Introduction to Adaptive Arrays

686 Pages·2011·8.25 MB·English

by  Robert A. Monzingo

Monzingo-7200014 monz7200014˙fm ISBN:XXXXXXXXXX November24,2010 16:30 iii
Introduction to Adaptive Arrays
22nndd EEddiittiioonn
Robert A. Monzingo
Randy L. Haupt
Thomas W. Miller
Raleigh,NC
scitechpub.com
Monzingo-7200014 monz7200014˙fm ISBN:XXXXXXXXXX November24,2010 16:30 iv
PublishedbySciTechPublishing,Inc.
911PaverstoneDrive,SuiteB
Raleigh,NC27615
[phone],fax[phone]
scitechpublishing.com
Copyright©2011bySciTechPublishing,Raleigh,NC.Allrightsreserved.
Nopartofthispublicationmaybereproduced,storedinaretrievalsystemortransmittedinanyformorbyany
means,electronic,mechanical,photocopying,recording,scanningorotherwise,exceptaspermittedunderSections
107or108ofthe1976UnitedStatedCopyrightAct,withouteitherthepriorwrittenpermissionofthePublisher,
orauthorizationthroughpaymentoftheappropriateper-copyfeetotheCopyrightClearanceCenter,222Rosewood
Drive,Danvers,MA01923,[phone],fax[phone],oronthewebatcopyright.com.Requeststothe
PublisherforpermissionshouldbeaddressedtothePublisher,SciTechPublishing,Inc.,911PaverstoneDrive,Suite
B,Raleigh,NC27615,[phone],fax[phone],[email protected].
Thepublisherandtheauthormakenorepresentationsorwarrantieswithrespecttotheaccuracyorcompletenessof
thecontentsofthisworkandspecificallydisclaimallwarranties,includingwithoutlimitationwarrantiesoffitness
foraparticularpurpose.
Editor:DudleyR.Kay
EditorialAssistant:KatieJanelle
ProductionManager:RobertLawless
Typesetting:MPSLimited,aMacmillanCompany
CoverDesign:BrentBeckley
Printer:SheridanBooks,Inc.
PrintedintheUnitedStatesofAmerica
10 9 8 7 6 5 4 3 2 1
ISBN:978-1-891121-57-9
LibraryofCongressCataloging-in-PublicationData
Monzingo,RobertA.,1938-
Introductiontoadaptivearrays/RobertA.Monzingo,RandyL.Haupt,
ThomasW.Miller.–2nded.
p.cm.
Includesbibliographicalreferences.
ISBN978-1-891121-57-9(hardcover:alk.paper)
1.Antennaarrays.I.Haupt,RandyL.II.Miller,ThomasW.III.Title.
TK7871.6.M662011
621.382’4–dc22
2010047941
Monzingo-7200014 monz7200014˙fm ISBN:XXXXXXXXXX November24,2010 16:30 xiv
Preface
This book is intended to serve as an introduction to the subject of adaptive array sensor
systems whose principal purpose is to enhance the detection and reception of certain
desiredsignals.Arraysensorsystemshavewell-knownadvantagesforprovidingflexible,
rapidly configurable, beamforming and null-steering patterns. The advantages of array
sensorsystemsarebecomingmoreimportant,andthistechnologyhasfoundapplications
inthefieldsofcommunications,radar,sonar,radioastronomy,seismologyandultrasonics.
The growing importance of adaptive array systems is directly related to the widespread
availability of compact, inexpensive digital computers that make it possible to exploit
certainwell-knowntheoreticalresultsfromsignalprocessingandcontroltheorytoprovide
thecriticalself-adjustingcapabilitythatformstheheartoftheadaptivestructure.
Thereareahostoftextbooksthattreatadaptivearraysystems,butfewofthemtake
thetroubletopresentanintegratedtreatmentthatprovidesthereaderwiththeperspective
toorganizetheavailableliteratureintoeasilyunderstoodparts.Withthefieldofadaptive
arraysensorsystemsnowamaturingtechnology,andwiththeapplicationsofthesesystems
growing more and more numerous, the need to understand the underlying principles of
suchsystemsisaparamountconcernofthisbook.Itisofcoursenecessarytoappreciate
the limitations imposed by the hardware adopted to implement a design, but it is more
informative to see how a choice of hardware “fits” within the theoretical framework of
theoverallsystem.Mostofthecontentsarederivedfromreadilyavailablesourcesinthe
literature,althoughacertainamountoforiginalmaterialhasbeenincluded.
Thisbookisintendedforusebothasatextbookatthegraduatelevelandasareference
workforengineers,scientists,andsystemsanalysts.Thematerialpresentedwillbemost
readily understood by readers having an adequate background in antenna array theory,
signalprocessing(communicationtheoryandestimationtheory),optimizationtechniques,
control theory, and probability and statistics. It is not necessary, however, for the reader
to have such a complete background since the text presents a step-by-step discussion of
the basic theory and important techniques required in the above topics, and appropriate
referencesaregivenforreadersinterestedinpursuingthesetopicsfurther.Fundamental
conceptsareintroducedandillustratedwithexamplesbeforemorecurrentdevelopments
are introduced. Problems at the end of each chapter have been chosen to illustrate and
extendthematerialpresentedinthetext.Theseextensionsintroducethereadertoactual
adaptive array engineering problems and provide motivation for further reading of the
background reference material. In this manner both students and practicing engineers
may easily gain familiarity with the modern contributions that adaptive arrays have to
offerpracticalsignalreceptionsystems.
The book is organized into three parts. Part One (Chapters 1 to 3) introduces the
advantages that obtain with the use of array sensor systems, define the principal system
components, and develop the optimum steady-state performance limits that any array
system can theoretically achieve. This edition also includes two new topics that have
practical interest: the subject of a performance index to grade the effectiveness of the
overalladaptivesystem,andtheimportantthemeofpolarizationsensitivearrays.PartTwo
xiv
Monzingo-7200014 monz7200014˙fm ISBN:XXXXXXXXXX November24,2010 16:30 xv
Preface xv
(Chapters 4 through 9) provides the designer with a survey of adaptive algorithms and
aperformancesummaryforeachalgorithmtype.Someimportantmoderndevelopments
in matrix inversion computation and random search algorithms are treated. With this
informationavailable,thedesignermaythenquicklyidentifythoseapproachesmostlikely
to lead to a successful design for the signal environment and system constrains that are
ofconcern.PartThree(Chapters10,11,and12)considerstheproblemofcompensation
foradaptivearraysystemerrorsthatinevitablyoccurinanypracticalsystem,exploresthe
importanttopicofdirectionofarrival(DOA)estimation,andintroducescurrenttrendsin
adaptive array research. It is hoped that this edition succeeds in presenting this exciting
fieldusingmathematicaltoolsthatmakethesubjectinteresting,accessible,andappealing
toawideaudience.
The authors would like to thank Northrop Grumman (Dennis Lowes and Dennis
Fortner),theNationalElectronicsMuseum(RalphStrongandMichaelSimons),Material
Systems Inc. (Rick Foster), and Remcom Inc. (Jamie Knapil Infantolino) for providing
someexcellentpictures.
Monzingo-7200014 monz7200014˙fm ISBN:XXXXXXXXXX November24,2010 16:30 ix
Contents
Preface xiv
PART I Adaptive Array Fundamental Principles: System
Uses, System Elements, Basic Concepts,
and Optimum Array Processing
1 Introduction 3
1.1 MotivationForUsingAdaptiveArrays 4
1.2 HistoricalPerspective 5
1.3 PrincipalSystemElements 6
1.4 AdaptiveArrayProblemStatement 7
1.5 ExistingTechnology 9
1.6 OrganizationoftheBook 21
1.7 SummaryandConclusions 22
1.8 Problems 23
1.9 References 24
2 Adaptive Array Concept 29
2.1 SignalEnvironment 30
2.2 ArrayElementSpacingConsiderations 33
2.3 ArrayPerformance 45
2.4 NullingLimitationsDuetoMiscellaneousArrayEffects 58
2.5 NarrowbandandBroadbandSignalProcessingConsiderations 62
2.6 AdaptiveArrayPerformanceMeasure—CoverageImprovement
Factor(CIF) 66
2.7 SummaryandConclusions 68
2.8 Problems 69
2.9 References 78
ix
Monzingo-7200014 monz7200014˙fm ISBN:XXXXXXXXXX November24,2010 16:30 x
x Contents
3 Optimum Array Processing 81
3.1 MathematicalPreliminaries 82
3.2 SignalDescriptionsforConventionalandSignalAlignedArrays 88
3.3 OptimumArrayProcessingforNarrowbandApplications 90
3.4 OptimumArrayProcessingforBroadbandApplications 103
3.5 OptimumArrayProcessingforPerturbedPropagationConditions 121
3.6 PolarizationSensitiveArrays 124
3.7 SummaryandConclusions 130
3.8 Problems 131
3.9 References 146
PART II Adaptive Algorithms
4 Gradient-Based Algorithms 153
4.1 IntroductoryConcepts 154
4.2 TheLMSAlgorithm 158
4.3 TheHowells–ApplebaumAdaptiveProcessor 171
4.4 IntroductionofMainBeamConstraints 191
4.5 ConstraintfortheCaseofKnownDesiredSignalPowerLevel 199
4.6 TheDSDAlgorithm 201
4.7 TheAcceleratedGradientApproach(AG) 209
4.8 GradientAlgorithmwithConstraints 213
4.9 SimulationResults 224
4.10 Phase-OnlyAdaptiveNullingUsingSteepestDescent 227
4.11 SummaryandConclusions 228
4.12 Problems 230
4.13 References 235
5 Direct Inversion of the Sample Covariance Matrix 239
5.1 TheDirectMatrixInversion(DMI)Approach 239
5.2 DiagonalLoadingoftheSampleCovarianceMatrix 251
5.3 FactorizationMethods 253
5.4 TransientResponseComparisons 257
5.5 SensitivitytoEigenvalueSpread 262
5.6 SummaryandConclusions 262
5.7 Problems 263
5.8 References 270
Monzingo-7200014 monz7200014˙fm ISBN:XXXXXXXXXX November24,2010 16:30 xi
Contents xi
6 Recursive Methods for Adaptive Array Processing 273
6.1 TheWeightedLeastSquaresErrorProcessor 273
6.2 UpdatedCovarianceMatrixInverse 277
6.3 KalmanFilterMethodsforAdaptiveArrayProcessing 284
6.4 TheMinimumVarianceProcessor 291
6.5 SimulationResults 295
6.6 SummaryandConclusions 299
6.7 Problems 299
6.8 References 301
7 Cascade Preprocessors 303
7.1 NolenNetworkPreprocessor 304
7.2 InterferenceCancellationwithaNolenNetworkPreprocessor 311
7.3 Gram–SchmidtOrthogonalizationPreprocessor 315
7.4 SimulationResults 324
7.5 SummaryandConclusions 328
7.6 Problems 328
7.7 References 332
8 Random Search Algorithms 335
8.1 LinearRandomSearch 336
8.2 AcceleratedRandomSearch 341
8.3 GuidedAcceleratedRandomSearch 344
8.4 GeneticAlgorithm 346
8.5 ComparisonofRandomSearchAlgorithms 353
8.6 SummaryandConclusions 358
8.7 Problems 359
8.8 References 362
9 Adaptive Algorithm Performance Summary 365
PART III Advanced Topics
10 Compensation of Adaptive Arrays 373
10.1 ArrayErrors 374
10.2 ArrayCalibration 377
Monzingo-7200014 monz7200014˙fm ISBN:XXXXXXXXXX November25,2010 21:3 xii
xii Contents
10.3 BroadbandSignalProcessingConsiderations 380
10.4 CompensationforMutualCoupling 396
10.5 MultipathCompensation 398
10.6 AnalysisofInterchannelMismatchEffects 406
10.7 SummaryandConclusions 415
10.8 Problems 416
10.9 References 418
11 Direction of Arrival Estimation and Related Topics 421
11.1 Periodogram 422
11.2 Capon’sMethod 423
11.3 MusicAlgorithm 423
11.4 TheMaximumEntropyMethod 426
11.5 ComparingDOAAlgorithmSpectra 436
11.6 SequentialImplementationofBayesOptimalArrayProcessor 437
11.7 ParameterEstimationviaSubspaceFitting 441
11.8 TheMaximumLikelihoodEstimate 443
11.9 Cramer–RaoLowerBoundonAOAEstimationError 449
11.10 FisherInformationMatrixandCRBoundforGeneralCases 451
11.11 SummaryandConclusions 452
11.12 Problems 452
11.13 References 459
12 Recent Developments in Adaptive Arrays 463
12.1 BeamSwitching 463
12.2 Space-TimeAdaptiveProcessing 465
12.3 MIMO 473
12.4 ReconfigurableAntennasandArrays 479
12.5 PerformanceCharacteristicsofLargeSonarArrays 484
12.6 AdaptiveProcessingforMonopulseTrackingAntennas 486
12.7 PartiallyAdaptiveArrays 488
12.8 SummaryandConclusions 503
12.9 Problems 503
12.10 References 504
AppendixA:FrequencyResponseCharacteristicsofTapped-DelayLines 507
A.1 References 510
AppendixB:ComplexEnvelopeNotation 511
B.1 References 513
Monzingo-7200014 monz7200014˙fm ISBN:XXXXXXXXXX November25,2010 21:3 xiii
Contents xiii
AppendixC:ConvenientFormulasforGradientOperations 515
C.1 References 516
AppendixD:UsefulMatrixRelationsandtheSchwartzInequality 517
D.1 References 518
AppendixE:MultivariateGaussianDistributions 519
E.1 RealGaussianRandomVectors 519
E.2 ComplexGaussianRandomVectors 521
E.3 References 524
AppendixF:GeometricAspectsofComplexVectorRelationships 525
F.1 Reference 526
AppendixG:EigenvaluesandEigenvectors 527
AppendixH:SelectedAnswers 529
Index 537
Monzingo-7200014 book ISBN:XXXXXXXXXX November24,2010 18:5 1
PART I
Adaptive Array
Fundamental Principles:
System Uses, System
Elements, Basic Concepts,
and Optimum Array
Processing
CHAPTER 1 Introduction
CHAPTER 2 Adaptive Array Concept
CHAPTER 3 Optimum Array Processing:
Steady-State Performance Limits
and the Wiener Solution