Methods of Signal Processing for Adaptive Antenna Arrays

233 Pages·2013·2.75 MB·English

by  Larysa Titarenko

Signals and Communication Technology 6
Forfurthervolumes:
http://www.springer.com/series/4748
Larysa Titarenko and Alexander Barkalov
Methods of Signal Processing
for Adaptive Antenna Arrays
ABC
Authors
Prof.Dr.LarysaTitarenko Prof.Dr.AlexanderBarkalov
InstituteofInformaticsandElectronics InstituteofInformaticsandElectronics
UniversityofZielonaGora UniversityofZielonaGora
ZielonaGora ZielonaGora
Poland Poland
ISSN1860-4862
ISBN978-3-642-32131-3 e-ISBN978-3-642-32132-0
DOI10.1007/978-3-642-32132-0
SpringerHeidelbergNewYorkDordrechtLondon
LibraryofCongressControlNumber:2012942953
(cid:2)c Springer-VerlagBerlinHeidelberg2013
Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpartof
thematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation,
broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,andtransmissionorinformation
storageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodology
nowknownorhereafterdeveloped.Exemptedfromthislegalreservationarebriefexcerptsinconnection
with reviews or scholarly analysis or material supplied specifically for the purpose of being entered
and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of
this publication or parts thereof is permitted only under the provisions of the Copyright Law of the
Publisher’slocation,initscurrentversion,andpermissionforusemustalwaysbeobtainedfromSpringer.
PermissionsforusemaybeobtainedthroughRightsLinkattheCopyrightClearanceCenter.Violations
areliabletoprosecutionundertherespectiveCopyrightLaw.
Theuseofgeneraldescriptivenames,registerednames,trademarks,servicemarks,etc.inthispublication
doesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevant
protectivelawsandregulationsandthereforefreeforgeneraluse.
Whiletheadviceandinformationinthisbookarebelievedtobetrueandaccurateatthedateofpub-
lication,neithertheauthorsnortheeditorsnorthepublishercanacceptanylegalresponsibilityforany
errorsoromissionsthatmaybemade.Thepublishermakesnowarranty,expressorimplied,withrespect
tothematerialcontainedherein.
Printedonacid-freepaper
SpringerispartofSpringerScience+BusinessMedia(www.springer.com)
Thebookisdedicatedto theblessed memory
ofLeonid Marchuk
Acknowledgements
WewouldliketothankourPhDstudentsSlawomirChmielewski,OlenaHebdaand
LukaszSmolinski.Theyhelpedusa lotwith preparationofthismanuscript.They
worked with us on initial planning of this work, distribution of tasks during the
project,andfinalassemblyofthisbook.
Contents
1 Introduction................................................... 1
2 GeneralCharacteristicofMethodsforSTSP ...................... 5
2.1 AnalysisofMethodsofNonadaptiveSpatialSignalProcessing .... 5
2.2 AnalysisofPeculiaritiesofAdaptiveSpatialSignalProcessing .... 9
2.3 AnalysisofNon-structuralMethodsofAdaptiveSTSP ........... 9
2.4 AnalysisofClassicalStructuralMethodsofAdaptiveSTSP ....... 10
References..................................................... 15
3 BackgroundofClassicalTheoryofASSP ......................... 17
3.1 AnalysisofTypicalDescriptionofSignal-NoiseSituation ........ 17
3.2 IntroductionintoSystemofCriteriaofOptimality ............... 19
3.3 AnalysisofAlgorithmsofAdaptiveSpace-TimeSignal
Processing ................................................ 26
References..................................................... 32
4 FeaturesofASSPunderDifferentLevelsofA-PrioriUncertainty.... 35
4.1 Analysis of Peculiarities of ASSP with DifferentLevelsof
A-PrioriUncertainty........................................ 35
4.2 NatureofaPrioriUncertaintyaboutPropertiesofSignaland
Noise..................................................... 37
4.3 MethodsofSSPunderGeneralizedParametricUncertaintyabout
theNoiseProperties ........................................ 40
4.4 MethodsofSP undera PrioryParametricUncertaintyabout
PropertiesofUsefulSignal................................... 44
References..................................................... 49
5 AlgorithmsofASSPwithNotExactlyKnownParameters .......... 51
5.1 MainApproachesforDevelopmentofAlgorithmsofASSPwith
NotExactlyKnownParameters............................... 51
X Contents
5.2 ProbabilisticApproachforSynthesisofRobustAlgorithmsof
ASSP .................................................... 53
5.3 Deterministic Approach:Robust Algorithms of ASSP for
ModifiedOptimizationTasks................................. 58
5.4 RestrictionsforValueofArbitraryDirectivityCharacteristicof
Antenna .................................................. 61
5.5 AdditionalLinearRestrictions................................ 67
5.6 RestrictionsofStandardDeviationforDirectivityCharacteristic
ofAAfromtheGivenValue ................................. 70
5.7 CorrelativeRestrictions ..................................... 73
5.8 RestrictionsfortheShapeofAmplitude-PhaseDistributionof
CurrentsinChannelsofAA.................................. 74
5.9 RestrictionforValueofModulusofOutputSignalofAA ......... 76
5.10 RestrictionsforValueofNormofWeightCoefficients............ 77
5.11 PeculiaritiesofRobustnizationforAlgorithmsofASSP .......... 77
5.12 ApproximationofControlVectorbySectionofTaylorSeries...... 78
5.13 ProjectionApproach........................................ 80
5.14 Robustnization of ASSP Algorithms Using Nonlinear
TransformationsofInputSignals.............................. 82
5.15 Restrictionsof Existed Methodsof ASPS with Not Exactly
KnownParameters ......................................... 83
References..................................................... 85
6 BackgroundofASSPwithNotExactlyKnownParameters ......... 87
6.1 ElementsofAxiomaticandSomeAnalogies.................... 87
6.2 GeneralizedLinearSystemsofRayleighandCentrosymmetric
Matrices .................................................. 90
6.3 AlgorithmsofASFBasingonOperators’ConstructioninBanach
Space .................................................... 91
6.4 MethodsofConstructionofOperators ......................... 95
6.5 MinimaxApproachforOperator’sConstructionandPrincipleof
Comparison ...............................................110
6.6 AdaptiveApproachforConstructionofOperators ...............118
6.7 OptimizationTaskswith SquaredRestrictionsoftheUnstrict
InequalitiesType...........................................120
6.8 ConstructionofOptimizationTaskswithMixedRestrictions ......128
6.9 ConstructionofOptimizationTaskswith GeneralizedMixed
Restrictions ...............................................132
6.10 Conclusion................................................134
References.....................................................136
7 SynthesisofASFAlgorithmsforNotExactlyKnownParameters....139
7.1 SynthesisofMinimaxAlgorithms.............................139
7.2 SynthesisofAdaptiveAlgorithms.............................148
Contents XI
7.3 SynthesisofAlgorithmsforAdaptationofStructures
ofOperatorstoCurrentSIE ..................................155
7.4 AnalysisofQualityforASFAlgorithmsforSignalswithNot
ExactlyKnownParameters ..................................162
References.....................................................165
8 AlgorithmsofASPforNotExactlyKnownParameters.............167
8.1 TaskofSynthesisforAlgorithmsofSpatialPartitioning
asaTaskofOperatorConstruction ............................167
8.2 ConstructingMinimaxOperators .............................171
8.3 SynthesisofAlgorithmsforAdaptiveSpatialSignalPartition......175
8.4 AnalysisofQualityofASFAlgorithms ........................185
8.5 AlgorithmofASFforLow-ElementAntennaArrays.............193
References.....................................................202
9 Conclusion ....................................................205
A PropertiesofBundlesandCentrosymmetricMatrices ..............209
References.....................................................218
B InequalitiesforMatrixNormsandProperValuesofBundlesof
HermitianForms ..............................................219
References.....................................................222
C MethodologyforConstructionofCentrosymmetricMatrices........223
D EquivalenceofOptimizationTasks...............................225
References.....................................................226
Index .............................................................227
Abbreviations
AA antennaarray
AAA adaptiveantennaarray
AE antennaelements
ASF adaptivespatialfiltration
ASSP adaptivespatialsignalprocessing
ASP adaptivespatialpartitioning
ASPSP adaptivespatial-temporalsignalprocessing
CFC complexfrequencycharacteristic
CM correlationmatrix
DC directivitycharacteristic
DL delayline
EW electromagneticwave
FC frequencycharacteristic
HF Hermetianform
MFL ModifiedfunctionofLagrange
MSD minimum for standard deviation of signal respectively to reference
signal
MPOSR minimumforpowerofoutputsignalunderrestrictions
MPSOS minimumforpowerofsummarizedoutputsignal
MRSI maximumofrelationforpowerofusefulsignaltototalpowerofin-
terferenceandnoise
OF objectivefunction
OLF optimallinearfiltration
PN propernumber
PV propervector
RSIN maximumofoutputrelationsignal/(interference+noise)
SF spacefilter
SFF space-frequencyfilter
SIE signal-interferenceenvironment
SP signalprocessing
SSP spatialsignalprocessing
XIV Abbreviations
STSP spatial-temporalsignalprocessing
TRW transmissionofradiowaves
VWC vectorofweightcoefficients