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Spatial Array Processing Signal and Image Processing Seminar Murat Torlak Telecommunications Spatial Array Processing Signal and Image Processing Seminar Murat Torlak Telecommunications

Spatial Array Processing Signal and Image Processing Seminar Murat Torlak Telecommunications - PDF document

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Spatial Array Processing Signal and Image Processing Seminar Murat Torlak Telecommunications - PPT Presentation

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