evaluation and comparison of beamforming algorithms for microphone array speech processing

119 Pages·2006·7.43 MB·English

EVALUATION AND COMPARISON OF BEAMFORMING
ALGORITHMS FOR MICROPHONE ARRAY SPEECH
PROCESSING
AThesis
Presentedto
TheAcademicFaculty
By
DanielJacksonAllred
InPartialFulfillment
oftheRequirementsfortheDegree
MasterofScience
in
ElectricalandComputer Engineering
SchoolofElectricalandComputer Engineering
GeorgiaInstituteofTechnology
August2006
Copyright ©2006byDanielJacksonAllred
EVALUATION AND COMPARISON OF BEAMFORMING
ALGORITHMS FOR MICROPHONE ARRAY SPEECH
PROCESSING
Approvedby:
Dr. PaulHasler,Committee Chair
Assoc. Professor,SchoolofECE
GeorgiaInstituteofTechnology
Dr. DavidAnderson,Advisor
Assoc. Professor,SchoolofECE
GeorgiaInstituteofTechnology
Dr. JamesHamblen
Assoc. Professor,SchoolofECE
GeorgiaInstituteofTechnology
DateApproved: July7,2006
Manyhandsmakelightwork.
-JohnHeywood
DEDICATION
To my wife, Erika, and our two daughters, Isabella and Julianne, for giving me the time, the
space,thelove,andtheencouragementtofinishthiswork.
ACKNOWLEDGMENT
Iwouldliketothankmyadvisor,Dr. DavidAnderson,forhisadvice,support,andencourage-
ment.
I would like to thank my fellow students for help given and offered, and for their constant
inquiriesastowhenIwouldfinallyfinishthisthing.
v
TABLE OF CONTENTS
ACKNOWLEDGMENT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v
LISTOF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii
LISTOF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix
LISTOF TERMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xii
SUMMARY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii
CHAPTER1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Organization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
CHAPTER2 BACKGROUND ANDHISTORY . . . . . . . . . . . . . . . . . . . . . 5
2.1 Radar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.2 Sonar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.3 Communications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.4 Astronomy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
CHAPTER3 BROADBANDACOUSTICARRAYSIGNALPROCESSING . . . . . 11
3.1 SignalsinSpaceandTime . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
3.1.1 AcousticWaveEquation . . . . . . . . . . . . . . . . . . . . . . . . . . 12
3.1.2 GeneralizedSolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
3.1.3 DefinitionofTermsandRelationships . . . . . . . . . . . . . . . . . . . 14
3.2 Wavenumber-Frequency Space . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
3.2.1 FourierTransformofSpatiotemporalSignals . . . . . . . . . . . . . . . 15
3.2.2 SupportofPropagating WavesinWavenumber-Frequency Domain . . . . 16
3.3 FilteringofSpace-TimeSignals . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
3.3.1 Time-DomainBroadbandBeamforming . . . . . . . . . . . . . . . . . . 18
3.3.2 Frequency-DomainBroadbandBeamforming . . . . . . . . . . . . . . . 20
3.4 Arrays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.4.1 ArrayConcepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.4.2 ArraysUsedforTheseExperiments . . . . . . . . . . . . . . . . . . . . 30
3.5 AcousticAssumptionsandApproximations forTheseExperiments . . . . . . . . 30
3.5.1 Far-fieldassumption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3.5.2 WavePropogationAssumptions . . . . . . . . . . . . . . . . . . . . . . 30
3.5.3 Uniform SensorResponse . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.5.4 StatisticalAssumptionsofInputSignals . . . . . . . . . . . . . . . . . . 32
vi
CHAPTER4 COMPARISONOFBEAMFORMINGALGORITHMS . . . . . . . . 35
4.1 ConventionalBeamforming . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
4.1.1 TheoreticalAnalysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
4.1.2 ExpectedPerformanceandGains . . . . . . . . . . . . . . . . . . . . . . 38
4.1.3 Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
4.2 LinearlyConstrainedMinimum VarianceBeamformer . . . . . . . . . . . . . . . 42
4.2.1 SolutiontoLCMV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
4.2.2 AlternatePerspective . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
4.2.3 Simulationresults . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
4.2.4 Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
4.3 ReviewofLeast-Mean-Squarealgorithms . . . . . . . . . . . . . . . . . . . . . 50
4.3.1 TraditionalLMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
4.3.2 ConstrainedLMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
4.4 ConstrainedAdaptation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
4.4.1 MinimumVarianceDistortionless Response . . . . . . . . . . . . . . . . 54
4.4.2 FrostAdaptiveBeamformer . . . . . . . . . . . . . . . . . . . . . . . . . 56
4.5 UnconstrainedAdaptation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
4.5.1 GeneralizedSidelobeCanceller . . . . . . . . . . . . . . . . . . . . . . . 59
4.5.2 Griffiths-Jim’sAdaptiveBeamformer . . . . . . . . . . . . . . . . . . . . 61
4.6 PracticalDetails . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
CHAPTER5 TESTPLATFORMIMPLEMENTATION . . . . . . . . . . . . . . . . 64
5.1 HardwareSystems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
5.1.1 AudioDaughter-board . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
5.1.2 FPGAandFPGADevelopmentBoard . . . . . . . . . . . . . . . . . . . 72
5.1.3 HostPC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
5.2 SoftwareSystems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
5.2.1 NiosIISoftware . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
5.2.2 HostPCSoftware . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
CHAPTER6 CONCLUSIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
APPENDIXA VHDLCODEFORAUDIOINTERFACE . . . . . . . . . . . . . . . . . 81
A.1 Audioboard.vhd: Top-levelofHardwareArchitecture . . . . . . . . . . . . . . . 81
A.2 ADInterface.vhd: ADCReadingModule . . . . . . . . . . . . . . . . . . . . . . 85
A.3 DAInterface.vhd: DACWriting Module . . . . . . . . . . . . . . . . . . . . . . 87
A.4 ADCSetup.vhd: ResetConfiguration Module . . . . . . . . . . . . . . . . . . . . 88
A.5 lrClkGenerate.vhd: SamplingclockGenerator . . . . . . . . . . . . . . . . . . . 90
A.6 clkDivideBy12.vhd: ClockDividertoMasterClock . . . . . . . . . . . . . . . . 91
APPENDIXB SCHEMATICSOFAUDIOBOARDDESIGN . . . . . . . . . . . . . . 92
APPENDIXC AUDIOBOARDPCBLAYOUTDIAGRAMS . . . . . . . . . . . . . . . 99
REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
vii
LIST OF TABLES
Table2.1 VariousFieldsofApplication forArrayProcessing. . . . . . . . . . . . . . . 5
Table4.1 Algorithms UnderTest. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
Table4.2 SNRGofconventionalbeamformer intermsofnumberofsensorsinarray,M. 39
Table4.3 SIRG for various weightings and number of sensors (data valid at critical
frequencyonly). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
Table5.1 Statusregisteroftheaudioboard interfaceperipheral. . . . . . . . . . . . . . 74
Table5.2 Control registeroftheaudioboardinterfaceperipheral. . . . . . . . . . . . . . 74
viii
LIST OF FIGURES
Figure1.1 Idealizeddirectionalresponseforvarioustypesofdirectionalmicrophones. . . 3
Figure2.1 Picture from the south of the VLA array,showing the Y configuration of the
individual sensors. Image courtesy of National Radio Astronomy Observa-
tory /AssociatedUniversities,Inc. /NationalScienceFoundation. . . . . . . 9
Figure2.2 Map with locations of VLBA sensors. Image courtesy of National Radio
Astronomy Observatory / Associated Universities, Inc. / National Science
Foundation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
Figure3.1 Ageneralformofatimedomainbeamformer. . . . . . . . . . . . . . . . . . 19
Figure3.2 Ageneralformofafrequencydomainbeamformer. . . . . . . . . . . . . . . 20
Figure3.3 Anexamplearrayshowingtwosources. . . . . . . . . . . . . . . . . . . . . 25
Figure3.4 The aperture smoothing function associated with the example array of Fig-
ure3.3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
Figure3.5 Theresultingspatialfrquencyresponsefromtheexamplearrayfortwosources. 27
Figure3.6 TheaperturesmoothingfunctionforthenineelementlineararrayusingDolph-
Chebychevwindowweighting. . . . . . . . . . . . . . . . . . . . . . . . . . 28
Figure3.7 Theresultingspatialfrequencyfromtheexamplearrayfortwosourcesusing
theDolph-Chebychevwindowing. . . . . . . . . . . . . . . . . . . . . . . . 29
Figure3.8 (a) The magnitude of the aperture smoothing function as a function of fre-
quencyandwavenumber,showingthevisibleregiongrowingwiderinwavenum-
ber as frequency increases. (b) A contour plot showing some divisions of the
wavenumber-frequency spacefortheaperturesmoothing. . . . . . . . . . . . 33
Figure3.9 (a) The magnitude of the aperture smoothing function as a function of fre-
quencyanddirectionofarrival,showingonlythevisibleregion. (b)Acontour
plotshowingof(a). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
Figure4.1 Response curves over frequencies of interest for a two microphone array
with inter-element spacing of 4.3 cm and (a) uniform weighting, (b) Dolph-
Chebychevweighting,and(c)Gaussianweighting. . . . . . . . . . . . . . . . 41
Figure4.2 TheLCMVbeamformerdecomposedintoanadaptivepartandanon-adaptive
part. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
Figure4.3 SimulatedLCMVbeamformerresponsesforoneinterferingsourceandarray
of (a) 2 microphones, (b) 3 microphones, (c) 4 microphones, (d) 8 micro-
phones,allwithinter-microphone spacingof4.31cm. . . . . . . . . . . . . . 45
ix
Figure4.4 SimulatedLCMVbeamformerresponsesfortwointerferingsourceandarray
of (a) 2 microphones, (b) 3 microphones, (c) 4 microphones, (d) 8 micro-
phones,allwithinter-microphone spacingof4.31cm. . . . . . . . . . . . . . 46
Figure4.5 Simulated LCMV beamformer responses for three interfering source and ar-
rayof(a)2microphones,(b)3microphones,(c)4microphones,(d)8micro-
phones,allwithinter-microphone spacingof4.31cm. . . . . . . . . . . . . . 47
Figure4.6 Simulated LCMV beamformer responses for four interfering source and ar-
rayof(a)2microphones,(b)3microphones,(c)4microphones,(d)8micro-
phones,allwithinter-microphone spacingof4.31cm. . . . . . . . . . . . . . 48
Figure4.7 Thegeneralstructureofatwo-channelblock-adaptivefrequency-domainbeam-
former. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
Figure4.8 TheFrostBeamformer. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
Figure4.9 Blockdiagramofthegeneralizedsidelobecanceller. . . . . . . . . . . . . . . 59
Figure4.10 BlockdiagramoftheGriffiths-Jimdynamicadaptivebeamformer. . . . . . . 62
Figure5.1 An overview of the system implementation used to obtain and process the
signalsfromamicrophone array. . . . . . . . . . . . . . . . . . . . . . . . . 64
Figure5.2 Top-side of the multi-channel audioboard used to digitize the microphone or
line-in data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
FigureB.1 BypasscapacitorsandADCcapacitors. . . . . . . . . . . . . . . . . . . . . . 92
FigureB.2 Clockdistribution circuitry. . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
FigureB.3 Digital interfacecircuitry neededforswitchingmodes. . . . . . . . . . . . . . 93
FigureB.4 Power supply system consisting of switchable unregulated supply inputs,and
twoDCvoltageregulators. . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
FigureB.5 HeaderinterfacetotheStratixFPGAboard. . . . . . . . . . . . . . . . . . . 94
FigureB.6 Analoginputcircuitry forchannels1and2. . . . . . . . . . . . . . . . . . . 95
FigureB.7 Analoginputcircuitry forchannels3and4. . . . . . . . . . . . . . . . . . . 95
FigureB.8 Analoginputcircuitry forchannels5and6. . . . . . . . . . . . . . . . . . . 96
FigureB.9 Analoginputcircuitry forchannels7and8. . . . . . . . . . . . . . . . . . . 96
FigureB.10 Analog-to-Digital Converters . . . . . . . . . . . . . . . . . . . . . . . . . . 97
FigureB.11 TheaudiooutputcircuitryconsistingofaDACandtheanalogoutputamplifiers 98
FigureC.1 Aschematicofthetopcopperlayerofthemulti-channel audioPCB. . . . . . 100
x