Eng The University of Texas at Austin brPage 2br Introduction A sensor array is a group of sensors located at spatially separated points Sensor array processing focuses on data collected at the sensors to carry out a given estimation task Applicatio ID: 36479
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SpatialArrayProcessingSignalandImageProcessingSeminar MuratTorlakTelecommunications&InformationSys.Eng.TheUniversityofTexasatAustin 1 IntroductionAsensorarrayisagroupofsensorslocatedatspatiallyseparatedpointsSensorarrayprocessingfocusesondatacollectedatthesensorstocarryoutagivenestimationtaskApplicationAreasSeismicexplorationAnti-jammingcommunicationsYES!Wirelesscommunications 2 ProblemStatement q1 2 D s1(t) s2(t) 1.Numberofsources2.Theirdirection-of-arrivals(DOAs)3.SignalWaveforms 3 IsotropicandnondispersivemediumUniformpropagationinalldirectionsFar-FieldRadiusofpropogationsizeofarrayPlanewavepropogationZeromeanwhitenoiseandsignal,uncorrelatedNocouplingandperfectcalibration 4 AntennaArray 123ArrayResponseVector–Far-FieldAssumptionDelayPhaseShifthift;ej2fc4sin=c=cSingleSourceCase 5 GeneralModelBysuperposition,forsignals, 6 Low-ResolutionApproach:BeamformingBasicIdeaUseDFT(orFFT)tondthefrequenciesfrequenciesF(w1)LookforthepeaksinTosmoothoutnoise NNXtjFx(t)j2 7 BeamformingAlgorithmAlgorithm1.Estimate 2.Calculate3.Findpeaksofforallpossible's.4.CalculateAdvantage-SimpleandeasytounderstandDisadvantage-Lowresolution 8 NumberofSourcesDetectionofnumberofsignalsfor }RsA+Efn(t)n(t)g| {z isthenoisepower.NonoiseandrankofEigenvaluesofwillbe;:::Realpositiveeigenvaluesbecauseisreal,Hermition-symmetricrankChecktherankoforitsnonzeroeigenvaluestodetectthenumberofsignalsNoiseeigenvaluesareshiftedbyDetectthenumberofprincipal(distinct)eigenvalues 9 SubspacedecompositionbyperformingeigenvalueistheeigenvectoroftheeigenvalueCheckwhich,whereisaprojectionmatrixSearchforallpossiblesuchthat AfterEVDofwherethenoiseeigenvectormatrix Foratrue=cisarootofof;z;:::;:::;z�1;:::;z�(M�1)]:Aftereigenvaluedecomposition,-Obtain-Form-Obtainrootsbyrooting-Pickrootslyingontheunitcircle-Solvefor EstimationofSignalParametersviaRotationallyInvariantTechniques(ESPRIT)DecomposeauniformlineararrayofsensorsintotwosubarrayswithNotetheshiftinvariancepropertyGeneralformrelatingsubarray(1)tosubarray(2)containssufcientinformationof isanonsingularunitarymatrixcomesfromaGrahm-SchmitorthogonalizationMultiplybothsidesbythepseudoinverseofmeansthepseudo-inverseEigenvaluesofarethoseof SuperresolutionAlgorithms1.Calculate 2.Performeigenvaluedecomposition3.Basedonthedistributionof,determine4.Useyourfavoritediraction-of-arrivalestimationalgorithm:(a)MUSIC:Findthepeaksoffor-Findcorrespondingthepeaksof(b)Root-MUSIC:Rootthepolynomial-Picktherootsthatareclosesttotheunitcircle (c)ESPRIT:Findtheeigenvaluesof 2c4 SignalWaveformEstimationGiven,recoverDeterministicMethodNonoisecase:ndsuchthatcandothejobWithnoise,Disadvantageincreasednoise StocasticApproachtominimizeUsetheLangrangemethodDifferentiatingit,weobtain;orCapon'sBeamformer SubspaceFrameworkforSinusoidLetusselectawindowofi.e.,,x(t);:::+1)]+1) {z }a(k)ke( k+k)t| isthewindowsize,thenumberofsinusoids,and SubspaceFrameworkforSinusoidTherefore,thesubspacemethodscanbeappliedtoThenndingisasimpleleastsquaresproblem. WirelessCommunications Personal Communications Services (PCS) Cellular Telephony Wireless LAN MultipathsDirect Path co-channel interference To Networks Direct PathMultipath Direct Path Outdoors IncreasingDemandforWirelessServicesUniqueProblemscomparedtoWiredcommunications ProblemsinWirelessCommunicationsScarceRadioSpectrumandCo-channelInterference 111342324 StationMultipathDirect PathMultipath Coverage/Range SmartAntennaSystemsEmploymorethanoneantennaelementandexploitthespatialdimensioninsignalprocessingtoimprovesomesystemoperatingparameter(s):Capacity,Quality,Coverage,andCost. User OneUser TwoMultiple RF ModuleConventionalCommunication ModuleAdvanced Signal ProcessingAlgorithms ExperimentalValidationofSmartUplinkComparisonofconstellationbefore(upper)andaftersmartuplinkprocessing(middleandlower) imaginary axisimaginary axisimaginary axis real axis Equalized Signal 2 real axis Equalized Signal 1 real axis Antenna Output SelectiveTransmissionUsingDOAsBeamformingresultsfortwosourcesseparatedby 1 1.5 2x 104 0 0.2 0.4 0.6 0.8 1 Power SpectrumFrequency [Hz], User #1 0.5 1 1.5 2x 104 0 0.2 0.4 0.6 0.8 1 Power SpectrumFrequency [Hz], User #2 SelectiveTransmissionUsingDOAsBeamformingresultsfortwosourcesseparatedby 1 1.5 2x 104 0 0.2 0.4 0.6 0.8 1 Power SpectrumFrequency [Hz], User #1 0.5 1 1.5 2x 104 0 0.2 0.4 0.6 0.8 1 Power SpectrumFrequency [Hz], User #2 FutureDirectionsAdaptthetheoreticalmethodstottheparticulardemandsinspecicapplicationsSmartAntennasSyntheticapertureradarUnderwateracousticimagingChemicalsensorarraysBridgethegapbetweentheoreticalmethodsandreal-timeapplications