XII SensorArray Processing MostafaKaveh UniversityofMinnesota 60ComplexRandomVariablesandStochasticProcesses DanielR.Fuhrmann Introduction • ComplexEnvelopeRepresentationsofRealBandpassStochasticProcesses • The MultivariateComplexGaussianDensityFunction • RelatedDistributions • Conclusion 61BeamformingTechniquesforSpatialFiltering BarryVanVeenandKevinM.Buckley Introduction • BasicTerminologyandConcepts • DataIndependentBeamforming • Statistically OptimumBeamforming • AdaptiveAlgorithmsforBeamforming • InterferenceCancellationand PartiallyAdaptiveBeamforming • Summary • DefiningTerms 62Subspace-BasedDirectionFindingMethods EgemenGonenandJerryM.Mendel Introduction • FormulationoftheProblem • Second-OrderStatistics-BasedMethods • Higher- OrderStatistics-BasedMethods • FlowchartComparisonofSubspace-BasedMethods 63ESPRITandClosed-Form2-DAngleEstimationwithPlanarArrays MartinHaardt, MichaelD.Zoltowski,CherianP.Mathews,andJavierRamos Introduction • TheStandardESPRITAlgorithm • 1-DUnitaryESPRIT • UCA-ESPRITforCircular RingArrays • FCA-ESPRITforFilledCircularArrays • 2-DUnitaryESPRIT 64AUnifiedInstrumentalVariableApproachtoDirectionFindinginColoredNoise Fields P.Stoica,M.Viberg,M.Wong,andQ.Wu Introduction • ProblemFormulation • TheIV-SSFApproach • TheOptimalIV-SSFMethod • AlgorithmSummary • NumericalExamples • ConcludingRemarks 65ElectromagneticVector-SensorArrayProcessing AryeNehoraiandEytanPaldi Introduction • TheMeasurementModel • Cram ´ er-RaoBoundforaVectorSensorArray • MSAE, CVAE,andSingle-SourceSingle-VectorSensorAnalysis • Multi-SourceMulti-VectorSensorAnal- ysis • ConcludingRemarks 66SubspaceTracking R.D.DeGroat,E.M.Dowling,andD.A.Linebarger Introduction • Background • IssuesRelevanttoSubspaceandEigenTrackingMethods • Summary ofSubspaceTrackingMethodsDevelopedSince1990 67Detection:DeterminingtheNumberofSources DouglasB.Williams FormulationoftheProblem • InformationTheoreticApproaches • DecisionTheoreticApproaches • ForMoreInformation 68ArrayProcessingforMobileCommunications A.PaulrajandC.B.Papadias IntroductionandMotivation • VectorChannelModel • AlgorithmsforSTP • ApplicationsofSpatial Processing • Summary • References c 1999byCRCPressLLC 69BeamformingwithCorrelatedArrivalsinMobileCommunications VictorA.N. BarrosoandJos´eM.F.Moura Introduction • Beamforming • MMSEBeamformer:CorrelatedArrivals • MMSEBeamformerfor MobileCommunications • Experiments • Conclusions 70Space-TimeAdaptiveProcessingforAirborneSurveillanceRadar HongWang MainReceiveApertureandAnalogBeamforming • DatatobeProcessed • TheProcessingNeedsand MajorIssues • TemporalDOFReduction • AdaptiveFilteringwithNeededandSample-Supportable DOFandEmbeddedCFARProcessing • Scan-To-ScanTrack-Before-DetectProcessing • Real- TimeNonhomogeneityDetectionandSampleConditioningandSelection • SpaceorSpace-Range AdaptivePre-SuppressionofJammers • ASTAPExamplewithaRevisittoAnalogBeamforming • Summary A SENSORARRAYSYSTEMconsistsofanumberofspatially-distributedelements,suchas dipoles,hydrophones,geophonesormicrophones,followedbyreceiversandaprocessor. Thearraysamplespropagatingwavefieldsintimeandspace.Thereceiversandtheprocessor varyinmodeofimplementationandcomplexityaccordingtothetypesofsignalsencountered, desiredoperation,andtheadaptabilityofthearray.Forexample,thearraymaybenarrowband orwidebandandtheprocessormaybefordeterminingthedirectionsofthesourcesofsignalsor forbeamformingtorejectinterferingsignalsandtoenhancethequalityofthedesiredsignalina communicationsystem.Thebroadrangeofapplicationsandthemultifacetednatureoftechnical challengesformodernarraysignalprocessinghaveprovidedafertilegroundforcontributionsby andcollaborationsamongresearchersandpractitionersfrommanydisciplines,particularlythose fromthesignalprocessing,statistics,andnumericallinearalgebracommunities. Thefollowingchapterspresentasamplingofthelatesttheory,algorithms,andapplicationsrelated toarraysignalprocessing.Therangeoftopicsandalgorithmsincludesomewhichhavebeeninuse formorethanadecadeaswellassomewhichareresultsofactivecurrentresearch.Thesectionson applicationsgiveexamplesofcurrentareasofsignificantresearchanddevelopment. Modernarraysignalprocessingoftenrequirestheuseoftheformalismofcomplexvariablesin modelingreceivedsignalsandnoise.Chapter60providesanintroductiontocomplexrandom processeswhichareusefulforbandpasscommunicationsystemsandarrays.Aclassicaluseforarrays ofsensorsistoexploitthedifferencesinthelocation(direction)ofsourcesoftransmittedsignalsto performspatialfiltering.SuchtechniquesarereviewedinChapter61. Anothercommonuseofarraysistheestimationofinformativeparametersaboutthewavefields impingingonthesensors.Themostcommonparameterofinterestisthedirectionofarrival(DOA) ofawave.SubspacetechniqueshavebeenadvancedasmeansofestimatingtheDOAsofsources, whichareveryclosetoeachother,withhighaccuracy.Thelargenumberofdevelopmentsin suchtechniquesisreflectedinthetopicscoveredinChapters62to66.Chapter62givesageneral overviewofsubspaceprocessingfordirectionfinding,whileChapter63discussesaparticulartype ofsubspacealgorithmwhichisextendedtosensingofazimuthandelevationangleswithplanar arrays.Mostestimatorsassumeknowledgeoftheneededstatisticalcharacteristicsofthemeasurement noise.ThisrequirementisrelaxedintheapproachgiveninChapter64.Chapter65extendsthe capabilitiesoftraditionalsensorstothosewhichcanmeasurethecompleteelectricandmagnetic fieldcomponentsandprovidesestimatorswhichexploitsuchinformation.Whensignalsources move,orwhencomputationalrequirementsforreal-timeprocessingprohibitbatchestimationofthe subspaces,computationallyefficientadaptivesubspaceupdatingtechniquesarecalledfor.Chapter66 presentsmanyoftherecenttechniqueswhichhavebeendevelopedforthispurpose.Beforesubspace methodsareusedforestimatingtheparametersofthewavesreceivedbyanarray,itisnecessaryto determinethenumberofsourceswhichgeneratethewaves.Thisaspectoftheproblem,oftentermed detection,isdiscussedinChapter67. Animportantareaofapplicationforarraysisinthefieldofcommunications,particularlyasit c 1999byCRCPressLLC pertains toemergingmobileandcellular systems. Chapter68 givesanoverview of anumber oftech- niquesforimprovingthereceptionofsignalsinmobilesystems,whileChapter69considersproblems which arise in beamforming in the presence of multipath signals—a common occurrence in mobile communications. Chapter70discussesradarsystemswhichemploysensorarrays,therebyproviding the opportunity for space-time signal processing for improved resolution and target detection. c 1999 by CRC Press LLC . BarryVanVeenandKevinM.Buckley Introduction • BasicTerminologyandConcepts • DataIndependentBeamforming • Statistically OptimumBeamforming • AdaptiveAlgorithmsforBeamforming • InterferenceCancellationand PartiallyAdaptiveBeamforming • Summary • DefiningTerms 62Subspace-BasedDirectionFindingMethods EgemenGonenandJerryM.Mendel Introduction • FormulationoftheProblem • Second-OrderStatistics-BasedMethods • Higher- OrderStatistics-BasedMethods • FlowchartComparisonofSubspace-BasedMethods 63ESPRITandClosed-Form2-DAngleEstimationwithPlanarArrays. HongWang MainReceiveApertureandAnalogBeamforming • DatatobeProcessed • TheProcessingNeedsand MajorIssues • TemporalDOFReduction • AdaptiveFilteringwithNeededandSample-Supportable DOFandEmbeddedCFARProcessing • Scan-To-ScanTrack-Before-DetectProcessing • Real- TimeNonhomogeneityDetectionandSampleConditioningandSelection • SpaceorSpace-Range AdaptivePre-SuppressionofJammers • ASTAPExamplewithaRevisittoAnalogBeamforming • Summary A SENSORARRAYSYSTEMconsistsofanumberofspatially-distributedelements,suchas dipoles,hydrophones,geophonesormicrophones,followedbyreceiversandaprocessor. Thearraysamplespropagatingwavefieldsintimeandspace.Thereceiversandtheprocessor varyinmodeofimplementationandcomplexityaccordingtothetypesofsignalsencountered, desiredoperation,andtheadaptabilityofthearray.Forexample,thearraymaybenarrowband orwidebandandtheprocessormaybefordeterminingthedirectionsofthesourcesofsignalsor forbeamformingtorejectinterferingsignalsandtoenhancethequalityofthedesiredsignalina communicationsystem.Thebroadrangeofapplicationsandthemultifacetednatureoftechnical challengesformodernarraysignalprocessinghaveprovidedafertilegroundforcontributionsby andcollaborationsamongresearchersandpractitionersfrommanydisciplines,particularlythose fromthesignalprocessing,statistics,andnumericallinearalgebracommunities. Thefollowingchapterspresentasamplingofthelatesttheory,algorithms,andapplicationsrelated toarraysignalprocessing.Therangeoftopicsandalgorithmsincludesomewhichhavebeeninuse formorethanadecadeaswellassomewhichareresultsofactivecurrentresearch.Thesectionson applicationsgiveexamplesofcurrentareasofsignificantresearchanddevelopment. Modernarraysignalprocessingoftenrequirestheuseoftheformalismofcomplexvariablesin modelingreceivedsignalsandnoise.Chapter60providesanintroductiontocomplexrandom processeswhichareusefulforbandpasscommunicationsystemsandarrays.Aclassicaluseforarrays ofsensorsistoexploitthedifferencesinthelocation(direction)ofsourcesoftransmittedsignalsto performspatialfiltering.SuchtechniquesarereviewedinChapter61. Anothercommonuseofarraysistheestimationofinformativeparametersaboutthewavefields impingingonthesensors.Themostcommonparameterofinterestisthedirectionofarrival(DOA) ofawave.SubspacetechniqueshavebeenadvancedasmeansofestimatingtheDOAsofsources, whichareveryclosetoeachother,withhighaccuracy.Thelargenumberofdevelopmentsin suchtechniquesisreflectedinthetopicscoveredinChapters62to66.Chapter62givesageneral overviewofsubspaceprocessingfordirectionfinding,whileChapter63discussesaparticulartype ofsubspacealgorithmwhichisextendedtosensingofazimuthandelevationangleswithplanar arrays.Mostestimatorsassumeknowledgeoftheneededstatisticalcharacteristicsofthemeasurement noise.ThisrequirementisrelaxedintheapproachgiveninChapter64.Chapter65extendsthe capabilitiesoftraditionalsensorstothosewhichcanmeasurethecompleteelectricandmagnetic fieldcomponentsandprovidesestimatorswhichexploitsuchinformation.Whensignalsources move,orwhencomputationalrequirementsforreal-timeprocessingprohibitbatchestimationofthe subspaces,computationallyefficientadaptivesubspaceupdatingtechniquesarecalledfor.Chapter66 presentsmanyoftherecenttechniqueswhichhavebeendevelopedforthispurpose.Beforesubspace methodsareusedforestimatingtheparametersofthewavesreceivedbyanarray,itisnecessaryto determinethenumberofsourceswhichgeneratethewaves.Thisaspectoftheproblem,oftentermed detection,isdiscussedinChapter67. Animportantareaofapplicationforarraysisinthefieldofcommunications,particularlyasit c 1999byCRCPressLLC pertains