.2 Alternating Maximization Algorithms ......... 1025
`8.6.3 Expectation Maximization Algorithm ......... 1031
`8.6.4
`Summary ............. 0.000500 2a ee 1037
`Polynomial Parameterization ©... 1 ee ee 1037
`8.7.1
`Polynomial Parameterization .............. 1038
`8.7.2
`Iterative Quadratic Maximum Likelihood (IQML)
`.. 1039
`8.7.3
`Polynomial WSF (MODE) ............... 1045
`8.7.4
`Summary ......-20 se ieee ewe we mS 1053
`Detection of Number of Signals ..............085 1054
`Spatially Spread Sighals ... 2. ee i eu eee ee ewe es 1055
`8.9.1
`Parameterized S(0,¢) 2... 6. eee ee ee 1055
`8.9.2
`Spatial ARMA Process ............00005 1062
`8.9.3
`Summary .... 2... 1062
`Beamspace algorithms ..............0-..050006. 1062
`8.10.1 Introduction 2... 2. ee 1062
`8.10.2 Beamspace Matrices ... 2.2... 0.00.00. ee 1065
`8.10.3 Beamspace Cramér-Rao Bound ............. 1073
`8.10.4 Beamspace Maximum Likelihood ............ 1081
`8.10.5 Summary .. 2... ee 1088
`Sensitivity, Robustness, and Calibration ............ 1088
`8.11.1 Model Perturbations
`................2.. 1089
`8.11.2 Cramér-Rao Bounds .......... 0.05 ee ae 1090
`8.11.3 Sensitivity of ML Estimators .............. 1098
`8.11.4 MAP Joint Estimation. .............0.04. 1099
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`8.11.5 Self&Calibration Algorithms ............... 1101
`8.11.6 Summary ... 1... ee 1102
`8.12 Summary .. 2... ee 1102
`8.12.1 Major Results... 2. ee 1102
`8.12.2 Related Topics ..........0..2.20 2222005 1105
`8.12.3 Algorithm complexity .. 1.6. ee ee ee es 1108
`8.13 Problems
`.. 1...ee 1109
`
`1139
`9 Parameter Estimation II
`9.1
`Introduction ......... 0200 eee ee ee 1139
`9.2 Quadratic Algorithms
`.. 2... 0.0.0 eee eee ees 1140
`9.2.1
`Introduction ......... 00.0000 eee ee ee 1140
`9.2.2 Beamscan Algorithms .............0004- 1142
`9.2.3 MVDR (Capon) Algorithm ............-..- 1144
`9.2.4 Root Versions of Quadratic Algorithms ........ 1147
`9.2.5
`Performance of MVDR Algorithms ........... 1148
`926 Summary .....: 642865 eRe tw ew 1149
`9.3 Subspace Algorithms... 1... ee 1155
`9.3.1
`Introduction ... 2.2.2... .0 00 2 ee eee eee 1155
`9.3.2 MUSIC .........2. 00.0.2 ee ee 1158
`9.3.3 Minimum-Norm Algorithm .............--. 1163
`93.4 ESPRIT....-. nn cnn re bw R EHD 1170
`9.3.5 Algorithm Comparison. .........-.-++-++-- 1189
`9.3.6
`Summary .. 2.6 cs os wee wee ee ee 1190
`9.4 Linear Prediction... 2... es 1194
`9.5 Asymptotic Performance... 2... 0 eee ee ee ee ee 1195
`9.5.1 Error Behavior ...... 2.2... 00050 ee eee 1195
`9.5.2 Resolution of MUSIC and Min-Norm.......... 1203
`9.5.3
`Small Error Behavior of Algorithms .......... 1211
`9.5.4
`Summary .. 2... ee es 1233
`9.6 Correlated and Coherent Signals .............-.-. 1233
`06.1
`Introdmclion
`«i: acuwt emi eer nen ne es wes 1233
`9.6.2
`Forward-Backward Spatial Smoothing ......... 1235
`9.6.3
`Summary... .. 2.2... 2 eee ee es 1241
`9.7 Beamspace Algorithms... 1... 2... ee ee es 1243
`9.7.1 Beamspace MUSIC........... 00502004. 1243
`9.7.2 Beamspace Unitary ESPRIT .............-. 1247
`9.7.3 BeamspaceSummary
`.........2++-++-0555 1251
`9.8 Sensitivity and Robustness ......-- ee ee eee eee 1251
`99 Planar Arrays... i sa i we twee ew Ee 1255
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`Standard Rectangular Arrays ........200040. 1255
`9.9.1
`9.9.2 Hexagonal Arrays
`.. 1.2.2.0... - 0000222 1272
`9.9.3
`Summary: Planar Arrays
`.. 1... 0.2.0.2. 0 00% 1279
`9.10 Summary .1. 1279
`9.10.1 Major Results... 2... .....0....02222020-. 1279
`9.10.2 Related Topics
`. 2... ee eee 1282
`9.10.8 Discussion... 2... le 1285
`Q11 Problems
`. 2.2... 0... 1285
`
`1318
`10 Detection and Other Topics
`10.1 Optimum Detection .. 2... ee ee ee ee 1318
`10.1.1 Classic Binary Detection... ......-...204. 1319
`10.1.2 Matched Subspace Detector... ..........4. 1320
`10.1.3 Spatially Spread Gaussian Signal Processes ..... . 1321
`10.1.4 Adaptive Detection... 2... 6... ee eee 1323
`10.2 Related Topics 2. 1... ee 1327
`10.3 Epilogue... ee 1329
`10.4 Problems 2... 1329
`
`1340
`A Matrix Operations
`A.1 Introduction. 2... ee 1340
`A.2 Basic Definitions and Properties ............---. 1341
`A.2.1 Basic Definitions .. 2... ee 1341
`A.2.2 Matrix Inverses . 2... ee 1347
`A.2.3 Quadratic Forms .........0. 200222220085 1348
`A.2.4 Partitioned Matrices... 1... ee ee ee ee 1349
`A.2.5 Matrix products
`.. 2... 0.0.0... 2 ee eee eee 1351
`A.2.6 Matrix Inequalities... 2... ee ee 1356
`A.3 Special Vectors and Matrices... 1... 0. ee ee eee 1356
`A.3.1 Elementary Vectors and Matrices. ...........- 1356
`A.3.2 The vec(A) matrix... ee 1358
`A.3.3 Diagonal Matrices... 2... 22 ee ees 1359
`A.3.4 Exchange Matrix and Conjugate Symmetric Vectors
`. 1361
`A.3.5 Persymmetric and Centrohermitian Matrices ..... 1362
`A.3.6 Toeplitz and Hankel Matrices. .......-.-.-.-. 1364
`A.3.7. Circulant Matrices 2... 1365
`A.3.8 Triangular Matrices
`.. 2... 0... 22 eee eee 1366
`A.3.9 Unitary and Orthogonal Matrices... .....--4. 1367
`A.3.10 Vandermonde Matrices... ......-2+++005- 1368
`A.3.11 Projection Matrices
`. 2... 1 ee ee 1369
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`A.3.12 Generalized Inverse... .....------022005 1370
`A.4 Ejigensystems .. 2... 0. ee es 1372
`A.4.1 Eigendecomposition ..........-+ 552200 - 1372
`A.4.2 Special Matrices 2... 6. ee 1376
`A.5 Singular Value Decomposition. ........-..--++5455 1381
`A.6 QR Decomposition... 00. ee 1387
`A.6.1
`Introduction ......4: 84s 06 sma we ww 1387
`A.6.2 QR Decomposition. .............2-2505.4 1388
`A.6.3 Givens Rotation . 1... 0... ee ee ee 1390
`A.6.4 Householder Transformation. .............. 1394
`A.7 Derivative Operations
`.. 1... ee