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Channel, spectrum, and waveform awareness in OFDM-based cognitive radio systems

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Title:
Channel, spectrum, and waveform awareness in OFDM-based cognitive radio systems
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English
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Yücek, Tevfik
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University of South Florida
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Subjects / Keywords:
Wireless communications
Multi-carrier transmission
Spectrum sensing
Adaptation
Parameter estimation
Dissertations, Academic -- Electrical Engineering -- Doctoral -- USF   ( lcsh )
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bibliography   ( marcgt )
theses   ( marcgt )
non-fiction   ( marcgt )

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ABSTRACT: The radio spectrum is becoming increasingly congested everyday with emerging technologies and with the increasing number of wireless devices. Considering the limited bandwidth availability, accommodating the demand for higher capacity and data rates is a challenging task, requiring innovative technologies that can offer new ways of exploiting the available radio spectrum. Cognitive radio arises to be a tempting solution to the spectral crowding problem by introducing the notion of opportunistic spectrum usage. Because of its attractive features, orthogonal frequency division multiplexing (OFDM) has been successfully used in numerous wireless standards and technologies. We believe that OFDM will play an important role in realizing the cognitive radio concept as well by providing a proven, scalable, and adaptive technology for air interface. The goal of this dissertation is to identify and address some of the challenges that arise from the introduction of cognitive radio.Specifically, we propose methods for obtaining awareness about channel, spectrum, and waveform in OFDM-based cognitive radio systems in this dissertation. Parameter estimation for enabling adaptation, spectrum sensing, and OFDM system identification are the three main topics discussed. OFDM technique is investigated as a candidate for cognitive radio systems. Cognitive radio features and requirements are discussed in detail, and OFDM's ability to satisfy these requirements is explained. In addition, we identify the challenges that arise from employing OFDM technology in cognitive radio. Algorithms for estimating various channel related parameters are presented. These parameters are vital for enabling adaptive system design, which is a key requirement for cognitive radio. We develop methods for estimating root-mean-square (RMS) delay spread, Doppler spread, and noise variance.The spectrum opportunity and spectrum sensing concepts are re-evaluated by considering different dimensions of the spectrum which is known as multi-dimensional spectrum space. Spectrum sensing problem in a multi-dimensional space is addressed by developing a new sensing algorithm termed as partial match filtering (PMF). Cognitive radios are expected to recognize different wireless networks and have capability of communicating with them. Algorithms for identification of multi-carrier transmissions are developed. Within the same work, methods for blindly detecting transmission parameters of an OFDM based system are developed. Blind detection is also very helpful in reducing system signaling overhead in the case of adaptive transmission where transmission parameters are changed depending on the environmental characteristics or spectrum availability.
Thesis:
Dissertation (Ph.D.)--University of South Florida, 2007.
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Includes bibliographical references.
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by Tevfik Yücek.
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Title from PDF of title page.
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Document formatted into pages; contains 185 pages.
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Includes vita.

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aleph - 001925099
oclc - 191563640
usfldc doi - E14-SFE0002160
usfldc handle - e14.2160
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IwishtothankDr.HavishKoorapaty,Dr.MiguelA.Labrador,Dr.WilfridoA.Moreno,andDr.ThomasM.Wellerforservinginmycommittee,fortheirvaluabletime,feedbackandsuggestions;andtoDr.DmitryB.Goldgofforchairingmydefense.Dr.ParisWiley,Dr.EliasK.Stefanakos,GaylaMontgomery,IreneWiley,MariaDu,BeckyBrenner,andNormaPazfromtheElectricalEngineeringadministrationandstadenitelydeservemanythanksforhelpingoutinnumerousissuesoverthepastyears. IowealottothepeopleofLogusBroadbandWirelessSolutionsInc.whonanciallysupportedmyworkforthemajorityofPh.D.duration.I'vealsospenttwosummersemestersduringmyPh.D.asaninternatLogus.IwouldespeciallyliketothanktoFrancisE.RetnasothieforprovidingmetheopportunitytoworkatLogusonsomerealresearchprojects.IenjoyedworkingwithLogusteam. IwouldliketothankalottomycolleaguesatUSF.IamgratefultomyroommateDr._IsmailGuvencwithwhomIstayedwithforthersttwoyearsofmyPh.D.,andtomyfriendsatwirelesscommunicationsandsignalprocessing(WCSP)group;HasariCelebi,SerhanYarkan,HishamA.Mahmoud,MustafaE.Sahin,SadiaAhmed,KemalOzdemirandothers.Wesharedmanythingstogether,includinglonggroupmeetings,conferencetravels,andfruitfuldiscussions;Iwishallofyouthebestinyourfuturecareersandlives. Mydeepestgratitudegoestomywifeforherencouragementandpatience.Youweretheretosharejoysanddisappointments,andtoprovidehopeandmotivationattimesIstartedlosingthem.IknowthatitwasverydiculttobethewifeofaPh.D.student,andIwillalwaysrememberyourunderstandingandsupport. Lastbutbynomeansleast,Iwouldliketothankmyparentsandtomydeargrandparents,forwhomthisdissertationisdedicated,fortheircontinuedsupport,encouragementandsacricethroughouttheyears,andIwillbeforeverindebtedtothemforallthattheyhavedone.

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LISTOFFIGURESvi ABSTRACTx CHAPTER1INTRODUCTION1 1.1OFDMTechnology2 1.2OFDM-BasedCognitiveRadio3 1.3AwarenessinCognitiveRadio4 1.4DissertationOutline5 1.4.1Chapter2:OFDMforCognitiveRadio:MeritsandChallenges7 1.4.2Chapter3:TimeDispersionandDelaySpreadEstimationforAdaptiveOFDMSystems8 1.4.3Chapter4:DopplerSpreadEstimationforWirelessOFDMSystems8 1.4.4Chapter5:MMSENoisePlusInterferencePowerEstima-tioninAdaptiveOFDMSystems8 1.4.5Chapter6:SpectrumSensingforCognitiveRadioApplications9 1.4.6Chapter7:SpectrumSensingforCognitiveRadioUsingPartialMatchFiltering9 1.4.7Chapter8:OFDMSignalIdenticationandTransmissionParameterEstimationforCognitiveRadioApplications10 1.4.8Chapter9:FeatureSuppressionforPhysical-LayerSecurityinOFDMSystems10 1.4.9OtherWorkDone10 1.5Notation11 CHAPTER2OFDMFORCOGNITIVERADIO:MERITSANDCHALLENGES12 2.1Introduction12 2.2ABasicOFDMSystemModel13 2.2.1CyclicExtensionofOFDMSymbols14 2.2.2WirelessChannel16 2.2.3ASimpleSystem19 2.2.4OFDMImpairments20 2.2.4.1FrequencyOset20 2.2.4.2Time-VaryingChannel23 2.2.4.3PhaseNoise24 2.2.4.4ReceiverTimingErrors25 2.2.4.5AdditiveNoise27 2.2.4.6Peak-to-AveragePowerRatio27 2.2.5Multiple-AccessingWithOFDM28 2.3WhyOFDMisaGoodFitforCognitiveRadio28 2.3.1AdaptingtoEnvironment28i

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2.3.1.2AdaptationinMobileOFDMSystems36 2.3.2SpectrumSensingandAwareness38 2.3.3SpectrumShaping39 2.3.4AdvancedAntennaTechniques40 2.3.5MultipleAccessingandSpectralAllocation41 2.3.6Interoperability42 2.4ChallengestoCognitiveOFDMSystems42 2.4.1SpectrumShaping43 2.4.2EectivePruningAlgorithmDesign44 2.4.3SignalingTransmissionParameters44 2.4.4Synchronization45 2.4.5MutualInterference45 2.5AStepTowardCognitive-OFDM:StandardsandTechnologies47 2.5.1WiMAX-IEEE802.1647 2.5.2IEEE802.2249 2.5.3IEEE802.1151 2.6Conclusion52 CHAPTER3TIMEDISPERSIONANDDELAYSPREADESTIMATIONFORADAP-TIVEOFDMSYSTEMS54 3.1Introduction54 3.2SystemModel56 3.3ProposedDelaySpreadEstimationAlgorithms57 3.3.1ChannelEstimationBasedAlgorithm58 3.3.2ChannelMagnitudeBasedAlgorithm60 3.3.3ReceivedSignalBasedAlgorithm62 3.3.4EstimationofRMSDelaySpreadandMaximumExcessDelay62 3.4NumericalResults63 3.5Conclusion67 CHAPTER4DOPPLERSPREADESTIMATIONFORWIRELESSOFDMSYSTEMS68 4.1Introduction68 4.2SystemandChannelModels69 4.3DopplerSpreadEstimation70 4.3.1ComputingfDfromAuto-CorrelationFunction72 4.3.2CoherenceTimeVersusDopplerSpread73 4.3.3ComplexityofProposedMethodVersusGains73 4.4NumericalResults74 4.5Conclusion75 CHAPTER5MMSENOISEPLUSINTERFERENCEPOWERESTIMATIONINADAP-TIVEOFDMSYSTEMS77 5.1Introduction77 5.2SystemModel79 5.3DetailsoftheProposedAlgorithm80 5.3.1RectangularWindow84 5.3.2EdgesandTimeAveraging85 5.4NumericalResults86 5.5Conclusion88ii

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6.1Introduction91 6.2Challenges94 6.2.1HardwareRequirements94 6.2.2HiddenPrimaryUserProblem94 6.2.3SpreadSpectrumPrimaryUsers94 6.2.4SensingTime95 6.2.5OtherChallenges95 6.3SpectrumSensingMethodsforCognitiveRadio95 6.3.1MatchedFiltering96 6.3.2WaveformBasedSensing96 6.3.3CyclostationarityBasedSensing98 6.3.4EnergyDetectorBasedSensing98 6.3.5RadioIdentication101 6.3.6OtherSensingMethods101 6.4CooperativeSensing102 6.4.1CentralizedSensing104 6.4.2DistributedSensing104 6.5ExternalSensing105 6.6UsingHistoryforPrediction106 6.7SensingFrequency107 6.8HardwareRequirementsandApproaches107 6.9Multi-DimensionalSpectrumAwareness108 6.10SpectrumSensinginCurrentWirelessStandards109 6.10.1IEEE802.11k110 6.10.2Bluetooth110 6.10.3IEEE802.22111 6.11Conclusions112 CHAPTER7SPECTRUMSENSINGFORCOGNITIVERADIOUSINGPARTIALMATCHFILTERING114 7.1Introduction114 7.2PartialMatch-Filtering115 7.2.1FeatureExtraction116 7.2.1.1FrequencyDomainFeatures116 7.2.1.2TimeDomainFeatures117 7.2.1.3OtherFeatures118 7.2.2DecisionMaking(Classication)118 7.2.3Multi-DimensionalSpectrumCharacterization119 7.3CaseStudy:EnergyDetectorBasedPMF119 7.3.1FrequencyDomainFiltering120 7.3.2ThresholdDetector121 7.3.3FeatureExtraction122 7.3.4Classication123 7.4NumericalResults125 7.5Discussion128 7.6ConclusionsandFutureResearch129iii

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8.1Introduction130 8.2SystemModel132 8.3ProposedAlgorithms134 8.3.1MLEstimationofOFDMSymbolLengthandCPSize134 8.3.2OFDMSignalIdentication138 8.3.3EstimationofNumberandFrequenciesofActiveSubcarriers139 8.3.3.1NumberofSubcarriers141 8.3.3.2FrequenciesofSubcarriers142 8.3.4FFTSizeandCommunicationStandard144 8.4NumericalResults145 8.5Conclusion149 CHAPTER9FEATURESUPPRESSIONFORPHYSICAL-LAYERSECURITYINOFDMSYSTEMS150 9.1Introduction150 9.2EectofCyclicPrexontheBER151 9.3BlindParameterEstimationandSynchronization152 9.4ProposedMethodsforCovertTransmission154 9.4.1InsertionofRandomSignals155 9.4.2AdaptiveCyclicPrexSize156 9.4.3PossibleExtensions156 9.5NumericalResults157 9.6Conclusion157 CHAPTER10CONCLUSIONANDFUTUREWORK161 10.1ListofSpecicContributions161 10.2FinalCommentsandFutureWork163 REFERENCES165 APPENDICES181 AppendixADerivationofChannelMagnitudeCorrelation182 AppendixBDerivationofCramer-RaoBound183 AppendixCLog-LikelihoodFunctionforOFDMParameterEstimation185 ABOUTTHEAUTHOREndPageiv

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Table2.2OFDM-basedwirelessstandards.43 Table2.3AdvancedantennafeaturesofWiMAX.50 Table3.1CharacteristicsoftheITU-R\VehicularA"channelmodel.64 Table6.1Blindradioidenticationalgorithms.102 Table6.2Localversuscooperativesensing.103 Table6.3Comparisonofsingle-radioanddual-radiosensingalgorithms.108 Table6.4Multi-dimensionalradiospectrumspaceandtransmissionopportunities.113v

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Figure1.2Thethreeelementsthatarestudiedinthisdissertation.6 Figure2.1PowerspectrumdensityoftransmittedtimedomainOFDMsignal.14 Figure2.2PowerspectrumdensityofOFDMsignalwhenthesubcarriersatthesidesofthespectrumandatDCissettozero.15 Figure2.3Illustrationofcyclicprexextension.16 Figure2.4Illustrationofsomeoftheeectsofradiochannel:Localscattererscausefading;remotereectorscausemultipathandtimedispersion,leadingtoISI;mobilityofuserorscattererscausetimevaryingchan-nel,leadingtofrequencydispersion(Dopplerspread);reuseoffre-quencies,adjacentcarriersetc.causeinterference.17 Figure2.5Anexample2-dimensionalchannelresponse:AnexponentialPDPwithRMSdelayspreadof16sisused,mobilespeedisassumedtobe100km/h,andthecenterfrequencywas5.2GHz.ChanneltapsareobtainedusingmodiedJakes'model[1].18 Figure2.6BlockdiagramofanOFDMtransceiver.19 Figure2.7Modulationmodeselectionbasedonchannelqualityinsubbandadap-tiveOFDMsystems.32 Figure2.8BiterrorrateofanOFDMsystemintime-varyingchannelasafunc-tionofFFTsize.Thetransmissionbandwidthis3.5MHz,thecenterfrequencyis5.8GHzandthemobilespeedis100km/h.35 Figure2.9BiterrorrateofanOFDMsystemintime-varyingchannelasafunc-tionofFFTsizeandguardintervallength.Thetransmissionband-widthis3.5MHz,thecenterfrequencyis5.8GHz,themobilespeedis100km/handSNRis30dB.38 Figure2.10SpectrumsensingandshapingusingOFDM.40 Figure2.11OFDM-basedwirelesstechnologies.43 Figure2.12ResearchchallengesincognitiveradioandOFDM.44vi

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Figure2.14RolloeectonthePSDofasingleOFDMsubcarrier.46 Figure2.15IllustrationofOFDMAsignalstructureusedinWiMAX.49 Figure2.16Standardsandtechnologiesdevelopments.53 Figure3.1Magnitudeofchannelfrequencycorrelationwithperfectsynchroniza-tionandwithsynchronizationerrors.Analytical(Eqn.3.9)andsim-ulationresultsareshown.60 Figure3.2Illustrationofframestructureofthesystemusedfortestingthepro-posedalgorithms.64 Figure3.3Normalizedmean-square-errorperformancesoftheRMSdelayspreadestimatorsasafunctionofnumberofframesusedforestimation.65 Figure3.4Normalizedmean-square-errorperformancesoftheRMSdelayspreadestimatorsasafunctionofnumberofframesusedforestimation.66 Figure3.5Normalizedmean-square-errorperformancesoftheRMSdelayspreadestimatorsasafunctionofnumberofframesusedforestimationwhentherearetimingsynchronizationerrors.66 Figure3.6Normalizedmean-square-errorperformancesoftheRMSdelayspreadestimatorsasafunctionoftheSNR.Estimationisperformedover80frames.67 Figure4.1Averagepowersofthechannelcomponentsanddisturbancesintime-domain.72 Figure4.2MeansquarederrorasafunctionofsignaltonoiseratioforaxedDopperspreadof300Hz.74 Figure4.3MeansquarederrorasafunctionofaveragingsizeforxedDopperspreadof300HzandSNRvalueof15dB.75 Figure4.4MeansquarederrorasafunctionofthemaximumDopplerfrequencyforSNRvalueof15dB.76 Figure5.1Weightingcoecientsfordierentcolorednoisetowhitenoisepowerratios.84 Figure5.2Meansquarederrorfordierentalgorithmsasafunctionofthesta-tionaryinterferencetowhitenoisepowerratios.87 Figure5.3Meansquarederrorfordierentalgorithmsasafunctionofthenon-stationaryinterferencetowhitenoisepowerratios.87 Figure5.4Trueandestimatednoisevariancesinthepresenceofanarrowbandinterferer.88 Figure5.5Probabilityofdetectionofinterferenceasafunctionofinterferencetowhitenoisepowerratios.89vii

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Figure6.1Variousaspectsofspectrumsensingforcognitiveradio.93 Figure6.2Illustrationofhiddenprimaryuserproblemincognitiveradiosystems.95 Figure6.3ROCcurvesforenergydetectorbasedspectrumsensingunderdier-entSNRvalues.100 Figure6.4Binaryschemeusedformodelingspectrumoccupationin[2].106 Figure6.5Bluetoothtransmissionwithandwithoutadaptivefrequencyhopping(AFH).AFHpreventscollusionsbetweenWLANandBluetoothtransmissions.111 Figure7.1Blockdiagramofproposedalgorithm.116 Figure7.2Blockdiagramofenergydetectorbasedpartialmatch-lteringmethod.120 Figure7.3ROCcurvesfordierentSNRvalues.123 Figure7.4IllustrationofDUDEalgorithmforbandwidthandcenterfrequencyestimation.124 Figure7.5PowerspectraldensityoftestedWLANandBluetoothsignals.126 Figure7.6DetectionerrorratesfortheWLANandBluetoothsystemsatdier-entSNRvaluesforLt=15.127 Figure7.7DetectionerrorratesfortheWLANandBluetoothsystemsatdier-entSNRvaluesforLt=30.127 Figure7.8DetectionerrorratesfortheWLANandBluetoothsystemsatdier-entSNRvaluesforLt=15undermulti-pathfadingchannel.128 Figure8.1IllustrationofcyclicprexextensioninOFDMsystems.133 Figure8.2NumericalperformancecomparisonofML,suboptimalMLandtwo-stepalgorithms.NormalizedMSEofOFDMsymboldurationestima-tionversusSNRispresented.138 Figure8.3IllustrationofESPRITbasedsubcarrierestimation.142 Figure8.4SubcarriersestimatedbyESPRITalgorithmandpowerspectralden-sityofreceivedsignalunderAWGNandfadingchannelsareillus-trated.143 Figure8.5ProbabilityofincorrectdetectionforOFDMsignalfordierentnum-berofsymbolsunderAWGNandfadingchannels.146 Figure8.6NormalizedMSEofOFDMsymboldurationasafunctionofSNRfordierentnumberofsymbolsunderAWGNandfadingchannels.146viii

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Figure8.8ProbabilityoferrorfordetectingnumberofactivesubcarriersfordierentnumberofsymbolsunderAWGNandfadingchannels.147 Figure8.9HistogramofnumberofdetectedsubcarriersfordierentSNRvalues.Thenumberofemployedsubcarriersis44.148 Figure8.10Probabilityoferrorsforproposedsubcarrierdetectionalgorithm.Er-rorsincludebothfalsealarmsandmis-detectionsofsubcarriers.149 Figure9.1Illustrationofinter-symbolinterferenceduetomultipathfadingandshortcyclicprexsize.152 Figure9.2Illustrationofcyclicprexbasedmaximumlikelihoodestimation.153 Figure9.3Thecorrelationsobtainedbyusingthecyclicprexandtheresultingsynchronizationmetricobtainedbyaveraging.154 Figure9.4Illustrationoftheproposedtransmissionscheme.Theresultingcor-relationpeaksintheidealcaseisshownaswell.155 Figure9.5Cyclicautocorrelationfunction(CAF)ofaconventionalOFDMsystem.158 Figure9.6Cyclicfrequencydensity(CFD)ofaconventionalOFDMsystem.158 Figure9.7Cyclicautocorrelationfunction(CAF)obtainedbyinsertingrandomdatawithdierentlengthsbetweenOFDMsymbols.159 Figure9.8Cyclicautocorrelationfunction(CAF)obtainedbyusingdierentcyclicprexlengthsforeachOFDMsymbol.160ix

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Thegoalofthisdissertationistoidentifyandaddresssomeofthechallengesthatarisefromtheintroductionofcognitiveradio.Specically,weproposemethodsforobtainingawarenessaboutchannel,spectrum,andwaveforminOFDM-basedcognitiveradiosystemsinthisdissertation.Pa-rameterestimationforenablingadaptation,spectrumsensing,andOFDMsystemidenticationarethethreemaintopicsdiscussed. OFDMtechniqueisinvestigatedasacandidateforcognitiveradiosystems.Cognitiveradiofeaturesandrequirementsarediscussedindetail,andOFDM'sabilitytosatisfytheserequirementsisexplained.Inaddition,weidentifythechallengesthatarisefromemployingOFDMtechnologyincognitiveradio.Algorithmsforestimatingvariouschannelrelatedparametersarepresented.Theseparametersarevitalforenablingadaptivesystemdesign,whichisakeyrequirementforcognitiveradio.Wedevelopmethodsforestimatingroot-mean-square(RMS)delayspread,Dopplerspread,andnoisevariance.Thespectrumopportunityandspectrumsensingconceptsarere-evaluatedbyx

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Eventhoughthereisnoagreementontheformaldenition,andhencecapabilities,ofcognitiveradioasofnow,theconcepthasevolvedrecentlytoincludevariousmeaningsinseveralcontexts[5].Onemainaspectofitisrelatedtoautonomouslyexploitinglocallyunusedspectrumtoprovidenewpathstospectrumaccess.Otheraspectsincludeinteroperabilityacrossseveralnetworks;roamingacrossborderswhilebeingabletostayincompliancewithlocalregulations;adaptingthesystem,transmission,andreceptionparameterswithoutuserintervention;andhavingtheabilitytounder-standandfollowactionsandchoicestakenbytheiruserstobecomemoreresponsiveovertime.Cognitiveradioscanbeusedasasecondarysystemontopofcurrentallocationofuserswhicharecalledprimary(orlicensed)users.Inthiscase,secondary(cognitive)usersneedtodetecttheunusedspectruminordertobeabletoexploitit.Moreover,theradioshouldbeabletoshapeitswaveformsoastoexploitonlytheunusedpartofthespectrum.

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Inthisintroductorychapter,abriefintroductiontoorthogonalfrequencydivisionmultiplexing(OFDM)technologyisgivenandOFDMbasedcognitiveradioisexplained.Then,anoutlineofthedissertationispresented.1.1OFDMTechnology

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Policyengineprovidesinformationtothecognitiveengineconcerningthecurrentpoliciestobeconsideredbythesystemdependingonthelocationofthesystem.Thisensuresthatcognitiveradiodoesnotuseillegalwaveformsorbreachanypolicies.Ontheotherhand,localspectrumsensingunitprocessesthespectruminformationandidentieslicensedusersaccessingtospectrumandtheirsignalspecicationssuchastheirbandwidthandpowerlevel.Italsodetectsspectrumopportunitiesthatcanbeexploitedbycognitiveradio.Oncetherequiredinformationisavailable,decisionunitcanmakeaconclusiononthebestcourseofactionforthesystem.Thedecisionincludeschoosingtheappropriatechannelcoding,modulation,operationfrequencies,andbandwidth.Atthisstage,OFDMtechnologygetstheupperhandoverothersimilartransmissiontechnologieswithitsadaptivefeaturesandgreatexibility.ByonlychangingthecongurationparametersofOFDM(seeTable2.2forsomeexampleparameters)andradio,thecognitivesystemcancommunicatewithvariousradioaccesstechnologiesintheenvironment,oritcanoptimizethetransmissiondependingontheenvironmentalcharacteristics.Theradiocircuitisdividedintodigitalpart(digitalIF,analogtodigitalconverter(ADC),anddigitaltoanalogconverter(DAC))andanalogpart(softwaretunable

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DetailedstudyofcognitiveOFDMsystems(Chapter2).2. Estimationofcriticalchannelparametersforenablingadaptation(Chapters3{5)3. Spectrumsensingfordynamicspectrumaccessincognitiveradio(Chapters6and7)4. OFDMsystemidenticationandsecureOFDMtransmissionforcognitiveradioapplications(Chapters8and9) TherstpartgivenaboveexpandsonthecurrentchapterandprovidesdetailedinformationaboutOFDMtechnologyandcognitiveradio.Thelastthreepartscontainthemaincontributionofthedissertationandincludeoriginalresearchresults.TheconceptualrelationshipamongthesepartsisillustratedinFig.1.2.Asshowninthisgure,thegoalofthisdissertationistodevelopalgorithmsthatenabletheawarenesscapabilityofcognitiveradio.Whiledoingthis,weconsideranOFDM-basedphysicallayertechnology. WestartbyinvestigatingtherequirementsofcognitiveradioandhowOFDMfulllsthesere-quirementsinChapter2.ChallengesthatarisefromemployingOFDMincognitiveradiosystemsareidentiedandcognitivepropertiesofsomeOFDM-basedwirelessstandardsarediscussedinthesamechapter. Indesigningmobilewirelesssystems,thevariationofradiochannelcharacteristicsneedstobetakenintoaccount.Traditionaldesignsbuildhead-roomsothatthemobilesubscribersattheworst-casechannelconditionscanstillmaintainthecommunication.Thiswouldtranslatetolowerdata5

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Cognitiveradiosareexpectedtorecognizedierentwirelessnetworksandhavecapabilityofcommunicatingwiththem.Multi-carriertechniques,specicallyOFDM,arecommonlyusedinmoderncommunicationssystems.SomeexamplesincludeIEEE802.11a/gbasedWLANandIEEE802.16basedWMANsystems.Foridenticationofactivetransmissions,signalscanbeclassiedassingle-carrierandmulti-carrierrst.Hence,thesizeofcandidatesetcanbereduced.Moreover,transmissionparametersofanOFDMbasedsystemcanbedetectedblindlyifthesystemisnotknowntocognitiveradiobringinginwaveformawareness.Maximum-likelihood(ML)estimationisusedtoidentifytheOFDMwaveformandestimateitscrucialparametersinChapter8.Furthermore,wedevelopestimationofsignalparametersviarotationalinvariancetechniques(ESPRIT)-basedalgorithmforidentifyingactivesubcarriersinthecaseofacognitiveradioscenario.InChapter9,weproposenewalgorithmsforachievingtransmission-levelsecurityinOFDMsystemsforpreventingdetectionofOFDMparametersblindly.Hence,inasense,Chapter8andChapter9areoppositeofeachother. Performancesofdierentalgorithmsandtechniquesdiscussedaboveareanalyzedwithclosedformexpressionsand/orsimulations.Intherestofthischapter,weprovidemoredetailsregardingthecontentoftheseupcomingindividualchaptersandourcontributionsineachchapter.1.4.1Chapter2:OFDMforCognitiveRadio:MeritsandChallenges

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ThediscreteFouriertransform(DFT)ofadiscretesequencef(n)oflengthN,F(k),isdenedas[42]F(k)=1 N;(2.1) andinversediscreteFouriertransform(IDFT)isdenedasf(n)=N1Xk=0F(k)ej2kn N:(2.2) OFDMconvertsserialdatastreamintoparallelblocksofsizeN,andusesIDFTtoobtaintime-domainsignal.Time-domainOFDMsymbolcanbecalculatedasxm(n)=IDFTfXm(k)g(2.3)=N1Xk=0Xm(k)ej2nk=NNGnN1;(2.4) whereXm(k)isthesymboltransmittedonthekthsubcarrierofmthOFDMsymbolandNisthenumberofsub-carriers.SymbolsareobtainedfromthedatabitsusinganM-arymodulation,e.g.binaryphaseshiftkeying(BPSK),quadratureamplitudemodulation(QAM),etc.TimedomainsignaliscyclicallyextendedNGsamplestoavoidinter-symbolinterference(ISI)fromprevioussymbol(seenextsection).TransmittedsignalcanbeobtainedbyconcatenatingOFDMsymbolsasx(n)=1Xm=xm(nm(N+NG))(2.5) ThesymbolsXm(k)areinterpretedasfrequencydomainsignalandsamplesx(n)areinterpretedastimedomainsignal.Applyingthecentrallimittheorem,whileassumingthatNissucientlylarge,x(n)canbeshowntohavezero-meancomplex-valuedGaussiandistribution.Powerspectrum13

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Thesub-carriersattheendsidesofthespectrumareusuallysettozeroinordertosimplifythespectrumshapingrequirementsatthetransmitter,e.g.IEEE802.11a.Thesesubcarriersareusedasfrequencyguardbandandreferredasvirtualcarriersornullsubcarriersinliterature[43].ToavoiddicultiesinD/AandA/Dconverterosets,andtoavoidDCoset,thesubcarrierfallingatDCisnotusedaswell.ThepowerspectrumforsuchasystemisshowninFig.2.2.Numberofsub-carriersthataresettozeroatthesidesofthespectrumis11.2.2.1CyclicExtensionofOFDMSymbols

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Theratiooftheguardintervaltotheusefulsymboldurationisapplicationdependent.Ifthisratioislarge,theoverheadincreasescausingadecreaseinthesystemthroughput.Acyclicprexisusedfortheguardtimeforthefollowingreasons;1. Tomaintainthereceivertimesynchronization;sincealongsilencecancausesynchronizationtobelost.2. ToconvertthelinearconvolutionofthesignalandchanneltoacircularconvolutionandtherebycausingtheDFTofthecircularlyconvolvedsignalandchanneltosimplybetheproductoftheirrespectiveDFTs.3. Itiseasytoimplementindigitalsignalprocessors(DSPs)andeld-programmablegatearrays(FPGAs).15

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Dependingonthetransmissionbandwidth(orsymbolduration)andthetypeoftheenvironmentthatthecommunicationtakesplace,multipathcancausevariousproblems.Whenrelativetimedelaysaresmallcomparedtothetransmittedsymbolperiod,dierent\images"ofthesamesymbolarriveatthesametime,addingeitherconstructivelyordestructively.Theoveralleectisarandomfadingchannelresponse.Whentherelativepathdelaysareontheorderofasymbolperiodormore,thenimagesofdierentsymbolsarriveatthesametime.Forexample,whenaparticularsymbolarrivesatthereceiveralongonepath,theprevioussymbolisarrivingalonganother,delayedpath.Thisisanalogoustoanacousticechoandresultsinamorecomplicatedchannelresponse,whichisoftenreferredastimedispersivechannel(orfrequencyselectivechannel).Forexample,inocebuildings,theaveragedelayspreadisaround50nsandmaximumdelayspreadisaround300nsin5GHzband.Therefore,ifthetransmittedsymboldurationislessthanthemaximumexcessdelay(MED)ofthechannel,thedispersioncausesISI.Traditionally,insinglecarriersystems,ISIis16

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Thechannelresponsecanchangerapidlywithtimeduetothemobilityofthetransmitter,thereceiver,orthescatteringobjects.ThisphenomenoncausesspectralbroadeningwhichisalsoreferredasDopplerspread.Dopplerspreadaectsthesignaldierentlydependingonthetransmissionbandwidth.Asthetransmissionbandwidthincreases,therelativebroadeningofthechannelwithrespecttothetransmissionbandwidthisinsignicant.Inotherwords,thetimevariationwithinthetransmissionofasymbolisnegligible.Thisbringsaboutacommontrade-obetweenhighmobilityandhighdatarate.Anexampletwo-dimensionalchannelresponseisshowninFig.2.5.17

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Channelequalizersareusuallyusedtocompensatemultipatheects.Equalizerscanconsiderablyincreasethesystemcomplexityastheircomplexityincreasesexponentiallywiththenumberofchannelpaths.InOFDMsystem,however,theneedforequalizerscanbeavoidedbycarefulsystemdesign.ToavoidISI,symboldurationisextendedbyaddingaguardbandtothebeginningofeachsymbolasexplainedbefore.Ifwedenethedelayspread(ormultipathspread)ofthechannelasthedelaybetweentherstandlastreceivedpathsoverthechannel1,theCPshouldbelongerthanthatdelay.Ontheotherhand,frequencyselectivefadingisavoidedbydecreasingthesubcarrierspacingorconsequentlyincreasingthenumberofsubcarriers.Wedenethechannelcoherencebandwidthasthebandwidthoverwhichthechannelcouldbeconsideredat.SinceOFDMsignalcanbe

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Codedandinterleaveddataisthenbemappedtotheconstellationpointstoobtaindatasymbols.ThesestepsarerepresentedbytherstblockofFig.2.6.TheserialdatasymbolsarethenconvertedtoparallelandinversefastFouriertransform(IFFT)isappliedtotheseparallelblockstoobtain19

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Inthereceiverside,thereceivedsignalispassedthroughaband-passnoiserejectionlteranddownconvertedtobaseband.Afterfrequencyandtimesynchronization,cyclicprexisremovedandthesignalistransformedtothefrequencydomainusingfastFouriertransform(FFT)opera-tion.Finally,thesymbolsaredemodulated,deinterleavedanddecodedtoobtainthetransmittedinformationbits.2.2.4OFDMImpairments ThecharacteristicsofICIaresimilartoGaussiannoise,henceitleadstodegradationofthesignal-to-noiseratio(SNR).Theamountofdegradationisproportionaltothefractionalfrequencyosetwhichisequaltoratiooffrequencyosettocarrierspacing. Frequencyosetcanbeestimatedbydierentmethodse.g.usingpilotsymbols,thestatisticalredundancyinthereceivedsignal,ortransmittedtrainingsequences.In[46],afrequencyosetestimatorwhichusestherepeatedstructureoftrainingsignalisgiven.Theaveragephasedierencebetweentherstandsecondpartofthelongtrainingsequencesiscalculatedandthennormalizedtoobtainthefrequencyoset. AssumethatwehavethesymbolsX(k)tobetransmittedusinganOFDMsystem.ThesesymbolsaretransformedtothetimedomainusingIDFTasshownearlierin(2.4).Thisbasebandsignalis20

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N:(2.7) Theeectoffrequencyosetonx(n)isaphaseshiftof2n=N,whereisthenormalizedfrequencyoset.Therefore;y(n)=x(n)ej2n N(2.8)=N1Xk=0X(k)ej2kn Nej2n N(2.9)=N1Xk=0X(k)ej2n N(k+):(2.10) Finally,weneedtoapplyDFTtoy(n)forrecoveringthesymbolsY(k)=DFT(y(n))(2.11)=1 N(m+))ej2kn N(2.12)=1 N(mk+)(2.13)=1 N(mk+)):(2.14)21

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N(mk+))(2.15)=1 Intheabovederivationweusedthefactthatsin(x)xforsmallxvalues,andN1 Wecannowrelatethereceivedsymbolstothetransmittedsymbolsusing(2.20).ButwerstdeneSF(m;k)=sin((mk+)) Thersttermin(2.22)isequaltotheoriginallytransmittedsymbolshiftedbyaconstanttermthatcorrespondsto.ThistermSF(k;k)introducesaphaseshiftofandanattenuationofsin()=inmagnitude.Actually,thistermonlydependsonthevalueofosetbutnotcarrierindexk,sotheeectoffrequencyosetoneachsub-carrieristhesame.Thesecondtermin(2.22)representstheinterferencefromothersub-carrierswhichisadualtoISIintimedomainduetotimingosetanditisknownasICI.22

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BytakingFFTof(2.23)andignoringthechannelnoiseforthemoment,frequencydomainreceivedsymbolscanbeobtainedasY(k)=1 N(2.24)=1 N(2.25)=1 N(2.26)=N1Xm=0X(m)8>>>><>>>>:L1Xl=01 {z }Hl(mk)ej2ml N9>>>>=>>>>;:(2.27) Notethatwhenhl(n)=hl,i.e.whenthechannelisconstantovertheOFDMsymbol,Hl(mk)=hlandthereisnoICI.23

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N:(2.28) Notethat(2.28)alsoincludestheeectoffrequencyselectivechannel.Therefore,Y(k)=N1Xm=0X(m)(1 N)(2.29)=N1Xm=0X(m)SC(m;k)(2.30)=X(k)SC(k;k)+N1Xm=0;m6=kX(m)SC(m;k):(2.31) Asin(2.22),thesecondtermin(2.31)representstheinterferencebetweenthesubcarriers.whilethersttermisequaltotheoriginallytransmittedsymbolmultipliedbySC(k;k)which,inthiscase,dependsonthecarrierindex.Thistermcanbere-writtenasSC(k;k)=1 N(2.32)=L1Xl=01 N:(2.33) ThetermintheparenthesesisjustanarithmeticaverageofthevaryingCIRtapswithinanOFDMsymbol.Hence,thewholeexpressionisFouriertransformoftheaverageCIRwhichgivesthefrequencydomainchannel,i.eatransmittedsymbolismultipliedwiththevalueoffrequencydomainchannelatthatsub-carrier.2.2.4.3PhaseNoise

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NN1Xr=0X(r)N1Xn=0(n)ej(2=N)(rk)n(2.35)X(k)+jX(k)1 {z }jX(k)+j NN1Xr=0;r6=kX(r)N1Xn=0(n)ej(2=N)(rk)n| {z }ICIterm:(2.36) In(2.36),thesecondtermrepresentsacommonerroraddedtoeverysubcarrierthatisproportionaltoitsvaluemultipliedbyacomplexnumberj,i.e.arotationoftheconstellation.Thisrotationisthesameforallsubcarriers,soitcanbecorrectedbyusingaphaserotationequaltotheaverageofthephasenoise,=1 Thelasttermin(2.36)representstheleakagefromneighboringsubcarrierstotheusefulsignalofeachsubcarrier,i.e.,ICI.Thistermcannotbecorrected,sincebothphaseoset(n)andinputdatasequenceX(k)arerandom.ThereforeitcausesSNRdegradationoftheoverallsystem.Theonlywaytoreduceinterferenceduetothephasenoiseistoimprovetheperformanceoftheoscillator,withassociatedcostincrease[50]. AmoredetailedstudyoftheeectsofphasenoiseonOFDMsystemcanbefoundin[50{53].2.2.4.4ReceiverTimingErrors

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Theformulaforxb(n)isalreadyderived,andisgivenin(2.7).Timingerroriscausedbysamplingthereceivedsignalatawrongtime.So~xb(n)isnothingbuttheshiftedversionofxb(n)intimedomain.Hence,inthecaseofatimingerrorofitcanbewrittenas~xb(n)=xb(n)(2.38)=N1Xk=0X(k)ej2k N(n):(2.39) Herethesignofdependsonwhethersamplingisperformedbeforeorafterthecorrecttimeinstant.Assumingtobepositive,weuseaminussignhereafter.Now~X(k)canbecalculatedusing~xb(n)byDFTas~X(k)=1 N(n))ej2kn N(2.40)=1 N(mk)ej2m N)(2.41)=1 N(mk))| {z }N(mk)ej2m N(2.42)=N1Xm=0X(m)(mk)ej2m N(2.43)=X(k)ej2k N:(2.44) Equation2.44showsthatatimingosetofcausesonlyarotationontherecovereddatasymbols.Thevalueoftherecoveredsymboldependsonlyonthetransmitteddata,butnottheneighboringcarriers.Asaresult,timingerrordoesnotdestroytheorthogonalityofcarriersandtheeectoftimingerrorisaphaserotationwhichlinearlychangeswithcarrierorder.Therefore,timingsynchronizationisnotaveryseriousprobleminOFDMbasedsystems.Unlessotherwisestated,perfecttimingsynchronizationisassumedintherestofthisthesis.26

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Discrete-timePAPRofmthOFDMsymbolxmisdenedas[56]PAPRm=max0nN1jxm(n)j2 AlthoughPAPRismoderatelyhighforOFDM,highmagnitudepeaksoccurrelativelyrarelyandmostofthetransmittedpowerisconcentratedinsignalsoflowamplitude,e.g.maximumPAPRforanOFDMsystemwith32carriersandQPSKmodulationisobservedstatisticallyonlyoncein3.7millionyearsifthedurationofanOFDMsymbolis100s[57].Therefore,statisticaldistributionofthePAPRshouldalsobetakenintoaccountinadditiontoPAPRvalueonly.27

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Onewaytoavoidnon-lineardistortionistooperatetheamplierinitslinearregion.Unfor-tunatelysuchsolutionisnotpowerecientandthusnotsuitableforbatteryoperatedwirelesscommunicationapplications.MinimizingthePAPRbeforepoweramplierallowsahigheraveragepowertobetransmittedforaxedpeakpower,improvingtheoverallsignaltonoiseratioatthereceiver.ItisthereforeimportanttominimizethePAPR.Intherestofthisthesis,thedistortionofthesignalduetonon-lineareectsisignored.Intheliterature,dierentapproachesareusedtoreducePAPRofOFDMsignals(see[58]andreferencestherein).Someoftheseincludeclipping[59],scrambling[60],coding[61],phaseoptimization[56],tonereservation[62]andtoneinjection.2.2.5Multiple-AccessingWithOFDM

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OFDM'sStrength EcientSpectrumUtilizationWaveformcaneasilybeshapedbysimplyturningosomesubcarrierswhereprimaryusersexist. Adaptation/ScalabilityOFDMsystemscanbeadaptedtodierenttransmissionenvironmentsandavailableresources.Someparametersinclude:FFTsize,subcar-rierspacing,CPsize,modulation,coding,andsubcarrierpowers. AdvancedAntennaTechniquesMIMOtechniquesarecommonlyusedwithOFDMmainlybecauseofthereducedequalizercomplexity.OFDMalsosupportssmartanten-nas. InteroperabilityWithWLAN(IEEE802.11),WMAN(IEEE802.16).WRAN(IEEE802.22),WPAN(IEEE802.15.3a)allusingOFDMastheirphysicallayertechniques,interoperabilitybecomeseasiercomparedtoothertechnologies. MultipleaccessingandspectralallocationSupportformultiuseraccessisalreadyinheritedinthesystemdesignbyassigninggroupsofsubcarrierstodierentusers(OFDMA). NBIImmunityNBIaectonlysomesubcarriersinOFDMsystems.Thesesubcarrierscanbesimplyturnedo. transmitinanopenareaofspectrum,adaptthewaveformtocompensateforchannelfading,andnullaninterferingsignal[64]. TheadaptivityinOFDMsystemscanbedividedintotwogroups[65]:algorithm-selectionleveladaptivityandalgorithm-parameterleveladaptivity.Inclassicalwirelesssystems,usuallyparame-tersofthealgorithms,e.g.codingrate,havebeenadaptedinordertooptimizethetransmission.However,incognitiveOFDMsystems,algorithmtype,e.g.channelcodingmethod,canalsobeadaptedinordertoachieveinteroperabilitywithothersystemsand/ortofurtheroptimizethetransmission.Toachievesuchadaptivity,afullycongurablehardwareplatformwouldbeneeded. OFDMoersagreatexibilityinthisregardasthenumberofparametersforadaptationisquitelarge[17].Thetransmissionparametersthatcanbechangedbasedonthespectrumawarenessincludebandwidth,FFTsize,lters,windows,modulation,transmitpower,andactivesubcarriersusedfortransmission.Moreover,theparametersthatcanbeadapteddependingonthecharac-teristicsoftheenvironmentinordertooptimizethetransmissionincludecyclicprexsize,codingrate/type,modulationtype,interleavingmethod,pilotpatterns,preambles/midambles,duplexing29

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Adaptivemodulationandcodingprovideaframeworktoadjustmodulationlevelandforwarderrorcorrection(FEC)codingratedependingonthelinkquality.Higherordermodulationsallowmorebitstobetransmittedforagivensymbolrate.Ontheotherhand,theyarelesspowerecient,requiringhigherenergyperbitforagivenBER.Therefore,higherordermodulationsshouldbeusedonlywhenthelinkqualityishigh,astheyarelessrobusttochannelimpairments.Similarly,strongFECandinterleavingproviderobustnessagainstchannelimpairmentsattheexpenseoflowerdatarateandspectraleciency.Asaresult,byproperlyadaptingthecodingandmodulationdependingonthelinkquality,theaveragethroughputcanbemaximized,whichmakesitveryattractiveforwirelesspacketdatacommunication.Notethatformobileusers,theinstantaneousdataratesvarydependingonthelinkquality. Withoutpowercontrol,adaptivecodingandmodulationincreasethevariationofthroughputamonguserssuchthatuserswithgoodlinkqualityalwayshavehighthroughput,butuserswithbadlinkqualityalwayshavelowthroughput[66].Ontheotherhand,powercontroltriestoequalizethelinkqualityoftheuserssothatallthereceivershaveaconstantsignal-to-interferenceratio(SIR).Thisallowsreducingtheinterferencefromothersourceswhilemakingsurethateachusergetsjust30

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InOFDMsystems,itisalsopossibletoadaptthemodulationandpowerforeachsubcarrierindividually.NotethatsincethebandwidthsofOFDMsystemsaremuchlargerthanthecoherencebandwidthofthechannel,dierentcarriersexperiencedierentsignal-to-interference-plus-noiseratio(SINR).Therefore,themodulationlevelorthepowerondierentcarrierscanbechangeddependingonthelinkqualityobservedatthatcarrier[68]. Transmittingdierentmodulationoneachcarrierrequiresalargeoverheadforsignaling.There-fore,approachesthatgrouptheneighboringcarriersintosubsetsandusethesamemodulationineachgroupofcarriersarepreferred.ThisiscalledsubbandadaptiveOFDMandillustratedinFig.2.7.Thesignalingcanalsobeavoidedintimedivisionduplexing(TDD)systemsundercer-tainassumptions.Unlikefrequencydivisionduplexing(FDD)systems,wherethechannelonthedownlinkanduplinkaredierent,inTDDsystems,usingtheassumptionofthereciprocalandslowvaryingchannel,thetransmitterandreceivercanbeassumedtoexperiencethesamechannelresponse.Therefore,thismighteliminatetheneedforsignalingofthechannelstateinformationtothetransmitterifthechannelestimatesareusedasthelinkqualitymeasures.However,thereceiverstillneedstoknowwhichmodulationisusedatthetransmitterforeachgroup.Blindmodulationdetectiontechniquescanbeusedforthispurpose[69,70]asthereisenoughaprioriinformationtoestimatethemodulationtype.Notethatalthoughthechannelscouldbethesame,theinterferencesobservedintransmitterandreceiverarenotnecessarilythesamebecausetheinterferermaybephysicallyclosertotransmitterorreceiver. Eventhoughadaptivepowercontrolhasalongandrichhistoryforwirelesscommunicationsys-tems,theadaptivecodingandmodulationrecentlybecomepopularduetotheincreasedinterestforhighdataratecommunications,andtheyarebecominganintegralpartofmostofthenewgen-31

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CombiningadaptiveantennaswithOFDMforoperationinafadeddelay-spreadchannelisdiscussedin[72].Inthisadaptivebeamformingalgorithm,ashorttrainingprocessrstupdatestheweightvectorandthenadecision-directedtechniqueisusedforupdatingtheweightvector.Ithasbeendemonstratedthatthisalgorithmisabletoextractdesiredsignalswhilesuppressingco-channelinterferers. MIMOandmulti-antennasystemsbringaboutanewdimensiontowirelesschannel.Itcanprovidehugecapacityand/orimprovedperformancegainsbyexploitingspatialselectivityofthechannel.However,thesegains,inreality,dependheavilyonthestatisticalpropertiesofthechannelandthecorrelationsbetweenantennaelements.Oneofthefactorsthataectstheantennacorrela-tionisthecharacteristicsofthescatteringenvironment.Therefore,optimalwayofusingmultipleantennasystemsdependsonthesituationawareness.Ifthetransmitterknowstheinstantaneouschannelgains(theMIMOchannelmatrix),itcanadaptthetransmissiontomaximizethecapacityofMIMOsystem[73,74].Similarly,theinstantaneousantennacorrelationvaluescanbeexploitedtoadaptthetransmission.Inmanycases,estimationoftheperfectinstantaneouschannelstateandantennacorrelationinformation,andfeedingthisinformationbacktothetransmittermightnotbepossible.Thisisthecaseespeciallywhenthemobilityishigh.Instead,otherparametermeasureslikepartial(statistical)channelinformation,averagechannelselectivityorangularspreadwouldbeusefulforadaptingthetransmitterandreceiver.Advancedsignalprocessingtechniquestocalculatethesepartialchannelandcorrelationinformationareneeded. InMIMO-OFDM,theSNRnotonlyvariesovertimeandfrequencybutalsodependsonanumberofparametersincludingthewaythetransmittedsignalsaremappedandweighedontothetransmitantennas,theprocessingtechniqueusedatthereceiver,andtheantennapolarizationandpropagationparameterssuchasmutualcouplingbetweenantennas[75].Space-timeadaptationaimstochoosethebestwayofcombiningantennaseitherthroughspace-timecodingapproach,beamformingorusingtheBLASTarchitecture.ThoseapproachescanbecoupledwithadaptationofOFDMparameters,e.g.,oneachOFDMsubcarrier,adaptivespace-timecoding,beamformingalongwithadaptivepowerandbitloadingschemescanbeemployedyieldingaspace-timefrequencyadaptationscenario.TheprocesscanbegeneralizedformultiuserMIMO-OFDMsystems.33

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TheCPlengthcanbechangedadaptivelydependingonthechannelconditions,specicallymax-imumexcessdelayofthechannel.AdaptiveCPisstudiedin[48,77].IntheproposedalgorithmstheCPlengthisvariedaccordingtothecurrentdelayspreadofthechannelandthelengthinformationisconveyedtothereceiverbysignaling.Thisadaptationrequirestheknowledgeofthemaximumexcessdelayofthechannel,estimationofwhichisstudiedinChapter3.AdaptiveInterleaving:

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WhileincreasingsubcarrierspacingcurestheICIproblem,itmeansshortersymbolduration.Therefore,therelativesizeofrequiredCPbecomeslarger,decreasingbandwidtheciency.Theeectofnumberofsubcarriersonthesystemperformanceisinvestigatedin[80].Theoptimumnumberofsubcarriersisfoundtobeincreasingwithdelayspreadandthecoherencetime.Thecalculationofoptimumsubcarrierspacingfordierentchannelconditionsisstudiedin[48]bysimulationandanalyticallyin[81]. UsingvariableFFTsizesisproposedforIEEE802.16estandardtoimplementscalableOFDMA(see[82]andreferencestherein)inwhichaconstantsubcarrierspacingisobtainedbychangingtheFFTsizeandsystembandwidth.Dopplerspreadknowledgecanbeusedforselectingtheoptimumsubcarrierspacingadaptively.EstimationofDopplerspreadisdiscussedinChapter4.35

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Someotherimportantelementsforpilotarrangementscanbetheallocationofpowertothepilotswithrespecttothedatasymbols,thetransmittedmodulationforthepilottonesetc.Inmostcases,thepowerforpilottonesanddatasymbolsareequallydistributed,however,itdoesnothavetobeuniform.Forexample,thechannelestimationaccuracycanbeimprovedbytransmittingmorepoweratthepilottonescomparedtothedatasymbols.Yet,thisreducestheSNRoverthedatatransmissionforagiventotalpower. Itisclearfromtheabovediscussionaboutthepilotallocationthatabettersystemperformancecanbeobtainedwhenthesystemisadaptive[84{87].Inthiscase,theinformationaboutthechannelstatisticsbecomesverycritical.Thepilotallocationinthefrequencydirectionrequiresthedelayspreadestimation,whereastheoneintimedirectionrequiresDopplerspreadestimation.Iftheseestimatesareavailable,thenapilotschemeusingrelativelylesspilotsbutstillprovidinganacceptableperformancecanbeutilized.Ifthisinformationisnotavailable,thenthepilotschemecanbedesignedbasedontheworstchannelcondition,i.e.themaximumexpecteddelayspreadandmobilespeed.In[88],thepilotpatternsarechosenadaptivelybasedonthepredictionofthechannelestimationerroratthereceiver.ThetransmittertriestoguaranteetheminimumrequiredSNRbyusingtheminimumnumberofpilotsubcarriers.AdaptationisperformedoverablockofOFDMsymbols.2.3.1.2AdaptationinMobileOFDMSystems

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TheoutputofIFFTatthereceivercanbeobtainedas(2.31).Thesecondtermintherighthandsizeof(2.31)isthepowerleakagefromtheneighboringsubcarriersanditiscalledICI.Whenthereisnotimevariationinchannelduringablockperiod,e.g.hl(n)=hl,theresultingICIiszero. Foraxedtotalbandwidth,theICIcontributionincreasesasthenumberofsubcarriersincreases.ThishappenssincetheOFDMsymbolperiodincreasesandhencethevariationofchannelwithinthesymbolduration.AnalysisoftheeectsofDopplerspreadforOFDMsystemsisgivenin[47,90,91].TightandgeneralboundsforICIduetoDopplerspreadarefoundin[92].TheICIpowerisreportedtobelinearlyproportionalwiththesquareofmaximumDopplerfrequencyandsymbolduration(fDTS).Inotherwords,theratiobetweenthemaximumDopplerfrequencyandsubcarrierspacingdeterminestheeectofICI. WhileincreasingthesubcarrierspacingmaydecreasetheICI,itincreasestheenergylossduetothecyclicprexextensionofOFDMsystems.Hencetheoptimumwindowsizeisafunctionoffrequencyandtimeselectivityofthechannel.Thistrade-oisshowninFig.2.9.TheBERperformanceofanOFDMsystemwith3.5MHzbandwidthoperatingat5.8GHzcenterfrequencyisshownfordierentFFTsizesandCPlengths.TheSNRofthesystemis30dBandmobilespeedis100km/h.AsopposedtotheFig.2.8,theaectofenergylossduetoCPistakenintoconsiderationinthisgure.However,thelengthoftheCPischosenlargerthanthedelayspreadofthechannelinordertoonlyshowtheaectofCPandFFTsizes.Asthisgureshowsthesubcarrierspacing(orFFTsize)thatgivesoptimumperformanceisafunctionofthedelayspreadandDopplerspreadsofthechannel. Transmitteradaptationcanbeusedtoovercomethemobilityproblem.ThesubcarrierspacingcanbechangeddependingontheDoppleranddelayspreadofthechannelinordertoreduceICIwhilekeepingthebandwidthusagemaximum.Calculationoftheoptimumsubcarrierspacingindoublydispersivechannelsisinvestigatedin[48,81].TheICIproblemcanalsobesolvedusingadvancedreceiveralgorithmssuchasfrequencydomainequalizationorinterferencecancellation.However,thesealgorithmsarecomputationallycomplexandtheycanonlyeliminatesomeofthedisturbanceduetoICI. AnotherfactorthatneedstobeconsideredinmobileOFDMsystemsistheestimationoffastvaryingchannel.Whenthetrainingsymbolstransmittedbeforethedatasymbolsareusedfor37

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However,sinceforarentalsystemitisimportantnottointerferewithotherlicensedsystemsusingthespectrum,othermeasuresshouldbetakentoguaranteeaninterference-freecommunicationbetweenrentalusers.Oneapproachistosharethespectrumsensinginformationbetweenmultiplecognitiveradiodevicestodecreaseoreveneliminatetheprobabilityofinterferencewithlicensed38

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Whiletheeciencyofthespectrumsensingandanalyzingprocessisimportantforasuccessfulimplementationofcognitiveradio,theprocessingtimecanbeevenmoreimportant.Theperiodicityofspectrumsensingshouldbeshortenoughtoallowfordetectionofnewspectrumopportunitiesand,atthesametime,todetectlicensedusersaccessingthepreviously-identied-as-unusedpartsofthespectrum.Ontheotherhand,ifspectrumsensingisdonesofrequently,theoverheadofsharingsuchinformationincreasesreducingthespectrumeciencyofthewholesystemnottomentiontheincreaseinsystemcomplexity.InOFDMsystems,conversionfromtimedomaintofrequencydomainisachievedinherentlybyusingDFT.Hence,allthepointsinthetime-frequencygridcanbescannedwithoutanyextrahardwareandcomputationbecauseofthehardwarereuseofFFTcores.Usingthetime-frequencygrid,theselectionofbinsthatareavailableforexploitation(spectrumholes)canbecarriedoutusingsimplehypothesistesting[96].TheDFToutputscanbelteredacrosstimeandfrequencydimensionstoreducetheuncertaintyindetectionaswell[26,27].Notethattheresolutionofthefrequencygridisdependentonsubcarrierspacing.2.3.3SpectrumShaping Cognitiveusersshouldbeabletoexiblyshapethetransmittedsignalspectrum.Itisdesiredtohavecontroloverwaveformparameterssuchasthesignalbandwidth,powerlevel,centerfrequency,andmostofallaexiblespectrummask.OFDMsystemscanprovidesuchexibilityduetotheuniquenatureofOFDMsignaling.Bydisablingasetofsubcarriers,thespectrumofOFDMsignalscanbeadaptivelyshapedtotintotherequiredspectrummask.Assumingthespectrummaskisalreadyknowntothecognitiveradiosystem,choosingthedisabledsubcarriersisarelativelysimpleprocess[97]. ThemainparametersofanOFDMsystemthatcanbeusedtoshapethesignalspectrumarenumberofsubcarriers,subcarrier'spower,andpulse-shapinglters.Increasingthenumberofsub-carriersforaxedbandwidthallowstheOFDMsystemtohaveahigherresolutioninthefrequency39

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Subcarrierpowercanbeusedtoshapethesignalintothedesiredmask.Onereasontoassignsubcarriersdierentpowersistobettertintothechannelresponse[98].Forexample,subcarrierswithhigherSNRvaluescanbeassignedlowerpowerthanthosewithlowerSNRtoimprovetheoverallsystemBER.AnotherreasonistoreducetheadjacentchannelinterferencefromanOFDMsystembyreducingthepowerassignedtoedgesubcarriers. AnexampleofspectrumsensingandshapingproceduresinOFDM-basedcognitiveradiosystemsisillustratedinFig.2.10.TwolicensedusersaredetectedusingtheoutputofFFTblock,andsubcarriersthatcancauseinterferencetolicenseduserareturnedo.Thetransmitterthenusesthefreepartsofthespectrumforsignaltransmission.Inaddition,pulse-shapinglterscanalsobeusedtoreducetheinterferencetoadjacentbands.Morediscussionsonreducinginterferenceisintroducedinsection2.4.5.2.3.4AdvancedAntennaTechniques

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MIMOsystemscommonlyemployOFDMastheirtransmissiontechniquebecauseofsimplediversitycombinationandequalization,particularlyathighdatarates[101].InMIMO-OFDM,thechannelresponsebecomesamatrix.Sinceeachtonecanbeequalizedindependently,thecomplexityofspace-timeequalizersisavoidedandsignalscanbeprocessedusingrelativelystraightforwardmatrixalgebra.Moreover,theadvantagesofOFDMinmultipatharepreservedinMIMO-OFDMsystemasfrequencyselectivitycausedbymultipathincreasesthecapacity.2.3.5MultipleAccessingandSpectralAllocation OFDMA,aspecialcaseofFDMA,hasgainedtremendousattentionrecentlywithitsusageinmobileWorldwideInteroperabilityforMicrowaveAccess(WiMAX)[82,103].InOFDMA,subcar-riersaregroupedintosetseachofwhichisassignedtoadierentuser.Interleaved,randomized,orclusteredassignmentschemescanbeusedforthispurpose.Hence,itoersveryexiblemultipleaccessingandspectralallocationcapabilityforcognitiveradioswithoutanyextracomplexityorhardware.Theallocationofsubcarrierscanbetailoredaccordingtothespectrumavailability.TheexibilityandsupportofOFDMsystemsforvariousmultipleaccessingenablestheinteroperabilityandincreasestheadoptionofcognitiveradioaswell.41

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FFTSize64128,256,512,1024,20481024,2048,40962048,8192 whenOFDMtechniqueisemployedbycognitiveradiosystems.Inthefollowing,somechallengesandapproachesforsolvingthesearegiven.2.4.1SpectrumShaping

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Figure2.14RolloeectonthePSDofasingleOFDMsubcarrier.waytheinterferencecanbegreatlyreducedasmostoftheinterferencecomesfromtheneighboringsubcarriers.However,theobviousdisadvantageofthismethodisthereductionofspectraleciency.Insteadofdeactivatingtheneighboringsubcarriers,theirvaluescanbedeterminedactivelyinordertocanceltheinterferenceinthedeactivatedbands.Thistechniqueisproposedin[116]and[117]andreferredasactiveinterferencecancellationandcancellationcarriersrespectively.Itisshownthattheperformancecanbeimproved,however,determinationofthevaluesforcancellationsubcarriersis46

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Inadditiontotheaforementionedchallenges,thereareotherissuesforpracticalimplementationofOFDMcognitiveradiosystems.Whilecognitiveradioissuchapromisingtechnology,moreresearchisneededtobuildpracticalsystemwithaordablecomplexity.2.5AStepTowardCognitive-OFDM:StandardsandTechnologies

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InWiMAX-basedsystems,userscanbeassigneddierentbandwidths,timedurations,transmitpowerlevels,andmodulationorders(seeTable2.2)basedonvariousparameterssuchasusercarrier-to-interference-plus-noiseratio(CINR),receivedsignalstrengthindicator(RSSI)ortheavailablebandwidth.Moreover,OFDMAPHYoersmultipleFFTsizes,CPsizes,andpilotallocationschemes.TheFFTsizecanbeselectedas128,256,512,1024or2048dependingonthetransmissionbandwidth4.Similarly,theCPlengthcanbesetto1/4,1/8,1/16and1/32timetheOFDMsymbollength.TheCPsizecanbechangeddependingonthevariousenvironmentalcharacteristics.Withalltheseadaptivefeatures,WiMAXhastheabilitytoadapttovariouschannelconditionsandcommunicationscenarios.Indeed,aWiMAXBSmeasurestheavailablechannelandreceivedsignalparameters,makesaplanonwhatthemostappropriatesettingsforcommunicationwithcurrentsubscribers(withcertaingoalsinmindsuchasmaximumthroughput,qualityofservice(QoS).)is,andexecutesthisplan. WiMAXstandardisveryrichintermsofadvancedantennatechniquesaswell.Table2.3showstheMIMOfeaturesavailableinthemobile-WiMAXstandardIEEE802.16E-2005[103].Althoughtheseantennatechniquesarenotrequirements,theyarewellsuitedtocognitiveradioandusefulforachievinghighdatarates. TheamendmenttoIEEE802.16standardIEEE802.16h,whichiscurrentlybeingdeveloped,introducescognitivefeaturestoWiMAX.ThegoalistoachievecoexistenceofWiMAXdevicesinunlicensedbands.Furthermore,methodsforcoexistencewithprimaryusersarealsodeveloped.

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TheBSusesmultipleantennastoformthebeamsinthedirectionofasubcarrier. Extendedrangeandincreasedcapacitythankstolowerinterference. Space-timecoding(STC) TransmitdiversitysuchasAlamouticodeisused. Increaseinsystemgainthroughspatialdiversityandreducedfademargin. Spatialmultiplexing(SM) Independentandseparatelyencodeddatasig-nalsaretransmittedovermultipleantennas. Increaseincapacity(higherdatarates). CollaborativeSM TwoULuserscantransmitcollaborativelyinthesameslotasiftwostreamsarespatiallymul-tiplexedfromtwoantennasofthesameuser. Increasedcoverageandthroughput. Antennaselection Anycombinationofantennasareselected(on-otypeofselectionofgroupofantennasfromtheavailableantennas)basedonthechannelfeed-back. Ecientuseofavail-ablepower. Antennagrouping TheBScangroupmultipleantennasfordierentcarriersindierentwaybasedonthefeedbackfromBSs.Forexample,ifwehave3Txanten-nas,theBScangroupthersttwoantennasinsomecarriers,andthelast2antennasinsomeothercarriers. Maximumdiversity/capacitygain. MIMOprecoding Theantennaelementsareweightedwithama-trixbeforemappingthemtotransmitantennasbasedonthefeedbackfromSSs.Thisschemeissimilartoawater-pouringalgorithm. Increasedcapacitygain. STCsub-packetcombining Intheinitialtransmission,thepacketsaretrans-mittedinafullMIMOspatialmultiplexingmode(nodiversity).Ifthedatacannotbede-codedcorrectly(CRCdidnotcheck),thenthepacketsaresentinfullSTCmode(fulltransmitdiversitymode).Thereceivercombinestheini-tialdataandthelaterdataforbetterdetection. Providesincrementalredundancy. Frequencyhoppingdiversitycoding(FHDC) Thisscheme(asforSTC)transmitstwocomplexsymbolsusingthemultipleinputsingleoutputchannel. AdaptiveMIMOSwitch(AMC) STCorSMisselectedadaptivelytoadoptchan-nelconditions. Optimumspectralef-ciencyisachieved. thoughthisstandardisnotnalizedyet,itisanticipatedthatitwillbebasedonOFDMtransmissionaswell.50

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The802.22standardisdesignedforaxedpoint-to-multipointcommunicationtopologywheretheBSactsasthemastermandatingalltheoperationparametersofuserswithitscell.Andwhiletheusers(slaves)cansharesensinginformationwiththeBSthroughdistributedsensing,itisuptotheBStochangeauser'stransmitpower,modulation,codingoroperatingfrequency.Insuchtopology,itistheresponsibilityoftheserviceprovidertoensurethatuserssignaliscausingnointerferencetotheincumbentsignalsbywithinthecoveragearea.ThisisacrucialissueforthecoexistenceofthestandardwiththealreadyexistingTVservices. Anotherchallengeindesigningthe802.22standardistheinitializationofnewuserswhodesiretocommunicatewiththeBS.Unlikecurrentwirelesstechnologies,thefrequencyandtimedurationoftheinitializationchannelisnotpredened.Inotherwords,initialuserswillhavetoscanparts(ifnotall)oftheTVbandstondthecurrentBSoperatingfrequencyandtime.Inaddition,usersshouldbeabletodierentiatebetweenincumbentsignalsandtheBSsignal.ThiscouldprovetobeverychallengingespeciallyiftheBSisoperatingoveracombinationofmultiplefrequencybands. Adiscussionoftheaforementionedchallengesandmoreissuesrelatedtothedesignofthe802.22standardcanbefoundin[121].2.5.3IEEE802.11 TheDFSdetectsdevicesusingthesameradiochannelandthesystemswitchestootherradiochannelsifnecessaryavoidinginterferencewithotherexistingprimaryusers.WLANstationreports51

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Ontheotherhand,IEEE802.11kstandardisproposedforradioresourcemanagement.TheaimistoimprovethetracdistributioninaWLAN.Thestandarddenesalistofseveralradioparameterstobeestimatedbythesystem.WhilethislistislimitedandaimedforIEEE802.11standards,itisfurtherenhancedcomparedtoearlierstandards.WLANdevicescanbeupgradedtosupportthenewstandard,sinceitisdesignedtobeimplementedinsoftware.Thestandardallowsaccesspointstocollectdatafromclientsregardingaccesspointstheycanhearandtheirsignalpower.Afterthecollecteddataisanalyzed,accesspointswithinrangeofaclientareorderedintoalistaccordingtotheirsignalstrength,services,andencryptiontypessupportedbytheclient.Thislistiscalledsitereport.Theaccesspointsprovidetheclientswiththesitereportandthusimprovetheroamingdecisionsandincreasetheoverallnetworkthroughput. TheaccesspointcouldgatherinformationfromclientsabouttheRFchannel.Forexample,theaccesspointcouldrequesttheclienttomeasurethechannelnoiselevel,ortoprovidetheaccesspointwithinformationregardingthetracloadonthechannelandthetimedurationoverwhichthechannelisoccupied.Usingthisinformation,theaccesspointcanmakeadecisionwhetheracertainchannelisbeingcrowdedorifthechannelcontainshighlevelofnoise/interference. Otherfeaturesincludingtrackingofhiddennodesandsharingclients'statisticsareincludedinthestandard.Byapplyingboth802.11hand802.11kstandardstocurrent802.11-basedWLANsystems,theperformanceandeciencyofwirelessnetworkingcanbeimprovedsignicantly.Addingcognitivefeaturessuchaschannelsensingandestimation,statisticsdistribution,DFS,TPCtoWLANdeviceswillsoonbepossible.Itisimportanttorememberthat802.11standardsmainlyuseOFDMmakingitthesignalingofchoiceforfuturetechnologies.Fig.2.16showsanillustrationofthediscussedcurrentandfuturetechnologiesandstandards.2.6Conclusion

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InOFDMsystems,thecyclicprex(CP)lengthneedstobelargerthanthemaximumexcessdelayofthechannel.Ifthisinformationisnotavailable,theworstcasechannelconditionisusedforsystemdesignwhichmakesCPasignicantportionofthetransmitteddata.OnewaytoincreasethespectraleciencyistoadaptthelengthoftheCPtothechangingmultipathconditionswhichrequiresthechannelexcessdelayknowledge[48,77].Adaptivelteringforchannelestimationisanotherareawheretimedispersioninformationofthechannelisuseful.Atwo-dimensionalWienerlter,implementedasacascadeoftwoone-dimensionallters,isusedforchannelestimationin[125].Thebandwidthofthesecondlter,whichisinthefrequencydirection,ischangeddependingontheestimateddelayspreadofthechanneltokeepthenoiselowandthustoimprovethechannelestimationperformance.Similarly,thecoecientsofthefrequencydomainchannelestimationlter54

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Characterizationofthefrequencyselectivityoftheradiochannelisstudiedin[127,128]usinglevelcrossingrate(LCR)ofthechannelinfrequencydomain.FrequencydomainLCRgivestheaveragenumberofcrossingsperHzatwhichthemeasuredamplitudeintersectsathresholdlevel.However,LCRisverysensitivetonoisewhichincreasesthenumberoflevelcrossingsandseverelydeterioratestheperformanceoftheLCRmeasurements[129].Filteringthechannelfrequencyresponse(CFR)reducesthenoiseeect,butndingtheappropriatelterparameterscouldbeaproblem.Ifthelterisnotdesignedproperly,onemightendupsmoothingtheactualvariationofthefrequencydomainchannelresponse.Timedispersionofthechannelcanbeestimatedusingthechannelimpulseresponse(CIR)estimatesaswell.In[84,125],theCIRisobtainedbytakingtheinversediscreteFouriertransform(IDFT)ofthefrequencydomainchannelestimatewhichiscalculatedatpilotlocations.In[130],instantaneousroot-mean-squared(RMS)delayspreadisobtainedbyestimatingtheCIRintimedomain.Thedetectedsymbolsinthefrequencydomainareusedtore-generatethetimedomainsignalthroughIDFTandthenthissignaliscorrelatedwiththereceivedsignalinordertoobtaintheCIR.Sincethedetectedsymbolsarerandom,theymightnothavegoodautocorrelationproperties,whichcanbeaproblemespeciallywhenthenumberofcarriersissmallandSNRislow.Timingsynchronizationerrorscreateaproblemwiththetimedomainestimation;ifsynchronizationisperformedindependentlyoverdierentframes(orsymbols),theestimatedCIRsshouldbetimealignedasthetimingerrorswillbedierentforeachCIRestimate.TechniquesexploitingtheCPareproposedfordelayspreadestimationin[131,132].ThechangeofgradientofthecorrelationbetweentheCPandthelastpartoftheOFDMsymbolisusedasastrategytodetectthedispersionparametersin[131].Usingthechangeofgradientinthecorrelation,theamplitudeanddelayofeachtapiscalculatedandthedelayspreadinformationisextractedfromthisinformation.Thismethodrequirescomputationallycomplexoptimizationandtheaccuracyofthetechniquecanbeexpectedtodegradeforcloselyspacedandweakmultipathcomponents.55

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Inthischapter,timedispersionoftheradiochannelisestimatedusingfrequencydomainchannelestimates.InOFDMsystems,channelcanbeestimatedinfrequencydomaineasily,andthisisusuallythepreferredmethodasbothestimationandequalizationinfrequencydomainaresimplerthantheirtimedomainequivalents.Sincethetimingerrorsarefoldedintothechannelestimatesinfrequencydomainasasubcarrier-dependentphaseterm,themagnitudesofthechannelestimatesareusedfordelayspreadestimationinordertoremovethephasedependence.Asathirdalgorithm,themagnitudeofthereceivedfrequencydomainsignalisusedwhenaconstantenvelopemodulationisemployed.TheproposedalgorithmsestimatethechannelPDPwhichisthenusedtoextractthetimedispersionparameters:RMSdelayspreadandmaximumexcessdelayofthechannel. Thischapterisorganizedasfollowing.InSection3.2,systemmodelwillbeintroduced,andtheproposedalgorithmswillbepresentedinSection3.3.NumericalresultswillbegiveninSection3.4andthechapterwillbeconcludedinSection3.5.3.2SystemModel Atthereceiver,thesignalisreceivedalongwithnoise.Aftertimeandfrequencysynchronization,down-sampling,andremovalofCP,thesimpliedbasebandmodelofthereceivedsamplescanbe56

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whereListhenumberofsample-spacedchanneltaps,andthetimedomainCIRformthOFDMsymbol,hl;m,isgivenasatime-invariantlinearlter.ThetimingerrormiscausedbytheimperfectsynchronizationanditsstatisticsdependsontheSNRandthesynchronizationalgorithmused.Inthiscase,aftertakingdiscreteFouriertransform(DFT)ofthereceivedsignalym(n+m),thesamplesinfrequencydomaincanbewrittenas1[133]Ym(k)=DFTfym(n+m)g=Xm(k)Hm(k)ej2km=N+Wm(k)0kN1;(3.2) whereHandWareDFTsofhandwrespectively.Theleastsquares(LS)estimateoftheCFR^Hmcanbecalculatedusingthereceivedsignalandtheknowledgeoftransmittedsymbolsas^Hm(k)=Ym(k) {z }~Hm(k)+Wm(k) {z }Zm(k):(3.4) TheLSchannelestimationconsistsofthedesiredchannelwithafrequencydependentphasetermduetotimingerrorsandanadditiveestimationerrortermduetonoise.3.3ProposedDelaySpreadEstimationAlgorithms

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whereEt;k[]istheexpectationovertrainingsymbolstandoversubcarriersk(averagingwithinanOFDMsymbol).Assumingthatthechannelandnoisetermsareuncorrelated,thecorrelationgivenin(3.5)canbewrittenasR^H()=R~H()+RZ();(3.6) whereR~H()isthecorrelationoftheeectivechannelandRZ()isthecorrelationofchannelestimationerror.RZ()becomesadeltafunctionwhentheestimationerrorsatdierentsubcarriersareuncorrelated,i.e.whenitiswhite.However,aschannelestimationisalteringoperation,thisnoiseisusuallycoloredanditcreatesabiasontheestimatesobtainedusingR^H,hencecareshouldbetaken.WhenthechannelestimatesareobtainedusingtheLSmethodgiveninSection3.2,however,thenoisebecomeswhiteastheadditivenoiseonthereceivedsignalW(k)isassumedtobewhiteanduncorrelatedwiththetransmittedsignalaswellasthechannel.Inthiscasethecorrelation(3.5)canbewrittenasR^H()=R~H()+()2z;(3.7) where2zisthevarianceofchannelestimationerrorZ(k),and()istheKroneckerdeltafunction. Using(3.4)and(3.5),thechannelcorrelationwithtimingerrorscanbeobtainedasR~H()=RH()Ethej2t=Ni:(3.8) Theexpectationin(3.8)isafunctionofthestatisticsoftheestimationerrortwhichdependsonchannelconditionsandthealgorithmusedforsynchronization.Thisexpectationcanbewrittenin58

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whereminandmaxaretheminimumandmaximumsynchronizationvaluesrespectively.P()istheprobabilityofhavingthesynchronizationerrorandinthecaseofperfectsynchronizationitbecomesadeltafunction,i.e.P()=().Inthischapter,thetimingerrorsareassumedtohaveaGaussiandistributionwithzeromeanandthevarianceof2[134]. Ascanbeseenfrom(3.7)and(3.8),therearetwoimpairmentsthataectthecorrelationestimates.Werstassumeperfecttimingsynchronizationandconcentrateonthenoiseterm.Inasimilarproblemforadierentcontext,aparabolaisttedtothelagswithnon-zeroindexforndingthevalueatthezero-thlagoftimedomainchannelcorrelationin[135].Inthischapter,weusethesamealgorithmforremovingthecorrelationtermduetonoisein(3.7).Thisalgorithmconsistsofthefollowingsteps: Oncetheeectofnoiseisremoved,thePDPcanbeestimatedfromtheCFCestimateR0~HbysimplyapplyingIDFToperationasPl=IDFTR0~H()(3.10)=1 wherePl=Emjhl;mj2isthelthtapofthechannelPDP.AsthePDPcoecientsarereal,theCFCexhibitsaconjugatesymmetrythatcanbeusedtodecreasethenumberofcorrelationlagstobecalculatedbyhalf. Timingerroristheotherimpairmentthatdegradestheperformanceofthechannelestimationbasedalgorithm.Fig.3.1showsthecorrelationmagnitudeasafunctionofsubcarrierseparationforperfectsynchronizationandforsynchronizationerrorswithazero-meanGaussiandistributionandvarianceof2t2s,i.e.2=2,wheretsisthesamplingfrequency.Bothanalyticalresultsobtained59

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Byinserting(3.4)into(3.12),thecorrelationcanbesimpliedtoRj^Hj2()=RjHj2()+(1+())2RH(0)2z+4z;(3.13)60

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Theeectofnoiseon(3.13)attherstcorrelationlag,i.e.=0,istwotimestheeectofnoiseontheotherlags.Therefore,ifthevalueoftherstcorrelationlagiscalculatedusingotherlags,theoveralleectofthenoisecanbesubtractedfromthecorrelationremovingtheeectofthenoise.TheparabolattingalgorithmdescribedinSection3.3.1isusedforremovingthenoisecontributioninthismethodaswell. Notethatthersttermintheright-handside(RHS)of(3.15)isequaltoRjHj2(0)=2andthesecondandthirdtermstogetherareequaltothemagnitudesquareofthecorrelationofthechannelresponse,RH().Usingthesefacts,thefollowingequalitycanbeobtainedRjHj2()RjHj2(0) 2=RH()RH();(3.16) whereRH()isthecorrelationofH(k)asdenedbefore.Notethattheleft-handside(LHS)ofthisequationcanbeestimatedusingthereceivedsignal.TheRHSisamultiplication,andwhenIDFTisappliedonthisterm,itbecomesaconvolutionofPDPwiththeippedversionofitselfintimedomain.ThisfollowsfromthepropertiesofDFT[42]andfromthefactthattheIDFToftheCFCisequaltothePDP.TheresultingequationcanthenbewrittenasIDFTRjHj2()RjHj2(0) 2=IDFTfRH()RH()g(3.17)=L1Xi=0PliPhiiN:(3.18) HavingtheLHSoftheequalitycalculatedusingthereceivedsignal,wecanestimatethePDPusing(3.18)andbysolvingthenon-linearsetofequations.Forthispurpose,leastsquaresoptimizationis61

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Afterexpanding(3.19),thesimpliedversioncanbewrittenasRjYj2()=RjHj2()RjXj2()+(1+())2RH(0)RX(0)2w+4w:(3.20) ForconstantenvelopemodulationsRjXj2()=RX()=1,andtherefore(3.20)reducesto(3.13)as2RjYj2()=Rj^Hj2():(3.21) ThereforethealgorithmgiveninSection3.3.2canbeusedforestimatingPDPusingY(k)insteadof^H(k).ThisenablesustouseallofthereceivedOFDMsymbolswhichresultsinbothnoiseaveragingandgettingbettercorrelationestimates.3.3.4EstimationofRMSDelaySpreadandMaximumExcessDelay

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PL1l=0Pl2l wherel=ltsisthedelayoflthmultipathcomponent.InordertodecreasetheeectoferrorsinthePDPestimation,tapswithpower25dBbelowthemostpowerfullagaresettozero.Moreover,weconsiderthemaximumexcessdelayof25dB,i.e.themaximumexcessdelayisequaltothedelayofthelastnon-zerotap. Thestatisticsofthechannelmightbechangingintimebecauseoftheenvironmentalchangesorbecauseofthemobilityofthetransmitterorreceiver.Inthiscase,thecorrelationestimatescanbeupdatedusinganalphatrackerinordertocapturethisvariation.Forchannelmagnitudebasedalgorithm,forexample,thecorrelationvaluescanbeupdatedasRmjHj2()=(1)RjHmj2()+Rm1jHj2()(3.23) whereRjHmj2()isthecorrelationvalueobtainedusingmthsymbol.Theforgettingfactor01isadesignparameteranditshouldbeselecteddependingonhowfastthechannelparametersarechanging.3.4NumericalResults

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Relativedelay(ns)0310710109017302510 Figure3.2Illustrationofframestructureofthesystemusedfortestingtheproposedalgorithms. Theestimationisassumedtobedoneinuplinkforauserwith20OFDMsymbolsinaframewith10msframeduration.TheframestructureoftheconsideredsystemisillustratedinFig.3.2.Inuplink,eachuserisassumedtohaveatrainingsymbolforsynchronizationandchannelestimationpurposes.Thechannelestimationbasedalgorithmsusethechannelestimatesobtainedusingthetrainingsymbolswhilethereceivedsignalpowerbasedalgorithmusesallofthe20transmittedsymbols(1trainingsymboland19datasymbols)forestimationofPDP.Therst5non-zerocorrelationvaluesareusedforobtainingtheparametersoftheparabolawhichisusedtoremovetheeectofnoiseoncorrelationestimates,i.e.M=5. NormalizedMSEisusedasaperformancemeasureoftheestimatorasitreectsboththebiasandthevarianceoftheestimator.ThenormalizedMSEofrmsisdenedasNMSE(rms),E(^rmsrms)2=2rmswhere^rmsistheestimateofrms.Fig.3.3showsthenormalizedmean-squared-error(MSE)oftheRMSdelayspreadasafunctionofthenumberofframesusedforestimation.Inthisgure,perfectchannelandtiminginformationisassumedtobeavailableandCramer-Raolowerbound(CRLB)fortheestimation(B.7)isalsopresented.Theproposedalgo-rithmsarelabeledasAlgorithmA,B,andCrespectively.Themultipathchannelcomponentsatdierentframesareassumedtobeindependentinthisgureinordertoshow.?.Thechannelestimationbasedalgorithmyieldscloseresultstotheboundandtheperformancelossinthechan-nelmagnitudebasedalgorithmcanbeexplainedbytheinformationlostbynotutilizingthephaseinformationofchannelestimates.Figs.3.4and3.5showthenormalizedMSEoftheRMSdelay64

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ThenormalizedMSEasafunctionofSNRfor80framesisshowninFig.3.6forperfecttimingsynchronization.TheperformancesofallthreealgorithmsincreaseastheSNRisincreasing.How-ever,afteracertainSNRlevel(around10dB),theperformancedoesnotchangesignicantlywithincreasingSNR.65

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Figure3.5Normalizedmean-square-errorperformancesoftheRMSdelayspreadestimatorsasafunctionofnumberofframesusedforestimationwhentherearetimingsynchronizationerrors.66

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Theaforementionedreasonsmotivatedtheuseofadaptivealgorithmsinnewgenerationwirelesscommunicationsystems.Adaptationaimstooptimizewirelessmobileradiosystemsperformance,enhanceitscapacityandutilizeavailableresourcesinanecientmanner.However,adaptationrequiresaformofaccurateparametermeasurements.OnekeyparameterinadaptationofmobileradiosystemsisthemaximumDopplerspread.Itprovidesinformationaboutthefadingrateofthechannel.KnowingDopplerspreadinmobilecommunicationsystemscanimprovedetectionandhelptooptimizetransmissionatthephysicallayeraswellashigherlevelsoftheprotocolstack[140].Specically,knowingDopplerspreadcandecreaseunnecessaryhand-os,adjustinterleavinglengthstoreducereceptiondelays,updaterateofpowercontrolalgorithms,etc.Inaddition,inOFDMsystems,ifthechannelvariesconsiderablywithinoneOFDMsymbolbecauseofhighMSSmobility,orthogonalitybetweensubcarriersislost,leadingtointer-carrierinterference(ICI)[89].DopplerinformationcanhelpinselectionofappropriatetransmissionprolesthatareimmunetoICIandhencetheoverallsystemperformancewillbeimproved.68

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Theorganizationofthischapterisasfollows.InSection4.2,briefsystemandchannelmodelsarepresented.Then,theDopplerspreadestimationalgorithmisdiscussedinSection4.3.SimulationresultsarepresentedandanalyzedinSection4.4.Finally,Section4.5concludesthechapter.4.2SystemandChannelModels wherelisthepropagationdelayassociatedwithlthpath.Thepathgainshl(n)arezero-meanstochasticprocesseswithnormalizedoverallpower,sothatE[(hl(n))]=0andPLl=1Ehjhl(n)j2i=1.Assumingwide-sensestationaryuncorrelatedscattering(WSSUS)channelmodel,andwithuni-69

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whereJo(:)isthezerothorderBesselfunctionoftherstkind.ThemaximumDopplershiftfDisdeterminedbythemobilevelocityandthewavelength.Afterpassingthrougharadiochannel,themthreceivedtime-domainOFDMsignalym(n)canbewrittenasafunctionofthetransmittedsignal,thechanneltransferfunction,andAWGNasym(n)=xm(n)h(n;)+wm(n);1nN:(4.3) AfterperformingthefastFouriertransform(FFT)operationatreceiver,thereceivedfrequency-domainsignalYm(k)canbeexpressedas[144]Ym(k)=Xm(k)Hm(k)+Im(k)+Wm(k);(4.4) whereHm(k)isthechanneltransferfunctionatthekthsubcarrierandIm(k)istheICIterm.TheinterferencetermdependsontransmittedsymbolsandthevariationofthechanneloveranOFDMsymbol.ItcanbeformulatedasIm(k)=N1Xu=0;u6=kL1Xl=0Xm(u)1 Notethattheinterferencepowerincreaseswithincreasingvariationinthechannelresponse,i.ewithincreasingvelocityorDopplerspread.4.3DopplerSpreadEstimation

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ThesecondtermontherighthandsideisthebiasintheestimateduetoICIandcanhaveaneectontheestimationiftheDopplerfrequencyisrelativelyhigh.However,theICItermdependsonthesignalvaluesmodulatedonalltheothersubcarriers.Since,weareinterestedinthecorrelationofthechannelestimateatkthsubcarrierintime,ICIappearsuncorrelated.Hence,itcanbetreatedasadditionalnoise.Thelasttermin(4.6)representstheAWGN. Itisknownthatthechannelintimedomainislimitedtothemaximumexcessdelayofthechannel.Thedatamappedintovarioussubcarriersarezero-meanrandomvariables.ThusICIappearsfastvaryingoversubcarriers.ThesameholdstrueforthetotallyrandomAWGNsamplesinfrequencydomainwhichchangeveryfastoverOFDMsubcarriers.Therefore,bytransformingthefrequencydomainchannelcomponents,thetruechannelandnoisecomponents(ICIandAWGN)canbeseparated.WhenIFFTisappliedtothechannelfrequencyresponse(CFR),theCIRwillbeconcentratedontherstfewtaps,whilenoiseandICItermswillbespreadoverallIFFTsize.Fig.4.1illustratesthisfactforaMSSwithmoderatevehicularspeed.Theaveragepowerlevelsofthecomponentsinthechannelestimateareplottedforauniformpowerdelayprole(PDP). Inthischapter,weproposetousetimedomainchannelestimationinsteadoffrequencydomainestimationinordertoincreasetheimmunitytowhitenoiseandtoICIinthechannelestimation.SimilarapproachesareusedinOFDMliteratureforchannelestimation,andarecommonlyreferredtoastransform-domainmethods[145].Inthetime-domain,therstfewtapscanbeusedtoestimatetheDopplerspreadwithlowerestimationerror.Besides,thiscanallowuseoflessnumberofsymbolstondtheautocorrelationandsowecanreducememoryusageandcomputationtimeneededforfastadaptation.Byusing(4.2)andfollowingtheassumptions,wecanobtaintheautocorrelationofaCIRtapasEh^h(n)^h(n+sTS)i=J0(2fDsTS)+2r(l)(4.7) where^histheestimateofthetimedomainchanneltaps,sisthedierenceinOFDMsymbolnumberand2risthecombinedreducedvarianceofICIandAWGN.71

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Wenoteherethatalthoughthezero-crossingmethodusedin[147]avoidstheinuenceofnoiseonndingzero-crossingpointifperfectmatchwithBesselfunctionisassumed,thisisunlikelytooccurespeciallyinrelativelylowDopplervalueswherethehighlagsarenotreliableduetoinsucientsamplesforcorrelationcomputation.ThemethodwillrequireverylargenumberofsymbolsforACFcomputation.Onthecontrary,hereweassumeuseoflesssymbolstoobtaintheACF.72

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ThecomputationofthecoherencetimecanbeeasilyobtainedfromtheACFoftheavailablechannelestimatesifacertainthresholdisattainedwithinanamountoftimelags.Commonly,whenthetimeelapsedforACFtodroptohalfofitsmaximumzerolagvalue,thiscanberegardedasameasureofthecoherencetime.ItisobviousthatourproposedmethodwillalsoallowareliableestimateofthecoherencetimeduetoitsimmunitytonoiseandICIperturbations.4.3.3ComplexityofProposedMethodVersusGains

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ForobtainingtheDopplervalues,allofthesubcarriersintheCFRbasedmethodandallofthetapsintheCIRmethodareused.Thecorrelationsfromdierenttapsareaddeduptoobtainmaximumratiocombining. Fig.4.2showsthenormalizedmeansquareerror(NMSE)ofDopplerestimationwhenestimationisdoneusingCFRandwhenitisdoneusingCIRasproposed.300OFDMsymbolsareusedtoobtainthecorrelationvaluesandtheDopplerspreadwas300Hz.WecanseeaconsiderablegainachievedbytheproposedmethodespeciallyinlowSNR(5-10dB)conditionswheretheeectofnoiseismorevisible.74

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TheNMSEversusthecorrelationlengthisshowninFig.4.3.TheDopplerspreadisxedto300HzandSNRis15dB.Itisevidentthatourmethodreducesthecorrelationlengthtomanyfoldslessthanconventionalmethodforsameestimationperformance.Ingeneral,theresultsobtainedindicaterobustnessofthismethodforDopplerspreadestimationinRayleighfadingchannels. Finally,Fig.4.4showstheMSEasafunctionofthemaximumDopplerfrequencyforaxedSNRof15dB.Asthisgureshows,theMSEincreasesforbothtimeandfrequencydomainestimationswithincreasingDopplerfrequency.ThisiscausedbytheincreasedICIpowerduetolargerDopplerfrequencies.4.5Conclusion

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Thesignal-to-noiseratio(SNR)isbroadlydenedastheratioofdesiredsignalpowertonoisepowerandhasbeenacceptedasastandardmeasureofsignalqualityforcommunicationsystems.AdaptivesystemdesignrequirestheestimateofSNRinordertomodifythetransmissionparame-terstomakeecientuseofsystemresources.Poorchannelconditions,reectedbylowSNRvalues,requirethatthetransmittermodiestransmissionparameterssuchascodingrate,modulationmodeetc.inordertocompensateforthechannelandtosatisfycertainapplicationdependentconstraintssuchasconstantbit-error-rate(BER)andthroughput.Dynamicsystemparameteradaptationre-quiresareal-timenoisepowerestimatorforcontinuouschannelqualitymonitoringandcorrespondingcompensationinordertomaximizeresourceutilization.In[152{154],bitloadinginDMTsystemsisperformedusingtheknowledgeofSNRinformationineachsubcarrierposition,andadaptivebit-loadingisappliedtoOFDMsystemsin[155,156].Inthesepapers,SNRisassumedtobeperfectlyknown.In[157]theeectofimperfectSNRinformationonadaptivebit-loadingisinvestigated,buttheerrorsareassumedtobecausedbychannelestimationandnoisevarianceisassumedto77

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Whitenoiseisrarelythecaseinpracticalwirelesscommunicationsystemswherethenoiseisdominatedbyinterferences,whichareoftencoloredinnature.ThisismorepronouncedinOFDMsystemswherethebandwidthislargeandthenoisepowerisnotthesameoverallofthesub-carriers.Colorofthenoiseisdenedasthevariationofitspowerspectraldensityinfrequencydomain.Thisvariationofspectralcontentaectscertainsub-carriersmorethantheothers.Therefore,anaveragednoiseestimateisnottheoptimaltechniquetouse.TheSNRcanbeestimatedusingregularlytransmittedtrainingsequences,pilotdataordatasymbols(blindestimation).Inthischapter,werestrictourselvestodataaidedestimation.Acomparisonoftime-domainSNRestimationtechniquescanbefoundin[158].ThereareseveralotherSNRmeasurementtechniqueswhicharegivenin[159]andreferenceslistedtherein.IntheliteratureofOFDMSNRestimation,thenumberofrelatedworksislimited.InconventionalSNRestimationtechniques,thenoiseisusuallyassumedtobewhiteandanSNRvalueiscalculatedforallsubcarriers[160{163].In[161],channelestimationforanOFDMsystemwithmultipletransmitandreceiveantennasisstudied.Usingtheintermediatesignalsfromchannelestimation,noisevarianceisalsocalculated.Pilotsareusedforestimationandonlyonenoisevarianceisestimatedforthewholesubcarrierrange.In[162],thenoisevariance(assumedtobeconstantforeachsubcarrier)isestimatedbyndingtheeigenvaluedecompositionofthechannelfrequencycorrelation(CFC).Theeigen-decompositionwillpartitionthesignalintonoisesubspaceandsignalsubspace.Ifthelengthofthemultipathchannelisknown,whichisestimatedfromtheeigenvaluesusingminimumdescriptivelength(MDL)estimationmethod,onecangetnoisevarianceandchannelpower.SNRestimationforanOFDMsystemunderAWGNchannelisgivenin[163],whereestimationisperformedusingtheBPSKmodulatedpreamblesymbolsofHiperLAN/2.In[164,165],theassumptionthatthenoisevarianceisconstantoversubcarriersisremovedbycalculatingSNRvaluesforeachsubcarrier.However,thecorrelationofthenoisevarianceacrosssubcarriersisnotusedineitherpaperasnoisevarianceiscalculatedforeachsubcarrierseparately.Blind(expectationmaximization(EM))anddecision-directednoisevarianceestimationalgorithmsaregivenin[164].Thenoisevariancesarecalculatedseparatelyforeachsubcarrierbyassumingtheyareconstantovertime.Therefore,thenoisevarianceateachsubcarrierisassumedtobeindependentofeachotherandthesamealgorithmisappliedforeachsubcarrier.Forthedecision78

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Inthischapter,thewhitenoiseassumptionisremovedandvariationofthenoisepoweracrossOFDMsub-carriersaswellasacrossOFDMsymbolsisconsidered.ThenoisevariancesateachsubcarrierareestimatedusingatwodimensionalMMSElterwhosecoecientsarecalculatedusingstatisticsofthenoise.Theseestimatesareespeciallyusefulforadaptivemodulation,optimalsoftvaluecalculationforimprovingchanneldecoderperformance,andforopportunisticspectrumusageforcognitiveradios.Moreover,itcanbeusedtodetectandavoidnarrowbandinterference.Thechapterfocusesmoreonestimationofnoisepower,andassumesthatthesignalpower,andhenceSNR,canbeestimatedfromthechannelestimates. Thischapterisorganizedasfollows.Inthenextsection,oursystemmodelisdescribed.Sec-tion5.3explainsthedetailsoftheproposedalgorithms.NumericalresultsarepresentedinSec-tion5.4andtheconclusionsaregiveninSection5.5.5.2SystemModel {z }Zm(k)0kN1;(5.1) whereIm(k)isthecolorednoisecausedbyinterferersorprimaryusers.Weassumethattheim-pairmentsduetoimperfectsynchronization,transceivernon-linearitiesetc.areincorporatedintoWm(k)andthechannelfrequencyresponse(CFR)doesnotchangewithintheobservationtime.

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TheautocorrelationoftheeectivenoisepowerisdenedasR02(;)=Em;kh0m;k20m+;k+2i;(5.2) whereEm;k[]representsexpectationoverOFDMsymbolsandsubcarriers.Whenthetimedepen-dencyisdropped,thecorrelationofvarianceinthefrequencydimensioncanbeexpressedasR02()=Ekh0k20k+2i:(5.3)5.3DetailsoftheProposedAlgorithm

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where^Xm(k)isthenoiselesssampleofthereceivedsymboland^Hm(k)isthechannelestimateforthekthsub-carrierofnthOFDMsymbol.Thebiascausedbyincorrecthypothesisofdatasymbols^Xm(k)canberemovedbyusingalook-uptableorstatisticalrelationbetweenthetrueandestimatedSNRvalues[164]. Weproposetolterthenoisevarianceestimatescalculatedateachsubcarrierj^Zm(k)j2usingatwodimensionallter.Filteringwillremovethecommonassumptionofhavingthenoisetobewhiteanditwilltakethecoloredinterference(bothintimeandfrequency)intoaccount.Letusrepresenttheweightingcoecientofthelterateachsubcarrierwithu;l.Inthiscase,theestimateofthenoisepoweratkthsubcarrierofnthOFDMsymbolcanbewrittenas^02m;k=UXu=ULXl=Lu;lj^Zn+u;k+lj2;(5.5) where2U+1and2L+1arethedimensionsofthelterintimeandfrequencydirectionsrespectively.Theweightingcoecientsshouldhaveaunitypower,i.e.PuPlu;l=1.Thetwodimensionalltergivenby(5.5)canbecomplexforpracticalimplementation.Toreducethecomplexity,twocascadedonedimensionalltersintimeandfrequencyareusedinstead.Thisapproachisvalidasthevariationofthenoisevarianceintimeandfrequencydimensionsareindependent.Fortherestofthechapter,lteringinthefrequencydirectionwillbeconsideredandsymbolindexwillbedroppedfornotationalclarity.Timedomainlteringisthedualofthefrequencydomaincounterpart,andthesamealgorithmcanbeappliedforltering.Theestimatorinfrequencydomainonlycanberepresentedas^02k=LXl=Llj^Zk+lj2;(5.6) wherelsatisesPLl=Ll=1.TheltercoecientslcanbecalculatedusingthestatisticsoftheinterferenceplusnoiseZ(k).Inthischapter,weuseaminimummean-squareerror(MMSE)approachforndingthesecoecients.81

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Notethattheinstantaneouserrors(5.8)willbeafunctionoftheltercoecientsl,theinterferencestatistics,averageinterferencepower,andaveragenoisepower.Hence,ideallytheoptimumvaluesforweightingcoecientswillbedierentforeachsubcarrier.However,thisrequiresknowledgeoflocalstatisticsandhasalargecomplexity.Inordertoovercometheseproblems,weusethesamecoecientsforthewholesubcarrierrange. Theltercoecientscanbecalculatedbyminimizingthemean-squared-error(MSE),i.ebyminimizingtheexpectedvalueofthesquareof(5.8).TheMSEcanbeformulatedas=Ek"(k)2(5.9)=Ek24LXl=Llj^Z(k+l)j20k2!235(5.10)=Ek"LXl=LLXu=Lluj^Z(k+l)j2j^Z(k+u)j220k2LXl=Llj^Z(k+l)j2+0k4#;(5.11) whereEk[]representsexpectationoversubcarriers.Byfurthersimplication,(5.11)canbewrittenintermsoftheauto-correlationofthevarianceofthenoisecomponentR02(;)andtheltercoecientsas=1+LXl=L2l!R02(0)2LXl=LlR02(l)+LXl=LLXu=LluR02(lu):(5.12) Theweightingcoecientsthatminimize(5.12)yieldtheMMSEsolution.Inordertondthissolution,thederivativeofMSEwithrespecttoltercoecientscanbesettozero.Wecanwrite(5.12)inmatrixformforsimplifyingthecalculations.Let=[L0L]Tbethecoecientvector,r=[R02(L)R02(0)R02(L)]Tbethecorrelationvector,andC02bethecovariancematrixofsize(2L+1)(2L+1)withcoecientsC02(i;j)=02(ij).Usingthese82

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Thederivativeof(5.13)withrespecttotheltercoecientsisd d=2R02(0)2r+2C02:(5.14) Bysettingthederivativetozero,i.e.d=d=0,andarrangingtheterms,thecoecientvectorcanbecalculatedas=(C02+R02(0)I)1r;(5.15) whereIis(2L+1)(2L+1)identitymatrix.Thevarianceoftheproposedestimatorcanbefoundbyinserting(5.15)into(5.13)as=R02(0)rT(C02+R02(0)I)1r:(5.16) Someexampleweightingfactors3inthefrequencydomainareshowninFig.5.1fordierentinterferencetowhitenoisepowerratioswhichisdenedasINRdB,10log10PN1k=0EjI(k)j2 PN1k=0E[jW(k)j2]:(5.17) Asthenoisebecomesmorecolored(highdecibelvaluesinthegure),thelterbecomesmorelocalizedinordertobeabletocapturethevariationofnoisevariance.Ontheotherhand,lterturnsintoarectangularwindowwhenwhitenoisebecomesmoredominant.Notethattheweightingcoecientsdependonthestatisticsofinterferenceandwhitenoise.Thesestatisticscanbeobtainedwithaveragingbyassumingthenoiseprocessistime-stationaryinagiveninterval.However,thestatisticsshouldbeupdatedintimeastheymightbechanging.Inordertoachievethis,atrackingmethodsuchasanalpha-trackercanbeemployed.

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where2Lw+1isthelengthofrectangularwindow.Forcalculatingtheoptimumwindowsize,theMSEgivenin(5.12)canbeminimizedbyexcessivesearching[25].Notethatinthiscaselshouldbereplacedwith0l.84

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OurresultsshowthatbothmethodsforcalculatingLwyieldverycloseresults,andthesecondmethod,i.e.calculationusing(5.19),isusedinthischapterforndingthelengthofrectangularwindow. Forcalculatingthenoisevarianceatonesubcarrier,2LmultiplicationsandadditionsarerequiredintheMMSElteringalgorithm.Ontheotherhand,only2Lwadditionsand1divisionisrequiredintherectangularwindowalgorithm.Although,thereductioninthecomputationalcomplexityislarge,theperformancelossduetotherectangularwindowingisnotverybigaswillbediscussedlater.5.3.2EdgesandTimeAveraging Inthiscase,thesameformulaforgivenin(5.15)canbeusedforcalculatingtheweightingcoecients.However,thedenitionofandrshouldbeupdatedas=[L0]Tandr=[R02(L)R02(0)]T. Asimilarproblemtotheedgeprobleminfrequencydomainisobservedinthetimedomainltering(acrossOFDMsymbols)iftheestimationisdelaysensitive.Inthiscase,theestimatormightnothaveOFDMsymbolsafterthecurrentsymbolandhencelteringshouldbeappliedasdenedin(5.20).Therefore,thenoisevarianceorotherrelatedparameterscanbeestimatedusingonlythepreviousOFDMsymbols.85

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PN1k=00k4:(5.21) TheMSEperformancesoftheconventional,MMSEltering,andrectangularwindowalgorithmsaregiveninFigs.5.2and5.3.Fig.5.2givestheMSEsasafunctionofthestationaryinterferencetowhitenoisepowerratioandFig.5.3givestheMSEsasafunctionofthenon-stationaryinterferencetowhitenoisepowerratio.Theinterferencetonoiseratioisasdenedin(5.17),andthetotalnoiseplusinterferencepoweriskeptconstantforbothgures.Whentheratioisverysmall(e.g.-20dB),thetotalnoisecanbeconsideredaswhitenoise,andtheconventionalalgorithmperformsbestbecauseitsinherentwhitenoiseassumptionisvalid.Theestimationerrorincreasesasthetotalnoisebecomesmorecoloredforallthreemethods.Theproposedlteringalgorithmshaveconsiderableperformancegainovertheconventionalone.TherectangularwindowbasedalgorithmhasverycloseperformancetotheMSEltering,anditmaybepreferableinpracticalapplicationsbecauseofitslowercomplexity.NotethatFigs.5.2and5.3showtheMSEsinlogarithmicscale.ThegainobtainedbyusingtheproposedalgorithmsathighpowerratiosismuchlargerthantheMSElosscomparedtoconventionalalgorithmatlowpowerratios(whitenoisecase). Finally,theapplicationoftheproposedmethodstonarrowbandinterferencedetectionisstudied4.Fig.5.4showsthetrueandestimatedpowerlevelsforanon-stationaryinterference/primaryuser.Figs.5.5and5.6showtheprobabilityofdetectionandprobabilityoffalsealarmratesforasingle

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Figure5.3Meansquarederrorfordierentalgorithmsasafunctionofthenon-stationaryinterfer-encetowhitenoisepowerratios.87

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Figure5.6Probabilityoffalsealarmratesasafunctionofinterferencetowhitenoisepowerratios.89

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Beingthefocusofthischapter,spectrumsensingbyfaristhemostimportanttaskamongothersfortheestablishmentofcognitiveradio.Spectrumsensingincludesawarenessabouttheinterferencetemperatureandexistenceofprimaryusers.Asanalternativetospectrumsensing,geolocationanddatabaseorbeacons1canbeusedfordeterminingthecurrentstatusofthespectrumusage[167,168].Inthischapter,wefocusonspectrumsensingperformedbycognitiveradiosbecauseofitsbroaderapplicationareaswhilereferringothermethodsasneeded.Althoughspectrumsensingistraditionallyunderstoodasmeasuringthespectralcontent,ormeasuringtheinterferencetemperatureoverthespectrum;whentheultimatecognitiveradioisconsidered,itisamoregeneraltermthatinvolvesobtainingthespectrumusagecharacteristicsacrossmultipledimensionssuchastime,space,frequency,andcode.Italsoinvolvesdeterminingwhattypeofsignalsareoccupying

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VariousaspectsofspectrumsensingtaskareillustratedinFig.6.1.Thegoalofthischapteristopointoutseveralaspectsofspectrumsensingasshowninthisgure.Theseaspectswillbediscussedintherestofthischapter.WestartbyexplainingsomechallengesassociatedwithspectrumsensinginSection6.2.Section6.3explainsthemainspectrumsensingmethods.CooperativesensingconceptanditsvariousformsareintroducedinSection6.4,followedbyadiscussionofexternalsensingalgorithmsinSection6.5.StatisticalmodelingofnetworktracandutilizationofthesemodelsforpredictionofprimaryuserbehaviorisstudiedinSection6.6.Section6.7explainsthefactorsondecidingthefrequencyofspectrumsensing.HardwareperspectiveofsensingproblemisdiscussedinSection6.8.Weintroducethemulti-dimensionalspectrumsensingconceptinSection6.9.Finally,sensingfeaturesofsomecurrentwirelessstandardsareexplainedinSection6.10andourconclusionsaregiveninSection6.11.92

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Letusassumethatthereceivedsignalhasthefollowingsimpleformy(n)=s(n)+w(n);(6.1)

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whereNisthelengthofknownpattern.Intheabsenceoftheprimaryuser,themetricvaluebecomesM=Re"NXn=1w(n)s(n)#:(6.3) Similarly,inthepresenceofaprimaryuser'ssignal,thesensingmetricbecomesM=NXn=1js(n)j2+Re"NXn=1w(n)s(n)#:(6.4) ThedecisiononthepresenceofaprimaryusersignalcanbemadebycomparingthedecisionmetricMagainstaxedthresholdW.Thisisequivalenttodistinguishingbetweenthefollowingtwohypotheses:H0:y(n)=w(n);(6.5)H1:y(n)=s(n)+w(n):(6.6) Theperformanceofthedetectionalgorithmcanbesummarizedwithtwoprobabilities:proba-bilityofdetectionPDandprobabilityoffalsealarmPF.PDistheprobabilityofdetectingasignalontheconsideredfrequencywhenittrulyispresent,thuslargedetectionprobabilityisdesired.ItcanbeformulatedasPD=Pr(M>WjH1);(6.7) whereWisthethresholdvalue.PFistheprobabilitythatthetestincorrectlydecidesthattheconsideredfrequencyisoccupiedwhenitactuallyisnot,anditcanbewrittenasPF=Pr(M>WjH0):(6.8)

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Thecyclicspectraldensity(CSD)functionofreceivedsignal(6.1)canbecalculatedas[183]S(f;)=1X=Ry()ej2f;(6.9) whereRy()=Ey(n+)y(n)ej2n(6.10) isthecyclicautocorrelationfunction(CAF),andisthecyclicfrequency.TheCSDfunctionoutputspeakvalueswhenthecyclicfrequencyisequaltothefundamentalfrequenciesoftransmittedsignalx(n).Cyclicfrequenciescanbeassumedtobeknown[177,182]ortheycanbeextractedandusedasfeaturesforidentifyingtransmittedsignals[180].6.3.4EnergyDetectorBasedSensing

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Usingthesamemodelgivenin(6.1),decisionmetricforenergydetectorcanbewrittenasM=NXn=0jy(n)j2:(6.11) Thewhitenoisecanbemodeledasazero-meanGaussianrandomvariablewithvariance2w,i.e.w(n)=N(0;2w).Forasimpliedanalysis,letusmodelthesignaltermasazero-meanGaussianvariableaswell4,i.e.s(n)=N(0;2s).Becauseoftheseassumptions,thedecisionmetricMfollowschi-squaredistributionwith2Ndegreesfreedom,22Nandhence,itcanbemodeledasM=8>><>>:2w Forenergydetector,theprobabilitiesPFandPDcanbecalculatedas[184]5PF=1LfLt;E whereEisthedecisionthreshold,and(a;x)istheincompletegammafunctionasgivenin[192](seeEquation6.5.1).Fig.6.3showsthereceiveroperatingcharacteristics(ROCs)fordierentSNRvalues.SNRisdenedastheratiooftheprimaryuser'ssignalpowertonoisepower,i.e.SNR=2s=2w.Theaveragingsizeissetto15inthisgure,N=15.Asthisgureclearlyshows,theperformanceofthethresholddetectorincreasesathighSNRvalues.

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Thethresholdusedinenergydetectorbasedsensingalgorithmsdependsonthenoisevariance.Consequently,smallnoisepowerestimationerrorscausesignicantperformanceloss[193].Asasolutiontothisproblem,in[194],noiselevelisestimateddynamicallybyapplyingareduced-rankeigenvaluedecompositiontoincomingsignal'sautocorrelation.Then,theestimatedvalueisusedtochoosethethresholdforsatisfyingaconstantfalsealarmrate. Measurementresultsareanalyzedin[174,175]usingenergydetectortoidentifytheidleandbusyperiodsofWLANchannels.EnergylevelforeachGSMslotismeasuredandcomparedin[186]foridentifyingtheidleslotsforexploitation.Thesensingtaskinthisworkisdierentinthesensethatthecognitiveradiohastobesynchronizedtotheprimaryusernetworkandthesensingtimeislimitedtoslotduration.Asimilarapproachisusedin[195]aswellforopportunisticexploitationofunusedcellularslots.In[187],powerattheoutputoffastFouriertransform(FFT)ofincomingsignaliscomparedwithathresholdvalueinordertoidentifythenumberofusedTVchannels.FFTisperformedonthedatasampledat45kHzaroundthecenteredTVcarrierfrequencyforeachTVchannel.Theperformanceofenergydetectorbasedsensingovervariousfadingchannelsisinvestigatedin[184].Closed-formexpressionsforprobabilityofdetectionunderAWGNand100

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Palicot[200]Channelbandwidthanditsshape:thisfeatureisfoundtobethemostdiscrimi-natingparameterusingtablesandcross-tables,i.e.bycomparingwithotherpa-rameters. Radialbasisfunction(RBF)neu-ralnetworks. Gandetto[201] Thestandarddeviationoftheinstanta-neousfrequencyandthemaximumdu-rationofasignal(Time-Frequencyanal-ysis). Feedforwardback-propagationneuralnetworks(FFBPNNs)andsupportvectormachines(SVMs)withRBF. Fehske[180]Spectralcorrelationdensity(SCD)andspectralcoherencefunction(SCF). Multilayerlinearperceptionnet-work(MLPN)neuralnetworks. Oner[177]Spectralcorrelationdensity(SCD)andspectralcoherencefunction(SCF). Statisticaltestsforidentifyingthepresenceofcyclostationarity. ofthismethodislessthanthemaximumlikelihoodestimator,itisstillcomputationallydemanding.RandomHoughtransformofreceivedsignalisusedin[202]foridentifyingthepresenceofradarpulsesintheoperatingchannelsofIEEE802.11systems.Thismethodcanbeusedtodetectanytypeofsignalswithperiodicpatternsaswell.In[203],waveletsareusedfordetectingedgesinthePSDofawidebandchannel.Oncetheedges,whichcorrespondtotransitionsfromoccupiedbandtoemptybandorviceversa,aredetected,thepowerwithinbandsbetweentwoedgesareestimated.Usingthisinformationandedgepositions,thePSDcanbecharacterizedasoccupiedoremptyinabinaryfashion.Theassumptionsmadein[203],however,needtoberelaxedforbuildingapracticalsensingalgorithm.6.4CooperativeSensing

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-Computational&implementationsimplicity -Hiddennodeproblem-Multipathandshadowing Cooperativesens-ing -Higheraccuracy(closetooptimal) -Reducedsensingtime[188] -Shadowingeectandhiddennodeproblemscanbeprevented -Complexity(complexityofsensor,complexityofwithin-systemcooper-ation,complexityofamong-systemcooperation) -Tracoverhead -Theneedforacontrolchannel offalsealarmsconsiderably.Inaddition,cooperationcansolvethehiddenprimaryuserproblemandcandecreasesensingtime[176,188,189]. Theinterferencetoprimaryuserscausedbycognitiveradiodevicesemployingspectrumaccessmechanismsbasedonsimplelisten-before-talk(LBT)schemeisinvestigatedin[190]viaanalysisandcomputersimulations.Resultsshowthatevensimplelocalsensingcanbeusedtoexploretheunusedspectrumwithoutcausinginterferencetoexistingusers.Ontheotherhand,itisshownanalyticallyandthroughnumericalresultsthatcollaborativesensingprovidessignicantlyhigherspectrumcapacitygainsthanlocalsensing.Thefactthatcognitiveradioactswithoutanyknowledgeaboutthelocationoftheprimaryusersinlocalsensingdegradestheperformance. Thechallengesofcooperativesensingincludedevelopingecientinformationsharingalgorithmsandincreasedcomplexity[204].Theadvantagesanddisadvantagesoflocalandcooperative(orcollaborative)sensingmethodsaretabulatedinTable6.2. Incooperativesensingarchitectures,thecontrolchannelcanbeimplementedusingdierentmethodologies.Theseincludeadedicatedband,unlicensedbandsuchasindustrial,scienticandmedical(ISM)band,andunderlayultrawideband(UWB)system[205].Dependingonthesystemrequirements,oneofthesemethodscanbeselected.Thesharedinformationcanbesoftorharddecisionsmadebyeachcognitivedevice[206].Furthermore,varioustechniquesforcombiningsensingresultscanbeemployed.Theperformancesofequalgain-combining(EGC),selectioncombining(SC),andswitchandstaycombining(SSC)areinvestigatedin[184]forenergydetectorbasedspectrumsensingunderRayleighfading.TheEGCmethodisfoundtohaveagainofapproximatelytwoordersofmagnitudewhileSCandSSChavingoneorderofmagnitudegain.Asfarasthe103

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Cooperativesensingcanbeimplementedintwofashions:centralizedordistributed[207].Thesetwomethodswillbeexplainedinthefollowingsections.6.4.1CentralizedSensing Thehard(binary)sensingresultsaregatheredatacentralplacewhichisknownasaccesspoint(AP)in[109].Thegoalistomitigatethefadingeectsofthechannelandincreasedetectionperformance.Resultingdetectionandfalsealarmratesaregivenin[208]forthesensingalgorithmusedin[109].In[206],thesensingresultsarecombinedinacentralnode,termedasmasternode,fordetectingTVchannels.Hardandsoftinformationcombiningmethodsareinvestigatedforreducingtheprobabilityofmissedopportunity.Theresultspresentedin[109,206]showthatsoftinformation-combiningoutperformshardinformation-combiningmethodintermsoftheprobabilityofmissedopportunity.6.4.2DistributedSensing AnincrementalgossipingapproachtermedasGUESS(gossipingupdatesforecientspectrumsensing)isproposedin[209]forperformingecientcoordinationbetweencognitiveradiosindis-tributedcollaborativesensing.Theproposedalgorithmisshowntohavelow-complexitywithre-ducedprotocoloverhead.TheGUESSalgorithmhasfastconvergenceandrobusttonetworkchangesasitdoesnotrequireasetupphasetogeneratetheclusters.Incrementalaggregationandrandom-izedgossipingalgorithmsarealsostudiedin[209]forecientcoordinationwithinacognitiveradionetwork.Adistributedcollaborationalgorithmisproposedin[189].Thecollaborationisperformedbetweentwosecondaryusers.Theuserclosertoprimarytransmitter,whichhasabetterchangeof104

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Asensornodedetectorarchitectureisusedin[210].Thepresenceofpassivereceivers,viz.televisionreceivers,isdetectedbymeasuringthelocaloscillator(LO)powerleakage.Onceareceiverandthechannelisdetected,thesensornodenotiescognitiveradiosintheregionofpassiveprimaryuserviaacontrolchannel.Similarto[210],asensornetworkbasedsensingarchitectureisproposedin[181].Adedicatednetworkcomposedofonlyspectrumsensingunitsisusedtosensethespectrumcontinuouslyorperiodically.Theresultsarecommunicatedtoasink(central)nodewhichfurtherprocessesthesensingdataandsharestheinformationaboutthespectrumoccupancyinthesensedareawithopportunisticradios.Theseopportunisticradiosusetheinformationobtainedfromsensingnetworkforselectingthebands(andtimedurations)oftheirdatatransmissions.Thesensingresultscanalsobesharedviaapilotchannelsimilartonetworkaccessandconnectivitychannel(NACCH)[211].ExternalsensingisoneofthemethodsproposedforidentifyingprimaryusersinIEEE802.22standardaswell(SeeSection6.10).105

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Channelaccesspatternsofprimaryusersareidentiedandusedforpredictingspectrumusagein[212].AssumingaTDMAtransmission,periodicitypatternofchanneloccupancyisextractedusingcyclostationarydetection.Thisparameteristhenusedtoforecastthechannelidleprobabilityforagivenchannel.Furthermore,[212]proposestousehiddenMarkovmodels(HMMs)inordertomodelthechannelusagepatternsofprimaryusers.Amultivariatetimeseriesapproachistakenin[2]tobeabletolearntheprimaryusercharacteristicsandpredictthefutureoccupancyofneighboringchannels.Abinaryscheme(emptyoroccupied)isusedtoreducethecomplexityandstoragerequirementsasshowninFig.6.4.Itisnotedin[174]thatthestatisticalmodelofprimaryusers'behaviorshouldbekeptsimpleenoughtobeabletodesignoptimalhigherorderprotocols.Ontheotherhand,itwillbeuselessiftheprimaryuser'sbehaviorcouldnotbepredictedwell.Inordertostrikeabalancebetweencomplexityandeectiveness,continuous-timesemi-MarkovprocessmodelisusedtodescribethestatisticalcharacteristicsofWLANchannelsthatcanbeusedbycognitiveradiotopredicttransmissionopportunities.TheinvestigationofvoiceoverInternetprotocol(VoIP)106

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Advantages -Lowercost -Higherspectrumeciency -Bettersensingaccuracy -Poorsensingaccuracy -Highercost -Higherpowerconsumption -Highercomplexity spectrumopportunities.Moreover,highspeedprocessingunits(DSPsorFPGAs)areneededforperformingcomputationallydemandingsignalprocessingtaskswithrelativelylowdelay. Sensingcanbeperformedviatwodierentarchitectures:single-radioanddual-radio[181,199].Inthesingle-radioarchitecture,onlyaspecictimeslotisallocatedforspectrumsensing.Asaresultofthis,onlyacertainaccuracycanbeguaranteedforspectrumsensingresults.Moreover,thespectrumeciencyisdecreasedassomeportionoftheavailabletimeslotisusedforsensinginsteadofdatatransmission.Theobviousadvantageofsingle-radioarchitectureisitssimplicityandlowercost.Inthedual-radiosensingarchitecture,oneradiochainisdedicatedfordatatransmissionandreceptionwhiletheotherchainisdedicatedforspectrummonitoring.Thedrawbackofsuchanapproachistheincreasedpowerconsumptionandhardwarecost.Notethatonlyoneantennawouldbesucientforbothchainsassuggestedin[199].Acomparisonofadvantagesanddisadvantagesofsingleanddual-radioarchitecturesisgiveninTable6.3.Inconclusion,onemightpreferonearchitectureovertheotherdependingontheavailableresources,andperformanceand/ordataraterequirements.6.9Multi-DimensionalSpectrumAwareness

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Itisofcrucialimportancetodenesuchann-dimensionalspaceforspectrumsensing.Spectrumsensingshouldincludetheprocessofidentifyingoccupancyinalldimensionsofthespectrumspaceandndingspectrumholes,ormorepreciselyspectrumspaceholes.Forexampleacertainfrequencycanbeoccupiedforagiventime,butitmightbeemptyinanothertime.Hence,temporaldimensionisasimportantasfrequencydimension.ThisexamplecanbeextendedtotheotherdimensionsofspectrumspacegiveninTable6.4.Asaresultofthisrequirement,advancedspectrumsensingalgorithmsthatoerawarenessinmultipledimensionsofthespectrumspaceshouldbedeveloped.6.10SpectrumSensinginCurrentWirelessStandards

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Thesensing(ormeasurement)informationisusedtoimprovethetracdistributionwithinanetworkaswell.WLANdevicesusuallyconnecttotheAPthathasthestrongestsignallevel.Sometimes,suchanarrangementmightnotbetheoptimumandcancauseoverloadingononeAPandunderutilizationofothers.In802.11k,whenanAPwiththestrongestsignalpowerisloadedtoitsfullcapacity,newsubscriberunitsareassignedtooneoftheunderutilizedAPs.Despitethefactthatthereceivedsignallevelisweaker,theoverallsystemthroughputisbetterthankstomoreecientutilizationofnetworkresources.6.10.2Bluetooth AFHrequiresasensingalgorithmfordeterminingwhetherthereareotherdevicespresentintheISMbandandwhetherornottoavoidthem.Thesensingalgorithmisbasedonstatisticsgatheredtodeterminewhichchannelsareoccupiedandwhichchannelsarenotoccupied.Channelstatistics110

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AnotherapproachformanagingthespectruminIEEE802.22devicesisbasedonacentralizedmethodforavailablespectrumdiscovery.TheBSswouldbeequippedwithaglobalpositioningsystem(GPS)receiverwhichwouldallowitspositiontobereported.ThelocationinformationwouldthenbeusedtoobtaintheinformationaboutavailableTVchannelsthroughacentralserver.Forlow-powerdevices7operatingintheTVbands,externalsensingisproposedasanalternative

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Whatneedstobesensed? Comments Illustrations Opportunityinthefre-quencydomain. Availabilityinpartofthefrequencyspectrum.Theavailablespectrumisdividedintonarrowerchunksofbands.Spectrumopportunityinthisdimensionmeansthatallthebandsarenotusedsimultaneouslyatthesametime,i.e.somebandsmightbeavailableforopportunisticusage. Time Opportunityofaspecicbandintime. Thisinvolvestheavailabilityofaspe-cicpartofthespectrumintime.Inotherwords,thebandisnotcontinu-ouslyused.Therewillbetimeswhereitwillbeavailableforopportunisticusage. Geographicalspace Location(latitude,lon-gitude,andelevation)anddistanceofprimaryusers. Thespectrumcanbeavailableinsomepartsofthegeographicalareawhileitisoccupiedinsomeotherpartsatagiventime.Thistakesad-vantageofthepropagationloss(pathloss)inspace. Thesemeasurementscanbeavoidedbysimplylookingattheinterferencetemperature.Nointerferencemeansnoprimaryusertransmissioninalocalarea.However,oneneedstobecarefulbecauseofhiddenterminalproblem. Code Thespreadingcode,timehopping(TH),orfrequencyhopping(FH)sequencesusedbytheprimaryusers.Tim-inginformationisalsoneededsothatsecondaryuserscansynchronizetheirtransmissions.Thesynchronizationestima-tioncanbeavoidedwithlongandrandomcodeusage.However,partialinterferenceinthiscaseisunavoidable. Thespectrumoverawidebandmightbeusedatagiventimethroughspreadspectrumorfrequencyhop-ping.Thisdoesnotmeanthatthereisnoavailabilityoverthisband.Si-multaneoustransmissionwithoutin-terferingwithprimaryuserswouldbepossibleincodedomainwithanor-thogonalcodewithrespecttocodesthatprimaryusersareusing.Thisrequirestheopportunityincodedo-main,i.e.notonlydetectingtheus-ageofthespectrum,butalsodeter-miningtheusedcodes,andpossiblymultipathparametersaswell. Angle Directionsofprimaryusers'beam(azimuthandelevationangle)andlocationsofprimaryusers. Alongwiththeknowledgeoftheloca-tion/positionordirectionofprimaryusers,spectrumopportunitiesinan-gledimensioncanbecreated.Forex-ample,ifaprimaryuseristransmit-tinginaspecicdirection,thesec-ondaryusercantransmitinotherdi-rectionswithoutcreatinginterferenceontheprimaryuser. Signal Signalpolarizationandwaveformsofprimaryusers. Primaryusersandsecondaryusersmightbetransmittingawaveformataspecicbandforagiventimeinageographicalareainallthedirec-tionsbutsecondaryuserscanexploitthesignaldimensiontotransmitanorthogonalwaveformsothatitdoesnotcreateinterferencewithprimaryusers.Thisrequiresnotonlyspec-trumestimationbutalsowaveformidentication.

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Thischapterisorganizedasfollows.ProposedPMFalgorithmispresentedinSection7.2.Section7.3discussesenergydetectorbasedPMFfollowedbynumericalresultsinSection7.4.SomediscussionsarepresentedinSection7.5,andnally,theconcludingremarksaregiveninSection7.6.114

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Extractionofapredenedsetoffeaturesfromthereceivedsignal,2. Usingtheextractedfeaturesformakingdecisionsonthepresenceofananticipatedtransmis-sion,3. Exploitingthegainedknowledgeabouttheactiveprimaryusersformulti-dimensionalspec-trumcharacterization. SystemmodelforPMFbasedcognitiveradioisshowninFig.7.1.TheblocksthatrepresentthethreemainstepsofPMFaremarkedwithcorrespondingstepnumbers.Cognitiveenginegovernstheselectionofbandsfortransmissionandcommunicateswithradio,user,andopensystemsinter-connectionreference(OSI)layers.Radioidenticationisperformedbasedontheextractedfeaturesofreceivedsignal,environmentalinformationandcognitiveradio'spriorknowledge.Thesetofpos-sibleRATsandtheirtransmissionparameterscanbecollectedbycognitivedevicesusingpreviousdecisions(blind)ortheycanbebroadcastedbyacentralunit(assisted).Alternatively,thesepa-rameterscanbepre-conguredtocognitiveradioduringhardwaredesign.FederalCommunicationsCommission(FCC)LicensingandInternationalTelecommunicationUnion(ITU)frequencyalloca-115

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Thedimensionofthefeaturesetisadesignparameter.Someoralloftheparameterscanbeextractedfromthereceiveddataandusedforclassication.However,thelargerthedimensionofthefeatureset,themorecomplexthesystem,andthemorereliabletheclassicationresults.Selectionoftheemployedfeaturescanbeperformedbyconsideringthecharacteristicsofpotentialsystems.Thefeaturesetcanberepresentedasavectorfwhichisapointinmulti-dimensionalfeaturespace.Then,thisvectorcanbeusedforclassifyingthedetectedtransmissionintooneofKcandidatetransmissionsusingaclassierthatwillbediscussedinthenextsection.7.2.2DecisionMaking(Classication) Priorprobabilitiesofdierentsystemsplayanimportantroleduringclassication.Forexample,wemayhavewirelessuniversalserialbus(USB)withmuchlessoccurrenceprobabilitythanWLANs.Similarly,Channels1,6,and11ofWLANsystemsareusedmorecommonlythenotherbands.Thispriorinformationcanbeusedduringclassication.Notethatthisparametercannotbeobtainedfromreceivedsignals,butitisanaprioriinformationthatcognitiveradiocancollectaftereachclassication.118

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TheproposedalgorithmisespeciallysuitableforcognitivedevicesusingOFDMastheirtrans-missiontechnology,suchassystemssimilarto[97].TheavailabilityofFFTcircuitryinthesesystemseasestherequirementsonthehardware.Moreover,thecomputationalrequirementofthespectrumsensingalgorithmisreducedasreceiverneedstoapplyFFTfordatadetection.

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TheblockdiagramoftheproposedalgorithmisshowninFig.7.2.Thesignalthatarrivestocognitiveusery(t)isrstlteredwithabandpasslter(BPF)toextractthesignalinthefrequenciesofinterest.Thisltercanbeadjustableandcontrolledbyacontrolunitinordertoscanawiderrange[222].TheoutputofthelterissampledatNyquistrateandN-pointFFTisappliedtoobtainthefrequencydomainsampleswhichcanbemodeledasYm(k)=8>><>>:Wm(k)H0;Sm(k)+Wm(k)H1;k=1;;N(7.1) whereSm(k)isthetransmittedsignalbyprimaryusersattheoutputofmthFFToperation,Wm(k)isthewhitenoisesampleatkthfrequencysample,andNistheFFTsize.H0andH1representthenullhypothesisandalternatehypothesisrespectively.Thewhitenoiseismodeledasazero-meanGaussianrandomvariablewithvariance2w,i.e.W(k)=N(0;2w).Thesignaltermisalsomodeledasazero-meanGaussianvariablewhosevarianceisafunctionoffrequency,i.e.S(k)=N(0;2k),wherekisthelocalstandarddeviation.Thevariationofkacrossfrequencydependsonthecharacteristicsofprimaryuserssignalsandoperatingfrequency.Hence,bychangingthesignalvarianceacrossfrequency,PSDsforvarioustechnologiescanberepresented. SomecriticalblocksfortheproposedenergydetectorbasedPMFalgorithmwillbediscussedinthefollowing.7.3.1FrequencyDomainFiltering

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wherebcrepresentstheoorfunction,andLtandLfaretheaveraginglterlengthsintimeandfrequencydirectionsrespectively.7.3.2ThresholdDetector AsY(k)hasGaussiandistribution,thedecisionstatistics~Y(k)followschi-squaredistributionwith2LfLtdegreesfreedom,22LfLt.Hence,~Y(k)canbemodeledas~Y(k)=8>><>>:2w where2wand2kareasdenedbefore.Theperformanceofthedetectionalgorithmcanbesumma-rizedwithtwoprobabilities:probabilityofdetectionPDandprobabilityoffalsealarmPF.PDistheprobabilityofdetectingasignalontheconsideredfrequencywhenitistrulypresent,thuslargedetectionprobabilityisdesired.ItcanbeformulatedasPD=Pr~Y>jH1;(7.6)121

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2w;(7.8)PD=1LfLt; 2w+2k;(7.9) where(a;x)istheincompletegammafunctionasgivenin[192](seeEquation6.5.1).Ingeneral,PDandPFareinverselyproportional.Fig.7.3showsthereceiveroperatingcharacteristics(ROCs)forasinglefrequencysampleattheoutputofthresholddevice(seeFig.7.2)fordierentsignal-to-noiseratio(SNR)values.SNRisdenedastheratiooftheprimaryuser'ssignalpowertonoisepower,i.e.SNR=2k=2w.Theaveragingsizeissetto15inthisgure.Asthisgureclearlyshows,theperformanceofthethresholddetectorincreasesathighSNRvalues. ThedecisionthresholdcanbeselectedforndinganoptimumbalancebetweenPDandPF.However,thisrequirestheknowledgeofnoiseanddetectedsignalpowersasseenin(7.8)and(7.9).Noisepowercanbeestimated,butthesignalpowerisdiculttoestimateasitchangesdependingontheongoingtransmissioncharacteristicsandthedistancebetweenthecognitiveradioandprimaryuser.Inthischapter,itisassumedthatthenoisevarianceisestimatedandthethresholdischosentoobtainafalsealarmrateof0:1percent.7.3.3FeatureExtraction

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whereP(!i)isthepriorprobabilityofclass!i,andP(xj!i)istheclassconditionalprobabilitywhichisassumedtohavemultivariatenormaldistributionwithmeanvectoriandcovariancematrixi.Undersuchanassumption,thediscriminantfunctionscanbeobtainedas[224]gi(f)=1 2(fi)T1i(fi)1 2logjij+logP(!i):(7.11) Theclassicationregionsdenedby(7.11)arequadraticfunctions.Therefore,gi(x)isknownasnormal-basedquadraticdiscriminantfunction.Theclassicationrulecannowbewrittenas:assignafeaturevectorftoasystem!iifgi(f)>gj(f)forallj6=i. Thediscriminantfunctiongi(f)islocallyestimated.Whencollaborativesensingisused,clas-sicationresultscanbesharedamongcognitiveradios.Alternatively,insteadofprovidingharddecisionscognitiveradioscansharethediscriminantfunctionvalues.Then,thecentralunitcancombinethesevaluesandmakeamoreoptimumdecisionbasedonthediscriminantfunctionvaluesfromallcognitiveradiospresentintheenvironment. Themeanvectoricanbeobtainedbyusingtheexpectedvaluesoffeatures,e.g.bandwidthandcenterfrequencyinthiscase.Inpractice,thecovariancematrixiisunknownandcanbe124

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whereDisthelengthofthetrainingdata.Furthermore,thecovariancematrixcanbeassumedtobethesameforallclassesusingthesameRAT.Forexample,alltheclassesusingWLANareexpectedtohavethesamecovariancematrixasonlycenterfrequencyischanged.Whentheestimatedfeaturesarenotcorrelatedtoeachother,thecorrelationmatrixbecomesadiagonalmatrix.Dierentfeatureswillhavedierentunitsandhencepropernormalizationofthisfeaturesneedstobeestablished.Moreover,thevaluesofdiagonalelementsgivetheweightsforeachfeature,anddierentweightscanbeassignedtodierentfeatures.7.4NumericalResults Thefeatures,transmissionbandwidthandcenterfrequency,arecalculatedasexplainedinSec-tion7.3afterpassingtheFFToutputthroughathresholddeviceandndingcontinuousfrequencieswithpowerlargerthanthethreshold.Thethresholdischosentohavealowfalsealarmrateof0.1125

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Figs.7.6and7.7showtheerrorratesindetectingtheWLANandBluetoothsignalsforadditivewhiteGaussiannoise(AWGN)channels.Theerrorrateforidentifyinganon-existentsystem(orasysteminanotherband)isshownaswell.ThetimeaveragingLtforFig.7.6andFig.7.7aresettobe15and30respectively.Hence,sensingdurationscorrespondto184sand368s.TheclassicationisquitesuccessfulevenatverylowSNRscenariosandperformanceincreaseswithincreasingaveragingduration.NotethattheerrorratesforWLANaresmallerforagivenSNRvalue.ThisisbecauseofthelargebandwidthandlargeseparationofcenterfrequenciesofWLANsignals. Fig.7.8showstheperformanceofenergydetectorbasedalgorithmwhenthereceivedsignalispassedthroughamultipathchannelwithexponentialdelaypowerdelayprole(PDP)withroot-mean-squared(RMS)delayspreadvalueof50ns.TheperformanceoftheBluetoothsignaldetectionisaectedverylittlewhiletheperformanceofWLANdetectionisdecreased.Thepoweructuations126

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Figure7.7DetectionerrorratesfortheWLANandBluetoothsystemsatdierentSNRvaluesforLt=30.127

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Whenthereceivedsignalisweak(lowSNRvalues),thesignalpowerfallsbelowthenoiseoor.Insuchcases,thecomparatoryieldszerooutputmostlyduetothelowPFsettings.Hence,notransmissionscanbedetected.Asaresultofthis,theprobabilityofmissingongoingtransmissionsbecomesoneandprobabilityofdetectinganon-existentsignalapproachestozero.7.5Discussion

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Anotherproblemariseswhenthexedfrequencysignalsoverlapinthefrequencyorwhentheyareveryclosetoeachother.Energydetectorbasedalgorithmdiscussedinthischaptermightnotbeabletodierentiatethetwotransmissionsandcanregardthetransmissionasasingletransmissionwithawiderbandwidth.ThiswillinturnaecttheclassicationoutputofPMFandyieldinaccuratespectrumknowledge. Theseproblemscanbesolvedbysupportingtheenergydetectorbasedalgorithmwithcare-fullydesignedsignalprocessingtechniquesorextrafeaturesforPMFcanbeobtainedusingothersignalprocessingtoolssuchascyclostationaritybasedorwaveletbasedmethods.AsexplainedinSection7.2.1,theselectionoffeaturesandalgorithmsforextractingthesefeaturesshouldbedonebyconsideringtheinitialsetofparametersandprocessingcapabilitiesofcognitiveradio.Inthischapter,wehaveexploredenergydetector-basedmethodasanexampleforPMFbecauseofitssimplicity.7.6ConclusionsandFutureResearch

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OFDMsignalscanbeconsideredasacompositionoflargenumberofindependentrandomsignals.Hence,sampledOFDMsignalcanbeassumedtohaveaGaussiandistributionthankstocentrallimittheorem.Thisobservationisusedin[221,225,226]forclassicationofsignalsassingle-carrierormulti-carrierbyapplyingnormalityteststoincomingsignal.However,inthepresenceofmultipath-fadingandinterference,single-carriersignalsatthecognitiveradioreceivercanalsohaveGaussiandistribution.Thisisespeciallytrueforlowsignal-to-noiseratio(SNR)scenarios.Furthermore,whenpowercontrolisemployedintime-multiplexedOFDM(suchasIEEE802.16),theGaussianapproximationdoesnotholdanymore,andasaconsequence,classicationbasedonnormalitytestsmayfail. VariousparameterestimationalgorithmsforOFDMsystemsaredevelopedinliterature.MethodsforndingtheOFDMsymbolandcyclicprex(CP)durationsaremostlybasedonexploitationofthecyclostationarityofOFDMsignalingduetocyclicprexextension[221,226{230].In[227],130

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NumberofsubcarriersordiscreteFouriertransform(DFT)sizeisanotherkeyparameterforOFDMsystems.Analgorithmbasedonmultiplesignalclassication(MUSIC)techniqueisusedin[231]forndingtheDFTsize.Basically,eigen-decompositionisusedtodiagonalizethecorrelationmatrixofthereceivedsignal.Then,usingAkaike'scriteria,numberofsub-spacesorsub-carriersisestimated.However,zerosareusedforgeneratingOFDMsignalinsteadofcyclicprexin[231].In[221],onceCPandsymboldurationsareestimated,DFTsizeisfoundbytestingallhypothesisDFTsizevalues.ThefactthattheDFToutputgivesmodulateddatasymbols,whichdonothaveGaussianproperties,whenDFTsizeismatchedtocorrectoneisexplored.DFToutputsaretestedforGaussianitytondthecorrectDFTsize.Ifnotallofthesubcarriersareemployedfortransmission,activesubcarriersshouldbeidentied.ThiscanbeperformedbyanalyzingthepowerlevelattheoutputofFFT[232].However,suchmethodsneedtheknowledgeofFFTsizeandrequiresynchronizationtothereceivedsignal. OFDMsignalbandwidthcanbeausefulelementforsignalidenticationandndingwhitespacesinthespectrum.Inliterature,thebrick-wallshapeofthespectrumisusedforestimatingtheOFDMbandwidth[233,234].Spectralbreakingpointsareidentiedusingedgedetectionalgorithmsandbandwidthinformationisextractedbyusingthespectralbreakingpoints.Thesemethods,however,areonlyeectivewhenallofthesubcarriersareemployed. Inthischapter,classicationofcommunicationssystemsassingle-carrierormulti-carrierisconsidered,andmethodsforestimationoffundamentaltransmissionparametersinthecaseofmulti-carriertransmissionareproposed.Ourcontributionscanbesummarizedasfollowing:

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Thechapterisorganizedasfollows.Section8.2describesthesystemmodel.ProposedOFDMidenticationandparameterextractionalgorithmsaregiveninSection8.3,followedbynumericalresultsinSection8.4.Finally,thechapterisconcludedinSection8.5.8.2SystemModel TDTGt
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whereListhenumberofsample-spacedchanneltapsandlisthedelayoflthtap.Inthischapter,thechannelisassumedtobeconstantoveranOFDMsymbol,buttime-varyingacrossOFDMsymbols,whichisareasonableassumptionforlowandmediummobility. Atthereceiver,thesignalisreceivedalongwithnoise.Afterdown-conversion,simpliedbase-bandmodelofthereceivedsignalcanbeformulatedasy(t)=ej2t[x(t)?h(t)]+w(t)(8.4)=ej2tZx()h(t)d+w(t)(8.5)=ej2tLXl=1x(tl)hl(l)+w(t);(8.6) wherecorrespondstothefrequencyosetduetoinaccuratefrequencysynchronizationwiththereceivedsignal.Theaveragereceivedsignalpowerisdenotedby2s. Itisassumedthatthereceiverdoesnotknowthecorrectsamplingrate2andsamplesthereceivedsignalwithasamplingtimeoft.Now,thediscrete-timereceivedsignalcanbeobtainedfromcontinuoustimesignalasy[n]:=y(nt):(8.7) Indiscrete-timerepresentation,ND,NGandNSareusedtorepresentthenumberofsamplescorrespondingtodata,CPandtotalsymboldurationsrespectively.Thetimedurationscanbecalculatedbymultiplyingthesenumberswiththesamplingperiod,e.g.TS=NSt.ThereceivedsignalisassumedtohaveDsampleswhichcontainsanunknownsingle-carriersignalorunknown

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MaximumlikelihoodestimatesoftheunknownparametersND,NG,andcanbeobtainedbymaximizingthelog-likelihoodfunctionoftheobservationsy.Log-likelihoodfunctioncanbe

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wherep()istheprobabilitydensityfunction(PDF)oftheobservedsamplesandp(;)isthejointPDF.Theset0containsthesamplesofOFDMdatathatarecopiedtoCP.AssumingthatyhasajointlyGaussiandistribution,itisshowninAppendixCthatthelog-likelihoodfunctioncanbeobtainedas(C.5)whereaandareasgivenin(C.4)and(C.6)respectively.Pleasenotethat,MLestimationobtainedbymaximizingthelikelihoodfunctiongivenby(C.5)isasymptoticallyoptimalwhenthefollowingassumptionsaresatised:1. Noiseiswhite,Gaussian,anduncorrelatedwiththetransmissionsignal.2. Alsonotethat,theMLestimationalgorithmcanbemodiedtoestimatethefrequencyosetaswell. Thevalueofa,2sand2warediculttoestimateinanon-cooperativescenario.AtlowSNRvalues,thesecondandthirdtermsof(C.5)approachestozeroandcanbedropped.Therefore,asuboptimalMLestimationispossiblewithlesscomplexityandnoneedfortheknowledgeofnoiseandsignalvariances.Modiedlikelihoodfunctioncannowbeobtainedfrom(C.5)as4~(y;ND;NG;)=D ND+NGXm=0NGXp=1y[m(ND+NG)+p+]y[m(ND+NG)+ND+p+]:(8.12) Hence,theproposedsub-obtimumMLestimationalgorithmis^ND;^NG;^=argmaxND;NG;n~(y;ND;NG;)o(8.13)=argmaxND;NG;D ND+NGXm=0NGXp=1y[m(ND+NG)+p+]y[m(ND+NG)+ND+p+]:(8.14)

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Maximizationgivenin(8.14)isacomputationallydemandingprocess.Inordertoreducethecomplexity,maximizationcanbeperformedintwosteps.First,OFDMsymbollengthNDisesti-mated,andthentheestimatedNDvalueisusedtondCPdurationNGandtimingosetinthesecondstep.Aswillbeshownlater,thesimplicationonthecomputationalcomplexitycomeswiththeexpenseofperformancedegradation.Step1 Assumingenoughstatisticalaveraging,thecorrelationcanbeobtainedasRy()=8>>>>>><>>>>>>:2s+2w=0;NG Hence,theauto-correlationbasedestimationofNDcanbeformulatedas^ND=argmaxfjRy()jg;>0:(8.17) Inordertosimplifytimeandfrequencysynchronization,knownsequencesaretransmittedinOFDMbasedsystems.Thesesequencesincludepreamblesandpseudo-randompilot(data)sym-bols.OFDMpreambleisusuallycomposedofidenticalsequencesthatcanbeusedtofacilitatesynchronizationusingauto-correlation.However,fortheblindestimationmethodgivenby(8.17),thecorrelationpeakduetorepetitioninthepreamblecauseambiguityasthevalueofthispeakcanbelargerthanthepeakgeneratedbythecyclicprex.AssumethatthereceivedsignalhasnDOFDMdatasymbols,nPpreamblesymbols,andpowerofthepreambleisboostedby.Theworstcasehappenswhenthepreamblehaslargenumberofidenticalparts.Assumingthatthenumberof136

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ForIEEE802.11a/gbasedwirelesslocalareanetwork(WLAN),forexample,theminimumnumberofOFDMsymbolsforcorrectdetectionis8.Inordertoremovethisambiguityinndingthesymbolduration,werstndCpeakvaluesinthecorrelationandusethecorrespondingNDvaluesforMLestimationofCPduration.Then,thenalvalueofNDisselectedinthesecondstep.Step2 Usually,theCPlengthischosenasamultipleofOFDMsymbolduration.InIEEE802.16systems,forexample,availablesizesare1/4,1/8,1/16and1/32[103].Therefore,inordertofurtherreducethecomplexity,theCPsizehypothesescanbelimitedtotheseratiosoftheestimatedNDvaluefrompreviousstep. AnumericalcomparisonofML,suboptimalML,andtwo-steplow-complexityalgorithmsisgiveninFig.8.2whichshowsthenormalizedmean-squared-error(MSE)ofOFDMdatadurationestimationforAWGNandmulti-pathfadingchannelsforaWLANsystem[10](seeSection8.4formoredetailsoftheusedOFDMsystemandchannelmodel).Ascanbeseenfromthisgure,theperformancelossforthesuboptimalmethodisaround1-1.5dBascomparedtotheMLmethod.PleasenotethatforMLalgorithm,perfectnoiseandsignalvarianceknowledgeisassumed;andtheperformanceofMLalgorithmisexpectedtodecreasewhentheseparametersarenotperfectlyknown.Another2dBperformancelossisobservedwhenlow-complexitytwostepmethodisusedinsteadofcalculating(8.14).Intherestofthechapter,weusetwo-stepestimationalgorithmbasedonmodiedlikelihoodfunctionforobtainingperformanceresultsoftheproposedmethod.137

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Eqn.(8.20)givesusthelikelihoodofreceivingyforanOFDMsystemwhichhastheestimatedparameters.ForOFDMsignals,asthenumberofsamplesincreases,convergestojD whereH0andH1representthenullhypothesisandalternatehypothesis,i.e.thereceivedsignalisnotOFDMsignaloritisanOFDMsignal,respectively.Thisobservationisusedforclassicationof138

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Thevalueofdecisionthresholddependsontheincoming(OFDM)signalpoweranddesiredprobabilityoffalsealarm(orprobabilityofmiss).SignalpowercanbefoundusingthetotalsignalifSNRisknown.Innon-cooperativeenvironments,SNRknowledgeisusuallyunavailable.Insuchacase,alowSNRvaluecanbeassumed.InSection8.4,itisshownthatsuchanapproachgivesrobustresultsforawiderangeofSNRvalues.8.3.3EstimationofNumberandFrequenciesofActiveSubcarriers WhenonlyasingleOFDMsymbolisconcerned,timedomainsignalcanbeconsideredasasumofsinusoidswhosenumberisequaltothenumberofactivesubcarriers.Hence,high-resolutionmethodscanbeusedtoestimatethenumberandpositions(frequencies)ofsubcarriers.OFDMsignalsareinherentlyshift-invariantastime-shiftcausesonlyasubcarrier-dependentphaseshifttothesubcarriers.InOFDM,shift-invarianceiscausedbytheadditionofcyclicprex.Inthissection,weexploitshift-invarianceofsignalsubspacesofsinusoidsusingESPRITalgorithmforestimatingthenumberandfrequenciesofusedsubcarriers.UsingtheresultsofSection8.3.1,observationvectorsforeachOFDMsymbolcanbeconstructedasxm=[ym[1]ym[2]ym[ND]]T(8.22)ym=[ym[2]ym[3]ym[ND+1]]T;(8.23)139

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Using(8.1)and(8.7),theobservationvectorscanbeexpressedinmatrixnotationasxm=Asm+wm;(8.24)ym=Asm+w0m;(8.25) whereA=[a1a2aK]isNDKVandermondematrixwhosecolumnsaregivenasak=[1ej!kej2!kej(ND1)!k]T:(8.26) Thefrequencyofeachsubcarriercanbeobtainedusing(8.1)as!k=2t TD(k)k=1;2K:(8.27) TheKKmatrixcontainsthephasedierenceduetoshiftinganditisgivenby=diagej!1;;ej!K:(8.28) Thecolumnvectorsmisgivenassm=[Hm(1)Xm(1)Hm(2)Xm(2)Hm(K)Xm(K)]T:(8.29) whereHm(k)correspondstotheeectofmultipathfadingchannelonthekth(active)subcarrierofmthOFDMsymbol,i.e.thechannelfrequencyresponse(CFR)atkthsubcarrierposition. Theauto-covariancematrixofxmcanbecalculatedasRxx=EmxmxHm=ASAH+2wI:(8.30) Similarlycross-covariancematrixofxmandymareobtainedasRxy=EmxmyHm=ASHAH+2wL;(8.31)140

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itcanbeshownthatSbecomesadiagonalmatrixwhosediagonalelementsareequaltoaveragechannelpowerateachusedsubcarrierposition.HenceScanbewrittenasS=EmsmsHm=diag2H(1);2H(2);;2H(K):(8.33) where2H(k)=EjHm(k)j2istheaveragechannelpoweratkthsubcarriers. Inthefollowing,weuseauto-covarianceandcross-covariancematicesofobservationvectorstoestimatethenumberandfrequenciesofactivesubcarriersofreceivedOFDMsignal.8.3.3.1NumberofSubcarriers 2k(2NDk)logD;(8.34) where12NDdenotetheeigenvaluesofRxx.Hence,theestimatorcanbewrittenas^K=argminkfMDL(k)g:(8.35) In[237],itisshownthatthisestimatorbasedonMDLcriterionisconsistent.Therefore,thevalueobtainedusing(8.35)convergestotruevalueofnumberofsignalsassamplesizegrows.SimulationresultspresentedinSection8.4areconsistentwiththeseconclusionsaswell.141

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ESPRITalgorithmdoesnotassumeanypriorknowledgeaboutthe(complex)sinusoids.Byinvestigating(8.27),however,weseethatthefrequenciesinourproblemhavearegularstructure.142

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whereis^2wthenoisevarianceestimatewhichisestimatedas^2w=1 SimilarlyCxyisdenedas,Cxy=Rxy^2wLASHAH:(8.38) Now,letusconsiderthematrixpenciloftheformCxxej!iCxy=AS(Iej!iH)AH(8.39)143

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TDi.Ifi2,onerowofIej!iHbecomeszero.Consequently,thedeterminantofIej!iHandhencethedeterminantofCxxej!iCxybecomezero.Therefore,activesubcarrierscanbeidentiedastheivaluesthatmakesthedeterminantofCxxej!iCxyzeroandthefrequenciesofeachsubcarriercanbeobtainedas2t TDi.Hence,thestepsofproposedESPRITbasedsubcarrierdetectionalgorithmcanbesummarizedasfollowing:1. Usingreceivedsignalandsynchronizationknowledge,constructobservationvectorsxmandym.2. Constructauto-correlationandcross-correlationmatricesRxxandRxy.3. ComputetheeigenvaluesofRxxandndnumberofsubcarriers^Kusing(8.35).4. ComputeCxxCxyusing(8.36)and(8.38)respectively.5. CalculatethedeterminantofCxxej!iCxyfori=0toi=ND.6. Theivalueswhichproducethe^Ksmallestdeterminantsareselectedasactivesubcarriers.8.3.4FFTSizeandCommunicationStandard Itisstraightforwardtondthecommunicationstandardthatthereceivedsignalbelongsonceitsparametersarecalculated.Theestimatedparameterscanbecomparedwiththeaprioristandardparameters.Forthispurpose,themostdistinguishingparameterscanbeselectedandbasedontheseparametersasimpletree-basedclassicationcanbeperformed.In[226],forexample,onlythelengthofCPisusedforndingwhichstandardthereceivedsignalbelongs.Alternatively,morecomplexandaccuratemethodssuchasstatisticalclassicationalsobeused[31].144

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Fig.8.5showstheprobabilityofincorrectclassicationofthesimulatedOFDMsignalassingle-carrierinAWGNandmulti-pathfadingchannels.Asthisgureshows,theclassicationissuccessfulevenatlowSNRvaluesandnoerrorisobservedfor10dBorhigherSNRvalues.NotethatforAWGNchannel,0dBisadecisionboundaryforclassication.ThereasonforthisboundaryistheselectedthresholdMCwhichcorrespondsto0dBSNRassumptionforthereceivedsignal.IfSNRinformationisavailable,thedecisionthresholdMCcanbechangedadaptivelydecreasingthefalsealarmandmis-detectionrates.ThenormalizedMSEsforTDandTGaregiveninFigs.8.6and8.7respectively.TheestimationismoreaccurateforAWGNchannelthanmulti-pathfadingchannelasexpected.ItisnotedthatthenumberofavailableOFDMsymbolsusedforestimationaectstheperformanceoftheestimationbecauseofnoiseaveraging. ForobservingtheperformanceofmodiedESPRITalgorithm,knowledgeofsymbolandCPdurationsandperfectsynchronizationisassumed.TheproposedmethodisappliedtothesameOFDMsystemwhoseparametersaregiveninthissection.TheprobabilityoferrorfordetectingthenumberofsubcarriersisgiveninFig.8.8for100,250and500OFDMsymbols.TheprobabilitiesofnumberofidentiedsubcarriersfordierentSNRvaluesinmultipathfadingchannelaregiveninFig.8.9.Theresultsareobtainedfor250OFDMsymbols.Notethatthetotalnumberofused145

PAGE 160

Figure8.6NormalizedMSEofOFDMsymboldurationasafunctionofSNRfordierentnumberofsymbolsunderAWGNandfadingchannels.146

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Figure8.8ProbabilityoferrorfordetectingnumberofactivesubcarriersfordierentnumberofsymbolsunderAWGNandfadingchannels.147

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WhileapplyingthemodiedESPRITalgorithm,falsealarmsormissdetectioncanhappenduetochannelandnoise.Theformercorrespondstoidentifyingadeactivatedsubcarrierasactiveandlattermeansthatanactivesubcarrierismissedbythealgorithm.Fig.8.10showstheprobabilityoferrorsforthesubcarrierdetectionalgorithm.Bothfalsealarmandmiss-detectionareconsideredaserrors.148

PAGE 164

Inorthogonalfrequencydivisionmultiplexing(OFDM),linearconvolutionofthetransmittedsignalwiththechannelimpulseresponse(CIR)isconvertedtocircularconvolutionbycyclicallyextendingtheOFDMsymbols.Thisway,transmitteddatasymbolscanberecoveredusingasim-plesingle-tapfrequencydomainequalizer.Theredundancyintroducedbythecyclicprex(CP),however,canbeusedfordetectingthetransmissionparameters[221,226{229]aswellaschanneles-timation[235,239]andsynchronization[240{242].Hence,whilehavingtheaforementionedbenets,CPmaybeundesiredforapplicationswhichrequirecovertness.TheperiodicityintroducedbytheCPcanbeexploredbyundesireduserstosynchronizetotransmittedsignal.NotethatthecyclicfeaturesinconventionalOFDMsystemsarenotsuspendedevenwhenfrequencyhopping(FH)isused[243]. Varioustechniquesaredevelopedtoachievetransmission-levelsecurityandcovertnessinOFDMsystems.OFDMdatasymbolsareembeddedintoanotchedultrawideband(UWB)noisesignalin[244].Theaimistodesignaspectrallyundetectablesystemforbuildinganetworkamong150

PAGE 165

Inthischapter,methodstopreventunwantedexploitationoftheCPforeavesdroppingtothetransmittedsignal,whilemaintainingtheadvantagesofCP,aredeveloped.ThisisachievedbysuppressingthecyclicfeaturesofOFDMsignalsinorderto1)preventidenticationofsignalingpa-rametersand2)avoidundesireduserstoachievesynchronizationtotransmittedsignal.Specically,weproposetochangethesizeoftheCPsizeinapseudonoise(PN)fashionandappendrandomsignalstosomeoftheOFDMsymbolstoscramblethecorrelationpeaksintimedomain.Thesetwomethodspreventenemydetectionofthetransmittedsignalevenifaninitialsynchronizationisachievedbyundesiredusers. Thechapterisorganizedasfollows.Section9.2explainstheeectsofshortCPontheBERperformanceoftheOFDMsystems,followedbyanoverviewofCPbased(timeandfrequency)synchronizationandparameterestimationalgorithmsinSection9.3.ThedevelopedtechniquesaregiveninSection9.4.SomenumericalresultsarepresentedinSection9.5andconclusionsaregiveninSection9.6.9.2EectofCyclicPrexontheBER

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2jH(k)j2N whereH(k)isthechannelfrequencyresponse(CFR)atkthsubcarrier,NisthefastFouriertransform(FFT)size,ListheCIRlength,andhlisthelthtapofCIR.Ascanbeseenin(9.1),thedegradationdependsontheratiobetweenthetailpoweroftheCIRandtotalpowerofCIR.Unlessequalizationisused,shortCPsizecausesperformancedegradation.9.3BlindParameterEstimationandSynchronization TheredundancyinthecyclicprexofOFDMsystemscanalsobeexploitedinordertoobtaintimeandfrequencysynchronizationoncethesymboldurationandCPsizeareestimated/known.Synchronizationalgorithmsbasedonthemaximumlikelihood(ML)[240],minimummean-square152

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TheMLsynchronizationmethodisillustratedinFig.9.2whereonlyoneOFDMsymbolisshown.ThesynchronizationmetricobtainedbyoneOFDMsymbolcanbewrittenasM(m)=NG1Xn=0y(mn)y(mn+ND);(9.2) wherey(n)isthereceivedsignal,NGisthelengthofCPandNDisthelengthoftheusefuldatapart.Using(9.2),thetimingpositioncanbefoundas^=argmaxmfjM(m)jg;(9.3) andfrequencyosetestimateis^=1 2\M(^):(9.4) Inpracticalapplications,extractionofthesynchronizationparametersbyusingtheCPwithonlyoneOFDMsymbolisverydicultifnotimpossible,sincetheCPisperturbedbymultipathcomponentsandadditivenoise.Moreover,thepresenceoffrequencyosetdecreasesthecorrelationbetweentherepeatedparts.Inordertoovercomethisproblem,averagingoveranumberofOFDMsymbolsshouldbeperformed.Fig.9.3showsthenoisycorrelationoutputsfromdierentOFDMsymbolsandtheresultingsynchronizationmetricwhichisobtainedbyaveragingthesecorrelations.TheresultsareobtainedforanOFDMsystemwith64subcarriersand1=4CPratio.Pleasesee153

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Forsynchronization,aPN-basedpreamblecanbeusedasdonein[245].Sincethetransmittedsignalisknownonlybythedesireduser,eavesdropperscannotsynchronizetothetransmittedsig-nal.Thedesiredusers,however,canusetheknowledgeofscramblingpatternandtheredundancycontainedintheCPtoobtainsynchronizationinformationbycombiningthecorrelationoutputsfromeachOFDMsymbol.Furthermore,synchronizationinformationfromthepreambleandsyn-chronizationinformationfromtheCPcanbecombinedusinganappropriatemethodforincreasingaccuracyattheexpenseofincreasednumericalcomplexity. Thecodesequenceforprependingtherandomsignalcanbethesamewiththepreamblesequence(ifused)fordecreasingsignalingoverhead.However,usingthesamesequencereducesthesecurity155

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Adaptivecyclicprexmethodcanbecombinedwithchannelcodingandchannelequalizer.Thecyclicprexdoesnothavetobethesameasthemaximumexcessdelayofthechannel;itcanbesmallerbutnotlargerforsecurity.Ifitissmaller,thentheperformancelossneedstobecompensatedbyadditionalcodingpowerorchannelequalizersneedtobeused.Inthelimitingcase,noCPisusedandtheISIiscompensatedbyusingveryhighcodingorchannelequalizersasproposedin[245]. Adaptivecyclicprexmethodrequirestheknowledgeofthemaximumexcessdelayofthewirelesschannel.VariousalgorithmsaredevelopedinliteratureforthispurposewhichusesCFR[128]orchannelfrequencycorrelation(CFC)[22].ChangingthelengthoftheCPadaptivelyalsoprovidesecientchannelutilizationsincetheoverallCPtimeisminimized.9.4.3PossibleExtensions ThesizeoftherandomsignalinsertedbetweenOFDMsymbolscanbechangeddependingonaPNsequence.Thisprovidesextrascramblingofthecorrelationpeaks.2. Forrandomdatainsertion,insteadofusingtotallyrandomsignal,aknownPNsequencecanbeused.ThereceivercanexploittheknowledgeofusedPNsequenceforsynchronizationorchannelestimation.Thisway,thebandwidthlossduetothetransmissionoftherandomsignalcanbereduced.156

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TheFFT/IFFTsizesofeachOFDMsymbolcanbechangedbasedonaPNsequence.Thisprovidestwotypesofsecuritybymakingsynchronizationanddemodulationofreceivedsignaldicultforundesiredusers.9.5NumericalResults ThemethodgiveninSection9.4.1isrealizedbyinsertingrandomsequencesoflength4,8,and12samplesorbynotinsertinganydata.Eachfourcaseisassumedtohaveequalprobability.TheCAFforthetransmittedsignalwithrandomsignalinsertionisgiveninFig.9.7.Thecyclicfrequenciesareclearlyremovedfromthecorrelationfunction.CSDisnotpresentedbecauseofspacelimitation.PleasenotethatthisinformationcanbeobtainedfromCAF. Fig.9.8showstheCAFforthecasewheredierentCPsizesareusedforeachOFDMsystem.FourdierentCPsizescontaining8,12,16and20samplesareusedrandomly.Thecyclicfeaturesaresomewhatremoved,butwecanseethatthismethodisnotaseectiveaspreviousoneintermsofremovingcyclicfeatures.9.6Conclusion

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Figure9.6Cyclicfrequencydensity(CFD)ofaconventionalOFDMsystem.158

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Below,werstpresentalistofspeciccontributionsindierentchaptersofthedissertation.Then,possibleextensionsoftheworkdonearediscussed.10.1ListofSpecicContributions

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Inthisdissertation,wehavediscussedsomechallengesanddevelopedmethodsforaddressingthose.Specically,estimationalgorithmsforachievingawarenessincognitiveradioareproposed.ThisawarenesscapabilitycanbeusedforadaptationofOFDMsystemsandopportunisticspectrumaccess. WehaveidentiedsomeoftheopenresearchareasforOFDMbasedcognitiveradiosystemsinChapter2.Thesetopicsincludespectrumshaping,eectivepruningalgorithmdesign,designingro-bustsynchronizationmethodsforcognitiveradioapplications,andreducingmutualinterferenceduetopowerleakagetounusedsubcarriers.Inadditiontothesegeneralareas,thefollowingextensionstotheworkinthisdissertationarepossible.163

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M.Sternad,T.Ottosson,A.Ahlen,andA.Svensson,\Attainingbothcoverageandhighspec-traleciencywithadaptiveOFDMdownlinks,"inProc.IEEEVeh.Technol.Conf.,Orlando,Florida,USA,Oct.2003.[15] B.A.Fette,CognitiveRadioTechnology.Newnes,2006.[17] H.ArslanandT.Yucek,AdaptationTechniquesinWirelessMultimediaNetworks.NovaSciencePublishers,2006,ch.AdaptationofWirelessMobileMulti-carrierSystems.[18] H.Mahmoud,T.Yucek,andH.Arslan,CognitiveRadio,SoftwareDenedRadio,andAdaptiveWirelessSystems.Springer,2007,ch.OFDMforCognitiveRadio:MeritsandChallenges.[19] ||,\OFDMforcognitiveradio:Meritsandchallenges,"submittedtoIEEEWirelessCom-mun.Mag.,2007.[20] H.ArslanandT.Yucek,\Delayspreadestimationforwirelesscommunicationsystems,"inProc.IEEESymposiumonComputersandCommun.,Antalya,Turkey,June/July2003,pp.282{287.[21] ||,\EstimationoffrequencyselectivityforOFDMbasednewgenerationwirelesscommu-nicationsystems,"inProc.WorldWirelessCongress,SanFrancisco,CA,USA,May2003.[22] T.YucekandH.Arslan,\DelayspreadandtimedispersionestimationforadaptiveOFDMsystems,"inProc.IEEEWirelessCommun.andNetworkingConf.,LasVegas,Nevada,USA,Apr.2006.[23] ||,\DispersionanddelayspreadestimationforadaptiveOFDMsystems,"submittedtoIEEETrans.Veh.Technol.,2006.[24] T.Yucek,R.A.Tannious,andH.Arslan,\DopplerspreadestimationforwirelessOFDMsystems,"inProc.IEEESarnoSymposium,Princeton,NewJersey,USA,Apr.2005,pp.233{236.[25] T.YucekandH.Arslan,\NoiseplusinterferencepowerestimationinadaptiveOFDMsys-tems,"inProc.IEEEVeh.Technol.Conf.,vol.2,Stockholm,Sweden,May2005,pp.1278{1282.[26] ||,\MMSEnoisepowerandSNRestimationforOFDMsystems,"inProc.IEEESarnoSymposium,Princeton,NewJersey,USA,Mar.2006.[27] ||,\MMSEnoiseplusinterferencepowerestimationinadaptiveOFDMsystems,"IEEETrans.Veh.Technol.,2007.[28] ||,\NoiseplusinterferencepowerestimationmethodforOFDMsystems,"U.S.U.S.Pro-visionalPatentApplicationUSFRef.No.05A011PR,2005.[29] H.ArslanandT.Yucek,CognitiveRadio,SoftwareDenedRadio,andAdaptiveWirelessSystems.Springer,2007,ch.SpectrumSensingforCognitiveRadioApplications.[30] T.YucekandH.Arslan,\Asurveyofspectrumsensingalgorithmsforcognitiveradioappli-cations,"submittedtoIEEECommunicationsSurveysandTutorials,2007.166

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||,\Spectrumcharacterizationforopportunisticcognitiveradiosystems,"inProc.IEEEMilitaryCommun.Conf.,Washington,D.C.,USA,Oct.2006,pp.1{6.[32] ||,\Spectrumsensingforcognitiveradiousingpartialmatchltering,"submittedtoEURASIPJournalonWirelessCommunicationsandNetworking,2007.[33] ||,\Amethodforspectrumsensingviaradioidentication,"U.S.U.S.ProvisionalPatentApplication,2007.[34] ||,\OFDMsignalidenticationandtransmissionparameterestimationforcognitiveradioapplications,"inProc.IEEEGlobalTelecomm.Conf.(Globecom),Washington,D.C.,USA,Nov.2007.[35] ||,\OFDMsignalidenticationandtransmissionparameterestimationforcognitiveradioapplications,"submittedtoIEEETrans.WirelessCommun.,2007.[36] ||,\Featuresuppressionforphysical-layersecurityinOFDMsystems,"insubmittedtoProc.IEEEMilitaryCommun.Conf.,2007.[37] ||,\CovertOFDMtransmissionusingcyclicprex,"U.S.PatentapplicationUS2006/0050626,2004.[38] F.E.Retnasothie,M.K.Ozdemir,T.Yucek,J.Zhang,H.Celebi,andR.Muththaiah,\Wire-lessIPTVoverWiMAX:Challengesandapplications,"inProc.IEEEWamicon(invitedpa-per),Clearwater,FL,Dec.2006.[39] T.Yucek,M.K.Ozdemir,H.Arslan,andF.E.Retnasothie,\AcomparativestudyofinitialdownlinkchannelestimationalgorithmsformobileWiMAX,"inProc.IEEEMobileWiMAXSymposium,Orlando,Florida,USA,Mar.2007,pp.32{37.[40] T.YucekandH.Arslan,\CarrierfrequencyosetcompensationwithsuccessivecancellationinuplinkOFDMAsystems,"inProc.IEEEVeh.Technol.Conf.,Montreal,QuebecFrench,Canada,Sept.2006.[41] ||,\CarrierfrequencyosetcompensationwithsuccessivecancellationinuplinkOFDMAsystems,"IEEETrans.WirelessCommun.,2007,toappear.[42] S.K.Mitra,DigitalSignalProcessing:AComputer-BasedApproach,2nded.NewYork,NY,USA:McGraw-Hill,2000.[43] D.HuangandK.Letaief,\CarrierfrequencyosetestimationforOFDMsystemsusingsub-carriers,"IEEETrans.Commun.,vol.54,no.5,pp.813{823,May2006.[44] W.Henkel,G.Taubock,P.Odling,P.Borjesson,andN.Petersson,\ThecyclicprexofOFDM/DMT-ananalysis,"inInternationalZurichSeminaronBroadbandCommunications.Access,Transmission,Networking.,Zurich,Switzerland,Feb.2002,pp.1{3.[45] F.Tufvesson,\Designofwirelesscommunicationsystems{issuesonsynchronization,channelestimationandmulti-carriersystems,"Ph.D.dissertation,LundUniversity,Aug.2000.[46] P.H.Moose,\Atechniquefororthogonalfrequencydivisionmultiplexingfrequencyosetcorrection,"IEEETrans.Commun.,vol.42,no.10,pp.2908{2914,Oct.1994.[47] P.RobertsonandS.Kaiser,\TheeectofDopplerspreadsinOFDM(A)mobileradiosys-tems,"inProc.IEEEVeh.Technol.Conf.,vol.1,Amsterdam,TheNetherlands,Sept.1999,pp.329{333.167

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D.T.HarvatinandR.E.Ziemer,\OrthogonalfrequencydivisionmultiplexingperformanceindelayandDopplerspreadchannels,"inProc.IEEEVeh.Technol.Conf.,vol.3,no.47,Phoenix,Arizona,USA,May1997,pp.1644{1647.[49] A.Demir,A.Mehrotra,andJ.Roychowdhury,\Phasenoiseinoscillators:Aunifyingtheoryandnumericalmethodsforcharacterization,"IEEETrans.CircuitsSyst.IFundamentalTheoryandApplications,vol.47,no.5,pp.655{674,2000.[50] A.G.Armada,\Understandingtheeectsofphasenoiseinorthogonalfrequencydivisionmultiplexing(OFDM),"IEEETrans.Broadcast.,vol.47,no.2,pp.153{159,June2002.[51] T.Pollet,M.VanBladel,andM.Moeneclaey,\BERsensitivityofOFDMsystemstocarrierfrequencyosetandWienerphasenoise,"IEEETrans.Commun.,vol.43,no.234,pp.191{193,Feb./Mar./Apr.1995.[52] K.SathananthanandC.Tellambura,\PerformanceanalysisofanOFDMsystemwithcarrierfrequencyosetandphasenoise,"inProc.IEEEVeh.Technol.Conf.,vol.4,AtlanticCity,NewJersey,USA,Oct.2001,pp.2329{2332.[53] L.PiazzoandP.Mandarini,\AnalysisofphasenoiseeectsinOFDMmodems,"IEEETrans.Commun.,vol.50,no.10,pp.1696{1705,Oct.2002.[54] E.P.Lawrey,\AdaptivetechniquesformultiuserOFDM,"Ph.D.dissertation,JamesCookUniversity,Dec.2001.[55] T.MayandH.Rohling,\Reducingthepeak-to-averagepowerratioinOFDMradiotransmis-sionsystems,"inProc.IEEEVeh.Technol.Conf.,vol.3,Ottawa,Ont.,Canada,May1998,pp.2474{2478.[56] S.MullerandJ.Huber,\AcomparisonofpeakpowerreductionschemesforOFDM,"inProc.IEEEGlobalTelecomm.Conf.(Globecom),vol.1,Phoenix,Arizona,USA,Nov.1997,pp.1{5.[57] H.OchiaiandH.Imai,\Onthedistributionofthepeak-to-averagepowerratioinOFDMsignals,"IEEETrans.Commun.,vol.49,no.2,Feb.2001.[58] S.HanandJ.Lee,\Anoverviewofpeak-to-averagepowerratioreductiontechniquesformulticarriertransmission,"IEEEWirelessCommun.Mag.,vol.12,no.2,pp.56{65,Apr.2005.[59] H.OchiaiandH.Imai,\Performanceofthedeliberateclippingwithadaptivesymbolselectionforstrictlyband-limitedOFDMsystems,"IEEEJ.Select.AreasCommun.,vol.18,no.11,pp.2270{2277,Nov.2000.[60] P.VanEetvelt,G.Wade,andM.Tomlinson,\PeaktoaveragepowerreductionforOFDMschemesbyselectivescrambling,"IEEElectron.Lett.,vol.32,no.21,pp.1963{1964,Oct.1996.[61] A.Jones,T.Wilkinson,andS.Barton,\Blockcodingschemeforreductionofpeaktomeanenvelopepowerratioofmulticarriertransmissionschemes,"IEEElectron.Lett.,vol.30,no.25,pp.2098{2099,Dec.1994.[62] E.LawreyandC.Kikkert,\PeaktoaveragepowerratioreductionofOFDMsignalsusingpeakreductioncarriers,"inSignalProcessingandItsApplications,1999.ISSPA'99.ProceedingsoftheFifthInternationalSymposiumon,vol.2,Brisbane,Qld.,Australia,Aug.1999,pp.737{740.168

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S.Haykin,\Cognitiveradio:brain-empoweredwirelesscommunications,"IEEEJ.Select.AreasCommun.,vol.3,no.2,pp.201{220,Feb.2005.[64] M.Uhm,\MakingtheadaptivityofSDRandcognitiveradioaordable,goingbeyondexi-bilitytoadaptivityinFPGAs."XcellDSPMagazine,pp.25{27,May2006.[65] Q.Zhang,F.Hoeksema,A.Kokkeler,andG.Smit,MobileMultimedia:CommunicationEngi-neeringPerspective.NovaSciencePublishers,2006,ch.TowardsCognitiveRadioForEmer-gencyNetworks.[66] M.Ahmed,H.Yanikomeroglu,andS.Mahmoud,\Fairnessenhancementoflinkadaptationtechniquesinwirelessaccessnetworks,"inProc.IEEEVeh.Technol.Conf.,vol.3,Oct.2003,pp.1554{1557.[67] M.Ahmed,H.Yanikomeroglu,D.Falconer,andS.Mahmoud,\Performanceenhancementofjointadaptivemodulation,codingandpowercontrolusingcochannel-interfererassistanceandchannelreallocation,"inProc.IEEEWirelessCommun.andNetworkingConf.,vol.1,May2003,pp.306{310.[68] T.KellerandL.Hanzo,\AdaptivemodulationtechiniquesforduplexOFDMtransmission,"IEEETrans.Veh.Technol.,vol.49,no.5,pp.1893{1906,Sept.2000.[69] S.B.Reddy,T.Yucek,andH.Arslan,\AnecientblindmodulationdetectionalgorithmforadaptiveOFDMsystems,"inProc.IEEEVeh.Technol.Conf.,Orlando,Florida,USA,Oct.2003.[70] T.YucekandH.Arslan,\Anovelsub-optimummaximum-likelihoodmodulationclassicationalgorithmforadaptiveOFDMsystems,"inProc.IEEEWirelessCommun.andNetworkingConf.,Atlanta,Georgia,USA,Mar.2004.[71] S.Anderson,H.Dam,U.Forssen,J.Karlsson,F.Kronestedt,S.Mazur,andK.J.Molnar,\AdaptiveantennasforGSMandTDMAsystems,"IEEEPersonalCommun.Mag.,vol.6,pp.74{86,June1999.[72] L.M.Tuan,P.V.Su,J.Kim,andG.Yoon,\AnewRLS-basedadaptivebeamformingalgorithmforsmartantennasappliedtoanOFDMsystem,"inProc.Int.Conf.onMicrowaveandMillimeterWaveTechnology,Aug.2002.[73] E.Telatar,\CapacityofmultiantennaGaussianchannels,"AT&TBellLaboratories,Tech.Rep.,June1995.[74] G.J.FoschiniandM.J.Gans,\Onlimitsofwirelesscommunicationsinafadingenvironmentwhenusingmultipleantennas,"WirelessPersonalCommun.,vol.6,no.3,pp.311{335,Mar.1998.[75] S.Catreux,V.Erceg,D.Gesbert,andJ.Heath,R.W.,\AdaptivemodulationandMIMOcodingforbroadbandwirelessdatanetworks,"IEEECommun.Mag.,vol.40,no.6,pp.108{115,2002.[76] S.Celebi,\Interblockinterference(IBI)andtimeofreference(TOR)computationinOFDMsystems,"IEEETrans.Commun.,vol.49,no.11,pp.1895{1900,Nov.2001.[77] Z.-Y.ZhangandL.-F.Lai,\AnovelOFDMtransmissionschemewithlength-adaptivecyclicprex,"JournalofZhejingUniversityScience,vol.5,no.11,pp.1336{1342,2004.[78] S.LeiandV.Lau,\AdaptiveinterleavingforOFDMinTDDsystems,"IEEProc.Commun.,vol.48,no.12,pp.77{80,Apr.2001.169

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K.Challapali,S.Mangold,andZ.Zhong,\Spectrumagileradio:Detectingspectrumoppor-tunities,"inProc.Int.SymposiumonAdvancedRadioTechnologies,Boulder,Colorado,USA,Mar.2004.[203] Z.TianandG.B.Giannakis,\Awaveletapproachtowidebandspectrumsensingforcognitiveradios,"inProc.IEEEInt.Conf.CognitiveRadioOrientedWirelessNetworksandCommun.(Crowncom),MykonosIsland,Greece,June2006.[204] T.Weiss,J.Hillenbrand,A.Krohn,andF.Jondral,\Ecientsignalingofspectralresourcesinspectrumpoolingsystems,"inProc.IEEESymposiumonCommun.andVeh.Technol.,Eindhoven,Netherlands,Nov.2003.[205] D.Cabric,S.Mishra,D.Willkomm,R.Brodersen,andA.Wolisz,\Acognitiveradioapproachforusageofvirtualunlicensedspectrum,"inProc.ISTMobileandWirelessCommunicationsSummit,Dresden,Germany,June2005.[206] E.Visotsky,S.Kuner,andR.Peterson,\OncollaborativedetectionofTVtransmissionsinsupportofdynamicspectrumsharing,"inProc.IEEEInt.SymposiumonNewFrontiersinDynamicSpectrumAccessNetworks,Baltimore,Maryland,USA,Nov.2005,pp.338{345.[207] I.F.Akyildiz,W.Y.Lee,M.C.Vuran,andS.Mohanty,\NeXtgeneration/dynamicspectrumaccess/cognitiveradiowirelessnetworks:Asurvey,"ComputerNetworksJournal(Elsevier),Sept.2006.[208] J.Hillenbrand,T.Weiss,andF.Jondral,\Calculationofdetectionandfalsealarmprobabilitiesinspectrumpoolingsystems,"IEEECommun.Lett.,vol.9,no.4,pp.349{351,Apr.2005.[209] N.Ahmed,D.Hadaller,andS.Keshav,\GUESS:gossipingupdatesforecientspectrumsens-ing,"inProc.InternationalworkshoponDecentralizedresourcesharinginmobilecomputingandnetworking,LosAngeles,California,USA,2006,pp.12{17.[210] B.WildandK.Ramchandran,\Detectingprimaryreceiversforcognitiveradioapplications,"inProc.IEEEInt.SymposiumonNewFrontiersinDynamicSpectrumAccessNetworks,Baltimore,Maryland,USA,Nov.2005,pp.124{130.[211] D.Hunold,A.Barreto,G.Fettweis,andM.Mecking,\Conceptforuniversalaccessandconnectivityinmobileradionetworks,"inProc.IEEEInt.SymposiumonPersonal,IndoorandMobileRadioCommun.,vol.2,London,UK,Sept.2000,pp.847{851.[212] T.ClancyandB.Walker,\Predictivedynamicspectrumaccess,"inProc.SDRForumTech-nicalConference,Orlando,Florida,USA,Nov.2006.[213] C.Cordeiro,K.Challapali,andD.Birru,\IEEE802.22:Anintroductiontotherstwirelessstandardbasedoncognitiveradios,"Journalofcommunications,vol.1,no.1,Apr.2006.[214] P.Kolodzyetal.,\Nextgenerationcommunications:Kickomeeting,"inProc.DARPA,Oct.2001.[215] R.Matheson,\Theelectrospacemodelasafrequencymanagementtool,"inInt.SymposiumOnAdvancedRadioTechnologies,Boulder,Colorado,USA,Mar.2003,pp.126{132.[216] W.D.Horne,\Adaptivespectrumaccess:Usingthefullspectrumspace,"inProc.AnnualTelecommunicationsPolicyResearchConf.,Arlington,Virginia,Oct.2003.[217] J.Andrews,\Interferencecancellationforcellularsystems:acontemporaryoverview,"IEEEWirelessCommun.Mag.,vol.12,no.2,pp.19{29,2005.178

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E.Kerherve,W.Akmouche,andA.Quinquis,\OFDMbandwidthestimationusingMorlet'swaveletdecomposition,"inProc.IEEE/AFCEAInf.SystemsforEnhancedPublicSafetyandSecurity,Munich,Germany,May2000,pp.62{66.[234] P.Liu,B.Li,Z.Lu,andF.Gong,\AnOFDMbandwidthestimationschemeforspectrummonitoring,"inProc.Int.Conf.WirelessCommun.,NetworkingandMobileComputing,vol.1,Maui,Hawaii,USA,Sept.2005,pp.248{251.[235] R.HeathJrandG.Giannakis,\Exploitinginputcyclostationarityforblindchannelidenti-cationinOFDMsystems,"IEEETrans.SignalProcessing,vol.47,no.3,pp.848{856,Mar.1999.[236] H.Nogami,S.Tsuruga,andN.Morinaga,\AtransmissionmodedetectorforOFDMsystems,"ElectronicsandCommunicationsinJapan(PartICommunications),vol.86,no.8,pp.79{94,Mar.2003.[237] M.WaxandT.Kailath,\Detectionofsignalsbyinformationtheoreticcriteria,"IEEETrans.Acoust.,Speech,SignalProcessing,vol.33,no.2,pp.387{392,Apr.1985.[238] R.Roy,A.Paulraj,andT.Kailath,\ESPRIT{asubspacerotationapproachtoestimationofparametersofcisoidsinnoise,"IEEETrans.Acoust.,Speech,SignalProcessing,vol.34,no.5,pp.1340{1342,Oct.1986.[239] B.Muquet,M.deCourville,P.Duhamel,andB.Stepmind,\Subspace-basedblindandsemi-blindchannelestimationforOFDMsystems,"IEEETrans.SignalProcessing,vol.50,no.7,pp.1699{1712,July2002.[240] J.vandeBeek,M.Sandell,andP.Borjesson,\MLestimationoftimeandfrequencyosetinOFDMsystems,"IEEETrans.SignalProcessing,vol.45,no.7,pp.1800{1805,July1997.[241] M.Speth,F.Classen,andH.Meyr,\FramesynchronizationofOFDMsystemsinfrequencyselectivefadingchannels,"inProc.IEEEVeh.Technol.Conf.,vol.3,Phoenix,Arizona,USA,May1997,pp.1807{1811.[242] T.Keller,L.Piazzo,P.Mandarini,andL.Hanzo,\Orthogonalfrequencydivisionmultiplexsynchronizationtechniquesforfrequency-selectivefadingchannels,"IEEEJ.Select.AreasCommun.,vol.19,no.6,pp.999{1008,June2001.[243] R.MeyerandM.Newhouse,\OFDMwaveformfeaturesuppression,"inProc.IEEEMilitaryCommun.Conf.,vol.1,Anaheim,California,USA,Oct.2002,pp.582{586.[244] S.C.SurenderandR.M.Narayanan,\Synchronizationforwirelessmulti-radarcovertcommu-nicationnetworks,"inProceedingsofSPIEDefenseTransformationandNet-CentricSystems,Orlando,Florida,USA,Apr.2007.[245] X.Wang,P.Ho,andY.Wu,\RobustchannelestimationandISIcancellationforOFDMsystemswithsuppressedfeatures,"IEEEJ.Select.AreasCommun.,vol.23,no.5,pp.963{972,May2005.[246] I.Reed,\OnamomenttheoremforcomplexGaussianprocesses,"IEEETrans.Inform.The-ory,vol.8,no.3,pp.194{195,Apr.1962.[247] S.Kay,Fundamentalsofstatisticalsignalprocessing:estimationtheory.UpperSaddleRiver,NewJersey,USA:Prentice-HallInc.,1993.180

PAGE 196

Using(A.1)anddenitionofcorrelation,thecorrelationofCFRmagnitudecanbeformulatedasRjHj2()=Em;kjHm(k)j2jHm(k+)j2(A.2)=1 Thesummandsin(A.3)equatetozeroexceptforthefollowingcases1.

PAGE 197

where()Tdenotesthetransposeand@g(P)=@Pisdenedas@g(P) UsingthedenitionofRMSdelayspread(3.22),thepartialswithrespecttoeachtapcanbeobtainedas@g(P) 2rms"2i TheLLmatrixI(P)istheFisherinformationmatrixanditisdenedby[I(P)]ij=E@2lnp(h;P) wherep(h;P)isthelikelihoodfunctionofchannelimpulseresponse(CIR)vectorh=[h1h2hL]conditionedonP.WemodelchanneltapshiasindependentcomplexGaussianrandomvariables.Hence,p(h;P)canbeeasilyformulated.Wheneachchanneltapisassumedtobeindependentofeachother,theFishermatrixbecomesadiagonalmatrixwhosediagonalentriescanbecalculatedas[I(P)]ii=Nf whereNfisthenumberofavailableCIRs,i.e.numberofframesoverwhichtheestimationisperformed.Consequently,theinverseofI(P)caneasilybeobtainedasI1(P)ii=P2i

PAGE 199

Itfollowsfrom(C.1)thatthesecondproducttermin(8.11)canbedroppedasp(y[n])isnotafunctionofunknownparametersset.Then,thelog-likelihoodfunctioncanbewrittenas(y;ND;NG;)=Xn2logp(y[n];y[n+ND]) Thenumeratorof(C.2)hasabivariatecomplexGaussiandistribution,whosePDFcanbefoundusing(8.9)as[240].p(r[n];r[n+ND])=1 wherethevariableaisgivenasa=2s Byinserting(C.1)and(C.3)into(C.2),andaftersomesimplications,thelog-likelihoodfunctioncanbefoundas(y;ND;NG;)=Xn2y(n)y(n+ND)Xn2a 2a(2s+2w)(1a2)log(1a2):(C.5) PleasenotethattheCPsetisnotknownanddependsonthesymbolandcyclicprex(CP)durations.Thissetisdenedasfollowing:=nnm(ND+NG)+p+;m=f0;1;;D ND+NG1g;p=f1;2;;NGg;=f0;1;;ND1go:(C.6)185


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Channel, spectrum, and waveform awareness in OFDM-based cognitive radio systems
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ABSTRACT: The radio spectrum is becoming increasingly congested everyday with emerging technologies and with the increasing number of wireless devices. Considering the limited bandwidth availability, accommodating the demand for higher capacity and data rates is a challenging task, requiring innovative technologies that can offer new ways of exploiting the available radio spectrum. Cognitive radio arises to be a tempting solution to the spectral crowding problem by introducing the notion of opportunistic spectrum usage. Because of its attractive features, orthogonal frequency division multiplexing (OFDM) has been successfully used in numerous wireless standards and technologies. We believe that OFDM will play an important role in realizing the cognitive radio concept as well by providing a proven, scalable, and adaptive technology for air interface. The goal of this dissertation is to identify and address some of the challenges that arise from the introduction of cognitive radio.Specifically, we propose methods for obtaining awareness about channel, spectrum, and waveform in OFDM-based cognitive radio systems in this dissertation. Parameter estimation for enabling adaptation, spectrum sensing, and OFDM system identification are the three main topics discussed. OFDM technique is investigated as a candidate for cognitive radio systems. Cognitive radio features and requirements are discussed in detail, and OFDM's ability to satisfy these requirements is explained. In addition, we identify the challenges that arise from employing OFDM technology in cognitive radio. Algorithms for estimating various channel related parameters are presented. These parameters are vital for enabling adaptive system design, which is a key requirement for cognitive radio. We develop methods for estimating root-mean-square (RMS) delay spread, Doppler spread, and noise variance.The spectrum opportunity and spectrum sensing concepts are re-evaluated by considering different dimensions of the spectrum which is known as multi-dimensional spectrum space. Spectrum sensing problem in a multi-dimensional space is addressed by developing a new sensing algorithm termed as partial match filtering (PMF). Cognitive radios are expected to recognize different wireless networks and have capability of communicating with them. Algorithms for identification of multi-carrier transmissions are developed. Within the same work, methods for blindly detecting transmission parameters of an OFDM based system are developed. Blind detection is also very helpful in reducing system signaling overhead in the case of adaptive transmission where transmission parameters are changed depending on the environmental characteristics or spectrum availability.
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Wireless communications.
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Spectrum sensing.
Adaptation.
Parameter estimation.
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