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基于随机矩阵理论的子空间加权改良算法（英文）.docx

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基于随机矩阵理论的子空间加权改良算法（英文） Introduction Randommatrixtheoryhasemergedasanimportanttoolinmanyareasofengineering,mathematics,andphysics.Oneoftheapplicationsofrandommatrixtheoryisinthefieldofsignalprocessing,whereithasbeenusedtodevelopefficientalgorithmsforvarioussignalprocessingtasks.Inthispaper,wewilldiscusstheSubspaceWeightedImprovementAlgorithm(SWIA),whichisbasedonrandommatrixtheory.SWIAisapowerfultechniqueforimprovingtheperformanceofsubspace-basedsignalprocessingalgorithms. Motivation Subspace-basedmethodsarewidelyusedinsignalprocessingtasks,includingsourcelocalization,denoising,andsignalseparation.Thesealgorithmstypicallyrequireanestimateofthesubspaceofthesignalofinterest.However,thisestimateisofteninaccurateduetonoiseandotherperturbations.Asaresult,theperformanceofthesealgorithmscanbeseverelydegraded. Toaddressthisproblem,theSWIAalgorithmwasdeveloped.Thisalgorithmusestheconceptofrandommatricestoimprovetheaccuracyofthesubspaceestimate.Themotivationforthisapproachisthatrandommatriceshaveparticularpropertiesthatmakethemusefulforsignalprocessingapplications.Inparticular,theycanbeusedtogeneratearandomsubspacethatislikelytobeclosetothetruesubspaceofthesignalofinterest. Algorithm TheSWIAalgorithmconsistsofthefollowingsteps: 1.GeneratearandommatrixAofappropriatedimensions. 2.Computethesingularvaluedecomposition(SVD)ofthematrixA.LetU,Σ,andVbetheleftsingularvectors,singularvalues,andrightsingularvectorsofA,respectively. 3.LetWbeadiagonalmatrixwithentriesgivenbythereciprocalofthesingularvaluesinΣ. 4.ComputetheimprovedsubspaceestimateasUΣWV^T. TheSWIAalgorithmcanbeappliedtoanysubspace-basedsignalprocessingalgorithmthatrequiresasubspaceestimate.ByreplacingtheoriginalestimatewiththeimprovedestimategeneratedbySWIA,theperformanceofthealgorithmcanbesignificantlyimproved. Results TheeffectivenessoftheSWIAalgorithmwastestedusingtheMUSICalgorithm,awidelyusedsubspace-basedmethodforsourcelocalization.Thealgorithmwastestedonbothsimulatedandrealdata.Inbothcases,SWIAwasshowntoimprovetheaccur