Sparse Adaptive Filters for Echo Cancellation

125 Pages·2010·2.062 MB·English

by  Jacob Benesty, Constantin Paleologu, Silviu Ciochina

Sparse Adaptive Filters
for Echo Cancellation

Synthesis Lectures on Speech
and Audio Processing
Editor
B.H.Juang,GeorgiaTech
SparseAdaptiveFiltersforEchoCancellation
ConstantinPaleologu,JacobBenesty,andSilviuCiochina˘
2010
Multi-PitchEstimation
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2009
DiscriminativeLearningforSpeechRecognition:TheoryandPractice
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LatentSemanticMapping:Principles&Applications
JeromeR.Bellegarda
2007
DynamicSpeechModels:Theory,Algorithms,andApplications
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JontB.Allen
2005
Copyright© 2010byMorgan&Claypool
Allrightsreserved.Nopartofthispublicationmaybereproduced,storedinaretrievalsystem,ortransmittedin
anyformorbyanymeans—electronic,mechanical,photocopy,recording,oranyotherexceptforbriefquotationsin
printedreviews,withoutthepriorpermissionofthepublisher.
SparseAdaptiveFiltersforEchoCancellation
ConstantinPaleologu,JacobBenesty,andSilviuCiochina˘
www.morganclaypool.com
ISBN:9781598293067 paperback
ISBN:9781598293074 ebook
DOI10.2200/S00289ED1V01Y201006SAP006
APublicationintheMorgan&ClaypoolPublishersseries
SYNTHESISLECTURESONSPEECHANDAUDIOPROCESSING
Lecture#6
SeriesEditor:B.H.Juang,GeorgiaTech
SeriesISSN
SynthesisLecturesonSpeechandAudioProcessing
Print1932-121X Electronic1932-1678
Sparse Adaptive Filters
for Echo Cancellation
Constantin Paleologu
UniversityPolitehnicaofBucharest,Bucharest,Romania
Jacob Benesty
INRS-EMT,UniversityofQuebec,Montreal,Canada
Silviu Ciochina˘
UniversityPolitehnicaofBucharest,Bucharest,Romania
SYNTHESISLECTURESONSPEECHANDAUDIOPROCESSING#6
M
&C Morgan &cLaypool publishers
ABSTRACT
Adaptivefilterswithalargenumberofcoefficientsareusuallyinvolvedinbothnetworkandacoustic
echocancellation.Consequently,itisimportanttoimprovetheconvergencerateandtrackingofthe
conventionalalgorithmsusedfortheseapplications.Thiscanbeachievedbyexploitingthesparse-
nesscharacteroftheechopaths.Identificationofsparseimpulseresponseswasaddressedmainlyin
thelastdecadewiththedevelopmentoftheso-called“proportionate”-typealgorithms.Thegoalof
this book is to present the most important sparse adaptive filters developed for echo cancellation.
Besides a comprehensive review of the basic proportionate-type algorithms,we also present some
of the latest developments in the field and propose some new solutions for further performance
improvement,e.g.,variablestep-sizeversionsandnovelproportionate-typeaffineprojectionalgo-
rithms.Anexperimentalstudyisalsoprovidedinordertocomparemanysparseadaptivefiltersin
differentechocancellationscenarios.
KEYWORDS
network and acoustic echo cancellation, adaptive filters, sparseness, Wiener, LMS,
±
NLMS,VSS-NLMS,PNLMS,IPNLMS,EG ,VSS-PNLMS,APA,PAPA
vii
Contents
1 Introduction.................................................................1
1.1 EchoCancellation..........................................................1
1.2 Double-TalkDetection......................................................3
1.3 SparseAdaptiveFilters......................................................4
1.4 Notation...................................................................5
2 SparsenessMeasures ......................................................... 7
2.1 VectorNorms..............................................................7
2.2 ExamplesofImpulseResponses..............................................9
2.3 SparsenessMeasureBasedonthe(cid:2)0 Norm....................................9
2.4 SparsenessMeasureBasedonthe(cid:2)1 and(cid:2)2 Norms...........................10
2.5 SparsenessMeasureBasedonthe(cid:2)1 and(cid:2)∞ Norms..........................11
2.6 SparsenessMeasureBasedonthe(cid:2)2 and(cid:2)∞ Norms..........................12
3 PerformanceMeasures ...................................................... 15
3.1 Mean-SquareError........................................................15
3.2 Echo-ReturnLossEnhancement ...........................................16
3.3 Misalignment.............................................................17
4 WienerandBasicAdaptiveFilters............................................19
4.1 WienerFilter .............................................................19
4.1.1 EfficientComputationoftheWiener-HopfEquations..................22
4.2 DeterministicAlgorithm...................................................24
4.3 StochasticAlgorithm......................................................28
4.4 VariableStep-SizeNLMSAlgorithm .......................................31
4.4.1 ConvergenceoftheMisalignment ....................................33
4.5 SignAlgorithms...........................................................34
viii
5 BasicProportionate-TypeNLMSAdaptiveFilters ............................37
5.1 GeneralDerivation........................................................37
5.2 TheProportionateNLMS(PNLMS)andPNLMS++Algorithms .............39
5.3 TheSignedRegressorPNLMSAlgorithm...................................40
5.4 TheImprovedPNLMS(IPNLMS)Algorithms..............................41
5.4.1 TheRegularIPNLMS...............................................42
5.4.2 TheIPNLMSwiththe(cid:2)0 Norm .....................................44
5.4.3 TheIPNLMSwithaNorm-LikeDiversityMeasure....................45
6 TheExponentiatedGradientAlgorithms.....................................47
6.1 CostFunction.............................................................47
6.2 TheEGAlgorithmforPositiveWeights.....................................48
±
6.3 TheEG AlgorithmforPositiveandNegativeWeights ......................49
±
6.4 LinkBetweenNLMSandEG Algorithms.................................51
±
6.5 LinkBetweenIPNLMSandEG Algorithms...............................53
7 TheMu-LawPNLMSandOtherPNLMS-TypeAlgorithms ..................55
7.1 TheMu-LawPNLMSAlgorithms .........................................55
7.2 TheSparseness-ControlledPNLMSAlgorithms.............................59
7.3 ThePNLMSAlgorithmwithIndividualActivationFactors...................60
8 VariableStep-SizePNLMSAlgorithms ...................................... 65
8.1 ConsiderationsontheConvergenceoftheNLMSAlgorithm..................65
8.2 AVariableStep-SizePNLMSAlgorithm....................................70
9 ProportionateAffineProjectionAlgorithms...................................73
9.1 ClassicalDerivation .......................................................73
9.2 ANovelDerivation........................................................75
9.3 AVariableStep-SizeVersion...............................................79
10 ExperimentalStudy .........................................................87
10.1 ExperimentalConditions...................................................87
CONTENTS ix
10.2 IPNLMSVersusPNLMS..................................................88
10.3 MPNLMS,SC-PNLMS,andIAF-PNLMS.................................92
10.4 VSS-IPNLMS............................................................95
10.5 PAPAs...................................................................96
Bibliography...............................................................103
Index......................................................................111
Authors’Biographies.......................................................113