UNITED STATES PATENT AND TRADEMARK OFFICE
`
`
`
`
`
`
`BEFORE THE PATENT TRIAL AND APPEAL BOARD
`
`
`
`
`
`
`
`
`
`Google LLC,
`
`Petitioner
`
`v.
`
`Vocalife LLC,
`
`Patent Owner
`
`
`
`
`Case No. IPR2022-00004
`
`U.S. Patent No. RE47,049
`____________________________________________
`
`
`Declaration of Shauna L. Wiest Regarding Van Trees
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`
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`
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`Page 1 of 52
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`GOOGLE EXHIBIT 1019
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`
`
`I.
`
`Introduction
`1.
`I have prepared this Declaration in connection with the Petition for
`
`Declaration of Shauna L. Wiest
`
`
`Inter Partes Review of U.S. Patent No. RE47,049, which I understand will be
`
`filed concurrently with this Declaration.
`
`2.
`
`I am currently a contract research analyst with the Research &
`
`Information Services team at Finnegan, Henderson, Farabow, Garrett &
`
`Dunner, LLP, located at 901 New York Avenue, NW, Washington, DC 20001-
`
`4413.
`
`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
`
`University of North Carolina at Chapel Hill in 1999, and a Bachelor of Arts in
`
`Political Science from the University of California at San Diego in 1985. I
`
`have worked as a librarian for over twenty years. I have been employed in the
`
`Research & Information Services Department at Finnegan Henderson since
`
`2021. Before that, from 2000-2015, I was employed as a Law Librarian at
`
`Stoel Rives LLP. And from 2015-2016, I was employed as a Competitive
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`Intelligence Specialist for Nossaman LLP.
`
`
`
`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
`5.
`
`practices regarding the receipt, cataloging, and shelving of materials. I have
`
`knowledge of and experience with the Machine-Readable Cataloging (MARC)
`
`system, an industry-wide standard that libraries use to catalog materials.
`
`6.
`
`Based on standard library practice, when a library receives an item, it
`
`stamps the item with the library name and often with a date within a few days or
`
`weeks of receipt. The library will then catalog the item within a few days or weeks
`
`of receiving it.
`
`7.
`
`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
`
`shared among libraries. By the mid-1970s, MARC had become the international
`
`standard for bibliographic data. And it is still used today.
`
`8.
`
`After an item is cataloged, the public may access the item by
`
`searching the catalog and requesting the item from the library. Standard library
`
`practice is to shelve an item within a few days or weeks of cataloging it.
`
`9.
`
`Given the matter of a few days or weeks between receiving an
`
`item and cataloging it, and the matter of a few days or weeks between
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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
`
`
`shelving it is usually a matter of a couple of weeks or months.
`
`III. MARC Records
`10. Many libraries provide public access to their MARC records via the
`
`Internet and/or their electronic cataloging system at the library. In a MARC record,
`
`each field provides information about the cataloged item. MARC uses a simple
`
`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
`
`title, other title information, and the statement of responsibility). Field 250
`
`identities the edition of the work. Field 260 identifies the publication information
`
`of the work. Field 264 identifies the Production, Publication, Distribution,
`
`Manufacture, and Copyright Notice information for the work. Field 020 identifies
`
`the International Standard Book Number (ISBN) for the work. Field 008 provides
`
`the date that the item was cataloged (Date entered on file). The first six characters
`
`of field 008 are always in the “YYMMDD” format. Finally, MARC fields 500-
`
`59X provide general bibliographic notes about a work.
`
`IV. Library and MARC Records for Van Trees Part IV
`11. Appendix A to this declaration is a true and correct copy of the
`
`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,
`
`and Modulation Theory” (“Van Trees”), published by John Wiley & Sons, Inc.
`
`
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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
`
`
`(Hardback). I understand that excerpts of Van Trees have been submitted as
`
`Exhibit 1009 in this proceeding.
`
`12. Appendix B to this declaration includes a true and accurate copy of
`
`the MARC record from the Washington Research Library Consortium
`
`(“WRLC”) for its copy of Van Trees, downloaded from https://wrlc-
`
`amu.primo.exlibrisgroup.com/discovery/sourceRecord?vid=01WRLC_AMU:prod
`
`&docId=alma9911024289504101&recordOwner=01WRLC_NETWORK on
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`August 23, 2021.
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`13.
`
`In this WRLC MARC record, the Title Statement field 245
`
`denotes the title and statement of responsibility for the work as “Optimum
`
`array processing” by Harry L. Van Trees. (App’x B at 1.) Field 264 denotes
`
`the publisher, location, and copyright date of the work. (App’x B at 1.) Field
`
`300 denotes the complete physical description of this work. (App’x B at 1.)
`
`Field 500 denotes that the work is “Pt. 4 of Detection, estimation and modulation
`
`theory.” (App’x B at 1.)
`
`14.
`
`In this WRLC MARC record, Field 008 lists the first six
`
`characters “020410s2002” in typical “YYMMDD” format, indicating that Van
`
`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
`
`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
`
`
`the public via print and/or online library catalogs.
`
`15. Appendix C to this declaration is a true and accurate copy of the
`
`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
`
`“020308m20019999nyua b 001 0 eng,” which includes the up to forty character
`
`positions numbered from 00 to 39 often found within MARC Field 008 to better
`
`define an item. This record indicates that Van Trees was cataloged by the Library
`
`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
`
`standard library practices, Van Trees would have been shelved and made available
`
`to the public a few days or weeks after March 8, 2002. Additionally, Library of
`
`Congress MARC field tag 955 denotes “local function identifying information,”
`
`including subfield code “c” which indicates that Van Trees was added to the main
`
`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,
`
`including “pt. 4. Optimum array processing.” (App’x C at 2.).
`6
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`16.
`
`The United States Copyright Office, a part of the Library of
`
`Declaration of Shauna L. Wiest
`
`
`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
`
`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
`
`same title as found in Van Trees. The date of publication field in Appendix D is
`
`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
`
`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
`
`
`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),
`
`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
`
`for cross-examination within the United States during the time allotted for
`
`cross-examination.
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`
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`
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`8
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`21.
`
`I declare that all statements made herein of my knowledge are true,
`
`Declaration of Shauna L. Wiest
`
`
`that all statements made on information and belief are believed to be true, and that
`
`these statements were made with the knowledge that willful false statements and
`
`the like so made are punishable by fine or imprisonment, or both, under Section
`
`1001 of Title 18 of the United States Code.
`
`
`Executed on October 7, 2021, in Washington, DC.
`
`
`
`
`Shauna L. Wiest
`
`
`
`9
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`Page 9 of 52
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`APPENDIX A
`APPENDIX A
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`Page 10 of 52
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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)
`
`Optimum Array Processing
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`Page 11 of 52
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`Optimum Array Processing
`Part IV of Detection, Estimation,
`and Modulation
`Theory
`
`Harry L. Van Trees
`
`WILEY-
`INTERSCIENCE
`
`A JOHN WILEY & SONS,
`
`INC., PUBLICATION
`
`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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`

`

`To Diane
`
`and
`support
`For her continuing
`encouragement
`during
`the many years
`that
`this book was discussed,
`researched,
`and finally written.
`More
`importantly,
`for her loyalty,
`love, and
`understanding
`during
`a sequence
`challenging
`periods,
`
`of
`
`and
`
`to
`
`whose
`
`Davenport,
`Professor Wilbur
`me to random
`book
`introduced
`friend,
`and who was a mentor,
`processes
`and supporter
`during my career
`at
`Massachusetts Institute of
`Technology.
`
`Page 14 of 52
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`

`

`Contents
`
`Preface
`
`1
`
`Introduction
`.........................
`1.1 Array Processing
`............................
`1.2 Applications
`...........................
`1.2.1
`Radar
`.....................
`1.2.2
`Radio Astronomy
`...........................
`1.2.3
`Sonar
`.....................
`1.2.4
`Communications
`.....................
`1.2.5
`Direction
`Finding
`........................
`1.2.6
`Seismology
`.......................
`1.2.7
`Tomography
`...............
`1.2.8
`Array Processing
`Literature
`....................
`1.3 Organization
`of the Book
`.........................
`1.4
`Interactive
`Study
`
`Filters
`and Spatial
`2 Arrays
`............................
`Introduction
`2.1
`Frequency-wavenumber
`Response and Beam Patterns
`2.2
`......................
`2.3 Uniform
`Linear Arrays
`2.4 Uniformly Weighted
`Linear Arrays
`2.4.1
`Beam Pattern Parameters
`..........................
`2.5 Array Steering
`..................
`2.6 Array Performance Measures
`........................
`2.6.1
`Directivity
`2.6.2
`Array Gain vs. Spatially White Noise
`2.6.3
`Sensitivity
`and
`the Tolerance
`Factor
`.........................
`2.6.4
`Summary
`.........................
`Linear Apertures
`
`2.7
`
`...............
`................
`
`(A,)
`..........
`
`xix
`
`1
`2
`6
`6
`7
`8
`9
`10
`10
`11
`12
`12
`14
`
`17
`17
`23
`37
`42
`46
`51
`59
`60
`63
`66
`70
`71
`
`.....
`
`......
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`Viii
`
`Contents
`
`Response
`Frequency-wavenumber
`2.7.1
`.....................
`Aperture
`Sampling
`2.7.2
`................
`Element
`Patterns
`2.8 Non-isotropic
`2.9
`Summary
`.............................
`2.10 Problems
`.............................
`
`............
`
`and Apertures
`Arrays
`of Linear
`Synthesis
`........................
`3.1 Spectral Weighting
`and
`the z-Transform
`3.2
`Array
`Polynomials
`........................
`3.2.1
`z-Transform
`...................
`3.2.2
`Real Array Weights
`3.2.3
`Properties
`of the Beam Pattern Near a Zero
`............
`Pattern
`Sampling
`in Wavenumber
`Space
`...................
`3.3.1
`Continuous
`Aperture
`.......................
`3.3.2
`Linear Arrays
`3.3.3
`Discrete
`Fourier
`Transform
`...........................
`3.3.4 Norms
`.........................
`3.3.5
`Summary
`3.4 Minimum
`Beamwidth
`for Specified Sidelobe Level
`.......................
`3.4.1
`Introduction
`................
`3.4.2
`Dolph-Chebychev
`Arrays
`....................
`3.4.3 Taylor Distribution
`................
`3.4.4
`Villeneuve
`fi Distribution
`.............
`Least Squares Error Pattern
`Synthesis
`3.5
`.........................
`3.6 Minimax
`Design
`......
`3.6.1
`Alternation
`Theorem
`3.6.2
`Parks-McClellan-Rabiner
`.........................
`3.6.3
`Summary
`...........................
`3.7. Null Steering
`.....................
`3.7.1
`Null Constraints
`3.7.2
`Least Squares Error Pattern
`........................
`Asymmetric
`Beams
`Spatially
`Non-uniform
`Linear Arrays
`.......................
`3.9.1
`Introduction
`3.9.2
`Minimum
`Redundancy
`Arrays
`39.3
`Beam Pattern
`Design Algorithm
`......................
`3.10 Beamspace
`Processing
`................
`3.10.1
`Full-dimension
`Beamspace
`.............
`3.10.2 Reduced-dimension
`Beamspace
`................
`3.10.3 Multiple
`Beam Antennas
`
`71
`74
`75
`78
`79
`
`90
`95
`109
`109
`110
`114
`118
`118
`120
`122
`126
`128
`128
`128
`130
`143
`147
`149
`156
`159
`160
`163
`165
`165
`166
`173
`178
`178
`179
`183
`192
`192
`193
`200
`
`...
`
`3.3
`
`,3.8
`3.9
`
`............
`
`...............
`
`......
`
`.......
`
`Y.
`Algorithm
`
`...........
`..........
`
`Synthesis
`
`with Nulls
`
`..............
`
`.............
`............
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`Page 16 of 52
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`Contents
`
`.........................
`3.10.4 Summary
`........................
`3.11 Broadband
`Arrays
`.............................
`3.12 Summary
`.............................
`3.13 Problems
`
`4
`
`....
`
`and Apertures
`Arrays
`Planar
`........................
`Arrays
`4.1 Rectangular
`..............
`4.1.1
`Uniform Rectangular
`Arrays
`..................
`4.1.2
`Array Manifold
`Vector
`.............
`4.1.3
`Separable Spectral Weightings
`.....................
`4.1.4
`2-D z-Transforms
`.................
`4.1.5
`Least Squares Synthesis
`4.1.6
`Circularly
`Symmetric Weighting
`and Windows
`.........
`4.1.7 Wavenumber
`Sampling
`and 2-D DFT
`4.1.8
`Transformations
`from One Dimension
`to Two Dimen-
`............................
`sions
`.......................
`Null Steering
`4.1.9
`......................
`4.1.10 Related Topics
`..........................
`4.2 Circular Arrays
`4.2.1
`Continuous
`Circular Arrays
`......................
`4.2.2
`Circular Arrays
`4.2.3
`Phase Mode Excitation
`Beamformers
`........................
`4.3 Circular
`Apertures
`..................
`4.3.1
`Separable Weightings
`4.3.2
`Taylor Synthesis
`for Circular Apertures
`4.3.3
`Sampling
`the Continuous
`Distribution
`.....................
`4.3.4
`Difference Beams
`.........................
`4.3.5
`Summary
`.........................
`4.4 Hexagonal
`Arrays
`.......................
`4.4.1
`Introduction
`..................
`4.4.2
`Beam Pattern Design
`4.4.3
`Hexagonal Grid
`to Rectangular
`Grid Transformation
`.........................
`4.4.4
`Summary
`.........................
`4.5 Nonplanar
`Arrays
`....................
`4.5.1
`Cylindrical
`Arrays
`.....................
`4.5.2
`Spherical Arrays
`.............................
`Summary
`4.6
`.............................
`4.7 Problems
`
`(Ring Apertures)
`
`.....
`
`..........
`
`........
`.........
`
`ix
`
`200
`200
`204
`207
`
`231
`233
`233
`249
`251
`251
`253
`259
`260
`
`264
`269
`272
`274
`275
`280
`284
`289
`290
`294
`298
`299
`304
`305
`305
`307
`. 314
`316
`316
`317
`320
`321
`322
`
`Page 17 of 52
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`X
`
`Contents
`
`Processes
`
`.
`
`....
`
`332
`332
`333
`334
`349
`352
`353
`353
`359
`361
`365
`369
`369
`374
`375
`377
`385
`390
`393
`393
`394
`394
`395
`407
`408
`414
`414
`415
`
`of Space-time
`5 Characterization
`............................
`5.1
`Introduction
`5.2 Snapshot Models
`.........................
`..........
`5.2.1
`Frequency-domain
`Snapshot Models
`5.2.2 Narrowband Time-domain Snapshot Models ......
`.........................
`5.2.3
`Summary
`5.3 Space-time Random Processes ..................
`............
`5.3.1
`Second-moment
`Characterization
`.............
`5.3.2
`Gaussian
`Space-time
`Processes
`5.3.3 Plane Waves Propagating
`in Three Dimensions
`.................
`5.3.4
`1-D and 2-D Projections
`......................
`5.4 Arrays and Apertures
`...........................
`5.4.1
`Arrays
`.........................
`5.4.2
`Apertures
`.....................
`5.5 Orthogonal
`Expansions
`....................
`5.5.1
`Plane-wave
`Signals
`5.5.2 Spatially Spread Signals .................
`................
`5.5.3
`Frequency-spread
`Signals
`..................
`5.5.4
`Closely Spaced Signals
`..................
`5.5.5
`Beamspace
`Processors
`5.5.6
`Subspaces
`for Spatially
`Spread Signals
`................
`5.6 Parametric Wavenumber Models
`...........
`5.6.1
`Rational
`Transfer
`Function Models
`...................
`5.6.2
`Model Relationships
`........
`5.6.3
`Observation
`Noise
`.........................
`5.6.4
`Summary
`.............................
`Summary
`.............................
`Problems
`
`.........
`
`..........
`
`2
`
`.
`
`5.7
`5.8
`
`428
`Estimation
`Waveform
`6 Optimum
`6.1
`Introduction
`. . . . . . . . . . . . . . . . . . . . . . . . . . . . 428
`6.2 Optimum
`Beamformers
`. . . . . . . . . . . . . . . . . . . . . 439
`Minimum
`Variance Distortionless
`Response
`(MVDR)
`6.2.1
`Beamformers
`. . . . . . . . . . . . . . . . . . . . . . . 440
`Minimum
`Mean-Square
`Error
`(MMSE)
`Estimators
`. . 446
`Maximum
`Signal-to-Noise
`Ratio
`(SNR)
`. . . . . . . . 449
`Minimum
`Power Distortionless
`Response
`(MPDR)
`Beam-
`formers
`. . . . . . . . . . . . . . . . . . . . . . . . . . 451
`Summary
`. . . . . . . . . . . . . . . . . . . . . . . . . 452
`Interference
`. . . . . . . . . . . . . . . . . . . . . . . 452
`
`6.2.5
`Discrete
`
`6.3
`
`6.2.2
`6.2.3
`6.2.4
`
`Page 18 of 52
`
`

`

`64 .
`
`65 .
`
`66 .
`
`67 .
`
`68 .
`
`69 .
`
`......
`
`...
`
`........
`........
`........
`
`Contents
`
`Xi
`
`Signal
`
`..........
`
`453
`Interfering
`Single Plane-wave
`6.3.1
`465
`Interferers
`6 3.2 Multiple
`Plane-wave
`471
`..........................
`63.3
`Summary:
`Interference
`Discrete
`473
`..................
`Spatially
`Spread
`Interference
`473
`..................
`6.4.1 Physical Noise Models
`474
`......................
`6.4.2
`ARMA Models
`477
`...................
`Multiple
`Plane-wave Signals
`477
`...................
`6.5.1
`MVDR
`Beamformer
`485
`....................
`6.5.2
`MMSE Processors
`488
`Mismatched MVDR and MPDR Beamformers .........
`488
`6.6.1
`Introduction
`.......................
`490
`......................
`6.6.2
`DOA Mismatch
`501
`...................
`6.6.3
`Array Perturbations
`505
`.....................
`6.6.4
`Diagonal
`Loading
`510
`.........................
`6.6.5
`Summary
`513
`and LCMP
`LCMV
`................
`Beamformers
`514
`...................
`6.7.1
`Typical Constraints
`526
`6.7.2
`Optimum
`LCMV
`and LCMP
`Beamformers
`528
`.............
`6.7.3
`Generalized
`Sidelobe Cancellers
`532
`6.7.4
`Performance
`of LCMV
`and LCMP
`Beamformers
`547
`..........
`6.7.5
`Quiescent
`Pattern
`(QP) Constraints
`554
`................
`6.7.6 Covariance Augmentation
`555
`6.7.7
`Summary
`.........................
`556
`....................
`Eigenvector
`Beamformers
`560
`6.8.1
`Principal-component
`(PC) Beamformers
`567
`6.8.2
`Cross-spectral
`Eigenspace
`Beamformers
`569
`6.8.3
`Dominant-mode
`Rejection
`Beamformers
`573
`6.8.4
`Summary
`.........................
`575
`Beamspace Beamformers .....................
`576
`....................
`6.9.1
`Beamspace MPDR
`583
`....................
`6.9.2
`Beamspace
`LCMP
`585
`......
`Processors
`6.9.3
`Summary:
`Beamspace Optimum
`. . . . . . . . . . . . 585
`6.10 Quadratically
`Constrained
`Beamformers
`6.11 Soft-constraint
`Beamformers
`. . . . . . . . . . . . . . . . . . 593
`6.12 Beamforming
`for Correlated
`Signal and
`Interferences
`. . . . . 599
`6.12.1
`Introduction
`. . . . . . . . . . . . . . . . . . . . . . . 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
`. . . . . . . . . . . . . . . . . . . . . . . . . 620
`
`Page 19 of 52
`
`

`

`Xii
`
`Contents
`
`6.13
`
`6.14
`6.15
`
`.....................
`Bearnformers
`Broadband
`.......................
`6.13.1
`Introduction
`....................
`6.13.2 DFT Beamformers
`Beamformers
`6.13.3 Finite
`impulse
`response
`(FIR)
`............
`6.13.4 Summary:
`Broadband
`Processing
`.............................
`Summary
`.............................
`Problems
`
`......
`
`621
`621
`627
`647
`664
`666
`669
`
`710
`710
`712
`714
`717
`718
`726
`726
`727
`727
`728
`731
`739
`739
`751
`751
`752
`752
`756
`763
`766
`768
`773
`777
`778
`778
`779
`789
`789
`791
`799
`805
`
`....
`
`....
`
`Beamformers
`7 Adaptive
`............................
`7.1
`Introduction
`............
`7.2
`Estimation
`of Spatial Spectral Matrices
`................
`7.2.1
`Sample Spectral Matrices
`...................
`7.2.2
`Asymptotic
`Behavior
`..............
`7.2.3
`Forward-Backward
`Averaging
`.........
`7.2.4
`Structured
`Spectral Matrix
`Estimation
`7.2.5
`Parametric
`Spatial Spectral Matrix
`Estimation
`..............
`7.2.6
`Singular Value Decomposition
`.........................
`7.2.7
`Summary
`.................
`Sample Matrix
`Inversion
`(SMI)
`7.3.1
`SINRsmi
`Behavior:
`MVDR
`and MPDR
`............
`7.3.2
`LCMV
`and LCMP
`Beamformers
`.................
`7.3.3
`Fixed Diagonal
`Loading
`...................
`7.3.4
`Toeplitz Estimators
`.........................
`7.3.5
`Summary
`.................
`7.4 Recursive
`Least Squares
`(RLS)
`...............
`7.4.1
`Least Squares Formulation
`................
`7.4.2
`Recursive
`Implement
`ation
`of LSE Beamformer
`7.4.3
`Recursive
`Implementation
`.............
`7.4.4
`Generalized
`Sidelobe Canceller
`.............
`7.4.5
`Quadratically
`Constrained
`RLS
`..........
`7.4.6
`Conjugate
`Symmetric
`Beamformers
`.........................
`7.4.7
`Summary
`Efficient Recursive
`Implementation
`.......................
`7.5.1
`Introduction
`7.5.2
`QR Decomposition
`(QRD)
`.......................
`7.6 Gradient
`Algorithms
`.......................
`7.6.1
`Introduction
`7.6.2
`Steepest Descent: MMSE Beamformers
`7.6.3
`Steepest Decent:
`LCMP
`Beamformer
`.........................
`7.6.4
`Summary
`
`Algorithms
`
`........
`
`...............
`
`........
`.........
`
`........
`
`7.3
`
`7.5
`
`Page 20 of 52
`
`

`

`Contents
`
`7.7
`
`...........
`..........
`
`LMS Algorithms
`.........................
`of the LMS Algorithms
`7.7.1
`Derivation
`of the LMS Algorithms
`7.7.2
`Performance
`................
`7.7.3
`LMS Algorithm
`Behavior
`..................
`7.7.4 Quadratic Constraints
`...............
`7.7.5
`Summary:
`LMS algorithms
`............
`7.8 Detection of Signal Subspace Dimension
`..................
`7.8.1
`Detection
`Algorithms
`...............
`7.8.2
`Eigenvector
`Detection
`Tests
`7.9 Eigenspace and DMR Beamformers ...............
`.....
`7.9.1
`Performance
`of SMI Eigenspace
`Beamformers
`7.9.2 Eigenspace and DMR Beamformers: Detection of Sub-
`space Dimension
`......................
`....................
`Subspace
`tracking
`7.9.3
`.........................
`Summary
`7.9.4
`.....................
`7.10 Beamspace
`Beamformers
`......................
`7.10.1 Beamspace SMI
`.....................
`7.10.2 Beamspace RLS
`7.10.3 Beamspace
`LMS
`.....................
`7.10.4 Summary:
`Adaptive
`Beamspace
`.....................
`7.11 Broadband
`Beamformers
`7.11.1 SMI Implementation
`...................
`7.11.2
`LMS
`Implementation
`...................
`Lattice Filters
`7.11.3 GSC: Multichannel
`.........................
`7.11.4 Summary
`.............................
`7.12 Summary
`.............................
`7.13 Problems
`
`Processing
`
`......
`
`...........
`
`I: Maximum
`Estimation
`8 Parameter
`...........................
`Introduction.
`81 .
`82 .
`a posteriori
`Maximum
`Likelihood
`and Maximum
`8.2.1 Maximum
`Likelihood
`(ML) Estimator
`8.2.2
`Maximum
`a posteriori
`(MAP)
`Estimator
`...................
`8.2.3
`Cramer-Rao
`Bounds
`..................
`Parameter
`Estimation
`Model
`..................
`8.3.1
`Multiple
`Plane Waves
`...................
`8.3.2
`Model Perturbations
`8.3.3
`Parametric
`Spatially
`Spread Signals
`.........................
`8.3.4
`Summary
`.......................
`Cramer-Rao
`Bounds
`
`Likelihood
`
`Estimators
`.........
`.......
`
`..........
`
`83 .
`
`84 .
`
`Xiii
`
`805
`806
`813
`817
`822
`826
`82'7
`828
`841
`845
`846
`
`850
`860
`863
`864
`865
`869
`872
`873
`874
`875
`878
`884
`885
`885
`887
`
`917
`917
`. 920
`922
`924
`925
`933
`933
`936
`938
`938
`938
`
`Page 21 of 52
`
`

`

`xiv
`
`Contents
`
`8.4.1
`8.4.2
`
`.......
`........
`
`.....
`
`......
`Signal Spectrum
`Gaussian Model: Unknown
`Gaussian Model: Uncorrelated
`Signals with Unknown
`...........................
`Power
`Gaussian Model: Known Signal Spectrum
`8.4.3
`Nonrandom
`(Conditional)
`Signal Model
`8.4.4
`................
`Known Signal Waveforms
`8.4.5
`.........................
`Summary
`8.4.6
`................
`8.5 Maximum
`Likelihood
`Estimation
`............
`8.5.1
`Maximum
`Likelihood
`Estimation
`8.5.2
`Conditional
`Maximum
`Likelihood
`Estimators
`...............
`8.5.3 Weighted
`Subspace Fitting
`.................
`8.5.4
`Asymptotic
`Performance
`....................
`8.5.5 Wideband
`Signals
`.........................
`8.5.6
`Summary
`...................
`8.6 Computational
`Algorithms
`................
`8.6.1
`Optimization
`Techniques
`8.6.2
`Alternating
`Maximization
`Algorithms
`8.6.3
`Expectation
`Maximization
`Algorithm
`.........................
`8.6.4
`Summary
`..................
`8.7 Polynomial
`Parameterization
`..............
`8.7.1
`Polynomial
`Parameterization
`8.7.2
`Iterative Quadratic Maximum
`Likelihood
`...............
`8.7.3
`Polynomial WSF
`(MODE)
`.........................
`8.7.4
`Summary
`.................
`8.8 Detection
`of Number
`of Signals
`.....................
`8.9 Spatially
`Spread Signals
`..................
`8.9.1
`Parameterized
`S(&+)
`.................
`8.9.2
`Spatial ARMA
`Process
`.........................
`8.9.3
`Summary
`......................
`8.10 Beamspace
`algorithms
`.......................
`8.10.1
`Introduction
`...................
`8.10.2 Beamspace Matrices
`8.10.3 Beamspace Cramer-Rao
`Bound
`8.10.4 Beamspace Maximum
`Likelihood
`.........................
`8.10.5 Summary
`8.11 Sensitivity,
`Robustness,
`and Calibration
`..................
`8.11.1 Model Perturbations
`...................
`8.11.2 Cram&-Rao
`Bounds
`..............
`8.11.3 Sensitivity
`of ML Estimators
`..................
`8.11.4 MAP
`Joint Estimation
`
`.........
`.........
`
`(IQML)
`
`.............
`............
`
`............
`
`939
`
`958
`967
`971
`978
`980
`984
`984
`1004
`1009
`1014
`1015
`1018
`1018
`1018
`1025
`1031
`1037
`1037
`1038
`. . 1039
`1045
`1053
`1054
`1055
`1055
`1062
`1062
`1062
`1062
`1065
`1073
`1081
`1088
`1088
`1089
`1090
`1098
`1099
`
`Page 22 of 52
`
`

`

`Contents
`
`...............
`
`Algorithms
`8.11.5 Self-Calibration
`.........................
`8.11.6 Summary
`.............................
`8.12 Summary
`.......................
`8.12.1 Major Results
`......................
`8.12.2 Related Topics
`..................
`8.12.3 Algorithm
`complexity
`.............................
`8.13 Problems
`
`xv
`
`1101
`1102
`1102
`1102
`1105
`1108
`1109
`
`1139
`1139
`1140
`1140
`1142
`1144
`1147
`1148
`1149
`1155
`1155
`1158
`1163
`1170
`1189
`1190
`1194
`1195
`1195
`1203
`1211
`1233
`1233
`1233
`1235
`1241
`1243
`1243
`1247
`1251
`1251
`1255
`
`..........
`..........
`
`.........
`
`II
`Estimation
`9 Parameter
`...........................
`9.1
`Introduction
`......................
`9.2 Quadratic
`Algorithms
`.......................
`9.2.1
`Introduction
`..................
`9.2.2
`Beamscan Algorithms
`...............
`9.2.3 MVDR
`(Capon) Algorithm
`........
`9.2.4
`Root Versions of Quadratic
`Algorithms
`...........
`9.2.5
`Performance
`of MVDR
`Algorithms
`.........................
`9.2.6
`Summary
`.......................
`9.3 Subspace Algorithms
`.......................
`9.3.1
`Introduction
`..........................
`9.3.2 MUSIC
`9.3.3 Minimum-Norm
`Algorithm
`..........................
`9.3.4
`ESPRIT
`9.3.5
`Algorithm
`Comparison
`.........................
`9.3.6
`Summary
`.........................
`Linear Prediction
`9.4
`.....................
`9.5 Asymptotic
`Performance
`......................
`9.5.1
`Error Behavior
`9.5.2
`Resolution
`of MUSIC
`and Min-Norm
`9.5.3
`Small Error Behavior
`of Algorithms
`.........................
`9.5.4
`Summary
`9.6 Correlated
`and Coherent Signals
`.......................
`9.6.1
`Introduction
`9.6.2
`Forward-Backward
`Spatial Smoothing
`........................
`Summary.
`9.6.3
`......................
`9.7 Beamspace Algorithms
`....................
`9.7.1
`Beamspace MUSIC
`..............
`9.7.2
`Beamspace Unitary
`ESPRIT
`..................
`9.7.3
`Beamspace Summary
`...................
`9.8 Sensitivity
`and Robustness
`...........................
`9.9 Planar Arrays
`
`........