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Advanced transceiver algorithms for OFDM(A) systems

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Advanced transceiver algorithms for OFDM(A) systems
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Mahmoud, Hisham A
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Wireless communications
Cognitive radio
Initial ranging
Channel estimation
Spectrum shaping
Dissertations, Academic -- Electrical Engineering -- Doctoral -- USF   ( lcsh )
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non-fiction   ( marcgt )

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ABSTRACT: With the increasing advancements in the digital technology, future wireless systems are promising to support higher data rates, higher mobile speeds, and wider coverage areas, among other features. While further technological developments allow systems to support higher computational complexity, lower power consumption, and employ larger memory units, other resources remain limited. One such resource, which is of great importance to wireless systems, is the available spectrum for radio communications. To be able to support high data rate wireless applications, there is a need for larger bandwidths in the spectrum. Since the spectrum cannot be expanded, studies have been concerned with fully utilizing the available spectrum. One approach to achieve this goal is to reuse the available spectrum through space, time, frequency, and code multiplexing techniques. Another approach is to optimize the transceiver design as to achieve the highest throughput over the used spectrum.From the physical layer perspective, there is a need for a highly flexible and efficient modulation technique to carry the communication signal. A multicarrier modulation technique known as orthogonal frequency division multiplexing (OFDM) is one example of such a technique. OFDM has been used in a number of current wireless standards such as wireless fidelity (WiFi) and worldwide interoperability for microwave access (WiMAX) standards by the Institute of Electrical and Electronics Engineers (IEEE), and has been proposed for future 4G technologies such as the long term evolution (LTE) and LTE-advanced standards by the 3rd Generation Partnership Project (3GPP), and the wireless world initiative new radio (WINNER) standard by the Information society technologies (IST). This is due to OFDM's high spectral efficiency, resistance to narrow band interference, support for high data rates, adaptivity, and scalability.In this dissertation, OFDM and multiuser OFDM , also known as orthogonal frequency division multiple access (OFDMA), techniques are investigated as a candidate for advanced wireless systems. Features and requirements of future applications are discussed in detail, and OFDM's ability to satisfy these requirements is investigated. We identify a number of challenges that when addressed can improve the performance and throughput of OFDM-based systems. The challenges are investigated over three stages. In the first stage, minimizing, or avoiding, the interference between multiple OFDMA users as well as adjacent systems is addressed. An efficient algorithm for OFDMA uplink synchronization that maintains the orthogonality between multiple users is proposed. For adjacent channel interference, a new spectrum shaping method is proposed that can reduce the out-of-band radiation of OFDM signals.Both methods increase the utilization of available spectrum and reduce interference between different users. In the second stage, the goal is to maximize the system throughput for a given available bandwidth. The OFDM system performance is considered under practical channel conditions, and the corresponding bit error rate (BER) expressions are derived. Based on these results, the optimum pilot insertion rate is investigated. In addition, a new pilot pattern that improves the system ability to estimate and equalize various radio frequency (RF) impairments is proposed. In the last stage, acquiring reliable measurements regarding the received signal is addressed. Error vector magnitude (EVM) is a common performance metric that is being used in many of today's standards and measurement devices. Inferring the signal-to-noise ratio (SNR) from EVM measurements has been investigated for either high SNR values or data-aided systems.We show that using current methods does not yield reliable estimates of the SNR under other conditions. Thus, we consider the relation between EVM and SNR for nondata-aided systems. We provide expressions that allow for accurate SNR estimation under various practical channel conditions.
Thesis:
Dissertation (Ph.D.)--University of South Florida, 2009.
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Includes bibliographical references.
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by Hisham A. Mahmoud.
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Document formatted into pages; contains 159 pages.
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Includes vita.

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usfldc doi - E14-SFE0002891
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AdvancedTransceiverAlgorithmsforOFDM(A)Systems by HishamA.Mahmoud Adissertationsubmittedinpartialfulllment oftherequirementsforthedegreeof DoctorofPhilosophy DepartmentofElectricalEngineering CollegeofEngineering UniversityofSouthFlorida MajorProfessor:HuseyinArslan,Ph.D. KenChristensen,Ph.D. RichardD.Gitlin,Sc.D. JosephMitolaIII,Ph.D. RaviSankar,Ph.D. DateofApproval: March25,2009 Keywords:Wirelesscommunications,cognitiveradio,initialranging,channelest imation,spectrum shaping,IQimbalances,errorvectormagnitude,SNRestimation. c r Copyright2009,HishamA.Mahmoud

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DEDICATION Tomyparents.

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ACKNOWLEDGEMENTS First,IwouldliketothankDr.HuseyinArslanforhissupportandadvicet hroughoutthe durationofmystudyatUSF.Withoutthelengthydiscussionswehadandwithouthisg uidance, thisdissertationwouldnotbethesame.IwishtothankDr.KenChristensen,Dr. RichardD. Gitlin,Dr.JosephMitolaIII,andDr.RaviSankarforagreeingtoservei nmycommittee;andfor theirvaluabletime,feedback,andsuggestions.IamalsothankfultoDr.Nagar ajanRanganathan forchairingmydefense.IwouldliketoacknowledgeDr.ParisWiley,Gayla Montgomery,Irene Wiley,BeckyBrenner,andNormaPazfromtheElectricalEngineeringDepartmentat USFwho havebeenalwayshelpfulandunderstanding.Toallofyou,Iamverythankful. IowemuchtoDr.KemalOzdemirandFrancisRetnasothieatLogusBroadbandWireless SolutionsInc.whosupportedmyresearchnanciallyforthemajorityofmyPh.D. durationand continuouslyoeredtheiradviceandhelp.IamalsogratefultomycolleaguesatUSF andmyfriends attheWirelessCommunicationsandSignalProcessing(WCSP)group.Iwouldlike toespecially mentionDr.TevkYucek,Dr.IsmailGuvenc,Dr.HasariCelebi,AliGorcin,Serhan Yarkan,and MustafaEminSahin. Lastbutbynomeansleast,Ithankmyparents,mygrandparents,mysister,mytw obrothers, andmywife.Iwouldliketoexpressmydeepestgratitudetomyparentswhomthisw orkisdedicated to.Withoutyourunconditionalsupport,yourkindwords,andyoursoundadvice,Iwoul dnotbe thepersonIamtoday.

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TABLEOFCONTENTS LISTOFTABLES iv LISTOFFIGURES v LISTOFACRONYMS viii ABSTRACT xiii CHAPTER1INTRODUCTION 1 1.1OFDMTechnology 2 1.2DissertationOutline 3 1.2.1Chapter2:OFDMforCognitiveRadio,MeritsandChallenges81.2.2Chapter3:SynchronizationinOFDMAUplinkSystems81.2.3Chapter4:SpectrumShapingofOFDM-basedCognitive RadioSignals 8 1.2.4Chapter5:AnalysisandOptimizationofOFDMAUplink SystemsOverTime-VaryingFrequency-SelectiveRayleighFadingChannels 9 1.2.5Chapter6:IQImbalanceCorrectionforOFDMAUplinkSystems91.2.6Chapter7:ErrorVectorMagnitudeBasedSNREstimation inBlindReceivers 10 CHAPTER2OFDMFORCOGNITIVERADIO:MERITSANDCHALLENGES11 2.1Introduction 11 2.2ABasicOFDMSystemModel 12 2.3OFDM-BasedCR 17 2.4WhyOFDMisaGoodFitforCR 17 2.4.1SpectrumSensingandAwareness 18 2.4.2SpectrumShaping 20 2.4.3AdaptingtotheEnvironment 21 2.4.4AdvancedAntennaTechniques 22 2.4.5MultipleAccessingandSpectralAllocation222.4.6Interoperability 23 2.5ChallengestoCognitiveOFDMSystems 24 2.5.1MultibandOFDMSystemDesign 25 2.5.2LocationAwareness 28 2.5.3SignalingtheTransmissionParameters292.5.4Synchronization 30 2.5.5MutualInterference 30 2.6AStepTowardCognitive-OFDM:StandardsandTechnologies32 2.6.1IEEE802.16 32 2.6.2IEEE802.22 35 2.6.3IEEE802.11 36 i

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2.7Conclusion 38 CHAPTER3SYNCHRONIZATIONINOFDMAUPLINKSYSTEMS39 3.1Introduction 39 3.2SystemModel 41 3.3ExistingRangingAlgorithms 43 3.4ProposedAlgorithm 44 3.4.1EnergyDetector 45 3.4.2TimingOsetEstimation 48 3.4.3CodeDetector 51 3.5ComputationalComplexity 52 3.6SimulationResults 54 3.6.1SystemSetup 54 3.6.2ChannelModel 55 3.6.3ProposedAlgorithmPerformance 57 3.7Conclusions 61 CHAPTER4SPECTRUMSHAPINGOFOFDM-BASEDCOGNITIVERADIOSIGNALS64 4.1Introduction 64 4.2SystemModel 65 4.3ActiveCancellationCarriers 65 4.4CycliclyExtendedOFDMSignals 68 4.5RaisedCosineWindowing 70 4.6CombiningCancellationCarriersandRaisedCosineWindowing734.7ProposedAlgorithm 73 4.7.1ProposedSystemModel 75 4.7.2AdaptiveSymbolTransition 75 4.7.3SimulationResults 78 4.8Conclusions 79 CHAPTER5ANALYSISANDOPTIMIZATIONOFOFDMAUPLINKSYSTEMSOVER TIME-VARYINGFREQUENCY-SELECTIVERAYLEIGHFADINGCHAN-NELS 81 5.1Introduction 81 5.2SystemModel 83 5.2.1ChannelModel 83 5.2.2SignalModel 84 5.3ChannelEstimationandEqualization 86 5.4BitErrorRateAnalysis 88 5.5OptimumTileDimensions 92 5.6SimulationResults 94 5.7Conclusion 99 CHAPTER6IQIMBALANCECORRECTIONFOROFDMAUPLINKSYSTEMS102 6.1Introduction 102 6.2SystemModel 103 6.3Channel/IQEqualization 105 6.4Channel/IQEstimation 108 6.5SimulationResults 110 6.6Conclusion 112 ii

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CHAPTER7ERRORVECTORMAGNITUDEBASEDSNRESTIMATIONINBLIND RECEIVERS 114 7.1Introduction 114 7.2SignalModel 116 7.3ErrorVectorMagnitude 116 7.4RelatingEVMtoSNR 117 7.5EVM-SNRforNondata-AidedReceivers 119 7.5.1DetectionOverAWGNChannels 119 7.5.2DetectionoverRayleighFadingChannels1277.5.3DetectionwithOtherImpairments128 7.6SimulationResultsandDiscussion 131 7.7Conclusion 137 CHAPTER8CONCLUSIONANDFUTUREWORK 138 8.1Contributions 138 8.2FinalRemarksandFutureWork 140 REFERENCES 142 APPENDICES 152 AppendixA 153 AppendixB 155 AppendixC 156 AppendixD 158 ABOUTTHEAUTHOR EndPage iii

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LISTOFTABLES Table2.1OFDM-basedwirelessstandards. 18 Table2.2OFDMpropertiesvs.CRrequirements. 19 Table2.3AdvancedantennafeaturesofWiMAX. 34 Table3.1SINRvs.numberofusersperOFDMAsymbol.51Table3.2Proposedalgorithm'scomputationalcomplexity.54Table3.3CharacteristicsoftheITUVehicularAchannelenvironment.55Table4.1IncreaseinaverageOFDMsymbolenergy E r .68 Table5.1SimulationparametersforatypicalOFDMAULsystemI.94Table6.1SimulationparametersforatypicalOFDMAULsystemII.110 iv

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LISTOFFIGURES Figure1.1BasicelementsofthePHYindigitalcommunicationsystems.4Figure1.2OFDMsubcarrierassignmentwithinusedavailablebandsinCRsyst ems.5 Figure2.1BlockdiagramofagenericOFDMtransceiver.13Figure2.2OFDMwaveform. 14 Figure2.3Multipathchannels. 15 Figure2.4OFDM-basedCRsystemblockdiagram. 18 Figure2.5SpectrumsensingandshapingusingOFDM. 20 Figure2.6OFDM-basedwirelesstechnologies. 23 Figure2.7ResearchchallengesinCRandOFDM. 24 Figure2.8FillingspectrumholesusingSB-OFDMorMB-OFDMsignals.26Figure2.9FillingspectrumholesusingSB-OFDMorMB-OFDMsignals.27Figure2.10Sub-bandsofMB-OFDM-basedUWBsystemsinfrequencydomain.28Figure2.11PowerspectrumdensityofasingleOFDMsubcarrier.30Figure2.12RCwindowingwithdierentrollo( )values.31 Figure2.13RolloeectonthePSDofasingleOFDMsubcarrier.31Figure2.14IllustrationofOFDMAsignalstructureusedinWiMAX.35Figure2.15Standardsandtechnologiesdevelopments. 37 Figure3.1 P fa and P md fordierentnoiselevels. 48 Figure3.2NormalizedmeasuredenergyontherangingchannelatSNR=10dB.49Figure3.3 E f ~ E r ( u ) j u = k g and E f ~ E r ( u ) j u 6 = k g fordierentnumbersofrangingusers. 51 Figure3.4Theeectofsynchronizationerrorontheconstellationpointsof a typicalBPSK-modulatedOFDMAsymbolreceivedoverAWGNanddispersivechannels. 56 v

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Figure3.5Pr fj ~ E r ( u ) j > 2 j u = k g andPr fj ~ E r ( u ) j > 2 j u 6 = k g fordierent valuesof 2 overnondispersiveanddispersivechannels.57 Figure3.6Probabilityofmisseddetection. 58 Figure3.7Probabilityoffalsealarm. 59 Figure3.8Standarddeviationoftimingerrors. 60 Figure3.9Computationalcomplexityreductionusingtheproposedalgorithm.6 1 Figure3.10Probabilitiesofmisseddetectionandfalsealarmfor N =1024and N =512. 62 Figure3.11Standarddeviationoftimingerrorsfor N =1024and N =512.63 Figure4.1NumberofCCeectonthesignalPSD. 67 Figure4.2GapsizeeectoneectonthesignalPSD. 68 Figure4.3CPsizeeectonthesignalPSD. 70 Figure4.4RollofactoreectontheRC-windowedsignalPSD.72Figure4.5GapsizeeectontheRC-windowedsignalPSD.72Figure4.6CombinedRCwindowingandCCeectonthesignalPSD.74Figure4.7SystemModel. 75 Figure4.8OutputoftheASTblock. 77 Figure4.9SpectrumofanOFDMsignalwith32subcarriersgap.79Figure4.10SpectrumofanOFDMsignalwith12subcarriersguardband.80Figure5.1ULframestructureandsubcarriermappingtotiles.85Figure5.2ThesubindexofoneOFDMAULtile. 86 Figure5.3UncodedBERofOFDMAULsystemoverPedestrianBchannel.95Figure5.4UncodedBERofOFDMAULsystemoverVehicularAchannel.95Figure5.5UncodedBERofOFDMAULsystemoverIndoorAchannel.96Figure5.6MaximumthroughputofOFDMAULsystemwith64QAMmodulationatSNR=35dBoverVehicularAchannel.97 Figure5.7EectivethroughputofOFDMAULsystemwith64QAMmodulation andrate1/2convolutioncoding,atSNR=35dBoverVehicularAchannel.97 Figure5.8MaximumthroughputofOFDMAULsystemwithQPSKmodulation atSNR=15dBoverPedestrianBchannel. 98 vi

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Figure5.9EectivethroughputofOFDMAULsystemwithQPSKmodulation andrate1/2convolutioncoding,atSNR=15dBoverPedestrianBchannel.98 Figure5.10UncodedBER,codedBER,andFERofOFDMAULsystemwith QPSKmodulationoverPedestrianBchannelwhere n t =3and k t =4.99 Figure5.11UncodedBER,codedBER,andFERofOFDMAULsystemwith QPSKmodulationoverPedestrianBchannelwhere n t =9and k t =12.100 Figure5.12EectivethroughputofOFDMAULsystemwith64QAMmodulation andrate1/2convolutioncodingoverVehicularAchannel.100 Figure5.13EectivethroughputofOFDMAULsystemwithQPSKmodulation andrate1/2convolutioncodingoverPedestrianBchannel.101 Figure6.1ULframestructureandsubcarriermappingtotiles.106Figure6.2Receiverblockdiagramof(a)conventionalOFDMA-ULsystem,and (b)AnOFDMA-ULsystemforsignalswithIQdistortion.107 Figure6.3Subcarrierindexingofatilepair. 108 Figure6.4AverageuncodedBERofQPSKsignalsreceivedoverPedestrianB channelandwithIQimpairments. 112 Figure6.5AverageuncodedBERofQPSKsignalsreceivedoverVehicularA channelandwithIQimpairments. 113 Figure6.6AverageuncodedBERofQPSKsignalsreceivedoverIndoorAchannelandwithIQimpairments. 113 Figure7.1MeasuredversusidealEVMmeasurementsinnondata-aidedreceivers.119Figure7.2MeasuredversusidealandtrueEVMmeasurementsinnondata-aided receiversoverAWGNchannels. 131 Figure7.3MeasuredversusidealandtrueEVMmeasurementsinnondata-aided receiversoverRayleighfadingchannels. 132 Figure7.4MeasuredversusidealandtrueEVMmeasurementsinnondata-aided receiverswithIQimpairmentsandAWGNnoise.133 Figure7.5NormalizedMSEofSNRestimatorsfordierentvaluesof N .134 Figure7.6NormalizedMSEoftrue-EVM-basedSNRestimatorunderdierent impairmentsandfordierentvaluesof N 135 Figure7.7NormalizedMSEofideal-EVMdata-aidedandtrue-EVMnondataaidedSNRestimatorsunderdierentchannelestimationerrorlevelsandfordierentvaluesof N 136 vii

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LISTOFACRONYMS 3GPP3rdGenerationPartnershipProjectAASadaptiveantennasystemsACIadjacentchannelinterferenceADCanalogtodigitalconverterADSLasymmetricdigitalsubscriberlineAMSadaptiveMIMOswitchingAPaccesspointASTadaptivesymboltransitionAWGNadditivewhiteGaussiannoiseBEMbasisexpansionmodelBERbiterrorrateBPSKbinaryphaseshiftkeyingBSbasestationBSCbinarysymmetricchannelCCcancellationcarrierCCIco-channelinterferenceCDFcumulativedistributionfunctionCDMAcodedivisionmultipleaccessCFRchannelfrequencyresponseCINRcarrier-to-interference-plus-noiseratioCIRchannelimpulseresponseCPcyclicprexCRcognitiveradio viii

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CRCcyclicredundancycheckCSMAcarriersensemultipleaccessingDABdigitalaudiobroadcastingDACdigitaltoanalogconverterDFSdynamicfrequencyselectionDLdownlinkDS-CDMAdirectspreadcodedivisionmultipleaccessDVBdigitalvideobroadcastingDVB-TterrestrialdigitalvideobroadcastingEVMerrorvectormagnitudeFDMAfrequencydivisionmultipleaccessingFECforwarderrorcorrectionFERframeerrorrateFFTfastFouriertransformFHDCfrequencyhoppingdiversitycombiningIinphaseICIinter-carrierinterferenceIEEEInstituteofElectricalandElectronicsEngineersIFintermediatefrequencyIFFTinversefastFouriertransformi.i.d.independentandidenticallydistributedISIinter-symbolinterferenceISTInformationsocietytechnologiesITUInternationalTelecommunicationUnionLNAlownoiseamplierLOlocaloscillatorLOSline-of-sight ix

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LSleastsquaresLTElongtermevolutionLUlicenseduserMACmediumaccesscontrolMB-OFDMmulti-bandOFDMMC-CDMAmulti-carriercodedivisionmultipleaccessMIMOmultiple-inputmultiple-OutputMLmaximumlikelihoodMMSEminimummean-squareerrorMSEmean-squared-errorMUImultiuserinterferenceNBInarrow-bandinterferenceNLOSnon-line-of-sightOFDMorthogonalfrequencydivisionmultiplexingOFDMAorthogonalfrequencydivisionmultipleaccessPApoweramplierPAMpulseamplitudemodulationPAPRpeak-to-average-powerratioPDFprobabilitydensityfunctionPHYphysicallayerPSAMpilot-symbol-aidedmodulationPSDpowerspectraldensityQquadratureQAMquadratureamplitudemodulationQPSKquadraturephaseshiftkeyingRCraisedcosineRFradiofrequency x

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RMSroot-mean-squaredRSSIreceivedsignalstrengthindicatorRTDroundtripdelayRUrentaluserSB-OFDMsingle-bandOFDMSDRsoftwaredenedradioSERsymbolerrorrateSINRsignal-to-interference-plus-noiseratioSMspatialmultiplexingSNRsignal-to-noiseratioSSsubscriberstationSTCspacetimecodingSVDsingularvaluedecompositionTDMAtimedivisionmultipleaccessTOAtimeofarrivalTPCtransmitpowercontrolUCDuplinkchanneldescriptorULuplinkUWBultrawidebandVSAvectorsignalanalyzerWiFiwirelessdelityWiMAXworldwideinteroperabilityformicrowaveaccessWINNERwirelessworldinitiativenewradioWLANwirelesslocalareanetworkWMANwirelessmetropolitanareanetworkWPANwirelesspersonalareanetworkWRANwirelessregionalareanetwork xi

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WSSwide-sensestationaryZFzero-forcing xii

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ADVANCEDTRANSCEIVERALGORITHMSFOROFDM(A)SYSTEMS HishamA.Mahmoud ABSTRACT Withtheincreasingadvancementsinthedigitaltechnology,futurewirelesssyst emsarepromising tosupporthigherdatarates,highermobilespeeds,andwidercoverageareas,amongo therfeatures. Whilefurthertechnologicaldevelopmentsallowsystemstosupporthighercomputati onalcomplexity, lowerpowerconsumption,andemploylargermemoryunits,otherresourcesremainlim ited.One suchresource,whichisofgreatimportancetowirelesssystems,istheavai lablespectrumforradio communications.Tobeabletosupporthighdataratewirelessapplications,ther eisaneedfor largerbandwidthsinthespectrum.Sincethespectrumcannotbeexpanded,studieshavebeenconcernedwithfullyutilizingtheavailablespectrum.Oneapproachtoachievethisg oalistoreuse theavailablespectrumthroughspace,time,frequency,andcodemultiplexingtechniques.A nother approachistooptimizethetransceiverdesignastoachievethehighestthroughputov ertheused spectrum. Fromthephysicallayerperspective,thereisaneedforahighlyrexibleandecientmo dulation techniquetocarrythecommunicationsignal.Amulticarriermodulationtechnique knownasorthogonalfrequencydivisionmultiplexing(OFDM)isoneexampleofsuchatechnique.OF DMhas beenusedinanumberofcurrentwirelessstandardssuchaswirelessdelity(WiFi)a ndworldwide interoperabilityformicrowaveaccess(WiMAX)standardsbytheInstitute ofElectricalandElectronicsEngineers(IEEE),andhasbeenproposedforfuture4Gtechnologiessuchas thelongterm evolution(LTE)andLTE-advancedstandardsbythe3rdGenerationPartnershipPr oject(3GPP), andthewirelessworldinitiativenewradio(WINNER)standardbytheInfor mationsocietytechnologies(IST).ThisisduetoOFDM'shighspectraleciency,resistancetonarrowbandi nterference, supportforhighdatarates,adaptivity,andscalability. xiii

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Inthisdissertation,OFDMandmultiuserOFDM,alsoknownasorthogonalfreq uencydivision multipleaccess(OFDMA),techniquesareinvestigatedasacandidateforadvancedwi relesssystems. Featuresandrequirementsoffutureapplicationsarediscussedindetail,andOFDM's abilitytosatisfytheserequirementsisinvestigated.Weidentifyanumberofchallengesthat whenaddressedcan improvetheperformanceandthroughputofOFDM-basedsystems.Thechallengesarein vestigated overthreestages.Intherststage,minimizing,oravoiding,theinterferenceb etweenmultiple OFDMAusersaswellasadjacentsystemsisaddressed.AnecientalgorithmforOFD MAuplink synchronizationthatmaintainstheorthogonalitybetweenmultipleusersispr oposed.Foradjacent channelinterference,anewspectrumshapingmethodisproposedthatcanreducetheout-of-bandradiationofOFDMsignals.Bothmethodsincreasetheutilizationofavail ablespectrumandreduce interferencebetweendierentusers. Inthesecondstage,thegoalistomaximizethesystemthroughputforagivenav ailablebandwidth.TheOFDMsystemperformanceisconsideredunderpracticalchannelconditions,andthecorrespondingbiterrorrate(BER)expressionsarederived.Basedontheseresults ,theoptimum pilotinsertionrateisinvestigated.Inaddition,anewpilotpatternthatim provesthesystemability toestimateandequalizevariousradiofrequency(RF)impairmentsisproposed. Inthelaststage,acquiringreliablemeasurementsregardingthereceivedsignali saddressed. Errorvectormagnitude(EVM)isacommonperformancemetricthatisbeingused inmanyof today'sstandardsandmeasurementdevices.Inferringthesignal-to-noiseratio(SN R)fromEVM measurementshasbeeninvestigatedforeitherhighSNRvaluesordata-aidedsystems .Weshowthat usingcurrentmethodsdoesnotyieldreliableestimatesoftheSNRunderotherconditions.Th us, weconsidertherelationbetweenEVMandSNRfornondata-aidedsystems.Weprovideex pressions thatallowforaccurateSNRestimationundervariouspracticalchannelconditions. xiv

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CHAPTER1 INTRODUCTION Withtheincreasingdemandformoreapplicationstobecomewireless,wirelesssy stemsare challengedtomeethigherdataraterequirements.Consideringthefrequencyspectrumasbei nga limitedandvaluableresource,wirelessdevicesarefacedwiththenecessitytoutili zetheavailable opportunitiesofthespectrumandcoexistwithotherlegacyorotherwisefuturesy stems. Studiestoincreasethesystemthroughputhavebeenconcernedwithimprovingsignaldetection algorithmsandreducingtheimpactofvariouspracticalimpairmentstowireless signals.Timing andfrequencyosets,radiochannelpropagationeects,andbasebandmodulatorgainand phase imbalancesareexamplesofsignaldegradationsourcesthatneedtobeestimatedandeq ualized. Minimizingtheeectsoftheseimpairmentsincreasetheeectivesignal-to-noisera tio(SNR)atthe receiverandallowthesystemtosupporthighermodulationordersandconsequentlyhig herdata rates.Thisapproachcanbeconsideredasmaximizingthesystemspectraleciencyfo ragiven allocatedspectrumorbandwidth. Recently,anewdirectionforutilizingtheavailablespectrumhasbeensuggested.This approach callsforallowingnon-licensedusers,alsocalledrentalorsecondaryusers,toop eratewithinlicensed bandsthatarenotheavilyoccupiedbytheirintendedusers,alsocalledlicensedorprimary users. Thesecondaryusers,however,canonlyoperatewithinlicensedbandgiventheydonotinter fereor blocktheprimaryusers.Recentmeasurementsshowthatwiderangesofthelicensedspect rumare rarelyusedmostofthetime,whileotherbandsareheavilyoccupied[1].Thisindicates thatthe aboveapproachcansignicantlyimprovethespectrumutilization.Thisoppor tunisticuseofthe spectrumhasbeenproposedbytheuseofcognitiveradio(CR)[2{4].Theforma ldenitionofCR hasnotbeenagreeduponatthemoment,butCRcanbedenedasanintelligentwirelesss ystem thatisawareofitssurroundingenvironmentthroughsensingandmeasurements;as ystemthatuses itsgainedexperiencetoplanfutureactionsandadapttoimprovetheoverallcommuni cationquality 1

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andmeetuser'sneeds.Itisnoteworthytomentionthatsystemsbasedontheabove approachhas alsobeenreferredtoasspectrumsharingsystemsandoverlaysystems. Consideringtheabovetwoapproachestodesigningfuturewirelesssystems,itcan beinferredthat thereisaneedforaphysicallayer(PHY)whichishighlyrexible,adaptable,andspect rumecient. Ononehand,detectedspectrumopportunitiesshouldbeexploitedbyshapingthetransmittedsignalaccordingly.Ontheotherhand,thesystemshouldbeabletoutilizeavailabl emeasurements regardingtheoperationalenvironmenttomaximizethespectraleciencyonusedbands .Theability tosupportmultipleusersisalsoanimportantaspectofwirelesssystems .Orthogonalfrequency divisionmultiplexing(OFDM)technologyisaspecialcaseofmulticarriersy stemsthat,webelieve, hasthepotentialoffulllingtheaforementionedrequirements. Inthischapter,abriefintroductiontoOFDMtechnologyisgivenfollowedbya noutlineofthe remainderofthisdissertation.1.1OFDMTechnology OFDMisoneofthemostwidelyusedtechnologiesincurrentcommunicationsystems. Theuse ofOFDMcanbefoundinthePHYoflegacystandardssuchasthewirelesslocalarea network (WLAN)[5{7],wirelessmetropolitanareanetwork(WMAN)standards[8 ,9],andasymmetric digitalsubscriberline(ADSL)[10].InEurope,OFDMisusedbythedigitalaudi obroadcasting (DAB)[11]andterrestrialdigitalvideobroadcasting(DVB-T)[12]standa rds.OFDMisalsoastrong candidateforfuturetechnologiessuchasthewirelesspersonalareanetwork(WPA N)standard[13] bytheInstituteofElectricalandElectronicsEngineers(IEEE),thelongtermevo lution(LTE)and LTE-Advanced[14]standardsproposedbythe3rdGenerationPartnershipProject( 3GPP),the wirelessworldinitiativenewradio(WINNER)[15]standardproposedby theInformationsociety technologies(IST),andnallywirelessregionalareanetwork(WRAN)standard whichisknownas therstcognitiveradiostandard[16]. OneofthemainreasonsforchoosingOFDMasamulticarriermodulationmethodi sdueto itsrobustnessandhighspectraleciencyspeciallyforhighdataratesystems.OF DMdividesthe allocatedspectrumintosubbandsthataremodulatedwithorthogonalsubcarriers .Overfrequencyselectivechannels,thesubcarrierbandwidthbecomessmallerthanthechannelcoherencebandwidth.Thiseectallowsthesystemtousesingle-tapchannelequalizers,insteadofthecompl exequalizers thatareusuallyneededforhighbandwidthsinglecarriersignals.Anotherresultoft hissubcarrier 2

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divisionisthateverysymbolismodulatedoveralongertimedurationwhich reducestheinter-symbol interference(ISI)eectscausedbymultipathpropagation.OtheradvantagesofOFDMi ncludeits scalabilityandeasyimplementationusingfastFouriertransform(FFT)m ethods. AspecialcaseofOFDMthatisofinteresttothisstudyisthemultipleuserOFDMt echnology, knownasorthogonalfrequencydivisionmultipleaccess(OFDMA).Byassignings ubcarrierswithin thesamesymbolandoverdierentsymbolstomultipleusers,OFDMAenablesmult ipleuseraccess overfrequencyandtimedomains,respectively.Inaddition,bymaintainingtheor thogonalitybetweensubcarriersbelongingtodierentusers,OFDMAisabletoachievehigherspectr aleciency whencomparedtoothermultipleaccesstechnologies.1.2DissertationOutline Fortheremainderofthisdissertation,advantagesandchallengestoOFDMtechnolo gywhen appliedtofuturecommunicationsystemsareidentied.Further,anumberofthesechal lengesthat improvestheperformanceandincreasesthethroughputofOFDM-basedcommunicationsyst emsare addressed.Inthissection,thestudiespresentedintheremainderofthisdissertationa remotivated andthefollowingchaptersareoutlined. ToidentifychallengestoOFDM-basedsystems,theblockdiagramofagenericdigi talcommunicationsystemisconsideredinFig.1.1.Theguresshowsthebasicelementsoft hePHY.Atthe transmitterside,therawbits,usuallypassedtothePHYbythemediumaccesscontr ol(MAC) layer,areencodedbyintroducingsomeredundancytotheinformationsequence.Theencodingprocessallowsforforwarderrorcorrection(FEC)atthereceiverandimprov esthereliabilityofthe receiveddatathrougherrordetectiontechniques.Encodeddataarethenmodulatedtoanyoneofpossiblewaveformstoallowthesignaltobetransmittedoverthecom municationchannel.In OFDM-basedsystems,thisstepalsoinvolvesloadingmodulatedsymbolstoo rthogonalsubcarriers.Atthereceiver,demodulatedsymbolsarecomparedtooriginallytransmit tedsymbolstoobtain channelmeasurementssuchaserrorvectormagnitude(EVM).Themeasurementscouldbe obtained eitherusingknowntransmittedsymbolsorblindlybyremodulatingdetectedsymbol s. Partoftransmittedsymbolsarereservedforpilotsorpreambles.Thisst epallowsthereceiver toestimateandequalizethechanneleect,mostlymodeledasalterresponse,impos edonthe transmittedsignal.Thechanneleectisusuallyconsideredasthecombinedeectsofthepro pagationchannelandotherradiofrequency(RF)impairments(e.g.timingandfrequencyos ets,lters 3

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Encoding Modulation Insert pilots/ preamble Pulse/spectrum shaping DAC + RF circuitry Noisy channel ADC + RF circuitry Synchronization Channel estimation/ equalization Demodulation Decoding PHY Raw bits Raw bits Maintain orthogonality, reduce interference Optimize performance, increase throughput Obtain measurements Figure1.1BasicelementsofthePHYindigitalcommunicationsystems. response).Theratiooftheenergyornumberofsymbolsdedicatedforpilotstot heenergyornumber ofsymbolsdedicatedfordataisoneofthefactorsthatdeterminetheoverallsy stemeciencyand throughput. ThelaststepinthePHYistopassthesignalthroughapulseshapinglter.Incon ventional communicationsystems,thisprocessimprovesthespectrumcharacteristicsofthe modulatedsignal andlimitsornegatestheISIbetweenconsecutivesymbols.InCRsystems,thepro cessmayalso involveshapingthesignalspectrumadaptivelytotintoadesiredspectrumprole whichallowsfor multiplerentaluser(RU)accessorminimizeinterferencetolicensedusers(LU)curren tlyoperating withintheusedband. AdetailedstudyofOFDMadvantagesandchallengeswhenusedinCRsystemsispresented in Chapter2.Examiningtheelementsdiscussedabove,theissuestoaddressforfuturewi relesssystems whenOFDMisemployedcanbedividedintrothreemainissues: Maintainorthogonalityandreduceinterference. Optimizeperformanceandincreasethroughput. Obtainsignalmeasurements. Fig.1.1showsthesethreeissuesandtheirrelationstothePHYcomponents. Therstissuetoconsiderismaintainingorthogonalityandreducinginterference.OFD Misable toachievehighspectrumeciencybecauseoftheorthogonalitybetweenitssubcarrier s.Fig1.2 showsamultipleuserOFDM,oranOFDMA,systemoperatingwithinlicensedband.If theorthogonalitybetweensubcarriersislostduetosynchronizationerrors,thenadj acentsubcarrierswill 4

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FrequencyAmplitude Licensed band RU-1 bandRU-2 bandRU-3 band Figure1.2OFDMsubcarrierassignmentwithinusedavailablebandsinCRsyst ems. interferewitheachothercausinginter-carrierinterference(ICI).Operatingunders uchconditions candegradetheperformanceoftheOFDMsystemsignicantly.Thisisactuallyone ofthedrawbacksofOFDMsystems;itssensitivitytotimingandfrequencyosets.Fors ingleuserOFDM systems,allsubcarriersaremodulatedbythesameuser.Inthiscase,thereceiv eronlyneedsto synchronizetothesignalofthatusertoavoidsynchronizationerrorsandmai ntainsorthogonality betweensubcarriers.However,thisdoesnotapplytotheuplink(UL)signalofOFDMA systems, wheredierentsubcarriersareassignedtodierentusers.Inthiscase,theorthog onalityismaintainedonlyifallusers'signalsreachthereceiversynchronously.Thesynchroniza tioninOFDMA ULsystemsisdiscussedindetailinChapter3. ConsideringCRsystems,therearepossiblyoneormoreLUoperatingwithin theusedband. Inthiscase,theOFDMsystemneedstoavoidinterferingwiththeseLUbandsthroughs pectrum shapingtechniques.Althoughdisablingthesetofsubcarriersthatlaywithintheli censedbandas showninFig.1.2canreducetheradiationleakedtothelicensedband,thereisstill asignicant amountofinterferencetotheLU.Thereasonforthishighadjacentchannelinterfer ence(ACI)isdue tothehighsidelobesofOFDMsubcarriers.TofurtherminimizeOFDMout-of-bandradi ationto neighboringbands,itisconventionaltodisablesubcarriersthatoperateatt heedgeofusedbands, alsoknownasguardsubcarriers.Thisprocessleadstolowerspectrumeciencyasthe vacantbands arenotfullyutilized.InChapter4,someoftheadvancedmethodsusedtoshapethespect rumof OFDMsignalsarediscussed.WealsointroduceanovelmethodforOFDMspectrumshapi ngthat canoutperformcurrentmethods. 5

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Intherstissuediscussedabove,theconcernistoutilizetheavailablespectrumo pportunities whileminimizingoravoidingtheinterferencebetweenmultipleusersofthesamesy stemaswell asbetweenRUsandLUssharingthesameband.Basedonthevacantbandsofthespectrumandtheusedspectrumshapingmethod,thenumberofusableOFDMsubcarriersaredetermined.Partofusedsubcarriersarethendedicatedtopilotsorpreamblestoaidinthechannel estimation andequalizationprocessatthereceiver.Increasingthenumberofpilotsubcarriersi mprovesthe channelestimationwhichreducesthebiterrorrate(BER)atthereceiver.However,us ingtoo manysubcarriersforpilotsreducestheoverallthroughputofthesystem.Ontheother hand, aninsucientnumberofpilotsubcarriersleadstoworsechannelestimationandi ncreasestheBER whichinturnsdecreasesthesystemthroughput.Thus,thereisusuallyanoptimumnumber ofpilots thatmaximizethesystemthroughputdependingonthechannelstatisticsandtheusedchannelestimationmethod.TheoptimumpilotinsertionrateforOFDMsystemshasbeen presentedin theliterature.MethodsthatweredevelopedforOFDMsystemsassumedallavaila blepilotscould beusedforchannelestimationandequalizationsincetheybelongtoasingleuser.I naddition, optimumchannelestimationtechniqueswereassumed.WhenconsideringOFDMA-ULsystems, the problemismorecomplicatedsincemultipleuseraccessmeansthereceivedsignalisactual lyasumof multiplesignalsreceivedoverdierentchannels.Moreover,sincepilotsaredivided amongusers,the numberofpilotsperchannelarenotsucientforoptimumchannelestimationtechniques .Recently, somestudiesinvestigatedpossiblechannelestimationtechniquesforOFDMA-UL systems.However, thesestudiesdidnotprovideneithertheBERperformanceofthesystemunderchannelestimat ion errorsnortheoptimumpilotinsertionrate.InChapter5,theperformanceofOFD MA-ULsystems overtime-varyingfrequency-selectivechannelsisconsidered.WeprovideBERexpressionsf orthe receivedsignalunderchannelestimationerrors.Basedonthederivedexpressions,ano ptimum pilotinsertionrate,inbothtimeandfrequencydirections,thatmaximizesthes ystemthroughput isidentied. Adirectconversionreceiver,alsoknownaszero-IFreceiver,isanattractivear chitecturefor OFDMsystemssinceitavoidscostlyintermediatefrequency(IF)lters,reducespow erconsumption, andallowsforeasierintegrationthansuper-heterodynestructure[17].Howev er,directconversion receiverscausemoredistortionstothebasebandsignalduetotheimbalancebetweenthe inphase(I) andquadrature(Q)branches.TheIQimbalanceresultsinadegradationinthesystem performance. ThisdrawbackofdirectconversionreceiversbecomesmoresignicantwithOFDMsy stemsasthey 6

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areknowntobesensitivetoreceiverfront-endnon-idealities[18].Asmentioned earlier,channel estimationandequalizationprocesstakesintoaccountnotonlythechannelpropaga tioneectsbut alsootherimpairmentstothesignal.InChapter6,theeectsofIQimbalanceon OFDMA-UL systemsareconsidered.Methodstoestimateandequalizedboththemultiuserchannelsa ndIQ distortionsareinvestigated.Anovelpilotpatternisdesignedwhichisthenused bytwoproposed methodstoecientlymitigatesignaldistortionscausedbythecombinedeectsoft hewireless communicationchannelsandIQimbalancesofmultipleusers.ComparedtoChapter5where we investigateoptimumpilotinsertionrate,inChapter6,weinvestigateo ptimumpilotpatterns. Finally,thethirdissuetoconsiderisobtainingreliablemeasurementsoftherecei vedsignal quality.BERandEVMaretwoprimaryspecicationsthatdeterminetheperform anceofthe wirelesssystemintermsoftransmittedandreceivedsymbols.WhileBERis usefulasaconceptual gureofmerit,itsuersfromanumberofpracticaldrawbackssuchasthecomplex ityanddelay requiredforcalculation.Inaddition,ithaslimiteddiagnosticvalue.IftheB ERvaluemeasured exceedsacceptedlimits,itoersnoclueregardingtheprobablecauseorsourceofsignaldeg radation. Hence,EVMhasbeenconsideredasaviablealternativetestmethodwhenlookingforag ureof meritinwirelesschannels.EVMiscalculatedbycomparingoriginallymodulated symbols(atthe outputofthemodulator)toreceivedsymbols(attheinputtothedemodulator)indat aaided cases.Innondataaidedcases,detectedsymbolsattheoutputofthedemodulatorareremo dulated andusedasareferenceinstead.EVMcanoerinsightfulinformationonthevario ustransmitter imperfections,includingcarrierleakage,IQmismatch,nonlinearity,localosci llator(LO)phasenoise andfrequencyerror[19].RequirementsonEVMarealreadypartofmostwireless communications standardssuchastheIEEE802.11a-1999standard[6]andtheIEEE802.16 e-2005standard[9]. RelatingEVMtootherperformancemetricssuchasSNRandBERisanimportan tresearchtopic astheserelationsallowthereuseofalreadyavailableEVMmeasurementstoi nfermoreinformation regardingthecommunicationsystem.Moreover,usingEVMmeasurementscouldreducethe system complexitybygettingridoftheneedtohaveseparatemodulestoestimateormeas ureothermetrics. InChapter7,weconsidertherelationbetweenEVMandSNRfornondata-aidedreceivers.T he signaldegradationsourcesaremodeledasadditivewhiteGaussiannoise(AWG N),Rayleighfading channels,andIQimbalances.TheexactvalueofEVMfornondata-aidedsymboldetection isderived andexpressedintermsoftheSNR.TheresultsshowthatSNRcanbeaccuratelyestimat edusing measuredEVMevenwhensymbolsequencesareunknown,andtheSNRlevelislow. 7

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Intheremainderofthischapter,amoredetailedoutlineofthefollowingchapters inthisdissertationareintroduced.1.2.1Chapter2:OFDMforCognitiveRadio,MeritsandChallenges CRisanovelconceptthatallowswirelesssystemstosensetheenvironment,adapt, andlearn frompreviousexperiencetoimprovethecommunicationquality.However,CRneedsarex ibleand adaptivePHYinordertoperformtherequiredtaskseciently.Inthischapter, CRsystemsand theirrequirementsofthePHYarediscussedandOFDMtechniqueisinvestigatedasa candidate transmissiontechnologyforCR.ThechallengesthatarisefromemployingOF DMinCRsystems areidentied.ThecognitivepropertiesofsomeOFDM-basedwirelessstandardsare alsodiscussed inordertoindicatethetechnicaltrendtowardamoreCR. 1 1.2.2Chapter3:SynchronizationinOFDMAUplinkSystems SynchronizationisoneofthemostimportantprocessesintheOFDMA-basedsyst emssuchas themobileworldwideinteroperabilityformicrowaveaccess(WiMAX)sta ndard.Synchronization betweenabasestation(BS)andalluserswithinacellaredonethroughwhatiskno wnastheranging process.Inthischapter,thedetailsoftherangingprocessarepresented.Someofthepr oposed algorithms,aswellasanovelalgorithmtocarryoutasuccessfulrangingproces sarediscussed. Performancecurvesandcomputationalcomplexitycomparisonsbetweenproposedalgo rithmand currentalgorithmsarepresented.Thesystemperformanceisevaluatedforboth AWGNchannels andpracticalfrequency-selectivefadingchannelswithmultiuserinterference(MUI).It isshown thattheproposedalgorithmoersareducedcomplexityrangingmethodthatcanbeempl oyedin practicalOFDMA-basedBSs. 2 1.2.3Chapter4:SpectrumShapingofOFDM-basedCognitiveRadio Signals Inthischapter,OFDMspectrumshapingusingvarioustechniquestoreduceACIisinvesti gated.Thetrade-osbetweeninterferencelevelandspectraleciency,powerconsumption,andcomputationalcomplexityarediscussed.Simulationresultsalongwithdetaileda nalysisshowing theadvantagesanddisadvantagesofconsideredtechniquearepresented.Inaddition,w eintroduce anewmethodforOFDMsidelobesuppression.AnextensionisaddedtoOFDMsymbolstha tis 1 Contentsofthischapterwerepublishedinpartsin[20,21]. 2 Contentsofthischapterwerepublishedinpartsin[22,23]. 8

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calculatedusingoptimizationmethodstominimizeACIwhilekeepingtheextensionpo weratan acceptablelevel.Usingthistechnique,interferencetoadjacentsignalsisreducedsignican tlyat thecostofasmalldecreaseintheusefulsymbolenergy.Theproposedmethodcanbeus edbyCR systemstoshapethespectrumofOFDMsignalsandtominimizeinterferencetoLU s,ortoreduce thesizeofguardbandsusedinconventionalOFDMsystems. 3 1.2.4Chapter5:AnalysisandOptimizationofOFDMAUplinkSystem sOverTimeVaryingFrequency-SelectiveRayleighFadingChannels Channelestimationandequalizationisonetheprocessesthatsignicantlyimpacts theoverallperformanceofOFDMAsystems.Inthischapter,theperformanceofOFDMA-U Lsystems overtime-varyingfrequency-selectiveRayleighfadingchannelsisinvestigated.Ex pressionsforthe BERperformanceforquadraturephaseshiftkeying(QPSK)andquadratureamplitudem odulation (QAM)signalsunderchannelestimationerrorsarederived.BasedonBERperforma nce,theoptimumpilotinsertionratesforatile-basedOFDMAsystemtomaximizetheovera llsystemthroughput areinvestigated.1.2.5Chapter6:IQImbalanceCorrectionforOFDMAUplinkSystems Directconversionreceiversareattractiveforlowcostsystemsastheyavo idIFlters.However, thedirectconversionfromRFtocomplexIandQbasebandsignalsinonemixingstep introduces additionalfront-enddistortions.TheseIQdistortionsleadtoadegradation inthesystemperformance.TheproblembecomesmoresignicantinOFDMAsystemswheremultipleusersigna lswith dierentIQimpairmentsarecombinedintheULsignal.Inthischapter,detectionm ethodsfor OFDMA-ULsignalscorruptedbyIQdistortionsareinvestigated.Thereceivedsi gnalasafunction oftransmittedsignals,IQparameters,andcommunicationchannelsismathemat icallyformulated. Wedesignedanovelpilotpatternthatisusedbytwoproposedestimationandcomp ensationmethodsfortheIQimpairmentsinthesignal.Throughsimulations,proposedmet hodswereshownto signicantlyimprovethesystemperformance. 4 3 Contentsofthischapterwerepublishedinpartsin[24,25]. 4 Contentsofthischapterwerepublishedinpartsin[26]. 9

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1.2.6Chapter7:ErrorVectorMagnitudeBasedSNREstimationinBl indReceivers EVMisoneofthewidelyacceptedgureofmeritsusedtoevaluatethequalityofcomm unication systems.Intheliterature,EVMhasbeenrelatedtoSNRfordata-aidedreceivers,w herepreamble sequencesorpilotsareusedtomeasuretheEVM,orundertheassumptionofhighSNRval ues.In thischapter,thisrelationisexaminedfornondata-aidedreceiversandisshowntop erformpoorly, especiallyforlowSNRvaluesorhighmodulationorders.TheEVMfornondata-ai dedreceiversis thenevaluatedanditsvalueisrelatedtotheSNRforQAMandpulseamplitudemodulat ion(PAM) signalsoverAWGNchannelsandRayleighfadingchannels,andforsystemswithI Qimbalances. TheresultsshowthatderivedequationscanbeusedtoreliablyestimateSNRvaluesus ingEVM measurementsthataremadebasedondetecteddatasymbols.Thus,presentedworkcan bequite usefulformeasurementdevicessuchasvectorsignalanalyzers(VSA)orotherwireless standards, whereEVMmeasurementsarereadilyavailable. 5 5 Contentsofthischapterwerepublishedinpartsin[27]. 10

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CHAPTER2 OFDMFORCOGNITIVERADIO:MERITSANDCHALLENGES 2.1Introduction Withemergingtechnologiesandwiththeincreasingnumberofwirelessdevices,thera diospectrumisbecomingincreasinglycongestedeveryday.Ontheotherhand,measurementsshowthatwiderangesofthespectrumarerarelyusedmostofthetime,whileotherbandsarehea vilyused. Dependingonthelocation,timeoftheday,andfrequencybands,thespectrumisactuallyf ound tobeunderutilized.However,thoseunusedportionsofthespectrumarelicensedandthus cannot beusedbysystemsotherthanthelicenseowners.Hence,thereisaneedforanoveltechnolog y thatcanbenetfromtheseopportunities.cognitiveradio(CR)arisestobeatem ptingsolutionto spectralcrowdingproblembyintroducingtheopportunisticusageoffrequencybandsthat arenot heavilyoccupiedbylicensedusers(LU)[2,4].CRcanbedenedasanintelligentwirel esssystem thatisawareofitssurroundingenvironmentthroughsensingandmeasurements;as ystemthatuses itsgainedexperiencetoplanfutureactionsandadapttoimprovetheoverallcommuni cationquality andmeetuser'sneeds. AmainaspectofCRistoautonomouslyexploitlocallyunusedspectrumtoimpro vespectrum utilization.Otheraspectsincludeinteroperabilityacrossseveralnetworks,devi ces,andprotocols; roamingacrossborderswhilebeingabletostayincompliancewithlocalregul ations;adaptingthe system,transmission,andreceptionparameterswithoutuserintervention;andha vingtheabilityto understandandfollowactionsandchoicestakenbytheiruserstolearnandbecomemor eresponsive overtime.Thefocusofthischapteristherstaspect,i.e.CR'sabilitytosense andbeawareofits operationalenvironment,anddynamicallyadjustitsradiooperatingparamet ersaccordingly.For CRtoachievethisobjective,thephysicallayer(PHY)needstobehighlyrexibleand adaptable. Aspecialcaseofmulticarriertransmissionknownasorthogonalfrequencydiv isionmultiplexing (OFDM)isoneofthemostwidelyusedtechnologiesincurrentwirelesscommunicatio nssystems. 11

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OFDMhasthepotentialoffulllingtheaforementionedrequirementsofCRinherent lyorwithminor modications.Becauseofitsattractivefeatures,OFDMhasbeensuccessfullyusedin numerous wirelessstandardsandtechnologies.WebelievethatOFDMwillplayanimport antroleinrealizing CRconceptaswellbyprovidingaproven,scalable,andadaptivetechnologyforairin terface. Inthischapter,OFDMtechniqueisinvestigatedasacandidateforCRsystems.C Rfeaturesand requirementsarediscussedindetail,andOFDM'sabilitytosatisfytheserequi rementsisexplained. Inaddition,wegothroughthechallengesthatarisefromemployingOFDMtechnolo gyinCR. Thischapterisorganizedasfollows.ThebasicsystemmodelofOFDMsystemsi sintroducedin Section2.2.InSection2.3,thestructureofanOFDM-basedCRispresented.Section2. 4discusses themeritsofOFDMtechnologyanditsadvantageswhenemployedbyCRsystems.C hallengestoa practicalOFDM-basedCRsystemandpossiblesolutionsareaddressedinSection2. 5.Section2.6 looksintopresentandfuturetechnologiesthatuseOFDMwithCognitivefeatur es.Section2.7 concludesthechapter.2.2ABasicOFDMSystemModel AsimpliedblockdiagramofabasicOFDMsystemisgiveninFig.2.1.Ina multipathfading channel,duetothefrequencyselectivity,eachsubcarriercanhavedierentattenuation. Thepower onsomesubcarriersmaybesignicantlylessthantheaveragepowerbecauseo fdeepfades.Asa result,theoverallbiterrorrate(BER)maybelargelydominatedbyafews ubcarrierswiththelowest powerlevel.Toreducethedegradationofsystemperformanceduetothisproblem,channel coding canbeusedpriortothemodulationofthebits.ChannelcodingcanreducetheBERsignican tly dependingonthecoderate,decodercomplexity,signal-to-noiseratio(SNR)levelamongo ther factors.Interleavingisalsoappliedtorandomizetheoccurrenceofbiterrorsand introducesystem immunitytobursterrors.Codedandinterleaveddatabitsarethenmappedtothecons tellation pointstoobtaindatasymbols.Thisstepisrepresentedbythemodulationbl ockofFig.2.1.The serialdatasymbolsarethenconvertedtoparalleldatasymbolswhichare fedtotheinversefast Fouriertransform(IFFT)blocktoobtainthetimedomainOFDMsymbols .Timedomainsamples 12

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Mod. S/P IFFT P/S Add CP DAC RF front end + Demod. P/S FFT S/P Remove CP ADC RF front end ChannelNoise Encoded data To decoder Transmitter Receiver Figure2.1BlockdiagramofagenericOFDMtransceiver. isrepresentedas x ( n )=IFFT f X ( k ) g = N 1 X k =0 X ( k )exp | 2 nk N ; 0 n N 1(2.1) where X ( k )isthetransmittedsymbolonthe k thsubcarrierand N isthenumberofsubcarriers. Timedomainsignaliscyclicallyextendedtoavoidresidualinter-symbolint erference(ISI)fromthe previousOFDMsymbols.Asimpliedbasebanddigitalsignalisconvertedtoanal ogsignalthrough thedigitaltoanalogconverter(DAC)block.Then,thesignalisfedtotheradi ofrequency(RF) frontend.TheRFfrontendup-convertsthesignaltotheRFfrequenciesusingmixers,am pliesit usingpowerampliers(PA),andtransmitsitthroughantennas. Inthereceiverside,thereceivedsignalispassedthroughaband-passnoiserejectionlter and down-convertedtobasebandbytheRFfrontend.Theanalogtodigitalconverter(ADC )digitizes theanalogsignalandre-samplesit.Afterfrequencyandtimesynchronization(whi charenotshown inthegureforsimplicity),cyclicprex(CP)isremovedandthesignalistra nsformedtothe frequencydomainusingthefastFouriertransform(FFT)block.Asimpliedbaseba ndmodelof thereceivedsymbolsinthefrequencydomaincanbewrittenas Y ( k )= H ( k ) X ( k )+ W ( k )(2.2) 13

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FrequencyAmplitude Subcarrier spacing Total Bandwidth Figure2.2OFDMwaveform. where Y ( k )isthereceivedsymbolonthe k thsubcarrier, H ( k )isthefrequencyresponseofthe channelonthesamesubcarrier,and W ( k )istheadditivenoiseplusinterferencesamplewhichis usuallyassumedtobeaGaussianvariablewithzeromeanandvarianceof N 0 = 2.NotethatOFDM convertstheconvolutionintimedomainintomultiplicationinfrequencydom ain,andhencesimple one-tapfrequencydomainequalizerscanbeusedtorecoverthetransmittedsymbols.A fterFFT, thesymbolsaredemodulated,deinterleavedanddecodedtoobtainthetransmittedinfo rmationbits. Fig.2.2showsatypicalOFDMwaveforminfrequencydomain.Thegureshowstheor thogonal subcarrierstomodulatethetransmitteddata.Foragivenbandwidth,thecommunica tionchannel aectssomeofthedesignparametersoftheOFDMsystem.Themainparameterofa nOFDM systemarethesymboltime,thesubcarrierspacing(orconsequentlythenumberof subcarriers),the CPlength.InordertodesignanOFDMsystemproperly,oneshouldrstunderstandthei mpact ofwirelesscommunicationchannelsonanOFDMsignal. Thetransmittedsignalusuallyarrivesattheintendedreceivereitherdirectlyinas traightline, alsocalledline-of-sight(LOS)communication,orafterbeingrerectedonsurfacesofbui ldings,cars, andothersurroundingsintheenvironment,alsocalledasnon-line-of-sight(NLOS).T heNLOS communicationismorecommonforlongrangewirelesssystems.Asaresulto fthesignalbeing rerectedonmultiplesurfaces,thereceivedsignalbecomesasumofthetransmittedsig nalwith dierentdelaysandgainscorrespondingtothemultiplepathsthesignaltraveledthr ough.Sucha channelisusuallyreferredtoasmultipathchannel(seeFig.2.3). Themaineectsofmultipathchannelonthereceivedsignalarefrequency-selectivefading and ISI.Frequencyselectivefadingmeansthatthechanneldoesnotaectallfrequencycomponentsof 14

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n r r n n n r n r Figure2.3Multipathchannels. thesignalequallywhichresultsinhighdistortionofthereceivedsignal.Ont heotherhand,ISIis theinterferencebetweenconsequentsymbolsofthesamesignal.Duetoreceivingmult iplecopiesof thesignalwithdierentdelays,asymbolcanleakapartofitsenergyintothe followingsymbol.If notdealtwith,bothfrequency-selectivefadingandISIcanresultinasignicantdegrada tiontothe systemperformance. ChannelEqualizersareusuallyusedtocompensatemultipatheects.Equalizerscancons iderably increasethesystemcomplexityastheircomplexityincreasesdependingonthenumberofcha nnel paths.InOFDMsystem,however,theneedforequalizerscanbeavoidedbycarefulsyst emdesign. ToavoidISI,symbolsdurationareextendedbyaddingaguardbandtothebeginningo feachsymbol inwhatisknownasCP.Ifwedenethedelayspread,ormultipathspread,ofthechannela sthedelay 15

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betweentherstandlastreceivedpathsoverthechannel,theCPshouldbeequaltoorlong erthan thatdelay.Ontheotherhand,thefrequency-selectivefadingisavoidedbydecreasingthesubcar rier spacingorconsequentlyincreasingthenumberofsubcarriers.Wedenethechannelcoherencebandwidthasthebandwidthoverwhichthechannelcouldbeconsideredrat.SinceODFMsignalcanbeconsideredasgroupofnarrowbandsignals,byincreasingthenumberofsubcar riers,the bandwidthofeachsubcarrier,alsoknownasthesubcarrierspacing,becomesnarrow er.Bychoosing thesubcarrierspacingtobelessthanthecoherencebandwidthofthechannel,eachsubcarrier is goingtobeaectedbyaratchannelandthuscomplexchannelequalizationisnotneeded. AnotherchanneleectthatshouldbeconsideredintheOFDMsystemsdesignisthemobility Forxedcommunicationsystems,thechannelcanbeconsideredconstantovertime.How ever,if eitherofthetransmitterorthereceiverismobile,thechannelisgoingtovaryover timeresultingin fastfadingofthereceivedsignal.Coherencetimeofthechannelisdenedasthetimeover whichthe channelisconsideredconstant.Toavoidfastfadingeect,OFDMsymboltimeisc hosentobeequal toorshorterthanthecoherencetimeofthechannel.Inthefrequencydomain,mobilityres ultsina frequencyspreadofthesignalwhichisdependentontheoperatingfrequencyandtherelativ espeed betweenthetransmitterandreceiver,alsoknowasDopplerspread[28].Dopplersprea dofOFDM signalsresultsininter-carrierinterference(ICI)whichcanbereducedbyincreasi ngthesubcarrier spacing. Inconclusion,whileincreasingthesymboltimereducesISIeect,shortersymboltim eisdesirable toavoidfastfadingofthesignal.AndwhiledecreasingsubcarrierspacingreducesIC I,narrower subcarrierspacinghelpsavoidingfrequencyselectivity.Asamatteroffact,thereexi stanoptimum valueoftheseparametersthatshouldbeusedtoimprovethesystemperformance[ 29]. Intheaforementioned,asingleusersystemmodelisrepresented,wheretheavailable channelis usedbyasingleuser.NotethatOFDMbyitselfisnotamultipleaccesstechnique.Ho wever,itcanbe combinedwithexistingmultipleaccessingmethodstoallowmultipleuserstoaccesst otheavailable channel.SomeofthemostcommonmultipleaccesstechniquesthatcanbeemployedbyOFDMsystemsaretimedivisionmultipleaccess(TDMA),carriersensemultiplea ccessing(CSMA)[6], frequencydivisionmultipleaccessing(FDMA),andcodedivisionmultipleaccess(C DMA)based schemes[30].Inaddition,amixofTDMAandFDMAknownasorthogonalfrequency division multipleaccess(OFDMA)[31]isalsopossible.Notethatintheabovesys temmodel,theinterference fromotherusersandothertechnologies,suchasco-channelinterference(CCI),adjacent channel 16

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interference(ACI),narrow-bandinterference(NBI),etc.;areallfoldedintot henoisetermforthe sakeofsimplicity.However,inreality,whenthereceivedsignalisimpaired byadominantinterferer, amoreaccuratemodelneedstobeused.2.3OFDM-BasedCR Inthischapter,weassumeaCRsystemoperatingasarentaluser(RU)inali censedband.The CRsystemidentiesavailableorunusedpartsofthespectrumandexploitthem.Theg oalisto achievemaximumthroughputwhilekeepinginterferencetoLUstoaminimum.Anexample ofsuch aCRsystemcouldbetheIEEE802.22standard-basedsystemwherethespectrumall ocatedforTV channelsisreused.Inthiscase,theTVchannelsaretheLUandthestandard-basedsystemsa re theRUs(seesection2.6.2formoredetails).AblockdiagramoftheCR-OFD Msystemconsidered inthischapterisshowninFig.2.4 1 .NotethatallofthelayerscaninteractwiththeCognitive engine.Thecognitiveengineisresponsibleformakingintelligentdecisionsandcong uringtheradio andPHYparameters.Thetransmissionopportunitiesareidentiedbythedecisio nunitbased ontheinformationfrompolicyengineaswellaslocalandnetworkspectrumsens ingdata.As farasthePHYlayerisconcerned,CRcancommunicatewithvariousradioaccesstechnol ogies intheenvironment,oritcanimprovethecommunicationqualitydependingontheenv ironmental characteristics,bysimplychangingthecongurationparametersoftheOFDMsys tem(seeTable2.1 forsomeexampleparameters)andtheRFinterface.Notethatcodingtype,codingr ate,interleaver pattern,andothermediumaccesscontrol(MAC)andhigherlayerfunctionalities,etc.,s houldalso bechangedaccordingly.2.4WhyOFDMisaGoodFitforCR OFDM'sunderlyingsensingandspectrumshapingcapabilitiestogetherwithitsrexibilit yand adaptivitymakeitprobablythebesttransmissiontechnologyforCRsyst ems.Inthefollowing,we presentsomeoftherequirementsforCRandexplainhowOFDMcanfullltheserequirem ents.A summaryoftheserequirementsandstrengthofOFDMinmeetingthemarepresentedinT able2.2. 1 SomeOFDMfunctionsareskippedorsimpliedinordertokeep theguresimple. 17

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UPPER LAYERS RADIO PHY Cognitive Engine DAC ADC PA Local Spectrum Sensing Policy Engine FEC/ Mapping S/P Digital RF Digital RF FFT IFFT P/S Equalizer FEC/ Demapping Synchronization & Channel estimation r Decision Unit Radio Configuration Local Policies Spectrum inf.from network Modulation, coding, etc. Wideband Antenna Subcarrier assignment LNA Figure2.4OFDM-basedCRsystemblockdiagram. Table2.1OFDM-basedwirelessstandards. StandardIEEE 802.11(a/g) IEEE802.16(d/e)IEEE802.22DVB-T FFTsize64128,256,512, 1024,2048 1024,2048,40962048,8192 CPsize/FFTsize 1/41/4,1/8,1/16, 1/32 variable1/4,1/8,1/16, 1/32 Bitpersymbol1,2,4,61,2,4,62,4,62,4,6 Pilots4variable96,192,38462,245 Bandwidth(MHz) 201.75to206,7,88 Multipleaccessing CSMAOFDMA,TDMAOFDMA,TDMAN/A 2.4.1SpectrumSensingandAwareness OneofthemostimportantelementsofCRconceptistheabilitytomeasure,sense,lea rn,and beawareofimportantoperatingconditions[32].Thisincludesparametersrel atedtotheradio channelcharacteristics,availabilityofspectrum,interferencetemperature,and radio'soperational environments.Inaddition,thesystemshouldbeawareofuserrequirementsanda pplications, availablenetworksinfrastructuresandnodes,localpoliciesandotheroperating restrictions.CR 18

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Table2.2OFDMpropertiesvs.CRrequirements. CRRequirementsOFDMStrengths SpectrumsensingInherentFFToperationofOFDMeasesspectrumsensingin frequencydomain. Ecientspectrumutilization WaveformcaneasilybeshapedbysimplyturningosomesubcarrierswhereLUsexist. Adaptation/scalabilityOFDMsystemscanbeadaptedtodierenttransmissio n environmentsandavailableresources.SomeadaptableparametersareFFTsize,subcarrierspacing,CPsize,modulation,coding,subcarrierpowers. Advancedantennatechniques Techniquessuchasmultiple-inputmultiple-Output(MIMO)arecommonlyusedwithOFDMmainlybecauseofthereducedequalizercomplexity.OFDMalsosupportssmartantennas. InteroperabilityWithwirelesslocalareanetwork(WLAN)(IEEE802.1 1), wirelessmetropolitanareanetwork(WMAN)(IEEE802.16).wirelessregionalareanetwork(WRAN)(IEEE802.22),WPAN(IEEE802.15.3a)allusingOFDMastheirPHYtechniques,interoperabilitybecomeseasiercomparedtoothertechnologies. Multipleaccessingandspectralallocation Supportformultiuseraccessisalreadyinheritedinthesystemdesignbyassigninggroupsofsubcarrierstodierentusers(i.e.OFDMA). NBIImmunityNBIaectsonlysomesubcarriersinOFDMsystems.These subcarrierscanbesimplyturnedo. shouldbeabletoidentifyandexploittheunusedpartsofthespectruminafastand ecientway. InOFDMsystems,conversionfromtimedomaintofrequencydomainisachieved byusingFFT. Hence,allthepointsinthetime-frequencygridoftheOFDMsystem'soperatingband canbe scannedwithoutanyextrahardwareorcomputationthankstothehardwarereuseofF FTcores. Usingthetime-frequencygrid,theselectionofbinsthatareavailableforexploit ation(spectrum holes)canbecarriedoutusingsimplehypothesistesting.In[33,34],FFTi sappliedtothereceived signal.ByusingtheoutputofFFT,thereceivertriestodetecttheexistenceofaLUint heband. In[34],morethanoneFFToutput(averagingintime)isused.However,averag ingintimeincreases thedelayortemporaloverhead.In[35],theaveragingsize(numberofFFTs)i sadaptedinorderto increasetheeciencyinacooperativesensingenvironment.TheLUsignalisusually spreadovera groupofFFToutputsamplesasthebandwidthofLUisexpectedtobelargerthantheco nsidered bandwidthdividedbytheFFTsize.Usingthisfact,theFFToutputislteredfornoise averaging inordertoobtainabetterperformance[36].Inthesesensingalgorithms,the availabilityofFFT circuitryinOFDMsystemseasestherequirementsonthehardware.Moreover,thecom putational 19

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0 5 10 15 20 25 Subcarrier indexAmplitude 0 5 10 15 20 25 Subcarrier indexAmplitude Sensing... Shaping... Licensed users Figure2.5SpectrumsensingandshapingusingOFDM. requirementsofthespectrumsensingalgorithmisreducedasthereceiveralreadyappliesF FTtothe receivedsignalinordertotransformthereceivedsignalintofrequencydomainfor datadetection. 2.4.2SpectrumShaping AfteraCRsystemscansthespectrumandidentiesactiveLUs,otherRUs,andavai lable opportunities;comesthenextstep:spectrumshaping.Ideally,itisdesiredtoallow RUstofreely useavailablebandsinthespectrum.Itisdesiredtohavearexiblespectrummaskand havecontrol overwaveformparameterssuchassignalbandwidth,powerlevel,andcenterfrequency.OF DM systemscanprovidesuchrexibilitythankstotheuniquenatureofOFDMsignaling. Bydisablinga setofsubcarriers,thespectrumofOFDMsignalscanbeadaptivelyshapedtotin totherequired spectrummask 2 .AssumingthespectrummaskisalreadyknowntotheCRsystem,choosingthe disabledsubcarriersisarelativelysimpleprocess. AnexampleofspectrumsensingandshapingproceduresinOFDM-basedCRsystemsisillustratedinFig.2.5.ThetwoLUsaredetectedusingtheoutputoftheFFTblock,and subcarriers thatcancauseinterferencetotheseLUsareturnedo.Thetransmitterthenusestheunoccupi ed partofthespectrumforsignaltransmission. 2 SeeSection2.5.5formoredetailsandformoreadvancedalgo rithms. 20

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2.4.3AdaptingtotheEnvironment AdaptivityisoneofthekeyrequirementsofCR.Bycombininggatheredinformati on(awareness) withknowledgeofcurrentsystemcapabilitiesandlimitations,CRcanperfor mvarioustasks.CR canadaptitswaveformtointeroperatewithotherfriendlycommunicationdevices ,choosethemost appropriatecommunicationchannelornetworkfortransmission,andallocateb estfrequencyto transmitinafreebandofthespectrum.Thesystemwaveformcanalsobeadapted tocompensate forchannelfading,andnullifyanyinterferingsignal.OFDMoersagreatrexibi lityinthisregardas thenumberofparametersforadaptationisquitelarge[37].AnOFDM-baseds ystemcanadaptively changethemodulationorder,coding,andtransmitpowerofeachindividualsubcarr ierbasedonuser needsorthechannelquality[38].Thisadaptiveallocationcanbeoptimizedtoac hievevariousgoals suchasincreasingthesystemthroughput,reducingBER,limitinginterferencetoLUs, increasing coverage,ortoprolongunitbatterylife.InmultiuserOFDMsystems,subcarrier sallocationtousers canbedoneadaptivelyaswelltoachievethesamegoals[39]. OneoftheattractivefeaturesofOFDMforbroadbandcommunicationsisitsabilit ytooperate usingsimpleonetapequalizers,inthefrequencydomain.Tomaintainthisfeature, thesubcarrier spacinginsettobelessthanthechannelcoherencebandwidth.Inaddition,toavoidISI,thesystemappendsaCPtoeachsymbolwithadurationlongerthanthechannelmaximum delay spread.Basedonestimatedchannelparameters,anOFDM-basedCRsystemcanadaptivel ychange thelengthoftheCPtomaintainanISI-freesignalwhilemaximizingthesys temthroughput[29]. Similarly,OFDMsystemcanadaptivelychangethesubcarrierspacingtoreduceICIo rpeak-toaverage-powerratio(PAPR)[29],thedatasubcarrierinterleavingtoreduceB ER[40],oreventhe usedpilotpatterns[41]. TheadaptivityinOFDMsystemscanbeperformedeitheratalgorithmlevelora tparameter level.Inclassicalwirelesssystems,usuallyalgorithmparameters,e.g.co dingrate,havebeenadapted inordertooptimizethetransmission.However,incognitiveOFDMsystems, algorithmtype,e.g. channelcodingtype,canalsobeadaptedinordertoachieveinteroperabilitywith othersystems and/ortofurtheroptimizesystemperformance.Toachievesuchadaptivity,aful lycongurable hardwareplatformwouldbeneeded. 21

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2.4.4AdvancedAntennaTechniques AdvancedantennatechniquesarenotnecessarilyrequiredforCRs.However,theyaredesir able astheyprovidebetterspectraleciencywhichistheprimarymotivationforCR .Smartantennas andmultiple-inputmultiple-Output(MIMO)systemscanbeusedtoexploitthespatialdimens ion ofspectrumspace,e.g.throughbeamforming,toimprovetheeciency.Inessence,multi -antenna systemscanhelptondspectralopportunitiesinthespatialdomainandcanhelpto exploitthese opportunitiesinfull.TheuseofMIMOtechniquesoersseveralimportantadva ntagesincluding spatialdegreeoffreedom,increasedspectraleciencyanddiversity[42].Theseadvan tagescanbe usedtoincreasethespectrumutilizationoftheoverallsystem.Furthermore,bea mforming,diversity combining,andspace-timeequalizationcanalsobeappliedtocognitiveOFDMsyst ems.Another applicationofadaptiveantennatechniquesisthereductionoftheinterferenceinOFDMs ystems[43]. MIMOsystemscommonlyemployOFDMastheirtransmissiontechniquebecauseofs imple diversitycombinationandequalization,particularlyathighdatarates.InM IMO-OFDM,the channelresponsebecomesamatrix.Sinceeachtonecanbeequalizedindependently,thecomplex ity ofspace-timeequalizersisavoidedandsignalscanbeprocessedusingrelativelyst raightforward matrixalgebra.Moreover,theadvantagesofOFDMinmultipatharepreserved inMIMO-OFDM systemasfrequencyselectivitycausedbymultipathincreasesthecapacity.2.4.5MultipleAccessingandSpectralAllocation TheresourcesavailabletoaCRhavetobesharedamongusers.Severaltechniquescanb e usedtoachievesuchatask.OFDMsupportswell-knownmultipleaccessingtechniquess uchas TDMA,FDMAandCSMA.Moreover,CDMAcanbeusedtogetherwithOFDM,inwhich casethe transmissionisknownasmulti-carriercodedivisionmultipleaccess(MC-CD MA)ormulticarrier directspreadcodedivisionmultipleaccess(DS-CDMA). OFDMA,aspecialcaseofOFDM,hasgainedsignicantattentionrecentlywithi tsusageinxed andmobileworldwideinteroperabilityformicrowaveaccess(WiMAX)sta ndard[9].InOFDMA, subcarriersaregroupedintosetseachofwhichisassignedtoadierentuser. Interleaved,randomized,orclusteredsubcarrierassignmentschemescanbeused.Therefore,OFDMAoersvery rexible multipleaccessingandspectralallocationcapabilityforCRwithoutanyextr ahardwarecomplexity. Theallocationofsubcarrierscanbetailoredaccordingtothespectrumavail ability.Therexibility 22

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WAN IEEE 802.22 3GPP* MAN IEEE 802.16 WiMAX HIPERMAN LAN IEEE 802.11a/g Wi-Fi HIPERLAN PAN IEEE 802.15.3a (MB-OFDM)* Proposed Figure2.6OFDM-basedwirelesstechnologies. andsupportofOFDMsystemsforvariousmultipleaccessingtechniquesenableintero perabilityand acceleratetheadaptationofCRinfuturewirelesssystems.2.4.6Interoperability Interoperabilityisdenedastheabilityoftwoormoresystemsorcomponent stoexchange informationandtousetheinformationthathasbeenexchanged[44].SinceCRsy stemsmayhave todealwithLUsaswellasotherRUs,theabilitytodetectandencodetheexistingsi gnalswithin theusedbandcanimprovetheperformanceofCRsystems.Furthermore,somerecentunf ortunate disastersmanifestedtheimportanceofinteroperabilityintermsofwirel esscommunicationsforthe rstresponders.CRhasthepotentialtoimprovethedisasterreliefoperatio nsbydevelopingthe coordinationamongrstresponders[45]. Toachieveinteroperability,OFDMisoneofthebestsignalingcandidates.OFDM signalinghas beensuccessfullyusedinvarioustechnologiesincludingtheIEEE802.11a[6]andIE EE802.11g[46] wirelesslocalareanetwork(WLAN)standards,theIEEE802.16e-2005[9]w irelessmetropolitan areanetwork(WMAN)standard,andtheEuropeandigitalaudiobroadcasting(DAB )anddigital videobroadcasting(DVB)standards.Fig.2.6showssomeoftheOFDM-basedwir elesstechnologies accordingtocommunicationrange.Asshowninthisgure,OFDMhasbeenusedinbothsho rtrange andlongrangecommunicationsystems.Hence,aCRsystememployingOFDMcancommunica te 23

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OFDM Challenges Cognitive Radio Challenges Cognitive radio-OFDM Specific Challenges • ICI• PAPR• Synchronization• ... • Spectrum sensing• Cross layer adaptation• Interference avoidance• ... Figure2.7ResearchchallengesinCRandOFDM. withsystemsusingotherOFDM-basedtechnologieswithmuchease.Onlytheknowledgeo fsignal parametersofintendedusersisneeded(seeTable2.1).However,forsuchtasktobe successful,the systemneedstoknowallstandard-relatedinformationrequiredtodecodethesignal, suchasthe dataandpilotmappingtothefrequencysubcarriers,framestructure,andthecodingtyp eandrate. Moreimportantly,theRFcircuitryoftheCRsystemneedstoberexibleenoughto accommodate dierentsignalbandwidthsandcenterfrequencies.Asaresult,CRshouldbebuiltaroundas oftware denedradio(SDR)architecturetoproviderequiredrexibilitytothesystem.2.5ChallengestoCognitiveOFDMSystems Asanintelligentsystemwithfeaturessuchasawareness,adaptivityandlea rning,CRrepresentsthefutureofwirelesssystemswiththepromiseofoeringsolutionst ovariouscommunication problems.However,withthisnewtechnology,newchallengesappear,raisinginteres tingresearch topics.ConsideringanOFDM-baseCRsystem,thechallengescanbegroupedintothr eecategories asillustratedinFig.2.7.Therstcategoryincludesthechallengesthatareuniq uetoclassical OFDMsystemssuchasPAPR,andsensitivitytofrequencyosetandphasenoise.The second categoryincludesproblemsfacedbyallCRssuchasspectrumsensing,crosslayeradapt ation,and interferenceavoidance.Ourmainfocusinthisarticleisonthethirdcategory:cha llengesthatarise whenOFDMtechniqueisemployedbyCRsystems.Inthefollowing,wediscussmajo rchallenges 24

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toapracticalsystemimplementationaswellassomeoftheproposedapproac hesforsolvingthese challenges.2.5.1MultibandOFDMSystemDesign Sofarwehaveconsideredthemoreconventionalsingle-bandOFDM(SB-OFDM)systems. In SB-OFDMsystems,theavailableportionofthespectrumisoccupiedbyasingleOF DMsignal.If LUexistwithintheusedband,theCRsystemshapestheOFDMsignalastoavoidin terference tothoseusersasshowninFig.2.5.Forsystemsutilizingwidebandsofthesp ectrum,multi-band signalingapproach,wherethetotalbandwidthisdividedintosmallerbands,canpro vetobemore advantageousoverusingsinglebandsignaling.Thisappearstobemoresignica ntifthedetected freepartsofthespectrumarescatteredoverarelativelywideband.Whileusingas ingleband simpliesthesystemdesign,processingawidebandsignalrequiresbuildinghighlycomplex RF circuitryforsignaltransmission/reception.HighspeedADCsarerequiredto sampleanddigitize thewidebandsignal.Inaddition,highercomplexitychannelequalizersarealsoneededtocapt ure sucientmultipathsignalenergyforfurtherprocessing.Ontheotherhand,multi-bandsig naling relaxestherequirementsonsystemhardwareassmallerportionsofthespectr umareprocessed separately.Dividingthespectrumintosmallerbandsallowsforbetterspectrum allocationaswell. ForOFDM-basedCR,thequestionbecomeswhentousemulti-bandandwhentousesingle band.Givenacertainscannedspectrumshape,choosingthenumberofbandsdependsonvari-ousparameters.Requiredthroughput,hardwarelimitations,computationalcomplex ity,numberof spectrumholesandtheirbandwidth,andinterferencelevelareexamplesofwhatcouldaectaC R choice.Wefurtherillustratetheimportanceofmulti-bandsignalingwiththenex texample. ConsiderthescenariowhereaCRsensesthespectrumandndstheresultsshowninFig.2.8 Twomainspectrumholesaredetectedwith10MHzand15MHzbandwidth.Oneofthespectr um holescontainsNBI.Thedetectedvacanciesinthespectrumare1GHzapart.Insuchscena rio, ifthesystemchoosestouseSB-OFDM,thenthebandwidthoftheOFDMsignalisgoingt obe 1.025GHz.AsignalwithsuchbandwidthrequiresADCswithasamplingrateo fatleast1.025GHz accordingtoNyquistrate.Inaddition,alargenumberofsubcarriersisrequir edtoguaranteethat subcarrierscanbettertintothespectrumholesaswellaskeepthesubcarrier'scha nnelrelatively rat.Unfortunately,largenumberofsubcarriersresultsinamorecomplexFFT operation.Moreover, inordertoavoidtheNBIinthe15MHzband,thesystemdropstwooutofthreesubca rriersthatare 25

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! #! $ % % &' () *+,. /0 (1 % 2 $3#! " $ 4 56789:; <=<>? @ 9A B = C DE F ; :A@ D @ <>? G HIJ KLM N 99 C ; N B FO 4 B 67 89:; <=<>? @9A B = C DE F ; :A@ D @ <>? MHIJKLM N 99 C ; N B FO 4 N 6 G A>@ <>? @ 9A B = C DE N >P PA =A B =<>? @ 9A B = C DE F ; :A@ O Figure2.8FillingspectrumholesusingSB-OFDMorMB-OFDMsignals. usedtollthespectrumhole,resultinginalowspectrumeciency.Now,let'sconsidermul ti-band OFDM(MB-OFDM). ByusingMB-OFDM,thespectrumholescanbelledwithtwoOFDMsignalswith15a nd 10MHzbandwidths.ADCswithasamplingrateof25MHzistheminimumrequirem entforthe system.AlargenumberofsubcarriersisnotnecessaryforeitherOFDMsignalsi nthatcase.In addition,thesystemhasmorecontroloverthesignalspectrumineachbandduetot hesmall subcarrierspacing.Hence,avoidingNBIisachievedwhilemaintainingahigherspectr aleciency. However,thesystemisnowprocessingtwoOFDMsignals.Whilesamplingfrequencyi sreducedin thisMB-OFDMcase,thesystemisperformingreceiveralgorithms(e.g.synchroni zation,channel estimationandequalization)separatelyforeachband.Anotherexampleisshowni nFig.2.9.In thisexampleaSB-OFDMcouldbeabetterchoiceforthesystemratherthanusingvebands ina MB-OFDMscheme.TheimprovementofspectrumeciencyintroducedbyusingMB-OFDMmaynotbeassignicantastheincreaseinsystemcomplexity. 26

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Q Q Q RS TUVWX Y Z [\ ] R Z [\ ]V ^ _`abcde fg fhi jck l g m no p e dkj n j fhi q rst uvw x cc m e x l py ^ l `a bcde fgfhi j ck l g m no p e dkj n jfhi wrstuvw x cc m e x l py ^ x ` q khj fhi j ck l g m no x hz zk gk l g fhi j ck l g m no p e dkj y Z [\ ]{ Z [\ ]| Z [\ ]U Figure2.9FillingspectrumholesusingSB-OFDMorMB-OFDMsignals. ItisworthmentioningthatMB-OFDMisemployedinsomeultrawideband(UWB) systems. InsteadofusingasinglebandUWBsignal,thespectrumisdividedintosub-bands(wit happroximately500MHzbandwidtheach)andOFDMsignalsareusedtotransmitdataoverea chband[47, 48].Fig.2.10showsanillustrationoftheUWBsignalinfrequencydomai n.However,whileUWB isoneoftheapplicationsofMB-OFDM,itisonlylimitedtoaspecicscenariowher eallsub-bands havealmostequalsize,andOFDMsignalsusedinsub-bandsareidenticalinotherparam eterssuch asCPsizeandsubcarrierspacing. Fromapracticalpointofview,designingacosteectivemulti-bandtransceiverwi thhighperformancehasbeenstudiedintheliterature[49{53].Onmostproposedtransceivers, directconversion architectureisusedtoeliminatetheneedforimagerejectionlters,andrelaxthe bandwidthrequirementsforthebasebandltersandconverters[49,50].Thechallengesthatfacethei mplementation ofabroadbandmulti-bandOFDMsystemincludestheneedforwiderangefrequencysynthesizers,broadbandcircuitsandmatching,gainswitchinthelownoiseamplier(LNA)w ithoutdegrading theinputmatch,broadbandtransmit/receiveswitchattheantenna,desensitization duetoadjacent LUinterference,andfastbandhoppingtoavoidinterferencetooccupiedbands[51].Frequencysynthesizersthatcanoperateinsevenbands[52,53],ninebands[50],andeven12bands [51]have beenpresentedrecently. 27

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3169 MHz3696 MHz4224 MHz4752 MHz Band #1Band #2Band #3 Frequency PSD Figure2.10Sub-bandsofMB-OFDM-basedUWBsystemsinfrequencydomain. Ifsingle-bandtransmissionisemployed,theremightbemanysubcarriersthat aredeactivated. Insuchacase,theeciencyofFFTalgorithmscanbeincreasedandtheexecutiontimeca nbe decreasedbyremovingoperationsoninputvalueswhicharezero;aprocessknownaspruni ng. DesigningeectivepruningalgorithmsspecictoCR-OFDMastoachievehigherperfor manceisan importantstudysubject[54].2.5.2LocationAwareness Geolocationinformationcanbeusedtoenablelocation-basedservices,optimize thenetwork trac,andadaptthetransceivertotheenvironment.Applicationsutilizinglocati oninformationcan begroupedintofourcategories;location-basedservices,networkoptimizatio n,transceiveralgorithm developmentandoptimization,andenvironmentcharacterization.Althoughsomeo ftheexisting wirelessnetworkshaveaminiatureutilizationoflocationinformation, CRisexpectedtohavea morecomprehensivelocationinformationutilization[55{57]. OFDMsignalingcanbeusedtoobtainthegeolocationinformationinCRswi thouttheneed foranyexternalpositioningsystems[58].Pilotsequences,orpreambles,whic harecommonlyused inOFDMsystemsforsynchronization,canbeusedforacquisitionandtracki ngofunits'locations. Intheliterature,bothtimeandfrequencydomaintechniquesareproposedtoestim atethetimeof arrival(TOA)usingreceivedOFDMsignal.ExistingWLANsystemsarebeing studiedforindoor positioningapplicationswhileMB-OFDM-basedUWBisproposedforhighprecisio napplications. SuchpositioningcapabilitieshelpOFDMtofulllanotherrequirementofCR. 28

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2.5.3SignalingtheTransmissionParameters InaCRsystem,communicationunitssensethesurroundingenvironmentandgatherupinf ormationthatcanbeusedtoimprovethecommunicationlink.Basedongatheredinfor mation,thesystem selectstransmissionparameterssuchasLUbands,spectralmask,operatingf requency,coding,and modulation.Whilesomeoftheseparameterscanbedetectedblindlybyintendedreceivers, other parametersneedtobeknownpriortoestablishingacommunicationlink.Distribut inginformation amongcommunicationunitsratherthanusinglocalsensingreducesthecomplexityandimpro ves theperformanceofthesystem.Thus,itiscrucialforthesuccessofCRtosuccessful lydistribute suchinformationtooperationalRUs. Oneapproachtothisproblemistodedicateacommunicationchannelfortheexchangeofmea suredinformationandtransmissionparametersamongRUs.However,thisr equiresthatachannel bepredened,orlicensed,forthatpurpose.Asaresult,theabilityofRUstoadaptively operate withinanygivenunlicensedbandbecomesdependentontheavailabilityofsuchachannel.M oreover,asthenumberofoperatingunitsinthesamecellincreases,theamountofinf ormationthat needstobedistributedincreasesaswell.Thiscanresultinahugeoverheadthatthededicat ed channelmaynotbeablehandle. Otherapproachessolvethedistributionproblembyeitherreducingtheinformationover head orbyimprovingtheperformanceofblinddetectors.Forexample,inOFDMsystems ,basedon thescannedchannel,waveformisadjustedbyturningosomesubcarriersinordertoex ploitthe availablespectrumholessimilartowhatisshowninFig.2.5.Thereceivers ,however,shouldbe informedaboutdetectedspectrumholes,orwhichsubcarriersaredeactivated.Theover headis reducedbybroadcastingthevectorcontainingdisabledsubcarriersratherthanexchanging thespectrumsensingresults.Onemethodtofurtherreducetheoverheadisproposedin[59],where the activation/deactivationofsubcarriersisperformedoverablockofsubcar riersinsteadofindividual subcarriers.Hence,thesignalingoverheadcanbereducedbyafactoroftheblocksize.On the otherhand,insteadofsharingthespectrumsensinginformation,tone-boostingcanbe usedtoRU ofwhichsubcarriersaredisabled[60].OnceaRUdetectsaLUsignalwithintheband, itsendsa tonewithmaximumpowerbutwithaveryshorttimedurationoverthedetectedsig nalband.The purposeistoinformotherRUsthataLUisoperatingwithinthisband.Asaresul t,theprobability ofinterferencetoLUsisreduced,whichisoneofthemainpurposesofspectrumsensing. Meanwhile, theshortdurationofthesetonescausesnosignicantinterferencetoLUs. 29

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f= ¢ fNormalizedPSD(dB) -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 -30 -25 -20 -15 -10 -5 0 Desiredsignalpower Interferencetorst adjacentsubband, I 1 I 2 I 3 Figure2.11PowerspectrumdensityofasingleOFDMsubcarrier. 2.5.4Synchronization SynchronizationisanimportantissuethatneedstobeaddressedinOFDMsystemdes ign.With theintroductionofCR,conventionalsynchronizationmethodsbecomeinsucient. Forexample, theNBIcandistortthepreamblethatisusedforsynchronization[61].Theincom pletesetofactive subcarriersisexpectedtoimpactthepreamble.Pilotsaswellmayfallintodeact ivatedsubcarriers. Moreover,ifmultipleaccessingisemployed,subcarriersareassignedtodierent users.Thus,tokeep theorthogonalitybetweensubcarriersandtoavoidinterference,allusersshould besynchronizedto thereceiverpriortotransmission.In[61],itisshownthatlongerpreamblesa rerequiredinCROFDMsystemsascomparedtoconventionalOFDMsystems.Inaddition,newpreamble structures areintroducedandtheirperformancesforthetimeandfrequencysynchronizationare investigated. 2.5.5MutualInterference ThesidelobesofmodulatedOFDMsubcarriersareknowntobelargeasshownin Fig.2.11.Asa result,thereispowerleakagefromOFDMsignalstoadjacentchannels.Inadditi on,usedsubcarriers' powerleakstonulledsubcarrierswhichcausesmutualinterferencetoLUs.Vario ustechniquesare proposedintheliteraturetoreducethisleakageandtoenableco-existenceofCR-OFDM systems withLUs.OnetechniqueistowindowthetimedomainOFDMsymbols[62,63]. In[64],araised cosine(RC)windowisapplied.Bychangingtheroll-ofactoroftheRCwindow,in terference reductionofupto6dBcanbeachieved.Fig.2.12andFig.2.13showtheRCwindows hapefor 30

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t=T sAmplitude -1 -0.5 0 0.5 1 0 0.2 0.4 0.6 0.8 1 =0 =0 : 25 =0 : 50 =0 : 75 =1 Figure2.12RCwindowingwithdierentrollo( )values. f= ¢ fNormalizedPSD(dB) 0 0.5 1 1.5 2 2.5 3 3.5 4 -60 -50 -40 -30 -20 -10 0 =0 =0 : 25 =0 : 50 =0 : 75 =1 Figure2.13RolloeectonthePSDofasingleOFDMsubcarrier. dierentroll-ovaluesandthecorrespondingpowerspectraldensities,respectively .However,the spectrumshapeimprovement,inthiscase,comesatthecostoflongerOFDMsymbol duration andthusareductioninthespectrumeciencyofthesystem.Anotherapproachistoincreas e thenumberofnulledsubcarrierstoachievelowerinterferencelevelstoLUbandsasm ostofthe interferenceiscausedbyneighboringsubcarriers.However,theobviousdisadvan tageofthismethod isagainthereductionofspectraleciency. Amethodthatreducesinterferencetospectrumholeswhilekeepinghighspectrumeciencyis proposedin[65]andin[66,67]andisreferredtoasactiveinterferencecancell ationandcancellation 31

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carriers,respectively.Insteadofdisablingsubcarriersadjacenttospectrumhol es,amuchsmaller numberofthoseadjacentsubcarriersisusedtoreducetheinterferenceleakedtospectrum holes.The cancellationsubcarriersarepre-calculatedtoreducesubcarriersidelobesinsidespectr umholes.This techniqueachievessignicantreductionofACI.Thedisadvantageofthistechniquei stheincrease inoverallsystemcomplexityduetothecalculationofcancellationcarrierval uesforeachsymbol. Inaddition,forlargerspectrumholes,morecancellationcarriersareneededtoma intainthedesired interferencelevel.Analogordigitallterscanalsobeusedtolter-outtheunwan tedspectral componentsoftheOFDMsignalpriortotransmission.However,sincethespectr ummaskofaCR signalneedstobeadaptive,theuseofanalogltersisnotpractical.Ontheotherhand,di gital ltersintroduceanincreaseinthesystemcomputationalcomplexityandprocessingdel ay.Other methodstoreduceOFDMinterferencetoadjacentchannelsarepresentedin[24,68].Adetai led discussiononthistopicispresentedinChapter4.2.6AStepTowardCognitive-OFDM:StandardsandTechnologies AsCRconceptisattractingmoreinteresteveryday,recentlydevelopedstandardsare considering morecognitivefeatures.Dynamicfrequencyselection(DFS),transmitpowercon trol(TPC),and spectrumsensingarejustafewexamplesoffeaturesthatareincludedinsomeofthecurr ent standards.Thesestandardscanbeconsideredasasteptowardthefutureimplementat ionofaCR. Inthissection,someoftheOFDM-basedstandardswhichutilizecognitivefeatures areintroduced. 2.6.1IEEE802.16 TherstWiMAXstandard,IEEE802.16a[69],operatesinthe10to66GHz range.Inthis frequencyrange,onlyLOScommunicationsarepossible.Thestandardlaterevolvedin 2004to theIEEE802.16-2004[8];alsoknowasIEEE802.16d.TheIEEE802.1 6-2004standardsupports theoperationinthe2to11GHzrangeallowingforaNLOScommunications.I tprovidespoint-tomultipointaccessforxedsubscribers.TheIEEE802.16e-2005[9]standardup datesandextends thisstandardtoallowformobilesubscriberstations(SS)travelingatvehicul arspeeds.Ascalable versionofOFDMAisintroducedimprovingtheoverallsystemperformance.Whil eIEEE'srole istodevelopstandardsforthePHYandMAClayers,WiMAXforumensurescompatibi lityand interoperabilitybetweenvendors'equipmentsthroughitscerticationprocess. 32

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OFDMAPHYmodeisprobablythemostinterestingmodesupportedbyWiMAX.Int hismode, aWiMAXbasestation(BS)isabletosupportmultiplexedormobileusersat thesametime.A BSsystemcanutilizetheavailablechannelbydividingtheavailablesubcarrier sintosubchannels. AnumberofsubchannelgroupedwithanumberofOFDMAsymbolsconstitutesatile. Atileis denedastheminimumdataallocationunit[8].Thetiledenitionshowsthatthesys temresources arebeingsharedbetweenusersintwodomains.Therstdimensionisfrequencywhichis represented bythenumberofsubcarriersineachtile.Theseconddimensionistimewhichisr epresentedby numberofOFDMAsymbols.Fig.2.14showstheOFDMAsignalstructureusedfo raWiMAX-based system.Notethatthisgureisonlyforillustrationpurposesandthusthen umberofsubcarriersor thetilesizedoesnotnecessarilyrerecttheactualnumbersusedbythestandard. AWiMAXBScanassignusersdierentbandwidths,timedurations,transmitpow erlevels, andmodulationordersbasedonvariousparameters(seeTable2.1)suchastheus ercarrier-tointerference-plus-noiseratio(CINR),receivedsignalstrengthindicator(RSSI)or theavailablebandwidth.Moreover,OFDMAPHYoersmultipleFFTsizes,CPsizes,andpilotallo cationschemes. TheFFTsizecanbeselectedas128,256,512,1024or2048dependingonthetrans missionbandwidth 3 .Similarly,theCPlengthcanbesetto1/4,1/8,1/16and1/32timestheOF DMsymbol length.TheCPsizecanbechangeddependingontheenvironmentcharacteristics.Witha llthese adaptivefeatures,WiMAXhastheabilitytoadapttovariouschannelconditionsand communication scenarios. WiMAXstandardisalsorichintermsofadvancedantennatechniquesaswell.Tabl e2.3shows MIMOfeaturesavailableintheIEEE802.16E-2005standard[9].Thesta ndarduseofthesetechniquesisnotdirectlyrelatedtoCR,butrathertoincreasethespectraleciencyandincreas ethe overallthroughputofthesystem.However,advancedantennatechniquescouldbeusedtoac hieve someoftheCRgoalsaswell.Forexample,theCRtransmittercanexploitlo cationawarenessto focusitsradiationonlyinthedirectionofintendedreceiversusingadaptivebeamf orming[4,70]. Ontheotherhand,theCRreceivercanusethesametechniquetoadaptivelycanceltheinterferencecausedbyunintendedtransmitters[71].Thegoalinbothcaseswouldbetoachiev ecoexistenceof WiMAXdevicesinunlicensedbands. 3 ThisisknownasscalableOFDMA.VariousFFTsizesareusedto keepthesubcarrierspacingconstantfordierent transmissionbandwidths 33

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Table2.3AdvancedantennafeaturesofWiMAX. TechniquesDetails Advantages Adaptiveantennasystems(AAS)-beamforming TheBSusesmultipleantennastoformthebeamsinthedirectionofasubcarrier. Extendedrangeandincreasedcapacitythankstolowerinterference. Spacetimecoding(STC) TransmitdiversitysuchasAlamouticodeisused.Increaseinsystem gainthroughspatialdiversityandreducedfademargin. Spatialmultiplexing(SM) Independentandseparatelyencodeddatasignalsaretransmittedovermultipleantennas. Increaseincapacity. CollaborativeSMTwouserscantransmitcollaborativelyinthe sametileasiftwostreamsarespatiallymultiplexedfromtwoantennasofthesameuser. Increaseincapacity. AntennaselectionAnycombinationofantennasareselected(on-o typeofselectionofgroupofantennasfromtheavailableantennas)basedonthechannelfeedback. Ecientuseofavailablepower. AntennagroupingTheBScangroupmultipleantennasfordierent carriersindierentwaysbasedonthefeedbackfromtheBS.Forexample,ifwehavethreetransmitantennas,theBScangroupthersttwoantennasinsomecarriers,andthelasttwoantennasinsomeothercarriers. Maximizediversityandincreasecapacity. MIMOprecodingTheantennaelementsareweightedwitha matrixbeforemappingthemtotransmitantennasbasedonthefeedbackfromSSs.Thisschemeissimilartoawater-pouringalgorithm. Increaseincapacity. STCsub-packetcombining Intheinitialtransmission,thepacketsaretransmittedinafullMIMOspatialmultiplexingmode,withnodiversity.Ifthedatacannotbedecodedcorrectly,i.e.cyclicredundancycheck(CRC)checkfailed,thenthepacketsaresentinfullSTCmode,orfulltransmitdiversitymode.Thereceivercombinestheinitialdataandthelaterdataforbetterdetection. Providesincrementalredundancy. Frequencyhoppingdiversitycombining(FHDC) Thisscheme,asforSTC,transmitstwocomplexsymbolsusingthemultipleinputsingleoutputchannel. AdaptiveMIMOswitching(AMS) STCorSMisselectedadaptivelytoadapttochannelconditions. Optimizespectraleciencyisachieved. 34

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Subchannel 1Subchannel 2Subchannel 3Subchannel 4Disabled subcarriersPilots Frequency Guard band Guard band DC subcarrier OFDMA symbols(Time dimension) Subchannels (Frequency dimension) One tile In this case, the tile is one subchannel by two OFDMA symbols User 1 User 2 User 3 User 5 User 3 User 4 Figure2.14IllustrationofOFDMAsignalstructureusedinWiMAX. 2.6.2IEEE802.22 IEEE802.22standardisalsoknownastherstCRstandardbecauseoftheam ountofcognitive featuresthatareemployedbyit.Thesecognitivefeaturesincludechannelsensing,LUsdet ection, DFS,andTPC.EventhoughIEEE802.22standardisnotnalizedyet,thecurrentdra ftproposal isbasedonOFDMtransmissionanditisanticipatedthatthenalversionwil lbethesame.The IEEE802.22standardisdesignedforaxedpoint-to-multipointcommunicati ontopologywherethe BSactsasthemastermandatingalltheoperationparametersofuserswithint hecell.Andwhile theuserscansharesensinginformationwiththeBSthroughdistributedsensing,i tisuptotheBS tochangeausertransmitpower,modulation,codingoroperatingfrequency. 35

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OneofthemostdistinctivefeaturesofIEEE802.22standardisitssensingreq uirementswhich isbasedontwostages:fastsensingandnesensing.Inthefastsensingstage,aco arsealgorithm isemployed,e.g.energydetector.Thenesensingstageisinitiatedbasedontheprevious stage results.However,amoredetailedandpowerfulsensingmethodsareusedintheseconds tage.The resultsarereturnedtotheBSwhichusestheseresultsformanagingtransmissio ns. OnechallengeindesigningtheIEEE802.22standardistheinitializationofnew userswhodesire tocommunicatewiththeBS.Unlikecurrentwirelesstechnologies,frequencyandtime durationof theinitializationchannelarenotpredened.Therefore,initialusershavetoscanparts ,ifnotall, oftheTVbandstondtheBSoperatingfrequencyandtime.Inaddition,usersshouldbeabl eto dierentiatebetweenincumbentsignalsandtheBSsignal.Thiscouldprovetobev erychallenging especiallyiftheBSisoperatingoveracombinationofmultiplefrequencybands.2.6.3IEEE802.11 TheWLANstandard,IEEE802.11a/g,isprobablythemostcommonlyknownOFD M-based standard.ThemainstandardisupgradedtohavecognitivefeatureswiththeIEEE 802.11hand theIEEE802.11kstandards.TheIEEE802.11hstandardisdesignedtoallo westimationofchannel characteristicsandDFS.Inaddition,TPCisincorporatedaswell,providingt hesystemwithmore controloversignalrangeandinterferencelevel.ThepurposeoftheIEEE802.1 1hstandardisto allowWLANsystemstosharethe5GHzspectrumwithLUs(e.g.military radarsystems). NotethattheDFSproposedfortheaforementionedstandardscanbeconsideredasc hannel switchingorfrequencyhoppingtechnique.Thus,itcanbeappliedtoanytransmission technology andisnotexclusivetoOFDM.However,itisalsonoteworthytomentionthat manyrecentpublished articleshaveproposednewmethodstofacilitateDFSuseforOFDMsystems.OFD Msubcarriers aresplitintosubchannelsthatcanbedisabled,enabled,orassignedtomultipleusers ,according tosensingmeasurements.Theserecentstudiescanbedividedintotwocategories:addres sing thereductionofinterferencebetweendierentsubchannels[24,65{68,72{75],anda ddressingthe optimizationofthesubcahnnelallocationprocess[76,77].Infollowingam endmentstowireless standards,weexpectthattheaboveadvancedOFDM-basedtechniqueswillbeconsideredfor DFS. Ontheotherhand,theIEEE802.11kstandardisproposedforradioresourcemanag ement. Itdenesseveraltypesofmeasurementssuchaschannelloadreport,noisehistogra mreport,and stationstatisticsreport.Thenoisehistogramreportprovidesmethodst omeasureinterferencelevels 36

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WRAN WMAN WLAN IEEE 802.22 IEEE 802.16 IEEE 802.11 Reuse TV bands (spectrum sensing)DFS, TPC 802.16-2004 & 802.16e-2005Adaptive FFT size, CP, pilots, bandwidth allocation 802.11h & 802.11kDFS, TPCSite reportRF channel measurementsHidden nodes sensingShared statistics Figure2.15Standardsandtechnologiesdevelopments. thatdisplayallnon-IEEE802.11energyonachannelasreceivedbytheSSs.Theaccesspoi nt(AP) collectschannelinformationfromeachunitandmakesitsownmeasurements.This dataisthen usedbytheAPtoregulateaccesstoagivenchannel. Otherfeaturessuchastrackingofhiddennodesandsharingclientsstatisticsareincl udedin thestandard.ByapplyingboththeIEEE802.11handtheIEEE802.11kstanda rdstocurrent IEEE802.11-basedWLANsystems,theperformanceandeciencyofwirelessnetwor kingcanbe improvedsignicantly.Addingcognitivefeaturessuchaschannelsensingandestimat ion,statistics distribution,DFS,TPCtoWLANdeviceswillsoonbepossible.Fig.2.15sho wsanillustrationof thediscussedcurrentandfuturetechnologiesandstandards. 37

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2.7Conclusion CRisanexcitingandpromisingtechnologythatoersasolutiontothespectrum crowding problem.Ontheotherhand,OFDMtechniqueisusedinmanywirelesssystemsandprovenas a reliableandeectivetransmissionmethod.OFDMcanbeusedforrealizingCRconceptb ecauseofits inherentcapabilitiesthatarediscussedindetailinthischapter.ByemployingOFDMt ransmissionin CRsystems;adaptive,awareandrexiblesystemscapableofinteroperatingwi thcurrenttechnologies canberealized.However,thechallengesidentiedinthischapterneedtoberesearchedfurt herin ordertoaddresstheopenissues.PracticalCRsystemscanbedevelopedusingtwoappr oaches: currentwirelesstechnologiescanevolvetosupportmorecognitivefeaturesover time,ornewsystems thatsupportfullcognitivefeaturescanbedeveloped.Ineithercase,weforeseethatOF DMwillbe oneofthedominantPHYtechnologiesforCR. 38

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CHAPTER3 SYNCHRONIZATIONINOFDMAUPLINKSYSTEMS 3.1Introduction Worldwideinteroperabilityformicrowaveaccess(WiMAX),asarelativ elynewtechnology,has receivedtheattentionofresearchersandwirelesscompanies.Thisnewwirelesstechnol ogypromises todeliverbothhighdataratesandlong-rangecoverage.Withtheapprovalofthe mobileWiMAX standard(IEEE802.16e-2005)atthebeginningoftheyear2006,thistechnolo gybecameevenmore exciting.UnlikeWiFi[78,79],whichisdesignedforindoorapplicationsandw irelesslocalarea network(WLAN),WiMAXisoptimizedforoutdoorapplicationsandwirelessmet ropolitanarea network(WMAN). OneoftheexcitingaspectsofWiMAXisthatitsmediumaccesscontrol(MAC)layer supportsmorethanonephysicallayer(PHY)mode[9].Thisfeaturenotonlyenabl escompaniesto dierentiatetheirproductsfromeachother,butalsomakesWiMAXanadaptivetec hnologythat cansatisfydierentneedsdependingontheapplication.OneofthemostpromisingPHYmo des supportedbyWiMAXstandardisorthogonalfrequencydivisionmultipleaccess(OF DMA)PHY mode.OFDMAPHYmodeenablesaWiMAXbasestation(BS)tosupportmultipleusera ccess, xedormobile,overbothtimeandfrequencydomains.Inthismode,aBSsystemutil izesthe channelbydividingavailablesubcarriersintosubchannelsthatcanbeassignedto multipleusersin asophisticatedandadaptiveway.Asamatteroffact,userscanbeassignedto dierentbandwidths, dierenttimedurations,anddierentmodulationordersbasedonvariousparamet erssuchasthe usercarrier-to-interference-plus-noiseratio(CINR)andtheavailablebandwidth. OneoftheproblemsthatfacesWiMAXsystems,andOFDMAsystemsingeneral,issy nchronizationbetweentheBSandsubscriberstations(SS)withinthecell.Whileotherorthog onalfrequency divisionmultiplexing(OFDM)receiverscaneasilysynchronizetothereceivedsigna l[80,81],this isnotthecaseforOFDMAreceivers.AtanOFDMAreceiver,wheremultipleusersarri veatthe 39

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sametime,ifusersarenotsynchronizedwiththereceiver,theywillinterferewi theachother,and thereforetheBSwillnotbeabletorecoverindividualsignalsofeachuser.Hence,fo rOFDMA PHYmodetoworkproperly,allusersshouldarriveattheBSatthesameti mewithaconsiderably hightimingaccuracy.ThiscanbeachievedifallusersaresynchronizedwiththeBS beforethe communicationlinkisestablished.Thestandardstatesthatforausertojointhe channel,rst,the roundtripdelay(RTD)betweentheuserandtheBSmustbeknowntotheuser[9].This delay estimationisusedbytheusertosynchronizeitssignalsuchthatitarrivesa ttheBSinitsallocated time.Theprocessinwhichthisdelayisestimatediscalledinitialranging,and thisismandatedfor allSSsthatdesiretosynchronizetothechannelinitially. AsstatedintheIEEE802.16e-2005standard[9],theMAClayerattheBSdenes aranging channelasagroupofsix(ormore)subchannels,whereasubchannelisagroupofsubcar riersthat arechosenaccordingtoarandomizationformula.Inaddition,usersareallow edtocollideinthis rangingchannel.AnySSthatattemptstoestablishacommunicationlinkisrequired tocarryout asuccessfulinitialrangingprocesswiththeBSovertherangingchannel.OnceaSSsensesaB S, fornetworkentry,itrstscansforadownlink(DL)channelandsynchronizesitself withtheBS. Then,theSSshallacquiretransmitparameters,whichareincludedintheuplinkchanneldescr iptor (UCD),uplink(UL)-MAP,andDL-MAP.Usingacquiredparameters,theSSinitiat estheinitial rangingprocessbysendingarangingcodeovertheULframe.Atthereceiverside,theBSisrequiredtodetectdierentreceivedrangingcodesandestimatethetimingosetandthepo werfor eachuserthatbearsaninitialrangingcode.TheBSthenbroadcaststhedetectedrangingco des withadjustmentinstructionsforthetimingandpowerlevel.Thestatusnoticat ionsofeithera successfulrangingprocessorretransmissionarealsobroadcasted. Ininitialranging,theSSchoosesoneoftheavailablerangingcodesrandomlyand transmitsit twiceovertwoconsecutiveOFDMAsymbolswithbinaryphaseshiftkeying(BPSK)m odulation. TheSSshouldtransmittherangingcodeduringtheULframeaslongasthereisarang ingopportunity.UL-MAPshowsifarangingopportunityisavailablethroughthenextUL frame.Another optionistosendtwoconsecutiverangingcodesoverfourOFDMAsymbolstoincrease theprobabilityofcodedetection[9].Inthisstudy,rangingovertwosymbolsisconsi deredsincethesame conceptcanbeappliedtothefoursymbolscase. SynchronizationformultiuserOFDMsystemshasbeendiscussedintheliterature.The useof ltersmatchedtotheintendeduser'ssubcarriers(inourcase,therangingchannelsubcar riers)and 40

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thenuseofcyclicprex(CP)redundancytoestimatethetimingosetisproposedin[8 1].However, inOFDMAsystemswithinterleavedsubcarrierassignmentsuchasWiMAX,t herangingsubcarriers arenotnecessarilyadjacent,whichmakesthelteringprocessinapplicable.In[82], itisproposed tosynchronizeuserstotheBSoneatatime,withtheassumptionthatotherusersa realready synchronized.ThismethodcannotbeusedforOFDMAwithmultipleuserscollidinginthe ranging channel.Inaddition,thisapproachrequirestheuserswhoarenotyetsynchronizedtothe system tobeawareofotherusersattempttosynchronize.Finally,in[83,84]itis proposedtouseabank ofcorrelators(correspondingtonumberofrangingcodes)intimeorinfrequencydo maintodetect receivedrangingcodes.Thedisadvantageofthisapproachisthatthecomputational complexity increasesasthenumberofavailablerangingcodesincreases. Inthischapter,anewalgorithmforOFDMA-ULsynchronizationorinitialrang ingisproposed. SystemparametersarechosenbasedontheWiMAXstandard,sinceitrepresentsthemo strecent standardthatemploysOFDMA.Theproposedalgorithmisexaminedusingtheoretica lanalysisand computersimulationsoveradditivewhiteGaussiannoise(AWGN)anddispersi vechannelsinthe presenceofmultiuserinterference.Aperformanceandcomplexitycomparisonbetweenthepr oposed algorithmandprioralgorithmsinpracticalsystemconditionsarepresented.I tisdemonstratedthat theproposedalgorithmoersasignicantreductionincomputationalcomplexity whilecarryingout asuccessfulinitialrangingprocess.Thereductionincomplexitymakestheproposeda lgorithmmore attractivetopracticalimplementationsofOFDMAsystems.Forexample,the proposedalgorithm canbeappliedtolow-costOFDMA-basedfemtocellBSimplementationswherethenumber ofusers perBSislimited. Theremainderofthischapterisorganizedasfollows.Thesystemmodelisintro ducedinSection3.2.Currentandproposedrangingalgorithmsarediscussedindetailin Sections3.3and3.4, respectively.InSection3.5,thecomputationalcomplexityoftheproposedalgo rithmiscalculated andcomparedtocurrentrangingalgorithms.Simulationresultsanddiscussionsdem onstrating theperformanceoftheproposedrangingalgorithmcomparedtootheralgorithm sarepresentedin Section3.6.Finally,theconclusionsareoutlinedinSection3.7.3.2SystemModel ThesystemmodelisbasedontheIEEE802.16e-2005standard[9].TheULofan OFDMAsystem with N subcarriersisconsidered.AfterassigningDCandguardsubcarriers,theremaining subcar41

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riers, N d ,aregroupedinto Q subchannels.Eachsubchannelhas N Q = N d =Q subcarriers,where Q ischosensuchthat N d isanintegermultipleof Q .EachuserintheULisassignedoneormoresubchannels.TheBSdenesagroupofsixsubchannels(ormore)forranging.Notethatthe subcarriers assignedtoeachsubchannelarechosenrandomlyandthustheyarenotnecessarilyadja cent.TheBS broadcastsalltheranginginformation(i.e.rangingopportunities,ranging channels,rangingcodes andsoon)intheUL-MAP.OnerangingtimeslotspanstwoOFDMAsymbolduratio n.The k th rangingusersignalinfrequencydomainisdenotedas c ( k ) p =[ c ( k ) p (1) ;c ( k ) p (2) ;:::;c ( k ) p ( L )] T ,where p is theindexoftherandomlychosenrangingcodeand L isthesizeoftherangingcode.Thesignalis thenextendedto N byinserting N L zeros,whichresultsin X ( k ) p =[ X ( k ) p (1) ;X ( k ) p (2) ;:::;X ( k ) p ( N )] T Notethat X ( k ) p ( m )= 8>><>>: c ( k ) p ( n ) ; if m = i r ( n ) ; 0 ; otherwise (3.1) where i r ( n )istheindexofthe n thsubcarrierwithintherangingchannelsubcarriersset i r = [ i r (1) ;i r (2) ;:::;i r ( L )] T .Thevector X ( k ) p isthenfedtoan N -pointinversefastFouriertransform (IFFT).TheresultingsignalintimedomainisextendedovertwoOFDMAsymbo lsbyrepeating x ( k ) p twiceandaddingthecyclicprexwithnophasediscontinuity,where x ( k ) p isthetimerepresentation of X ( k ) p .NotethattheBSreceiverusesanobservationwindowof( N + N g )toacquireOFDMA symbols,where N g isthesizeoftheCP.Finally,thetransmittedsignalisdenotedas s ( k ) p = [ s ( k ) p (1) ;s ( k ) p (2) ;:::;s ( k ) p (2 N +2 N g )] T ,where, s ( k ) p = h x ( k ) p ( N N g +1) ;:::;x ( k ) p ( N ) ;x ( k ) p (1) ;:::;x ( k ) p ( N ) ; x ( k ) p (1) ;:::;x ( k ) p ( N ) ;x ( k ) p (1) ;:::;x ( k ) p ( N g ) i T : (3.2) Thetransmittedsignal s ( k ) p isthenreceivedbytheBSafterbeingcorruptedbythecommunication channel.Inthefollowinganalysis,weassumethatthechannelisnondispersivea ndthatthereceivedsignalsfrommultipleusersareonlyaectedbycomplexAWGN.However,we willevaluate theproposedrangingalgorithmperformanceforbothAWGNanddispersivec hannels.Asimilar approachhasbeenusedin[85]toanalyzetheproposedalgorithm. Allusersotherthantheusersperforminginitialrangingareassumedtobealr eadysynchronized totheBS.ThisisavalidassumptionassynchronizingtotheBSismandatoryb eforeaSScan 42

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establishthecommunicationlink.Hence,itisguaranteedthatthereisnointerference fromsynchronizedusersignalstotherangingchannel.Notethatthisisnotthecaseforrang ingusersastheir unsynchronizedsignalcancauseinterferencetosynchronizedusers.Asthissituationi sunavoidable, initialrangingSSisrequiredbythestandardtostarttherangingprocesswith minimumpossible powerlevel.Then,aslongastheSSfailstogetaresponsefromtheBS,thepoweri sincreased incrementallyuntilaresponseisdetected.Ifthemaximumpowerlevelisreachedandt heSSstill cannotgetaresponsefromtheBS,theuserstartsfromtheminimumpowerlevelandt heprocess isrepeated.ThisshowshowimportantitisforaBStodetectranginguserswith thelowestsignal levelspossible.3.3ExistingRangingAlgorithms TodetectrangingcodesattheBS,oneapproachwouldbetocross-correlatethereceiveds ignal withallpossiblerangingcodesintimedomain[83].Toreducethehighcomputat ionalcomplexity ofthisprocess,onecaninsteadauto-correlatethereceivedsignalwithitsdelayed replicatoexploit therepetitionintherangingcode.However,forthisapproachtoworkproperly ,thesystemneedsto extractothernon-rangingusersignalsfromthereceivedsignalastherangingusersar efrequencymultiplexedwiththosesynchronizedusers.Notonlydoessuchaprocessincreasethecom plexity anddelayofthealgorithm,butitisalsoaectedbytheperformanceofnon-ranging userssignal estimator.Inaddition,thecodesusedforrangingaremodulatedinfrequencydomain andperforming thecorrelationintimedomainweakenstheauto-correlation/cross-correlati onpropertiesofused codes. Anotherapproachtodetectrangingcodesistoperformthecross-correlationonthef requencydomainsignalattheoutputofthefastFouriertransform(FFT)[84].Int hiscase,acomplete OFDMArangingsymbolintheobservationwindowresultsinacorrectrangingcode inthefrequency domainevenifatimingosetexists.Theeectofthetimingosetistranslat edintoalinear phaseshift,alsocalledaphaserotation,inthefrequencydomain.Toestimatet hetimingoset oftherangingcode,thesystemappliesallpossiblelinearphaseshifts,correspo ndingtopossible timingosets,tothesignal.Then,thereceivedsignaliscorrelatedwithallr angingcodes.A thresholdissettodetecttheexistenceofarangingcodeinthecurrentobservationwindo wandits timingoset.Oneadvantageofperformingthecross-correlationprocessinf requencydomainisthat thereisnointerferencefromnon-ranginguserstotherangingchannel.Thus,theprobabili tyofa 43

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misseddetectionorafalsealarm,duetomultiuserinterference,isreduced.Anotheradva ntageof thisapproachisthatoperatinginfrequencydomainutilizestheauto-correlation/ cross-correlation propertiesofusedrangingcodes. Themaindisadvantageofthepreviouslymentionedalgorithmsisthehighcom putationalcomplexity.ConsiderthemaximumRTDtobe max T S ,where T S isthesamplingtime.Ifthetotal numberofcodesis K ,then K max cross-correlationoperationsareneededforeveryOFDMAsymbol.IntheWLANIEEE802.16a[69]andIEEE802.16a/b[86]standar dsconsideredin[83]and in[84],respectively,thenumberoflongrangingcodesusedforinitialrangingi sonly16.However, forIEEE802.16e-2005[9],thenumberofrangingcodesis256.Thesecodesaredi videdintothree categories:initialrangingcodes,periodicrangingcodes,andbandwidth-requestcodes.Ini tially,the BSisexpectedtoassignmorecodesforinitialrangingasuserswithinthecells tartenteringthe network.Ifweassumethat128codeswouldbeassignedforinitialranging,t henforOFDMAsystemsbasedonIEEE802.16e-2005,thecomputationalcomplexityfortheranging processwouldbe eighttimesasmuchasthecomplexityofIEEE802.16a/b.Otherrangingalgor ithmswereproposed intheliterature(e.g.,[87]and[88]).However,thosealgorithmsare notapplicabletotheconsidered standard.Hence,theyarenotconsideredinthisstudy.3.4ProposedAlgorithm Intheproposedalgorithm,weconcentratemoreonthetradeobetweencomputat ionalcomplexityandperformanceoftherangingprocesssothatthealgorithmcanbereali zedinpractical systems.WechooseanobservationwindowwithoneOFDMAsymbolsizeanda pplythealgorithm infrequencydomainfortheadvantagesofthismethodthatismentionedearlierin Section3.3. However,insteadofdirectlycross-correlatingwitheverypossiblecodeandevery possiblephase osetforeveryOFDMAsymbol,webreaktheinitialrangingprocessintothreem aintasks.Our rsttaskistondOFDMAsymbolscontainingrangingcodes.Thisstepallowst hesystemtond outwhichsymbolsitshouldprocessfurtherandwhichonesthesystemshouldjustdro psothatno additionalcomputationsareperformedonemptyOFDMAsymbols.Energydetectors ,whichare discussedinmoredetailinSection3.4.1,areusedtodetectOFDMAsymbolsconta iningranging codesintherangingchannel.Next,thealgorithmndshowmanycodestherearewithindetect ed OFDMAsymbolsfromsteponeanddeterminethetimingosets(orlinearphaseshi fts)foreach code.Again,inthisstepthesystemfurtherreducesthecomputationalcomplexitybyrst nding 44

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thetimingosetofthecodesbeforeperformingthecross-correlationwithal lpossiblecodesfor everypossiblelinearphaseshift.Section3.4.2discussesthedetailsofthisstep. Thelaststepinthe algorithmisidenticationofmultiusercodesbycross-correlatingdetectedcodeswit hallpossible rangingcodesafterremovalofanytimingosets.ThisstepiscoveredinSection 3.4.3.Usingthis approach,thecomputationalcomplexityisgreatlyreducedwhiletheperformanceiss tillacceptable asshowninSections3.5and3.6.3.4.1EnergyDetector IfthereisarangingopportunityinthenextULframe,therangingchannelwillbea vailable throughtheentireULsubframeduration.TheBSsamplesthereceivedsignalandgro upsitinto N + N g samples.TheCPisremovedandtheremaining N samplesarefedtotheFFTunit.The rangingchannelcontainsnoiseandenergyfromrangingusers.Thereceivedunsynchronizedsi gnal ofaranginguserconsistsoftworangingsymbolswithnophasediscontinuity .TheOFDMAsymbols processedbytheBScanbeonlyoneofthreepossiblecases: a )emptysymbolscontainingonlynoise, b )symbolscontainingincompletepartsoftherangingsignal,whichcauseinter ferencetosubcarriers otherthantherangingsubcarriersandthusinterferewithsynchronizedusers,and c )symbolsthat areentirelylledwiththerangingsignal,referredtoassymbolswithcom pleterangingsignal.We areinterestedindetectingthethirdkind,asitcontainstherequiredinformatio ntodetectthe userrangingcode.Foreveryrangingusersignal,atleastonesymbolwithcomplete rangingsignal shouldbereceivedbytheBSsincetherangingsignalspanstwoOFDMAsymbols.Em ptysymbols shouldbeignoredsincetheycontainnoinformation.TheinformationincludedinOF DMAsymbols withincompleterangingsignal(i.e.therangingcode,itstimingoset,andsig nalpower)canbe extractedfromthesymbolswithcompleterangingsignal.Therefore,amissed detectionofsymbols withincompletesignalshouldnotaecttheperformanceofthealgorithm.Inor dertodetectsymbols withacompleterangingsignalweuseasimpleenergydetectorinfrequencydomain.Theener gy detectormeasurestheenergywithintherangingchannel.Thismethodhastwoadvantages: a )since theenergyismeasuredinthefrequencydomainandsincetherangingsubcarriersarenota djacent, thelikelihoodofapulseofnoisetriggeringtheenergydetectorbymistakeisl ow, b )theenergyis alreadymeasuredtoobtainthenoisevarianceofthechannelandcanalsobeusedlat ertomeasure thesignalpowerofrangingusers.Therefore,noadditionalcomputationalcomplexit yisrequiredfor thisstep. 45

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Themeasuredenergyintherangingchannelis, E g = L 1 X n =0 j Y ( m ) j 2 (3.3) where m = i r ( n )and Y isthe N vectorattheoutputoftheFFTunitatthereceiverside. Aftermeasuringtheenergywithintherangingchannel,athreshold 1 isusedtodecideifthe OFDMAsymbolcontainsarangingcodeornot.Tondthebestvaluefor 1 ,theprobabilityof afalsealarm P fa andtheprobabilityofmisseddetection P md arecalculated.Theprobabilityofa falsealarmisdenedastheprobabilityofnoiseenergyinemptyOFDMAsymbolsex ceeding 1 Inthesamemanner,theprobabilityofmisseddetectionisdenedastheprobabilityof theenergy ofanOFDMAsymbolnotexceeding 1 whilecontainingacompleterangingsignal.Notethatthe caseofanOFDMAsymbolcontainingincompleterangingsignalisignoredinthe calculationof P md asmissingthissymboldoesnotaectthealgorithmperformance.Infact,detecti nganincomplete rangingsignalcanadditionallyprovidecorrectranginginformationiftheti mingosetisrelatively small.IfthecurrentOFDMAsymbolcontainsnorangingcode,then Y ( m )= W ( m ),where W is avectorofcomplexAWGNsampleswithzeromeanand N 0 = 2variance.From(3.3), E g = L 1 X n =0 j W ( m ) j 2 ; = L 1 X n =0 W 2 < ( m )+ L 1 X n =0 W 2 = ( m )(3.4) where W < ( m )and W = ( m )aretherealandimaginarypartsof W ( m ),respectively.Theenergy inthiscaseisthesumof2 L samplesofthesquareofnormally-distributedrandomvariableswith zeromeanand N 0 = 2variance.Hence,themeasuredenergycanbedescribedasarandomvariable withChi-squaredistributionhavingamean 1 = LN 0 andvariance 2 1 = LN 2 0 .Usingthecentral limittheorem,andassuming2 L islargeenough,theenergydistributioncanbeapproximatedasa normally-distributedrandomvariablewiththesamemeanandvariance.Basedo nthestandard[9], L ortherangingcodelengthisequalto144whichislargeenoughtovalidatethea boveapproximation. Theprobabilityofafalsealarmthenbecomes[89], P fa =0 : 5erfc 1 1 p 2 2 1 (3.5) 46

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whereerfcisthecomplementaryerrorfunction.ForanOFDMAsymbolcontaininga complete rangingsignal,ifauser k signalhasatimingosetof k samples 1 ,thentheOFDMAsymbolwith completerangingsignalcontainsacopyoftherangingcodewhichiscyclicallyshi ftedby k samples. TheOFDMAsymbolinthefrequencydomainhasalinearphaseshiftof2 n k =N where n isthe subcarrierindex.Inthiscase, E g = L 1 X n =0 c ( k ) p ( m )exp[ | m ( k )]+ W ( m ) 2 (3.6) where m ( k )=2 m k =N .SinceBPSKmodulationisused, c ( k ) p ( m )= 1.Thus, E g = L 1 X n =0 1+ W 2 < ( m )+ W 2 = ( m )+ 2 c ( k ) p ( m )cos[ m ( k )] W < ( m )+2 c ( k ) p ( m )sin[ m ( k )] W = ( m ) : (3.7) Usingthecentrallimittheorem,thedistributionofthisenergycanbeapproxima tedasanormallydistributedrandomvariablewithmean 2 = L + LN 0 andvariance 2 2 = LN 2 0 +2 LN 0 asshownin AppendixA.Hence,theprobabilityofamisseddetectionbecomes, P md =1 0 : 5erfc 1 2 p 2 2 2 : (3.8) Fig.3.1shows P fa and P md againstnormalized 1 (normalizedby L and N 0 )fordierentsignalto-noiseratio(SNR)levels.Notethat P fa doesnotchangeastheSNRchangessince 1 isnormalized andsince P fa dependsonlyon N 0 .Inthisstudy, N 0 isassumedtobeavailableforchoosingthe bestvalueof 1 .ThisisavalidassumptionsincetheBSneedstoestimatethenoiselevelfor calculationsofdierentusersSNR.AnexampleofareceivedULframewithranging codesisshown inFig.3.2.Thereceivedsymbolsofrangingusersareshownintimedomain. Also,thegureshows themeasuredenergyontherangingchannelforeveryOFDMAsymbolandforanSNRof10 dB. Notethatintheaboveanalysis,itisassumedthatonlyonecompleteranging signalexistsinthe receivedsymbol.Thisassumptionisbasedonworstcasescenario,since P md getsevenlowerifmore thanonecompletesignalexistsinthereceivedsymbolasshowninFig.3.2. 1 Weonlyconsidertimingosetthatisintegermultipleofthe samplingtime.Thenon-integerpartofthedelayis insignicanttotheOFDMAsystemperformanceandisusually incorporatedaspartofthecommunicationchannel. 47

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0 5 10 15 20 25 30 35 40 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 NormalizedThreshold 1 (2 =LN 0 )Probability P fa P md ; SNR=0dB P md ; SNR=5dB P md ; SNR=10dB Figure3.1 P fa and P md fordierentnoiselevels. 3.4.2TimingOsetEstimation Inthepreviousstep,thesystemdetectsOFDMAsymbolscontainingoneormorecompl ete rangingsignals.Thenextstepistoidentifyhowmanycodesareineachsymbol andestimate thetimingosetforeachofthesecodes.Sincetheproposedalgorithmisappliedin frequency domain,timingosetwouldbedirectlytranslatedintoalinearphaseshift.I nthiscase,whatis estimatedisactuallythelinearphaseshiftforeachcodeinthecurrentOFDMAsym bol.Thiscan bedonebycross-correlatingtherangingchannelofthecurrentOFDMAsymbolwitha llpossible codesafterapplyingallpossiblelinearphaseshiftstothesymbol.Thecorrela toroutputisfollowed byathresholddetectortodetectdierentrangingcodesandtheirphaseshiftswithinthecurr ent symbol.However,thisiscomputationallycomplex.Weintendedtoreducethecomplexi tyofthis operationbyexploitingthefactthattimingosetsonlyaectthephaseofthef requencydomain signal.SinceBPSKmodulationisused,thesignalshouldnothaveanimaginarypar t.Ifthereare K ranginguserswithinthecurrentOFDMAsymbol,eachuserhasatimingoset k samples,where 0 < k < max and max isthemaximumRTDbetweentheSSandtheBSwithinthecurrentcell. 48

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0 2 4 6 8 10 12 0 100 200 300 400 OFDMA symbolNormalized measured energy 0 2 4 6 8 10 12 TimeSymbols S1S1 S2S2 S3S3 S4S4 S5S5 Figure3.2NormalizedmeasuredenergyontherangingchannelatSNR=10dB. Then, Y ( m )= K 1 X k =0 c ( k ) p ( m )exp[ | m ( k )]+ W ( m )(3.9) where m = i r (0) ;i r (1) ;:::;i r ( L 1).Ascanbeseenin(3.9),iftherewerenotimingosets(i.e. k =0for k =0 ; 1 ;:::;K 1),thewholeenergyoftheranginguserwillbeonlyintherealpart ofthesignalandtheimaginarypartwillcontainonlynoise.Byapplyingall possiblelinearphase shiftsandtakingtheenergyoftherealpartofthesignal,wehave, E r ( u )= L 1 X n =0 < 2 f Y ( m )exp[ | m ( u )] g = L 1 X n =0 K 1 X k =0 c ( k ) p ( m )cos[ m ( k u )]+ ^ W < ( m ) 2 (3.10) where u =0 ; 1 ;:::; max ^ W ( m )= W ( m )exp[ | m ( u )]and ^ W < ( m )=
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of k forallvaluesof k .Themeasuredrealenergyisnormalizedwithrespecttotheaveragereal energyofthesymbol E r suchthat, ~ E r ( u )= E r ( u ) E r = E r (3.11) where, E r = 1 K K 1 X u =0 E r ( u ) : (3.12) AsshowninAppendixB, E fE r ( u ) g 8>><>>: L ( K +1+ N 0 ) = 2 ; for u = k L ( K + N 0 ) = 2 ; for u 6 = k : (3.13) From(3.12)and(3.13)weget, E r = KE fE r ( u ) j u = k g +( max K ) E fE r ( u ) j u 6 = k g max : (3.14) Theaboveequationisvalidgiventhat K< max ,whichisareasonableassumptionsince,depending onthecellradius, max cangoupto N= 2,whilethenumberofranginguserswithinthesameOFDMA symbolisusuallymuchlowerthanthisvalue.Fig.3.3shows E f ~ E r ( u ) j u = k g and E f ~ E r ( u ) j u 6 = k g fordierentvaluesof K andforSNR=10dB.Forsimulatedresults,weusethesystemsetup presentedinSection3.6.1.Assumingallrangingusersarereceivedwithequalpow er,thesignal-tointerference-plus-noiseratio(SINR)levelforagivennumberofrangingusersperOFD MAsymbol andforanSNRlevelof10dBiscalculatedinTable3.1,whereSINRisdenedastherat ioofthe powerofoneusersignaltothepoweroftheremaininguserssignalsplusnoisepow er.Thegure showsthatasthenumberofrangingusersincreases,theprobabilityofamisseddetect ionincreases sincethedierencebetweenthetwomeansdecreases.Inaddition,thevarianceofthemeasuredenergyalsoincreaseswiththenumberofrangingusers,sincetheyactasinterferencenoi sefor u 6 = k asshownin(3.10).Notethatsince K isusuallyverysmallcomparedto max ,thenfrom(3.14), E r E fE r ( u ) j u 6 = k g and E n ~ E r ( u ) j u 6 = k o 0,asshowninFig.3.3. 50

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1 2 3 4 5 6 7 8 9 10 -0.2 0 0.2 0.4 0.6 0.8 1 Ranging users per OFDMA symbolNormalized energy level E f ~ E r ( u ) j u = k g ; theoritical E f ~ E r ( u ) j u = k g ; simulated E f ~ E r ( u ) j u 6 = k g ; theoritical E f ~ E r ( u ) j u 6 = k g ; simulated Figure3.3 E f ~ E r ( u ) j u = k g and E f ~ E r ( u ) j u 6 = k g fordierentnumbersofrangingusers. Table3.1SINRvs.numberofusersperOFDMAsymbol. Number ofusers SINR (dB) Number ofusers SINR (dB) 110 : 0 6 7 : 1 2 0 : 4 7 7 : 9 3 3 : 2 8 8 : 5 4 4 : 9 9 9 : 1 5 6 : 1 10 9 : 6 3.4.3CodeDetector Intheprevioustwostepsofthealgorithm,OFDMAsymbolscontainingranging codeswere detectedandtheirtimingosetswereestimated.Thelaststageistoidentifywhi chcodeswere transmittedoutoftheavailablerangingcodes, P ,where P isthenumberofcodesassignedbythe BSforinitialranging.Inthisstep,thelinearphaseshiftcorrespondingtoeach detectedranging codeisremovedandthenacross-correlationwithallpossiblerangingcodesisp erformed.The correlatoroutputis, E ( v ) c ( i )= L 1 X n =0
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where i =0 ; 1 ;:::;P 1,and^ v istheestimatedtimingosetofthe v thuser.Thevector E ( v ) c is calculatedforeverydetectedrangingcode, v ,where v =0 ; 1 ;:::; ^ K 1,and ^ K isthetotalnumber ofdetectedrangingcodesinthesecondstep. E ( v ) c isthencomparedtoathreshold, 3 ,toidentify whichrangingcodeiswithinthecurrentOFDMAsymbol.Notethat 3 isnormalizedbytheroot meansquarevalueof E ( v ) c .Sincethisstepshouldnotbereachedunlessatleastonerangingcode existsinthecurrentOFDMAsymbol,thecodewithmaximumcorrelationcouldj ustbechosen foreveryvalueof v .However,athresholdisusedsothatthealgorithmcandetectmultiplecodes withthesametimingosetwhichwouldbeinterpretedasasinglecodeinthes econdstepofthe algorithm.Inthiscase, ^ K isupdatedtorerecttheincreaseinthenumberofdetectedrangingcodes. Inaddition,iftwousershappentousethesamerangingcodeandboththeirsignals arereceived inthesamesymbolbutwithdierenttimingosets,thesystemdeclaresacolli sionandbothcodes aredropped.Thecorrespondingusersthenhavetoretryinthenextavailablerangingo pportunity. 3.5ComputationalComplexity Forpracticalapplications,thecomputationalcomplexityofanalgorithmisi mportant.Inthis section,weevaluatethecomplexityoftheproposedalgorithmandcompareitto otheralgorithms. Theproposedalgorithmiscomparedwiththetwoproposedalgorithmsin[8 3]and[84],which arereferredtoasalgorithm1andalgorithm2,respectively.Foralgori thm1,anobservationwindow withtheOFDMAsymbolsizeisused.Abankofcorrelators,equaltothenumberof available rangingcodes P ,isusedtoseparaterangingcodesinthereceivedsignal.Ifthemaximumpossible delayis max ,then( max +1) P cross-correlationoperationsareperformedforeveryOFDMAsymbol withrangingopportunity.AssumingthecurrentULconsistsof N UL OFDMAsymbols,where N UL isrequiredbythestandardtobeanintegermultipleof3,thenthetotalnumber ofcorrelation operationsperformedwouldbe N UL ( max +1) P .Thesamenumberappliesforthresholdcomparison operations.Algorithm2,ontheotherhand,performsthecross-correlationi nfrequencydomain. Thus,toperformthecross-correlationateverypossibletimingoset,al inearphaseshiftof m ( u ) where u =0 ; 1 ;:::; max ,isappliedtothefrequencydomainsignalpriortothecross-correlatorsbank. Asaresult,algorithm2hasanadditionof max +1linearphaseshiftsaddedtoitscomputational complexity.However,sincethecorrelationisperformedinthefrequencydomain,a ndsinceBPSK modulationisused,thecorrelationsaredoneonreal-signalsunlikealgorithm 1whichhastoperform complex-signalcorrelations. 52

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Intheproposedalgorithm,theenergyoftherangingchannelforeveryOFDMAsymbo lis calculated.Asaresult, N UL energycalculationoperationsandthresholdcomparisonsareneeded. Theenergycalculationisalreadyperformedfor N 0 estimation.Assumingthateveryrangingsymbol triggerstheenergydetectorovertwoOFDMAsymbols,thenatmost2 K OFDMAsymbolswillreach thenextstageofthealgorithm,where K isthetotalnumberofranginguserswithinthecurrentUL frame.Ofcourse,ifoneormorecodescollide,thenlessOFDMAsymbolswillreach thenextstage. Inthesecondstage,allpossiblelinearphaseshiftsareappliedtotheOFDMAsy mbol(i.e.from0 to max ).Theenergyoftherealpartofthesignalismeasuredandcomparedtoathreshold.Th us, (1+ max )linearphaseshifts,realenergycalculation,andcomparisonoperationsareper formed.A maximumof K rangingcodes,within2 K rangingOFDMAsymbols,willreachthethirdandlast stage.Across-correlationwithallpossiblecodesisperformed.Asaresult ,2 KP correlationsand comparisonoperations(CMPs)areperformedatthisstage. Table3.2showsthenumberofadditions(ADDs)andmultiplications(MULs)needed foreach operation.UsingTable3.2,thecomputationalcomplexityofthealgorithms underinvestigationis, Algorithm1: N UL P ( max +1)(4 L 2)ADD+4 LN UL P ( max +1)MUL+ N UL P ( max +1)CMP Algorithm2: ( max +1)(2 L + N UL PL N UL P )ADD+ L ( max +1)(4+ N UL P )MUL+ N UL P ( max +1)CMP ProposedAlgorithm: h N UL (4 L 2)+2 K ( max +1)(3 L 1)+2 KP ( L 1) i ADD+ h 2 L ( KP +2)+10 KL ( max +1) i MUL+ h N UL +2 K ( max + P +1) i CMP Finally,thecomplexityofallthreealgorithmsiscalculatedforapractical system 2 .Weassume N UL =12OFDMAsymbols, P =256codes(maximum), L =144bits(standard-based[9]),and 2 UsingCPUcyclecountsbasedonXilinXDSP48slice. 53

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Table3.2Proposedalgorithm'scomputationalcomplexity. OperationADDMUL Correlation,complex2( L 1)+2 L 4 L Correlation,real L 1 L Energycalc.,complex2( L 1)+2 L 4 L Energycalc.,real L 1 L Phaseshift2 L 4 L max =512samplesfor N =1024.Thenumberofcyclesneededbyeachalgorithmisasfollows, Algorithm1:3 : 629 10 9 cycles ; Algorithm2:9 : 088 10 8 cycles ; ProposedAlgorithm:2 : 963 10 6 cyclesfor K =1 ; 5 : 909 10 7 cyclesfor K =20 : Thedierenceincomputationalcomplexityisevident.Thecomplexityoftheproposeda lgorithm isafewordersofmagnitudelowerthanthecomplexityofalgorithms1and2.Whi lebothof algorithm1and2maintainxedcomplexityregardlessofthenumberofranging users K ,the proposedalgorithmcanupdateto K ,whichgivesitthelowestlimitincomputationalcomplexity. Notethattheaboveresultsareoptimisticasweassumetherearenofals ealarmsintherstand secondstagesoftheproposedalgorithm.Acomplexitycomparisonforatypica lWiMAXsystem operatinginapracticalwirelessenvironmentispresentedinthefollowingsect ion. 3.6SimulationResults3.6.1SystemSetup AnOFDMAsystemmodelbasedon[9,90]isusedwiththefollowingparameters: N =1024, N g =128samples, N UL =12OFDMAsymbols, L =144bits.Thesystemisassumedtobeoperating at2GHzcenterfrequencywithabandwidthof10MHzandasamplingfrequencyof11.2MH z.The maximumRTDconsideredis45 : 71 S( max =512samples)allowingforacellradiusof6 : 86Km. Thetotalnumberofrangingcodesis256codes.Intheconsideredsystem,allcodesare assigned toinitialranging,i.e. P =256.Therangingchannelismadeupofsixsubchannelsandspanning 144subcarriersperOFDMAsymbol.Ranginguserschoosetwoconsecutivesymbo lsrandomlyto 54

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Table3.3CharacteristicsoftheITUVehicularAchannelenvironment. TapRelative delay(nS) Average power(dB) 100 : 0 2310 1 : 0 37104 9 : 0 41090 10 : 0 51730 15 : 0 62510 20 : 0 sendtheirrangingcodeduringtheULframewithequalprobability.Ineachsimulat ion,10 ; 000UL framesor120 ; 000OFDMAsymbolsareusedtoevaluatethesystemperformance. 3.6.2ChannelModel TheperformanceoftheproposedrangingalgorithmisevaluatedinbothanAW GNchannel andanoutdoordispersivechannel.Forthedispersivechannel,weuseoneofthesta ndardchannel modelsdenedbyInternationalTelecommunicationUnion(ITU)[90,91].Thetime-v aryingchannel impulseresponseforthesemodelscanbedescribedby h ( ;t )= X ` h ` ( t ) ( ` ) : (3.16) Thisequationdenestheimpulseresponseofatapped-delaychannelwitheverytap ` havinga delayof ` andgainof ` ( t ).Inthisstudy,weconsidertheVehicularAchannelenvironment[91]. Thetaps'relativedelaysandaveragepowersareshowninTable3.3.Thecha nneltaps ` ( t )are complexGaussianprocesses,andareindependentfordierentpaths.Dierentuserchannelsa re assumedindependentandthechannelsarealsoindependentbetweenULframes. Themultipathfadingchannelisexpectedtodegradetheperformanceoftherangingalgo rithms underinvestigation.Fortheproposedalgorithm,onlythesecondandthirdstepsa resignicantly aectedbythemultipathchannel.Theimpactofchannelmodelsonthethirdstep,wherethesignaliscorrelatedwithallpossiblecodes,hasalreadybeendiscussedin[84] wherealgorithm2is presented.Therefore,wearemainlyinterestedinexaminingtheeectofadispersive channelonthe secondstepwherewedetectrangingcodeswithintheOFDMAsymbolandestimatetheirti ming osets. 55

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-2 0 2 -2 -1 0 1 2 (a) AWGN channel, no timing offset RealImaginary -2 0 2 -2 -1 0 1 2 (b) AWGN channel, with timing error RealImaginary -2 0 2 -2 -1 0 1 2 (c) Dispersive channel, no timing offset RealImaginary -2 0 2 -2 -1 0 1 2 (d) Dispersive channel, with timing error RealImaginary Figure3.4Theeectofsynchronizationerrorontheconstellationpointsof atypicalBPSKmodulatedOFDMAsymbolreceivedoverAWGNanddispersivechannels. Asdiscussedearlier,thesubcarriersofanOFDMAsymbolwithatimingerror exhibitalinear phaseshift.Therefore,byapplyingtheappropriatelinearphaseshifttothereceiveds ymbols, thiseectiscompensated.Fig.3.4showsthateectontheconstellationpointso fatypicalBPSKmodulatedOFDMAsymbolreceivedoverAWGNchannelwithSNR=10dBandoverthedisper sive channelreferredtoearlier.Asseeninthegure,thelinearphaseshiftcausesthesymbol energy tobedistributedequallybetweentherealandimaginarypartsofthesignal.Ont heotherhand, atthecorrecttimingoset,theenergyismoreconcentratedintoasingleaxis. Theeectofthe dispersivechannelisthatatthecorrecttimingoset,thesignalismorenoisy andthereisalso arandomgainandphaseshift.However,thecorrecttimingosetisstilldetectabl ecomparedto thesamesignalwithwrongtimingoset.Therealpartofthesignalcontai ns50%ofthetotal symbolenergywhenatimingosetispresentregardlessofthewirelesschannel.Int heabove exampleandwithnotimingoset,therealpartofthesignalholds99%and69%o fthetotal symbolenergyoverAWGNandmultipathfadingchannels,respectively.Tofurtheril lustratethis eect,computersimulationswereusedtocalculatetheprobabilitiesPr fj ~ E r ( u ) j > 2 j u = k g and Pr fj ~ E r ( u ) j > 2 j u 6 = k g fordierentvaluesof 2 overnondispersiveanddispersivechannels.The 56

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0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 2 Probability Pr fj ~ E r ( u ) j > 2 j u = k g ,nondispersive Pr fj ~ E r ( u ) j > 2 j u = k g ,dispersive Pr fj ~ E r ( u ) j > 2 j u 6 = k g ,nondispersive Pr fj ~ E r ( u ) j > 2 j u 6 = k g ,dispersive Figure3.5Pr fj ~ E r ( u ) j > 2 j u = k g andPr fj ~ E r ( u ) j > 2 j u 6 = k g fordierentvaluesof 2 over nondispersiveanddispersivechannels.resultsareshowninFig.3.5.Notethatweconsider j ~ E r ( u ) j astoavoidnegativevaluesthatcan resultfromphaseshiftsintroducedbythechannel.Asexpected,thePr fj ~ E r ( u ) j > 2 j u = k g is signicantlyhigherthanthePr fj ~ E r ( u ) j > 2 j u 6 = k g foragiventhresholdlevel 2 .Thegureshows thatforbothchannels,Pr fj ~ E r ( u ) j > 2 j u 6 = k g exhibitsthesamebehaviorwhereitdecaysatafast rateas 2 increases.Pr fj ~ E r ( u ) j > 2 j u = k g ontheotherhand,decreasesas 2 increasesonlyfor dispersivechannels.3.6.3ProposedAlgorithmPerformance ThesystemperformanceisevaluatedatanSNR=10dBoverbothAWGNandVehicular A dispersivechannels.Theproposedalgorithmperformanceiscomparedtothatof algorithm2.The performanceisinvestigatedfordierentnumbersofrangingusersperULfram e.Tobeableto fairlyevaluatethesystemperformancefordierentnumbersofrangingusers, itisassumedthat allrangingsignalsarereceivedwithequalpowers.However,boththepropos edalgorithmand algorithm2canoperatewhendierentusershavedierentpowerlevels.Fortheres ultspresented inthischapter,theSINRcorrespondingtoagivennumberofusersperOFDMAsymbol isshown inTable3.1.BasedonouranalysisandthesimulationresultsshowninFi g.3.1andFig.3.5,the 57

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1 2 3 4 5 6 7 8 9 10 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 Number of ranging users per UL frameProbability of missed detection Proposed alg., dispersive Alg. 2, dispersive Proposed alg., AWGN Alg. 2, AWGN Figure3.6Probabilityofmisseddetection. thresholds( 1 2 3 )fortheproposedalgorithmarechosentobe(3,0 : 2,6)forAWGNchannels and(3,0 : 1,6)fordispersivechannels.Fig.3.6andFig.3.7showtheprobabilityof misseddetection andtheprobabilityoffalsealarm,respectively,forboththeproposedal gorithmandalgorithm2, andfordierentnumbersofrangingusersperULframe.OverAWGNchannels,bothal gorithm performancesarealmostidenticalwithzeroprobabilityoffalsealarm.Ov erdispersivechannels, theproposedalgorithmsuersfromahigherprobabilityofmisseddetectioncompa redtoalgorithm 2.Thedierencebetweenthetwoalgorithmsincreasesasthenumberofusersincreases.On the otherhand,theproposedalgorithmshowsamuchlowerprobabilityoffalseala rmthanalgorithm 2especiallyforlownumberofrangingusers.Evenwithupto8rangingusersperU Lframe,the proposedalgorithmisabletodetectmorethan75%ofreceivedcodeswithafalse alarmprobability lessthan0 : 2%. Animportantmeasureoftherangingalgorithmqualityisthetimingesti mationaccuracy.For dispersivechannels,thetimingerrordenitionisambiguous[81].Inthisstudy, weconsiderthe timingerrorrelativetothechanneltapwithmaximumaveragepower,orrs ttapintheconsidered dispersivechannel.Thestandarddeviationsforthetimingestimatorerrorsf orboththeproposed algorithmandalgorithm2areshowninFig.3.8.Bothalgorithmssho wzerotimingerrorsforAWGN 58

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1 2 3 4 5 6 7 8 9 10 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.05 Number of ranging users per UL frameProbability of false alarm Proposed alg., dispersive Alg. 2, dispersive Proposed alg., AWGN Alg. 2, AWGN Figure3.7Probabilityoffalsealarm. channels.Overdispersivechannels,theproposedalgorithmtimingestimatorsho wsahighererror standarddeviationthanthatofalgorithm2.Overall,bothalgorithmss howanaccuratetiming estimationcapabilitywithanaveragestandarddeviationof5and3fort heproposedalgorithmand algorithm2,respectively.Amoreimportantmeasureofrangingaccuracyis theprobabilityofthe timingerrorfallingoutsideagiveninterval.Forexample,ifweassumet hetimingerrorstobea normally-distributedrandomvariablewithzeromean[81],theprobabilityof thetimingerrorto exceed32samples(25%oftheCP)islessthan1%forbothalgorithms. Next,weconsiderthecomputationalcomplexityoftheproposedalgorithm.Forb othalgorithms underconsideration,correlatingthereceivedsignalwithallpossiblerangingcodesco nstitutesthe majorityofthealgorithmcomputations.Assuch,thenumberoftimesthisfunct ioniscalledby therangingalgorithmisusedasameasureofhowcomplexthealgorithmsare.In thisregard, algorithm2hasaxedcomputationcomplexityregardlessofthenumberofranging opportunities orthenumberofranginguserswithinthereceivedULframeasshowninsection3. 5.Thereduction ofcomputationalcomplexitygainedbyusingtheproposedalgorithmoveralgor ithm2isevaluated andtheresultsareshowninFig.3.9.Thecomputationalcomplexityarenorma lizedbythenumber ofdetectedcodes(1 P md )totakeintoconsiderationthedierentprobabilitiesofmisseddetection 59

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1 2 3 4 5 6 7 8 9 10 -1 0 1 2 3 4 5 6 7 8 9 10 Number of ranging users per UL frameStandard deviation Proposed alg., dispersive Alg. 2, dispersive Proposed alg., AWGN Alg. 2, AWGN Figure3.8Standarddeviationoftimingerrors. betweenbothmethods.Theproposedalgorithmreducesthecomputationalcomplexityby over98% overAWGNchannels.Overdispersivechannels,thecomplexityreductionrangesfrom96 %to80% dependingonthenumberofrangingusersperULframe. Finally,anothersetofsystemparametersfromtheWiMAXsystemprolesiscons ideredto verifytheperformanceoftheproposedalgorithm.Thenewsetofsystemparamet ersare: N =512, N g =32samples.Inaccordancetothestandard,thesignalbandwidth,inthiscase,is5MH zand thesamplingfrequencyis5.6MHz.Forfairnessofcomparison,themaximumRTD, thenumberof OFDMAsymbolsperULframe,andthenumberofframesusedtoevaluatethesimul ationresults remainconstant.Theprobabilitiesofmisseddetectionandfalsealarmfort herstandsecond setsofsystemparametersarecomparedinFig.3.10.Inbothsystemproles ,theperformancesare almostidentical.ThisisduetothefactthatWiMAXstandardmaintainsxeds ubcarrierspacing regardlessofthesignalbandwidthorFFTsize.Asaresult,therangingchannel,whic hconsistsofa xednumberofsubcarriers,hasaxedbandwidthfordierentsignalbandwidths.InFig .3.11,the standarddeviationsoftimingerrorsforbothcasesaswellasforbothcons ideredrangingalgorithms arecompared.Notethatasthebandwidthisreduced,thesamplingtimeisincreasedwhich leads 60

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1 2 3 4 5 6 7 8 9 10 80% 82% 84% 86% 88% 90% 92% 94% 96% 98% 100% Number of ranging users per UL frameComputational complexity reduction Dispersive AWGN Figure3.9Computationalcomplexityreductionusingtheproposedalgorithm. toareductionintimingerrors(insamples).Inthiscase,thetimingestimat ionperformancesofthe proposedalgorithmandalgorithm2arealmostequal.3.7Conclusions AnovelalgorithmforOFDMAinitialrangingprocessbasedontheIEEE802.16 e-2005standard isproposed.Theproposedalgorithmperformsmultiusercodedetectionandtiming osetestimation forrangingusers.Thealgorithmisdividedintothreestages.Intherststa ge,thesystemdetects OFDMAsymbolscarryingrangingusers.Thesecondstageisresponsiblefordetect ionofcodesand estimationoftimingosetsforeachuserwithincurrentOFDMAsymbol.Fi nally,thelaststage identiesuserrangingcodes.Theproposedalgorithmperformancewasevaluatedfor bothAWGN channelsanddispersivechannels.Acomplexitycomparisonbetweentheproposedalgo rithmand otherexistingalgorithmswascarriedoutaswell.Theresultsshowthatpropo sedalgorithmreduces thecomputationalcomplexityby80%to96%dependingonthenumberofranginguserswhi le maintainingthetimingerrorstandarddeviationunder5%oftheguardinterval .Simulationresults showedthattheproposedalgorithmcanperformwellwithashighas10usersp errangingchannel 61

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1 2 3 4 5 6 7 8 9 10 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 Number of ranging users per UL frameProbability Probability of missed detection, N =512 Probability of missed detection, N =1024 Probability of false alarm, N =512 Probability of false alarm, N =1024 Figure3.10Probabilitiesofmisseddetectionandfalsealarmfor N =1024and N =512. inagivenULframe.Hence,itisbelievedthattheproposedalgorithmcanbereal izedinpractical OFDMA-basedBSs. 62

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1 2 3 4 5 6 7 8 9 10 -1 0 1 2 3 4 5 6 7 8 9 10 Number of ranging users per UL frameStandard deviation Proposed alg., N =1024 Alg. 2, N =1024 Proposed alg., N =512 Alg. 2, N =512 Figure3.11Standarddeviationoftimingerrorsfor N =1024and N =512. 63

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CHAPTER4 SPECTRUMSHAPINGOFOFDM-BASEDCOGNITIVERADIOSIGNALS 4.1Introduction Recently,opportunisticusageoflicensedfrequencybandshasbeenproposedasasolutio nto spectralcrowdingproblembyusingcognitiveradio(CR)systems[2,60].ACR systemwould beabletooperateinlicensedbandsbyutilizingvacantpartsofthesebands.Akeypo intfor thesuccessofCRistheabilitytoshapeitssignalspectrumtoachieveminimumi nterferenceto licensedusers(LU).Orthogonalfrequencydivisionmultiplexing(OFDM)hasbeenpropo sedas acandidatesignalingtechnologyforsuchapplications.Bydividingthespectrumin tosubbands thataremodulatedwithorthogonalsubcarriers,OFDMspectrumcanbeshapedwi thmoreease comparedtoothersignalingtechniques.However,modulatedOFDMsubcarrierssuerfr omhigh sidelobes,whichresultinadjacentchannelinterference(ACI).Thus,disablingaset ofOFDM subcarrierstocreateaspectrumnullmaynotbesucienttoavoidinterferenceto LU.Ontheother hand,usinglterscanincreasethesystemcomplexityandintroducelongdelays.Usingg uardbands onbothsidesofusedOFDMspectrumandwindowingthetimedomainsignalhavebeeni nvestigated in[64].In[65{67],theuseofinterferencecancellationcarriers(CC)ispr oposed.Otherproposed methodsincludetheuseofsubcarrierweighting[74]ormultiple-choicesequences[75]. Inthischapter,wediscusssomeofthecurrentmethodsandtechniquesproposedintheli terature forspectrumshapingofanOFDMsignaltoavoidorminimizeinterferencetoLUs .Weinvestigate theeectofvarioussystemparameters(suchastheLUbandwidth,cyclicprex(CP)leng th, andnumberofCCs)andtheireectsonthesystemperformanceintermsofinterfer encelevel, spectraleciency,computationalcomplexity,andpowerconsumption.Simulationresul tsshowing thesystemperformanceareprovidedalongwithdiscussionsoftheadvantagesa nddisadvantagesof eachtechnique.Wethenproposeanewmethod,referredtoasadaptivesymboltransit ion(AST), tosuppressOFDMsidelobesandshapethesignalspectrum.Similartothewindowingt echnique, 64

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theOFDMsymbolsareextendedintimetoreducetheeectofsymboltransition.Ho wever,instead ofusingapredenedltershape,thetransitionsignalisoptimizedadaptivelybasedon transmitted dataanddetectedLUbandstoreducetheinterferencetoLUs.4.2SystemModel Throughoutthischapter,weassumeaCRsystememployingOFDMasthesignalingtec hnique. TheCRisassumedtobeawareofthesurroundingenvironmentandtheradiochannelcha racteristics. Afterscanningthechannel,theCRshouldbeabletoidentifyLUsoperatingwithint hetargeted band[92].Thegoalistoexploitidentiedspectrumopportunitiesandachievehighes tpossible spectraleciencywhilekeepingtheinterferencetodetectedLUstominimum.Inthesystem, the encodeddataismodulatedandthenfedtoan N -pointinversefastFouriertransform(IFFT)unit. Wedene F N 1 ;N 2 = f F n 1 ;n 2 g asthe N 1 -pointFouriertransformmatrixofavectoroflength N 2 where F n 1 ;n 2 =exp j 2 n 1 n 2 N 1 : (4.1) ThetimedomainsignalattheoutputoftheIFFTis x = 1 N F N;N X ; (4.2) where N istheIFFTsize,( ) isthecomplexconjugateoperator, 1 N F istheinverseFourier transformmatrix,and X =[ X (1) ;X (2) ;:::;X ( N )] T isthemodulateddatavector.Thesignalis thenextendedusingaCPconsistingof N g samples.Thesignalgoesthroughapulseshapinglter beforebeingsentthroughthecommunicationchannel.4.3ActiveCancellationCarriers ActiveCCstechniquewasproposedin[65{67]whereafewtonesatbothedgesoft hespectrum holeareusedtocanceltheinterferencetoLUs.First,westartbyexaminingthep erformanceof CCswithnocyclicextensionorpulseshapingusedtosimplifytheanalysis.How ever,theeectof CPisdiscussedlaterinSection4.3.Thetimedomainsignalisupsampledbyafa ctorof andthe signalspectrumiscalculatedasfollows S = F N N x = QX ; (4.3) 65

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where Q = 1 N F N N F N N : (4.4) Notethat correspondsalsotothenumberofpointspersidelobethatareconsideredinthes pectrum shapingprocess.Unlessotherwisementioned,thevalueof issettoeight.ALUisdetectedwithin theOFDMbandspanningover B subcarriers X ( i +1) ;X ( i +2) ;:::;X ( i + B ),where i f istheLU signalosetwithrespecttotheOFDMsignal, B f istheLUsignalbandwidth,and f isthe frequencysubcarrierseparation.Iftheabovesubcarriersaredisabledandremaini ngsubcarriersare usedfordatatransmission,theinterferencetoLUbandis I L = Q B X B ; (4.5) where Q B isasubsetof Q containingonlytherowsof Q thatcorrespondstotheLUband, ( i +1) to ( i + B ),and X B isthesameas X butwithinterferencesubcarriers, X ( i +1)to X ( i + B ),set tozero.Assume c CCsoneachedgeofthespectrumgapareusedtocanceltheinterferencetoLU band.Inthiscase,subcarriers X ( i +1 c )to X ( i + B + c )aresettozeroin X B tomeasurethe interferencetoLUband.WiththeuseofCCs,interferencepowertoLUis, P I = k Q I X I + I L k 2 : (4.6) where Q I isasubsetof Q B containingonlythecolumnscorrespondingtodisabledsubcarriers, i +1 c to i + B + c ,and X I isavectorofrequiredvaluesofdisabledsubcarrierstominimizethe interference.Themean-squared-error(MSE)solutiontotheaboveequationis, X I = ( Q HI Q I ) 1 Q HI I L ; (4.7) where( ) H istheHermitiantranspose.From(4.5),(4.7)canbewrittenas X I = W I X B ; (4.8) where W I = ( Q HI Q I ) 1 Q HI Q B .Notethat W I needstobecalculatedonlyonceforthesame spectrumshapewhile X I iscalculatedforeveryOFDMsymbol[65]. 66

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20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 -90 -80 -70 -60 -50 -40 -30 -20 -10 0 10 Normalized frequency (subcarrier index)Normalized PSD (dB) No CCs 2 CC 4 CC Licensed user band Figure4.1NumberofCCeectonthesignalPSD. ToexaminetheperformanceoftheCCtechnique,anOFDMsystemwith N =256isconsidered. TheDCsubcarrier X (0)isdisabled.ALUisdetectedspaningthebandbetweensubcarriers X (26) and X (28).Tokeepspectrumeciencyconstant,sevensubcarriersaredisabled, X (24)to X (30),in allconsideredcases.First,thenormalizedpowerspectraldensity(PSD)isestim atedwithdisabled subcarrierssettozeroanddatasubcarrierscarryingbinaryphaseshiftkeying(BP SK)signals.Next, twoandfourCCsareconsidered,withhalfofCCsoneachsideofthegap.Theresul tsareshown inFig.4.1.WhenCCsarenotused,theinterferenceleveliskeptunder 10dBoftheoriginal signalpowerlevel.TwoandfourCCsreducetheinterferenceleveltoaround 35dBand 75dB, respectively.CCtechniquereducestheinterferencesignicantlyatthecostofanincreas einthe computationalcomplexityandsymbolenergy. Next,theeectoftheLUbandwidthisconsidered.ForaxednumberoffourCCs,thePSD ofthetransmittedsignalwithagapof7,17,and27subcarriers,assumi ngLUswithbandwidths of3,13,and23subcarriers,areshowninFig.4.2.Asthegapbandwidthincr eases,theeciency ofCCsisreduced.Moreover,peaksemergeonthesignalspectrumjustbeforethespect rumgap. Thesepeaks'powerincreasesasthegapbandwidthincreasesindicatingthatmorepower isusedby theCCs.Tofurtherinvestigatethiseect,increasesintheaveragesymbolenerg y E r duetoCCsis 67

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8 13 18 23 28 33 38 43 48 -80 -70 -60 -50 -40 -30 -20 -10 0 10 20 Normalized frequency (subcarrier index)Normalized PSD (dB) 27 subcarriers gap 17 subcarriers gap 7 subcarriers gap Figure4.2GapsizeeectoneectonthesignalPSD. Table4.1IncreaseinaverageOFDMsymbolenergy E r Disabled subcarriers 2CCs4CCs 71%3% 172%15%2725%26% measured(seeTable4.1),where E r =( E S E S ) =E S E S istheaveragesymbolenergywithnoCCs, and E S istheaveragesymbolenergywithCCs.Foraxedoverallsymbolenergy,the increasein energyconsumedbyCCsreducestheusefuldataenergyleadingtoadecreaseinthesystemecientsignal-to-noiseratio(SNR).Thismayresultinanincreaseinthebiterrorr ate(BER).Thus,a CRsystemfacesatradeobetweenreducingtheinterferenceleveltoLUandkeepingthespectrumeciencyandtheoverallBERofthesystemwithinacceptablelevels.4.4CycliclyExtendedOFDMSignals InpracticalOFDMsystems,symbolsarecyclicallyextendedtomitigateint er-symbolinterference (ISI)andsynchronizationerrors[93].TheeectsofCPonCCsarepresentedin [72]butaveryshort CPvaluewasconsideredinthesimulation(0.04ofsymboltime).CPextensi onresultsinalossof 68

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orthogonalitybetweenOFDMsubcarriers.Notethatatthereceiver,theCPisrem ovedpriortothe fastFouriertransform(FFT)blockandthustheorthogonalityisrestor ed.Sinceorthogonalityis lostintransmittedsignal,sidelobesofadjacentsubcarriersaremisali gned.Thisreducestheability ofonesubcarriertoreducetheinterference,causedbythesidelobes,ofadjacentsubcarri ers.Infact, onlysidelobesofsubcarrierswith N=N g separationarealignedtoeachother.Onelastnoteisthat increasingtheCPintervalcausesthePSDofsidelobestodecayfaster. TotaketheCPeectintoaccountintheCCtechnique,wedene C = 0BBBB@ 0 N g N N g I N g I N N g 0 N N g N g 0 N g N N g I N g 1CCCCA N + N g N ; (4.9) where 0 isthezeromatrixand I istheidentitymatrix.Thesignalspectrumisthenmodiedtobe S = F N N + N g Cx ; (4.10) For(4.3)tohold, Q in(4.4)ismodiedbasedon(4.10)tobe Q = 1 N F N N + N g CF N N : (4.11) Fig.4.3showsthenormalizedPSDofthetransmittedsignalforthesamesy stemusedtogenerate Fig.4.1with4CCsanddierentCPsizes.For N g =N =1/32,1/8,1/4,and1/2, E r wasfoundto be3%,75%,29%,and1%respectively.ThegureshowsthatashortCP,asint hecaseof N g =N =1/32,hasanegligibleeectonthesystemperformanceinbothpowerandinter ferencelevel. AlongerCPwith N g =N =1/8reducestheCCseectivenessbyaround20dBand,evenworse, increasestheenergyconsumedbyCCstoasignicantlyhighervalueof75%.As N g =N increases, theperformancelossduetotheCPdecreasesandsodoes E r .Thiscanbeexplainedasfollows.For N g =N =1/8,noneoftheCCssidelobesarealignedforthecaseunderconsideration.Asares ult,the CCsspectraareaddednon-coherentlyandthussomepartsoftheirsignalsarecancelled outwhich reducesthesystemeciency.Asaresult,morepowerisneededtoachieveminimuminterferencelevel.Ontheotherhand,for N g =N =1/4,subcarriers X (25)and X (29)arealignedandthusthe systemregainsomeoftheperformanceloss.However,morepowerisstil lneededbytheCCssince 69

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20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 -80 -70 -60 -50 -40 -30 -20 -10 0 10 20 Normalized frequency (subcarrier index)Normalized PSD (dB) N / N g = 1/32 N / N g = 1/8 N / N g = 1/4 N / N g = 1/2 Figure4.3CPsizeeectonthesignalPSD. theothertwosubcarriersarenotmatched.Finally,for N g =N =1/2,allCCsarematchedandthus boththeperformancelossandconsumedpowerarelow.Infact,thepowerconsumed byCCsfor N g =N =1/2isevenlessthanforthecaseofnoCP.ThisisduetothefactthatalongCPr esultsin lowerinterferencelevelstoadjacentbands.AconclusioncanbemadethatCPlength,gap location andCCslocationsareallparametersthatcansignicantlyaectboththeperf ormanceandpower consumptionofCCs.4.5RaisedCosineWindowing ApossibletechniquetoreducetheinterferencetoLUistheuseoftimewindowing.The timedomainOFDMsymbolsaremultipliedwithashapingwindowtoimprovethespectr umcharacteristics ofthesignal[64].Raisedcosine(RC)windowsareusuallyused,wherethelterv ector g = f g n g is denedas: g n = 8>>>>>><>>>>>>: 1 2 + 1 2 cos + n N T ; for0 n
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where N T = N + N g isthesymbollength(insamples)and istherollofactor.Thetotalsymbol lengthis(1+ ) N T .However,adjacentsymbolspartiallyoverlapoveralengthof N T fromeach side,causingtheactualsymboltimetobe N T .TomaintaintheorthogonalitybetweentheOFDM subcarriersandthesystemresistancetoISI,thesymbolsareextendedusingboth prexandpostx. Thedurationsforboththeprexandpostxextensions( N pre and N post respectively)arechosen suchthattheycovertheoverlappingperiodofthesymbols.Theadvantageofwi ndowingisitslow complexityandsimpleimplementation.Thedrawbackisthetimeextensionofthe symbolwhich reducesthesystemthroughput. Thesystemperformancewasevaluatedfordierentvaluesof .Thesystemhadsevendisabled subcarriers, N=N g =1 = 32, N post = N T ,and N pre = N T + N g .Thus, N T =( N + N g ) = (1 ). TheresultsareshowninFig.4.4.Theaverageinterferencelevel(indB)withi nLUbandwasfound tobe 23, 40, 55for =0.12,0.25,and0.4,respectively.Theincreaseinsymbolenergywas calculatedforallcases.For =0.12,0.25,and0.4, E r wasfoundtobe10%,25%,and51%, respectively.Moreover,thesymboltimeincreasedby14%,33%,and67%.Co mparedtotheresults inFig.4.1,itappearsthatCCsaresuperiortowindowinginbothspectra leciencyandpower. However,itisimportanttopointoutthatwindowingrequiresmuchlesscomput ationsthanCCs. Inaddition,windowingismorerobustsinceitisindependentofthegapposition,w idth,orsymbol datavalues.NotethatwindowingreducesthesidelobesofallOFDMsubcarrierswhich improves notonlythetargetgapbutalsotheout-of-bandemissionsaswell.Fig.4.5show stheRCwindowed systemwith =0 : 25,andvariousgapsizes.Itisseenthatasthegapbandwidthincreases, theinterferenceleveldecreases.Sincewindowingincreasesthedecayrateofmodulatedsubcarr ier sidelobes,thistechniqueperformsbetterwithlargergaps.ComparedtoCCss howninFig.4.2, windowedsystemachieves10dBlowerinterferencelevelfora27subcarriersgapwi thalmostthe samepowerconsumption.However,CCshavetheadvantageofmaintainingana lmostratspectrum overtheLUband. 71

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20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 -70 -60 -50 -40 -30 -20 -10 0 10 Normalized frequency (subcarrier index)Normalized PSD (dB) =0 =0 : 12 =0 : 25 =0 : 4 Licensed user band Figure4.4RollofactoreectontheRC-windowedsignalPSD. 8 13 18 23 28 33 38 43 48 -80 -70 -60 -50 -40 -30 -20 -10 0 10 Normalized frequency (subcarrier index)Normalized PSD (dB) 7 subcarriers gap 17 subcarriers gap 27 subcarriers gap Figure4.5GapsizeeectontheRC-windowedsignalPSD. 72

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4.6CombiningCancellationCarriersandRaisedCosineWindow ing Inthissection,thecombinationofbothCCsandRCwindowingisconsidered.TheCCs calculationismodiedtotaketheRCwindowingintoaccount.Wedene D = 0BBBBBBB@ 0 N pre N N pre I N pre I N N pre 0 N N pre N pre 0 N pre N N pre I N pre I N post 0 N post N N post 1CCCCCCCA (1+ ) N T N ; (4.13) where D modelstheeectofaddingbothprexandpostxtothetimesignal.Wealsodene R C =diag f g g ,where R C isadiagonalmatrixholdingtheelementsof g asitsmaindiagonal.The valueof S and Q arethenmodiedaccordinglyto S = F N (1+ ) N T R C Dx ; (4.14) and Q = 1 N F N (1+ ) N T R C DF N N : (4.15) Again,aLUspanningthreesubcarriersisconsideredandagapofsevensubcarriersis used. N g =N = 1 = 8and =0 : 25.ThePSDsofthesystemusingonlyRCwindowingandusingcombinationofRC andCCstechniqueareshowninFig.4.6.ThegurealsoshowsthePSDforagap of17subcarriers. Notethatinthiscase,RCwindowingincreasesthesymboltimeby33%and E r to13%.Inthe caseofsevensubcarriersgap,thecombinedsystemreducestheinterferencelevelbyanextr a20dB. Inaddition,theincreasein E r duetoCCsisaround0.02%.Inotherwords,CCscausealmostno increaseinsymbolenergy.However,forthewidergapof17subcarriers,therei salmostnogainfor thecombinedsystemovertheRCsystem.Thus,combiningCCtechniquewithRCwindowi ngis onlybenecialforthesystemtocombineCCsandRCwindowingforsmallgaps.4.7ProposedAlgorithm Inprevioussections,sidelobesuppressiontechniquessuchasCCtechnique,RCwindowing ,and acombinationofboth,wereconsidered.Ononehand,alowcomplexitytechniquesuchasthe RC windowingdoesnotprovidesucientsidelobesuppression.Ontheotherhand,theCCtechnique, 73

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8 13 18 23 28 33 38 43 48 -80 -70 -60 -50 -40 -30 -20 -10 0 10 Normalized frequency (subcarrier index)Normalized PSD (dB) RC RC + 4 CCs RC RC + 4 CCs 7 subcarriers 17 subcarriers Figure4.6CombinedRCwindowingandCCeectonthesignalPSD. whichprovidesignicantsidelobesuppressionforsmallergaps,isineectivef orlargergapsizes.In addition,CCtechniqueresultsinanincreaseinthesystempeak-to-average-powerr atio(PAPR), andtheperformanceissensitivetotheCPsize.DuetothehigherpowerusedfortheC Cs,usingthis techniqueaectsthespectralratnessofthetransmittedsignalandcanincreasethei nter-carrier interference(ICI)incaseofaDopplerspreadorafrequencyoseterroratthereceiver .Other methodsthatwerenotconsideredinthisstudysuchasthesubcarrierweightingmethod[ 74]causes anincreaseinthesystemBER,andtheinterferencereductionisnotassignicantas itiswiththe CCmethod. Inthissection,weproposeanewmethod,referredtoasadaptivesymboltransit ion(AST),to suppressOFDMsidelobesandshapethesignalspectrum.Similartothewindowingtechni que,the OFDMsymbolsareextendedintimetoreducetheeectofsymboltransition.Howev er,insteadof usingapredenedltershape,thetransitionsignalisoptimizedadaptivelybasedontr ansmitted dataanddetectedLUbandstoreducetheinterferencetoLUs. 74

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Mod. Subc. Mapper IFFT P/S Add CP AST Unit Encoded data To channel Cognitive Radio Transmitter Cognitive Engine X ( m ) x ( m ) y ( m ) Disabled Subcarriers Index Figure4.7SystemModel. 4.7.1ProposedSystemModel TheproposedsystemmodelisshowninFig.4.7.Theencodeddataismodulatedandfed to an N -pointIFFTunit.ThesignalisthenextendedwithaCPconsistingof N g samplesandthe extendedsymbols y ( m ) arefedtotheASTblock.Meanwhile,thecognitiveenginepassesrequired informationregardingLUsoperatinginthesamebandtoboththesubcarrier mapperandtheAST block.ThisinformationisusedtodisablesubcarriersoperatingintheLUba ndsandtosuppress theinterference{causedbyOFDMsidelobes{toLUsasexplainedinthefollowingsect ion. 4.7.2AdaptiveSymbolTransition In[64],windowingofOFDMsymbolswasinvestigatedasamethodtosuppress OFDMsidelobes. Thetimedomainsymbolsarepassedthroughalter(usuallyRCltersareused) ,andconsecutive symbolsareallowedtooverlap.Theprocesssmoothsthetransitionbetween OFDMsymbolsandthus improvesthespectralcharacteristicsoftheOFDMsignal.Tokeeptheorthogona litybetweenOFDM subcarriers,thesymbolsarecyclicallyextendedtocovertheoverlappingregion.T headvantage ofthisapproachisitslowcomputationalcomplexity.Thedisadvantageist hereducedspectral eciencyduetothesymbolextension.Similartowindowing,theASTtechniquesuppressesOFD M sidelobesbyextendingOFDMsymbolsandusingtheextensionstosmooththetransit ionbetween consecutivesymbols.However,insteadofusingapredenedwindowshape,suchRC,wepro posean adaptivemethodthatcalculatesthevalueofthesymbolextensionbasedonLUscent erfrequency andbandwidth. Onceagain,weassumetheCRsystemdetectsanLUsignalspanningover K subcarriers X ( i +1), X ( i +2),... X ( i + K ).TheabovesubcarriersetisdisabledtoavoidinterferingwiththeLU.To further suppresstheinterference,theASTblockaddsanextension a ( m ) =[ a (1) ( m ) a (2) ( m ) ,... a ( C ) ( m ) ] T 75

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toeveryOFDMsymbol y ( m ) asshowninFig.4.8,where( m )isthesymbolindexand C isthe numberofsamplesin a ( m ) y ( m ) and y ( m 1) areusedtocalculate a ( m ) inthefollowingmanner. First,weexaminetheinterferencetotheLU.Thesignalisupsampledbyafactor ,orinother words,weconsider pointspersubcarrier.Thesignalspectrumoftwoconsecutivesymbolscanbe obtainedas, S ( m ) = F N; 266664 y ( m 1) a ( m ) y ( m ) 377775 | {z } z ( m ) ; (4.16) where =2 N +2 N g + C .TheinterferencetotheLUisthen, I L = F K z ( m ) K ; (4.17) where F K isasubsetof F N; containingonlytherowsthatcorrespondstotheLUband(rows ( i +1)to ( i + K ))and z ( m ) K isthesameas z ( m ) butwith a ( m ) =[ 0 ] C 1 .Tominimizeinterference power,theASTblockchooses a ( m ) suchthat, a ( m ) =argmin a ( m ) rrr F I a ( m ) + I L rrr 2 ; (4.18) where F I isasubsetof F K containingonlythecolumnsthatcorrespondsto a ( m ) ;columns N + N g to N + N g + C 1. TheMSEsolutionto(4.18)wasfoundtoresultinveryhighvaluesfor jj a ( m ) jj .Thisleadsto increaseintheextensionpower.Asaresult,theusefulsymbolenergyisreducedcompared tothe totalsymbolenergyresultinginanincreaseinthesystemBER.Tomitigat ethiseect,weadda constraintontheminimizationin(4.18)suchthatthesymbolextensionp owerisbelowagivenlevel 2 rrr a ( m ) rrr 2 2 (4.19) 76

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y ( m ) y ( m +1) y ( m +2) y ( m ) y ( m+ 1) y ( m+2 ) a Input: conventional OFDM symbols Output: extended OFDM symbols ( m +1) a ( m ) a ( m +2) Figure4.8OutputoftheASTblock. Theoptimizationin(4.18)and(4.19)isknownaslinearleastsquarespro blemwithaquadratic inequalityconstraint[94].Usingsingularvaluedecomposition(SVD),we get, U H F I V = 264 D F I 0 375 (4.20) and, D F I =diag( 1 ;:::; C ) ; i 0 ; (4.21) where[ U ] and[ V ] C C areunitary,and= ( K 1)+1.UsingthemethodofLagrange multiplierswegetthefollowingequation, f ( )= C X i =1 2 i j ~ I L;i j 2 ( 2 i + ) 2 = 2 ; (4.22) where ~ I L = U H I L =[ ~ I L; 1 ;:::; ~ I L; ] T .Ifasolutionexisttotheoptimizationproblem,thefunction f ( )willhaveauniquepositiverootandithasbeenshownthatthisisthedesiredr oot[94].The solutioncanthenbeobtainedas, a ( m ) = V [ 1 ~ I L; 1 = ( 2 1 + ~ ) ;:::; C ~ I L;C = ( 2 C + ~ )] T ; (4.23) where ~ istheuniquepositiverootof(4.22).Fortunately,foragivenspectrums hape, F I isxed andthus,only I L needstobeupdatedforeveryOFDMsymbol.Thecomputationalcomplexityof theoptimizationproblemisreducedsignicantlyduetothisfact. 77

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AnimportantparameterforOFDMsystemsisthePAPRwhichaectsthedynami crangeover whichthesystemshouldbelinear.Bychoosing 2 suchthat, 2 = C= ( N + N g ) E S ; (4.24) thesignalaveragepoweriskeptatthesamelevel,where E S isthesymbolenergypriortotheAST block.SincetheASTsignalisoptimizedtosmooththesymboltransition,it doesnotintroduceany peakstothesignal(conrmedbysimulationresults)and,thus,thePAPRofthe systemdoesnot increase.Nevertheless,theASTreducestheusefulsymbolenergy.Using(4.24),themaxi mumSNR loss r is, r =10log 10 E S + 2 E S =10log 10 1+ C N + N g dB : (4.25) Bycontrolling C andforaxedPAPR,thesystemhasatradeobetweenreducing r (byreducing C ),orimprovingtheinterferencesuppression(byincreasing C ). NotethatsinceASTtechniqueisperformedontime-domainsymbols,theperfor manceisnot sensitivetotheCPsize.Inaddition,theASTdoesnotintroduceanyISItothesyst emasthe leakagefromthesymbolextensioniscontainedintheCP.Theintendedreceivercan removethe ASTextensionalongwiththeCPtomaintainanISI-freesignal.4.7.3SimulationResults Inthissection,theperformanceoftheproposedmethodisinvestigatedusingcom putersimulations.WeconsideranOFDM-basedCRsystemwith N =256and N g =16.TheASTmethodis usedwith C =16, =16,and,basedon(4.24), 2 =0 : 06 E S .TheDCsubcarrierisdisabled.Data subcarriersaremodulatedwithaquadraturephaseshiftkeying(QPSK)signal.Al lresultsshown areaveragedover10 ; 000OFDMsymbols.Weconsidertwocasesforperformanceevaluation.In therstcase,anLUisdetectedspaning24OFDMsubcarriers.Thesystemdisables32sub carriers leavingaguardbandof4subcarriersoneachsideoftheLUband.Theguardbandsaret oallowthe signalpowertodecaywhiletheASTblockperformstheoptimizationoverthe24 {subcarrierband. ThenormalizedPSDofthesignalattheoutputoftheASTblockismeasuredandtheresul tsare showninFig.4.9.ThesystemperformanceiscomparedwithaconventionalOF DMsystemwithout anysymbolextension,andwithanOFDMsystemusingRCwindowingandasymbol durationequal totheASTsystem.TheconventionalOFDMsystemsuersaninterferencelevelof 22dB.The 78

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-128 -96 -64 -32 0 32 64 96 127 -70 -60 -50 -40 -30 -20 -10 0 Normalized frequency (subcarrier index)Normalized PSD (dB) Conventional RC windowed AST LU Band Figure4.9SpectrumofanOFDMsignalwith32subcarriersgap. RC-windowedsystemsuppressestheinterferenceto 33dB,whiletheASTreducestheinterference furthertolessthan 50dB.TheASTmethodachievesa28dBgainoverconventionalsystemswhile keepingtheSNRlosslessthan0 : 25dB. Finally,weconsiderthesecondcasewhereASTmethodisusedtoreducethenumberofdisabled subcarriersusedasguardbandsincurrentOFDMsystems.Forexample,aworldwidei nteroperabilityformicrowaveaccess(WiMAX)systememployinga256subcarriersOF DMsystemdisables 55subcarriers(28and27ontheleftandrightsides,respectively)tolimit out-of-bandradiations. Usingsidelobesuppressiontechniques,therequiredguardbandcanbereducedforanincreas ein systemcomplexity.Weconsiderusing24subcarriers(12oneachside)asguardbands N N g C ,and 2 arethesameastherstcase.ThenormalizedPSDoftheleftsideofthesignalis shown inFig.4.10.TheASTmethodsuppressesthesignalpowerto 50dBbytheendofthein-band signalcomparedto 32dBforRC-windowmethodand 20dBforconventionalsystems. 4.8Conclusions Inthischapter,weinvestigatedthreetechniquesforOFDMspectrumshaping.CCstec hniquehas theadvantageoflowerinterferencelevelespeciallyforsmallgapsizes.How ever,CCperformance 79

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-128 -124 -120 -116 -112 -108 -104 -100 -70 -60 -50 -40 -30 -20 -10 0 Normalized frequency (subcarrier index)Normalized PSD (dB) Conventional RC windowed AST Figure4.10SpectrumofanOFDMsignalwith12subcarriersguardband. issensitivetotheCPsize,andasthegapsizeincreases,theperformancedegradat ion,andthe consumedpowerbyCCsincreases.Alternatively,RCwindowingtechniqueisamorer obustsolution withlowercomplexity.Thesidelobesuppressioncomesatthecostofanincreasei nthesymbol durationwhichreducesthespectraleciency.However,RCwindowingisinferiortoCCs forsmall gapsizes.ThecombinedCCsandRCwindowingtechniqueperformsverywellforsmal lgaps regardlessoftheCPsize.Moreover,thepowerconsumedbyCCsisminimalinthis case.The disadvantageisthatthesystemexhibitsbothlowspectraleciencyduetosymbo lextensionand highercomputationalcomplexityduetotheuseofCC.Inaddition,thecombinedtechniquedo es notintroduceanygainoverRCwindowingforlargegapsizes. Basedontheaboveobservations,weinvestigatedanewmethodthatcanovercom ethedrawbacks ofRCwindowingandCCtechnique.TheproposedASTmethodextendsOFDMsymbolsandusestheextensiontoreduceACItootherusersoperatinginthesameband.Simulationresul tsshow thatASTcanachieveasignicantgainoverconventionalsidelobesuppressiontec hniqueswhile maintaininglowincreaseinsymbolenergy.Moreover,ASTdoesnotincreasethesi gnalPAPRand theperformanceisnotsensitivetotheCPsize. 80

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CHAPTER5 ANALYSISANDOPTIMIZATIONOFOFDMAUPLINKSYSTEMSOVER TIME-VARYINGFREQUENCY-SELECTIVERAYLEIGHFADINGCHANNEL S 5.1Introduction Duetoitsattractivefeatures,orthogonalfrequencydivisionmultipleaccess( OFDMA)has beenproposedforavariouswirelessstandardssuchasWiMAX[9],LTE-Advanced [14],andISTWINNER[15].Mostofthesesystemsareexpectedtoprovidebroadbandservicesf ormobileusers. Assuch,itisexpectedthatreceiverswillsuerfromtime-varyingfrequency-selective propagation eects.Thequalityofchannelestimation,insuchcase,cansignicantlyimpactthe overallsystem performance. TosupportmultipleuseraccessinOFDMAuplink(UL)systems,theOFDMAsignalis divided intosmallerunits,calledtilesorchunks,consistingofanumberofsubcarri ersthatareadjacentin timeandfrequency.Oneormoreofthesetilescanbeassignedtomultipleusersbyt hescheduler inanadaptiveorrandommanner.Sinceadjacenttilesarenotnecessarilyassignedto thesame user,itisexpectthatdierenttilesarereceivedoverdierentwirelesschannels.Ass uch,the channelestimationandequalizationneedstobeperformedonatile-by-tilebasis [95,96].Pilotsare placedwithineachtiletoenablethechannelestimationprocess.Theoptimumalloca tionofpilots withinatiletoreducethechannelestimationmean-squared-error(MSE)isinvestig atedin[97, 98]consideringthefrequencyandtimedimensions.Theauthorsconcludedthatpilotsshouldb e placedatthecornersofthetileatlowsignal-to-noiseratio(SNR)valuesanda t1 = p 3ofthetile duration/bandwidthathighSNRvalues.Inthiswork,pilotsplacementatthecorners ofeachtile isconsidered[9]. ThestructureofpilotassignmentsinOFDMAULinthetime-frequencygridisanal ogoustothat ofpilot-symbol-aidedmodulation(PSAM)insingleuserorthogonalfrequencydiv isionmultiplexing (OFDM).However,sinceinOFDMAULsystems,pilotsinadjacenttilescannotbe usedforchannel estimation,optimumalgorithmssuchas2DWienerltering[99]orhigherordera lgorithmssuch 81

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assincinterpolationcannotbeused[100].Inaddition,techniquessuchasmini mummean-square error(MMSE)channelestimation[101]areinapplicable,sincethenumberofpilot symbolsper user/channelisnotnecessarilysucienttoreliablyestimatethechannelstatistics .Oneapproach forchannelestimationinthiscaseistoobtainleastsquares(LS)estimates atpilotsymbolsand usearstordertime-frequencyinterpolation(bilinearinterpolation)toesti matethechannelat datasymbols.Anotherapproachistouseiterativechannelestimationmethods whichutilizedata symbolstoimprovethechannelestimationprocess[95].Thedrawbackofthis approachisthe increasedcomplexity,andconsequentlythedelay,neededtoperformmultipleiterations .Thisis especiallytrueforlargertilesizes,sincethereceiverneedstobuertheentiretile duration(upto 7560subcarriersinsomecases).In[96],theauthorsproposetousebasis expansionmodel(BEM) todescribethetime-frequencyselectivityofthechannelwithineachtile,insteadofa linearmodel. Whilethismethodcanimprovethechannelestimationperformance,thechannelDopplers pread anddelayspreadvaluesareneededtocorrectlymodelthechannel.Hence,fromapracticalpoin tof view,usingbilinearinterpolationmaybethemostattractiveapproachf orOFDMAULsystems[97]. Inalltheaforementionedstudies,analysisofthebiterrorrate(BER)oro ptimumpilotinsertion ratefortile-basedOFDMAULsystemarenotconsidered. Inthischapter,theperformanceofOFDMAULsystemovertime-varyingfrequency-sel ective Rayleighfadingchannelsisconsidered.Itisassumedthatthesystemusesatile-basedc hannel estimationandequalizationapproach.Consideringtime-frequencyinterpolatio nlter,thevariances ofthechannelestimatesandchannelestimationerrorsareevaluated.Expressionsf ortheBER performanceunderchannelestimationerrorsforquadraturephaseshiftkeying(QPSK)a ndquadratureamplitudemodulation(QAM)signalsarederived.Basedonthepresentedresult s,ananalysis ofoptimumtiledimensions(orequivalentlypilotinsertionrate)thatmaxi mizetheoverallsystem throughputisinvestigated. Theremainderofthischapterisorganizedasfollows.InSection5.2,thesystem modeland consideredchannelmodelareintroduced.Evaluationofthechannelestimationandequali zation usingtime-frequencyinterpolationispresentedinSection5.3.AnalysisoftheB ERperformance forQPSKandQAMsignalsisderivedinSection5.4.InSection5.5,optimumtiledi mensionsfor maximumsystemthroughputisdiscussed.Simulationresultsareusedtoverifythet heoretically resultsinSection5.6.Finally,concludingremarksarepresentedinSection5.7. 82

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5.2SystemModel5.2.1ChannelModel Thecomplexbasebandrepresentationofamobilewirelesschannelimpulseresponse(CI R)is describedas[101], h ( t; )= X ` h ` ( t ) ( t ` ) ; (5.1) where ` isthedelayofthe l thpathand h ` ( t )isthecorrespondingcomplexamplitude.Notethat h ` ( t )'sarewide-sensestationary(WSS)narrowbandcomplexGaussianprocesses,andar eindependentfordierentpaths.Withoutthelossofgenerality,thechannelisassumedtobe normalized suchthat X ` 2 ` =1 (5.2) where 2 ` = E n j h ` ( t ) j 2 o (5.3) and E fg istheexpectationoperator.Thechannelfrequencyresponse(CFR)attime t is, H ( t;f )= X ` h ` ( t )exp( | 2 f ` ) : (5.4) ThechannelfadingintimeismodeledusingtheclassicalDopplerspectrum[102].Thus ,foran OFDMsystemwithsymbolduration T S andsubcarrierspacing f ,thecorrelationfunctionbetween thechannelresponsesattwosubcarriers( n;k )and( n + n;k + k )is[101], R H ( n; k )= J 0 (2 nf d ) X ` 2 ` exp( | 2 k f ` )(5.5) where J 0 isthezeroth-orderBesselfunctionoftherstkind, f d isthemaximumDopplershift,and n and k arethesymbolindexandsubcarrierindex,respectively,suchthat R H ( n; k ) R H ( nT S ; k f ) : (5.6) 83

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5.2.2SignalModel InOFDMAsystems,usedsubcarriersaredividedintosmallerblocks,alsok nownastilesor chunks,whichrepresenttheminimumallocationunit.Thetilesarethenassignedt osubchannels eitherrandomlyordependingonuserchannels.TheoverallreceivedULframeisasumofal lcurrent usersignals,whicharetransmittedoverdierentcommunicationchannels. AnexampleofhowtheULframeisdividedintotilesisshowninFig.5.1.U sedsubcarriersare dividedinto Q tiles,usuallywithequalnumberoftilesoneachsideoftheDCsubcarrier.Thr ee dierenttilestructuresareshowninthegure,wheretiledimensionsarethreesym bolsbyfour subcarriers.Inthisexample,thetilebandwidth, B tile =3 f ,andthetileduration, T tile =2 T S Fortheremainderofthischapter,TileCstructureisconsidered.Notethatasimil arframestructure isemployedbythemobileworldwideinteroperabilityformicrowaveaccess( WiMAX)standard[9]. AnOFDMA-ULsystememploying N subcarrierspersymbolisconsidered.TheDCsubcarrier andguardsubcarriersaredisabled.Theremainingsubcarriers N u areusedfordatatransmission withequalnumberofsubcarriersoneachsideoftheDCsubcarrier.Theabovea ssumptionsare commonformostpracticalimplementationsofOFDMAsystems. ConsideringtheoutputofthefastFouriertransform(FFT)unitatthereceiver,the received signalofauser u atsubcarrier( n;k )is Y ( n;k )= H ( u ) ( n;k ) X ( u ) ( n;k )+ I ( n;k )+ W ( n;k ) ; (5.7) where X ( u ) ( n;k )and H ( u ) ( n;k )arethe u thusertransmittedsignalandCFRatsubcarrier( n;k ), respectively, W ( n;k )istheadditivewhiteGaussiannoise(AWGN)withzeromeanandvariance 2 n = N 0 = 2,and I ( n;k )istheinter-carrierinterference(ICI)duetoDopplerspreading.Itisshown in[103]that, I ( n;k )= 1 N N X i =0 ;i 6 = k X ( n;i ) N 1 X m =0 H ( n;i;m )exp( | 2 m ( i k ) =N )(5.8) where H ( n;i;m )istheCFRatsubcarrier( n;i )andsamplinginstant m ,asthechannelisassumed tobetimevariant.Wheneverthesamplingindexisdropped,itistoindicateaverag ingisperformed 84

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symbolssubcariers PilotData Tile A Tile B Tile C one tile tile duration, T tiletile bandwidth, B tile DC subcarrier tile q tile 1 tile Q tile q+ 1 Figure5.1ULframestructureandsubcarriermappingtotiles. overallsamplesofthecurrentsymbol,suchthatin(5.7) H ( m ) ( n;k )= 1 N N 1 X m =0 H ( m ) ( n;k;m ) : (5.9) Itisassumedthatoneormoretilescanbeassignedtoanygivenuserinthesy stembutasingle tilecanonlybeassignedtooneuser.Inaddition,itisassumedthattheprocesso ftileassignment 85

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} ~€ ‚ } } ƒ€„ … †† ‡ˆ †} ‰ Š ‹Œ  ‰ ‹ Œ ‰ Š Ž   ‘ ’ “  ” Œ  ‰ ” Œ ‹ ” • ” Œ • ”– • ‹ – • ‹ Œ Figure5.2ThesubindexofoneOFDMAULtile. tomultipleusersisdoneinarandomfashion,suchthatadjacenttilesdonotnecessari lybelongto thesameuser.Thus,thereceiverperformsthechannelestimationandequalization onatile-by-tile basis.Finally,channelstatisticssuchasthenumberofpaths,thedelayspread,o rDopplerspread ofeachuser'schannelisassumedtobeunknowntothereceiver.Fortheremainderofthis chapter, theusersuperscript( u )isdroppedforsimplicity. 5.3ChannelEstimationandEqualization Inthissection,theprocessofchannelestimationandequalizationinanOFDMAUL system isexamined.Sinceeachtileisprocessedseparately,thesubindexofsubcarrierswithin eachtileis considered.Thus,ifthetilesizeischosentobe n t symbolsby k t subcarriers,thenpilotsareassigned tosubcarriers(1 ; 1),(1 ;k t ),( n t ; 1),and( n t ;k t )asshowninFig.5.2. ThechannelLSestimatesarecalculatedbydividingthereceivedsubcarriers Y ( n;k )atpilot locationswithknownpilotsymbols P ( n;k ).From(5.7),theLSestimateofthechannelis ^ H LS ( n;k )= H ( n;k )+ I ( n;k ) P ( n;k ) + W ( n;k ) P ( n;k ) (5.10) 86

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where n 2f 1 ;n t g and k 2f 1 ;k t g ,foreachtile.Withoutthelossofgenerality,itisassumedthat datasymbolsandpilotsymbolsarenormalizedsuchthat E fj X ( n;k ) j 2 g = E fj P ( n;k ) j 2 g =1.Thus, thesecondorderstatisticsof I ( n;k )and W ( n;k )arenotchangedwhendividedby P ( n;k ).TheICI canbemodeledasanadditiveGaussianprocesswithzeromeanandvariance 2 ICI [104].Anupper boundon 2 ICI fortheclassicalDopplerspectrumisintroducedin[105]as 2 ICI 1 24 (2 f d T s ) 2 : (5.11) AssumingtheICIandAWGNvaluesateachsubcarrierareindependentandidenticallydi stributed (i.i.d.),thecorrelationfunctionbetweentheLSestimatesattwosubcarrier s( n;k )and( n + n;k + k )canbeshown,using(5.10)and(5.6),tobe R H; LS ( n; k )= 8>><>>: 2 H + 2 ICI + 2 n ; for n = k =0 ; R H ( n; k ) ; otherwise (5.12) where 2 H = E h j H ( n;k ) j 2 i : (5.13) Sincethechannelisassumedtobenormalized,thenfrom(5.2),weconcludethat 2 H =1. Thereceiverestimatesthechannelatdatasubcarriersusingbilinearinterpolation andthefour LSestimates.Foradatasubcarrier( n;k )thatbelongstothecurrenttile,thebilinearchannel estimateiscalculatedasfollows ^ H BL ( n;k )= 1 n T k T n t n 1 264 ^ H LS (1 ; 1) ^ H LS (1 ;k t ) ^ H LS ( n t ; 1) ^ H LS ( n t ;k t ) 375 264 k t k 1 375 (5.14) where n 1 = n 1 ; n t = n t n; n T = n t 1 ; k 1 = k 1 ; k t = k t k; k T = k t 1 ; (5.15) 87

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asshowninFig.5.2.Usingzero-forcing(ZF)equalizer,theequalizedOFDMAsubca rrierisgiven by ^ X ( n;k )= Y ( n;k ) ^ H BL ( n;k ) = X ( n;k ) ( n;k ) ^ H BL ( n;k ) X ( n;k )+ I ( n;k ) ^ H BL ( n;k ) + W ( n;k ) ^ H BL ( n;k ) (5.16) where ( n;k )= ^ H BL ( n;k ) H ( n;k )(5.17) isthechannelestimationerroratdatasubcarrier( n;k ). 5.4BitErrorRateAnalysis Inthissection,theBERofOFDMAULsystemsoperatinginmultipathslowfa dingchannels isevaluated.TheBERofsystems,includingOFDMsystems,underchannelestimationerr orshas beenstudiedintheliterature[100,106{112].EvaluationofBER,assum ingthechannelenvelopand phasearetwoindependentrandomprocesses,isintroducedin[106]withoutconsideringIC Iand in[107,110]whiletakingICIintoconsideration.In[110,111],theB ERisevaluatedwhiletaking intoaccountthecorrelationbetweentheenvelopandthephaseofthechannel.In[100 ],theresults areextendedtoRiceanfadingchannelsandmultichannelreceivers.However,thecalculation ofBER inmostoftheabovereferencesinvolvestheevaluationofthree-fold(orevenfo ur-fold)integraland yieldshighly-complexexpressions.AnapproximationoftheBERforOFDM-basedwi relesslocal areanetwork(WLAN)systemswithchannelestimationerrorsisintroducedin [108].Theauthors assumedthatforrelativelysmallchannelestimationerrors,theestimated channelresponseandthe channelestimationerrorsareuncorrelated.Inthiswork,weusetheresultsint roducedin[108],since theyyieldsimpliedexpressionswithminimalerrormarginforconsideredapplica tion(asveried bycomputersimulationsinSection5.6). From(5.16),itcanbeseenthatthesourcesofdegradationarethebilinearchannel estimates, thechannelestimationerror,theICI,andtheAWGN,withpowers(orvaria nces) 2 BL 2 2 ICI and 2 n ,respectively.Notethatthesymbolpowerisnotconsideredhere,sinceitisassum edthat symbolsarenormalized.ToevaluatetheBER,theinstantaneousSNRisobtained atanysubcarrier 88

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( n;k )using(5.16)suchthat SNR( n;k )= ^ H BL ( n;k ) 2 j ( n;k ) j 2 + 2 ICI + 2 n : (5.18) TheinstantaneousBERisevaluatedforagivenmodulationtypeusing(5.18) ,andtheaverageBER isobtainedbyaveragingovertheprobabilitydensityfunctions(PDF)ofboththe channelestimation errorandthechannelestimates.TheBERforaQPSKsignalis[108] P QPSK 1 2 1 s 2 BL 2 2 exp( )erfc p # (5.19) whereerfc( )isthecomplementaryerrorfunctionand = 2 BL +2 2 ICI +2 2 n 2 2 : (5.20) ForsquareQAMsignals,i.e.withevennumberofbitspersymbol,andwithG raybitmapping,the BERis[108] P QAM 2 log 2 M 1 1 p M 1 s 3 2 BL 2( M 1) 2 exp( M )erfc p M # (5.21) where M isthemodulationorderand M = 3 2 BL +2( M 1)( 2 ICI + 2 n ) 2( M 1) 2 : (5.22) Forlowchannelestimationerrors, and M yieldlargevalues,ascanbeseenfrom(5.20)and(5.22). However,evaluatingtheerfc( )oflargevaluescanleadtoinaccurateresults.Toovercomethis problem,wefurthersimplifytheexpressionsin(5.19)and(5.21)byusingana pproximationofthe erfc( ).Itcanbeshownfrom[113]thattheerfc( )isboundedby L 0 ( x ) < erfc( x ) R 0 ( x )(5.23) 89

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where L 0 ( x )= 2exp( x 2 ) p x + p x 2 +2 (5.24) and R 0 ( x )= 2exp( x 2 ) p x + p x 2 +4 = : (5.25) Forlargevaulesof x ,suchasinconsideredapplication,wenotethat erfc( x ) L 0 ( x ) : (5.26) Applying(5.26)to(5.19)and(5.21),theBERforQPSKsignalsreducesto P QPSK 1 2 1 s 2 2 BL 2 1 p + p +2 # (5.27) andforQAMsignalsreducesto P QAM 2 log 2 M 1 1 p M 1 s 6 2 BL ( M 1) 2 1 p M + p M +2 # : (5.28) TheabovetwoexpressionsfortheBERhavetheadvantagesofbeingmuchsimpler comparedwith exactBERexpressionsintheliterature,canbeevaluatedaccuratelyforlowchanneles timation errors(noerfc( )),andprovideverycloseresultstotheexactBERasshowninSection5.6. TousetheBERexpressionspresentedin(5.27)and(5.28),thepowerofthechannel estimates 2 BL andchannelestimationerrors 2 needtobecalculated.Thevalueof 2 BL isexpressedas 2 BL = 1 n t k t 4 X n X k 2 BL ( n;k )(5.29) and 2 BL ( n;k )= E ^ H BL ( n;k ) 2 (5.30) 90

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wherethesummationsareoveralldatasubcarrierswithinthetileand 2 BL ( n;k )isthevarianceof thechannelestimatesatsubcarrier( n;k ).From(5.10)and(5.14),andsince I ( n;k )and W ( n;k ) arei.i.d.zeromeanrandomvariables,itcanbeshownthat 2 BL ( n;k )= 1 n 2T k 2 T ( n 2t k 2 t + n 21 k 2 t + n 2t k 2 1 + n 21 k 2 1 )
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Similarto 2 LS ,thevarianceofthechannelestimationerrorcanbecalculatedfrom(5.17)as follows 2 = 1 n t k t 4 X n X k 2 ( n;k )(5.37) and 2 ( n;k )= 2 H + 2 BL 2 < E h H ( n;k ) ^ H BL ( n;k ) i | {z } R B ( n;k ) : (5.38) From(5.14),itcanbeshownthat R B ( n;k )= 1 n T k T n t n 1 264 R H ( n 1 ; k 1 ) R H ( n 1 ; k t ) R H ( n t ; k 1 ) R H ( n t ; k t ) 375 264 k t k 1 375 : (5.39) Basedontheresultsin(5.29),(5.32),(5.36),(5.37),(5.38),a nd(5.39);thevaluesof 2 BL and 2 can becalculatedusingthechannelautocorrelationfunctionandtheconsideredtiledimensio ns( n t and k t ). 5.5OptimumTileDimensions Next,optimizationofthetiledimensions,usingtheresultspresentedisthischa pter,isconsidered.Forthesystemunderconsideration,itisassumedthatharddecisiondetectionanddecodi ng isusedatthereceiver.Similaranalysiscanbeappliedtothesoftdecisiondetectio ncase.However,calculationsofsoftdecisionmetricsoverRayleighchannelswithchannelesti mationerrorsis quitecomplicated[114,115]andisoutofthescopeofthiswork.Twoapproa chesareconsidered underharddecisioncriteria.Therstapproachistochoosethetiledimensionthat maximizes thesystemthroughput,assumingoptimumchannelcoding.Thesecondapproachistoconsiderthetiledimensionsthatmaximizethesystemeectivethroughputunderpracticalchannelcodi ng conditions. Withsucientinterleaving,thechannelcanbemodeledasabinarysymmetricchannel( BSC) withBER P b whichcanbeobtainedusing(5.27)and(5.28).Inthiscase,thechannelcapacity 92

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is[89,p.382] C = P b log 2 (2 P b )+(1 P b )log 2 2(1 P b ) : (5.40) Fromthenoisychannelcodingtheorem[116],themaximumcodingratethatcanachieve errorfreetransmissionisequalto C .Thus,forgiventiledimensions( n t k t ),themaximumachievable throughputis T max = C log 2 M n t k t 4 n t k t N u T S : (5.41) Itcanbeseenfrom(5.41)thatincreasingthetiledimensions,whicheectivelyr educesthepilot insertionrate,canincreasethesystemthroughput.However,largertiledimensio nsdegradethe channelestimationperformanceleadingtohighBER, P b andconsequentlylowerchannelcapacity, C .Assuch,thereisanoptimumvaluefor n t and k t atwhichthethroughputismaximized. Theoptimumtiledimensionsinthatsensecanbeobtainedusingnumericalmethodsassho wnin Section5.6. Achievingthechannelcapacityusingchannelcodingisusuallyverydicultinpractice.Thus, usingtheaboveapproachmayresultintiledimensionsthatarenotoptimumfor apracticalsystem. Inthiscase,thesystemdesignmayconsiderchoosingthetiledimensionsthatmaxi mizethesystem eectivethroughput,wheretheeectivethroughputisdenedas T e = r c (1 P f )log 2 M n t k t 4 n t k t N u T S ; (5.42) where r c isthechannelcodingrate,whichisusuallypredenedinapracticalsystem,and P f isthe frameerrorrate(FER).Theaboveexpressionisbasedonthefactthatfor practicalsystems,the decodedframesarecheckedforerrorsanderroneousframesaredropped.Thus,theactual system throughputisbasedontherateofframesthatarereceivedsuccessfully.Similarto theprevious approach,whileincreasingthetiledimensionscanincreasethesystemthroughput,itl eadstohigher FERwhichmaycancelanyincreasetotheoverallsystemthroughput.Therefore,itis expectedthat thereshouldbeoptimumtiledimensions,thatmaximizetheeectivethroughput. 93

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Table5.1SimulationparametersforatypicalOFDMAULsystemI. ParameterValue Carrierfrequency2 : 5GHz FFTsize1024CPsize128Numberofusedsubcarriers840Samplingfrequency11 : 2MHz 5.6SimulationResults AnOFDMULsystemthatisbasedontheWiMAXstandard[9]isconsidered.Typicals imulation parametersarechosenbasedon[90]andaresummarizedinTable5.1.Similar toWiMAXOFDMA systems,itisassumedthateachtilespansthreesymbols n t =3,andfoursubcarriers k t =4. Basedontheabovetiledimensions,theULframesizeinsymbolsisalwa ysconsideredasaninteger multipleofthree.Thereare210tilesperthreeOFDMAsymbolswhichareassi gnedrandomlyto oneormoreusers.ThemodulationschemesconsideredfordatasubcarriersareQPSK,1 6QAM,and 64QAM.ThesystemistestedoverthreechannelsbasedontheITUchannelmodels[91]:I ndoorA, PedestrianB,andVehicularA,withDopplerspreadof0Hz(0km/h),6.9Hz(3km /h),and138.9Hz (60km/h),respectively.Itisassumedthatthechannelisindependentbetweendierentfr amesand betweendierentusers.Thereceiverprocesseseachframeindividually.Atthereceiver,t heuncoded BERismeasuredandaveragedoverallusers.Forcomparison,thetheoreticalBER curvesbased ontheresultspresentedin(5.27)and(5.28)areconsidered.Theresultsforbot hsimulationsand theoreticalvaluesarepresentedinFig.5.3,Fig.5.4,andFig.5.5forPedes trianB,VehicularA, IndoorAchannelmodels,respectively.TheguresshowthatderivedBERvaluesareinver ygood agreementwithsimulationresultswithonlylittlemismatchathigherB ERvalues. Next,weinvestigatetheoptimumtiledimensionsfortwooperationproles .Therstproleis foranOFDMAULsystemoperatinginaVehicularAchannelwith64QAMmodulation. Inthe secondprole,thesystemisoperatinginPedestrianBchannelwithQPSKmodulation.I nboth cases,thesystemusesaconvolutionalcodewithrate r c =1 = 2,constraintlengthof7,andgenerator polynomialsof(133,171)inoctalform.Thiscodeachievesthemaximumf reedistanceforthegiven rateandconstraintlength[117].Thecondingblockischosentobe70bytes.A tthereceiver,hard decisionViterbidecoderisusedtodecodethedemodulatedsymbols.Insearchforoptimum tile dimensions,themaximumandeectivethroughputsforvarioustilesizesareevalua tedusing(5.41) 94

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10 15 20 25 30 35 40 45 50 10 -5 10 -4 10 -3 10 -2 10 -1 10 0 SNR (dB)Uncoded BER Theory Simulation QPSK 64QAM 16QAM Figure5.3UncodedBERofOFDMAULsystemoverPedestrianBchannel. 10 15 20 25 30 35 40 45 50 10 -5 10 -4 10 -3 10 -2 10 -1 10 0 SNR (dB)Uncoded BER Theory Simulation 64QAM 16QAM QPSK Figure5.4UncodedBERofOFDMAULsystemoverVehicularAchannel. 95

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10 15 20 25 30 35 40 45 50 10 -5 10 -4 10 -3 10 -2 10 -1 10 0 SNR (dB)Uncoded BER Theory Simulation QPSK 16QAM 64QAM Figure5.5UncodedBERofOFDMAULsystemoverIndoorAchannel. and(5.42),respectively.Toevaluatetheeectivethroughput,theFERneedstobecal culated. Unfortunately,therearenoexactexpressionsforthecodedBERandtheFERforconvo lutional codes.Thus,upperboundsontheBERandtheFERarecalculatedusingresultsfrom[89, 118]. ThedisadvantageofusingunionboundsisthattheydivergeforhigherBERvalues(or relatively lowSNRvalues).Themaximumandeectivethroughputfortherstandsecondproleare shown inFig.5.6,Fig.5.7,Fig.5.8,andFig.5.9,respectively.Inallg uresthethroughputsurfaceshows aconvexshapewhichindicatesamaximumvalueatagiventiledimensions.Theser esultsarein agreementwiththeconclusionsdrawninSection5.5.Theguresalsoshowthattheopt imumtile dimensionsarequitelargerthattheoneusedinitially(i.e. n t =3, k t =4). Toverifytheaboveresults,computersimulationsweregeneratedforbothprol es.Notethat whenchoosingthetiledimensionsfortheOFDMAsystem,therearesomelimita tions.First,the tiledurationinsymbols n t islimitedbythetotalallowedframeduration.Second,thenumberof usedsubcarriers N u shouldbeanintegermultipleofthetilebandwidthinsubcarriers k t .Basedon theselimitations,thebestpossibletiledimensionsforbothsystemprol esunderconsiderationwere foundtobe n t =9and k t =12.Consideringthesecondsystemprole,simulationresultsforthe uncodedBER,codedBER,andtheFERareshowninFig.5.10andFig.5.11forti ledimensions 96

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4 6 8 10 12 14 4 6 8 10 12 14 3.7 3.8 3.9 4 4.1 4.2 x 10 7 Subcarriers SymbolsMaximum Throughput (bits/sec) Figure5.6MaximumthroughputofOFDMAULsystemwith64QAMmodulationatSN R=35dB overVehicularAchannel. 4 6 8 10 12 14 4 6 8 10 12 14 2 2.1 2.2 2.3 2.4 x 10 7 Subcarriers SymbolsEffective Throughput (bits/sec) Figure5.7EectivethroughputofOFDMAULsystemwith64QAMmodulationandr ate1/2 convolutioncoding,atSNR=35dBoverVehicularAchannel. 97

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5 10 15 20 5 10 15 20 1.15 1.2 1.25 1.3 1.35 x 10 7 Subcarriers Symbols Maximum Throughput (bits/sec) Figure5.8MaximumthroughputofOFDMAULsystemwithQPSKmodulationatSNR= 15dB overPedestrianBchannel. 5 10 15 20 5 10 15 20 6.5 7 7.5 8 x 10 6 Subcarriers Symbols Effective Throughput (bits/sec) Figure5.9EectivethroughputofOFDMAULsystemwithQPSKmodulationandrat e1/2 convolutioncoding,atSNR=15dBoverPedestrianBchannel. 98

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10 11 12 13 14 15 16 17 18 10 -7 10 -6 10 -5 10 -4 10 -3 10 -2 10 -1 10 0 SNR (dB)Error rate Theory Simulation uncoded BER FER coded BER Figure5.10UncodedBER,codedBER,andFERofOFDMAULsystemwithQPSKmodulat ion overPedestrianBchannelwhere n t =3and k t =4. ( n t =3, k t =4)and( n t =9, k t =12),respectively.TheoreticalvaluesfortheuncodedBERas wellasupperboundsforthecodedBERandtheFERareincludedforreference.ThetheoreticalandsimulatedvaluesfortheuncodedBERarematchingwell.Theupperboundsconvergeswi th simulatedresultsathigherSNRvalues. Finally,simulationresultsoftheeectivethroughputsforbothsystemprol esandbothconsideredtiledimensionsareshowninFig.5.12andFig.5.13.Duetotheuseofupp erboundsforthe FER,thetheoreticalresultsfortheeectivethroughputactaslowerboundsforsimul atedvalues. ThelowerboundsconvergewithsimulatedresultsathigherSNRvalues.Theresultss howthata signicantincreaseinthesystemthroughput(around40%increase)canbeachievedbyca refully choosingtheusedtiledimensions.5.7Conclusion Inthischapter,channelestimationinOFDMAULsystemsovertime-varyingmult ipathRayleigh fadingchannelsisconsidered.Tile-basedchannelestimationisassumedwithnoknowledge of multipleuserchannelstatisticssuchasDoppleranddelayspreads.Approximateexpres sionsof 99

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10 11 12 13 14 15 16 17 18 10 -7 10 -6 10 -5 10 -4 10 -3 10 -2 10 -1 10 0 SNR (dB)Error rate Theory Simulation uncoded BER coded BER FER Figure5.11UncodedBER,codedBER,andFERofOFDMAULsystemwithQPSKmodulat ion overPedestrianBchannelwhere n t =9and k t =12. 20 21 22 23 24 25 26 27 28 29 30 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 x 10 7 SNR (dB)Effective throughput (bits/sec) Theory Simulation n t = 9, k t = 12 n t = 3, k t = 4 Figure5.12EectivethroughputofOFDMAULsystemwith64QAMmodulationand rate1/2 convolutioncodingoverVehicularAchannel. 100

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10 11 12 13 14 15 16 17 18 3 4 5 6 7 8 9 x 10 6 SNR (dB)Effective throughput (bits/sec) Theory Simulation n t = 9, k t = 12 n t = 3, k t = 4 Figure5.13EectivethroughputofOFDMAULsystemwithQPSKmodulationandra te1/2 convolutioncodingoverPedestrianBchannel.theBERforQPSKandQAMsignalswithchannelestimationerrorsarederivedwhenbi linear interpolationisusedforchannelestimation.UsingBERtheoreticalexpressio ns,theoptimumtile dimensions(oroptimumpilotinsertionrate)inthetime-frequencygridareinves tigated.Both analyticalandsimulatedresultsshowthatcarefulchoiceofthetiledimensionsca nsignicantly increasethesystemthroughput(upto40%insomecases). 101

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CHAPTER6 IQIMBALANCECORRECTIONFOROFDMAUPLINKSYSTEMS 6.1Introduction Thedirectconversionreceiverisanattractivearchitectureforthephysicalla yer(PHY)oforthogonalfrequencydivisionmultipleaccess(OFDMA)systemssinceitavoidscost lyintermediate frequency(IF)lters,reducespowerconsumption,andallowsforeasierintegration thansuperheterodynestructure[17].However,directconversionreceiverscausemoredistort ionstothebasebandsignalduetotheimbalancebetweentheinphase(I)andquadrature(Q)branches.TheIQimbalanceresultsinadegradationinthesystemperformance.Thisdrawbackofdi rectconversion receiversbecomesmoresignicantwithorthogonalfrequencydivisionmultiplexing (OFDM)systems astheyareknowntobesensitivetoreceiverfront-endnon-idealities[18].Thus, thereisaneedfor methodstonullifyorreducetheIQdistortions. SeveraltechniqueshavebeenproposedtoreducethedegradationcausedbyIQimbalancein OFDM-basedsystems[119].In[120{122],theIQimbalancecausedbythereceiver front-endis investigated.ThecombinedeectsofIQimbalanceatthetransmitterandreceiverfro nt-endsis investigatedin[123{126].AninterestingapproachthatusestheinruenceofIQ imbalancetoobtain diversitygainisproposedin[127]. Inalloftheabove,theeectsofIQimbalanceonmultiuserOFDMsystemsarenot considered. InOFDMA-uplink(UL)systems,IQimbalanceproblembecomesmorecomplicated.Firs t,thenonidealitiesinmultipleuserfront-endsareexpectedtobedierent.Second,thetotalIQ imbalance eectsonOFDMAsystemsresultsinmultiuserinterference(MUI)asopposedtoin ter-carrierinterference(ICI)inOFDMsystems.Inaddition,inOFDMA-ULsystems,preamblesare notusedfor channelestimation.Instead,thechannelisdividedintosubchannels-thatcanbeassigned touserswithdedicatedpilotsforeachsubchannel.Withoutpreambles,manyofproposedalg orithmsabove areinapplicable. 102

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Inthischapter,weconsidertheeectofIQimbalanceontheOFDMA-ULsystem.Thereceiv ed signalasafunctionofmultiusertransmittedsignals,IQparameters,andcom municationchannelsis mathematicallyformulated.Thissignalmodelisthenusedtoinvestigatedmetho dstoestimateand equalizedboththemultiuserchannelsandIQdistortions.Anovelpilotpatternisdes ignedwhichis thenusedbytwoproposedmethodstoecientlymitigatesignaldistortionscaus edbythecombined eectofmultipathdispersivechannelsandIQimbalancesofmultipleusers.Thepropo sedmethods areshowntosignicantlyreducetheimpactofIQimbalanceonOFDMAsignals.6.2SystemModel WeconsideranOFDMA-ULsystememploying N subcarrierspersymbol.TheDCsubcarrier andguardsubcarriersaredisabled.Theremainingsubcarriers N u areusedfordatatransmission withequalnumberofsubcarriersoneachsideoftheDCsubcarrier.Theabovea ssumptionsare commonformostpracticalimplementationsofOFDMAsystems.Usedsubcarri ersaredividedinto M subchannels,theindexesofeachsubchannel m isintheset M m .Subchannelscanthenbe assignedtomultipleusers.Everyuser m generatesasequenceofmodulatedsymbols x m whichare mappedtosubcarriersofassignedsubchannels.Thesignalinthenfedtoaninvers efastFourier transform(IFFT)blockandthecyclicprex(CP)isadded.The n thsampleofthetransmitted symbolofuser m is, s m ( n )= X k 2M m x m ( k )exp | 2 nk N ; N g n N 1(6.1) where N g + N isthetotalnumberofsamplespersymboland N g isthesizeoftheCP. TheIQimbalancedistortstheidealTxsignalasfollows[121], e s m = m s m + m s m ; (6.2) where( ) isthecomplexconjugate,and m and m arerelatedtotheIQimbalanceasfollows, m =cos m + j m sin m ; (6.3a) m = m cos m j sin m ; (6.3b) 103

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where m and m arethegainimbalanceandthephasemismatch,respectively.Fortheremainder ofthechapter, m and m arereferredtoastheIQparameters.Atthereceiver,thesumofall transmittedusersignalsisreceived, y ( n )= K X m =1 r m ( n )+ w ( n ) ; (6.4) where K isthetotalnumberofusersinthesystematthecurrentsymbol, w ( n )isthermalnoise, and r m isthereceivedsignalofthe m thuser. r m ( n )= X i s m ( i ) h m ( n i ) ; (6.5) where h m ( n )isthesampledchannelimpulseresponse(CIR)ofthe m thuserattime t = nT S and T S isthesamplingtimeofreceivedsignal.Inordertoeliminateanyinterferenceb etweenadjacent OFDMAsymbols,i.e.inter-symbolinterference(ISI),theCPsize, N g ischosensuchthat N g T S islargerthatthemaximumdelayspreadofthechannelforallusers.Atthereceiver, theCPis removedandthesignalisfedtoan N -pointfastFouriertransform(FFT)block.Theoutputofthe FFTcanbeexpressedas, Y ( k )= N 1 X n =0 y ( n )exp | 2 nk N ; 0 k N 1 ; (6.6) where k isthesubcarrierindex.IfreceivedsignalisISIfree,thenreceivedsubcarriersofuser u are, Y ( k )= u H u ( k ) x u ( k )+ v H v ( k ) x v ( k )+ ( k ) ;k 2M u (6.7) where ( k )ismodeledasadditivewhiteGaussiannoise(AWGN)withzeromeanandvari ance N 0 = 2, k isthemirroredsubcarrierof k overtheDCsubcarrier, v 2f 1 ;:::;K g istheindexofuserwhich subcarrier k isassignedto,and H m isthe m thuserchannelfrequencyresponse(CFR).If H u is perfectlyknowntothereceiver,thentheequalizedsignalofuser u is, e Y ( k )= u x u ( k ) | {z } desiredsignal + v H v ( k ) H u ( k ) x v ( k ) | {z } interference + ( k ) H u ( k ) ;k 2M u : (6.8) 104

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Itcanbeseenfromtheaboveequationthatthersttermisthedesiredsignalwi thanattenuation u ,thesecondtermrepresentstheICIfor v = u ortheMUIfor v 6 = u ,andthelasttermrepresents thenoise.Theinterferencetermcanbecanceledbyjointlydetecting x u ( k )and x v ( k ).Insucha case,thereceiverneedstoestimate H m for m =1 ;:::;K .Thepilotsubcarriers N p aredivided amongusers/subchannels. InanIQdistortionfreeOFDMAsystem,thesystemestimatesthechannelrespo nseat N u subcarriersusing N p pilots.However,forasystemsueringfromIQdistortion,everyuser m transmittingoversubcarriers k 2M m causesinterferenceat k aswell,asshownin(6.7).This meansthatinworstcasescenario,where k= 2M m 8 k ,theusereectivelytransmitsovertwicethe numberofassignedsubcarriers.Receiverthenneedstoestimatetwouserchannelspersubca rrieror atotalof2 N u channelresponsesusingthesamenumberofpilots.Inaddition,estimationof K sets ofIQparameters f m ; m g isneededtofullycanceltheinterferenceintroducedbyimagecarriers asshownin(6.8).6.3Channel/IQEqualization Inthissection,equalizationofthechanneleectsandIQdistortionsinthereceiveds ignalisdiscussed.First,theULframestructureneedstobeintroduced.InOFDMAsystems,useds ubcarriers aredividedintosmallerunits,alsoknownastilesorchunks,whichrepresent theminimumallocation unit(seeFig.6.1).Thetilesarethenassignedtosubchannelseitherrandomlyordep endingonuser channels.TheoverallreceivedULframeisasumofallcurrentusersignals,which aretransmitted overdierentcommunicationchannels.Theuseofsophisticatedchannelestimational gorithmsat thereceivercansignicantlyincreasethesystemcomplexityandprocessingdelay.Theref ore,pilotsareassignedwithineachtile.Thereceivercanthenperformchannelestimati ononeachtile individuallyusinglowcomplexitychannelestimationtechniquessuchasbilinearint erpolation. AnexampleofhowtheULframeisdividedintotilesisshowninFig.6.1.U sedsubcarriersare dividedinto Q tiles,withequalnumberoftilesoneachsideoftheDCsubcarrier.Thismeanst hatfor everytile q ,thereisanimagetile q = Q q +1.Threedierenttilestructuresareshowninthegure, whereonetiledimensionsarethreesymbolsbyfoursubcarriers.Thetilebandwi dth, B tile =3 f where f isthesubcarrierspacing,andthetileduration, T tile =3 T sym ,where T sym =( N + N g ) T S isthesymbolduration.Fortheremainderofthischapter,TileCstructureisused. Notethata 105

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— ™š› œ —  Ÿ  ¡¢ £ ¤¢ ¦œ › § ¨ § ¦œ ¦œ ¦œ › § ¦œ § ¦œ § ¦ › £ ¤ Ÿ ¡ £ ¨ — š ¦ § ¦œ § ¦œ § ¦œ § ¦œ Figure6.1ULframestructureandsubcarriermappingtotiles. similarframestructureisemployedbythemobileworldwideinteroperabil ityformicrowaveaccess (WiMAX)standard[9]. InasystemwithnoIQdistortion,thereceiverwouldconsidereachtileindependently .Thefour pilotswithinatilewouldbeusedtoobtainleastsquares(LS)estimates.T heLSestimatesarethen usedtoestimatethechannelattheremainingdatasubcarriersusingbilinearinterpo lation.Ifthe receivedsignalisdistortedbytheIQimbalance,thereceiverprocesseseachtile q alongwithits 106

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RF front-end Parallel-to-Serial & Permutation FFT Serial-to-Parallel Subcarriers-to-tiles Mapper 1-tile channel estimation & equalization k = 1 N q = 1 Q 1-tile channel estimation & equalization (a) RF front-end Parallel-to-Serial & Permutation FFT Serial-to-Parallel Subcarriers-to-tiles Mapper 2-tile channel+distortion estimation & equalization k = 1 N q = 1 Q (b) Q /2 Q /2+1 2-tile channel+distortion estimation & equalization Figure6.2Receiverblockdiagramof(a)conventionalOFDMA-ULsystem,and( b)AnOFDMA-UL systemforsignalswithIQdistortion.imagetile q .SimpliedblockdiagramsofbothaconventionalOFDMAreceiverandanIQdisto rted OFDMAreceiveraredepictedinFig.6.2.Withoutthelossofgenerality,weassum ethattile q is assignedtouser u andtile q isassignedtouser v 6 = u .Thereceivedsubcarriersoftile q and q are, y ( i;j )= u H u ( i;j ) x ( i;j )+ v H v ( i;j ) x ( i; j ) ;y ( i;j ) 2 q; (6.9a) y ( i; j )= v H v ( i; j ) x ( i; j )+ u H u ( i; j ) x ( i;j ) ;y ( i; j ) 2 q; (6.9b) wheretheindex( i;j )representsthe i thOFDMAsymboland j thsubcarrierasshowninFig.6.3. Using(6.9a)and(6.9b),thereceivedsignalsasfunctionoftransmittedsig nals,users'CFR,and users'IQparametersisexpressedas, 264 y ( i;j ) y ( i; j ) 375 = 264 u H u ( i;j ) v H v ( i;j ) u H u ( i; j ) v H v ( i; j ) 375 | {z } Z ( i;j ) 264 x ( i;j ) x ( i; j ) 375 (6.10) Tojointlydetecttransmittedsubcarrier x ( i;j )anditsimage x ( i; j ),thereceiverneedstoestimate eightunknowns(fourCFRsamplesandfourIQparameters),iftheestimationof thechannelre107

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symbols subcarriers jj +1 j +2 j +3 j -3 j -2 j -1 j i i +1 i +2 Tile q Tile q DC Figure6.3Subcarrierindexingofatilepair. sponsesandIQimbalancesaredoneseparately.Alternatively,thereceivercanestim ateonlythefour unknownsof Z ( i;j ),iftheeectsofthechannelsandIQimbalancesareestimatedjointly.However, inthiscase,thereceiverdoesnothaveanestimateoftheIQdistortionintroduced byeachuser. TheLSestimationoftransmittedsignalisgivenby, 264 x ( i;j ) x ( i; j ) 375 = Z 1 ( i;j ) 264 y ( i;j ) y ( i; j ) 375 (6.11) 6.4Channel/IQEstimation Let'sassumethat x ( i;j ), x ( i; j ), x ( i;j +3),and x ( i; j 3)arepilotsasshowninFig.6.3.Knowing thevalueofthetwopilotsin(6.10)isnotsucienttoestimatethechannel/I Qparametersmatrix Z ( i;j ).Twomethodsareproposedtosolvethisproblem.Therstproposedmethod,Metho dA, assumesthatthetilebandwidth, B tile islessthanthechannelcoherencebandwidth, B C ,forall users.Inthiscase,theCFRoverthetilebandisalmostconstant,i.e. H m ( i;j ) H m ( i;j +3) for m 2f 1 ;:::;K g .Basedontheaboveassumption,thesecondpairofpilotsatsymbol i and subcarriers f j +3 ; j 3 g canberepresentedas, 264 y ( i;j +3) y ( i; j 3) 375 = 264 u Hu ( i;j +3) v H v ( i;j +3) u H u ( i; j 3) v H v ( i; j 3) 375 264 x ( i;j +3) x ( i; j 3) 375 Z ( i;j ) 264 x ( i;j +3) x ( i; j 3) 375 (6.12) 108

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Using(6.10)and(6.12),thesystemcansolvefor Z ( i;j ).Thesameprocedureisthenrepeatedfor thetwopilotpairsatsymbol i +2toobtain Z ( i +2 ;j ).Toinsurethatthissetofequationshasa uniquesolution,pilotvectorpairsarechosentobeorthogonal[128,129]s uchthat, x ( i;j ) x ( i; j ) 264 x ( i;j +3) x ( i; j 3) 375 =0 ; (6.13a) x ( i +2 ;j ) x ( i +2 ; j ) 264 x ( i +2 ;j +3) x ( i +2 ; j 3) 375 =0 : (6.13b) Next, Z ( i +1 ;j )canbeestimatedusing1-Dinterpolationbetween Z ( i;j )and Z ( i +2 ;j ).Finally, using(6.11), f Z ( i;j ) ; Z ( i +1 ;j ) ; Z ( i +2 ;j ) g areusedtoestimatetheremainingdatasubcarriersat symbols f i;i +1 ;i +2 g ,inthisorder.Thereceiverrepeatsthisprocessforeachpairoftiles( Q= 2 times). Thesecondproposedmethod,MethodB,assumesthatthetileduration, T tile islessthanthe coherencetimeofthechannel, T C ,forallusers.Inthiscase, H m ( i;j ) H m ( i +2 ;j )for m 2 f 1 ;:::;K g .Basedontheaboveassumption,thesecondpairofpilots(tobecoupledwith(6 .10))at symbols f i;i +2 g andsubcarriers f j; j g canberepresentedas, 264 y ( i +2 ;j ) y ( i +2 ; j ) 375 Z ( i;j ) 264 x ( i +2 ;j ) x ( i +2 ; j ) 375 (6.14) Using(6.10)and(6.14),thesystemsolvesfor Z ( i;j ).Similarly,thepilotpairsatsubcarriers f j +3 ; j 3 g canbeusedtosolvefor Z ( i;j +3).Next,thereceiveruseslinearinterpolationto calculate f Z ( i;j +1) ; Z ( i;j +2) g from f Z ( i;j ) ; Z ( i;j +3) g .Finally,theabovevaluesof Z areused toestimatetheremainingdatasubcarriersinbothtiles.Theprocedureisthenrep eatedforeach pairoftiles.Thepilotsorthogonalityisachievedasfollows, x ( i;j ) x ( i; j ) 264 x ( i +2 ;j ) x ( i +2 ; j ) 375 =0 ; (6.15a) x ( i;j +3) x ( i; j 3) 264 x ( i +2 ;j +3) x ( i +2 ; j 3) 375 =0 : (6.15b) 109

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Table6.1SimulationparametersforatypicalOFDMAULsystemII. ParameterValue Carrierfrequency2 : 5GHz FFTsize, N 1024 CPsize, N g 128 Numberofusedsubcarriers, N u 840 Samplingfrequency,1 =T S 11 : 2MHz Numberoftiles, Q 210 Numberofsubchannels, M 35 Toenablethereceivertouseeithermethods,weproposetousethefollowingpilotpat tern,which satisestheconditionsin(6.13a),(6.13b),(6.15a),and(6.15b). 264 x ( i;j ) x ( i;j +3) x ( i +2 ;j ) x ( i +2 ;j +3) 375 = 264 d 2 d 1 d 1 d 2 375 ; (6.16a) 264 x ( i; j 3) x ( i; j ) x ( i +2 ; j 3) x ( i +2 ; j ) 375 = 264 d 2 d 1 d 1 d 2 375 ; (6.16b) where d 1 and d 2 arearbitrarysymbolsthatbelongtothemodulationsymbolsetusedforpi lots. Theabovepilotpatternachievesorthogonalitybetweenpilotpairsinbotht hesubcarrierdimension andthesymboldimension.Thus,thereceivercanimprovethesystemperformanceby adaptively usingeitherMethodAorMethodBdependingontheuserchannelconditions(i.e.delayspreadandDopplerspread)orbyusingbothmethodsandchoosingtheestimateswiththeleaster rorvector magnitude(EVM)values.6.5SimulationResults AsystembasedontheWiMAXstandard[9]isconsidered.Typicalsimulationpara metersare chosenbasedon[90]andaresummarizedinTable6.1.Weassumethreeusersare transmittinginall ULframes.Theavailable35subchannelsaredividedamonguserswith12,12,a nd11subchannels assignedtouser1,user2,anduser3,respectively.SubchannelsassignedtoULusersar erandomized foreveryframe.Themodulationusedfordatasubcarriersisquadraturephaseshi ftkeying(QPSK), andforpilots,binaryphaseshiftkeying(BPSK)isused( d 1 = d 2 =1).Thesystemistestedover threechannelsbasedontheITUchannelmodels[91]:IndoorA,PedestrianB,andVehicular A, withDopplerspreadof0Hz(0km/h),6 : 9Hz(3km/h),and138 : 9Hz(60km/h),respectively.It 110

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isassumedthatthechannelisindependentbetweendierentframesandbetweendierentusers.Thereceiverprocesseseachframeindividually.Atthereceiver,theuncodedbiterrorrate (BER)is measuredandaveragedoverallusers. Forallgeneratedsimulations,itisrstassumedthattherearenoIQimbalances introducedto thesignal.Thereceiverusesallpilotspertiletoestimateandequalizeonlythe channeleects using2-Dlinearinterpolationtechnique.Thiscaseislabeledas\IdealIQ".Next ,theULuser signalsaredistortedbyIQimbalances.TheIQgainimbalanceandphasemisma tchofuser1, user2,anduser3are f 0 : 2 ; 2 g f 0 : 35 ; 5 g ,and f 0 : 5 ; 8 g ,respectively.TheuncodedBERis measuredwhilethereceiveroperatesassumingnoIQimbalanceispresent.Theresultsa relabeled as\IQImbalance/Nocompensation".Finally,MethodAandMethodBareusedtoest imateand equalizethecombinedchannelandIQdistortions.TheresultsareshowninFig.6.4 ,Fig.6.5,and Fig.6.6.Inallgures,thesystemperformancedegradessignicantlywhentherecei verignoresthe IQdistortionstothesignal.Atasignal-to-noiseratio(SNR)of35dB,t heIQdistortionsincrease theBERbytwoordersofmagnitude.Ontheotherhand,proposedmethodsmanagetoreducetheBERconsiderably.FortheresultsoverthePedestrianBchannelinFig.6.4,thedela yspreadishigh whiletheDopplerspreadislow.Asaresult,MethodBoutperformsMethodA,since itassumes lowDopplerspreading.MethodBsignicantlyreducestheIQdistortioneectonthesig nal.The lossisaround2dBfromtheidealIQcaseatBER=10 3 .FortheresultsovertheVehicularA channelinFig.6.5,bothdelayspreadandDopplerspreadarehigh.Inthiscase,Metho dAslightly outperformsMethodB,sinceitsapproximationismoreaccurate.Whileboth methodsAandB improvetheBERsignicantly,thelossfromtheidealIQcaseisconsiderable.U ndersuchhighly selectivechannelsandwithIQdistortions,thesystemcanchoosetoreducesignal bandwidthwhich leadstoanimprovedperformanceofMethodA.Finally,fortheresultsoverthe IndoorAchannelin Fig.6.6,bothdelayspreadandDopplerspreadarelow.Asexpectedinthiscase,b othmethodsA andBperformverywell.TheBERdegradationduetotheIQdistortionsisrecover edwitharound 2 : 5dBlossfromtheidealIQcaseatBER=10 3 .NotethatthereisalossfromtheidealIQ caseeveninchannelswithlowDopplerspreadanddelayspread.Thislossisaresultof thenoise averagingeect.Inidealcase,theestimationofchannelresponse,whichisalmos tconstantoverslot bandwidthand/orslotduration,isaveragedbythebilinearinterpolationover twicethenumberof pilotscomparedtoproposedmethods.AreceivercapableofdetectingthepresenceofIQdisto rtions 111

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10 15 20 25 30 35 40 45 50 10 -4 10 -3 10 -2 10 -1 10 0 SNR (dB)BER IQ Imbalance / No compensation IQ Imbalance / Method-A IQ Imbalance / Method-B Ideal IQ Figure6.4AverageuncodedBERofQPSKsignalsreceivedoverPedestrianBchannelandwi thIQ impairments.canavoidthislossbyswitchingtoconventionalchannelestimatorifreceived signalisfreefromIQ distortions.6.6Conclusion Inthischapter,amodelforOFDMA-ULsystemswithIQimpairmentsisintro duced.Thereceivedsignalasafunctionoftransmittedsignals,IQparameters,andcommunica tionchannelsis mathematicallyformulated.Thesignalmodelisusedtodesignanoveltwo-dimensio nalorthogonalpilotpattern.TwolowcomplexitymethodsareproposedtoequalizeanddetectIQdi storted signalsusingdesignedpilotpattern.Proposedmethodswereshowntoimprovethes ystemperformancesignicantlyoverconventionaldetectionmethodsforsignalssueringfrom multipleuserIQ distortions. 112

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10 15 20 25 30 35 40 45 50 10 -4 10 -3 10 -2 10 -1 10 0 SNR (dB)BER IQ Imbalance / No compensation IQ Imbalance / Method-B IQ Imbalance / Method-A Ideal IQ Figure6.5AverageuncodedBERofQPSKsignalsreceivedoverVehicularAchannelandwith IQ impairments. 10 15 20 25 30 35 40 45 50 10 -4 10 -3 10 -2 10 -1 10 0 SNR (dB)BER IQ Imbalance / No compensation IQ Imbalance / Method-A IQ Imbalance / Method-B Ideal IQ Figure6.6AverageuncodedBERofQPSKsignalsreceivedoverIndoorAchannelandwithI Q impairments. 113

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CHAPTER7 ERRORVECTORMAGNITUDEBASEDSNRESTIMATIONINBLIND RECEIVERS 7.1Introduction Inwirelesscommunicationsystems,complexdigitalmodulationschemesareused formeeting stringentspectralandsignal-to-noiseratio(SNR)requirements[130].In suchsystems,theoverall qualityofthetransmissionandreceptionaredeterminedbyvariousbasebandandR Fsystemspecications.Amongthese,biterrorrate(BER)anderrorvectormagnitude(EVM)a retwoprimary specicationsthatdeterminetheperformanceofthewirelesssystemintermsoftr ansmittedand receivedsymbolscorrespondingtoagivendigitalmodulationscheme.WhileBER isusefulasaconceptualgureofmerit,itsuersfromanumberofpracticaldrawbacksthatcomprom iseitsvalue asastandardtestinmanufacturingormaintenance[131].CalculationofBE Rrequiresdedicated equipment,thusincreasingthecostandcomplexityofthetestsystem.Inaddition,i thaslimited diagnosticvalue.IftheBERvaluemeasuredexceedsacceptedlimits,itoersnocluereg ardingthe probablecauseorsourceofsignaldegradation. Formeasurementsandtestingdevices,EVMisaviablealternativetestmethodwhen looking foragureofmeritinnon-regenerativetransmissionlinks.EVMcanoerinsi ghtfulinformation onthevarioustransmitterimperfections,includingcarrierleakage,IQmisma tch,nonlinearity,localoscillator(LO)phasenoiseandfrequencyerror[19].RequirementsonEVMar ealreadypart ofmostwirelesscommunicationsstandardssuchastheIEEE802.11a-1999st andard[6]andthe IEEE802.16e-2005worldwideinteroperabilityformicrowaveaccess(Wi MAX)standard[9].EVM measurementsandsimulationscanbefoundin[131{133].TheimpactofIQimba lance,aswellas LOphasenoiseonEVMisinvestigatedin[134]andEVMasafunctionofthese impairmentsis derived.Thisworkhasbeenexpandedin[19],wheretheeectsofcarrierleakage,nonlinear ityand LOfrequencyerroronEVMareconsidered. 114

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RelatingEVMtootherperformancemetricssuchasSNRandBERisanimportan tresearch topic,aswell[135,136].Theserelationsarequiteusefulsinceitallowst hereuseofalreadyavailable EVMmeasurementstoinfermoreinformationregardingthecommunicationsyst em.Moreover,using EVMmeasurementscouldreducethesystemcomplexitybygettingridoftheneedtohaves eparate modulestoestimateormeasureothermetrics.WhenrelatingEVMtoSNR,oneassum ptionthat hasbeenmadeisthattheEVMismeasuredusingknowndatasequences(e.g.preamblesorpilo ts) orthattheSNRishighenoughthatsymbolerrorsarenegligible[135,136]. Anotherassumption wasthatoneortwosystemimperfectionsaredominant;theremainingimperfect ionsaremodeled asGaussiannoise[19,134].However,theaboveanalysesdidnotconsidermea suringEVMblindly forlowSNRlevelswheresymbolerrorsarepossible.Withnewtechnologiesfo rspectrumdetection andutilization[4,92],thereisaneedtodetectsignalsatmediumtoverylowSNRv alues.The signalqualitymetricsincludingEVMandSNRarepossiblymeasuredoverunknowndat asequences (nondata-aided)aswell. Inthischapter,weconsidertherelationbetweenEVMandSNRfornondata-aidedreceivers ThesignaldegradationsourcesaremodeledasadditivewhiteGaussiannoise(A WGN),Rayleigh fadingchannels,andIQimbalances.Itisshownthatforhighermodulationordersor lowSNR values,usingpreviouslymadeassumptionsleadstoinaccurateresults.Theexactval ueofEVMfor nondata-aidedsymboldetectionisderivedandexpressedintermsoftheSNR.Thederivedr elations arethenusedtoestimatetheSNRusingmeasuredEVMvaluesforQAMandPAMsignals andover limitednumberofsymbols.TheresultsshowthatSNRcanbeaccuratelyestimat edusingmeasured EVMevenwhensymbolsequencesareunknown,andtheSNRlevelislow. Theremainderofthischapterisorganizedasfollows.InSection7.2,thesignal modeland assumptionsarepresented.TheEVMisdenedandmathematicallyexpressedinSection7.3 RelationbetweenEVMandSNRfordata-aidedreceiversanditsapplicationtonondata -aided receiversarediscussedinSection7.4.InSection7.5,theEVMrelationtoSNRis derivedforQAM andPAMsignals.Computer-basedsimulationsareperformedtoexaminethecorr ectnessofderived expressions;thoseresultsarediscussedinSection7.6.Finally,concludingremark saregivenin Section7.7. 115

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7.2SignalModel Weassumeadigitalbasebandsignal x istransmittedoveracommunicationchannelwitha channelimpulseresponse(CIR) h .Inaddition,thereceivedsignaliscorruptedbycomplexAWGN, w .Thus,the n threceivedbasebandsymbolcanbeexpressedasfollows, r ( n )= 1 X l = 1 x ( l ) h ( n l )+ w ( n ) : (7.1) Notethat h canalsoincludetheeectsoftransmitter/receiverltersinadditiontothechannel.I fa modulationorderof M isused,then x ( n ) 2f S 1 ;S 2 ;:::S M g .Throughoutthechapter,itisassumed thatallsymbolsaresentwithequalprobability. Thereceiver,usuallyameasurementinstrumentsuchasvectorsignalanalyzers(VSA) ,acquires thesignal,performssynchronization,andchannelestimationandequalization. Thedetectedsignal canberepresentedby, y ( n )= g ( n ) x ( n )+ ( n ) ; (7.2) where g ( n )and ( n )representthemultiplicativeandadditiveimpairmentstodetectedsignal.The multiplicativeimpairmentscanbearesultofchannelestimationerrorsorI Qimbalances,forexample. Theadditiveimpairmentsisusuallyduetothermalnoiseandaremodeledasanindep endentand identicallydistributed(i.i.d.)complexAWGNsampleswithpowerspectraldensi ty(PSD)of N 0 = 2. Inthischapter,threemodelsareconsideredforthedetectedsignal.Therstcaseiswhen the additivenoiseisthedominantdegradationsourceand g ( n ) 1.Thesecondcaseisforsignals detectionoverRayleighfadingchannels.Finally,thethirdcaseisforsignals detectionwithother impairmentssuchaschannelestimationerrors,interference,orIQimbalances.7.3ErrorVectorMagnitude EVMcanbedenedastheroot-mean-squared(RMS)valueofthedierencebetweenacollection ofmeasuredsymbolsandidealsymbols[136].ThevalueoftheEVMisavera gedovertypicallya largenumberofsymbolsanditisoftenexpressedasapercentage(%)orindB .TheEVMcanbe 116

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representedas[137], EVM RMS = vuuuut 1 N N X n =1 j S r ( n ) S t ( n ) j 2 P 0 ; (7.3) where N isthenumberofsymbolsoverwhichthevalueofEVMismeasured, S r ( n )isthenormalized received n thsymbolwhichiscorruptedbyGaussiannoise, S t ( n )istheideal/transmittedvalueofthe n thsymbol x ( n ),and P 0 iseitherthemaximumnormalizedidealsymbolpowerortheaveragepower ofallsymbolsforthechosenmodulation.Fortheremainderofthischapter,the latterdenitionof P 0 isused.Insuchcase, P 0 = 1 M M X m =1 j S m j 2 : (7.4) TheEVMvalueisnormalizedwiththeaveragesymbolenergytoremovethedependencyo fEVMon themodulationorder.In(7.3), S r ( n )isthedetectedsymbol y ( n )and S t ( n )couldbeeitherknown tothereceiver(data-aided)ifpilotsorpreamblesareusedtomeasuretheEVM,orest imatedfrom y ( n )(nondata-aided)ifdatasymbolsareusedinstead. 7.4RelatingEVMtoSNR LetusconsiderthecasewherethesignalisonlycorruptedbyAWGN.Fordata-aidedEVM calculations,(7.3)isreducedto, EVM RMS = vuuuut 1 N N X n =1 j ( n ) j 2 P 0 : (7.5) IftheEVMismeasuredoverlargevaluesof N ,then[135,136,138], EVM RMS r N 0 P 0 = r 1 SNR ; (7.6) where N 0 = 2= 2 n isthenoisePSD. TheaboveEVM-SNRrelation,however,onlyholdsfordata-aidedreceivers.Fornondat a-aided receivers,thetransmittedsymbolsareestimatedandthoseestimates^ x ( n )areusedtomeasurethe 117

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EVMvalue.Thus,forlowSNRvalues,errorsaremadewhenestimating x ( n ).ThemeasuredEVM valueinthiscaseisexpectedtobelessthanitsactualvalueasthesymbolest imatortendsto assignreceivedsymbolstotheirclosestpossibleconstellationpoint.F oraBPSKsignal,thesymbol estimatorcriterionisasfollows, ^ x ( n )= 8>><>>: S 1 ; if y < ( n ) > 0 ; S 2 ; if y < ( n ) < 0 ; (7.7) where y < ( n )istherealpartof y ( n ).Notethatfor y < ( n )=0,^ x ( n )= S 1 or S 2 withequalprobability. Assuch,errorsinestimating x ( n ),andconsequentlyinmeasuringtheEVM,occurseverytimea constellationpointpassestoanotherpointdecisionregion.Tofurtherillust ratetheeectofsuch errorsontheEVM-SNRrelation,theEVMversusSNRcurvesforvariousmodulatio nordersare plottedinFig.7.1.Theresultsareaveragedover100 ; 000modulatedsymbols.Theidealvalueof EVM(=1 = p SNR)isalsoplottedforreference.Twoobservationscanbedrawnfromthisgure. First,themeasuredEVMvaluesarelessthantheidealEVM,asexpected.Second,themeas ured EVMdeviationfromitsidealvalueincreaseswiththemodulationorder.Thisi sduetothefact thatforhighermodulationorders,andforthesameSNRlevel,theprobabilityof asymbolerroris higher[89], P S =1 2 1 1 p M Q r 3 M 1 SNR !# 2 ; (7.8) where P S isthesymbolerrorrate(SER), M isthemodulationorder, Q ( v )=1 = 2erfc( v= p 2),and erfc( )isthecomplementaryerrorfunction.NotethattheaboveequationholdsforQAM signals butnotforBPSKsignals.Basedontheabove,themeasuredEVMfornondata-aidedrecei vers becomesdependentonthemodulationorderevenwiththenormalizationin(7.3).Mo reover,using themeasuredEVMasanindicationoftheSNRasin(7.6)canbemisleading,especi allyforlowSNR levels.Thus,thereisaneedforamoreaccurateEVMtoSNRrelationfornondata-a idedreceivers. 118

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-5 0 5 10 15 0 20 40 60 80 100 120 140 160 180 SNR (dB)EVM (%) Data-aided EVM (= 1/SNR 1/2 ) Nondata-aided EVM, BPSK Nondata-aided EVM, QPSK Nondata-aided EVM, 16QAM Nondata-aided EVM, 64QAM Figure7.1MeasuredversusidealEVMmeasurementsinnondata-aidedreceivers. 7.5EVM-SNRforNondata-AidedReceivers7.5.1DetectionOverAWGNChannels Considerthedetectedsignalin(7.2)where g ( n ) 1.Fornondata-aidedreceivers,theEVMis, EVM RMS = vuuuut 1 N N X n =1 j y ( n ) ^ x ( n ) j 2 P 0 : (7.9) Forlargevaluesof N ,thenumeratorin(7.9)canbeapproximatedas, 1 N N X n =1 j y ( n ) ^ x ( n ) j 2 E n j y ( n ) ^ x ( n ) j 2 o ; (7.10) where E f x g istheexpectedvalueof x .Forsimplicity,theindex n isdroppedfortheremainderof thischapter. 119

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WerststartbyconsideringBPSKsignals.Inthiscase, x and^ x arerealsignals.Thus,wecan rewrite(7.10)asfollows, E n j y ^ x j 2 o = E n ( y < ^ x ) 2 o + E 2 = ; (7.11) where y < = x + < ,andthesubscripts < and = representtherealandimaginarycomponentsofthe signal,respectively.Notethat < and = areuncorrelatedrandomprocessesthathaveaGaussian distributionwithzeromeanand 2 n variance.Thus, E 2 = = 2 n : (7.12) Toevaluate E f ( y < ^ x ) 2 g ,thestatisticalpropertiesof y < isexamined.SinceBPSKmodulation isconsidered,then x 2f a;a g ,where a isthesymbolamplitude.Thus,theconditionalprobability densityfunction(PDF)ofreceivedsignalis, f ( y < j x = S i )= 1 n y < S i n ; (7.13) where, ( v )= 1 p 2 exp v 2 2 (7.14) and ( )thePDFofastandardnormaldistribution.Basedonthecriterionin(7.7) ,theprobability of^ x = a is, P (^ x = a )= P ( x = a ) Z 1 0 f ( y < j x = a )d y < + P ( x = a ) Z 1 0 f ( y < j x = a )d y < : (7.15) Itisassumedthat, P ( x = a )= P ( x = a )= 1 2 : (7.16) Assuch,itcanbeshownthat, f ( y < j ^ x = a )= 1 C f ( y < j x = a )+ f ( y < j x = a ) ;y < > 0 ; (7.17) 120

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and f ( y < j ^ x = a )= 1 C f ( y < j x = a )+ f ( y < j x = a ) ;y < < 0 ; (7.18) where C isaconstantchosensuchthat, Z 1 1 f ( y < j ^ x = S i )d y < =1 : (7.19) Inthiscase, C =1.Using(7.17)and(7.18), E ( y < ^ x ) 2 = P (^ x = a ) Z 1 1 ( y < + a ) 2 f ( y < j ^ x = a )d y < + P (^ x = a ) Z 1 1 ( y < a ) 2 f ( y < j ^ x = a )d y < : (7.20) Sincethedecisionpoint( y < =0)isequallyspacedbetweenthetwopossiblevaluesof x andsince f ( y < j x = S i )issymmetricaround x ,then, P (^ x = a )= P (^ x = a )= 1 2 : (7.21) Since f ( y < j ^ x = a )= f ( y < j ^ x = a ),thenbyexchanging y < with y < inthesecondintegral in(7.20)andwithsomemanipulationitcanbeshownthat, Z 1 1 ( y < + a ) 2 f ( y < j ^ x = a )d y < = Z 1 1 ( y < a ) 2 f ( y < j ^ x = a )d y < : (7.22) Thus,using(7.21)and(7.22),(7.20)canbereducedto, E ( y < ^ x ) 2 = Z 1 1 ( y < a ) 2 f ( y < j ^ x = a )d y < : (7.23) From(7.18)and(7.13),theintegralin(7.23)canbeexpressedas, E ( y < ^ x ) 2 = 1 n Z 1 0 ( y < a ) 2 y < + a n d y < + 1 n Z 1 0 ( y < a ) 2 y < a n d y < ; = 1 n Z 1 a v 2 v +2 a n d v + 1 n Z 1 a v 2 v n d v; (7.24) 121

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where v = y < a .Thelasttwointegralsin(7.24)arerelatedto E f V 2 g where V isarandom variablethathasalow-truncatednormaldistribution[139].Tosolve(7. 24),wedeneanewfunction z ( A;; ),where, z ( A;; ) 1 Z 1 A v 2 v d v (7.25) ItisshowninAppendixCthat, z ( A;; )= ( A + ) A +( 2 + 2 ) Q A (7.26) Using(7.25),thesolutionto(7.24)is, E ( y < ^ x ) 2 = z ( a; 2 a; n )+ z ( a; 0 ; n ) = 3 a n a n +(4 a 2 + 2 n ) Q a n a n a n + 2 n Q a n : (7.27) Notethat ( v )= ( v )and Q ( v )+ Q ( v )=1.Assuch,(7.27)isreducedto, E ( y < ^ x ) 2 = 2 n 4 a n a n +4 a 2 Q a n (7.28) Then,substituting(7.28)and(7.12)into(7.11), E n j y ^ x j 2 o =2 2 n 4 a n a n +4 a 2 Q a n : (7.29) Withoutthelossofgenerality,weassumethattheaveragesymbolpower, P 0 =1(i.e. a =1). Therefore SNR= P 0 N 0 = 1 2 2 n : (7.30) TorelateEVMtoSNRfornondata-aidedreceiversandforBPSKsignaling,theresult sfrom(7.29), (7.30)aresubstitutedinto(7.9)asfollows, EVM BPSK = 1 SNR 4 p 2SNR p 2SNR +4 Q p 2SNR # 1 = 2 ; (7.31) 122

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ormoreconvenientlyusingtheexponentialanderrorfunctionsas, EVM BPSK = 1 SNR 2 p SNR exp( SNR)+2erfc p SNR # 1 = 2 : (7.32) Notethattherstsquare-rootedtermin(7.32)representstheidealEVMvalue.T hesecondand lasttermsrepresenttheerrorscausedbythesymbolestimationprocess.Forhi ghvaluesofSNR,the lasttwotermsconvergetozeroandtheEVMapproachesitsidealvalue.Thisisexpl ainedbythe factthatforhighSNRvalues,theprobabilityofsymbolerrorgoestozero.Thi sisalsoconrmed bythesimulationresultsinFig.7.1.Thevalidityof(7.32)isfurther investigatedinSection7.6. Next,weconsidersquareQAMsignals(i.e.withevennumberofbitspersymbols uchasQPSK, 16QAM,64QAM,etc).ForaQAMsignaloforder M ,themodulatedsymbolsare, x =(2 i k ) a + | (2 m k ) a;i;m =0 ; 1 ;:::;k (7.33) where k = p M 1.Inthiscase, E fj y ^ x j 2 g = E f ( y < ^ x < ) 2 g + E f ( y = ^ x = ) 2 g : (7.34) Duetotheindependenceandsymmetrybetweentherealandimaginarypartsofthesignal, E f ( y < ^ x < ) 2 g = E f ( y = ^ x = ) 2 g .Thus,itissucienttocalculateonlyoneoftheaboveexpectations.For non-squareQAMsignals,theaboveequalitydoesnothold.Itisshownlaterinthi ssectionhowto calculatetheexpectedEVMvalueinsuchcase. Inthefollowinganalysis,therealpartofthesignalisconsidered.Generalizing theexpression in(7.20), E f ( y < ^ x < ) 2 g canbeobtainedbyaveragingoverallpossiblevaluesof^ x < asfollows, E f ( y < ^ x < ) 2 g = k X i =0 P (^ x < = S i ) E f ( y < S i ) 2 j ^ x < = S i g = k X i =0 P (^ x < = S i ) Z 1 1 ( y < S i ) 2 f ( y < j ^ x < = S i )d y < ; (7.35) 123

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where S i =(2 i k ) a ,istherealvalueofthemodulationsymbol.Similarto(7.17),itbes hownthat foranyarbitraryvalueof i f ( y < j ^ x < = S i )= 1 C i 24 k X j =0 f ( y < j x < = S j ) 35 ;y < 2 D i = 1 C i 24 k X j =0 1 n y < S j n 35 ;y < 2 D i (7.36) where D i isthedecisionregionforsymbol S i suchthat, for i =0 ; 1
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From(7.38)and(7.40),itcanbeseenthat P (^ x < = S i )= C i = ( k +1).Thus,using(7.36),(7.38), and(7.40),theexpressionin(7.35)isreducedto, E f ( y < ^ x < ) 2 g = 1 k +1 k X i =0 k X j =0 Z D i 1 n ( y < S i ) 2 y < S j n d y < ; (7.41) Byusing v = y < S i E f ( y < ^ x < ) 2 g = 1 k +1 k X i =0 k X j =0 Z ~ D i v 2 n v ji n d v | {z } I ji (7.42) where ~ D i = D i S i and ji =2 a ( j i )= S j S i .Toevaluatetheintegralin(7.42) I ji ,weneed toconsidertwocases.Therstcaseisthesingly-truncateddecisionregions(i.e. i =0 ;k ),andthe secondcaseisthedoubly-truncateddecisionregions(i.e.1 i k 1).Duetothesymmetry aroundzero,thevaluesof I ji areequalfor i =0and i = k (orgenerallyforany i and k i ).Thus, I j 0 = I jk = 1 n Z 1 a v 2 v jk n d v = z ( a; jk ; n ) : (7.43) Fordoubly-truncatedregions, I ji = Z a a v 2 v ji n d v = z ( a; ji ; n ) z ( a; ji ; n ) ; 1 i k 1 : (7.44) Substituting(7.43)and(7.44)into(7.42), E f ( y < ^ x < ) 2 g = 1 k +1 0@ 2 k X j =0 z ( a; jk ; n )+ k 1 X i =1 k X j =0 h z ( a; ji ; n ) z ( a; ji ; n ) i 1A : (7.45) ItisshowninAppendixDthat(7.45)reducesto, E f ( y < ^ x < ) 2 g = 2 n 8 a n k X i =1 r i i a n +8 a 2 k X i =1 r i i Q i a n ; (7.46) 125

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where r i =1 i k +1 ; and i =2 i 1 : (7.47) Combining(7.30),(7.34),and(7.46),andexchanging and Q withtheexponentialanderror functions, E fj y ^ x j 2 g = 1 SNR 8 a p SNR k X i =1 r i exp( 2 i a 2 SNR)+8 a 2 k X i =1 r i i erfc i a p SNR : (7.48) ForanormalizedQAMsystem, a = s 3 2( M 1) : (7.49) From(7.9),(7.48),and(7.49),theEVMforQAMsignalsis EVM QAM = 1 SNR 8 s 3 2 ( M 1)SNR p M 1 X i =1 r i exp 3 2 i SNR 2( M 1) + 12 ( M 1) p M 1 X i =1 r i i erfc s 3 2 i SNR 2( M 1) !# 1 = 2 ; (7.50) where r i =1 i p M ; and i =2 i 1 : (7.51) Inviewoftheaboveresults,someremarksareinorder.First,simila rtotheEVMofaBPSKsignal in(7.32),theEVMofaQAMsignalin(7.50)canbedividedintotwoparts .Therstpartis1 = SNR, whichrepresentstheidealEVMwhennoerrorsareintroducedtothesymboldetection.T hesecond part,whichinQAMcaseisasumofexponentialanderrorfunctions,representsther eductionin measuredEVMduetodetectionerror.Theseconderrorpartisafunctionofboththemo dulation order M andtheSNRlevel,anditgoestozeroforhighvaluesofSNR.Notethatasthesumma tion index i in(7.50)increases,thevalueoftheexponentialanderrorfunctionsdecreasesrapidl y.Hence, forhighmodulationorder,anapproximationoftheEVMvaluecanbeobtained byconsideringonly therstfewtermsofthesummations. 126

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Second,theexpressionin(7.46)canbeusedtoevaluatetheEVMforQAMsystemswi thodd numberofbitspersymbol.Inthiscase,the E f ( y < ^ x < ) 2 g and E f ( y = ^ x = ) 2 g arenotequal. Using(7.46), E f ( y < ^ x < ) 2 g and E f ( y = ^ x = ) 2 g canbeevaluatedfor k = k 1 1and k = k 2 1, where M = k 1 k 2 ,and k 1 and k 2 representsthenumberofconstellationpointsontherealand imaginarypartsofthesignal,respectively.Finally,theEVMcanbeevalua tedbysubstitutingthe abovevaluesinto(7.34)andrepeatingasimilarprocesstotheonein(7.4 8)and(7.50). Third,notethattheEVMforanormalizedPAMsignalcanbeobtainedfrom(7.4 6)byadding 2 n ,setting k to M 1,and a to p 3 = ( M 2 1),suchthat EVM PAM = 1 SNR 4 s 3 ( M 2 1)SNR M 1 X i =1 r i exp 3 2 i SNR ( M 2 1) + 12 ( M 2 1) M 1 X i =1 r i i erfc s 3 2 i SNR ( M 2 1) !# 1 = 2 ; (7.52) where r i =1 i M ; and i =2 i 1 : (7.53) Forexample,bysetting M =2in(7.52),theEVMforBPSKsignalsin(7.29)canbeobtained. 7.5.2DetectionoverRayleighFadingChannels ForsignalsdetectedoverRayleighfadingchannels[89], y ( n )= exp( | ) x ( n )+ ( n ) ; (7.54) where and aretheattenuationandphaseshiftintroducedbythefadingchannel,and isa Rayleigh-distributedrandomvariable.Slowfadingisassumedsuchthatthechannelres ponseis constantoveratleastonesymbolinterval.Ifthechannelfadingissuciently slow,thephase shift canbeestimatedfromthereceivedsignalwithouterror.Inthiscase,itcanbes hownthat theinstantaneousSNRischi-square-distributed[89].ToevaluatetheaverageEV Mvalue,werst considertheinstantaneousEVMvalueforagiven .Inthefollowinganalysis,QAMsignalsare 127

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considered.Thus,from(7.50),theinstantaneousEVMis, EVM QAM ( )= 1 SNR 8 s 3 2 ( M 1)SNR p M 1 X i =1 r i exp 3 2 2 i SNR 2( M 1) + 12 2 ( M 1) p M 1 X i =1 r i i erfc s 3 2 2 i SNR 2( M 1) !# 1 = 2 ; (7.55) where r i and i areasin(7.51).ThePDFof is, f ( )=2 exp( 2 ) ; 0 : (7.56) TheexpectedvalueofEVMisevaluatedbyaveragingover EVM QAM = Z 1 0 EVM QAM ( ) f ( )d : (7.57) Theevaluationoftheintegralin(7.57)isskippedhereforbrevity.TheEV Misfoundtobe, EVM QAM = 1 SNR + 4 SNR 2 s 3 2( M 1) p M 1 X i =1 r i 3 2 i 2( M 1) + 1 SNR 3 = 2 + 12 ( M 1) p M 1 X i =1 r i i 1 s 3 2 i SNR 2( M 1)+3 2 i SNR 1+ ( M 1) 2( M 1)+3 2 i SNR !# 1 = 2 (7.58) 7.5.3DetectionwithOtherImpairments Intheprevioussection,theeectofRayleighfadingchannelsonthemeasuredEVMofrecei ved signalswasconsidered.Sinceitwasassumedthatthephaseshiftcausedbythechannelcanb e perfectlyestimatedfromthereceivedsignal,therewasnointerferencebetweentherea landimaginary partsofthesignal.Inthissection,weconsiderthecasewherethemultiplicative term, g ( n )in(7.2), canhaveacomplexvaluethatisunknowntothereceiver.Since g ( n )iscomplex-valued,therewill beinterferencebetweentherealandimaginarypartsofthesignal.Thiscasecanb eusedtomodel receivedsignalswithimpairmentssuchastheIQimbalance[124]orchannelesti mationerrors[114]. 128

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Thereceivedsignalcanberepresentedusingitsrealandimaginarypartsas 264 y < y = 375 = 264 g 11 g 12 g 21 g 22 375 264 x < x = 375 + 264 < = 375 ; (7.59) wheretheindex n isdroppedtosimplifythepresentation.Inthefollowing,QAMsignalsare considered.Assumethetransmittedsignalisasin(7.33).Inthiscase,andfo ragivenvalueof g theexpectedvalueoftherealandimaginarypartsofthedetectedsignalsare, E f y < j i;m g =(2 i k ) ag 11 +(2 m k ) ag 12 < ( i;m ) ; (7.60) E f y = j i;m g =(2 i k ) ag 21 +(2 m k ) ag 22 = ( i;m ) : (7.61) Ideally,thesignalshouldbedetectedsuchthat( g 11 = g 22 )and( g 12 = g 21 =0).Theprevioustwo equalitiesarelostiftheIQmodulatorissueringfromgainandphaseimbal ances,respectively.In thiscase,thereisinterferencebetweentherealandimaginarypartsof x inthedetectedsignal y Sinceitisassumedthat g isunknowntothereceiver,thedecisionregionsarethesameasin(7.37). FollowingthesameanalysispresentedinSection7.5.1,similarresultst o(7.45)areobtainedas follow, E f ( y < ^ x < ) 2 g = 1 M k X i =0 k X m =0 0@ 2 z ( a; ( R ) imk ; n )+ k 1 X j =1 h z ( a; ( R ) imj ; n ) z ( a; ( R ) imj ; n ) i 1A ; (7.62) E f ( y = ^ x = ) 2 g = 1 M k X i =0 k X m =0 0@ 2 z ( a; ( I ) imk ; n )+ k 1 X j =1 h z ( a; ( I ) imj ; n ) z ( a; ( I ) imj ; n ) i 1A ; (7.63) where ( R ) imj = < ( i;m ) (2 j k ) a; (7.64) ( I ) imj = = ( i;m ) (2 j k ) a: (7.65) Notethatinthiscase,thesymmetrybetweentherealandimaginarycomponentso fthedetected signal y islost.Thus,tomeasurethenalEVMvalue,expectationsofboththerealandi maginary partsofthesignalneedstobeconsidered.Thesymmetryisrestoredif j g 11 j = j g 22 j and j g 12 j = j g 21 j Inaddition,duetotheinterferencebetweentheIandQbranchesoftheIQmodulator,theex pected 129

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valueneedstobeaveragedoverallpossiblevaluesoftheQsignalinadditiont otheIsignal.Hence, ascomparedto(7.45),theexpressionsin(7.62)and(7.63)containanext rasummationover m Furthersimplicationof(7.62)and(7.63)isnotpossiblesince ( R ) imj and ( I ) imj havedistinctivevalues foreachsetof i m ,and j (unlike ij in(7.45)whosevaluesdependonlyonthedierence i j ). Finally,theaverageEVMcanbeevaluatedas, EVM QAM ( g )= E f ( y < ^ x < ) 2 g + E f ( y = ^ x = ) 2 g 1 = 2 : (7.66) While g isusuallyconsideredconstantsuchasinthecaseofIQimbalances,insomeotherca ses g canbemodeledasarandomprocess.Forexample,channelestimationerrorscanbemo deledas amultiplicativerandomvariablewithGaussiandistribution[114].In thiscase,theEVMexpected valuecanbeobtainedbyaveragingoverthePDFof g similarto(7.57). Toexaminethevalidityoftheresultspresentin(7.62)and(7.63),weconsi derthecasewhere theSNRissucientlyhighand g I suchthattheprobabilityofasymboldetectionerroriszero, where I istheidentitymatrix.Thisisequivalenttoassumingthatthetransmitted sequence x ( n )is knowntothereceiver.Inthiscase, z ( a; ( R ) imk ; n )= 8>><>>: h ( R ) kmk i 2 + 2 n ; for i = k 0 ; otherwise ; z ( a; ( R ) imj ; n ) z ( a; ( R ) imj ; n )= 8>><>>: h ( R ) jmj i 2 + 2 n ; for i = j 0 ; otherwise ; (7.67) Substituting(7.67)in(7.62)and(7.63),andassuminganormalizedQAMsig nal,theEVMisfound tobe, EVM QAM ( g )= r 1 SNR +1+ 1 2 ( g 2 11 + g 2 12 + g 2 21 + g 2 22 ) ( g 11 + g 22 ) : (7.68) Itisconventionaltoassume,withoutthelossofgenerality,thattheimpair mentsmatrix g isnormalizedsuchthat( g 2 11 + g 2 12 + g 2 21 + g 2 22 =2).Inthiscase, EVM QAM ( g )= r 1 SNR +2 Tr( g ) ; (7.69) 130

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-5 0 5 10 15 0 20 40 60 80 100 120 140 160 180 SNR (dB)EVM (%) Ideal EVM True EVM Measured EVM, BPSK Measured EVM, QPSK Measured EVM, 16QAM Measured EVM, 64QAM Figure7.2MeasuredversusidealandtrueEVMmeasurementsinnondata-aidedreceiverso ver AWGNchannels.whereTr( g )isthetraceofmatrix g .Theexpressionin(7.69)isidenticalto(27)in[140]withzero DCosets,whereitisassumedthattherearenodetectionerrors.7.6SimulationResultsandDiscussion Inthissection,thevalidityoftheEVM-SNRrelationsderivedinSection7.5isex aminedusing computersimulations.EVMvaluesaremeasuredforBPSK,QPSK,16QAMand64QAMmodula ted signalsandareaveragedover100 ; 000symbols.OverAWGNchannels,theEVMmeasurementsare comparedwiththeidealEVMbasedon(7.6)andwhatwedeneastrueEVMbasedon(7. 32), and(7.50).TheresultsareshowninFig.7.2.ThegureshowsthattrueEVM valuesalign perfectlywithmeasuredEVMvalues.SimilarresultsareobtainedoverRayleig hfadingchannels andareshowninFig.7.3,wheretrueEVMinthiscaseisbasedon(7.58). Next,signalscorruptedwithIQgainandphaseimbalancesandreceivedoverAWGNcha nnels areconsider.Forasystemwithgainimbalance t andphaseimbalance t ,thereceivedsignalis 131

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-5 0 5 10 15 0 20 40 60 80 100 120 140 160 180 SNR (dB)EVM (%) Ideal EVM True EVM Measured EVM, QPSK Measured EVM, 16QAM Measured EVM, 64QAM Figure7.3MeasuredversusidealandtrueEVMmeasurementsinnondata-aidedreceiverso ver Rayleighfadingchannels.modeledas[134,141], 264 y < y = 375 = s 2 1+ g 2 t 264 g t cos t 2 sin t 2 g t sin t 2 cos t 2 375 264 x < x = 375 + 264 < = 375 ; (7.70) where g t = t +1istheratiobetweentheIandQgainsintheIQmodulator[141].Thegain imbalanceindBiscalculatedas20log( g t ).Fig.7.4showsEVMmeasurementsfora16QAMsignal withaphaseimbalanceof2 andvaryinggainimbalance.ThemeasuredEVMiscomparedwith thetheoreticalidealandtrueEVMbasedon(7.69)and(7.66),respectively.At SNR=45dB,ideal andtrueEVMmatcheswithmeasuredEVM.AtSNR=10dB,detectionerrorsoccurandthe ideal EVMdeviatesfromtheactualmeasuredEVMbyaround5%fornondata-aidedsystems. Onthe otherhand,trueEVMmatchestomeasuredEVM,asdetectionerrorprobabilitywereta keninto consideration. TheanalysisdoneinSection7.5iseventuallymeanttobeusedtorelateEVMto SNR.EVMis readilyavailableinmostmeasurementdevices,aswellasarequirementformos twirelessstandards (e.g.IEEE802.11a-1999[6]andIEEE802.16e-2005[9]).Reliablyest imatingtheSNRfromthemea132

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0 0.5 1 1.5 2 2.5 3 0 5 10 15 20 25 30 35 40 Gain imbalance (dB)EVM (%) Ideal EVM True EVM Measured EVM SNR = 10 dB SNR = 45 dB Figure7.4MeasuredversusidealandtrueEVMmeasurementsinnondata-aidedreceiversw ithIQ impairmentsandAWGNnoise.suredEVMcanreducethesystemcomplexitybyeliminatingtheneedformodulesthatisreq uired toseparatelyestimatetheSNR.Usually,theestimatedSNRvaluesarequanti zedwithapredened value.Forexample,theIEEE802.16e-2005standardstatesthatthecarrier-to -interference-plusnoiseratio(CINR)shouldbequantizedin1dBincrementsrangingfromaminim umof 20dBtoa maximumof40dB.Ingeneratedsimulations,thequantizationlevelissetto0 : 1dBformoreaccurate results.TwosetsoflookuptablesaregeneratedthatrelatesthemeasuredEVMto theSNRbased onidealEVMandtrueEVM.BothSNRestimatorsarecomparedtothemaximuml ikelihood(ML) SNRestimator,wheretheML-estimatedSNRiscomputedas[142], [ SNR ML = 1 N N X n =1 ( y < ( n )^ x < ( n )+ y = ( n )^ x = ( n )) # 2 1 N N X n =1 j y ( n ) j 2 1 N N X n =1 ( y < ( n )^ x < ( n )+ y = ( n )^ x = ( n )) # 2 : (7.71) Theeectofnumberofsamples N ontheSNRestimationisinvestigatedforQPSKsignals.Thenormalizedmean-squared-error(MSE) E Norm oftheSNRestimationsisevaluatedforallthreemethods 133

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-5 0 5 10 15 10 -4 10 -3 10 -2 10 -1 10 0 10 1 SNR (dB)Normalized MSE ML estimator Ideal-EVM-based estimator True-EVM-based estimator N = 100 N = 10,000 N = 1,000 Figure7.5NormalizedMSEofSNRestimatorsfordierentvaluesof N overAWGNchannelsandtheresultsareshowninFig.7.5,where[142] E Norm ( [ SNR)= E [ SNR SNR 2 SNR 2 : (7.72) Ingeneral,itisexpectedthattheperformancewouldimproveforlarger N .Duetodetection errors,bothMLestimatorandideal-EVM-basedestimatorperformpoorly atlowSNRvalues, independentof N .AstheSNRincreases,theperformancesshowimprovementforlarger N .Note thatforsucientlyhighSNRvalues,performancesofallestimatorsarealm ostequalasthereare nodetectionerrors.Consideringtrue-EVM-basedestimator,theperformanceisalw aysbetterfor larger N regardlessoftheSNRlevel.Inaddition,theperformanceisalmostindependentofthe SNRvalue. Theperformanceofthetrue-EVM-basedSNRestimatorisfurtherinvestigatedbyco nsidering variousimpairmentstoreceivedsignal.Fig.7.6showsthenondata-aidedSNRest imatorperformance forsignalscorruptedbyAWGN,signalsreceivedoverRayleighfadingchannels,a ndsignalswith IQimbalances(2 phaseimbalanceand1dBgainimbalance).Forreference,theperformanceof ideal-EVM-basedSNRestimatorisprovidedunderbestcasescenariowheretheestimatio nisdone 134

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-5 0 5 10 15 10 -4 10 -3 10 -2 10 -1 10 0 SNR (dB)Normalized MSE True EVM, nondata aided, IQ imbalance True EVM, nondata aided, AWGN True EVM, nondata aided, Rayleigh Ideal EVM, data aided, AWGN N = 100 N = 1,000 N = 10,000 Figure7.6NormalizedMSEoftrue-EVM-basedSNRestimatorunderdierentimpairmen tsand fordierentvaluesof N overknowndatasequences(data-aided)andthereceivedsignalisonlycorruptedbyAWGN.T he gureshowsthattheperformanceofthetrue-EVM-basedestimatorisconsistentunderv arious impairments.Thedeviationfromthebestcaseperformanceislowandindependento f N .This showsthatevenforsystemswithpilotsorpreamblesavailabletothereceiver, measuringtheEVM overdatasymbolsaswellaspilotscanproducebetterSNRestimation.Thisises peciallytrue consideringthatpilotsymbolsareusuallymuchlessthandatasymbolsinmo stpracticalsystems. NotethattheperformanceshowninFig.7.6isobtainedundertheassumptionthat impairments tothesignal(e.g. and g )areknown.Inpracticalsystems,suchimpairmentsareestimatedeither usingpreamblesandpilots,orblindlybyusingdatasymbols.Theestimationand equalization processisusuallynotperfect.Thus,theestimationerroreectonthesystemperf ormanceis considered.ForasignalreceivedoverRayleighfadingchannel,thechannelestimationo utputcan berepresentedas, ^ = + ; (7.73) 135

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-2 0 2 4 6 8 10 12 14 16 10 -4 10 -3 10 -2 10 -1 10 0 SNR (dB)Normalized MSE N = 100 N = 1,000 N = 10,000 True EVM, nondata aided, e = 10% Ideal EVM, data aided, e = 10% True EVM, nondata aided, e = 1% Ideal EVM, data aided, e = 1% True EVM, nondata aided, e = 0.1% Ideal EVM, data aided, e = 0.1% Figure7.7NormalizedMSEofideal-EVMdata-aidedandtrue-EVMnondata-aidedSNResti mators underdierentchannelestimationerrorlevelsandfordierentvaluesof N where istheadditiveestimationerror.Thechannelestimationerror isismodeledasarandom variablethathasaGaussiandistribution[140]withzeromean(unbiasedest imator)andvariance 2 est .SincetheestimatorperformanceisaectbytheAWGNinthesignal[108],the estimationerror varianceisconsideredasapercentageofthenoisevariance 2 n suchthat, 2 est = 2 n .Inthissense, onecouldconsider tobeameasureofthechannelestimatorquality,whereabetterestimatorwoul d havealower .TheperformanceoftheidealEVMdata-aidedandtrueEVMnondata-aidedSNR estimatorsisconsideredinthiscaseundervariousvaluesof .TheresultsareshowninFig.7.7. TheerrorinSNRestimationcanbeattributedtobothchannelestimationerro rsandthenoise averaging(i.e.thenumberofsymbolsusedforestimation, N ).At N =100,theMSEduetonoise averagingisdominantandtheperformancesofbothdata-aidedandnondata-aidedesti matorsare notaectbythechannelestimatorquality(or ).As N increasesto1 ; 000and10 ; 000,thechannel estimatorqualitystartstoaecttheperformanceoftheSNRestimator.I nallcases,itisshownthat forthesame N and thedierencebetweenthedata-aidedandnondata-aidedSNRestimatorsis almostconstant.Thisimpliesthatthegainachievedbyusingthetrue-EVM-basedSN Restimator isconsistentregardlessofestimationerrors. 136

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7.7Conclusion Inthischapter,measuredEVMisrelatedtoSNRfornondata-aidedreceivers,calledtr ueEVM. TrueEVMisrelatedtotheSNRforQAMandPAMsignals.TheEVM-SNRrelationi sevaluated forsignalsdetectedoverAWGNchannels,andRayleighfadingchannels;andforsigna lswithIQ impairments.Thederivedexpressionsareveriedusingcomputersimulations.Thepres entedresults showthatwhenconsideringnondata-aidedreceivers,usingEVM-SNRrelationsderivedfordat aaidedreceivers(orassuminghighSNR)resultsinpoorSNRestimationespeciall yforhighmodulation ordersorlowSNRvalues.Ontheotherhand,usingproposedtrueEVMexpressionsresults in accurateSNRestimationindependentofmodulationorderandSNRvalue. 137

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CHAPTER8 CONCLUSIONANDFUTUREWORK Inthisdissertation,weconsideredthetransceiverdesignfororthogonalfrequencydi visionmultiplexing(OFDM)andorthogonalfrequencydivisionmultipleaccess(OFDMA)advanced systems. InChapter2,weintroducedOFDMtechnologyanddiscusseditsadvantagesanddisadva ntages whenappliedtofuturewirelesssystems.Fortheremainderofthedissertation,we focusedonsome oftheimportantchallengesthatfaceOFDM-basedsystems.Practicalimplement ationaspectssuch ascomputationalcomplexity,powerconsumption,biterrorrate(BER),andadja centchannelinterference(ACI)areconsidered.Partsoftheworkpresentedinthisdissertationhav ebeenaccepted forpublication[20{27]andhasbeenrecognizedbythewirelessresearchcommunityt hroughcitations[143{150].Thestudywepresentedin[22]hasbeenthesecondmostaccesseddocum entonthe IEEEXplore R r [151]forthemonthofJune,2008.Someofthespeciccontributionspresentedin thisdissertationarelistedbelow.8.1Contributions SynchronizationinOFDMAUplinkSystemsAnovelalgorithmforOFDMAinitialrangingprocessbasedontheIEEE802.16 e-2005standardispresentedinChapter3.Theproposedalgorithmperformsmultiusercodedetect ion andtimingosetestimationforrangingusers.Itwasshownthatthepropos edalgorithm reducesthecomputationalcomplexityby80%to96%dependingonthenumberofuserswhilemaintainingthestandarddeviationofthetimingerrorunder5%oftheguardint erval.Simulationresultsshowedthattheproposedalgorithmcanperformwellwithashig has10usersper rangingchannelinagivenuplink(UL)frame.Hence,theproposedalgorithmcanbehig hly desirableforpracticalOFDMA-basedbasestations(BS). 138

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SpectrumShapingforOFDMSystemsWeproposedanewmethod,calledadaptivesymboltransition(AST),tosuppressOF DM sidelobesadaptivelyandallowthesystemtoshapethetransmittedsignalsp ectrum.The proposedASTmethodextendsOFDMsymbolsandusestheextensiontoreduceACItootherusersoperatinginthesameband.SimulationresultsshowthatASTcanachieveasi gnicant gainoverconventionalsidelobesuppressiontechniqueswhilemaintaininglowi ncreaseinsymbolenergy.Moreover,ASTdoesnotincreasethesignalpeak-to-average-powerratio (PAPR) andtheperformanceisnotsensitivetoothersystemparameterssuchasthecyclic prex(CP) size. OFDMAPerformanceunderChannelEstimationErrorsWederivedtheBERexpressionsforOFDMsignalsreceivedovertime-varyingfrequency-selectivechannelswithchannelestimationerrors.Theresultswereusedtoobtain theoptimum tiledimensions(oroptimumpilotinsertionrate)inthetime-frequencygrid.Bot hanalytical andsimulatedresultsshowthatcarefulchoiceofthetiledimensionscansignicant lyincrease thesystemthroughput. OFDMAChannelEstimationwithIQImbalancesWhenconsideringtheULsignalinOFDMA-basedzero-IFsystems,imperfectionsoftheI Qmodulatorscausesmultiuserinterference(MUI).Wedesignedatwo-dimensionalortho gonal pilotpatterntobeusedforchannelestimationandequalizationinthiscase.Tw olowcomplexitymethodsareproposedtoequalizeanddetectIQdistortedsignalsusingdesigned pilot pattern.Proposedmethodswereshowntoimprovethesystemperformancesignica ntlyover conventionaldetectionmethodsforsignalssueringfrommultipleuserIQdistor tions. EVM-basedSNREstimationinBlindReceiversWederivedtheerrorvectormagnitude(EVM)tosignal-to-noiseratio(SNR)rel ationsfor signalsdetectedoveradditivewhiteGaussiannoise(AWGN)channels,andRaylei ghfading channels;andforsignalswithIQimpairments.Thepresentedresultsshowthatw henconsideringblindreceivers,usingEVM-SNRrelationsderivedfordata-aidedreceivers(orass uming highSNR)resultsinpoorSNRestimationespeciallyforhighmodulationor dersorlowSNR values.Ontheotherhand,usingproposedtrueEVMexpressionsresultsinaccurateSNRestimationindependentofmodulationorderandSNRvalue. 139

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8.2FinalRemarksandFutureWork OFDMsystemoersanumberofadvantagesforhighdataratewirelesssystem s,butsuersfrom somedrawbacks.Throughoutthedissertation,wetriedtoaddresssomeofthei mportantchallenges thatfaceOFDMimplementationinpracticalwirelesssystems.Meanwhile,there wereotherresearch topicsthatwefeelarecloselyrelatedtoourworkandcanbeapossibleextensio ntothestudies presentedinthisdissertation.Adiscussionofthesetopicsispresentedinthissect ion. NoncoherentDetectioninOFDMAUplinkSystemsForOFDMAsystemtomaintainorthogonalityandreducemultiuserinterference( MUI),synchronizationbetweenusersshouldbemaintained.TheapproachweproposedinChapt er3can beusedinprimarynetworks,wherethebasestation(BS)canmandatethetransm issiontime ofeachuser.However,forsecondarynetworks,suchasfemtocell,userscannotbesy nchronized priortotransmission.Inthatcase,thereisaneedforanalgorithmtodetectrecei vedsignal underMUIeectsthroughinterferencedetectionandcancellationmethods.Assuch,thede-signandimplementationofOFDMAsystemsinfemtocellrepresentsaninterest ingresearch topic. Low-ComplexitySpectrumShapingforOFDMSystemsThemethodweproposedinChapter4,aswellasmostothersidelobesuppressiontec hniques proposedintheliterature,suerfromhighcomputationalcomplexity.However, spectrum shapingincognitiveradio(CR)systemsneedstobeperformedonlinewithminim umdelayas totakeadvantageofavailablespectrumopportunities.Thus,thereisaneedf oranecient yetlow-complexitymethodsforOFDMspectrumshaping.Wearecurrentlyworkingon suboptimaladaptivesymboltransition(AST)algorithmthatcanshapethes pectrumofOFDM signalswithreducedcomputationalcomplexity. OFDMACapacityunderVariousImpairmentsWeevaluatedtheperformanceofOFDMAsystemsoverwirelessselectivechannelsand under channelestimationerrorsaswellasIQimbalancesinChapters5and6.Therearet hree directionsinwhichthisworkcanbeextended.First,theperformanceofOFDMAsys tems canbeexaminedunderanumberofotherpracticalimpairmentssuchastimingandfrequencyosetsorsamplingclockerrors. 140

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Second,sincetilesintheOFDMAuplinkbelongtomultipleusers,weassumedthereceivercarriesouttheestimationandequalizationonatile-by-tilebasis.Aposs ibleimprovementto thechannelestimationcanbeattainedifthesystemhastheabilitytodetectanduse pilots thatbelongtothesameuserbutoverdierenttiles.Toachievethisgoalthesyst emneedsto havepriorknowledge,tosomeextend,oftheuserchannelcorrelationovertimeandfr equency. Third,theoptimumtiledimensionsintroducedinChapter5wereobtainedforharddecisi on receiversusingchannelcapacityandupperboundsonconvolutionalcodes.Thisworkcanbeextendedtoobtaintheoptimumtiledimensionsforsoftdecisionreceivers.Inthi scase, weneedtoderivetheprobabilitydistributionsofreceivedsignalasfunctionofthew ireless selectivechannelandthechannelestimationerrorsforagivensystemmodel. 141

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[99]P.Hoeher,S.Kaiser,andP.Robertson,\Two-dimensionalpilot-symbol-ai dedchannelestimationbyWienerltering," Proc.IEEEInt.Conf.onAcoust.,Speech,andSignalProcess (ICASSP) ,vol.3,pp.1845{1848,Apr.1997. [100]P.TanandN.C.Beaulieu,\Eectofchannelestimationerroronbiterror probabilityin OFDMsystemsoverrayleighandriceanfadingchannels," IEEETrans.Commun. ,vol.56, no.4,pp.675{685,Apr.2008. [101]Y.Li,L.J.Cimini,andN.R.Sollenberger,\Robustchannelestimatio nforOFDMsystems withrapiddispersivefadingchannels," IEEETrans.Commun. ,vol.46,no.7,pp.902{915, Jul.1998. [102]W.C.Jakes, Microwavemobilecommunications .Wiley,NewYork,1974. [103]Y.-S.Choi,P.J.Voltz,andF.A.Cassara,\Onchannelestimationand detectionformulticarriersignalsinfastandselectiverayleighfadingchannels," IEEETrans.Commun. ,vol.49, no.8,pp.1375{1387,Aug.2001. [104]M.RussellandG.L.Stuber,\InterchannelinterferenceanalysisofOFDMin amobileenvironment,"in Proc.IEEEVeh.Technol.Conf.(VTC) ,vol.2,Jul.1995,pp.820{824. [105]Y.LiandL.J.Cimini,\BoundsontheinterchannelinterferenceofOFDMint ime-varying impairments," IEEETrans.Commun. ,vol.49,no.3,pp.401{404,Mar.2001. [106]X.Tang,M.-S.Alouini,andA.J.Goldsmith,\Eectofchannelestimatio nerroronM-QAM BERperformanceinRayleighfading," IEEETrans.Commun. ,vol.47,no.12,pp.1856{1864, Dec.1999. [107]I.Gaspard,\ImpactofthechannelestimationontotheBER-performance ofPSAM-OFDM systemsinmobileradiochannels,"in Proc.IEEEVeh.Technol.Conf.(VTC) ,vol.1,May 2001,pp.673{677. [108]H.CheonandD.Hong,\EectofchannelestimationerrorinOFDM-basedWLA N," IEEE Commun.Lett. ,vol.6,no.5,pp.190{192,2002. [109]M.-X.ChangandY.T.Su,\PerformanceanalysisofequalizedOFDMsystems inRayleigh fading," IEEETrans.WirelessCommun. ,vol.1,no.4,pp.721{732,Oct.2002. [110]J.Chen,Y.Tang,S.Li,andY.Li,\Eectofchannelestimationerroront otheBERperformanceofPSAM-OFDMinRayleighfading,"in Proc.IEEEVeh.Technol.Conf.(VTC) vol.4,Oct.2003,pp.2444{2448. [111]L.CaoandN.C.Beaulieu,\Exacterror-rateanalysisofdiversity1 6-QAMwithchannel estimationerror," IEEETrans.Commun. ,vol.52,no.6,pp.1019{1029,Jun.2004. [112]M.Al-GharaballyandP.Das,\OntheperformanceofOFDMsystemsint imevaryingchannels withchannelestimationerror," Proc.IEEEInt.Conf.Commun.(ICC) ,vol.11,pp.5180{5185, Jun.2006. [113]P.O.BorjessonandC.-E.W.Sundberg,\Simpleapproximationsoftheerro rfunction Q ( x ) forcommunicationsapplications," IEEETrans.Commun. ,vol.27,no.3,pp.639{643,Mar. 1979. [114]M.M.Wang,W.Xiao,andT.Brown,\Softdecisionmetricgenerationf orQAMwithchannel estimationerror," IEEETrans.Commun. ,vol.50,no.7,pp.1058{1061,2002. 148

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[115]W.Xiao,\OptimaldetectionofM-QAMsignalwithchannelestimationerr or," Proc.IEEE Int.Conf.Commun.(ICC) ,vol.5,pp.3251{3255,May2003. [116]C.E.Shannon,\Amathematicaltheoryofcommunication," BellSyst.Tech.J. ,vol.27,no.3, pp.379{423,Jul.1948. [117]K.Larsen,\Shortconvolutionalcodeswithmaximalfreedistanceforra tes1/2,1/3,and1/4," IEEETrans.Inf.Theory ,vol.19,no.3,pp.371{372,May1973. [118]P.Frenger,P.Orten,andT.Ottosson,\Convolutionalcodeswithoptimum distancespectrum," IEEECommun.Lett. ,vol.3,no.11,pp.317{319,Nov.1999. [119]A.R.WrightandP.A.Naylor,\I/Qmismatchcompensationin zero-IFOFDMreceivers withapplicationtoDAB,"in Proc.IEEEInt.Conf.onAcoust.,Speech,andSignalProcess (ICASSP) ,vol.2,2003. [120]A.TarighatandA.H.Sayed,\OnthebasebandcompensationofIQimbalancesi nOFDM systems,"in Proc.IEEEInt.Conf.onAcoust.,Speech,andSignalProcess .(ICASSP) ,vol.4, 2004. [121]J.Tubbax,B.Come,L.VanderPerre,L.Deneire,S.Donnay,andM.Engels,\Co mpensation ofIQimbalanceinOFDMsystems,"in Proc.IEEEInt.Conf.Commun.(ICC) ,vol.5,2003. [122]H.ShaeeandS.Fouladifard,\CalibrationofIQimbalanceinOFDMtrans ceivers,"in Proc. IEEEInt.Conf.Commun.(ICC) ,vol.3,2003. [123]J.LinandE.Tsui,\Jointadaptivetransmitter/receiverIQimbala ncecorrectionforOFDM systems,"in Proc.IEEEInt.Sym.onPers.,IndoorandMobileRadioCommun .(PIMRC) vol.2,2004. [124]A.TarighatandA.H.Sayed,\OFDMsystemswithbothtransmittera ndreceiverIQimbalances,"in Proc.IEEEWorkshoponSignalProcess.Adv.inWirelessComm un.(SPAWC) 2005,pp.735{739. [125]T.C.W.Schenk,P.F.M.Smulders,andE.R.Fledderus,\Estimationandcom pensationof TxandRxIQimbalanceinOFDM-basedMIMOsystems,"in Proc.IEEERadioandWireless Sym.(RWS) ,2006,pp.215{218. [126]M.Valkama,Y.Zou,andM.Renfors,\OnI/QimbalanceeectsinMIMOs pace-timecoded transmissionsystems,"in Proc.IEEERadioandWirelessSym.(RWS) ,2006,pp.223{226. [127]Y.Jin,J.Kwon,Y.Lee,D.Lee,andJ.Ahn,\ObtaineddiversitygaininOFDMs ystems undertheinruenceofIQimbalance," IEICETrans.onCommun. ,vol.91,no.3,p.814,2008. [128]L.Giugno,V.Lottici,andM.Luise,\Low-complexitygainandphaseI/ Qmismatchcompensationusingorthogonalpilotsequences,"in EuropeanSignalProcess.Conf.(EUSIPCO) ,Sep. 2006. [129]R.ChrabiehandS.Soliman,\IQimbalancemitigationviaunbiasedtra iningsequences,"in Proc.IEEEGlobalTelecommun.Conf.(GLOBECOM) ,Nov.2007,pp.4280{4285. [130]A.HaiderandA.Chatterjee,\Low-costalternateEVMtestforwireless receiversystems,"in Proc.IEEEVLSITestSym. ,May2005,pp.255{260. [131]R.Hassun,M.Flaherty,R.Matreci,andM.Taylor,\Eectiveevalua tionoflinkqualityusing errorvectormagnitudetechniques,"in Proc.IEEEWirelessCommun.Conf. ,Aug.1997,pp. 89{94. 149

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[132]T.NakagawaandK.Araki,\EectofphasenoiseonRFcommunications ignals,"in Proc. IEEEVeh.Technol.Conf.(VTC) ,vol.2,Sep.2000. [133]M.Helfenstein,E.Baykal,K.Muller,A.Lampe,P.Semicond,andS.Zurich,\ Errorvector magnitude(EVM)measurementsforGSM/EDGEapplicationsrevisedunderproductioncon-ditions,"in Proc.IEEEInt.Sym.onCircuitsandSyst.(ISCAS) ,May2005,pp.5003{5006. [134]A.Georgiadis,\Gain,phaseimbalance,andphasenoiseeectsonerrorvecto rmagnitude," IEEETrans.Veh.Technol. ,vol.53,no.2,pp.443{449,2004. [135]K.M.Gharaibeh,K.G.Gard,andM.B.Steer,\AccurateEstimationofDi gitalCommunicationSystemMetrics{SNR,EVMand inaNonlinearAmplierEnvironment," IEEETrans. Commun. ,pp.734{739,Sep.2005. [136]R.A.Shak,M.S.Rahman,A.R.Islam,andN.S.Ashraf,\OntheErrorV ectorMagnitude asaPerformanceMetricandComparativeAnalysis," InternationalConferenceonEmerging Technologies(ICET) ,pp.27{31,2006. [137]S.Forestier,P.Bouysse,R.Quere,A.Mallet,J.M.Nebus,andL.Lapierre, \JointOptimizationofthePower-AddedEciencyandtheError-VectorMeasurementof20-GHzpHEMTAm plierThroughaNewDynamicBias-ControlMethod," IEEETrans.Microw.TheoryTech. vol.52,no.4,pp.1132{1141,2004. [138]F.L.LinandH.R.Chuang,\EVMandBERSimulationofanNADC-TDM ARadiophone InruencedbytheOperator'sBodyinUrbanMobileEnvironments," WirelessPersonalCommunications ,vol.17,no.1,pp.135{147,2001. [139]N.L.JohnsonandS.Kotz, Distributionsinstatistics:Continuousunivariatedistr ibutions JohnWiley&Sons,1970,vol.1. [140]M.Al-GharaballyandP.Das,\OntheperformanceofOFDMsystemsint imevaryingchannels withchannelestimationerror,"in Proc.IEEEInt.Conf.Commun.(ICC) ,vol.11,Jun.2006, pp.5180{5185. [141]J.K.CaversandM.W.Liao,\Adaptivecompensationforimbalanceand osetlossesindirect conversiontransceivers," IEEETrans.Veh.Technol. ,vol.42,no.4,pp.581{588,Nov.1993. [142]D.R.PauluzziandN.C.Beaulieu,\AcomparisonofSNRestimationtechniq uesforthe AWGNchannel," IEEETrans.Commun. ,vol.48,no.10,pp.1681{1691,Oct2000. [143]S.SoundararajanandP.Agrawal,\AschedulingalgorithmforIEEE80 2.16andIEEE802.11 hybridnetworks,"in Proc.IEEEInt.Conf.BroadbandCommun.,Netw.andSys.(BRO ADNETS) ,2007,pp.320{322. [144]D.H.LeeandH.Morikawa,\Non-synchronizedrandomaccessprocessofsingl ecarrierFDMA system,"in TechnicalreportofIEICERadioCommun.Sys.(RCS) ,vol.107,no.147,2007, pp.137{142. [145]||,\AnalysisonrandomaccessprocessofsinglecarrierFDMAsystem,"i n Proc.ICSTInt. Conf.onWirelessInternet(WICON) ,2007,pp.1{9. [146]J.ZengandH.Minn,\AnovelOFDMArangingmethodexploitingmultiuserdivers ity,"in Proc.IEEEGlobalTelecommun.Conf.(GLOBECOM) ,Nov.2007,pp.1498{1502. [147]||,\DiversityexploitingMIMO-OFDMAranging,"in Proc.IEEEInt.Conf.Information, Commun.andSignalProcess.(ICICS) ,Dec.2007,pp.1{5. 150

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[148]||,\AninvestigationintoinitialrangingmethodformobileOFDM Asystems,"in Proc. IEEESarnoSymposium ,Apr.2008,pp.1{5. [149]L.Sanguinetti,M.Morelli,andH.V.Poor,\AnESPRIT-basedapproach forinitialranging inOFDMAsystems,"in Proc.IEEEWorkshoponSignalProcess.Adv.inWirelessComm un. (SPAWC) ,Jul.2008. [150]G.Bansal,M.J.Hossain,andV.K.Bhargava,\Optimalandsuboptim alpowerallocation schemesforOFDM-basedcognitiveradiosystems," IEEETrans.WirelessCommun. ,vol.7, no.11,pp.4710{4718,Nov.2008. [151]http://ieeexplore.ieee.org. 151

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APPENDICES 152

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AppendixA From(3.7),theexpectedvalueof E g is, E [ E g ]= E L + L 1 X n =0 W 2 < ( m )+ L 1 X n =0 W 2 = ( m )+2 L 1 X n =0 c ( k ) p ( m )cos[ m ( k )] W < ( m ) +2 L 1 X n =0 c ( k ) p ( m )sin[ m ( k )] W = ( m ) : (A.1) Notethat, E h c ( k ) p ( m ) i =0 ; (A.2) and, E [ W < ( m )]= E [ W = ( m )]=0 : (A.3) Since m valuesarerandomlychosenbetween0and N t 1, m ( k )canbeapproximatedasa uniformly-distributedrandomvariablebetween and .Thus, E [cos[ m ( k )]]= E [sin[ m ( k )]]=0 : (A.4) Thereforetheexpectedvalueofthelasttwotermsin(A.1)goestozeroforlar gevaluesof L Then, E [ E g ]= L + E L 1 X n =0 W 2 < ( m ) # + E L 1 X n =0 W 2 = ( m ) # = L + LN 0 : (A.5) Next,wecalculate E E 2 g from(3.7).Notethat, E 24 L 1 X n =0 W 2 < ( m ) 2 35 = 1 2 LN 2 0 + 1 4 L 2 N 2 0 ; (A.6) 153

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AppendixA(Continued) E 24 2 L 1 X n =0 c ( k ) p ( m )cos[ m ( k )] W < ( m ) 2 35 = LN 0 ; (A.7) E L 1 X n =0 W 2 < ( m ) L 1 X n =0 W 2 = ( m ) !# = 1 2 L 2 N 2 0 : (A.8) Then, E E 2 g = L 2 + LN 2 0 + L 2 N 2 0 +2 LN 0 +2 L 2 N 0 : (A.9) 154

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AppendixB From(3.10), E r ( u )= L 1 X n =0 ( K 1 X k =0 c ( k ) p ( m )cos[ m ( k u )] ) 2 + L 1 X n =0 ^ W 2 < ( m ) + L 1 X n =0 2 ^ W < ( m ) K 1 X k =0 c ( k ) p ( m )cos[ m ( k u )] # = L 1 X n =0 K 1 X k =0 cos 2 [ m ( k u )] + L 1 X n =0 K 1 X k =0 K 1 X v =0 v 6 = k ( c ( k ) p ( m ) c ( v ) p ( m )cos[ m ( k u )]cos[ m ( v u )] ) + L 1 X n =0 ^ W 2 < ( m )+ L 1 X n =0 ( 2 ^ W < ( m )cos[ m ( u )] K 1 X k =0 c ( k ) p ( m )cos[ m ( k u )] ) : (B.1) Theexpectedvalueofthesecondandlasttermsin(B.1)iszero.Therefore, E [ E r ( u )]= E L 1 X n =0 K 1 X k =0 cos 2 [ m ( k u )] # + E L 1 X n =0 ^ W 2 < ( m ) # : (B.2) E [ E r ( u )]= 8>>>>>>>>>><>>>>>>>>>>: 1 2 LK + 1 2 L + 1 2 LN 0 ,for u = k for onlyonevalueof k: 1 2 LK + 1 2 LN 0 ,for u 6 = k for allvaluesof k: (B.3) Theassumptionthat u = k foronlyonevalueof k impliesthatinthesamesymbolandforagive timingoset u ,onlyonecodeexist. 155

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AppendixC Theprobabilitydensityfunction(PDF)ofarandomvariable V thathasadoubly-truncated normaldistributionis[139], f ( v )= 1 v B A ;A V B; (C.1) where and 2 arethemeanandvarianceoftheuntruncatedrandomvariable,respectively,and ( v )=1 Q ( v )isthecumulativedistributionfunction(CDF)ofthestandardnormaldistri bution. Themean v ,andvariance 2 v of V are[139], v = + A B B A ; (C.2) and, 2 v = 2 + A A B B B A 2 2664 A B B A 3775 2 2 : (C.3) Forarandomvariablethathaslower-truncatednormaldistribution, B !1 .Inthiscase, ( 1 )=0 and( 1 )=1.Since 2 v = E f V 2 g 2v ,then,using(C.2)and(C.3),itcanbeshownthatif V has lower-truncatednormaldistribution, E f V 2 g = 2 v + 2v = ( A + ) A Q A + 2 + 2 : (C.4) 156

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AppendixC(Continued)Notethatfrom(C.1)andas B !1 E f V 2 g = 1 Q A Z 1 A v 2 v d v: (C.5) Wedeneanewfunction z ( A;; ),where z ( A;; )= 1 Z 1 A v 2 v d v: (C.6) From(C.5),thesolutionto(C.6)is, z ( A;; )= E f V 2 g Q A = ( A + ) A +( 2 + 2 ) Q A (C.7) 157

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AppendixD From(C.7),andsince ( v )= ( v )and Q ( v )+ Q ( v )=1,thefollowingpropertiesofthe z -functioncanbeinferred, z ( A;; )+ z ( A; ; )= 2 + 2 ; (D.1) andfrom(D.1), z ( A;; ) z ( A;; )= z ( A; ; ) z ( A; ; ) : (D.2) From(7.45),intherstsummation, jk canbesubstitutedwith i ,for i;j =0 ;:::;k ,where i =2 ai .Inthesecondsummation,thedoublesummationcanbereducedtoonesummationby substituting ji ,for i =1 ;:::;k 1and j =0 ;:::;k with i ,for i = k +1 ;:::;k 1.The expressionin(7.45)canthenberewrittenas, E f ( y < ^ x < ) 2 g = 1 k +1 2 k X i =0 z ( a; i ; n )+ 1 X i = k +1 ( k + i ) h z ( a; i ; n ) z ( a; i ; n ) i +( k 1) h z ( a; 0 ; n ) z ( a; 0 ; n ) i + k 1 X i =1 ( k i ) h z ( a; i ; n ) z ( a; i ; n ) i = 1 k +1 ( k 1) h z ( a; 0 ; n ) z ( a; 0 ; n ) i +2 k X i =0 z ( a; i ; n ) +2 k 1 X i =1 ( k i ) h z ( a; i ; n ) z ( a; i ; n ) i : (D.3) Byusingthepropertyin(D.2)onthelastsummationin(D.3), E f ( y < ^ x < ) 2 g = 1 k +1 ( k 1) h z ( a; 0 ; n ) z ( a; 0 ; n ) i +2 k X i =0 z ( a; i ; n ) +2 k 1 X i =1 ( k i ) h z ( a; i ; n ) z ( a; i ; n ) i : (D.4) 158

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AppendixD(Continued)Aftersomemanipulation,wehave, E f ( y < ^ x < ) 2 g = 1 k +1 ( k +1) h z ( a; 0 ; n )+ z ( a; 0 ; n ) i +2 k 1 X i =0 ( k i ) h z ( a; i +1 ; n ) z ( a; i ; n ) i : (D.5) Using(D.1)and(C.7),andaftersomemoremanipulation, E f ( y < ^ x < ) 2 g = 2 n 8 a n k X i =1 r i i a n +8 a 2 k X i =1 r i i Q i a n ; (D.6) where r i =1 i k +1 ; and i =2 i 1 : (D.7) 159

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ABOUTTHEAUTHOR HishamAbdelazizMahmoudreceivedtheB.S.(withhighesthonors)degreeinelectricaleng ineeringfromCairoUniversityatFayoum,Fayoum,Egypt,in2002,andtheM .S.degreeinelectrical engineeringfromCairoUniversity,Cairo,Egypt,in2005.Heiscurrently pursuinghisPh.D.degree attheElectricalEngineeringDepartment,UniversityofSouthFlorida,Tampa,F L.Hisresearch interestsincludewirelesssystems,OFDM-basedsystems,synchronization,channeles timation,spectrumsensingandshapingforcognitiveradio,andchannelcoding.


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Advanced transceiver algorithms for OFDM(A) systems
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ABSTRACT: With the increasing advancements in the digital technology, future wireless systems are promising to support higher data rates, higher mobile speeds, and wider coverage areas, among other features. While further technological developments allow systems to support higher computational complexity, lower power consumption, and employ larger memory units, other resources remain limited. One such resource, which is of great importance to wireless systems, is the available spectrum for radio communications. To be able to support high data rate wireless applications, there is a need for larger bandwidths in the spectrum. Since the spectrum cannot be expanded, studies have been concerned with fully utilizing the available spectrum. One approach to achieve this goal is to reuse the available spectrum through space, time, frequency, and code multiplexing techniques. Another approach is to optimize the transceiver design as to achieve the highest throughput over the used spectrum.From the physical layer perspective, there is a need for a highly flexible and efficient modulation technique to carry the communication signal. A multicarrier modulation technique known as orthogonal frequency division multiplexing (OFDM) is one example of such a technique. OFDM has been used in a number of current wireless standards such as wireless fidelity (WiFi) and worldwide interoperability for microwave access (WiMAX) standards by the Institute of Electrical and Electronics Engineers (IEEE), and has been proposed for future 4G technologies such as the long term evolution (LTE) and LTE-advanced standards by the 3rd Generation Partnership Project (3GPP), and the wireless world initiative new radio (WINNER) standard by the Information society technologies (IST). This is due to OFDM's high spectral efficiency, resistance to narrow band interference, support for high data rates, adaptivity, and scalability.In this dissertation, OFDM and multiuser OFDM also known as orthogonal frequency division multiple access (OFDMA), techniques are investigated as a candidate for advanced wireless systems. Features and requirements of future applications are discussed in detail, and OFDM's ability to satisfy these requirements is investigated. We identify a number of challenges that when addressed can improve the performance and throughput of OFDM-based systems. The challenges are investigated over three stages. In the first stage, minimizing, or avoiding, the interference between multiple OFDMA users as well as adjacent systems is addressed. An efficient algorithm for OFDMA uplink synchronization that maintains the orthogonality between multiple users is proposed. For adjacent channel interference, a new spectrum shaping method is proposed that can reduce the out-of-band radiation of OFDM signals.Both methods increase the utilization of available spectrum and reduce interference between different users. In the second stage, the goal is to maximize the system throughput for a given available bandwidth. The OFDM system performance is considered under practical channel conditions, and the corresponding bit error rate (BER) expressions are derived. Based on these results, the optimum pilot insertion rate is investigated. In addition, a new pilot pattern that improves the system ability to estimate and equalize various radio frequency (RF) impairments is proposed. In the last stage, acquiring reliable measurements regarding the received signal is addressed. Error vector magnitude (EVM) is a common performance metric that is being used in many of today's standards and measurement devices. Inferring the signal-to-noise ratio (SNR) from EVM measurements has been investigated for either high SNR values or data-aided systems.We show that using current methods does not yield reliable estimates of the SNR under other conditions. Thus, we consider the relation between EVM and SNR for nondata-aided systems. We provide expressions that allow for accurate SNR estimation under various practical channel conditions.
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