Efficient and Robust Beamforming Algorithms for Broadband Antenna Array Processors

243 Pages·2014·2.33 MB·English

Efficient and Robust Beamforming
Algorithms for Broadband Antenna Array
Processors
by
Md. Selim Hossain
B.ScEng.,M.ScEng.
ATHESISSUBMITTEDFORTHEDEGREEOF
DOCTOROFPHILOSOPHY
SCIENTIA
MANU ET M E N T E
SchoolofEngineeringandInformationTechnology(SEIT)
UniversityofNewSouthWales
Canberra,ACT,Australia
August06,2013
Originality Statement
I hereby declare that this submission is my own work and to the best of my knowledge
and belief, it contains no material previously published or written by another person,
nor material which to a substantial extent has been accepted for the award of any other
degree or diploma at UNSW or any other educational institution, except where due
acknowledgement is made in the thesis. Any contribution made to the research by
colleagues, with whom I have worked at UNSW or elsewhere, during my candidature,
isfullyacknowledged.
I also declare that the intellectual content of this thesis is the product of my own work,
except to the extent that assistance from others in the project’s design and conception
orinstyle,presentationandlinguisticexpressionisacknowledged.
Md. SelimHossain
UNSW,Canberra,Australia
August06,2013.
i
Acknowledgements
I would like to take this opportunity to thank my principle supervisor, Dr. Greg N.
Milford, School of Engineering and Information Technology, UNSW, Canberra, who
provided endless support, guidance, and motivation to fulfill this work. His technical
guidance,moralsupportandthoughtfulapproachofstudying,havemademyselftrained
tocompletethiswork.
I am also grateful to my co-supervisor, Dr. Mark C. Reed, School of Engineering and
InformationTechnology,UNSW,Canberra,forhisenormousencouragementsandsup-
ports in the weekly meetings as well as in the entire candidature. I give a special thank
to both my supervisors for their deep concentration on the writing of my publication,
andthisthesis.
I also would like to thank my previous principle supervisor Associate Professor Lal C.
Godara, School of Engineering and Information Technology, UNSW, Canberra, whom
I have started my research. He has given me guidance and support about research unto
hisretirementfromthisuniversity.
I like to thank the School of Engineering and Information Technology for providing
me a full-fee studentship, and sponsoring my attendance at conferences. I also thank
theUniversityofNewSouthWalesforprovidingmetheInternationalPostgraduateRe-
searchScholarship(IPRS),oneoftheprestigiousscholarshipsinAustralia,tocomplete
thisresearch.
Thanks to my friends and colleague Rakibul Islam and Presila Israt for their valuable
discussionaboutmyresearch.
I warmly thank my wife and sons for their patience and support, especially during the
finalstagesofpreparingthisthesis.
Lastbutnotleast,Iwishtothankmydearestparents. Theyhaveprovidedbeyondtheir
meansformyeducationandIamgreatlyindebttothem.
ii
Abstract
Broadband beamforming plays an important role in many applications involving an-
tenna array signal processing such as communications, radar, sonar, imaging, geophys-
ical exploration, astrophysical exploration and biomedical diagnostics. The traditional
approaches to broadband beamforming use tapped delay line filter architectures, where
the weights of the filters are chosen by optimization algorithms. Unfortunately, these
approaches have some limitations. Firstly, large matrices need to be manipulated to es-
timatethefiltercoefficientsandthenecessarysteeringdelaysarecumbersometoimple-
ment,withimplementationerrorscausinglossofsystemperformance. Secondly,when
someimperfectionsoccurinthearray,theresultingmismatchinarrayresponsescauses
degradationinthebeamformerperformance. Therefore,theneedforrobustbeamform-
ing arises in many practical applications. Additionally, the placement of nulls in the
array pattern is also a vital issue for cancelling slow moving jammers and known un-
wanted directional sources. Moreover, the traditional techniques have difficulties in
controllingsidelobelevelregardlessofthemainlobepositioninthearraypattern.
This thesis presents algorithms for broadband beamforming that overcomes these lim-
itations. The result is a computationally efficient beamformer that does not require
presteering delays. A unique feature of these new algorithms is inherent robustness to
array imperfections, giving the user some degree of flexibility in choosing array pa-
rameters. The thesis also discusses techniques for broadband pattern synthesis. These
techniques are designed to produce isolated point and broad sector spatial nulls in the
presence of array imperfections. Moreover, a robust Chebyshev broadband antenna ar-
ray pattern synthesis technique is proposed to achieve a specified side lobe level with
interferencecancellationcapabilities.
The thesis also presents broadband arrays having circular and concentric circular an-
tenna element geometries, where these arrays are able to scan a beam through entire
spacewithlittlechangeineitherthebeamwidthorthesidelobelevel. Theperformance
of this proposed processor is compared with the performance of existing broadband
processorsandshowsthatthelimitationsofsteeringdelays,computationalcost,robust-
ness,equalsidelobelevel,nullplacementandarraygeometriescanbeovercomebythe
useoftherobustbroadbandmethodspresentedinthisthesis.
iii
Contents
Declaration i
Acknowledgements ii
Abstract iii
ListofFigures viii
ListofTables xiv
ListofAcronyms xv
ListofNotations xvi
ListofPublications xix
1 Introduction 1
1.1 ProblemIdentification . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.1.1 RobustnessAgainstArrayImperfections . . . . . . . . . . . . 5
1.1.2 ComputationallyEfficientRobustBroadbandArrayProcessor . 6
1.1.3 SelectiveNullPlacementonArrayPattern . . . . . . . . . . . . 7
1.1.4 RequireEqualSidelobeonArrayPattern . . . . . . . . . . . . 8
1.1.5 BeamScanningThrough360◦ . . . . . . . . . . . . . . . . . . 8
1.2 Thesisobjectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.3 ThesisOutline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2 LiteratureReviewandProposedResearch 13
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.2 ArraySignalProcessingOverview . . . . . . . . . . . . . . . . . . . . 13
2.2.1 NarrowbandRobustMethods . . . . . . . . . . . . . . . . . . 14
2.2.2 BroadbandRobustMethods . . . . . . . . . . . . . . . . . . . 15
2.2.3 RobustAntennaArrayPatternSynthesis . . . . . . . . . . . . 17
2.2.4 BroadbandChebyshevAntennaArray . . . . . . . . . . . . . 19
2.2.5 RobustPartitionProcessor . . . . . . . . . . . . . . . . . . . 20
2.2.6 BroadbandCircularAntennaArray . . . . . . . . . . . . . . . 21
2.3 ResearchContributions . . . . . . . . . . . . . . . . . . . . . . . . . . 23
iv
2.4 SystemModelAssumptions . . . . . . . . . . . . . . . . . . . . . . . 24
2.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3 BackgroundandSystemModel 26
3.1 Outlines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.2 SignalModel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.3 SystemModel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.3.1 NarrowbandBeamforming . . . . . . . . . . . . . . . . . . . . 31
3.3.2 ConventionalBeamformer . . . . . . . . . . . . . . . . . . . . 36
3.3.3 OptimalBeamformer . . . . . . . . . . . . . . . . . . . . . . . 38
3.4 BroadbandBeamforming . . . . . . . . . . . . . . . . . . . . . . . . . 39
3.4.1 BroadbandBeamformerwithPresteeringDelays . . . . . . . . 40
3.4.2 BroadbandBeamformerwithoutPresteeringDelays . . . . . . 43
3.4.3 FrequencyResponse . . . . . . . . . . . . . . . . . . . . . . . 47
3.4.4 OptimizationoftheBroadbandBeamformer . . . . . . . . . . 49
3.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
4 RobustandEfficientBroadbandBeamforming 51
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
4.2 RobustBroadbandProcessorwithConvolutionConstraints . . . . . . . 52
4.2.1 RobustAlgorithms . . . . . . . . . . . . . . . . . . . . . . . 53
4.2.1.1 FixedLoading . . . . . . . . . . . . . . . . . . . . . 53
4.2.1.2 OptimalLoading . . . . . . . . . . . . . . . . . . . . 54
4.2.1.3 VariableLoading . . . . . . . . . . . . . . . . . . . 54
4.2.1.4 LinearCombination . . . . . . . . . . . . . . . . . . 55
4.3 BroadbandEfficientRealisationTechnique . . . . . . . . . . . . . . . 56
4.4 RobustAlgorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
4.4.1 FixedDiagonalLoading . . . . . . . . . . . . . . . . . . . . . 59
4.4.2 EigenvaluebasedDiagonalLoading . . . . . . . . . . . . . . . 59
4.4.3 OptimalDiagonalLoading . . . . . . . . . . . . . . . . . . . . 60
4.4.3.1 ExplicitErrorMethod . . . . . . . . . . . . . . . . . 60
4.4.3.2 ImplicitErrorMethod . . . . . . . . . . . . . . . . . 61
4.4.4 VariableOptimalLoadingTechnique . . . . . . . . . . . . . . 61
4.4.5 GeneralLinearCombinationTechnique . . . . . . . . . . . . . 61
4.4.5.1 ExplicitErrorMethod . . . . . . . . . . . . . . . . . 62
4.4.5.2 ImplicitErrorMethod . . . . . . . . . . . . . . . . . 62
4.4.6 NewVariableLoadingTechnique . . . . . . . . . . . . . . . . 63
4.5 PerformanceEvaluation . . . . . . . . . . . . . . . . . . . . . . . . . . 64
4.5.1 OutputSINR . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
4.5.2 EffectofFilterLength . . . . . . . . . . . . . . . . . . . . . . 67
4.5.3 EffectofInterferencesPower . . . . . . . . . . . . . . . . . . 67
4.5.4 MultichannelPropertiesonEfficientProcessor . . . . . . . . . 68
4.5.5 EffectofElementsNumberonAntennaArray . . . . . . . . . . 68
4.5.6 BandwidthVariationonAntennaArray . . . . . . . . . . . . . 69
v
4.5.7 RobustPerformance . . . . . . . . . . . . . . . . . . . . . . . 70
4.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
5 RobustPatternSynthesisforBroadbandAntennaArray 87
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
5.2 ProblemFormulation . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
5.3 DesignPhilosophy . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
5.4 AGeneralOptimisationProblem . . . . . . . . . . . . . . . . . . . . . 91
5.5 TheMinimumMeanOutputPowerProblem . . . . . . . . . . . . . . . 92
5.5.1 MinimumPowerMethodwithQuadraticConstraints . . . . . . 92
5.5.2 MinimumPowerMethodwithEigenvectorConstraints . . . . 95
5.5.3 MinimumPowerMethodwithMultipointConstraints . . . . . 96
5.6 TheMinimumNormProblem . . . . . . . . . . . . . . . . . . . . . . 100
5.6.1 MinimumNormMethodwithQuadraticConstraints . . . . . . 100
5.6.2 MinimumNormMethodwithEigenvectorConstraints . . . . . 101
5.6.3 MinimumNormMethodwithMultipointConstraints . . . . . . 102
5.7 TheLeastSquareProblem . . . . . . . . . . . . . . . . . . . . . . . . 104
5.7.1 LeastSquareMethodwithQuadraticConstraints . . . . . . . . 104
5.7.2 LeastSquareMethodwithEigenvectorConstraints . . . . . . . 105
5.7.3 LeastSquareMethodwithMultipointConstraints . . . . . . . . 106
5.8 ResultsandDiscussions . . . . . . . . . . . . . . . . . . . . . . . . . . 108
5.8.1 ComparisonwithExistingTechniques . . . . . . . . . . . . . . 108
5.8.2 ComputationalComplexity . . . . . . . . . . . . . . . . . . . . 109
5.8.3 Robustness . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
5.9 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
6 RobustConstrainedPartitionedBroadbandProcessor 114
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
6.2 PartitionedBroadbandProcessor . . . . . . . . . . . . . . . . . . . . . 115
6.2.1 ConstrainedPartitionedRealisation . . . . . . . . . . . . . . . 116
6.3 ConvolutionConstrainedRobustPartitionedProcessor . . . . . . . . . 119
6.4 EfficientConstrainedPartitionedProcessor . . . . . . . . . . . . . . . 123
6.5 PerformanceEvaluation . . . . . . . . . . . . . . . . . . . . . . . . . . 125
6.5.1 Beamwidth . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
6.5.2 Robustness . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
6.5.3 PatternSynthesis . . . . . . . . . . . . . . . . . . . . . . . . . 132
6.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
7 ChebyshevBroadbandAntennaArray 136
7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
7.2 DesignofChebyshevAntennaArray . . . . . . . . . . . . . . . . . . 138
7.2.1 BroadbandChebyshevAntennaArray . . . . . . . . . . . . . 138
7.3 PerformanceEvaluation . . . . . . . . . . . . . . . . . . . . . . . . . . 141
7.3.1 InterferenceCancellation . . . . . . . . . . . . . . . . . . . . . 143
7.3.2 Robustness . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
vi
7.3.3 PatternSynthesis . . . . . . . . . . . . . . . . . . . . . . . . . 147
7.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
8 BroadbandCircularAntennaArrayProcessor 151
8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
8.2 ProblemFomulation . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
8.3 ConvolutionConstraintsbasedCircularArray . . . . . . . . . . . . . . 155
8.3.1 OutputPower . . . . . . . . . . . . . . . . . . . . . . . . . . . 156
8.3.2 OutputSINR . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
8.3.3 Robustness . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
8.4 EfficientRobustAlgorithmforCircularArray . . . . . . . . . . . . . . 159
8.5 ResultsandDiscussion . . . . . . . . . . . . . . . . . . . . . . . . . . 161
8.5.1 Robustness . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164
8.5.2 PatternSynthesis . . . . . . . . . . . . . . . . . . . . . . . . . 168
8.5.3 SensitivityAnalysis . . . . . . . . . . . . . . . . . . . . . . . 170
8.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172
9 BroadbandConcentricCircularAntennaArray 173
9.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173
9.2 ProblemFomulation . . . . . . . . . . . . . . . . . . . . . . . . . . . 175
9.2.1 SteeringAngleMismatch . . . . . . . . . . . . . . . . . . . . 177
9.2.2 SensorPositionError . . . . . . . . . . . . . . . . . . . . . . . 177
9.2.3 MutualCouplingEffect . . . . . . . . . . . . . . . . . . . . . 179
9.3 ConvolutionConstraintsbasedBroadbandCCAA . . . . . . . . . . . 180
9.4 EfficientRobustAlgorithmforCCAA . . . . . . . . . . . . . . . . . . 181
9.5 PerformanceAnalysis . . . . . . . . . . . . . . . . . . . . . . . . . . 184
9.5.1 Robustness . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187
9.5.2 SynthesiswithCCAA . . . . . . . . . . . . . . . . . . . . . . 188
9.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188
10 ConclusionsandFutureResearch 189
10.1 ThesisAchievements . . . . . . . . . . . . . . . . . . . . . . . . . . . 189
10.2 FutureResearch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191
AppendixA 193
A.0.1 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197
AppendixB 200
References 204
vii
List of Figures
1.1 Blockdiagramofanarraysystem[1] . . . . . . . . . . . . . . . . . . . 4
1.2 Blockdiagramofacommunicationsystemusinganantennaarray[1] . 4
3.1 Coordinate system for a receiving array showing a source and array
elementattheirrespectivelocations. . . . . . . . . . . . . . . . . . . . 27
3.2 GeometryoflinearantennaarrayshowingLelementsuniformlyspaced
alongx-axiswithonedesiredandmultipleinterferingsignalsources. . 28
3.3 NarrowbandbeamformerstructureconsistingofLantennaelementsand
wcomplexweightssummedtoproduceantennaarrayoutputy(t). . . . 32
3.4 Delay-and-sum beamformer showing two elements separated by dis-
tanced. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
3.5 Broadbandbeamformerstructurewithpresteeringdelays[1]. . . . . . . 41
3.6 Broadbandtimedomainbeamformerstructurewithoutpresteeringdelays. 44
4.1 Blockdiagramofbroadbandbeamformerwithefficientrealisationtech-
nique. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
4.2 3-D power pattern of the broadband efficient processor with steering
angle and frequency variations with number of elements = 10, number
of taps = 125, signal power = 1.0, signal direction = 70◦, number of
interferences = 4, interference power = 10.0, interference directions =
[40◦,100◦,120◦,160◦],backgroundnoise=0.1. . . . . . . . . . . . . . 64
4.3 OutputSINRcomparisonbetweenefficientrealisationmethodandcon-
volutionconstrainedmethodforscenario1ofTable4.2. . . . . . . . . 65
4.4 Output SINR as a function of filter lengths using efficient realisation
methodforscenario1ofTable4.2. . . . . . . . . . . . . . . . . . . . 66
4.5 EffectofinterferencespoweronoutputSINRusingefficientrealisation
methodforscenario2ofTable4.2. . . . . . . . . . . . . . . . . . . . 67
4.6 Output SINR using efficient realisation method for scenario 1 of Ta-
ble4.3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
4.7 Effect of elements number on broadband processor for scenario 2 of
Table4.3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
4.8 EffectofbandwidthonoutputSINRpatternofbroadbandefficientpro-
cessorforscenario2ofTable4.4. . . . . . . . . . . . . . . . . . . . . 70
4.9 Output signal power versus look direction error using various methods
forscenario1ofTable4.4. . . . . . . . . . . . . . . . . . . . . . . . . 71
4.10 Output SINR versus look direction error using different methods for
scenario1ofTable4.4. . . . . . . . . . . . . . . . . . . . . . . . . . . 72
viii
4.11 Output SINR versus look direction error using EEM for scenario 2 of
Table4.4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
4.12 OutputsignalpowerversuslookdirectionerrorusingEEMforscenario
2ofTable4.4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
4.13 OutputSINRatlookdirectionerrorusingIEMforscenario2ofTable4.4. 76
4.14 OutputsignalpoweratlookdirectionerrorusingIEMforscenario2of
Table4.4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
4.15 Output signal power at look direction error for NVL processor using
EEMandIEMforscenario2ofTable4.4. . . . . . . . . . . . . . . . . 78
4.16 OutputsignalpowerasafunctionofnoiselevelusingEEMforscenario
2ofTable4.4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
4.17 Output SINR as a function of noise level using IEM for scenario 2 of
Table4.4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
4.18 Output SINR versus filter length of the processor using IEM for sce-
nario1ofTable4.5. . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
4.19 Output signal power versus filter length of the processor using IEM for
scenario1ofTable4.5. . . . . . . . . . . . . . . . . . . . . . . . . . . 82
4.20 PowerpatternoftheprocessorusingIEMoftheNVLrobusttechniques
forscenario2ofTable4.5. . . . . . . . . . . . . . . . . . . . . . . . . 83
4.21 FrequencyresponseoftheprocessorusingIEMoftheNVLrobusttech-
niqueforscenario2ofTable4.5. . . . . . . . . . . . . . . . . . . . . . 84
4.22 FrequencyresponseoftheNVLbasedbeamformerinthedirection300
forscenario2ofTable4.5. . . . . . . . . . . . . . . . . . . . . . . . . 85
4.23 PowerpatternoftheprocessorusingIEMoftheNVLrobusttechniques
withfourdifferentMCmatrixforscenario2ofTable4.5. . . . . . . . . 86
5.1 Output SNR of the beamformer with quadratic constraints minimum
mean output power problem for number of elements = 16, number of
taps=125,signalpower=1.0,broadnull . . . . . . . . . . . . . . . . 93
5.2 Output SNR of the beamformer with placing point null at 100◦ for the
sameconfigurationofFigure5.1. . . . . . . . . . . . . . . . . . . . . 94
5.3 Power pattern of the beamformer for minimum mean output power
problemwiththesameconfigurationofFigure5.1. . . . . . . . . . . . 96
5.4 Desired frequency response for minimum mean output power problem
forthesamescenarioofFigure5.3. . . . . . . . . . . . . . . . . . . . 97
5.5 Frequencyresponseforminimummeanoutputpowerproblemwiththe
sameconfigurationofFigure5.3. . . . . . . . . . . . . . . . . . . . . 98
5.6 Effect of parameter ξ on broadband SNR pattern for minimum mean
outputpowerproblemwithquadraticconstraints. . . . . . . . . . . . . 99
5.7 Power pattern of the beamformer for minimum norm problem with
samescenarioofFigure5.3. . . . . . . . . . . . . . . . . . . . . . . . 102
5.8 Effect of the trace parameter on the output SNR for eigenvector con-
strainedbasedminimumnormproblem. . . . . . . . . . . . . . . . . . 103
5.9 Powerpatternofthebeamformerforleastsquareproblemwiththesame
scenarioof 5.7. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
ix