Spectrum Management in Multi-Hop Cognitive Radio Networks

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Title:
Spectrum Management in Multi-Hop Cognitive Radio Networks Architecture, Modeling and Design
Physical Description:
1 online resource (215 p.)
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english
Creator:
Pan, Miao
Publisher:
University of Florida
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Gainesville, Fla.
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Thesis/Dissertation Information

Degree:
Doctorate ( Ph.D.)
Degree Grantor:
University of Florida
Degree Disciplines:
Electrical and Computer Engineering
Committee Chair:
Fang, Yuguang
Committee Members:
Sahni, Sartaj
Khargonekar, Pramod
Chen, Shigang

Subjects

Subjects / Keywords:
architecture -- cognitiveradio -- modeling -- networking -- optimization
Electrical and Computer Engineering -- Dissertations, Academic -- UF
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Electrical and Computer Engineering thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

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Abstract:
Cognitive radio technology is a promising solution to the dilemma between the ever-increasing spectrum demand brought by the booming growth of wireless services and the exhaustion of available spectrum. Multi-hop cognitive radio networks have also been widely accepted as an indispensable component of next-generation communication systems to improve spectrum utilization and to facilitate ubiquitous network access from anywhere at any time. Although offering significant benefits, they also provide unique research challenges over other wireless networks. Of note are the issues associated with the architecture, modeling and design of spectrum management in multi-hop cognitive radio networks. In this dissertation, we aim to address these challenging and fundamental issues in multi-hop cognitive radio networks, cognitive vehicular ad hoc networks, spectrum auction mechanisms, and spectrum trading systems. Our contributions are mainly sixfold. First, due to the unpredictable activities of the primary users, we propose metrics to evaluate the potential loss for opportunistic spectrum accessing. Second, considering uncertain spectrum supply, we propose a novel architecture of CRNs for spectrum harvesting and sharing, and presented a theoretical study on the joint frequency scheduling and routing problem in multi-hop CRNs. Third, we have a comprehensive study on the path selection problem considering multiple factors including the price of the bands, budget constraints of CR source, link scheduling constraints, flow routing constraints, and activities of primary services. Fourth, under the proposed network architecture, we extend the per-user based spectrum trading into session based spectrum trading, which effectively simplifies the design of spectrum trading systems. Fifth, with a joint consideration of cooperative communications, we propose a cooperative communication aware link scheduling scheme to maximize the throughput for a session in cognitive vehicular ad hoc networks. Last, we incorporate cryptographic technique into the spectrum auction design, and propose a secure spectrum auction scheme leveraging Paillier cryptosystem to purge all the back-room dealings.
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In the series University of Florida Digital Collections.
General Note:
Includes vita.
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Includes bibliographical references.
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Description based on online resource; title from PDF title page.
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This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility:
by Miao Pan.
Thesis:
Thesis (Ph.D.)--University of Florida, 2012.
Local:
Adviser: Fang, Yuguang.
Electronic Access:
RESTRICTED TO UF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE UNTIL 2013-02-28

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lcc - LD1780 2012
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UFE0044645:00001


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SPECTRUMMANAGEMENTINMULTI-HOPCOGNITIVERADIONETWORKS:ARCHITECTURE,MODELINGANDDESIGNByMIAOPANADISSERTATIONPRESENTEDTOTHEGRADUATESCHOOLOFTHEUNIVERSITYOFFLORIDAINPARTIALFULFILLMENTOFTHEREQUIREMENTSFORTHEDEGREEOFDOCTOROFPHILOSOPHYUNIVERSITYOFFLORIDA2012

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c2012MiaoPan 2

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Toallwhonurturedmyintellectualcuriosity,academicinterests,andsenseof scholarshipthroughoutmylifetime,makingthismilestonepossible 3

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ACKNOWLEDGMENTS Firstandforemost,Iwouldliketoexpressmysinceregratitudetomyadvisor,Prof.YuguangFang,forhisinvaluableguidance,encouragementandsupportwithmyyearsinWirelessNetworksLaboratory(WINET).HeconvincedmetojointhePh.D.programatUFLsevenyearsago,andencouragedmeinmypursuitofanacademiccareeraftergraduation.Iamlookingforwardtoourcollaborationinthefuture.IalsowouldliketothankProfessorPramodKhargonekar,ProfessorSartajSahni,andProfessorShigangChenforservingonmysupervisorycommitteeandfortheirgreathelpinvariousstagesofmyworkandcareer.Iwouldnotbeasanegraduatestudentwithoutagroupofgreatfriends.IwouldliketoextendmythankstoallmycolleaguesinWINETforprovidingmeawarm,family-likeenvironmentandfortheircollaborationandinsightfuladvice.IspeciallythankDr.YounggooKwon,Dr.WenjingLou,Dr.WenchaoMa,Dr.Byung-SeoKim,Dr.WeiLiu,Dr.XiangChen,Dr.JingZhao,Dr.HongqiangZhai,Dr.YanchaoZhang,Dr.ShushanWen,Dr.JianfengWang,Dr.YunZhou,Dr.XiaoxiaHuang,Dr.PanLi,Dr.FengChen,Dr.JinyuanSun,Dr.YangSong,Dr.RongshengHuang,HaoYue,LinkeGuo,HuangLin,YuanxiongGuo,ZongruiDing,XinxinLiu,Hanzhao,Huai-leiFu,YanLong,JunjiNakamoto,Dr.SunmyengKim,Dr.NicolaScalabrino,Dr.RobertoRiggio,Dr.QiangShen,Dr.XiaoyanYin,Dr.LeifangHui,Dr.XiaobinTan,Dr.JianweiLiu,Dr.XiaoyanZhuandDr.GuoliangYaoformanyvaluablediscussionsandallthegoodmemories.SpecialthanksareduetotheFangfamily:myadvisorYuguangFangandhiswifeJenniferLu,whonotonlyconstantlyencouragedmeandhelpedmeinmanyways,butalsosharedtheirviewoflifewithme.Finally,Ioweaspecialdebtofgratitudetomybelovedparents.Withouttheirloveandunwaveringsupport,IwouldneverimaginewhatIhaveachieved. 4

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TABLEOFCONTENTS page ACKNOWLEDGMENTS .................................. 4 LISTOFTABLES ...................................... 9 LISTOFFIGURES ..................................... 10 ABSTRACT ......................................... 12 CHAPTER 1INTRODUCTION ................................... 14 1.1CognitiveRadioNetworks:AnOverview ................... 14 1.2ResearchChallenges ............................. 15 1.3ScopeandOrganizationoftheDissertation ................. 17 2THEXLOSS:BAND-MIXSELECTIONFOROPPORTUNISTICSPECTRUMACCESSING ..................................... 20 2.1ChapterOverview ............................... 20 2.2SystemModel ................................. 24 2.2.1SpectrumMarket ............................ 24 2.2.2SSP'sRevenueandRiskFunction .................. 25 2.3PrimaryConceptsforBand-MixSelection .................. 27 2.3.1Band-MixSelectionPrinciple ..................... 27 2.3.2TheEfcientOSACurve ........................ 27 2.3.3UtilityFunctionoftheSSP ....................... 28 2.4TheRiskMeasurementforOSA ....................... 28 2.4.1TheXLossforOSA .......................... 28 2.4.2TheExpectedXLossforOSA ..................... 30 2.4.3CharacterizationandDiscretizationoftheExpectedXLoss .... 31 2.5OptimalBand-MixSelectionBasedontheExpectedXLoss ........ 35 2.6PerformanceAnalysis ............................. 39 2.6.1SimulationSetup ............................ 39 2.6.2ConstructionofEfcientOSACurves ................. 40 2.6.3PerformanceComparison ....................... 42 2.7ChapterSummary ............................... 47 3SPECTRUMHARVESTINGANDSHARINGINMULTI-HOPCRNSUNDERUNCERTAINSPECTRUMSUPPLY ........................ 48 3.1ChapterOverview ............................... 48 3.2NetworkModel ................................. 54 3.2.1SpectrumHarvestingandOpportunisticSpectrumAccessing ... 54 3.2.2ModelingofUncertainSpectrumSupply ............... 56 5

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3.2.3OtherRelatedModels ......................... 57 3.2.3.1TransmissionRangeandInterferenceRange ....... 57 3.2.3.2LinkCapacity ......................... 57 3.3FrequencySchedulingandRoutingConstraintsforOpportunisticAccessing 58 3.3.1SchedulingandInterferenceConstraints ............... 58 3.3.2RoutingConstraints .......................... 61 3.4ProblemFormulationandaLowerBoundfortheCross-layerOptimization 62 3.4.1ProblemFormulation .......................... 64 3.4.1.1Bandwidthintegration .................... 64 3.4.1.2Bandwidthrequiredat ................... 65 3.4.1.3Formalformulation ...................... 66 3.4.2TheLowerBoundfortheCross-layerOptimization ......... 67 3.5AFastFixingAlgorithmforSub-optimalSolutionsUsingDFT-IDFT .... 67 3.5.1FastComputationoftheBandwidthIntegration ........... 68 3.5.2TheCoarse-grainedFixingProcedure ................ 68 3.6PerformanceAnalysis ............................. 71 3.6.1SimulationSetup ............................ 71 3.6.2ResultsandAnalysis .......................... 72 3.7ChapterSummary ............................... 74 4PATHSELECTIONUNDERBUDGETCONSTRAINTSINMULTI-HOPCRNS 76 4.1ChapterOverview ............................... 76 4.2RelatedWork .................................. 79 4.3NetworkModel ................................. 81 4.3.1SpectrumMarketandOpportunisticSpectrumAccessing ..... 81 4.3.2OtherRelatedModelsinCRNs .................... 83 4.3.2.1Probabilitymodelofprimaryservices ........... 83 4.3.2.2Transmissionrangeandinterferencerange ........ 83 4.44-DimensionalConictGraph,ConictCliquesandIndependentSetsinMulti-hopCRNs ................................. 84 4.4.1Constructionofthe4-DConictGraph ................ 84 4.4.2IndependentSetsandConictCliques ................ 86 4.5OptimalPathSelectionunderLinkScheduling,RoutingandBudgetConstraints 87 4.5.1PathCapacityunderCRLinkSchedulingConstraints ........ 87 4.5.2Single-RadiobasedCRRoutingConstraints ............. 89 4.5.3OptimalPathSelectionunderMultipleConstraints ......... 90 4.6AHeuristicPathSelectionAlgorithmforHighEnd-to-EndThroughput .. 92 4.6.1ACounterexamplefortheMaximalCliqueApproach ........ 92 4.6.2TheProposedAlgorithmforPathSelectioninCRNs ........ 93 4.6.3ComplexityAnalysis .......................... 100 4.7PerformanceEvaluation ............................ 101 4.7.1SimulationSetup ............................ 101 4.7.2ResultsandAnalysis .......................... 102 4.8ChapterSummary ............................... 105 6

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5SPECTRUMCLOUDS:ASESSIONBASEDSPECTRUMTRADINGSYSTEMFORMULTI-HOPCOGNITIVERADIONETWORKS ............... 108 5.1ChapterOverview ............................... 108 5.2RelatedWork .................................. 111 5.3NetworkModel ................................. 113 5.3.1SystemArchitectureforSpectrumClouds .............. 113 5.3.2NetworkConguration ......................... 115 5.3.3OtherRelatedModelsinMulti-hopCRNs .............. 116 5.3.3.1Transmissionrangeandinterferencerange ........ 116 5.3.3.2Linkcapacityandachievabledatarate ........... 117 5.3.3.3Uncertainspectrumsupply ................. 117 5.4OptimalSpectrumTradingunderCross-layerConstraintsinMulti-hopCRNs ...................................... 117 5.4.1ExtendedConictGraph,CliquesandIndependentSets ...... 118 5.4.1.1Constructionof3-dimensionalconictgraph ....... 118 5.4.1.2Threedimensionalindependentsetsandconictcliques 120 5.4.2CRLinkSchedulingandFlowRoutingConstraints ......... 121 5.4.2.1CRlinkschedulingconstraints ............... 121 5.4.2.2Bandwidthrequiredat ................... 122 5.4.2.3CRroutingconstraints .................... 122 5.4.3OptimalSpectrumTradingunderMultipleConstraints ........ 123 5.5TheUpperBoundfortheSessionBasedSpectrumTradingOptimization 125 5.6ABiddingValue-RateRequirementRatioBasedHeuristicAlgorithmforSpectrumTrading ................................ 125 5.6.1TheBVR3BasedRelax-and-FixAlgorithm ............. 126 5.6.2ACoarse-GrainedRelax-and-FixHeuristicAlgorithm ........ 129 5.7PerformanceEvaluation ............................ 130 5.7.1SimulationSetup ............................ 130 5.7.2ResultsandAnalysis .......................... 132 5.8ChapterSummary ............................... 136 6COOPERATIVECOMMUNICATIONAWARELINKSCHEDULINGFORCOGNITIVEVEHICULARAD-HOCNETWORKS ........................ 138 6.1ChapterOverview ............................... 138 6.2RelatedWork .................................. 142 6.3NetworkModel ................................. 144 6.3.1NetworkSettingofC-VANETs ..................... 144 6.3.2TransmissionModes .......................... 145 6.3.2.1Amplify-and-forward(AF) .................. 146 6.3.2.2Decode-and-forward(DF) .................. 146 6.3.2.3Directtransmission ..................... 147 6.3.3Transmission/InterferenceRange ................... 147 6.4CooperativeConictGraph,ConictCliquesandIndependentSetsinC-VANETs ................................... 148 7

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6.4.1ExtendingLinksintoCooperative/GeneralLinks ........... 148 6.4.2Establishingthe3-DCooperativeConictGraph .......... 149 6.4.3CooperativeIndependentSetsandConictCliques ......... 151 6.5OptimalCooperativeCommunicationAwareLinkSchedulingforHighEnd-to-EndThroughput ............................ 152 6.5.1CollisionsofRelaySelectionw.r.t.LinkScheduling ......... 152 6.5.2PathCapacitywithLinkSchedulingConsideration ......... 153 6.5.3FlowRoutingConstraintsinC-VANETs ............... 155 6.5.4MaximizingtheThroughputunderMultipleConstraints ....... 156 6.6AHeuristicPruningAlgorithmforCooperativeCommunicationAwareScheduling ................................... 158 6.6.1AnIterativeLink-bandPairPruningAlgorithm ............ 158 6.6.2IllustrativeExamplesfortheProposedPruningAlgorithm ...... 163 6.7PerformanceEvaluation ............................ 164 6.8ChapterSummary ............................... 169 7PURGINGTHEBACK-ROOMDEALING:SECURESPECTRUMAUCTIONLEVERAGINGPAILLIERCRYPTOSYSTEM ................... 170 7.1ChapterOverview ............................... 170 7.2SystemModel ................................. 173 7.2.1Overview ................................ 173 7.2.2DesignChallenges ........................... 175 7.3Preliminaries .................................. 177 7.3.1VCGAuction .............................. 177 7.3.2PaillierCryptosystem .......................... 179 7.4AuctionDesignofTHEMIS .......................... 180 7.4.1THEMIS:SpectrumAuctionProcedure ................ 180 7.4.2THEMIS:SecureSpectrumAuctionDesign ............. 183 7.4.2.1Representationofbiddingvalues .............. 184 7.4.2.2Securesubnetworkspectrumauction ........... 185 7.4.3THEMIS:AnExample ......................... 188 7.5SimulationandAnalysis ............................ 192 7.5.1PerformanceComparison ....................... 193 7.5.1.1Simulationsetup ....................... 193 7.5.1.2Resultsandanalysis ..................... 195 7.5.2SecurityAnalysis ............................ 196 7.5.3EfciencyAnalysis ........................... 197 7.6ChapterSummary ............................... 198 8CONCLUSION .................................... 199 REFERENCES ....................................... 203 BIOGRAPHICALSKETCH ................................ 215 8

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LISTOFTABLES Table page 2-1Spectrumvacancyfromtheprimaryserviceproviders. .............. 31 2-2XvsEXwith=0.9. ............................... 33 2-3Utilityfunctionswithriskatdifferentcondencelevels. .............. 42 3-1LowerandupperboundsofthebandwidthrequiredatforagivensetofCRsessionsatdifferent(,)levels. .......................... 75 5-1Spectrumtradingstatusofthecandidatesessionsw.r.t.thedescendingBVR3valuesinmulti-hopCRNs. .............................. 137 7-1Thecomparisonofdifferentspectrumauctiondesigns. .............. 192 7-2Thecommunicationcomplexity ........................... 196 7-3Thecomputationalcomplexity ............................ 196 9

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LISTOFFIGURES Figure page 2-1Systemmodelforspectrumtrading ......................... 26 2-2ThelossmetricsforOSA. .............................. 30 2-3Optimalband-mixselectionforOSAbasedontheXlossandtheexpectedXloss. .......................................... 41 2-4Performancecomparisonofband-mixselectionschemeswithtworiskmetricsatdifferentcondencelevels(=)]TJ /F7 11.955 Tf 9.3 0 Td[(0.6) ...................... 44 2-5Performancecomparisonofband-mixselectionschemeswithtworiskmetricsatdifferentcondencelevels(=)]TJ /F7 11.955 Tf 9.3 0 Td[(1.4) ...................... 45 3-1SimpleexamplesforCRsessionsunderuncertainspectrumsupplyinCRNs. 49 3-2Anovelarchitectureforspectrumharvestingandsharingunderuncertainspectrumsupplyinmulti-hopCRNs. .............................. 55 3-3AschematicillustratingavailablebandwidthforOSAandunpredictableoccupationofprimaryservicesinCRNs. ............................ 58 3-4Bandwidthrequiredatandoptimizationobjective. ............... 68 3-5Ratiooftheupperboundtothelowerboundatvarious(,)levels. ...... 72 3-6Theblockingratioofdifferentapproaches. ..................... 74 4-1SpectrummarketandopportunisticspectrumaccessingforpacketdeliveryunderCRsource'sbudgetconstraintsinmulti-hopCRNs. ............ 83 4-2Conictrelationshiprepresentedby4-DconictgraphinCRNs. ......... 85 4-3Anillustrativeexamplefortheproposedprocedurewithagivenpath. ...... 94 4-4ImpactofCRsource'sbudgetonpathselectioninmulti-hopCRNs. ....... 103 4-5Impactofthenumberofavailablelicensedbandsonpathselectioninmulti-hopCRNs. ......................................... 104 4-6PathcapacityfordifferentpathselectionalgorithmsinCRNs. .......... 107 5-1Anovelarchitectureforspectrumtradinginmulti-hopCRNs. .......... 114 5-2Conictrelationshiprepresentedby3-DconictgraphinCRNs. ......... 119 5-3ImpactofthenumberofavailablebandsjMjandradiointerfacesjHjonspectrumtradinginmulti-hopCRNs:gridtopology. ..................... 131 10

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5-4ImpactofthenumberofavailablebandsjMjandradiointerfacesjHjonspectrumtradinginmulti-hopCRNs:randomtopology. ................... 132 5-5RatiooftheupperboundtolowerboundsdeterminedbytheproposedalgorithmsatjHj=3andjMj=9. ................................ 133 6-1Illustrativetoytopologiesforcooperativecommunications. ............ 139 6-2Networksettingsandtheend-to-endtrafcdeliverywithtwodifferenttransmissionmodesinC-VANETs. ................................ 142 6-3Conictrelationshiprepresentedby3-Dcooperativeconictgraph. ....... 151 6-4Possiblecasesforrelayselectioncollisionsw.r.t.linkscheduling. ........ 154 6-5Twoillustrativeexamplesfortheproposedpruningalgorithmwithagivenpath:(a)onelicensedbandavailable;(b)twolicensedbandsavailable. ........ 161 6-6Comparisonbetweencooperativecommunicationsanddirecttransmissionsforathree-nodeschematic. ............................. 165 6-7Impactofthenumberofavailablelicensedbandsontheend-to-endthroughputinC-VANETs. ..................................... 167 6-8Impactofdistancebetweenthesourceanddestinationnodesontheend-to-endthroughputinC-VANETs. .............................. 168 7-1Systemarchitecture,conictgraph,andsecurespectrumauctionmemo. ... 174 7-2Challengestosecurespectrumauctiondesign .................. 176 7-3AnillustrativeexampleforTHEMIS. ........................ 189 7-4PerformancecomparisonofTHEMIS,VERITASandM-W ............ 194 11

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AbstractofDissertationPresentedtotheGraduateSchooloftheUniversityofFloridainPartialFulllmentoftheRequirementsfortheDegreeofDoctorofPhilosophySPECTRUMMANAGEMENTINMULTI-HOPCOGNITIVERADIONETWORKS:ARCHITECTURE,MODELINGANDDESIGNByMiaoPanAugust2012Chair:YuguangFangMajor:ElectricalandComputerEngineering Cognitiveradiotechnologyisapromisingsolutiontothedilemmabetweentheever-increasingspectrumdemandbroughtbytheboominggrowthofwirelessservicesandtheexhaustionofavailablespectrum.Multi-hopcognitiveradionetworkshavealsobeenwidelyacceptedasanindispensablecomponentofnext-generationcommunicationsystemstoimprovespectrumutilizationandtofacilitateubiquitousnetworkaccessfromanywhereatanytime.Althoughofferingsignicantbenets,theyalsoprovideuniqueresearchchallengesoverotherwirelessnetworks.Ofnotearetheissuesassociatedwiththearchitecture,modelinganddesignofspectrummanagementinmulti-hopcognitiveradionetworks. Inthisdissertation,weaimtoaddressthesechallengingandfundamentalissuesinmulti-hopcognitiveradionetworks,cognitivevehicularadhocnetworks,spectrumauctionmechanisms,andspectrumtradingsystems.Ourcontributionsaremainlysixfold.First,duetotheunpredictableactivitiesoftheprimaryusers,weproposemetricstoevaluatethepotentiallossforopportunisticspectrumaccessing.Second,consideringuncertainspectrumsupply,weproposeanovelarchitectureofCRNsforspectrumharvestingandsharing,andpresentedatheoreticalstudyonthejointfrequencyschedulingandroutingprobleminmulti-hopCRNs.Third,wehaveacomprehensivestudyonthepathselectionproblemconsideringmultiplefactorsincludingthepriceofthebands,budgetconstraintsofCRsource,linkschedulingconstraints,ow 12

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routingconstraints,andactivitiesofprimaryservices.Fourth,undertheproposednetworkarchitecture,weextendtheper-userbasedspectrumtradingintosessionbasedspectrumtrading,whicheffectivelysimpliesthedesignofspectrumtradingsystems.Fifth,withajointconsiderationofcooperativecommunications,weproposeacooperativecommunicationawarelinkschedulingschemetomaximizethethroughputforasessionincognitivevehicularadhocnetworks.Last,weincorporatecryptographictechniqueintothespectrumauctiondesign,andproposeasecurespectrumauctionschemeleveragingPailliercryptosystemtopurgealltheback-roomdealings. 13

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CHAPTER1INTRODUCTION 1.1CognitiveRadioNetworks:AnOverview DuetothepopularityofsmartmobiledevicessuchasiPhones,peoplenowadayscouldconducttheirbusinessoraccessinformationsuperhighwayviatheirmobiledevices.Manypeoplejustcouldnotlivewithouttheirmobiletoys!Thisleadstotremendoustrafcincreaseoverthewirelessaccessnetworksandadramaticincreaseinthedemandforradiospectrum.Inparallelwiththat,currentstaticspectrumallocationpolicyofFederalCommunicationsCommission(FCC)[ 3 20 73 ]resultsintheexhaustionofavailablespectrum,whilealotoflicensedspectrumbandsareextremelyunder-utilized.Experimentaltestsinacademia[ 9 72 ]andmeasurementsconductedinindustries[ 70 71 ]bothshowthateveninthemostcrowedregionofbigcities(e.g.,Washington,DC,Chicago,NewYorkCity,etc.),manylicensedspectrumbandsarenotusedincertaingeographicalareasandareidlemostofthetime. Observingsuchunbalancedspectrumutilization,FCCrevisiteditsspectrumpolicyandlookedintonewspectrummanagementpolicytoallowotherstoutilizetheunusedlicensedbandsaslongasitdoesnotcauseinterferencetotheservicesofferedtotheprimaryusers(e.g.,unlicensedusersisallowedtousetheunoccupiedlicensedband,butmustvacantthelicensedbandimmediatelywhenthelicensedusersreturntousethisband).Cognitiveradiosaredesignedtoaddresssuchopportunisticuseofunoccupiedspectrumbandsforunlicensedusers(secondaryusers). Comparedwithothertraditionalmulti-hopwirelessnetworks(e.g.,Adhocnetworks),multi-hopcognitiveradionetworks(CRNs)releasethespectrumfromshacklesofauthorizedlicenses,andallowopportunisticusageofthevacantlicensedspectrumbandsineithertemporalorspatialdomain.Duetothegreatpotentialofimprovingthespectrumutilization,CRNshaveattractedtremendousinterestinthelastfewyears,andpromotenumerouspossibleapplicationsinbattlecommunications, 14

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publicsafety,disasterrelief,searchandrescue,environmentmonitoring,andmanyothermilitaryandcivilianareas. 1.2ResearchChallenges Whileofferingsignicantbenets,multi-hopCRNsalsoprovideuniqueresearchchallengesoverotherwirelessnetworks.Thissubsectionoutlinesthemajorproblemsthatoughttobeaddressed. Firstofall,thedesignofcognitiveradioswithwidedynamicfrequencyrangemaybehard.Inmostofresearchactivities,itseemstoassumethatacognitiveradiocanbeoperatedacrossmultiplefrequencybands,say,rangingfromMHzbandssuchasTVwhitespacestoGHzbandssuchas2GHzPCSbandsor5GHzunlicensedband[ 14 73 97 110 ].Intheory,thismaybepossible,butitishardtoimplementinlightweightradios,whichmaybethelikelyscenariosforanybusinesspush.Althoughsomeofthedesiredfeaturesmayberealizedinthenearfuture,enormousamountoftimeandeffortsmustbespentinhardwaredesignsandsignalprocessinginordertoimplementtheseharshfrequency-agilerequirementsinlightweightradios[ 73 97 110 122 ]. Second,spectrumlicensedholdersmaynotbewillingtoletothersutilizetheirbandswithoutcompensationeventhoughFCCallowssecondarymarkettoutilizesuchunusedresourceandtheymaytryeverywaytomeddlewiththeusageofsecondaryusers[ 11 86 ].Thus,themorefeasibleeconomicalmodelmaybetoletprimaryspectrumholderstoparticipateinthebusinessthroughthespectrumtradingprocess(e.g.,spectrumauction).Thisiswhytherearemanyresearchpapersfocusingonthedesignofspectrumtradingsystems/mechanisms[ 48 100 124 135 136 ].Unfortunately,manyproposedspectrumtradingschemesassumetheexistenceofspectrumtraders/auctioneerswithoutspecifyingwhotheyareinCRNs[ 48 124 135 136 ].Someofpapersassumethattheprimaryusersactasthetraders/auctioneers,whichwouldcompromisetheimpartialityofthespectrumtraders/auctioneersandmake 15

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somespectrumtradingschemes,suchastheVCG,impracticalbecauseofthepartialityoftheprimaryusersandlackoftrustedmonitoringimpartialparty. Third,mostresearchworkassumesper-userbasedspectrumtrading,i.e.,eachcognitiveradiobidsandusesthepurchasedspectrumforcommunications[ 48 100 124 135 136 ].Therearetwoproblems:(1)itisnotreallyclearwhomawinningradiocommunicateswith(thereceiverisnotclearlyspecied)andwhatkindsofqualityofservice(QoS)itwouldgetexceptthatitcanusethepurchasedspectrumtotransmit;(2)itisnotclearhowtoenforcetheFCCrulefortheusageofthespectrum(itshouldnotimpacttheserviceoftheprimaryuser)andhowtocollecttherevenue,whichisparticularlydifcultwhenonlinespectrumtradingisonthescaleofminutesorevenhours[ 3 31 ].Thus,althoughsomeofonlinespectrumtrading/auctiontechniquesaretheoreticallyinteresting,theymaynotbepractical. Fourth,usertrafctendstobelocation-basedandtime-varying,andmosttrafcmaytargetatInternetservices,whilethecurrentspectrummanagementapproachestendtomostlyfavortheone-hoptrafcservices,andthusitisnotclearwhatkindsofcommunicationsCRNsaredesignedtosupport.Althoughgroup-basedspectrummanagementschemesintendtoconsiderthespectrumreuseandinterferencemitigationwithcertainefciencyoptimization,itmostlyconsidershowtooptimallyutilizethepurchasedorharvestedspectrumforthecommunicationsamongthecognitiveradiosthemselvesintheregionthatthespectrumcanbeusedintheadhocnetworking.Thisapplicationscenariomaynotbetrulyinterestinginpractice(whichcanbeobservedinmosthotspots). Fifth,sincethereturnsofprimaryusersareunpredictable,thusthespectrumbandsharvestedfromthelicensedusersisstochasticinnature[ 51 88 ],wemayhavetotakeadvantageofthestochasticmultiplexinginordertomaximizethespectrumefciency.Thiscanbedoneonlywhenmultipleuserscancollectivelysharetheharvested 16

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resource,whilethecurrentspectrummanagementincognitiveradionetworksmaynotbeenough. Finally,toattractcustomersforanynewtechnologies,itisalwaysgoodideatominimizethecomplexityonthecustomersside.Formulti-hopCRNs,itisalwaysagreatideatominimizethechangesontheusers'deviceswhileharvestingtheunusedresource(thewhitespaces).Thus,itmaybemoreviabletodeveloptechnologiestomaximizethespectralefciencywhileminimizingtheusers'sidecomplexity. 1.3ScopeandOrganizationoftheDissertation Thisdissertationcontributestothedevelopmentofnovelsolutionstoanumberofchallengingandfundamentalissuesofspectrummanagementinmulti-hopcognitiveradionetworks,whichareeitherignoredornotwelladdressedinpreviousresearch.Therestofthedissertationisorganizedasfollows. Consideringtheuncertainlicensedspectrumavailability,in 2 ,werstintroduceanintuitivemethod,theXloss,toquantifytheriskforsecondaryusersatagivencondentlevel.SincetheXlosstheoreticallyunderestimatesthepotentialriskforopportunisticspectrumaccessingandmathematicallylacksofsubadditivity,wefurtherproposetheexpectedXloss,amoresuitableriskmeasurementforopportunisticspectrumaccessingwithdesiredproperties. Basedontheproposedmetricscharacterizingthespectrumavailability,inChapter 3 ,weproposeanovelarchitectureofCRNsforspectrumharvestingandsharing,andpresentedatheoreticalstudyonthejointfrequencyschedulingandroutingprobleminmulti-hopCRNsunderuncertainspectrumsupply.Werstintroduceanewserviceprovider,SSP,andlettheSSPprovidecoverageinCRNswithlow-costCRmeshroutersinordertofacilitatetheaccessingofSUswithoutCRcapability.Wecharacterizethenetworkwithapairof(,)parameters,presentamathematicalformulationwiththegoalofminimizingtherequirednetwork-widespectrumresourceata(,)levelforasetofCRsessionswithraterequirements,providefeasiblesolutions 17

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totheformulatedoptimizationproblem,andshowthe(,)basedapproachisbetterthanexpectedbandwidthbasedoneintermsofblockingratioandspectrumutilization. UndertheproposednetworkarchitectureinChapter 3 ,Chapter 4 studiesthepathselectionprobleminmulti-hopCRNsunderowrouting,linkschedulingandCRsource'sbudgetconstraints.ConsideringtheinherentsingleradioconstraintofCRdevicesandthefeaturesofspectrumtrading,weproposea4-DconictgraphtodescribetheconictrelationsamongCRlinks,mathematicallyformulatethepathselectionproblemundermultipleconstraintsintoanoptimizationproblemwiththeobjectiveofmaximizingtheend-to-endthroughputforacertainCRsession,andsolveitbylinearprogramming. Asafollow-upinvestigationinChapter 4 ,inChapter 5 ,wefurtherextendtheper-userbasedspectrumtradingintotheper-sessionbasedone,wheremultiplesessionsexistinthenetwork,andproposeanovelspectrumtradingsystem,i.e.,spectrumclouds.Giventheraterequirementsandbiddingvaluesofcandidatetradingsessions,weformulatetheoptimalspectrumtradingintotheSSP'srevenuemaximizationproblemundertheavailabilityofspectrum,linkschedulingandowroutingconstraintsinmulti-hopCRNs.SincetheformulatedproblemisNP-hardtosolve,wederiveanupperboundfortheoptimizationbyrelaxingtheintegervariables,proposeheuristicalgorithmsforlowbounds,andshowthattheproposedsessionbasedspectrumtradinghassuperioradvantagesovertheper-userbasedoneinmulti-hopCRNs. Chapter 6 studiesthethroughputmaximizationproblemincognitivevehicularAdhocnetworksundermultipleconstraints(i.e.,CRdevices'inherentsingle-radioconstraint,theavailabilityoflicensedspectrum,transmissionmodeselectionandlinkscheduling).Consideringthespecialfeaturesofcooperativecommunications,weextendthelinksandclassifythemintocooperativelinks/generallinks.Dependingontheavailablebandsatdifferentextendedlinks,weconductcooperativecommunicationawarelinkschedulingtochoosetheoptimalrouteintermsofend-to-endthroughput. 18

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Securityissuesareimportantisthedesignofspectrummanagementinmulti-hopCRNsaswell.InChapter 7 ,againsttheuntrustworthyspectrumtrader,weincorporatecryptographictechniqueintothespectrumauctiondesignandproposeasecurespectrumauctionschemeleveragingPailliercryptosystemtopurgetheback-roomdealing. Finally,Chapter 8 summarizesthisdissertation. 19

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CHAPTER2THEXLOSS:BAND-MIXSELECTIONFOROPPORTUNISTICSPECTRUMACCESSING 2.1ChapterOverview Boominggrowthofwirelessnetworksandourishofvariouswirelessserviceshavebeenwitnessedinthepastdecade.Inparallelwiththat,currentstaticspectrumallocationpolicyofFederalCommunicationsCommission(FCC)[ 3 21 73 ]resultsintheexhaustionofavailablespectrum,whilemanylicensedspectrumbandsareextremelyunder-utilized(socalledwhitespace).Asoneofthemostpromisingsolutionstoimprovespectrumutilization,cognitiveradiotechnologyallowsthesecondaryusers(SUs)toopportunisticallyaccesstovacantbandsbelongingtoprimaryusers(PUs)ineithertemporalorspatialdomain[ 3 21 73 ]. Theideaofopeningupthelicensedspectrumbandsincognitiveradionetworksinitiatesthemarketofspectrumtrading,andpromotesabatchofinterestingresearchonrelatedtopics.Specically,in[ 35 ],Grandblaiseetal.generallydescribethepossiblescenariosandintroducesomemicroeconomicsinspiredmechanismsforopportunisticspectrumaccessing(OSA),andin[ 100 ],SenguptaandChatterjeeproposeaneconomicframeworkforOSAandservicepricingtoguidethedesignofdynamicspectrumallocationalgorithmsaswellasservicepricingmechanismsthattheserviceproviderscanpossiblyuse.Fromtheviewofsystemdesign,modelsingametheory,byWangetal.in[ 119 120 ],Panetal.in[ 84 ]andZhangetal.in[ 132 ],andauctiondesignsinmicroeconomics,byZhouetal.in[ 135 136 ],Jiaetal.in[ 48 ]andWuetal.in[ 124 ],areexploitedtoconstructthespectrumtradingmechanismswithdesiredproperties,suchaspowerefciency,allocationfairness,incentivecompatibility,Paretoefciency,etc.Fromtheviewoftheprimaryserviceprovider(PSP),Xingetal.in[ 125 ]andNiyatoetal.in[ 75 76 ]havewellinvestigatedthespectrumpricingissuesinthespectrummarket,wheremultiplePSPs,whosegoalistomaximizethemonetarygainswiththeirvacantspectrum,competewitheachothertoofferspectrumaccesstothe 20

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secondaryserviceprovider(SSP).FromtheviewoftheSSP,peopleareinterestedinhowtheSSPoptimallydistributesSUs'trafcdemandsoverthespectrumbandswhenthereismorethanoneunoccupiedlicensedband.MotamediandBahaiin[ 74 ]haveformulatedthisproblemasamulti-armedbanditproblemandproposeareinforcelearningalgorithmtoconsistentlytrackthebestbandintermsofbandconditions. However,theconceptofthebestbandforOSAtendstobeambiguousconsideringthecharacteristicsofdifferentbands.Asdescribedin[ 75 125 ],thespectrumbandsfromPSPsmaybeevaluatedunequallybytheSSPfromdifferentperspectives,suchasthefrequencyoftheavailableband,thesegmenttypeoftheband(i.e.,contiguoussegmentordiscontinuousone),thepriceoftheband,thelocationofthePSP,etc.Amongallthesefactors,thePUs'activitiesonthebandarethemostcrucialonefortheSSP,becausetheunexpectedreturningofprimaryservicesmayterminatetheSSP'sspectrumprovisiontotheSUsandincurenormousmonetaryriskfortheSSPonitsspectrumpurchasing.Therefore,itisnecessaryfortheSSPtondametrictoquantifythepotentialriskforOSAduetothePSPs'uncertainspectrumsupply. State-of-the-artworkoninvestigatingtheunpredictableactivitiesofprimaryservicescangenerallybeclassiedintotwocategories:i)spectrumsensing[ 12 26 27 51 65 134 ]andii)statisticalanalysisofthecollected/historicalspectrumvacancy/occupancydata[ 9 70 71 ].Inspiteoftheoverwhelmingwasteofsensingtimewhichcanbeusedformoretrafcdelivery,individualsensingistrappedbysensingaccuracysincebothfalsealarmprobabilityandmissingdetectionprobabilityarereallyhigh[ 12 26 51 ].Toovercometheweaknessofindividualsensing,cooperativesensingisproposedtoimprovethesensingaccuracybygroupingSUstosensetogetherandshareinformationamongthegroup[ 26 27 ].Butthetroubleisthatitistoodifculttosynchronize/scheduletheSUsinthegroupsensingsimultaneously/sequentially.Inaddition,cooperativesensinghastosetupacommonchannelforinformationexchange,whichwillincurenormouscommunicationoverhead.Ontheotherhand, 21

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in[ 9 21 34 70 71 ]1,researchersinacademiaaswellasengineersinindustrytrytoidentifythespectrumsupplyforOSAwiththestatisticsoflicensedspectrumutilizationratherthanattemptingtodetecttheactivitiesofprimaryservices.Theyhavecarriedoutspectrummeasurements,collectedandanalyzedthedataaboutspectrumutilization,summarizedthestatisticalcharacteristicsofthebandvacancy/occupancy,andstoredthesestatisticsintothedatabase.ThisdatabasearchitectureisadoptedbyFCCinitslatestreleasedrulefortheopportunisticusageofwhitespace[ 21 ],andmanycompaniesincludingSpectrumBridge,Microsoft,Google[ 34 ],etc.haveproposedtheirsolutionsandexperimentalprototypesbasedonthisarchitecture.Inaddition,authorsin[ 2 19 ]integratethehistoricaldatawiththesensingresultstoprovidebetterstatisticsorgivebetterpredictionfortheactivitiesofprimaryservices.ThesestatisticalresultscontainabundantinformationabouttheuncertainspectrumsupplyandprovideaniceguidetothebandselectionandpurchaseoftheSSPfortheSUs'OSA. Inspiredbythestatisticalcharacteristicsofspectrumbandsobtainedonobservationandexperimentsin[ 9 21 34 70 71 ],inthischapter,wenovellymodeltheunpredictableactivitiesofprimaryservicesonthelicensedbandsasavectorofrandomvariablesandproposemetricstoevaluatetheriskforOSA.Duetotheuncertainspectrumsupply,heapingallthetrafcononebandmakesthesecondaryservicesvulnerabletotheactivitiesoftheprimaryservices.Therefore,basedontheproposedlossmetrics,weillustratehowtheSSPoptimallysplitsthetrafcdemandsoftheSUsonaband-mix,whentherearemultipleavailablelicensedbands.Ourmajorcontributionsaresummarizedasfollows. 1Chenetal.in[ 9 ]carriedoutasetofspectrummeasurementsinthe20MHzto3GHzspectrumbandsat4locationsconcurrentlyinGuangdongprovinceofChina.Theyusedthesedatasetstoconductasetofdetailedanalysisoftherstandsecondorderstatisticsofthecollecteddata,includingchanneloccupancy/vacancystatistics,channelutilization,alsospectralandspatialcorrelationofthesemeasures. 22

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WerstintroducetheXlosstointuitivelyanswerthequestion:whatistheriskforOSAataspeciedcondencelevelwithuncertainspectrumsupplyfromthePSPs.DespitethesimplicityoftheXlossindenition,itinfactunderestimatesthepotentialriskoftheSSPandmathematicallylacksofsubadditivity(i.e.,theXlossofamixwithtwobandsmaybelargerthanthesumofindividualXlossesofthetwobands.),whichmakestheXlossunabletosupportthetrafcsplittingoverdifferentbands. BeyondtheXloss,weformallydenetheexpectedXloss,ameasurementwithdesirablepropertiesincludingsubadditivityandconvexity,toquantifytheriskforOSA.Besides,theexpectedXlosscansupportthetrafcsplittingwithoutanylimitationonthedistributionofprimaryservicesonthebands.DuetothedifcultyincalculationoftheexpectedXloss,wesimplifyitwithacharacteristicfunctionintoadiscritizedversion,whichisfeasibletobeusedinevaluatingtheriskforOSA. ToreducetheriskoftheSUsforOSA,weputeggsintodifferentbaskets[ 69 ],i.e.,wemaketheSSPsplitthetrafcdemandsfromSUsonamixofbandsinsteadofswarmingallthetrafcoveroneband.Thereasonisthatitisgenerallyimpossibleforbandswithdifferentfrequenciestoperformpoorlyatthesametime.Moreover,weintroducetheSSP'sband-mixselectioncriterion,i.e.,selectingtheband-mixfortrafcsplittingwithmaximumexpectedrewardforgivenriskforOSA,orwithminimumriskforgivenreward,aswellasotherconceptsrelatedtothespectrumband-mixselectionforOSA,suchasefcientOSAcurvesandutilityfunctionsoftheSSP. BasedontheexpectedXloss,wespecicallyillustratehowtheSSPoptimallyselectstheproportionalcompositionofthemixofbandsownedbythePSPsfortrafcsplittingwiththeriskforOSAatagivencondencelevel2.Furthermore,weformulatetheband-mixselectionforOSAintoanon-linearrevenuemaximizationproblem.ByreplacingtheexpectedXlosswithitsdiscritizedversionforriskestimation,weprovethatthetwoproblemsachievethesameresultsintermsoftheoptimalband-mixselectionforOSA,andwesolvethelatteroptimizationproblembylinearprogramming. 2Actually,theprocessofselectingtheband-mixforOSAcanbedividedintotwostages.Therststagestartswithsamplingandobservation,andendswithstatisticalvaluesaboutthefutureperformanceofavailablespectrumbandsfromPSPs.Chenetal.in[ 9 ]haveaccomplishedtherststageworkofband-mixselectionforOSA;thesecondstagestartswiththelateststatisticalvaluesrelatedtofuturespectrumsupplyfromPSPs,andendswiththeSSP'sriskquanticationandband-mixselectionforOSA.Inthischapter,weareonlyconcernedwiththesecondstage. 23

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Bycarryingoutnumericalsimulations,weprovidetheefcientOSAcurveswithriskforOSAatdifferentcondencelevels,andshowthatwiththedesignatedutilityfunctionoftheSSP,theproposedspectrumband-mixselectionschemeiseffectiveinimprovingthespectrumutilization,thesatisfactiondegreeofSUsandtheSSP'sprot. Therestofthischapterisorganizedasfollows.InSection 2.2 ,wedescribetherolesofthePSPsandtheSSPinthespectrumtradinganddenetherewardfunctionfortheSUsaswellastheriskfunctionforOSA.Weintroducerelatedconceptstoband-mixselectionincludingband-mixselectionrule,efcientOSAcurvesandtheSSP'sutilityfunctioninSection 2.3 .WeelaborateonthetwoproposedriskmetricsforOSA:theXlossandtheexpectedXlossinSection 2.4 .WiththediscritizedversionoftheexpectedXloss,weillustratetheoptimalband-mixselectionoftheSSPforOSAinSection 2.5 .Finally,weconductnumericalsimulationsandanalyzetheperformanceresultsinSection 2.6 ,anddrawtheconcludingremarksinSection 6.8 2.2SystemModel 2.2.1SpectrumMarket Weconsideraspectrummarketincognitiveradionetworks[ 75 ]withmultiplePSPsoperatingondifferentspectrumbandsandaSSPwhoservesagroupofSUsasshowninFig. 2-1A .TheSUscantakeopportunisticuseoftheselicensedspectrumbandswhentheprimaryservicesarenoton,butmustevacuatefromthesebandsimmediatelywhenprimaryservicesbecomeactive.Inaddition,weassumeallthespectrumtransactionstakeplaceatstartingtimeofeachperiod3asshowninFig. 2-1B ,andthepaymentforspectrumtradingisnon-refundable. 3Theselling/buyingperiod4tshouldnotbetoolong(e.g.,days,monthsoryears)tomakedynamicspectrumaccessinfeasible,anditshouldnotbetooshort(e.g.,millisecondsorseconds)toincuroverwhelmingoverheadinspectrumtrading.Thetypicaldurationisminutesorhoursasshownin[ 31 ].Intherestofthischapter,weassumethatallthespectrumtransactionsareofxedduration,sothatthetimeparameterisnotincludedinourformulation. 24

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Inthiscase,PSPswillsetreasonablepricesfortheunoccupiedbandsconsideringthequalityofthebandsaswellascompetitionamongthePSPsinthespectrummarket[ 48 75 125 ],andsellthosebandsperiodicallyformonetarygains.Correspondingly,iftheSSP(e.g.,thebasestation(BS)ortheaccesspoint(AP))realizesthereisnotenoughradioresourceforthetrafcdemandsofitsSUs,theSSPwillplaytheroleoftradingagentfortheSUs[ 100 ].Specically,theSSPwilltrytoselectamixofcurrentlyvacantlicensedbands,buythosebandsfromthePSPs,chargetheSUswiththepricessetbyPSPsandsharethebandspurchasedamongmultipleSUsinatime-divisionmultipleaccess(TDMA)manner. 2.2.2SSP'sRevenueandRiskFunction AssumetherearenavailablespectrumbandsownedbydifferentPSPswithidenticalbandwidth,whichequalsto1,withinthesensingrangeoftheSSP.Consideringtheunpredictableactivitiesofprimaryservices,theuncertainspectrumsupplyofdifferentbandsforagivenperiodisrepresentedbys=(s1,s2,,sn),wheresiisarandomvariable4withinthedomainof[0,1].SupposethetotaltrafcdemandfromtheSUsis1,andtheproportionalcompositionoftheband-mixthattheSSPpicksupis!=(!1,!2,,!n),!2W,wherePni=1!i=1.Then,thetotalspectrumresourcestheSSPcanobtainisPni=1si!i,andtheexpectedrewardfortheSSPcanbewrittenas (!)=rnXi=1E[si]!i.(2) 4Here,sicanbeinterpretedasunoccupiedtimeorunoccupiedbandwidthbyprimaryservicesforbandiduringonetimeperiod. 25

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AThearchitectureofspectrummarket BPeriodicalspectrumselling Figure2-1. Systemmodelforspectrumtrading whererisaconstant,representingtheSSP'srewardforsatisfyingoneunitoftrafc5.Correspondingly,theriskfunctionoftheSSPcanbeexpressedas `(!,s)=pT!)]TJ /F5 11.955 Tf 11.95 0 Td[(rsT!,(2) wherep=(p1,p2,,pn)isthechargingpricevectorsetbythePSPsforOSAperperiod,andpiisaconstantduringaspectrumtradingperiod.Notethatpipj,ifE(si)E(sj).Sincerisaxednumberandsisarandomvector,theriskforOSAdependsonboththestatisticalcharacteristicsofsandtheSSP'sselectionofbandsbelongingtothePSPs. 5Withtheassumptionthatrisxed,(!)canalsobeinterpretedastheexpectedtrafcdemandsthattheSSPisabletosupport. 26

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2.3PrimaryConceptsforBand-MixSelection 2.3.1Band-MixSelectionPrinciple Intuitively,theSSPisabletomaximizehisrevenuebypouringallthetrafcofsecondaryusersoveraparticularbandwiththemaximalexpectedreward.However,theriskofusingthatbandmaybequitehigh.Arationalorrisk-averseSSPisnotlikelytogambleallthetrafcononebandsincetherewardmaybeextraordinarilylowconsideringtheactivitiesofprimaryservices. Therefore,theexpectedrewardshouldnotbetheonlycriterioninchoosingthespectrumbandstoaccess;instead,theriskoftherewardmustbeconsideredbytheSSP.Itisreasonabletobelievethatifanytwoband-mixeshavethesameexpectedreward,theSSPwillprefertheonehavingthesmallerriskforOSA,andifanytwoband-mixeshavethesamerisk,theSSPwillprefertheonehavingthegreaterexpectedreward.So,thecriterionforband-mixselectionisasthefollows. R eward-R isk(Dual-R)Rule:TheSSPshouldchooseamixoflicensedbandswithmaximumexpectedrewardforgivenriskforOSA,orwithminimumriskforgivenexpectedrewardforOSA,withrespecttotheuncertainspectrumsupplyfromthePSPs. 2.3.2TheEfcientOSACurve Withallband-mixesthatcanbeconstructedfromthesetofvacantspectrumbandsfromPSPs,itisobviousthattheDual-RruleproducesnotanoptimalOSApointbutanefcientOSAcurvefortheSSP'sband-mixselection,ifweconsidertheSSPmaytoleratedifferentlevelsofriskforOSA.Givenaxedrisk,thecorrespondingband-mixontheefcientOSAcurvealwaysprovidesthehighestreward.Or,givenaxedexpectedreward,thecorrespondingband-mixontheefcientOSAcurvealwaysprovidesthelowestriskforOSA,i.e.,theefcientOSAcurveisthesetofalltheband-mixeswiththereward-riskpairswhicharenotdominatedbyanyotherband-mixesforOSA. 27

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2.3.3UtilityFunctionoftheSSP Todetermineaspecicband-mixselectionforOSAontheefcientOSAcurve,theSSPneedstospecifyhisutilityfunction,whichcanjointlymeasuretheSSP'ssatisfactionofreceivingacertainamountofrewardandtherisk-aversionassociatedwiththatreward.ArationalSSP'sgoalistondtheoptimalband-mixforOSAtomaximizetheexpectedutilitywithrespecttoallexpectedreward-riskpairsofpossibleband-mixesforOSA.Inthischapter,theSSP'sutilityfunctionisassumedtobeanincreasingandconcavefunction,whichmaybepolynomial,exponential,etc.,e.g.,theutilityfunctionoftheSSPcanbedenedasthedifferencebetweenthevalueofitsexpectedrewardandthevalueofitsriskformonetaryloss[ 69 106 107 ]duringtheopportunisticaccessingprocess. 2.4TheRiskMeasurementforOSA Inthissection,webeginwithanintuitiveway,theXloss,toquantifytheriskoftheSSPforOSAatagivencondencelevel.Then,wedwellontheexpectedXloss,amorereasonableandeffectivemetricwithdesirablepropertiesforriskevaluation. 2.4.1TheXLossforOSA Forconvenience,weassumetherandomvectors,whichrepresentstheuncertainspectrumsupplyfromPSPs,hasaprobabilitydensityfunctionf(s)6.FromEquation( 2 ),wendthattherisk,`(!,s),isarandomvariablehavingadistributiondependingonthatofs.Theprobabilityoftherisk,`(!,s),notexceedingathreshold2Risthengivenby F(!,)=Z`(!,s)f(s)ds.(2) 6ThisassumptionisnotessentialfortheexpectedXlossandcanberelaxed. 28

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Asafunctionofforxed!,F(!,)7isthecumulativedistributionfunctionfortheriskcausedbytheunpredictableactivitiesofprimaryservices. Givenanyspeciedcondencelevel2(0,1),theXlossforOSAassociatedwith!isdenotedas X(!)=inff2R:F(!,)g.(2) AccordingtoEquation( 2 ),theXloss8representsthepotentialriskthattheSSPneedstotakeforOSAwithaspeciedband-mix!atthecondencelevel. Ex.1:Letbeequalto0.9.Withagiven!,theprobabilitydistributionoftheriskforOSAissupposedtobelikethatshowninFig. 2-2A .Then,theareainshadeisequalto(1)]TJ /F3 11.955 Tf 11.95 0 Td[()=0.1,andX(!)=0.57. AlthoughtheXlossseemssimpletofollow,itsinherentweaknessmakesthismeasurementdifculttobeappliedinband-mixselectionandtrafcsplittingforOSAinoursetting.TheshortcomingsoftheXlossareasfollows: TheXlossunderestimatestheriskforOSA.FromEquation( 2 )andEx.1,wendtheXlossdenotestheriskthattheSSPsuffersinthebestcasesintermsoftheuncertainspectrumsupplyfromPSPs.Actually,withthegiven!,theSSPisnotinterestedinthelossintheleastcasesofriskirrespectivelyofhowserioustheriskinalltheothercasesis. TheXlossisnotvalidwhenshasafat-tailed(a.k.a.,heavy-tailed)distribution.However,recentworksontrafcmeasurements[ 9 46 ]showthatthetrafcofthe 7ThefunctionF(!,)isnondecreasingw.r.t.andweassumethatF(!,)iseverywherecontinuousw.r.t..Thisassumptionisalsomadeforsimplicity.8Comparedwiththeclassicalriskmetric(i.e.,thevarianceofthereward)inportfoliotheory[ 69 ],theproposedXlossandtheexpectedXlossexcludethenegativeeffectsofthevarianceapproach[ 38 ]andtakefulluseoftheinherentinformationcontainedinthestatisticsofbandvacancy[ 88 ]. 29

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ATheXlossforOSA. BTheexpectedXlossforOSA. Figure2-2. ThelossmetricsforOSA. primaryservicesmaystatisticallyexhibitnotonlyathin-tailed(a.k.a.,light-tailed)distributionbutalsoafat-taileddistribution9. TheXlosslackssubadditivity10andisnon-convexasafunctionof!,whichmakeitdifculttooptimizeaswellastoapplyinband-mixselectionfortrafcsplitting. 2.4.2TheExpectedXLossforOSA TheweaknessoftheXlossgivesustheimpetustoseekanothermeasurementfortheriskincurredbytheuncertainspectrumsupply.So,wedeneanalternativerisk 9Tobespecic,thedistributionofvoiceservicesinGSMmeasuredin[ 9 ]issaidtohaveathintail,andthedistributionofdatapacketservicesmeasuredin[ 46 ]issaidtohaveafattail.10PleaserefertoEx.2forbetterunderstanding. 30

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Table2-1. Spectrumvacancyfromtheprimaryserviceproviders. BandABandBB-mix(A+B)Probability 0.510.756%0.810.94%10.50.756%10.80.94%11180% metric,theexpectedXloss,as EX(!)=1 1)]TJ /F3 11.955 Tf 11.96 0 Td[(Z`(!,s)X(!)`(!,s)f(s)ds.(2) InEquation( 2 ),theprobabilitythat`(!,s)X(!)isequalto(1)]TJ /F3 11.955 Tf 11.99 0 Td[().Therefore,EX(!)comesoutastheexpectationoftheriskbeingX(!)orgreater. AsthecomparisonshowninFig. 2-2 ,theexpectedXlossconsiderstheriskforOSAingeneralcases,buttheXlossonlyconsiderstheriskforOSAinthebestcases.Moreover,theexpectedXlossissubadditivebuttheXlossisnot.Tobesimple,weillustratethispropertyinthefollowingexample. Ex.2:AssumetheSSPselectsaband-mixconsistingofbandAandB,where!A=(1,0),!B=(0,1)and!mix=(0.5,0.5).TheavailabilityofbandAandBforOSAisgiveninTab. 2-1 .Givenp=(p1,p2)=(1,1),r=1,and=0.9,theXlossandtheexpectedXlossforbandA,bandBandtheband-mixarecalculatedandlistedinTab. 2-2 .ObservationshowsthatX(!A)=X(!B)=0.2EX(!mix)=0.25,whichindicatestheexpectedXlossissubadditivebuttheXlossisnot. 2.4.3CharacterizationandDiscretizationoftheExpectedXLoss WiththedenitionoftheexpectedXloss,westillnditdifculttohandlebecauseX(!)isinvolvedinthecalculationofEX(!).Thus,wesimplifyEX(!)bycharacterizingitwiththefunction)]TJ /F6 7.97 Tf 6.78 -1.79 Td[(onWR,whichcanbedenotedas )]TJ /F6 7.97 Tf 6.77 -1.79 Td[((!,)=+1 1)]TJ /F3 11.955 Tf 11.95 0 Td[(Zs2Rn[`(!,s))]TJ /F3 11.955 Tf 11.96 0 Td[(]+f(s)ds,(2) 31

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where[t]+=maxf0,tg.Thecriticalfeaturesof)]TJ /F6 7.97 Tf 6.78 -1.79 Td[(areasfollows. Theorem2.1. Asafunctionof,)]TJ /F6 7.97 Tf 6.77 -1.8 Td[((!,)isconvexandcontinuouslydifferentiable.TheexpectedXlossassociatedwithany!2Wcanbedeterminedfromtheformula EX(!)=min2R)]TJ /F6 7.97 Tf 6.78 -1.8 Td[((!,).(2) Inthisformula,thesetconsistingofthevaluesof,forwhichtheminimumisattained,isanonempty,closed,boundedinterval(perhapsreducingtoasinglepoint),andinparticular,weobtain 8><>:X(!)2argmin2R)]TJ /F6 7.97 Tf 6.77 -1.79 Td[((!,)EX(!)=)]TJ /F6 7.97 Tf 27.6 -1.8 Td[((!,X(!)). (2) Proof. ThefollowinglemmaisessentialforestablishingTheorem 2.1 andTheorem 2.2 withrespecttooftheintegralexpressioninthedenitionof)]TJ /F6 7.97 Tf 6.77 -1.79 Td[((!,).Here,werelyontheassumptionthatF(!,)iscontinuouswithrespectto,whichisequivalenttosayingthatregardlessofthechoiceof!,thesetofswith`(!,s)=hasprobabilityzero,i.e., Z`(!,s)=f(s)ds=0. Lemma1. With!xed,letG()=Rs2Rng(,s)f(s)ds,whereg(,s)=[`(!,s))]TJ /F3 11.955 Tf 12.4 0 Td[(]+.Then,Gisaconvex,continuouslydifferentiablefunctionwithderivative @ @G()=F(!,))]TJ /F7 11.955 Tf 11.96 0 Td[(1. 32

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Table2-2. XvsEXwith=0.9. =90%BandABandBB-mix(A+B) X0.20.20.25EX0.380.380.25 Proof. ThelemmaaboveisfromProposition2.1in[ 102 ],wherethefollowingequationsareproved,i.e., @ @G()=E[@ @g(,s)]=Zs2Rn@ @g(,s)f(s)ds=Z`(!,s)@ @[`(!,s))]TJ /F3 11.955 Tf 11.96 0 Td[(]f(s)ds=F(!,))]TJ /F7 11.955 Tf 11.95 0 Td[(1. Inviewofthedeningformulafor\(!,),itcaneasilybededucedfromthelemmathat\(!,)isconvexandcontinuouslydifferentiablewithderivative @ @\(!,)=1+1 (1)]TJ /F3 11.955 Tf 11.96 0 Td[()[F(!,))]TJ /F7 11.955 Tf 11.95 0 Td[(1]=1 (1)]TJ /F3 11.955 Tf 11.96 0 Td[()[F(!,))]TJ /F3 11.955 Tf 11.95 0 Td[(]. Therefore,thevaluesofthatminimize\(!,)areexactlythoseforwhichF(!,))]TJ /F3 11.955 Tf 12.92 0 Td[(=0.Theyformanonemptyclosedinterval,inasmuchasF(!,)iscontinuousandnondecreasinginwithlimit1as!.ThisfurtherdemonstratesthevalidityoftheXformula.So,wehave min2R)]TJ /F6 7.97 Tf 6.77 -1.79 Td[((!,)=)]TJ /F6 7.97 Tf 27.59 -1.79 Td[((!,X(!))=X(!)+1 1)]TJ /F3 11.955 Tf 11.95 0 Td[(Zs2Rn[`(!,s))]TJ /F5 11.955 Tf 11.96 0 Td[(X(!)]+f(s)ds. 33

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Buttheintegralhereequals Z`(!,s)X(!)[`(!,s))]TJ /F5 11.955 Tf 11.95 0 Td[(X(!)]f(s)ds=Z`(!,s)X(!)`(!,s)f(s)ds)]TJ /F5 11.955 Tf 11.95 0 Td[(X(!)Z`(!,s)X(!)f(s)ds, wheretherstintegralontherightisbydenition(1)]TJ /F3 11.955 Tf 12.76 0 Td[()EX(!)andthesecondis1)]TJ /F5 11.955 Tf 11.96 0 Td[(F(!,X(!)).Moreover,F(!,X(!))=.Thus, min2R)]TJ /F6 7.97 Tf 6.78 -1.79 Td[((!,)=X(!)+1 1)]TJ /F3 11.955 Tf 9.96 0 Td[([(1)]TJ /F3 11.955 Tf 9.96 0 Td[()EX(!))]TJ /F5 11.955 Tf 9.96 0 Td[(X(!)(1)]TJ /F3 11.955 Tf 9.96 0 Td[()]=EX(!). Theproofisnished. Theorem2.2. MinimizingtheexpectedXlosswith!overall!2Wisequivalenttominimizing)]TJ /F6 7.97 Tf 6.77 -1.8 Td[((!,)overall(!,)2WR,i.e., min!2WEX(!)=min(!,)2WR)]TJ /F6 7.97 Tf 6.78 -1.79 Td[((!,),(2) Proof. TheclaimsinTheorem 2.2 aresimpleresultsoftheexpectedXlossformulainTheorem 2.1 andthefactthattheminimizationof)]TJ /F6 7.97 Tf 6.77 -1.79 Td[((!,)withrespectto(!,)2WRcanbecarriedoutbysequentialxingminimization[ 41 ],i.e.,rstminimizingover2Rforxed!andthenminimizingtheresultover!2W. Theconvexityclaimstartswiththeobservationthat)]TJ /F6 7.97 Tf 6.77 -1.79 Td[((!,)isconvexwithrespectto(!,)whenevertheintegrand[`(!,s))]TJ /F3 11.955 Tf 13.1 0 Td[(]+,intheequation:)]TJ /F6 7.97 Tf 6.78 -1.79 Td[((!,)=+1 1)]TJ /F6 7.97 Tf 6.59 0 Td[(Rs2Rn[`(!,s))]TJ /F3 11.955 Tf 12.64 0 Td[(]+f(s)dsfor)]TJ /F6 7.97 Tf 6.77 -1.79 Td[((!,),isitselfconvexwithrespectto(!,).Foreachs,thisintegrandisthecompositionofthefunction(!,)7!`(!,s))]TJ /F3 11.955 Tf 12.99 0 Td[(withthenondecreasingconvexfunctiont7![t]+,sobytherulesinTheorem5.1in[ 98 ],itisconvexaslongasthefunction(!,)7!`(!,s))]TJ /F3 11.955 Tf 12.68 0 Td[(isconvex.Thelatteristruewhen`(!,s)isconvexwithrespectto!.TheconvexityofthefunctionEX(!)canbeillustratedfromthefactthatminimizingofanextendedreal-valuedconvexfunctionof 34

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twovectorvariableswithrespecttooneofthesevariables,resultsinaconvexfunctionoftheremainingvariable[ 98 ]. AccordingtoTheorem 2.1 and 2.2 ,theSSPisnotnecessary,forthepurposeofdetermining!thatyieldstheminimumexpectedXlossforthegivenreward,toworkdirectlywiththefunctionEX(!),whichmaybetoodifculttodobecauseitsdenitioncontainsX(!),avaluewithtroublesomemathematicalproperties.Instead,theSSPcanoperateonthemuchsimplerexpression)]TJ /F6 7.97 Tf 6.78 -1.79 Td[((!,)withitsconvexityinthevariableandevenwithrespectto(!,). Moreover,theintegralin)]TJ /F6 7.97 Tf 6.77 -1.79 Td[((!,)canbeapproximatedbysamplingtheprobabilitydistributionofsaccordingtoitsdensityf(s)orbydirectlyusingthedatacollectedbyYinetal.in[ 9 ].Assumingthisproceduregeneratesacollectionofvectors(s1,s2,,sm),thenthecorrespondingapproximationto)]TJ /F6 7.97 Tf 6.77 -1.79 Td[((!,)canbewrittenas ~)]TJ /F6 7.97 Tf 6.77 -1.8 Td[((!,)=+1 m(1)]TJ /F3 11.955 Tf 11.95 0 Td[()mXk=1[`(!,sk))]TJ /F3 11.955 Tf 11.95 0 Td[(]+.(2) Since`(!,s)islinearw.r.t.!and)]TJ /F6 7.97 Tf 6.77 -1.79 Td[((!,)isconvex,thefunction~)]TJ /F6 7.97 Tf 6.77 -1.79 Td[((!,)isconvexandpiecewiselinear. 2.5OptimalBand-MixSelectionBasedontheExpectedXLoss BasedontheconceptoftheefcientOSAcurve,theSSPwillchoosetheproportionalcompositionoftheband-mix,!,tomaximizetheexpectedrewardforSUswithanexpectedXlossconstraint,ortominimizetheexpectedXlosswithanexpectedrewardconstraint,i.e., max!2W(!),EX(!),!2W(2) and min!2WEX(!),(!),!2W(2) 35

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Varyingtheparametersand,thetwoproblemsaboveareequivalentinthesensethattheyproducethesameefcientOSAcurves.Thus,wecanonlyworkonEquation( 2 ).Furthermore,wedemonstratethatthefunction)]TJ /F6 7.97 Tf 6.78 -1.79 Td[((!,)canbeusedinsteadofEX(!)inthisproblem. Theorem2.3. Thetworewardmaximizationproblemsbelow max!2W(!),EX(!),!2W(2) and max(,!)2WR(!),)]TJ /F6 7.97 Tf 31.74 -1.79 Td[((!,),!2W(2) areequivalentinthesensethattheirobjectivesachievethesamemaximumvalues. Proof. Themaximizationproblem max!2W(!),EX(!),!2W isthesameastheminimizationproblem min!2W)]TJ /F7 11.955 Tf 11.96 0 Td[((!),EX(!),!2W Meanwhile,themaximizationproblem max(,!)2WR(!),)]TJ /F6 7.97 Tf 31.74 -1.8 Td[((!,),!2W isthesameastheminimizationproblem min(,!)2WR)]TJ /F7 11.955 Tf 11.96 0 Td[((!),)]TJ /F6 7.97 Tf 31.75 -1.79 Td[((!,),!2W Therefore,toproveTheorem 2.3 isthesameasprovingthetwominimizationproblemsbelow min!2W)]TJ /F7 11.955 Tf 11.96 0 Td[((!),EX(!),!2W(2) 36

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and min(,!)2WR)]TJ /F7 11.955 Tf 11.96 0 Td[((!),)]TJ /F6 7.97 Tf 31.75 -1.8 Td[((!,),!2W(2) areequivalentinthesensethattheirobjectivesachievethesameminimumvalues. WithKuhn-Tacker(K-T)conditions11,thenecessaryandsufcientconditionsfortheproblemarestatedasfollows )]TJ /F7 11.955 Tf 9.3 0 Td[((!)+)]TJ /F6 7.97 Tf 6.78 -1.79 Td[((!,))]TJ /F7 11.955 Tf 21.92 0 Td[((!)+)]TJ /F6 7.97 Tf 6.78 -1.79 Td[((!,),()]TJ /F6 7.97 Tf 11.65 -1.8 Td[((!,))]TJ /F3 11.955 Tf 11.95 0 Td[()=0,0,!2W First,supposethat!isasolutiontotheprobleminEquation( 2 ).Letusshowthat(!,)isasolutiontotheprobleminEquation( 2 ).Usingnecessaryandsufcientconditions(K-Tconditions)andTheorem 2.1 ,wehave )]TJ /F7 11.955 Tf 9.3 0 Td[((!)+)]TJ /F6 7.97 Tf 6.77 -1.8 Td[((!,)=)]TJ /F7 11.955 Tf 9.3 0 Td[((!)+EX(!))]TJ /F7 11.955 Tf 21.92 0 Td[((!)+EX(!)=)]TJ /F7 11.955 Tf 9.3 0 Td[((!)+min2R)]TJ /F6 7.97 Tf 6.77 -1.79 Td[((!,))]TJ /F7 11.955 Tf 21.92 0 Td[((!)+)]TJ /F6 7.97 Tf 6.78 -1.79 Td[((!,), and ()]TJ /F6 7.97 Tf 11.65 -1.8 Td[((!,))]TJ /F3 11.955 Tf 11.96 0 Td[()=(EX(!))]TJ /F3 11.955 Tf 11.96 0 Td[()=0,0,!2W. Thus,K-Tconditionsaresatisedand(!,)isasolutiontotheprobleminEquation( 2 ). Now,letussupposethat(!,)achievestheminimumof)]TJ /F7 11.955 Tf 9.3 0 Td[((!)inEquation( 2 )and>0.Forxed!,thepointminimizesthefunction)]TJ /F7 11.955 Tf 9.29 0 Td[((!)+)]TJ /F6 7.97 Tf 6.77 -1.79 Td[((!,),and,consequently,thefunction)]TJ /F6 7.97 Tf 6.78 -1.79 Td[((!,).Since(!,)isasolutiontotheproblemin 11SeedetailsinTheorem2.5in[ 95 ]. 37

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Equation( 2 ),K-TconditionsandTheorem 2.1 implythat )]TJ /F7 11.955 Tf 9.3 0 Td[((!)+EX(!)=)]TJ /F7 11.955 Tf 9.3 0 Td[((!)+)]TJ /F6 7.97 Tf 6.78 -1.79 Td[((!,))]TJ /F7 11.955 Tf 21.92 0 Td[((!)+)]TJ /F6 7.97 Tf 6.77 -1.8 Td[((!,X(!))=)]TJ /F7 11.955 Tf 9.3 0 Td[((!)+EX(!), and (EX(!))]TJ /F3 11.955 Tf 11.95 0 Td[()=()]TJ /F6 7.97 Tf 11.65 -1.79 Td[((!,))]TJ /F3 11.955 Tf 11.96 0 Td[()=0,0,!2W. WeprovedthatK-Tconditionsaresatised,i.e.,!isasolutiontotheprobleminEquation( 2 ).Theorem 2.3 isproved. AsillustratedinSec. 2.4.3 ,thefunction)]TJ /F6 7.97 Tf 6.78 -1.79 Td[((!,)canbeapproximatedbythefunction~)]TJ /F6 7.97 Tf 6.77 -1.8 Td[((!,).Byusingdummyvariableszk,wherek=1,2,,m,thefunction~)]TJ /F6 7.97 Tf 6.77 -1.8 Td[((!,)canbereplacedbythelinearfunction+1 m(1)]TJ /F6 7.97 Tf 6.59 0 Td[()Pmk=1zkandthesetoflinearconstraints zk`(!,sk))]TJ /F3 11.955 Tf 11.95 0 Td[(,zk0,k=1,2,,m.(2) Belowwesummarizetheoptimalband-mixselectionproblemforOSAdescribedinthissection. max(,!)2WRrnXi=1E[si]!i,(2) s.t. +1 m(1)]TJ /F3 11.955 Tf 11.96 0 Td[()mXk=1zk, zk`(!,sk))]TJ /F3 11.955 Tf 11.95 0 Td[(,zk0,k=1,2,,m, !ii,i=1,,n, where!iiindicatesthattheSSPwouldnotdistributetrafconabandsimorethanagivenpercentioftheoveralltrafcdemandsfromSUs.Thisconstraintcanberelaxedbysettingi=1ifthereisnolimitationfortheproportionalcompositionoftheband-mixselectedforOSA. 38

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BysolvingprobleminEquation( 2 )withlinearprogramming,theSSPattainstheoptimalvector!andthecorrespondingmaximumexpectedrewardforSUs,whichequalsE[s]!.BysolvingproblemaboveforthedifferentlevelsoftheexpectedXlossthattheSSPcansuffer,,theSSPobtainstheefcientOSAcurvefortheband-mixselection. 2.6PerformanceAnalysis Bycarryingoutnumericalsimulations,inthissection,wefurtherdemonstratetheband-mixselectionproblemwiththeriskatdifferentcondencelevelsforOSA,wheretheriskisevaluatedbytheXlossortheexpectedXloss.WithoutthespecicutilityfunctionoftheSSP,webuilduptheefcientOSAcurvesontheReward-Riskplane,andanalyzethedifferencesbetweenefcientOSAcurvesbasedontheXlossandthosebasedontheexpectedXloss.Moreover,withtheSSP'sspeciedutilityfunctions,wecomparetheexpectedXlossbasedband-mixselectionwiththeXlossbasedband-mixselectionandthemaximumexpectedrewardbasedband-mixselection[ 85 88 126 ]intermsofthespectrumutilization,theSUs'satisfactionaswellastheprotoftheSSP. 2.6.1SimulationSetup WesetupthesimulationwithasimilarsettingtothatshowninFig. 2-1 ,wherethenumberofspectrumbandsfromPSPswithintherangeoftheSSPis6,andtheSSP,operatingasthetradingagentforSUs,selectsthemixofbandsfortrafcdelivering.Forillustrativepurpose,weassumetheoveralltrafcdemandfromSUsisequalto1,andtheSSP'srewardforsatisfyingoneunitoftrafc,r,isequalto120.AsfortheuncertainspectrumsupplyfromPSPs,werepresentitbyarandomvectors=(s1,s2,,sn),wheresi2[0,1]isarandomvariable.Moreover,weassumethepriceofthebandifromPSPs,pi,whichisascendingasE(si)increases,isintherangeof[80,130],fori=(1,2,,6).Basedonthetworiskmetricsinthischapter,i.e.,theXlossandthe 39

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expectedXloss,wecarryouttheband-mixselectionoptimizationwithcondencelevel=0.7,0.8and0.9,respectively12. Meanwhile,accordingtotheanalysisin[ 9 46 ],thedistributionoftheunpredictableprimaryservices,si,iseitherthin-tailedorfat-tailed.Asweknow,manytypesofdistributioncanbecategorizedasthin-taileddistribution,e.g.,normaldistribution,exponentialdistribution,etc.,andseveraltypesofdistributioncanberegardedasfat-taileddistribution,e.g.,log-normaldistribution,Cauchydistribution,etc.[ 5 24 ].Withoutlossofgenerality,weletsibenormallydistributedtorepresenttheunpredictableprimarytrafcwithathintailintherstsimulationscenario,andletsibelog-normallydistributedtorepresenttheunpredictableprimarytrafcwithafattailinthesecondone13,whiletheotherparametersarethesameinthetwosimulationscenarios. 2.6.2ConstructionofEfcientOSACurves InFig. 2-3A ,theXlossbasedefcientOSAcurvesforband-mixselectionandtheexpectedXlossbasedonesoverlapatdifferentcondencelevels,whichisnotsurprisingtoseebecausesiisnormallydistributed.AlittlemorethoughtisenoughtounderstandthatintheGaussianworldeverythingisproportionaltothestandarddeviation,whichinturnissubadditive.Therefore,whensihasnormaldistribution,theXlossissubadditive,andthereisnodifferencebetweentheefcientOSAcurveswithXlossandthosewiththeexpectedXloss.Inaddition,itshouldbenotedthattheriskforOSAbecomeslargerwiththeincreasingoftheSSP'scondencelevelsinageneralsense. 12Itdoesnotmakesenseforsimulationswith0.5,becauseitisthesameasguessing.13ByMonteCarlosimulations,thedistributionoftheprimaryservicescanbettedfromthedatacollected/sampled,asconductedin[ 9 ]. 40

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AEfcientOSAcurveswithdifferentcondencelev-els(siisnormallydistributed,andn=6.). BEfcientOSAcurveswithdifferentcondencelev-els(siislog-normallydistributed,andn=6.). Figure2-3. Optimalband-mixselectionforOSAbasedontheXlossandtheexpectedXloss. Withtheassumptionthattheprobabilitydistributionoftheuncertainspectrumsupplyislog-normal,theXlossbasedefcientOSAcurvesandtheexpectedXlossbasedonesarecomparedatdifferentcondencelevelsasdepictedinFig. 2-3B .Wendthatwithagiven,theXlossbasedefcientOSAcurvesforband-mixselectionseverelyunderestimatethepotentialriskforOSA,andmaketheSUsmoreliabletobeaffectedbytheunpredictableactivitiesofprimaryservices.Onthecontrary,the 41

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Table2-3. Utilityfunctionswithriskatdifferentcondencelevels. IndexUtilityFunctionRiskMetricCondenceLevel 1(!)+X(!)X(!)=0.702(!)+EX(!)EX(!)=0.703(!)+X(!)X(!)=0.804(!)+EX(!)EX(!)=0.805(!)+X(!)X(!)=0.906(!)+EX(!)EX(!)=0.90 expectedXlossbasedefcientOSAcurvesperformbetterinevaluatingtheriskforOSA,andprovidemoreaccurateguidefortheSSPwithvariouslevelsofrisktolerance. 2.6.3PerformanceComparison Inordertoselectaparticularband-mixforOSAbasedontheXlossortheexpectedXloss,itisnecessarytopresenttheutilityfunctionoftheSSPasabondbetweentheexpectedrewardoftheSSPandthepotentialriskforOSA,otherwiseitwillbedifcultfortheSSPtomakeachoiceamongtheband-mixesontheefcientOSAcurves.Thus,weadoptawidelyusedutilityfunction[ 49 106 107 ]andlistafewofitsvariationswiththetworiskmetricsatdifferentcondencelevelsinTab. 2-3 .Here,representstherisktolerancelevelsoftheSSPfortheOSA.Thevalueofisassumedtobewithintherangeof[,0],where=indicatesthattheSSPisextremelyrisk-averseandtheSSPwillneverbuythespectrumbandfromPSPs,and=0indicatesthattheSSPhasnoconcernabouttheriskforOSAandonlycaresaboutthemaximumexpectedreward.Usingtheseutilityfunctions,weletthenumberofavailablespectrumbandsofPSPsincrease14from1to6,andcomparetheXlossbasedband-mixselectionschemewiththeexpectedXlossbasedoneforopportunisticaccessingintermsofspectrumutilization,SUs'satisfactionandtheSSP'sprot. 14Inthesimulation,weassumethatthepriceofthebandandthecorrespondingriskforOSAincreasewiththeindexofthebands,e.g.,Band1isthecheapestband,andBand6isthemostexpensiveone. 42

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SincetheXlossbasedefcientOSAcurvesandtheexpectedXlossbasedefcientOSAcurvesoverlapforthenormallydistributedtrafcoftheprimaryservices,itisobviousthattheXlossbasedband-mixselectionschemeandtheexpectedXlossbasedonewillproducethesameperformance,providedthattheirutilityfunctionshavethesameparametersintherstscenario.Therefore,wejustneedtocomparetheperformanceoftheXlossbasedband-mixselectionschemeandtheexpectedXlossbasedoneinthesecondscenario,wherethedistributionoftheprimaryserviceshasafattail.Forillustrativepurposes,wecarryouttheperformancecomparisonwith=)]TJ /F7 11.955 Tf 9.3 0 Td[(0.6and=)]TJ /F7 11.955 Tf 9.3 0 Td[(1.4,respectively. InFig. 2-4A andFig. 2-5A ,weevaluatetheperformanceofspectrumutilizationwiththeXlossbasedband-mixselectionandtheexpectedXlossbasedband-mixselection.Notethatspectrumutilizationiscalculatedastheratiooftheutilizedbandstothetotalbands.Nomattertheportionofabandisusedbytheprimaryservicesorusedbythesecondaryservices,thisportionofspectrumbandshouldbeconsideredasutilized.ItisnotsurprisingtoseethattheperformanceofthemaximumexpectedrewardbasedbandselectionisworstsinceithasnoconsiderationabouttheriskandalwaysmakestheSSPswarmallthetrafconthemostriskybandfromthePSPsforOSA.Ontheotherhand,alltheband-mixselectionschemessupporttrafcsplittingonamixofbandstoreducetheriskforOSA,sothattheyaresuperiortothemaximumexpectedrewardbasedone. Amongtheband-mixselectionschemes,wendthattheexpectedXlossbasedband-mixselectionoutperformstheXlossbasedband-mixselection.Thereasonisthatwhentheprimarytrafchasafat-taileddistribution,theXlossbasedband-mixselectionoftenunderestimatestheriskforOSAandcausestheSSPmoreliabletobeaffectedbythereturningoftheprimaryservices;ontheotherhand,theexpectedXlossbasedband-mixselectionmakesmuchmoreaccurateestimationforthepotentialriskforOSAandhelpstheSSPtotakebetteruseoftheunoccupiedspectrumbandsfromPSPs. 43

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ASpectrumutilization(=)]TJ /F23 9.963 Tf 7.75 0 Td[(0.6) BSUs'satisfaction(=)]TJ /F23 9.963 Tf 7.75 0 Td[(0.6) CTheSSP'sprot(=)]TJ /F23 9.963 Tf 7.75 0 Td[(0.6) Figure2-4. Performancecomparisonofband-mixselectionschemeswithtworiskmetricsatdifferentcondencelevels(=)]TJ /F7 11.955 Tf 9.3 0 Td[(0.6) 44

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ASpectrumutilization(=)]TJ /F23 9.963 Tf 7.75 0 Td[(1.4) BSUs'satisfaction(=)]TJ /F23 9.963 Tf 7.75 0 Td[(1.4) CTheSSP'sprot(=)]TJ /F23 9.963 Tf 7.75 0 Td[(1.4) Figure2-5. Performancecomparisonofband-mixselectionschemeswithtworiskmetricsatdifferentcondencelevels(=)]TJ /F7 11.955 Tf 9.3 0 Td[(1.4) 45

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Besides,thespectrumutilizationratiooftheband-mixselectionwithriskforOSAathighercondencelevelsisgenerallybetterthanthatoftheband-mixselectionwithriskforOSAatlowercondencelevels.However,sometimesthedifferenceisnotsodistinct,becauseifthecondencelevelishigh,thatband-mixselectionschememaybeconservativefortheestimationofriskforOSA,e.g.,thespectrumutilizationratiooftheband-mixselectionwith=0.8andthatoftheband-mixselectionwith=0.9arecloseasshowninFig. 2-4A andFig. 2-5A SimilaranalysisalsoappliestotheSUs'satisfactionaswellastheSSP'sprot.SUs'satisfactionisdenedtobetheratioofsatisedtrafcdemandstooveralltrafcdemandsoftheSUs.Comparedwithband-mixbasedselectionforOSA,themaximumexpectedrewardbasedbandselectionisnotgoodenough.WiththeincreasingofthenumberofbandsavailablefromPSPs,itsperformanceevendegradestosomeextent,sincethereemergemoreriskybandswhentherearemorebandsforselection.TheSUs'satisfactorydegreeoftheXlossbasedband-mixselectionislowerthanthatoftheexpectedXlossbasedband-mixselectionduetothedistributiontypeoftheprimaryservices,especiallywhenthespectrumsupplyfromPSPsislimitedforthetrafcdemandsofsecondaryservicesasshowninFig. 2-4B andFig. 2-5B Fig. 2-4C andFig. 2-5C describetheperformancecomparisonofdifferentbandselectionschemesintermsoftheSSP'sprot,whichisdenedasthedifferencebetweentheSSP'srewardanditspaymentforspectrumpurchasingfromthePSPs.IftheSSPadoptsthemaximumexpectedrewardbasedbandselection,italwayshasnegativeprotforthetrafcdistributedonthatbandbecauseoftheunexpectedreturningofprimaryservices.AlthoughtheSSPplaytheroleoftradingagentforSUswiththegoalofsatisfyingasmuchdemandsoftheSUsaspossibleratherthanmaximizinghisprotasillustratedinSec. 2.2.1 ,negativeprotwilldiscouragetheSSPandreducetheSSP'sincentivefortradingspectrumwiththePSPs.Bycontrast,asshowninFig. 2-4C andFig. 2-5C ,theSSP'sprotisgenerallybetterwhenthe 46

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SSPtakestheband-mixselectionschemes,amongwhichtheexpectedXlossbasedband-mixselectionhasthebestperformanceinviewofitsaccurateriskestimationforOSA. 2.7ChapterSummary ConsideringtheuncertainspectrumsupplyfromthePSPs,inthischapter,werstintroduceanintuitivemethod,theXloss,toquantifytheriskforSUsatagivencondentlevel.SincetheXlosstheoreticallyunderestimatesthepotentialriskforOSAandmathematicallylacksofsubadditivity,wefurtherproposetheexpectedXloss,amoresuitableriskmeasurementforOSAwithdesiredproperties.BasedonthesimpliedexpectedXloss,weformulatetheSSP'sband-mixselectionfortrafcsplittingintoanoptimizationproblemandsolveitbylinearprogramming.Bynumericalsimulations,weshowthatcomparedwiththeXlossbasedband-mixselectionforOSA,theexpectedXlossbasedselectionnotonlyprovidesmuchmoreaccurateefcientOSAcurvesatdifferentcondencelevels,butalsogivesmuchbetterperformanceintermsofspectrumutilization,SUs'satisfactionandtheSSP'sprot,especiallywhenthedistributionoftheprimaryserviceshasafattail. 47

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CHAPTER3SPECTRUMHARVESTINGANDSHARINGINMULTI-HOPCRNSUNDERUNCERTAINSPECTRUMSUPPLY 3.1ChapterOverview Recentyearshaswitnessedtheboostinggrowthofwirelessnetworksandourishofvariouswirelessservices.Inparallelwiththat,currentstaticspectrumallocationpolicyofFederalCommunicationsCommission(FCC)[ 3 20 73 ]resultsintheexhaustionofavailablespectrum,whilealotoflicensedspectrumbandsareextremelyunder-utilized.Experimentaltestsinacademia[ 9 72 ]andmeasurementsconductedinindustries[ 70 71 ]bothshowthatmanylicensedspectrumblocksarenotusedincertaingeographicalareasandareidlemostofthetime.EveninthemostcrowdedareaneardowntownWashington,DC,wherebothgovernmentandcommercialspectrumuseisintensive,only38%ofthelicensedspectrumremainsoccupiedandtherestofspectrumresource(a.k.a.,whitespace/spectrumhole)iswasted.ThesestatisticsandstudiesspurtheFCCtoopenuplicensedspectrumbandsandpursuenewinnovativetechnologiestoencouragedynamicuseoftheunder-utilizedspectrum[ 20 ]. Asoneofthemostpromisingsolutions,cognitiveradio(CR)technologyreleasesthespectrumfromshacklesofauthorizedlicenses,andallowsopportunisticusageofthevacantlicensedspectrumbandsineithertemporalorspatialdomain.Duetothepotentialofgreatlyimprovingthespectrumutilization,CRtechnologypromotesnumerouspossibleapplicationsinvariousareas,e.g.,militarycommunications,publicsafety,disasterrelief,searchandrescue,environmentmonitoring,etc. However,toopportunisticallyaccesstothelicensedbands,CRdeviceshavetobefrequency-agile[ 73 97 ].ItisimperativefortheCRdevicestohavethecapabilityofexploringlicensedspectrumbands,reconguringRF,switchingfrequenciesacrossawidespectrumrange(i.e.,from20MHzto2.5GHz[ 14 97 110 ]),sendingandreceivingpacketsovernon-contiguousspectrumbands,etc.Althoughsomeofthedesiredfeaturesmayberealizedinfuture,enormousamountoftimeandeffortsmustbe 48

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AToytopologywithonesession. BTheprobabilitydensityfunctionsofavailablebandwidthforband1andband2. CToytopologywithtwosessions. Figure3-1. SimpleexamplesforCRsessionsunderuncertainspectrumsupplyinCRNs. spentinhardwaredesignsandsignalprocessinginordertoimplementthesefeaturesinlightweightradios[ 73 97 110 122 ].Inaddition,toattractcustomersforanynewtechnologies,thereisnoreasontoenforcetheuserstoreplacetheircommunicationdevicesortoincreasethecomplexityonthecustomers'side.Forcognitiveradionetworks(CRNs),itisalwaysagoodideatominimizethechangesonthehandsetsofsecondaryusers(SUs)whilemaximizingthespectralefciency.Thus,itmaybemoreviabletodesignanewarchitectureofnetworkstoeffectivelyharvestwhitespacewhileminimizingthecomplexityofSUs. Anotherkeyobstacletotheemploymentofmulti-hopCRNsliesintheuncertainlicensedspectrumsupply[ 3 19 73 ].SincetheCRservicesmustevacuatethelicensedbandswhenprimaryservicesareactive,thereturningofprimaryserviceshassignicantimpactonhowtoperformopportunisticspectrumaccessing(OSA),schedulingandinterferenceavoidance,andmulti-hopmulti-pathroutinginCRNs. 49

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State-of-the-artworkoninvestigatingtheunpredictableactivitiesofprimaryservicescangenerallybeclassiedintotwocategories:i)spectrumsensingandii)statisticalanalysisofthecollected/historicalspectrumvacancy/occupancydata. Inspiteoftheoverwhelmingwasteofsensingtimewhichcanbeusedformoretrafcdelivery,individualsensingistrappedbysensingaccuracysincebothfalsealarmprobabilityandmissingdetectionprobabilityarereallyhigh.Toovercometheweaknessofindividualsensing,cooperativesensingisproposedtoimprovethesensingaccuracybygroupingCRdevicestosensetogetherandshareinformationamongthegroup.ButthetroubleisthatitistoodifculttosynchronizetheCRdevicesinthegroupsensingsimultaneously.Inaddition,cooperativesensinghastosetupacommonchannelforinformationexchange,whichwillincurenormouscommunicationoverhead.Ontheotherhand,in[ 9 70 71 ],researchersaswellasengineerstrytoidentifythespectrumsupplyforOSAwiththestatisticsoflicensedspectrumutilizationratherthanattemptingtodetecttheactivitiesofprimaryservices.Theyhavecarriedoutspectrummeasurements,collectedandanalyzedthedataaboutspectrumutilization,andsummarizedthestatisticalcharacteristicsofthebandvacancy/occupancyindetails.ThesestatisticalresultscontainabundantinformationabouttheactivitiesofprimaryservicesandprovideaniceguidetotheCRdevicesforOSA. Resortingtothelatterapproachdealingwiththeunpredictablereturningofprimaryservices,inthischapter,westudythespectrumharvestingandsharingproblemformulti-hopCRNsunderuncertainspectrumsupply.Toeffectivelyharvestandsharetheunder-utilizedlicensedspectrum,weintroduceanewemergingserviceprovider,calledSecondaryServiceProvider(SSP).SupposethattheSSPhasitsownbands(i.e.,basicbands)andisabletocollectivelyharvesttheavailablelicensedbands.InordertofacilitatetheaccessingofSUswithoutCRcapability,weassumetheSSPhas 50

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alreadyestablishedsomepartialinfrastructurewithCRmeshrouters1atlowcosttoprovidecoverageintheareaofinterest.ThoseCRmeshroutershaveCRcapabilityandareequippedwithmultipleCRradios.SUscancooperatewithCRroutersforpacketdelivery.UndertheguidanceoftheSSP,SUsaccesstheirnearbyCRmeshroutersusingbasicbandsanddeliverpacketsviaCRmeshroutersusingbothbasicbandsandharvestedbands.InsuchaCRN,morespectrumreuseopportunitiescanbecreatedandthenetworkcapacitycanbeincreased. Asforspectrumsharing,wefocusonthejointfrequencyschedulingandroutingproblemamongCRmeshroutersinmulti-hopCRNs.SupposethatCRmeshrouterscollecttrafcfromendusers/SUsandformasetofCRsessions,eachofwhichischaracterizedbyapairofsourceanddestinationCRroutersandhasacertainraterequirement.TheSSPmayaskaninterestingquestion:howmuchbandwidthisatleastrequiredtomaintaintheseCRsessionsconsideringtheavailabilityofspectrumresourcesatacertaincondencelevelw.r.t.alltheconstraintsfrommultiplelayersinCRNs.Toputitinanotherway,inthischapter,wearetryingtoaddresshowtheSSPperformsOSA,frequencyschedulingandmulti-hopmulti-pathroutingsothattherequirednetwork-widespectrumresourceisminimized2,giventhefactthatthelicensedspectrumsupplycannotbeguaranteed. Inspiredbythestatisticsofspectrumbandsobtainedonobservationandexperimentsin[ 9 ]3,[ 70 71 ],wenovellymodeltheuncertainspectrumvacancyofalicensedband 1Intherestofthischapter,weusethewordsCRrouter/CRmeshrouter/routerinterchangeably.2Wefollowthesameobjectiveasthatin[ 42 43 ],wheretheso-calledspace-bandwidthproductdenedin[ 68 ]isadoptedastheperformancemetricinthesettingofmulti-hopCRNs.3Chenetal.in[ 9 ]carriedoutasetofspectrummeasurementsinthe20MHzto3GHzspectrumbandsat4locationsconcurrentlyinGuangdongprovinceofChina.Theyusedthesedatasetstoconductasetofdetailedanalysisaboutthestatisticsofthecollected 51

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(i.e.,availablebandwidthforOSA)asarandomvariablesatisfyingcertaindistribution.ThismodelingexplicitlydistinguishesthejointroutingandfrequencyschedulingprobleminCRNsfromthatinsingle-channelsingle-radionetworks[ 10 63 64 131 ]ormulti-channelmulti-radionetworks[ 4 18 45 53 57 61 115 ].Thereasonisthatinthosenetworks,thebandwidthisalwaysregardedasaconstantvalue.Evencomparedwithpriorworkintheliteratureofmulti-hopCRNs[ 23 42 43 114 ],theuniquefeatureofuncertainspectrumsupplymakestherouteselectionandschedulinginthischaptermuchmorechallengingaswell. Forexample,supposethereisatoyCRNconsistingof4CRmeshroutersand3bandsavailableforOSA.ThesourceCRroutercanchooseeithertherouteS-A-DortherouteS-B-DtodelivertrafcasshowninFig. 3-1A .Moreover,assumetheavailablebandwidthofBand1isnormallydistributedwithN(9,6),theavailablebandwidthofBand2isuniformlydistributedwithU(7,11),andBand3isnotthebottleneckfortrafcdelivery.AninterestingquestionforthesourceCRrouteriswhichrouteisbetter.Theanswerisnotstraight-forwardwhenthevacantbandwidthofBand1andthatofBand2arerepresentedbyrandomvariables.Anintuitivesolutionistoevaluatetheexpectedvalueoftheavailablebandwidth,i.e.,tomeasurewhichbandcansupportlargerowrateoraccommodatemoreowsonaverage4.Inthiscase,considertheprobabilitydensityfunctions(PDF)ofbandwidthforthetwobands,eachrandomvariablehasanexpectedvalueof9asshowninFig. 3-1B ,whichmakestherstorderstatisticsbasedrouteselectionimplausible.Furthermore,considerthetoytopologywithtwosessionsinFig. 3-1C .ProvidedthatallthoselicensedbandsofferuncertainspectrumsupplytoCR data,includingchanneloccupancy/vacancystatistics,channelutilization,alsospectralandspatialcorrelationofthesemeasures.4TheavailablebandwidthforOSAcandirectlybeinterpretedintolinkcapacityusingShannon-HartleytheoremasillustratedinSec. 5.3.3.2 52

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routers,wemustidentifyhowtocalculatethesumofrandomvariablefortheschedulingandrouting,whichmakesthisprobleminCRNsevenmorecomplex. Althoughwehavedevotedsomeeffortstoanalyzingthisproblemin[ 88 ],thereisalackofasolidsystemarchitecturetosupportourtheoreticalstudy.Meanwhile,requirementsofCRcapabilityareimposedonSUs'handsets,sincethereisnocooperationbetweenSUsandCRroutersforpacketdelivery. WithintheproposedarchitectureofCRNs,weexploitapairof(,)parameterstocharacterizetheSSP'sconcernsabouttheCRNsandmathematicallyformulatethejointfrequencyschedulingandroutingproblem.Specically,denotesthetargetedcondencelevelfortheavailabilityoftherequirednetwork-widespectrumresource,anddenotesthetargetedqualityofCRcommunications.Besides,wedemonstrateconstraintsfrommultiplelayersunderthesituationthatspectrumsupplyisuncertain.Inparticular,wepayspecialattentiontomodelingtheunpredictableactivitiesofprimaryservices,schedulingandinterferencemodels,andmulti-pathroutingconstraints.Wealsodwellonhowtointegratethebandwidthofdifferentbandsandcalculatethesumoflinkcapacity,whenthevacantbandwidthofeverylicensedbandisarandomvariable.Weformulateanoptimizationproblemwiththeobjectiveofminimizingtherequirednetwork-widespectrumresourceatan(,)level. Foraxedpairof(,),theformulatedoptimizationproblemfallsintoamixedintegernon-linearprogrammingandisprovedtobeNP-hard[ 29 ].Aimingtoderiveafeasiblesolution,wepresentasub-optimalalgorithmfortheNP-hardoptimization.Werstndalowerboundfortheobjectivebyrelaxingtheintegervariablesinschedulingandinterferenceconstraints.Then,weproposeacoarse-grainedxingalgorithmtoiterativelydeterminebinaryintegervariablesexploitingathreshold,wherethebandwidthintegrationandthesumoflinkcapacityfromdifferentbandsarecomputedusingdiscreteFouriertransform(DFT)andinversediscreteFouriertransform(IDFT).Aslongasxingalltheintegervariables,wecandetermineowroutingvariablesandsolvethe 53

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optimizationproblem.Sincethesolutionsattainedbythecoarse-grainedxingalgorithmisanupperboundfortheoptimizationobjective,wecompareitwiththelowerboundwehavedevelopedearlier.Simulationresultsshowthat(i)theproposedcoarse-grainedxingalgorithmisnear-optimalforany(,)level;(ii)comparedwiththeexpectedbandwidthbasedsolution,the(,)basedonehasbetterperformanceinthesensethatitlowersdowntheblockingratioofCRsessionsandimprovesthespectrumutilization. Therestofthischapterisorganizedasfollows.InSection 6.3 ,weproposeanovelarchitectureforspectrumharvestingandsharing,introducethemodelofspectrumuncertaintyandpresentotherrelatedmodelsinCRNs.InSection 3.3 ,wemathematicallydescribeschedulingandinterferenceconstraintsandmulti-hopmulti-pathroutinginCRNs.InSection 3.4 ,Weillustratethebandwidthintegration,denebandwidthrequiredat,andformulatejointroutingandschedulingasanNP-hardoptimizationproblem.Besides,wendalowerboundforthisoptimizationproblem.InSection 3.5 ,wedevelopacoarse-grainedalgorithmforasub-optimalsolution.Finally,weconductsimulationsandanalyzetheperformanceresultsinSection 6.7 ,anddrawconcludingremarksinSection 6.8 3.2NetworkModel 3.2.1SpectrumHarvestingandOpportunisticSpectrumAccessing Weconsideranovelmulti-hopCRNconsistingoftheSSP,agroupofSUs,N=f1,2,,n,,NgCRmeshroutersandasetofavailablelicensedspectrumbands5withunequalsizeofbandwidthsasshowninFig. 5-1A .TheSSPisanindependentwirelessserviceproviderwithitsownspectrum,i.e.,theSSP'sbasicbands(potentiallycongestedalready),andisabletocollectivelyharvesttheavailablelicensed 5Takingtheleast-utilizedspectrumbandsintroducedin[ 43 ][19]forexample,wefoundthatthebandwidthbetween[1240,1300]MHz(allocatedtoamateurradio)is60MHz,whilebandwidthbetween[1525,1710]MHz(allocatedtomobilesatellites,GPSsystems,andmeteorologicalapplications)is185MHz. 54

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Figure3-2. Anovelarchitectureforspectrumharvestingandsharingunderuncertainspectrumsupplyinmulti-hopCRNs. bands.TheSSPhasalsodeployedsomeCRmeshroutersatlowcosttofacilitatetheaccessingofSUs.SUsarejustend-usersnotsubscribedtoprimaryservices.NospecicrequirementsareimposedontheSUs'communicationdevices.Theycouldbeanydevicesusinganyaccessingtechnologies(e.g.laptopsordesktopcomputersusingWi-Fi,cellphonesusingGSM/GPRS,smartphonesusing3G/4G/NxtGaccessingtechnology,etc.).SUscanaccesstothebasicbandsownedbytheSSP,buttheycannotbetunedtotheharvestedlicensedfrequency.TheCRmeshroutersdeployedbytheSSPhaveCRcapabilityandareequippedwithmultipleCRradios. UndertheguidanceoftheSSP,SUsandCRmeshrouterscooperatewitheachotherforpacketdelivery.Specically,themobileSUsreporttheironlinetrafcrequeststotheirnearbyCRmeshroutersviabasicbands.ThexedCRmeshrouterscollecttrafcdemandsfromdifferentend-users,formuni-castCRcommunicationsessions,anddeliverpacketsusingboththeleftoverbasicbandsandharvestedbands.Forbetternetworkcapacity,reuseoftheSSP'sbasicspectrumandsharingoftheharvestedspectrum,theSSPcoordinatesthoseCRmeshroutersandjointlyconductsfrequencyschedulingandowroutingamongthemasshowninFig. 5-1A SupposethereareasetofLuni-castcommunicationsessionsamongtheseCRmeshrouters.Lets(l)/d(l)denotethesource/destinationCRrouterofsession 55

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l2L,andr(l)betheraterequirementofsessionl.AssumetheSUs'usageofbasicbandsinthemulti-hopCRNsisaprioriinformation.TheCRroutersareabletousetherestofbasicspectrumownedbytheSSP.TheCRroutersarealsoallowedtocommunicatewitheachotherbyopportunisticallyaccessingtothelicensedbandswhentheprimaryservicesarenotactive,buttheymustevacuatefromthesebandsimmediatelywhenprimaryservicesbecomeactive.ConsideringthegeographicallocationoftheCRrouters,theavailablespectrumbandsatoneCRroutermaybedifferentfromanotheroneinthenetwork.Toputitinamathematicalway,letM=f1,2,,m,MgbethebandsetincludingtheavailablebasicbandsandlicensedbandsforCRcommunications,andMiMrepresentthesetofavailablebandsatCRmeshrouteri2N.MimaybedifferentfromMj,wherejisnotequaltoi,andj2N,i.e.,possiblyMi6=Mj. 3.2.2ModelingofUncertainSpectrumSupply TheuniquefeatureofCRNsistheuncertainspectrumsupplyfromlicensedbands,orsay,theunpredictablebandwidthoccupancyofprimaryservices.TomodelthiskeyfeatureofCRNs,wemakeWmdenotetheunoccupiedbandwidthoftheavailablebandm2M,whereWmisarandomvariableconsideringtheunpredictableactivitiesofprimaryservices.Notethatforanavailablebasicband,theunoccupiedbandwidthisaconstantandthetransmissionsofCRroutersoverthisbandarenotaffectedbyprimaryservicesbecausethebasicbandbelongstotheSSP.However,inprobabilitytheory,aconstantcanberegardedasaspecialrandomvariablethattakesaconstantvalue,regardlessofanyeventthatoccurs[ 22 89 ].Therefore,themodelingofWmasarandomvariableisapplicablenotonlytotheavailablelicensedbandsbutalsototheavailablebasicbandsforCRcommunications. Generallyspeaking,people[ 85 111 ]wouldliketouseE(Wm),therstorderstatisticsofWm[ 9 ]topredictthewhitespaceasshowninFig. 6-2 .Althoughthismeasurementisintuitiveandeasytoquantify,itignoressomuchsignicantinformation 56

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w.r.t.theactivitiesofprimaryservicesthatitmayleadtothefailureoftrafcdeliverybetweenCRroutersasdepictedinthezoomed-inpictureofFig. 6-2 .ItshouldbenotedthatthestatisticalcharacteristicsofWmcontainabundantknowledgeabouttheavailablebandwidthofbandmforCRrouters'opportunisticaccessing.Forexample,assumeWmisnormallydistributedwithE(Wm)=2andWm=1,i.e.,WmsN(2,12).Then,theprobabilitythatWm3isequalto84.1%. 3.2.3OtherRelatedModels 3.2.3.1TransmissionRangeandInterferenceRange SupposeallCRmeshroutersusethesamepowerfortransmission,andthepowerspectraldensityfromthetransmitterisQ.Awidelyusedmodel[ 23 33 43 ]forpowerpropagationgainis gij=d)]TJ /F12 7.97 Tf 6.59 0 Td[(nij, (3) wherenisthepathlossfactor,isanantennarelatedconstant,anddijisthedistancebetweenCRroutersiandj.WeassumethatthedatatransmissionissuccessfulonlyifthereceivedpowerspectraldensityatthereceiverexceedsathresholdQT.Meanwhile,weassumeinterferencebecomesnon-negligibleonlyifitproducesapowerspectraldensityoverathresholdofQIatthereceiver.Thus,thetransmissionrangeforaCRrouterisRT=(Q=QT)1=n,whichcomesfrom(RT))]TJ /F12 7.97 Tf 6.59 0 Td[(nQ=QT.Similarly,basedontheinterferencethresholdQI(QIRTsinceQI
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Figure3-3. AschematicillustratingavailablebandwidthforOSAandunpredictableoccupationofprimaryservicesinCRNs. whereistheambientGaussiannoisedensity.Asweknow,tomathematicallymodelthelinkcapacityisimperativeinthesensethattheaggregateowratesoneachradiolinkcanneverexceedthislink'scapacity,whichisanimportantconstraintforrouting.Differentfrommodelingoflinkcapacityintheotherwirelessnetworks[ 64 111 ]orinexistingliterature[ 43 108 ],wearealsoawarethatcmijisnotaxednumberbutarandomvariablesincetheavailablebandwidthWmisuncertaininCRNs.Besides,notethatthedenominatorinsidethelogfunctioncontainsonly.Thisisbecauseofoneofourinterferenceconstraints,i.e.,whenCRrouteriistransmittingtoCRrouterjonbandm,thenalltheotherneighborsofrouterjwithinitsinterferencerangeareprohibitedfromusingthisband.Wewilladdresstheinterferenceconstraintsindetailsinthefollowingsection. 3.3FrequencySchedulingandRoutingConstraintsforOpportunisticAccessing 3.3.1SchedulingandInterferenceConstraints Schedulingcanbeconductedintimedomain,infrequencydomain,orinbothofthem.Inthischapter,weonlyfocusonfrequencybasedbandassignment,i.e.,howtoassignbandsataCRmeshrouterfortransmissionandreception.Aplausibleschedulingonfrequencybandsmustconsiderthelimitationsatthetransmittersideandguaranteenointerferenceatthereceiverside. 58

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Assumebandmisavailableatbothrouteriandrouterj,i.e.,m2MiTMj.Wedenote smij=8>>>><>>>>:1Ifrouteritransmitsdatatorouterjonbandm,0otherwise. (3) Forarouteri2Nandabandm2Mi,denoteTmithesetofCRroutersthatcanalsoopportunisticallyaccesstobandmandarewithinthetransmissionrangetorouteri,i.e., Tmi=fj:dijRT,j6=i,m2Mjg. (3) Fromtheviewofthetransmitter,CRrouteriisnotabletotransmittomultipleroutersonthesamefrequencyband.Thus,wehave Xq2Tmismiq1. (3) Fromtheviewofthereceiver,aCRroutercannotusethesamefrequencybandfortransmissionandreception6,duetoself-interferenceatthephysicallayer.Thatis,ifsmij=1,thenforanyq2Tmj,smjqmustbe0,i.e., smij+Xq2Tmjsmjq1. (3) Notethatin( 3 ),wearereferringtoaspecicrouterjtowhichrouteriistransmitting.Ifsmij=1,thenPq2Tmjsmjq=0,i.e.,CRrouterjisnotabletousethesamefrequencybandmfortransmission.Ontheotherhand,ifsmij=0,thenPq2Tmjsmjq1,i.e.,router 6Thislimitationappliestoboththetransmitterandreceiver.Thereasontocategorizeitintotheconstraintsofthereceiverisfortheeaseofwritingintherestofthischapter.Also,asforthisconstraint,therolesoftransmitterandreceiveraresymmetricandinterchangeable. 59

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jmayusebandmfortransmission,butcanonlyuseitforonereceivingrouterq2Tmj,whichisthesameasin( 3 ). Beyondtheconstraintsaboveatthereceiver,therearealsointerferenceconstraintsfromtheotherCRroutersinCRNs.Tobespecic,forafrequencybandm,ifCRrouteriusesthisbandfortransmittingdatatoaCRrouterj2Tmi,thenanyotherroutersthatmayproduceinterferenceonCRrouterjshouldnotusethisband7.Tomodelthisconstraint,weletPmjrepresentthesetofroutersthatcanproduceinterferenceatCRrouterjonbandm,i.e., Pmj=fp:dpjRI,p6=j,Tmp6=;g. (3) ThephysicalinterpretationofTmp6=;intheaboveformulaisthatCRrouterpmayusebandmforavalidtransmissiontoaCRrouterinTmpandthenmaycauseinterferencetorouterj.BasedonthedenitionofPmj,wehave smij+Xq2Tmpsmpq1(p2Pmj,p6=i). (3) In( 3 ),ifsmij=1,i.e.,routeriusesbandmtotransmittorouterj,thenanyCRrouterpthatmayinterferewithCRrouterjshouldnottransmitonthisband,i.e.,Pq2Tmpsmpq=0.Likewise,ifsmij=0,( 3 )reducesinto( 3 ),i.e.,routerpmaytransmitonbandmtoonerouterq2Tmp,i.e.,Pq2Tmpsmpq1. Now,weintegratetheconstraintsin( 3 )and( 3 )intoageneralconstraintatthereceiverside.Wedene Imj=fp:dpjRI,Tmp6=;g, (3) 7Hiddenterminalproblemisaspecialcaseunderthisconstraint. 60

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whichisequivalentto Imj=8><>:PmjSfjgIfTmj6=;,Pmjotherwise. (3) Inthisway,both( 3 )and( 3 )canbedescribedbythefollowinggeneralizedconstraint. smij+Xq2Tmpsmpq1(p2Imj,p6=i) (3) 3.3.2RoutingConstraints Asforrouting,asourceCRroutermayemployanumberofrelayCRrouterstoforwarddatapacketstowarditsdestinationCRrouter.Obviously,thereshouldbemorethanonepathinvolvedindatadeliverysincemulti-pathrouting8ismoreexibletoroutethetrafcfromasourceroutertoitsdestination.Followingtheroutingmodelin[ 43 108 ],wemathematicallypresenttheconstraintsatnetworklayerasfollows. Letfij(l)denotethedatarateonlink(i,j)thatisattributedtosessionl,wherei2N,j2Sm2MiTmi,andl2L.Tosimplifythenotation,letTi=Sm2MiTmi. IfCRrouteriisthesourcerouterofsessionl,i.e.,i=s(l),then Xj2Tifij(l)=r(l). (3) IfCRrouteriisanintermediaterelayrouterforsessionl,i.e.,i6=s(l)andi6=d(l),then j6=s(l)Xj2Tifij(l)=p6=d(l)Xp2Tifpi(l). (3) 8ThemultipleradiosofCRroutersallowformulti-pathrouting. 61

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IfCRrouteriisthedestinationrouterofsessionl,i.e.,i=d(l),then Xp2Tifpi(l)=r(l). (3) If( 6 )and( 6 )aresatised,itcanbeeasilyveriedthat( 6 )mustbesatised.Asaresult,itissufcienttolistonly( 6 )and( 6 )asroutingconstraintsintheproblemformulation. Inadditiontotheaboveowbalanceequationsateachrouteriforeachsessionl,theaggregateowratesoneachradiolinkcannotexceedthislink'scapacity,whichisdenedin( 5 ).Takinginterferenceconstraintsintoconsideration,thecalculationofthelinkcapacitycmijcanbefurthersimplied.Whensmij=0,wehavecmij=0.Thus,cmijshouldbewrittenas cmij=smijWmlog21+gijQ (3) Therefore,fortherequirementthattheaggregatedataratesoneachlink(i,j)cannotexceedthelink'scapacity,weobtain s(l)6=j,d(l)6=iXl2Lfij(l)Xm2MiTMjcmij=Xm2MiTMjsmijWmlog21+gijQ (3) 3.4ProblemFormulationandaLowerBoundfortheCross-layerOptimization TheessentialobjectiveofCRNsistoavoidthewasteofwhitespaceandtoimprovethespectrumutilization.Toputitinanotherword,forthegivenamountofradioresource,wetrytouseittosupportasmanyCRrouters'sessionsaspossible;correspondingly,forthegivennumberofCRrouters'sessions,wetrytouseaslittleradioresourceaspossibletosupportthem.Inthischapter,wemeasuretheradioresourceintermsofthetotalbandwidthrequiredbytheSSPtosupportasetof 62

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CRsessions,whichisthesimpliedformofthesocalledspace-bandwidthproductproposedin[ 68 ]withxedtransmissionpower. AsintroducedinSec. 6.3 ,thereisasetofsourceanddestinationpairs(CRrouters'sessions)inthenetwork,eachwithacertainraterequirement.EachCRrouterisentitledtoopportunisticallyaccesstoasetofspectrumbandswithuncertainsupplyforcommunications.Weseekforafeasiblesolutiontoassigningtheavailablefrequencybandstoeachrouter,schedulingbandsfortransmissionandreception,androutingtheowssothatthetotalradiobandwidthrequiredinthemulti-hopCRNsisminimized. Intuitively,theoptimizationproblemcanbeformulatedasfollows[ 42 43 ]. MinXi2NXm2MiXj2TmiWmsmij (3) s.t.Xq2Tmismiq1(i2N,m2Mi)smij+Xq2Tmpsmpq1(i2N,m2Mi,j2Tmi,p2Imj,p6=i)s(l)6=j,d(l)6=iXl2Lfij(l))]TJ /F14 11.955 Tf 17.31 11.36 Td[(Xm2MiTMjWmlog21+gijQ smij0 (3) (i2N,j2Ti)Xj2Tifij(l)=r(l)(l2L,i=s(l))j6=s(l)Xj2Tifij(l))]TJ /F12 7.97 Tf 11.96 15.66 Td[(p6=d(l)Xp2Tifpi(l)=0(l2L,i2N,i6=s(l),d(l))smij=0or1,fij(l)0(l2L,i2N,i6=d(l),j2Ti,j6=s(l)), wheresmijandfij(l)areoptimizationvariables,andgij,Q,andr(l)areallconstants. Notethatduetotheunpredictablereturningofprimaryservices,WmisnotmodeledasaconstantbutmodeledasarandomvariableinCRNsasillustratedinSec. 3.2.3 .Thisfeaturemakesthespectrumresourceminimizationprobleminthischapter 63

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fardifferentfromthatwithguaranteedspectrumsupplyinexistingworks[ 43 108 ].Therefore,twocriticalissuesneedtobeaddressedintheintuitiveformulationabove. First,bandwidthintegrationin( 3 )and( 3 )isthesumofaseriesofrandomvariablesinCRNsratherthanthesumofaseriesofdeterministicquantitiesinotherkindsofwirelessnetworks. Second,withdifferentchoicesofsmijandfij(l),wehavedifcultyincomparingresultsoftheoptimization,i.e.,Pi2NPm2MiPj2TmiWmsmij,becausetheyarerandomvariableswithdifferentkindsofdistribution. 3.4.1ProblemFormulation 3.4.1.1Bandwidthintegration Wetakeasimpleexampletoillustratehowtointegratethebandwidthofdifferentbands.WeletWc=Wa+Wb,whereWaandWbareindependent9,andbandsa,b2M.Furthermore,weassumetheprobabilitydensityfunction(PDF)andcumulativedistributionfunction(CDF)ofWaandWbarehWa(wa),hWb(wb),HWa(wa)andHWb(wb),respectively.Then,theCDFandPDFofWcarederivedasfollows. HWc(wc)=Pr(Wcwc)=Pr(Wa+Wbwc)=Z1Zwc)]TJ /F12 7.97 Tf 6.59 0 Td[(wahWa,Wb(wa,wb)dwbdwa. (3) GivenWaandWbareindependent,wefurthercalculate HWc(wc)=Z1Zwc)]TJ /F12 7.97 Tf 6.58 0 Td[(wahWa(wa)hWb(wb)dwbdwa=Z1hWa(wa)HWb)]TJ /F5 11.955 Tf 5.48 -9.69 Td[(wc)]TJ /F5 11.955 Tf 11.95 0 Td[(wadwa. (3) 9ThisassumptionisheldforanytwobandsinCRNsforthewholechapter. 64

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Moreover,theprobabilitydensityofWcisexpressedas hWc(wc)=Z1hWa(wa)@HWb)]TJ /F5 11.955 Tf 5.48 -9.68 Td[(wc)]TJ /F5 11.955 Tf 11.96 0 Td[(wa @wcdwa=Z1hWa(wa)hWb(wc)]TJ /F5 11.955 Tf 11.95 0 Td[(wa)dwa. (3) Thus,hWc(wc)istheconvolutionofhWa(wa)andhWb(wb)[ 89 ].Itcanbewrittenas hWc(wc)=hWa(wa)hWb(wb)=Om2fa,bghWm(wm), (3) whereNdenotestheoperatorfortheconvolutionofasequence,whichisanalogytotheuseofQastheproductoperatororPasthesummationsymbol.FromthecalculationofhWc(wc),wendthatthesumoftwoindependentrandomvariablesisassociativeandcommutative.Usingthesameapproachasin( 3 ),( 3 )and( 3 ),thispropertycaneasilybeextendedtothesumofanitenumberofrandomvariables.Forexample,forthebandwidthintegrationoflink(i,j),thePDFofW=Pm2MiTMjWmsmijis hW(w)=Om2MiTMjhWm)]TJ /F5 11.955 Tf 5.48 -9.68 Td[(wmsmij. (3) 3.4.1.2Bandwidthrequiredat Beforewere-formulatetheproblem,wemustquantifythebandwidthrequiredforOSAwhenthevacancyofthelicensedbandisuncertainandmodeledasarandomvariable.Thus,weleverageparametertodenebandwidthrequiredatforOSA.Inspiredbythemathematicalexpressionofvalueatrisk(VaR)in[ 39 ],weuseX(w)todenotebandwidthrequiredatanddeneitasfollows. 8>><>>:HW()=ZhW(w)dw,2RX(W)=inff:HW()g,2[0,1].(3) 65

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From( 5 ),wendthattheavailablebandwidthofthebandwidthintegrationforOSAislessthanX(W)atcondencelevelasshowninFig. 3-4A 3.4.1.3Formalformulation Basedonthedescriptionofbandwidthintegrationanddenitionofbandwidthrequiredat,theoptimizationproblemcanbereformulatedasfollows. MinXXi2NXm2MiXj2TmiWmsmij s.t.Xq2Tmismiq1(i2N,m2Mi) (3) smij+Xq2Tmpsmpq1(i2N,m2Mi,j2Tmi,p2Imj,p6=i) (3) Prs(l)6=j,d(l)6=iXl2Lfij(l)Xm2MiTMjWmlog21+gijQ smij(i2N,j2Ti) (3) Xj2Tifij(l)=r(l)(l2L,i=s(l))j6=s(l)Xj2Tifij(l))]TJ /F12 7.97 Tf 11.96 15.66 Td[(p6=d(l)Xp2Tifpi(l)=0(l2L,i2N,i6=s(l),d(l))smij=0or1,fij(l)0(l2L,i2N,i6=d(l),j2Ti,j6=s(l)). Comparedwiththeintuitiveformulation,thereformulatedproblemmathematicallysolvesthesumofrandomvariablesbyusingbandwidthintegrationandincorporatestheotherparametertorepresenttheSSP'srequirementsaboutqualityofCRcommunicationsaspresentedin( 3 ). Inaddition,theobjectiveoftheoptimizationisclaried,i.e.,tominimizebandwidthrequiredattosupporttheCRsessionswithraterequirements,whenjointschedulingandroutingconstraintsaresatised.TakeWandW"inFig. 3-4B forexample,assumetheyarebothintegratedbandwidthswhichsatisfyalltheconstraintslistedabove.We 66

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canchooseeitherWorW"forOSA.WecompareX0.9(W)andX0.9(W")asshowninFig. 3-4B ,anddecidetouseWforOSA.ThereasonisthatifwechooseW,theavailablebandwidthofbandwidthintegrationislessthanX0.9(W)=9atcondencelevelof90%;butifwechooseW",theavailablebandwidthofbandwidthintegrationislessthanX0.9(W")=90atcondencelevelof90%.Atan(,)level,thesmallerX(W)is,thelessspectrumrequiredtomaintainthesetofCRsessions.Thelessspectrumrequired,thelessCRsessionsareaffectedbytheactivitiesofprimaryservices. Nevertheless,theaboveoptimizationproblemitselfisamixed-integernonlinearprogrammingproblem,whichisprovedtobeNP-hard[ 29 ]. 3.4.2TheLowerBoundfortheCross-layerOptimization Foranarbitrarypairof(,),thecomplexityoftheproblemformulatedinSec. 3.4.1 arisesfromthebinarysmijvariables.Toreducethecomplexityandpursuealowerboundforthecross-layeroptimization,werelaxthebinaryrequirementonsmijandreplaceitwith0smij1.Duetotheenlargedoptimizationspace(causedbyrelaxationonsmij),thesolutiontothisrelaxedoptimizationproblemyieldsalowerboundfortheminimizationofbandwidthrequiredatprobleminSec. 3.4.1 .Althoughthelowerboundmaynotbeachievedbyafeasiblesolution,itoffersabenchmarktomeasurethequalityoffeasiblesolutions. 3.5AFastFixingAlgorithmforSub-optimalSolutionsUsingDFT-IDFT Whereaswehavethelowerboundasthebenchmark,westillseekforaneffectiveandefcientsolutiontotheproposedproblemsincethesmijvariablesarebinaryvaluesratherthanrealnumberswithin0and1.Giventhevaluesofthe(,)pair,inthissection,werstinvestigatehowtoreducethecomplexityofcomputingthePDFconvolutioninvolvedinthebandwidthintegration.Then,withtheknowledgeofbandwidthintegrationcomputation,wepresentacoarse-grainedxingproceduretoproduceafeasiblesolutiontothecross-layeroptimizationproblem[ 42 43 ]. 67

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AThegeometricalillustra-tionofX(w). BThegeometricalillus-trationofoptimizationobjective. Figure3-4. Bandwidthrequiredatandoptimizationobjective. 3.5.1FastComputationoftheBandwidthIntegration Followingthetypicalwaytoefcientlycalculatethelinearconvolutionin[ 78 ],weimplementthePDFconvolutionofbandwidthintegrationinSec. 3.4.1 infoursteps. Brieyspeaking,werstlyconvertthecontinuousPDFofWmintoadiscretesequencebyperiodicsampling.Then,wezero-padallthesequences,andcomputetheDFTofeachsequenceusingthefastFouriertransform(FFT)algorithm(e.g.,Cooley-Tukeyalgorithm).Afterthat,wepoint-by-pointmultiplytheDFTsofallthesequences,wheretheproductrepresentstheDFTofthePDFconvolutionofWm.Finally,wecomputetheIDFToftheproduct,andconvertthediscreteresultintocontinuousonetoreconstructthePDFconvolutionofthebandwidthintegration. 3.5.2TheCoarse-grainedFixingProcedure Now,theleftproblemishowtodeterminethesmijvariablesandxowroutingintheproblemformulationinSec. 3.4.1 .ThekeytosimplifyingtheNP-hardoptimization,xingfij(l)-variables,andattaininganeffectivesolutionisthedeterminationofthebinaryvaluesforthesmijvariables[ 42 43 ]. Todeterminethevaluesofallthesmij-variables,weiterativelysolveasequenceofrelaxedoptimizationproblems.Consideringinterferenceconstraints,ineachiteration,wecanxatleastonebinaryvalueforsomesmij.Specically,fortherstiteration,werelaxallbinaryvariablessmijto0smij1asinSec. 3.4.2 toobtainanewoptimization 68

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problem.WeintegratethebandwidthwiththePDFconvolutionandsolvethisnewproblem,sothatwehaveasolutionwitheachsmijbeingavaluebetween0and1.Then,weselectthesmijwiththelargestvalueamongallthesmij-values,andsetthisparticularsmijtobe1.Inparallelwiththisxing,by( 3 ),weshouldsetsmiq=0for(q2Tmi,q6=j).Meanwhile,by( 3 ),weshouldsetsmpqto0for(p2Imj,p6=i,q2Tmp).Inparticular,iftheresultincludesmorethanonesmij-variableswiththevalueof1,wecansetthosesmij-variablesto1andperformanadditionalxingforthelargestfractionalvariableinthecurrentiterationasillustratedabove. Havingxedsomesmij-variablesintherstiteration,weremoveallthetermsassociatedwiththosealreadyxedsmij-variables,eliminatetherelatedconstraintsin( 3 )and( 3 ),andupdatetheproblemtoanewonefortheseconditeration.Intheseconditeration,wesolvethenewoptimizationandthendeterminethevaluesofsomeotherunxedsmij-variablesbasedonthesameprocess10.Theiterationcontinuesuntilwexallsmij-variablestobeeither0and1.TheoverallgrainedxingprocedureissummarizedinAlg. 1 Consideringthenumberofbandswithdifferentfrequenciesandthespatialreuseinmulti-hopCRNs,wemayfurtherreducethecomplexityofthealgorithmandspeeduptheprocedurebyxingmoresmij-variablesinacoarse-grainedmannerduringeachiteration.Firstly,thetransmissioninonebandhasnointerferenceimpactonthetransmissioninanyotherbandswithdifferentfrequencies.Thus,foralink(i,j),wemayxmultiplebandswithinasingleiterationinthecoarse-grainedxingalgorithm.Then,fromtheviewofspatialreuse,abandcanbeusedbythelinksfarapartfromoneanother(i.e.,beyondtheinterferencerangeoftheroutersincommunicationswithalink). 10Providedthatsomesmij-variablesarexedintherstiteration,thecomputationcomplexityintheseconditerationislowerthanthatintherstiterationbecauseweonlyneedtodealwiththeremainingun-xedsmij-variables 69

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Thus,forabandm,wemayxmultiplelinksthathavenomutualinterferencewithinasingleiterationinthecoarse-grainedxingalgorithm. Tobespecic,weemployathreshold>0.5inthecoarse-grainedxingprocessandxallthesmij-variablesexceedingto1inasingleiteration.Tomakesurethattheconstraintsin( 3 )and( 3 )areheldintherelaxedproblem,wendthatatmostonevariablesmijisallowedtobelargerthaninthelocalareainCRNs.Therefore,>0.5issuitablefordeterminingthebinaryvaluesofsmij-values.Inthecasethatnoneofthesmij-variablesexceed,wewillresorttotheprocedurelistedinAlg. 1 forthecurrentiterationandsetthelargestvaluedsmij-variableto1. DifferentfromthelowerboundobtainedinSec. 3.4.2 ,theproposedfastalgorithmyieldsanupperboundtotheproblemformulatedinSec. 3.4.1 .Thequalityofoursub-optimalapproachcanbeassessedbycomparingitssolutiontothelowerboundatvarious(,)levels. Algorithm1TheGrainedFixingProcedure 1: Initializetheprocedurebyrelaxingallbinarysmij-variableswith0smij1. 2: CalculatethePDFconvolutionofbandwidthintegrationbyDFTandIDFT. 3: Withapairof(,)determinedbythenetworkplanner/operator,solvetherelaxedoptimizationproblem. 4: Searchforthesmijwiththelargestvalueamongallthesmij-variablesnotxedyet. 5: Setthefoundsmij=1;besides,setsmiq=0for(q2Tmi,q6=j)andsmpqto0for(p2Imj,p6=i,q2Tmp). 6: ifallthesmij-variablesarexedthen 7: SteptoLine 12 8: else 9: Reformulateaupdatedrelaxedoptimizationproblemwiththelatestxedsmij-variables. 10: SteptoLine 2 11: endif 12: Withallxedsmij-variables,solvetheoptimizationproblemandsettleallowrouting,i.e.,thefij(l)-variables. 70

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3.6PerformanceAnalysis 3.6.1SimulationSetup WeconductsimulationswithaCRNconsistingofjNj=25CRroutersina5050m2area.AmongtheseCRrouters,therearejLj=6activeCRsessions,eachsessionwitharandomraterequirementwithin[10,100]Mb/s.Weassumethatthetransmissionrangeofeachrouteris20m,thattheinterferencerangeis30m,andthatthepathlossindexnis4.Forthesimplicityofcomputation[ 42 43 ],weassumethethresholdQTisequaltotheambientGaussiannoisedensity,i.e.,.Thus,wehaveQI=(20 30)nQTandthetransmissionpowerspectraldensityQ=(20)nQT=1.6105accordingtotheanalysisinSec. 3.2.3 .WealsoassumethebasicbandsoftheSSParefullyutilizedbytheSUswithoutCRcapability. Asfortheuncertainspectrumsupply,weassumethattherearejMj=20licensedbandsthatcanbeopportunisticallyusedbyCRroutersinthewholenetwork.Thevacantbandwidthsofthesebandsarerepresentedbyaseriesofrandomvariables.Basedondatacollectedandthestatisticalanalysisonspectrumutilizationin[ 9 ],thoserandomvariablesareexponentiallydistributed11,i.e.,hWm(wm,m)=me)]TJ /F6 7.97 Tf 6.59 0 Td[(mwm,wherem2(0,3].Asweknow,availablebandsforeachCRrouterareasubsetofthese20bandsbasedonitslocation,andtheavailablebandsforanytwoCRroutersinthenetworkmaynotbethesame.Therefore,werandomlyselectasubsetofbandsfromthespectrumpoolof20bandsforeachrouterinthesimulations.Duetodifferentm-valuesandrandomselectionprocess,thesizeofavailablebandwidthineachbandmaybeunequal,whichtruthfullymirrorsthepracticalscenario. 11Theresultsandanalysiscaneasilybeextendedtootherdistributions(e.g.,normaldistribution,uniformdistribution,etc.),evenforthecasethatWmfromdifferentspectrumbandssatisesdifferentdistributions. 71

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Figure3-5. Ratiooftheupperboundtothelowerboundatvarious(,)levels. Itisnotsurprisingthattheremayexistnofeasiblesolutionforsomespecicdataset,becauseofdis-connectivity,inherentresourcebottleneckinahotspot,etc.Inthischapter,weonlyfocusonthedatasetswithfeasiblesolutionsandanalyzethecorrespondingresultsasshowninthenextsubsection. 3.6.2ResultsandAnalysis InFig. 3-5 ,weevaluatetheproposedcoarse-grainedxingalgorithm.Weset=0.75(i.e.,thethresholdforthecoarse-grainedxing),andcomparetheupperbounddeterminedbythecoarse-grainedxingalgorithmwiththelowerbounddevelopedinSec. 3.4.2 atdifferent(,)levels.Therangeof(,)valuesisfrom(50%,50%)to(90%,90%),andsimulationsforthecomparisonofboundsareconductedforevery10%increaseineitherorvalue.Foreachpairof(,),weemploy50datasetsthatcanproducefeasiblesolutionsandtaketheaveragevalueasaresult.Foreachdataset,were-generatethenetworktopology,source/destinationpairandbitrateofeachsession,andavailablefrequencybandsforeachCRrouter,whichfollowstheguidelineofsimulationsetup.AsshowninFig. 3-5 (theratioisdenotedbyballsinshade;thebenchmarkofvalue1isdenotedbythecontourareainterceptedandbythehollowsquaresatthesampled(,)pairs),theratiooftheupperboundtothelowerboundvia 72

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integerrelaxationisequaltoorslightlyaboveto1inalmostallthearea.Theaverageratiooftheupperboundtothelowerboundforallthesampleddatasetsis1.0506,andthestandarddeviationis0.0867.Itindicatesthatsincetheratiooftheupperboundtothelowerboundiscloseto1atany(,)level,andtheoptimalbandwidthrequiredatisbetweenthosebounds,thesolutionfoundbythecoarse-grainedxingalgorithmmustbeclosetotheoptimum. Figure 3-6 showsthecomparisonbetweentheproposed(,)basedapproachandtheexpectedbandwidthbasedapproachinwhichtheexpectedvalueofbandwidthisusedtocharacterizeboththeobjectiveoftheoptimizationandcorrespondingconstraints[ 85 ].Forillustrativepurposes,wecomparethesolutionoftheexpectedbandwidthbasedapproachwiththesolutionsobtainedbythecoarse-grainedxingalgorithmat(,)=(80%,80%),(,)=(90%,90%)and=80%withtheexpectedvalueofrequiredbandwidthastheobjective,respectively.WetaketheblockingratioofCRsessionsastheevaluationmetricandpresentsimulationresultsfor50datasets.FromtheresultsshowninFig. 3-6 ,threeobservationscanbemadeinorder.First,theperformanceoftheexpectedbandwidthbasedapproachisworstofallbecauseitignoresboththeuncertaintyofspectrumsupplyandthequalityofCRcommunicationswhenitselectsthesubsetoflicensedbandssatisfyingschedulingandroutingconstraintsforOSA.Theexpectedbandwidthwith=80%approachisworsethanthe(,)basedonebecauseitalsoneglectstheuncertainspectrumsupply,i.e.,theavailabilityofrequiredspectrum,asillustratedinSec. 3.4.1.3 .Bycontrast,takingbothfactorsintoconsideration,the(,)basedapproachperformsthebest.Second,forthe(,)basedapproach,theblockingratiodecreasesasthe(,)levelincreases.Third,sincetheblockingratioofCRsessionsiscloselyassociatedwiththespectrumutilizationratioinCRNs,i.e.,lowblockingratioisequivalenttohighspectrumutilizationratioforagivensetofCRsessions.Wecanclaimthatthe(,)basedapproachisbetterthantheexpectedbandwidthbasedoneintermsofspectrumutilizationaswell. 73

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Figure3-6. Theblockingratioofdifferentapproaches. WithaspecicsetofCRsessions(i.e.,thenetworktopology,thesource/destinationpairandtheraterequirementofeachsessionarexed),Table 3-1 presentsageneraltrendofchangeintermsofthebandwidthrequiredatinCRNsatdifferent(,)levels.Itisobviousthatas-valueincreases,boththelowerboundandtheupperboundofthebandwidthrequiredatincrease.Similarly,as-valueincreases,boththeboundsofthebandwidthrequiredatincreaseaswell.Thereasonisfromtwoaspects:i)Fromtheoptimizationobjective'spointofview,thelarger,thehighercondencelevelthenetworkoperatorrequestsfortheavailabilityofrequiredspectrum.Thehighercondencelevel,themorebandwidthrequiredatisneeded.ii)Fromtheconstraint'spointofview,thelarger,thebetterqualityofcommunicationsinCRNs.ThebetterqualityofCRcommunications,themorebandwidthrequiredatisneeded,providedthatthesetofCRsessionsisidentied. 3.7ChapterSummary Inthischapter,wehaveproposedanovelarchitectureofCRNsforspectrumharvestingandsharing,andpresentedatheoreticalstudyonthejointfrequencyschedulingandroutingprobleminmulti-hopCRNsunderuncertainspectrumsupply.Werstintroduceanewserviceprovider,SSP,andlettheSSPprovidecoveragein 74

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Table3-1. LowerandupperboundsofthebandwidthrequiredatforagivensetofCRsessionsatdifferent(,)levels. Index(%)(%)Lower-BsUpper-Bs 17080481.88496.0927580517.29517.2938080566.39594.3748580628.71631.1559080669.76690.0567085490.28493.2577585562.89573.3088085589.02595.1398585662.54664.74109085714.15725.87117090503.32506.09127590602.34606.50138090613.90631.76148590681.88696.09159090735.07741.68 CRNswithlow-costCRmeshroutersinordertofacilitatetheaccessingofSUswithoutCRcapability.Enlightenedbythestatisticsofspectrumutilization,wethenmodelthevacancyofanavailablebandwitharandomvariablesatisfyingcertainstatisticaldistribution.Afterthat,weelaborateonschedulingandinterferenceconstraintsaswellasroutingconstraintsw.r.t.theunpredictableactivitiesofprimaryservices.Furthermore,wecharacterizethenetworkwithapairof(,)parameters,andpresentamathematicalformulationwiththegoalofminimizingtherequirednetwork-widespectrumresourceata(,)levelforasetofCRsessionswithraterequirements.SincetheformulatedoptimizationproblemisNP-hard,wederivealowerboundfortheobjectivebyrelaxingtheintegervariables.Furthermore,weproposeacoarse-grainedxingalgorithmforafeasiblesolution.Throughsimulations,weshowthatthesolutionattainedbytheproposedalgorithmisnear-optimaltotheformulatedNP-hardproblematany(,)level;meanwhile,the(,)basedsolutionisbetterthanexpectedbandwidthbasedoneintermsofblockingratioandspectrumutilization. 75

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CHAPTER4PATHSELECTIONUNDERBUDGETCONSTRAINTSINMULTI-HOPCRNS 4.1ChapterOverview Nowadays,moreandmorepeople,familiesandcompaniesrelyonwirelessservicesfortheirdailylifeandbusiness,whichleadstoaboominggrowthofvariouswirelessnetworksandadramaticincreaseinthedemandforradiospectrum.Inparallelwiththat,currentstaticspectrumallocationpolicyofFederalCommunicationsCommission(FCC)[ 3 20 73 ]resultsintheexhaustionofavailablespectrum,whilealotoflicensedspectrumbandsareextremelyunder-utilized.Experimentaltestsinacademia[ 9 72 ]andmeasurementsconductedinindustries[ 70 71 ]bothshowthateveninthemostcrowedregionofbigcities(e.g.,Washington,DC,Chicago,NewYorkCity,etc.),manylicensedspectrumbandsarenotusedincertaingeographicalareasandareidlemostofthetime.ThosestudiesspurtheFCCtoopenuplicensedspectrumbandsandpursuenewinnovativetechnologiestoencouragedynamicuseoftheunder-utilizedspectrum[ 20 ].Asoneofthemostpromisingsolutions,cognitiveradio(CR)technologyreleasesthespectrumfromshacklesofauthorizedlicenses,andenablestheCRuserstoopportunisticallyutilizethevacantlicensedspectrumbandsineithertemporalorspatialdomain. Theideaofopportunisticusinglicensedspectruminmulti-hopcognitiveradionetworks(CRNs)hasinitiatedthemarketofspectrumtradingandpromotedabunchofinterestingresearchonrelatedtopics.Specically,in[ 35 ],Grandblaiseetal.generallydescribethepotentialscenariosandintroducesomemicroeconomicsinspiredmechanismsforopportunisticspectrumaccessing,andin[ 100 ],SenguptaandChatterjeeproposeaneconomicframeworkforopportunisticspectrumaccessingtoguidethedesignofdynamicspectrumallocationalgorithmsaswellasservicepricingmechanisms.Fromtheviewofsystemdesign,modelsingametheory,byWangetal.in[ 119 120 ],Panetal.in[ 84 ]andZhangetal.in[ 132 ],andauctiondesignsin 76

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microeconomics,byZhouetal.in[ 135 136 ],Jiaetal.in[ 48 ]andWuetal.in[ 124 ],areexploitedtoconstructthespectrumtradingmechanismswithdesiredproperties,suchaspowerefciency,allocationfairness,incentivecompatibility,Paretoefciency,andsoon.Fromtheviewoftheprimaryusers,Xingetal.in[ 125 ]andNiyatoetal.in[ 75 76 ]havewellinvestigatedthespectrumpricingissuesinthespectrummarket,wheremultipleprimaryusers,whosegoalistomaximizethemonetarygainswiththeirvacantspectrum,competewitheachothertoofferspectrumaccesstotheCRusers.FromtheviewoftheCRusers,Panetal.in[ 85 87 ]haveaddressedhowtheCRusersoptimallydistributetheirtrafcdemandsoverthespectrumbandstoreducetheriskformonetaryloss,whenthereismorethanoneunoccupiedlicensedband. Unfortunately,mostexistingworkassumeper-userbasedspectrumtrading(i.e.,eachCRuserpurchasesavailablebandsfromprimaryusersandusesthepurchasedspectrumforcommunications),whichconfrontsthosemechanismswithseveralcriticalproblemswhentheyaredeployedinmulti-hopCRNs.Forinstance,itisnotclearwhomaCRusercommunicateswith(i.e.,theCRreceiverisnotexplicitlyspecied);itisnotclearhowtondacommonbandbetweentwoCRuserstoestablishcommunications;itisnotclearwhatkindofqualityofservice(e.g.,throughput,delay,rateorbandwidthrequirement,etc.)canbesupported.Besides,althoughsomeofpriorspectrumtradingdesignsconsidertheimpactoffrequencyreuse[ 84 124 135 136 ],theyignorealmostalltheotherfactors,e.g.,activitiesofprimaryservices,linkscheduling,routeselection,etc.,whichmaysignicantlyaffecttheperformanceofCRsessionsinmulti-hopCRNs. Insteadofworkingonper-userbasedspectrumtrading,inthischapter,weinvestigatethesession-basedspectrumtrading.SupposethattheCRsourcehasaxedbudgetandpricesforopportunisticspectrumaccessingaredifferentfordifferentlicensedbandsorforthesamebandatdifferentlocations.GivenaCRsessionandmultipleroutesbetweentheCRsourceanddestination,weendeavortondapathwiththemaximumend-to-endthroughputundertheCRsource'sbudgetinmulti-hop 77

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CRNs.Toachievethisobjective,wehavetoconsiderthepriceofthebands,budgetconstraintsofCRsource,linkschedulingconstraints,owroutingconstraintsandpossiblereturningofprimaryservices,whenselectingthepathaswellasthelicensedbandsforopportunisticaccessing.Inthischapter,wemathematicallyformulatetheseconcernsintoanoptimizationproblemandprovidenear-optimalsolutionsusinglinearprogramming.Wealsoproposeaheuristicalgorithmtogivefeasiblesolutionstothepathselectionproblemundermultipleconstraints.Ourcontributionsaresummarizedasfollows. WeintroduceanovelserviceproviderforCRusers,calledsecondaryserviceprovider(SSP),intothenetworkandemploySSPtohelptheCRsessionselectthepathforpacketdelivery.OnbehalfoftheCRlinks,theSSPpurchaseslicensedbandsfromprimaryusersforCRnodes'opportunisticspectrumaccessingw.r.t.thepriceofthebandsaswellastheactivitiesofprimaryservices.Meanwhile,theSSPseeksthemaximumthroughputroutefortheCRsessionbyconductinglinkschedulingandpathselectionunderthebudgetofCRsource. Inspiredbythelinkconictgraphinsingle-radiosingle-channel(SR-SC)networks[ 10 131 ]andthe3-dimensionalconictgraphinmulti-radiomulti-channel(MR-MC)networks[ 61 ],weproposea4-dimensional(4-D)conictgraphtodescribetheconictrelationsamongCRlinksincompetingforbandsw.r.t.thepriceofbandsandtheprobabilityofprimaryservices'returninginmulti-hopCRNs.Similartothemethodologyusedin[ 61 ],weinterpreteachvertexinthegraphasabasicresourcepointforscheduling.Furthermore,werepresenteachresourcepointwithal ink-b and-p robability-p rice(LBP2)quadrupletandconstructthe4-DconictgraphconsistingofLBP2quadruplets. Basedonthe4-Dconictgraph,theSSPcanmathematicallyformulatethepathselectionasajointroutingandlinkschedulingoptimizationproblemundertheCRsource'sbudgetconstraint.GivenalltheindependentsetsinCRNs,theSSPcanrelaxtheintegervariablesintheformulation,solvetheoptimizationproblembylinearprogrammingandndtheoptimalpathwiththelargestend-to-endthroughputbetweenCRsourceanddestination. ItisNP-hardtondalltheindependentsetsinCRNs[ 30 ].ItiseventoocomplicatedfortheSSPtondallindependentsetsofagivenpathifthenumberoflinksortheavailablelicensedbandsislarge.Therefore,wedevelopaheuristicalgorithmtodealwiththepathselectionproblemusinglocalconictcliquesofLBP2quadruplets.WelettheSSPlayerthe4-Dconictgraphbythenumberoflicensedbands,switchLBP2quadrupletstomitigatetheco-bandinterference,and 78

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leveragetheconictcliquestondtheoptimalpathwiththelargestpathcapacityconsideringtheCRsource'sbudget. Bycarryingoutsimulations,wedemonstratetheimpactoftheCRsource'sbudget,thenumberofavailablebandsandthedistancebetweentheCRsourceanddestinationontheperformanceofpathselectioninCRNs.Wealsocomparethepathselectionalgorithmsincludingtheoptimalpathselection,theproposedheuristicpathselectionandthesingle-bandbasedpathselectionproposedin[ 131 ],andshowthattheheuristicalgorithmismuchbetterthanthesingle-bandbasedone,andisclosetotheoptimaloneintermsofthepathcapacity. Therestofthischapterisorganizedasfollows.InSection 6.2 ,wereviewrelatedworkoncross-layeroptimizationforSR-SCandMR-MCnetworksandstate-of-the-artonCRNs.InSection 6.3 ,weintroducethespectrummarketandrelatedmodelsinmulti-hopCRNs.InSection 6.4 ,wedescribethe4-Dconictgraphandpresenttheconceptofindependentsetsandconictcliquesin4-Dconictgraph.InSection 6.5 ,wemathematicallydescribeschedulingandroutingconstraintsinmulti-hopCRNs,formulatethepathselectionundermultipleconstraintsintoanoptimizationproblemandsolveitbylinearprogramming.InSection 6.6 ,wedevelopaheuristicalgorithmforthehighthroughputpathselection.Finally,weconductsimulationsandanalyzetheperformanceresultsinSection 6.7 ,anddrawconcludingremarksinSection 6.8 4.2RelatedWork Howtondthepathwiththelargestend-to-endthroughputunderjointlinkschedulingandroutingconstraintshasbeenextensivelystudiedinbothSR-SCnetworksandMR-MCnetworks.Jainetal.in[ 45 ]studiedtheimpactofinterferenceonperformanceofmulti-hopwirelessnetworkbasedonanNP-hardoptimizationproblem.ZhaiandFangin[ 131 ]investigatedthepathcapacityofagivenpathconsideringlinkschedulingandleveragedtheinterferencecliquetransmissiontimetodesignaroutingmetricforhighthroughputpathselectioninSR-SCnetworks.In[ 10 ],Chenetal.extendedthisworktomulti-rateSR-SCnetworks,andaddressedhowtondapathwithhighavailablebandwidthconsideringboththeinterferencefrombackgroundtrafcandthatalongthepath.InMR-MCnetworks,Lietal.in[ 61 ]proposeda3-dimensional(i.e., 79

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radio-link-channel)conictgraphandexploitedittoefcientlysolvetheoptimalpathcapacityproblemusinglinearprogramming. However,differentfromthemobiledevicewithasingleradioinSR-SCnetworksortheonewithmultipleradiosinMR-MCnetworks,theCRdevicehasonlyoneradiobuttheradioisasoftwaredenedone[ 3 20 73 ],whichissupposedtoswitchfrequenciesacrossawidespectrumrange(i.e.,from20MHzto2.5GHz[ 14 97 110 ]).Besides,theopportunisticspectrumusageoftheCRuserscloselydependsontheactivitiesofprimaryservices.ThelimitationsinCRhardwareandtheimpactofprimaryusersmakethepathselectionproblemmuchmorecomplexinCRNsthanthatinSR-SCnetworksandMR-MCnetworks. InCRresearchcommunity,therehavebeensomeeffortsdevotedtocross-layeroptimizationaswell.Tangetal.in[ 114 ]studiedthejointspectrumallocationandlinkschedulingproblemswiththeobjectivesofmaximizingthroughputandachievingcertainfairnessinCRNs.Houetal.in[ 43 ]investigatedthejointfrequencyscheduling1androutingproblemwiththeobjectiveofminimizingthenetwork-widespectrumresourceandpresentedacentralizedalgorithmforspectrumsharinginCRNs.Intheirfollowingwork,ShiandHouin[ 108 ]alsoprovidedadistributedapproachtoaddressthisissue.Consideringtheuncertainspectrumsupply,Panetal.in[ 88 ]proposedtomodelthevacancyoflicensedbandsasaseriesofrandomvariables,characterizedthemulti-hopCRNswithapairof(,)parametersandminimizedtheusageoflicensedspectrumtosupportCRsessionswithraterequirementsatcertaincondencelevels. Intheexistingliteratureofmulti-hopCRNs,thereremainsalackofstudyonthepathselectionproblembyjointlyconsideringroutingandlinkscheduling.Meanwhile, 1Inthischapter,frequencyschedulingreferstotheschedulinginfrequencydomainormeansfrequencybandallocation,andlinkschedulingreferstotheschedulingintimedomain. 80

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thereisalackofbondtoconnecttheresearchonspectrumtradingandtheresearchoncross-layeroptimizationinmulti-hopCRNs. Ourworkbridgesthegapbetweenthesetwoactiveresearchtopics,i.e.,spectrumtradingmechanismdesignandcross-layeroptimization,inmulti-hopCRNs.Wehaveacomprehensivestudyonthepathselectionproblemconsideringmultiplefactorsincludingthepriceofthebands,budgetconstraintsofCRsource,linkschedulingconstraints,owroutingconstraintsandactivitiesofprimaryservices.Thisworkextendstheper-userbasedspectrumtradingintosessionbasedspectrumtradingandmakesthosemicroeconomicsinspiredspectrumtradingmechanismspracticallyapplicableinmulti-hopCRNs. 4.3NetworkModel 4.3.1SpectrumMarketandOpportunisticSpectrumAccessing Weconsideraspectrummarketinmulti-hopCRNs[ 75 85 87 ]consistingofmultipleprimaryusersoperatingondifferentfrequencybandsandaSSP(e.g.,abasestation(BS)oranaccesspoint(AP))whoservesagroupofCRusersN=f1,2,,n,,Ng.SupposethatthesetoflicensedspectrumbandsB=f1,2,,b,,Bghavetheidenticalbandwidth,wherethesizeofthebandwidthisequalto1.WealsoassumethataCRuserhasonlyoneradio,buttheradiocanbetunedintoanyavailablefrequencybandforpacketdelivery,i.e.,aCRusercanonlyworkononeoftheavailablebandsatonetime.AsshowninFig. 6-2 ,somespectrumbandsatcertaingeographicallocations(thebandsfullyinshade)maybereservedfortheexclusiveusageofspecicprimaryservices(e.g.,restrictedareasformilitaryuseorpublicsafety,dangerareasofemergencyordisaster,etc.);someotherlicensedbands(thebandspartiallyinshade)areopenedandthewhitespaceisavailableforopportunisticaccessingofCRusers.Toputitinamathematicalway,letBiBrepresentthesetofavailablelicensedbandsatCRnodei2N.BimaybedifferentfromBj,wherejisnotequaltoi,andj2N,i.e.,possiblyBi6=Bj. 81

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Inthiscase,primaryuserswillsetreasonablepricesfortheavailablelicensedbandsconsideringtheunpredictableactivitiesoftheprimaryservicesaswellascompetitionamongprimaryusersinthespectrummarket[ 48 75 125 ],andsellthosebandsformonetarygains.Besides,weassumethespectrumtradingtakesplaceperiodically,wherethedurationofatradingperiodis,andthepaymentforspectrumtradingisnon-refundable2.InsteadofbeingthetradingproxyforCRusers[ 100 ],theSSPplaystheroleoftradingproxyforCRsessions.Supposethereisauni-castCRsessioninCRNs.Letsr/dtdenotethesource/destinationCRnodeofthissession,andEbethebudgetoftheCRsourcesr.Toforwardpacketstothedestination,thesourceCRnode3mustpayfortheopportunisticspectrumusageoftheCRlinksalongtheselectedpathtoprimaryusersviatheSSP.Meanwhile,theavailabilityofthepurchasedbandsarenotguaranteed.CRlinkscanopportunisticallyusethepurchasedlicensedbandswhentheprimaryservicesarenoton,buthavetostopusingthosebandswhenprimaryservicesbecomeactive.GivensuchaCRsession,inthiswork,theSSPcollectivelyharvestslicensedspectralresource,purchasesspectrumbandsforCRlinksatdifferentlocations,andjointlyconductlinkschedulingandrouteselectionunderthebudgetconstraintswiththeobjectiveofmaximizingtheend-to-endthroughput4. 2Thetradingperiodshouldnotbetoolong(e.g.,monthsoryears)tomakedynamicspectrumaccessinfeasible,anditshouldnotbetooshort(e.g.,millisecondsorseconds)toincuroverwhelmingoverheadinspectrumtrading.Thetypicaldurationisminutesorhoursasshownin[ 31 ].Intherestofchapter,weassumethatisofxedduration,sothatthetimeparameterisnotincludedinourformulation.3IncentiveissuesoftherelayCRnodesarenotconsideredinthischapter.4Byexchangingsmall-sizecontrolmessageswiththeCRusersoverthededicatedchannel(e.g.,cognitivepilotchannel),theSSPcanconductthespectrumtradingandschedulethetransmissionsoflarge-sizedatapacketsformultihopCRcommunications. 82

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Figure4-1. SpectrummarketandopportunisticspectrumaccessingforpacketdeliveryunderCRsource'sbudgetconstraintsinmulti-hopCRNs. 4.3.2OtherRelatedModelsinCRNs 4.3.2.1Probabilitymodelofprimaryservices ItisnecessarytomodeltheactivitiesofprimaryservicesbecausethetransmissionsofaCRlinkoverbandb2Bcloselydependontheavailabilityofbandb.Asshownin[ 26 51 60 ],thetrafcofprimaryservicescanbemodeledasatwostateON-OFFprocess,whereanONstaterepresentsthebandisoccupiedbyprimaryservices,andanOFFstaterepresentsthebandisavailableforCRusers'opportunisticaccessing.LetqbijrepresenttheprobabilitythatthebandbatlinklijisinOFFstate,and(1)]TJ /F5 11.955 Tf 12.56 0 Td[(qbij)representtheprobabilitythatthebandbatlinklijisinONstate,whereb2BiTBj. 4.3.2.2Transmissionrangeandinterferencerange Theinterferenceinwirelessnetworkscanbedenedaccordingtotheprotocolmodelorthephysicalmodel[ 37 ].SupposeallCRnodesusethesamepowerfortransmission.Then,inprotocolmodel[ 37 131 ],therewillbeaxedtransmissionrangeandaxedinterferencerange,wheretheinterferencerangeistypically2or3timesofthetransmissionrange.Thesetworangesmayvarywiththefrequencybands.Theconictrelationshipbetweentwolinksoverthesamebandcanbedeterminedbythespeciedinterferencerange.Theprotocolmodelisadoptedbymostoftheexistingwork[ 43 61 88 114 131 ],bywhichtheinterferenceoveranetworkcanbeabstractedintoaconictgraph.Wealsoexploittheprotocolmodeltocharacterizetheinterference 83

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relationshipamongCRlinksinthisresearch,andextendtheconictgraphinto4-DconictgraphconsideringthefeaturesofspectrumtradinginCRNs,whichwillbedescribedinthenextsection.Inaddition,ifweproperlysettheinterferencerange,wecanaccuratelytransformaprotocolmodelintoaphysicalmodelasillustratedin[ 109 ]. 4.44-DimensionalConictGraph,ConictCliquesandIndependentSetsinMulti-hopCRNs Topursuithighend-to-endthroughputorpathcapacity,itisnecessaryfortheSSPtojointlyconsiderowroutingandlinkscheduling.ToeffectivelyscheduledatatransmissionamongdifferentCRlinks,itisnecessaryfortheSSPtondtheindependentsetsintheconictgraphconstructedfromCRNs[ 10 131 ].Inthissection,weextendtheconictgraphtomulti-dimensioncaseandestablisha4-dimensional(4-D)conictgraphtocharacterizetheinterferencerelationamongCRlinks.Inthebackgroundof4-Dconictgraph,wealsore-deneindependentsetsandconictcliques,whichcanhelptheSSPmakedecisionsoflicensed-bandpurchasing,spectrumassignment,linkschedulingandowroutingunderthebudgetconstraintsinmulti-hopCRNs. 4.4.1Constructionofthe4-DConictGraph RegardingtheunpredictableactivitiesofprimaryservicesandthefeaturesofCRtransceivers,weintroducea4-DconictgraphtocharacterizetheinterferencerelationshipamongCRlinksinCRNs.Specically,weinterpretaCRNasafour-dimensionalresourcespace,withdimensionsdenedbylinks,bands,theprobabilitythatthebandisavailableforOSAandthechargingprice.Inparallelwiththis,ina4-DconictgraphG(V,E),eachvertexcorrespondstoal ink-b and-p robability-p rice(LBP2)quadruplet,whereanLBP2quadrupletisdenedas link-band-probability-price:(lij,b,qbij,pbij). 84

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AToytopologyinCRNs. B4-Dconictgraph. Figure4-2. Conictrelationshiprepresentedby4-DconictgraphinCRNs. TheLBP2quadrupletindicatesthattheCRlinklij(i,j2N)operatesonbandbw.r.ttheactivitiesoftheprimaryservicesoverthislink.Theavailabilityofbandbatlinklijisdenotedbyqbijandthepricechargedforlij'sopportunisticuseofbandbisrepresentedbypbij.AccordingtothedenitionofLBP2quadruplets,wecanenumerateallcombinationsofCRusers,bands,theavailabilityofbandsandthepriceofbands,whichcanpotentiallyenableaCRcommunicationlink. Obviously,theconictrelationshipamongLBP2quadrupletsinCRNsismorecomplexthanthatamonglinksinSR-SCnetworks,andthatamonglink-channelpairsinMR-MCnetworks.Twoquadrupletsaresaidtointerferewitheachotherifeitherofthefollowingtwoconditionsholds. Condition1:TwodifferentLBP2quadrupletshaveoneortwoCRnodesincommon. Condition2:IftwodifferentLBP2quadrupletsareusingthesameband,thereceivingCRnodeofoneLBP2quadrupletiswithintheinterferencerangeofthetransmittingCRnodeintheotherLBP2quadruplet. Basedontheseconditions,weconnecttwoverticesinVwithanundirectededgeinG(V,E),iftheircorrespondingLBP2quadrupletsinterferewitheachother. Forillustrativepurpose,wetakeasimpleexampletoshowhowtoconstructa4-Dconictgraph.InthistoyCRNsinFig. 5-2A ,weassumethereareveCRuserswithCRtransceivers,i.e.,A,B,C,DandE,andtwolicensedbands,i.e.,band1andband2.Dependingonthegeographiclocations,thesetofcurrentlyavailablefrequencybandsatoneCRlinkmaynotbethesameasthatatanotherCRlinkasmentionedinSec. 6.3.1 85

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Forexample,thecurrentlyavailablebandsetforlinklABisf1gandthebandsetforlinklBCisf1,2g.Meanwhile,theCRtransmissionsaresubjecttotheunpredictablereturningofprimaryservices,wheretheavailabilityofalicensedbandatalinkisdenotedbytheprobability.Forinstance,q1AB=0.7forband1atlinklAB,q1BC=0.6forband1atlinklBCandq2BC=0.8fortheband2atlinklBCasshowninFig. 5-2A .Furthermore,weused()torepresentEuclideandistanceandsupposethatd(A,B)=d(B,C)=d(C,D)=d(D,E)=DT=1 2DI,d(A,C)=p 2DT,d(A,D)=p 5DT,andd(A,E)=p 10DT,whereDTandDIarethetransmissionrangeandinterferencerangeoftheCRusers,respectively. GiventheaboveassumptionsandinformationabouttoyCRNs,wecanconstructthecorresponding4-Dconictgraph,whichisdepictedinFig. 5-2B .Inthegure,eachvertexcorrespondstoanLBP2quadruplet,forexample,vertex(lAB,1,0.7,1)inthe4-DconictgraphcorrespondstoLBP2quadruplet(lAB,1,0.7,1).Notethatthereareedgesbetweenvertices(lAB,1,0.7,1)and(lBC,1,0.6,1),and(lAB,1,0.7,1)and(lBC,2,0.8,2)becauselABandlBChaveaCRnodeBincommon.Thereareedgesbetweenvertices(lAB,1,0.7,1)and(lCD,1,0.9,3)becauselABisincidenttolCDoverband1.Moreover,thereisanedgebetweenvertices(lBC,1,0.6,1)and(lBC,2,0.8,2)becauseanyCRuserhasonlyoneradioandcanonlyworkononebandatonetime.Similaranalysisappliestotheotherverticesinthe4-Dconictgraphaswell. 4.4.2IndependentSetsandConictCliques Givena4-DconictgraphG=(V,E)representingCRNs,wedescribetheimpactofvertexi2Vonvertexj2Vasfollows, wij=8><>:1,ifthereisanedgeconnectingvertexiandj0,ifthereisnoedgebetweenvertexiandj, (4) wherethetwoverticescorrespondtotwoLBP2quadruplets,respectively. 86

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Providedthatthereisavertex/LBP2quadrupletsetIVandanLBP2quadrupleti2IsatisfyingPj2I,i6=jwij<1,thetransmissionatLBP2quadrupletiwillbesuccessfulevenifalltheotherLBP2quadrupletsbelongingtothesetIaretransmittingatthesametime.Ifanyi2Isatisestheconditionabove,wecanschedulethetransmissionsoveralltheseLBP2quadrupletsinItobeactivesimultaneously.Suchavertex/LBP2quadrupletsetIiscalledanindependentset.IfaddinganyonemoreLBP2quadrupletintoanindependentsetIresultsinanon-independentone,Iisdenedasamaximalindependentset.Besides,ifthereexistsavertex/LBP2quadrupletsetZVinGandanytwoLBP2quadrupletsiandjinZsatisfyingwij6=0(i.e.,vertexiandjcannotbescheduledtotransmitsuccessfullyatthesametime.),Ziscalledaconictclique.IfZisnolongeraconictcliqueafteraddinganyonemoreLBP2quadruplet,Zisdenedasamaximalconictclique. 4.5OptimalPathSelectionunderLinkScheduling,RoutingandBudgetConstraints Inthissection,westudyhowtheSSPcanndtheoptimalpathwiththehighestthroughputundermultipleconstraints.First,weaddresshowtocalculatethepathcapacityconsideringlinkschedulingforagivenpath.Then,wemathematicallydescribeowroutingconstraintsforsingle-radiobasedCRusers.Afterthat,weformulateanintegerlinearprogrammingoptimizationproblemtondthebestpossiblepathtoachievethemaximumend-to-endthroughputunderCRscheduling,routingandbudgetconstraintsinmulti-hopCRNs. 4.5.1PathCapacityunderCRLinkSchedulingConstraints ForagivenpathP,wecanestablishthe4-DconictgraphGP=(VP,EP)followingthesameapproachillustratedinSec. 6.4.2 .SupposewecanlistallindependentsetsasIP=fI1,I2,,Im,,IMg,whereMisjIPj,andImVPfor1mM.Then,atanytime,atmostoneindependentsetcanbeactivetotransmitpacketsforallLBP2quadrupletsinthatset.Letm0denotethetimesharescheduledtoindependentset 87

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Im,and X1mMm1,m0(1mM). (4) Letrbij(Im)bethedatarateforCRlinklijoverbandb,whererbij(Im)=0ifLBP2quadruplet(lij,b,qbij,pbij)62Im;otherwise,rbij(Im)isthechannelrate5forlijoverbandb.Therefore,byexploitingtheindependentsetIm,theowratethatlijcansupportoverbandbinthetimesharemismrbij(Im)qbij,consideringthepossiblereturningofprimaryservicesinCRNs.LetsrepresenttheowrateofagivenCRsession.ThisCRsessionisfeasibleatlinklijifthereexistsascheduleoftheindependentsetssatisfying ssij=MXm=1mjBiTBjjXb=1rbij(Im)qbij. (4) Tomaximizetheend-to-endthroughputofP,wemustconsiderthetrafctravelingthroughalllinksalongthegivenpathfromtheCRsourcetotheCRdestination,i.e., CP=maxminlij2Psij. (4) Letsedenoteminlij2Psij,whereeisthebottleneckCRlinkalongPfortheend-to-endthroughput.AsintroducedinSec. 6.3.1 ,thetimeisdividedintospectrumtradingperiodswiththedurationof.Eachtradingperiodisfurtherpartitionedintoasetoftimeslotsindexedbym(1mM),sothatthem-thtimeslothasalengthofm.Inthem-thtimeslot,allLBP2quadrupletsinthesetImwillbescheduledtotransmit.The 5Inthischapter,weassumechannelrateisdeterminedbythereceivedpowerandisequaltothemaximumavailableratesatisfyingtherequirementofreceiversensitivity.Asweknow,inmostofexistingliterature[ 43 61 88 ],thechannelrateisapproximatedbythephysicalchannelcapacityobtainedfromShannon-Hartleytheorem,eventhoughthecapacitycannotbeachieved.Moreover,thechannelrateherecaneasilybesubstitutedbythemorepracticaleffectivedatarate,whichisdenedin[ 131 ].Notethatalltheseapproximationsandsubstitutionswillnotaffectthetheoreticalresultsaswellasperformancecomparisoninthiswork. 88

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end-to-endthroughputofPisdeterminedbythethroughputofthebottlenecklink,i.e.,se.So,duringeachspectrumtradingperiodoflength,thepathcapacityofPis se=1 MXm=1mjBiTBjjXb=1rbe(Im)qbe=MXm=1mjBiTBjjXb=1rbe(Im)qbe, (4) whererbe(Im)andqberepresentthedatarateandspectrumavailabilityforthebottlenecklinkeoverbandb,respectively. 4.5.2Single-RadiobasedCRRoutingConstraints Asforrouting,theSSPwillhelpthesourceCRnodetondtheavailablepathsandemployanumberofrelayCRnodestoforwardthedatapacketstowarditsdestinationCRnode.Similartothemodelingin[ 28 88 ],wemathematicallypresenttheroutingconstraintsasfollows. LetfijrepresenttheowrateoftheCRsessionoverlinklij,wherei2Nandj2Sb2BiTbi.Here,TbiisthesetofCRnodeswithinCRnodei'stransmissionrange,whenbandb2Biisopportunisticallyused.Tosimplifythenotation,letTi=Sb2BiTbi. IfCRnodeiisthesourcenodeoftheCRsession,i.e.,i=sr,then Xj2Tifij=s. (4) Xj2Tifji=0. (4) Duetotheinherentsingle-radioconstraintofCRdevices,wefocusontheunicastandsingle-pathroutingproblem.Thus,weneedtomodifytheroutingconstraintin( 5 )asfollows: Xj2Tifijij=s, (4) 89

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whereij=1indicatesthatlijmayhaveanonzeroow,i.e., Xj2Tiij1,ij2f0,1g. (4) IfCRnodeiisanintermediaterelaynodefortheCRsession,i.e.,i6=srandi6=dt,then Xj2Tifijij=Xj2Tifjiji. (4) IfCRnodeiisthedestinationnodeoftheCRsession,i.e.,i=dt,then Xj2Tifjiji=s. (4) Notethatif( 6 ),( 6 ),( 6 )and( 6 )aresatised,itcanbeeasilyveriedthat( 6 )mustbesatised.Asaresult,itissufcienttolistonly( 6 ),( 6 ),( 6 )and( 6 )asroutingconstraintsintheproblemformulation. 4.5.3OptimalPathSelectionunderMultipleConstraints IfthereismorethanonerouteavailableforthedatadeliveryfromthesourceCRnodetothedestinationCRnode,theSSPwillselecttheoptimalpathonbehalfofthesourceCRnodeintermsoftheend-to-endthroughput.SincetheSSPpurchasesavailablelicensedbandsandchargesthesourceCRnodefortheCRsession'sopportunisticusageofthesebandsasmentionedinSec. 6.3.1 ,theSSPmustconsiderthebudgetofthesourceCRnodebesidestheCRlinkschedulingandroutingconstraints.Thus,theSSPseeksforafeasiblesolutiontotradingtheavailablefrequencybands,assigningthesebandstoCRnodes,schedulingbandsfortransmissionandreception,androutingtheCRowsothattheend-to-endthroughputoftheCRsessionismaximizedinmulti-hopCRNs. 90

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Theoptimalpathselectionproblemundermultipleconstraintsinmulti-hopCRNscanbeformulatedasfollows. Maximizes s.t.:Xj2Tifji=0(i=sr) (4) Xj2Tifijij=s(i=sr) (4) Xj2Tifijij=Xj2Tifjiji(i2Nnfsr,dtg) (4) Xj2Tiij1,ij2f0,1g,(i2N) (4) 0fijjIjXm=1mjBiTBjjXb=1rbij(Im)qbij (4) (i2N,j2Ti,b2Bi\BjandIm2I)jIjXm=1m1,m0 (4) jIjXm=1mX(lij,b,qbij,pbij)2ImpbijE (4) (i2N,j2Ti,b2Bi\BjandIm2I), wherepbijisthepricechargedforlij'susageofbandb,ifLBP2quadruplet(lij,b,qbij,pbij)2Im.AsmentionedinSec. 6.3.1 ,EisthebudgetofthesourceCRnode.Correspondingly,( 4 )meansthattheoverallexpenseofspectrumpurchasingshouldbewithinthebudgetofthesourceCRnode.Inaddition,( 6 ),( 6 ),( 6 )and( 6 )specifythatthereisatmostoneoutgoinglinkfromeachCRnodewithanonzeroow,andthatthereisonlyonepathselectedbytheSSPbetweentheCRsourceandtheCRdestination.( 6 ) 91

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and( 6 )indicatethattheowratesoverlijcannotexceedthecapacityofthisCRlink,whichisobtainedfromtheCRlinkschedulingasillustratedinSec. 6.5.2 NotethatIincludesallindependentsetsinCRNs.Givenallindependentsets6inthenetwork,wendthattheformulatedoptimizationisamixed-integerlinearprogrammingproblemsinceijonlyhasbinaryvalues.Itcannear-optimallybesolvedinpolynomialtimebysometypicalalgorithms(e.g.,sequentialxingalgorithm[ 88 108 ],branchandbound[ 94 ],etc.)orsoftwares(e.g.,CPLEX[ 79 ]),providedthatalltheindependentsetsalongdifferentpathscanbefoundinG(V,E). 4.6AHeuristicPathSelectionAlgorithmforHighEnd-to-EndThroughput Asweknow,tondallindependentsetsinG(V,E)isNP-hard[ 10 45 61 115 131 ].Eventhoughacandidatepathisgiven,itistoocomplexfortheSSPtondalltheindependentsetsalongthepath,ifthenumberoflinksofthepathorthenumberofavailablelicensedbandsforselectioninCRNsislarge.Therefore,inthissection,weproposea7-stepheuristicalgorithmforpathselectionwiththeobjectiveofmaximizingtheend-to-endthroughputforaCRsession.Insteadofusingindependentsets,weclassifytheedgesinthe4-Dconictgraphintotwotypes,layerthegraphbythenumberoflicensedbands,andleverageconictcliquestondthepathwiththehighestend-to-endthroughputfortheCRsessionunderbudgetconstraints. 4.6.1ACounterexamplefortheMaximalCliqueApproach InSR-SCnetworks,authorsin[ 10 131 ]leveragethemaximallocalcliquestoapproximatelyselectthepathwiththehighestthroughput.Unfortunately,thisapproachcannotbeappliedinCRNs.WetakeatoyCRpathshowninFig. 5-2A asacounterexample.Supposethatthepacketlengthis1andthetransmissiontimeofa 6Thatisageneralassumptionusedinexistingliterature[ 10 61 114 115 131 ]forobtainingthroughputboundsorperformancecomparison,wherebothlinkschedulingandowroutingareconsidered. 92

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packetoverallLBP2quadrupletsisthesame,whichisequaltoT.Accordingtothelocalcliqueapproach,CP1 4Tsincethemaximallocalcliquecontains4LBP2quadrupletsasshowninFig. 5-2B .However,ifweonlyconsiderband1forCRnodes'usageregardlessofprimaryservices'activities,CP1 3Tsincethemaximallocalcliquecontains3LBP2quadruplets.Intuitively,ifweconsiderbothband1and2forCRnodes'opportunisticaccessing,thethroughputofthetoypathshouldbefurtherimproved.TheparadoxaboveindicatesthatthemaximallocalcliquebasedalgorithmisnolongersuitableforpathselectioninCRNs. 4.6.2TheProposedAlgorithmforPathSelectioninCRNs ThedetailedprocedureoftheproposedheuristicalgorithmforpathselectioninCRNsispresentedasfollows. Step1:Constructionofthe4-Dconictgraph GivenacandidatepathP,werstsetupacorresponding4-DconictgraphGP(VP,EP)asillustratedinSec. 6.4.2 Step2:Decouplingthe4-Dconictgraphintolayers Withtheestablished4-Dconictgraphofthepath,wefurtherdivideGP(VP,EP)intodifferentlayersaccordingtothenumberofbands,i.e.,jBj.Toputitinanotherway,eachlayerrepresentsaband,andtheinterceptedconictgraphonlayerbdescribestheinterferencerelationshipamongtheCRlinksoverbandb,b2B. Forexample,forapathfromCRnodeAtonodeEasshowninFig. 5-2A ,webuildupthecorresponding4-DconictgraphanddividethegraphintotwolayersbecausethetotalnumberofavailablebandsinCRNsis2. Step3:Differentiatingtwotypesofedges Then,weclassifytheedgesonalayerofthe4-Dconictgraphintotwocategories.ForlayerbinGP,onekindofedgesconnecttwodifferentLBP2quadrupletswhohaveoneCRnodeincommon,i.e.,LBP2quadrupletsonlayerbsatisfyingCondition1.Wedenetheseedgesasnon-reducibleedges.Theotherkindofedgesconnecttwo 93

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Figure4-3. Anillustrativeexamplefortheproposedprocedurewithagivenpath. differentLBP2quadrupletswhohaveco-bandinterference,i.e.,LBP2quadrupletsonlayerbsatisfyingCondition2.Wedenetheseedgesasreducibleedges. Forexample,inFig. 4-3 ,edgesbetweenLBP2quadruplets(lAB,1,0.7,1)and(lBC,1,0.6,1),between(lBC,1,0.6,1)and(lCD,1,0.9,3),andbetween(lCD,1,0.9,3)and(lDE,1,0.7,1)onlayer1arenon-reducibleedges(denotedbysolidlines)duetothesingle-radioconstraint;correspondingly,edgesbetween(lAB,1,0.7,1)and(lCD,1,0.9,3)andbetween(lBC,1,0.6,1)and(lDE,1,0.7,1)onlayer1,andedgesbetween(lBC,2,0.8,2)and(lDE,2,0.7,1)onlayer2arereducibleedges(denotedbydashedlines).Theco-bandinterferencebetweenLBP2quadrupletsrepresentedbyreducibleedgesmaybemitigatedbyswitchingLBP2quadrupletstodifferentlayers. Step4:Selectingthebenchmarklayer IfthereisonlyonelayerinGP,selectitasthebenchmarklayer;ifthereismorethanonelayerinGP,selecttheonewhichhasthemostedges(eithernon-reducibleedgesorreducibleones)becausethislayercanmosteffectivelyshowtheinterferencerelationshipamongdifferentlinksalongthepathP.Forinstance,layer1isthebenchmarklayerforthetoyCRpathfromCRnodeAtonodeEasshowninFig. 4-3 Step5:Establishingthebenchmarkpathcapacity Afterchoosingthebenchmarklayer,wefurtherestimatethebenchmarkexpense.Tocalculatethebenchmarkexpense,weneedinformationfromtwosides:i)theunitpriceofthebandusedbyalinkandii)theactivetimeofthatlinkalongthepathPforonetimeperiod,undertheconditionthatlayerbofGPisselectedasthebenchmarklayer. 94

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LetlijbeaCRlinkalongthepathP,Eijbetheestimatedexpenseoflij,andQijrepresenttheLBP2quadrupletsetassociatedwithlij(e.g.,QDE=f(lDE,1,0.7,1),(lDE,2,0.7,1)gasshowninFig. 4-3 ).Givenlayerbasthebenchmarklayer,theunitpriceofthebandusedbylijiscalculatedasthefollowingthreecases. Case1:IfjQijj=1,thereisonlyoneLBP2quadrupletavailableforlij.Thus,theSSPcanonlychoosetheLBP2quadrupletforlijandpaythecorrespondingpriceforusingthebandenclosedinthatLBP2quadruplet. Case2:IfjQijj1and(lij,b,qbij,pbij)2Qij,therearemultipleLBP2quadrupletsavailableforlijincluding(lij,b,qbij,pbij).Sincelayerbisthebenchmarklayer,theSSPwillchooseLBP2quadruplet(lij,b,qbij,pbij)forlijtocalculatethebenchmarkexpenseandpaypbijforusingbandb,i.e.,Eij=pbij. Case3:IfjQijj1and(lij,b,qbij,pbij)62Qij,therearesomeotherLBP2quadrupletsavailableforlijexcept(lij,b,qbij,pbij).Inthiscase,theSSPcanrandomlychooseanLBP2quadruplet(lij,k,qkij,pkij)inQijforlijtoestimatethebenchmarkexpenseandpaythecorrespondingpriceforusingthebandenclosedinthatLBP2quadruplet,i.e.,Eij=pkij(k6=b). Then,weemployconictcliquesoverlayerbtoestimatetheactivetimeoflinksalongthepathPforonetimeperiod.Similartotheillustrationin[ 10 131 ],wedenetheinterferencecliquetransmissiontimeTZforoneconictcliqueZovertheselectedbenchmarklayeras TZ=X(lij,b,qbij,pbij)2ZT(lij,b,qbij,pbij) (4) whereT(lij,b,qbij,pbij)isthetransmissiontimeforapacketoverlijusingbandb.Assumethepacketlengthis1,consideringtheactivitiesofprimaryservices,T(lij,b,qbij,pbij)canbewrittenas T(lij,b,qbij,pbij)=1 rbijqbij (4) ForthegivenpathP,ndthesetZofallthemaximalinterferencecliqueZfortheLBP2quadrupletsonthebenchmarklayer.LetTPbethemaximalvalueofTZforall 95

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cliquesoverthebenchmarklayerand TP=maxZ2ZTZ (4) ConsideringthelinklijinZandanyonepacketsuccessfullydeliveredfromtheCRsourcetotheCRdestination,thepackettakestimeTPtotravelthroughalltheLBP2quadrupletsinZ,andlijcannotbescheduledtodoanyothertransmissionduringTP.ThatindicatesthatapackettakesatleasttimeTPatlinklijoverthebenchmarklayer,andthethroughputatlinklijislessthanorequalto1 TPoverthebenchmarklayer.Sincetheend-to-endthroughputcannotbelargerthanthethroughputofanylinkalongthepath,thebenchmarkpathcapacityCPcanbeapproximatedas1 TP[ 131 ]. Thisstatementholdsiftherearenooddcycles[ 15 ]inGP.Infact,theproblemcanbesimpliedfortheconictgraphconstructedfromgeneralpathswithoutoddcyclesasillustratedin[ 131 ].InsteadofndingallthemaximalcliquesincludingoneLBP2quadruplet,theSSPonlyneedstoconsiderotherLBP2quadrupletsclosetothisonealongthepath.Werefertothesecliquesasthelocalinterferencecliquesofapath.Forpathsoveracertainlayer,themaximalvalueoftheinterferencecliquetransmissiontimeofalllocalcliques(i.e.,^TPoverbenchmarklayer)isequaltothatforallcliques(i.e.,TPoverbenchmarklayer)7. Thus,wecanfurtherestablishthebenchmarkpathcapacity8using^TPasCP=1 TP=1 ^TP[ 131 ]. Step6:Establishingthebenchmarkexpense 7Somebrute-forcealgorithmscanbedesignedtondalllocalcliquesonaspeciclayer(i.e.,foraspecicband)inpolynomialtimeasillustratedin[ 131 ],whichisomittedinthischapterduetothelimitedspace.8Similarto[ 10 131 ],inthischapter,weonlyconsiderthedirectroutesasdenedin[ 131 ].Notethatfordirectroutes,CP=1 TP=1 ^TPholds. 96

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GiventhebenchmarkpathcapacityCP,theSSPwillestablishthebenchmarkexpenseP. ForaCRlinklijalongthepathP,iftheLBP2quadruplet(lij,b,qbij,pbij)2Qij,i.e.,theLBP2quadruplet(lij,b,qbij,pbij)isonthebenchmarklayerb,ittakesuptijforpacketdeliveryduringoneperiod,wheretijis tij=CP rbijqbij=T(lij,b,qbij,pbij) ^TP. (4) Correspondingly,thebenchmarkexpenseoflijis ij=Eij T(lij,b,qbij,pbij) ^TP=EijT(lij,b,qbij,pbij) ^TP. (4) Similarly,foraCRlinkluvalongthepath,wheretheLBP2quadruplet(luv,b,qbuv,pbuv)62Quvandbandkotherthanbandbisexploitedbyluvforpacketdelivery,thebenchmarkexpenseiswrittenas uv=EuvT(luv,k,qkuv,pkuv) ^TP. (4) Therefore,thebenchmarkexpenseofthepathPcanbeexpressedas P=X(lij,b,qbij,pbij)2QijT(lij,b,qbij,pbij) ^TPEij+X(luv,b,qbuv,pbuv)62QuvT(luv,k,qkuv,pkuv) ^TPEuv. (4) TheprocedureofStep5andStep6issummarizedinAlg. 2 Step7:Switchingquadrupletsforhighthroughput DependingonthevaluesofP,1 ^TPandthebudgetE,theSSPmayapplydifferenstrategiestoswitchLBP2quadruplets. IfPisbeyondE,i.e.,thebudgetoftheCRsource,theSSPwillswitchLBP2quadrupletstoreducetheoverallexpenseforthegivenpathP.NotethatPincreaseswhen^TPdecreasesasshownin( 4 ).Thus,theSSPwouldswitchtheLBP2quadrupletsonotherlayers(i.e.,(luv,k,qkuv,pkuv)in( 4 ),where(luv,b,qbuv,pbuv)62Quv)ratherthantheonesonthebenchmarklayer(i.e.,(lij,b,qbij,pbij)in( 4 ),where 97

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Algorithm2Establishingthebenchmarkexpense Require: InitializetheprocedureafterlayeringGPandselectinglayerbasthebenchmarklayer. 1: foralllij2Pdo 2: ifjQijj==1then 3: TheSSPchoosesthatLBP2quadrupletforlij. 4: elseifjQijj1and(lij,b,qbij,pbij)2Qijthen 5: TheSSPchooses(lij,b,qbij,pbij)forlijandsetEij=pbij. 6: elseifjQijj1and(lij,b,qbij,pbij)62Qijthen 7: TheSSPrandomlychooses(lij,k,qkij,pkij)2QijforlijandsetEij=pkij. 8: endif 9: Calculatethetransmissiontimeforlij2P. 10: endfor 11: Findthemaximumvalueofthelocalclique'stransmissiontime^TPandestimatethebenchmarkpathcapacitywith1 ^TP. 12: Giventhebenchmarkpathcapacity,calculatethetransmissiontimeandthecorrespondingbenchmarkexpenseatlij2P. 13: SumupthebenchmarkexpenseofeachlinkalongPandestablishthebenchmarkexpenseofP. (lij,b,qbij,pbij)2Qij)tolowerdowntheexpense.TheSSPwillreplace(luv,k,qkuv,pkuv)with(luv,h,qhuv,phuv),wherephuv
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TheSSPrstsortstheLBP2quadrupletsonthebenchmarklayer.AccordingtothenumberofreducibleedgesassociatedwiththeLBP2quadruplets,theSSPindexestheLBP2quadrupletsinadecreasingmanner,i.e.,themorereducibleedgesanLBP2quadrupletisassociatedwith,thesmallerindexnumbertheLBP2quadruplethas9. Then,theSSPstartstheswitchingprocesswiththeLBP2quadruplethavingthesmallestindex.LettheLBP2quadrupletbe(lij,b,qbij,pbij)onbenchmarklayerb.IfjQijj=1,thenthisLBP2quadrupletcannotbeswitched,andtheSSPcontinuestocheckthenextLBP2quadruplet.Otherwise,ifjQijj>1,theSSPneedstodecidewhether(lij,b,qbij,pbij)canbeswitchedinto(lij,k,qkij,pkij),where(lij,k,qkij,pkij)2Qijandk6=b.Let^TPbethetransmissiontimeoflocalcliquesonthebenchmarklayerbbeforequadrupletswitching,^T"Pbethelargesttransmissiontimeoflocalcliquesamongallthelayersafterswitching(lij,b,qbij,pbij)to(lij,k,qkij,pkij),and"PbetheexpenseofPafterswitching(lij,b,qbij,pbij)to(lij,k,qkij,pkij).Tomakethedecisionofquadrupletswitching,theSSPmustconsiderthefollowingtwocases. If^T"P^TPand"PE,theSSPwillswitch(lij,b,qbij,pbij)to(lij,k,qkij,pkij),eliminatereducibleedgesassociatedwithLBP2quadruplet(lij,b,qbij,pbij)onlayerb,andaddreducibleedgesassociatedwithLBP2quadruplet(lij,k,qkij,pkij)onlayerk.Inaddition,theSSPwillidentifythelayerwith^T"P,put^TP=^T"PandP="P,andsetthatlayerasnewbenchmarklayer.Afterthat,theSSPwillsortLBP2quadrupletsonthenewbenchmarklayerandcontinueswitchingprocess. If^T"P>^TPor"P>E,theSSPcannotswitch(lij,b,qbij,pbij)to(lij,k,qkij,pkij).TheSSPwillkeepthebenchmarklayerandbenchmarkexpenseunchanged,andcontinuetheprocesswiththenextLBP2quadruplet. Iterationsofquadrupletswitchingcontinueuntil^TPcannotbedecreasedfurtherundertheCRsource'sbudgetE.Then,theSSPcanestimatethethroughputofPasCP=1 ^TPasshowninAlg. 3 9IftherearemultipleLBP2quadrupletswiththesamenumberofreducibleedges,theSSPwilljustindextheminorderaccordingtotheirdistancefromtheCRsource. 99

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Algorithm3Switchingquadrupletsforhighthroughput Require: ThebenchmarklayerislayerbandPE. 1: SortandindextheLBP2quadrupletsonthebenchmarklayerinadecreasingmanneraccordingtothenumberofreducibleedgesassociatedwiththesequadruplets. 2: Set=1. 3: Starttheswitching-quadrupletprocessofthe-thquadruplet(lij,b,qbij,pbij)onthebenchmarklayer. 4: ifjQijj==1then 5: =+1.GotoLine 3 6: elseifjQijj1then 7: forall(lij,k,qkij,pkij)2Qijdo 8: Calculate^T"and"P 9: if^T"P>^TPor"P>Ethen 10: continue. 11: elseif^T"P^TPand"PEthen 12: Switch(lij,b,qbij,pbij)into(lij,k,qkij,pkij). 13: Deletethereducibleedgesassociatedwith(lij,b,qbij,pbij)onthebenchmarklayer. 14: Identifythelayerwith^T"P,andsetthatlayerasnewbenchmarklayer. 15: ^TP=^T"PandP="P.GotoLine 1 16: endif 17: endfor 18: =+1.GotoLine 3 19: endif 20: OutputthethroughputofP:CP=1 ^TP=1 ^TP. TheheuristicalgorithmprovidesausefulmetrictotheSSPforthepathselection.GivenpossiblepathsofaCRsession,theSSPcanexploittheproposedalgorithmabovetocalculatethethroughputofthesepathsbyusinglocalcliques,andselectthepathwiththehighestpathcapacity. 4.6.3ComplexityAnalysis ForaGP(VP,EP)constructedfromthecandidatepathP,itisNP-hardtoidentifyallthemaximalindependentsets.Givenallthemaximalindependentsetsandrelaxedij-variables,thecomplexityofsolvingsuchanoptimizationproblembystandardsolverssuchasCPLEX[ 79 ]isO(X3Y)[ 94 ],whereXisthenumberofvariablesandYisthenumberofbitsrequiredtostorethedata.Bycontrast,theproposedheuristicalgorithm 100

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candirectlycalculatethepathcapacityineachiteration.Thus,thecomplexityoftheproposedalgorithmmainlyliesinthenumberofrequirediterations.Notethatforagivencandidatepath,ineachiteration,wedeterminethestatusofanadditionallinkonanavailablebandforthesessionunderbudgetconstraints.LetjNPjbethenumberofCRnodesalongthepath,andjHj=maxi2NP,b2BijHbij,wherejHbijisthenumberofCRnodeswithinthelocalcliqueofioverbandb.EachlinkcouldbeactiveatmostjBjbands.So,forapathwithjNPjCRnodes,thenumberofiterationsfortheproposedprocedureisnomorethantheproductjNPj2jHjjBj,whichindicatesthattheproposedalgorithmhasapolynomial-timecomplexity. 4.7PerformanceEvaluation 4.7.1SimulationSetup Weconsideramulti-hopCRNconsistingofjNj=40CRnodesrandomlydistributedina800800m2area.WeassumeeachCRnodehasaxedtransmissionrangeof250mandinterferencerangeof500m[ 96 115 ].Regardingthereturningofprimaryservices,theavailabilityofalicensedbandoveraCRlinkatacertainlocationiswitharandomprobabilitywithin(0.5,1],i.e.,qbij2(0.5,1](8i,j2Nand8b2B).Correspondingly,thepriceforopportunisticusingabandforonetimeperiodiswithin(50,100].Thepriceofalicensedbandincreaseswiththeavailabilityofthatband,giventhefactthatallbandshavetheidenticalbandwidth.Forillustrativepurposes,weconductsimulationstostudythepathselectionprobleminCRNswithtwodifferentchannelrates,i.e.,18Mbps(802.11a)and11Mbps(802.11b),respectively. WextheCRnodenearesttotheupperleftcornerastheCRsourceandtheCRnodenearesttothelowerrightcornerastheCRdestination.Wecomparethepathselectionalgorithmsconsistingoftheoptimalpathselection,theproposedheuristicpathselectionandthesingle-bandbasedpathselectionillustratedin[ 131 ].Theperformancemetricistheend-to-endthroughput/pathcapacity.Notethattheoptimalpathselectionistheoneobtainedfromthemixedinteger-linearprogramming 101

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problemformulatedinSec. 6.5.4 .Givensuchasmallnetworktopologyinsimulations,wecanndtheindependentsets[ 61 131 ],relaxthebinaryrequirementonijandsolvetheoptimizationprobleminareasonabletimebyusingCPLEX[ 79 ].Besides,wedemonstratetheimpactofCRsource'sbudgetandtheimpactofthenumberofavailablelicensedbandsonthepathcapacityinCRNs,andpresenttheresultsinFig. 4-4 and 6-7 .WealsondthepathsfromtheCRsourcetoalltheotherCRnodesinthisarea,carryoutsimulationstoevaluatetheimpactofdistancefromtheCRsourceonthepathcapacitywithdifferentpathselectionalgorithms,andshowtheresultsinFig. 6-8 4.7.2ResultsandAnalysis InFig. 4-4 ,wecomparetheoptimalpathselectionwiththeproposedheuristicpathselectionatdifferentCRsource'sbudgetlevels,wherethenumberofavailablelicensedbandsjBjisequalto1,2and3,respectively.Meanwhile,wesetthepathcapacityobtainedfromthesingle-bandbasedpathselectionalgorithmin[ 131 ]asthebaseline,whereweassumethebudgetislargeenough.FromtheresultsshowninFig. 4-4A andFig. 4-4B ,fourobservationscanbemadeinorder.First,thesingle-bandbasedpathselectionhastheworstperformanceamongallthesealgorithms.Thatisnotsurprisingbecausethesingle-bandbasedpathselectionalgorithmin[ 131 ]isdesignedforSR-SCnetworks.ItneitherconsiderstheCRcapabilityoftheCRrelaynodesnorconsidersthepossiblereturningofprimaryservicesatdifferentCRlinks10inCRNs.Second,asthenumberofavailablebandsincreases,theend-to-endthroughputincreasesaswell.ThereasonisthatmorelicensedbandsavailablegivemoreopportunitiesforCRusers'accessing,sothatmoreCRlinksalongtheselected 10Inthesimulations,weassumethereexistperfectlinks,wherethedeliveryratioisequalto1.ThepacketlossofCRtransmissionsisonlycausedbythereturningofprimaryservices. 102

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APerformancecomparisonamongdifferentpathselec-tionalgorithms,wherechannelrateis18M. BPerformancecomparisonamongdifferentpathselec-tionalgorithms,wherechannelrateis11M. Figure4-4. ImpactofCRsource'sbudgetonpathselectioninmulti-hopCRNs. pathcanbeactivatedfortransmissionsimultaneously.Third,astheCRsource'sbudgetincreases,theend-to-endthroughputalsoincreases.ThatisbecausethebudgetisoneofthemostimportantconcernsoftheSSPwhenitjointlyconductstheowroutingandlinkschedulingforaCRsession.However,whenthebudgetofCRsourcenodeislargeenough(e.g.,beyond250),ithasnoimpactontheSSP'sdecisionofpathselectionandthepathcapacitywillnotincreaseanymore.Fourth,theperformanceof 103

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Figure4-5. Impactofthenumberofavailablelicensedbandsonpathselectioninmulti-hopCRNs. theheuristicalgorithmisclosetothatoftheoptimaloneatdifferentbudgetlevelsasshowninFig. 4-4A andFig. 4-4B Figure 6-7 presentstheimpactofthenumberofavailablebandsonthepathcapacityinCRNs,wherewecanhavethefollowingtwoobservations.i)Thepathcapacityobtainedfromtheheuristicpathselectionalgorithmisclosetothatfromtheoptimalone,especiallywhenthenumberofavailablelicensedbandsislargerthan4.ii)Theincrementofpathcapacitybasicallystopswhenthenumberofavailablebandsexceeds4.AsillustratedinSec. 6.4.2 andSec. 6.6 ,onlytheinterferencebetweenLBP2quadrupletssatisfyingCondition2canbereducedbyswitchingLBP2quadruplets,duetothesingleradioconstraintofCRdevices.Giventhenetworkscaleinthesimulation,therearealimitednumberofLBP2quadrupletssatisfyingCondition2inthemaximalconictcliques.Therefore,themaximumpathcapacitycanbeachievedbyfullexploitationof4licensedbands,evenconsideringthepotentialinterruptioncausedbyprimaryservicesinmulti-hopCRNs. Figure 6-8 showstheimpactofdistancebetweentheCRsourceanddestinationonthepathcapacityinCRNs.Forthesimplicityofcomputingindependentsets[ 61 ],weassumethereare3licensedbandsavailableinthenetwork.Exceptfortheobservations 104

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wealreadyhaveinFig. 4-4 andFig. 6-7 ,wendthatthelongerdistancethepathspans,themorelikelythepathcapacityisaffectedbythebudgetoftheCRsource.ItisobviousthatalongerpathmayincludemoreCRlinksalongthepath,whichimpliesthatmorelinkscouldbescheduledtotransmitatthesametime.Thus,theend-to-endthroughputofsuchapathdependsmoreonthebudgetoftheCRsource. 4.8ChapterSummary Inthischapter,wehavestudiedthepathselectionprobleminmulti-hopCRNsunderowrouting,linkschedulingandCRsource'sbudgetconstraints.WerstintroduceanovelserviceproviderforCRusers,SSP,andmaketheSSPhelpagivenCRsessiontopurchasethelicensedspectrumandselectthepathforpacketdelivery.Then,consideringtheinherentsingleradioconstraintofCRdevicesandthefeaturesofspectrumtrading,weproposea4-DconictgraphtodescribetheconictrelationsamongCRlinks.Afterthat,wemathematicallyformulatethepathselectionproblemundermultipleconstraintsintoanoptimizationproblemwiththeobjectiveofmaximizingtheend-to-endthroughputfortheCRsession.Givenallindependentsetsin4-Dconictgraph,wecanrelaxtheformulatedoptimizationproblemandsolveitbylinearprogramming.RegardingtheNP-hardnessofndingallindependentsets,weprovideaheuristicalgorithmaswell,whichlayersthe4-Dconictgraphandexploitsthemaximallocalcliquestoapproximatelyselectthepathwiththehighestthroughput.Bysimulations,wedemonstratehowtheCRsource'sbudget,thenumberofavailablebandsanddistancefromCRsourceaffecttheperformanceofpathselectionintermsofpathcapacity.Wealsocomparetheheuristicpathselectionalgorithmwiththeoptimaloneandshowthatthethroughputobtainedfromtheheuristicalgorithmisclosetothatobtainedfromtheoptimaloneinmulti-hopCRNs. Asaninitialstep,inthischapter,wejustconsiderasingle-owscenarioandignoretheinterferencefromtheotherowsaswellasthecompetitivebiddingforspectrumusagefromtheotherows.InaCRNwithmulti-ows,theCRsourcenodesneedto 105

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developsophisticatedbiddingstrategiesconsideringthecompetitionfromthepeerows,andtheSSPshouldjointlyconsiderthecross-layerfactorsandthebiddingvaluestodeterminethesharingoftheharvestedspectrum.Besides,thenetworkperformanceimprovementisstillhinderedbytheinherentsingle-radioofCRdevices.AnotherissueisthemobilityofCRusers,whichmayhavenegativeimpactonthescheduledtransmissions.Similartomulti-hopcellularnetworks,abetterCRNarchitectureinvolvingsomexedmulti-radioCRroutersmayfurtherincreasethenetworkcapacityandsolvethemobilityproblem.Themorecomplexdesignofpathselectionalgorithmsassociatedwithmulti-owsinmobileCRNswillbedeferredforthenextchapter. 106

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APerformancecomparisonamongdifferentpathselec-tionalgorithms,wherechannelrateis18M. BPerformancecomparisonamongdifferentpathselec-tionalgorithms,wherechannelrateis11M. Figure4-6. PathcapacityfordifferentpathselectionalgorithmsinCRNs. 107

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CHAPTER5SPECTRUMCLOUDS:ASESSIONBASEDSPECTRUMTRADINGSYSTEMFORMULTI-HOPCOGNITIVERADIONETWORKS 5.1ChapterOverview Nowadays,moreandmorepeople,familiesandcompaniesrelyonwirelessservicesfortheirdailylifeandbusiness,whichleadstoaboominggrowthofvariouswirelessnetworksandadramaticincreaseinthedemandforradiospectrum.Inparallelwiththat,currentstaticspectrumallocationpolicyofFederalCommunicationsCommission(FCC)[ 3 20 73 ]resultsintheexhaustionofavailablespectrum,whilealotoflicensedspectrumbandsareextremelyunder-utilized.Experimentaltestsinacademia[ 9 72 ]andmeasurementsconductedinindustries[ 70 71 ]bothshowthateveninthemostcrowedregionofbigcities(e.g.,Washington,DC,Chicago,NewYorkCity,etc.),manylicensedspectrumbandsarenotusedincertaingeographicalareasandareidlemostofthetime.ThosestudiesspurtheFCCtoopenuplicensedspectrumbandsandpursuenewinnovativetechnologiestoencouragedynamicuseoftheunder-utilizedspectrum[ 20 ].Asoneofthemostpromisingsolutions,cognitiveradio(CR)technologyreleasesthespectrumfromshacklesofauthorizedlicenses,andenablessecondaryusers(SUs)toopportunisticallyaccesstothevacantlicensedspectrumbandsineithertemporalorspatialdomain. Theideaofopportunisticusinglicensedspectrumbandshasinitiatedthespectrumtradinginmulti-hopcognitiveradionetworks(CRNs)andpromotedalotofinterestingresearchonthedesignofspectrumtradingsystems[ 35 48 100 124 135 136 ].Throughspectrumtrading,primaryusers(PUs)cansell/lease/auctiontheirvacantspectrumformonetarygains,andSUscanpurchase/rent/bidtheavailablelicensedspectrumiftheysufferfromthelackofradioresourcestosupporttheirtrafcdemands.However,totradethelicensedspectrumandopportunisticallyaccesstothesebands,SUs'handsetshavetobefrequency-agile[ 73 97 ].ItisimperativefortheSUs'devicestohavetheCRcapabilitysuchasexploringlicensedspectrumbands,reconguring 108

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RF,switchingfrequenciesacrossawidespectrumrange(i.e.,from20MHzto2.5GHz[ 14 97 110 ]),sendingandreceivingpacketsovernon-contiguousspectrumbands,etc.Althoughsomeofthedesiredfeaturesmayberealizedinfuture,enormousamountoftimeandeffortsmustbespentinhardwaredesignsandsignalprocessinginordertoimplementthesefeaturesinlightweightradios[ 73 97 110 ].Inaddition,toattractcustomersforanynewtechnologies,thereisnoreasontoenforcetheuserstoreplacetheircommunicationdevicesortoincreasethecomplexityonthecustomers'side.ForspectrumtradinginCRNs,itisalwaysappreciatedtominimizethechangesonthehandsetsofSUswhilefacilitatingthespectrumtradingtomaximizethespectralefciency. ExceptfortheharshrequirementsonSUs'devices,anotherprimarychallengeforspectrumtradinginmulti-hopCRNsishowSUsconductthemulti-hopCRcommunicationsusingthepurchasedspectrum.Mostexistingworkfocusesonper-userbasedspectrumtrading[ 48 124 135 136 ],i.e.,eachSUpurchasesavailablebandsfromPUsandusesthepurchasedspectrumforcommunications.Unfortunately,thosespectrumtradingdesignsareconfrontedwithseveralcriticalproblemswhentheyaredeployedinmulti-hopCRNs.Forinstance,itisnotclearwhomaSUcommunicateswith(i.e.,thedestinationSUorthereceiverisnotexplicitlyspecied);itisnotclearhowtondacommonbandbetweentwoSUstoestablishcommunications;itisnotclearwhatkindofqualityofservice(e.g.,throughput,delay,rateorbandwidthrequirement,etc.)canbesupported.Besides,althoughsomeofpriorspectrumtradingsystemsconsidertheimpactoffrequencyreuse[ 48 84 124 135 136 ],theyignorealmostalltheotherfactors,suchasinterferencemitigation,linkscheduling,owrouting,etc.,whichmaysignicantlyaffecttheperformanceofCRsessionsinmulti-hopCRNs. Toaddressthechallengesabove,inthischapter,weproposeasessionbasedspectrumtradingsystem,spectrumclouds,formulti-hopCRNs.InordertofacilitatethespectrumtradingofSUswithoutCRcapability,anovelnetworkarchitectureandnew 109

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networkentitiesareintroducedinspectrumclouds.UndertheproposedarchitectureofCRNs,westudythesessionbasedspectrumtradinginsteadofper-userbasedspectrumtrading.Giventheraterequirementsandbiddingvalues1ofcandidateCRsessions,weendeavortoconducttheoptimalspectrumtradingundermultipleconstraints(e.g.,theavailabilityofspectrumbands,thecompetitionamongdifferentCRsessions,linkschedulingconstraints,owroutingconstraints,etc.)inmulti-hopCRNs.Wemathematicallyformulatetheseconcernsintoanoptimizationproblemandprovideboththenear-optimalsolutionandthefeasiblesolutioninthiswork.Oursalientcontributionsarelistedasfollows. Differentfromthearchitectureoftraditionalspectrumtradingsystems,weintroduceanewemergingserviceprovider,calledSecondaryServiceProvider(SSP),inspectrumclouds,andassumetheSSPhasalreadyestablishedsomepartialinfrastructurewithCRmeshrouters2atlowcosttoprovidecoverageintheareaofinterest.SupposethattheSSPhasitsownbands(i.e.,basicbands)andcanharvesttheavailablelicensedspectrumbands.TofacilitatetheaccessingofSUswithoutCRdevices,alltheCRmeshroutersareequippedwithmultipleCRradios.UndertheguidanceoftheSSP,SUsaccesstheirnearbyCRmeshroutersusingbasicbandsanddeliverpacketsviaCRmeshroutersusingbothbasicbandsandharvestedbands.GivenraterequirementsandbiddingvaluesofCRsessionswithdifferentsource/destinationSUs,theSSPseekstooptimallytradethespectrumwithaobjectiveofmaximizinghisrevenueundermultipleconstraintsinmulti-hopCRNs,i.e.,thespectrumavailability,linkschedulingandowroutingconstraints. Similartothemulti-dimensionalconictgraphillustratedin[ 61 ],weemploya3-dimensional(3-D)conictgraphtocharacterizetheconictrelationsamongCRlinksinspectrumclouds.Basedonthe3-Dconictgraph,wemathematicallydescribethecompetitionamongCRsessionsforradiospectrumaswellasthelinkschedulingandroutingconstraints.Furthermore,weformulatetheoptimalsessionbasedspectrumtradingintotheSSP'srevenuemaximizationproblemunderthose 1Inthischapter,biddingvaluesgenerallyrepresenthowmuchtheSUsarewillingtopayforpurchasing/renting/biddingfortheavailablespectrum,whichcanbeusedforthetrafcdeliveryofcorrespondingCRsessions.2Intherestofthischapter,weusethewordsCRrouter/CRmeshrouter/routerinterchangeably. 110

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cross-layerconstraints.GivenalltheindependentsetsinCRNs,wecanrelaxtheintegervariablesintheformulation,solvetheoptimizationproblembylinearprogramming,andndtheupperboundoftheSSP'srevenueforsessionbasedspectrumtradinginmulti-hopCRNs. Sincethecompetitionrelationshipbetweenanytwosessionsisrepresentedbybinaryvalues,itisNP-hardtosolvetheformulatedoptimization,inwhichtheseintegerconstraintsareinvolved[ 88 94 ].Topursuefeasiblesolutions,wedeveloptheheuristicrelax-and-xalgorithmstodeterminethevaluesofintegervariables.Brieyspeaking,wedividealltheCRsessionsintodifferentsetsandrelax-and-xtheintegervariablesforCRsessionsinonesessionsetafteranother.Ifthereexistsafeasiblesolution,ityieldsalowerboundtotheoriginaloptimizationproblem. Bycarryingoutextensivesimulationsinbothgridtopologyandrandomtopology,wedemonstratethattheproposedsessionbasedspectrumtradingsystemhasgreatadvantagesovertheper-userbasedonesinmulti-hopCRNs.Wealsocomparetheupperboundandlowerboundsdeterminedbytheheuristicalgorithmsatdifferentdatasets,andshowthatthefeasiblesolutionsobtainedbytheproposedalgorithmsarereallyclosetotheoptimaloneintermsoftheSSP'srevenue. Therestofthischapterisorganizedasfollows.InSection 6.2 ,wereviewrelatedworkinCRcommunity.InSection 6.3 ,weintroducethesystemarchitectureofspectrumclouds,correspondingnetworksettingsandrelatedmodelsinmulti-hopCRNs.InSection 6.5 ,wemathematicallydescribelinkschedulingandroutingconstraintsinspectrumclouds,formulatethesessionbasedspectrumtradingundermultipleconstraintsintoanoptimizationproblemandnear-optimallysolveitbylinearprogramming.InSection 6.6 ,wedeveloptheheuristicalgorithmsforfeasiblesolutions.Finally,weconductsimulationsandanalyzetheperformanceresultsinSection 6.7 ,anddrawconcludingremarksinSection 6.8 5.2RelatedWork Priorworkhasinvestigatedspectrumtradingissuesfromdifferentaspects.Specically,in[ 35 ],Grandblaiseetal.generallydescribethepotentialscenariosandintroducesomemicroeconomicsinspiredspectrumtradingmechanisms,andin[ 100 ],SenguptaandChatterjeeproposeaneconomicframeworkforopportunisticspectrum 111

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accessingtoguidethedesignofdynamicspectrumallocationalgorithmsaswellasservicepricingmechanisms.FromtheviewofthePUs,Xingetal.in[ 125 ]andNiyatoetal.in[ 75 76 ]havewellinvestigatedthespectrumpricingissuesinthespectrummarket,wheremultiplePUs,whosegoalistomaximizethemonetarygainswiththeirvacantspectrum,competewitheachothertoofferspectrumaccesstotheSUs.FromtheviewoftheSUs,Panetal.in[ 85 87 ]haveaddressedhowtheSUsoptimallydistributetheirtrafcdemandsoverthespectrumbandstoreducetheriskformonetaryloss,whenthereismorethanonevacantlicensedspectrumband.Fromtheviewoftradingsystemdesign,modelsingametheory,byWangetal.in[ 119 120 ],Panetal.in[ 84 ]andZhangetal.in[ 132 ],andauctiondesignsinmicroeconomics,byZhouetal.in[ 135 137 ],Jiaetal.in[ 48 ],Panetal.in[ 86 ]andWuetal.in[ 124 ],areexploitedtoconstructspectrumtradingsystemswithdesiredproperties,suchaspowerefciency,allocationfairness,incentivecompatibility,Paretoefciency,collusionresistanceandsoon.Althoughthesedesignsconsidercertainfeaturesofwirelesstransmissions,theyaregenerallyper-userbasedspectrumtradingsystemsratherthansessionbasedones. Theimpactofmultiplesessionsontheperformanceofmulti-hopwirelessnetworkshasbeenextensivelyinvestigatedinexistingliterature.Jianetal.in[ 45 ]studiedhowtheinterferenceaffectstheperformanceofad-hocnetworksbasedonanNP-completeoptimizationproblem.ZhaiandFangin[ 131 ]developedahighthroughputroutingmetricunderlinkschedulingandroutingconstraintsinsingle-radiosingle-channelnetworks.Inmulti-radiomulti-channelnetworks,Lietal.in[ 61 ]proposedamulti-dimensionalconictgraphandexploitedittoefcientlysolvetheoptimalnetworkthroughputproblemusinglinearprogramming.InCRresearchcommunity,therehavebeensomeeffortsdevotedtocross-layeroptimizationaswell.Tangetal.in[ 114 ]studiedthejointspectrumallocationandlinkschedulingproblemswiththeobjectivesofmaximizingthroughputandachievingcertainfairnessinCRNs.Houetal.in[ 43 108 ]investigated 112

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thejointfrequencyscheduling3androutingproblemwiththeobjectiveofminimizingthenetwork-widespectrumusageinCRNs.Consideringtheuncertainspectrumsupply,Panetal.in[ 88 ]proposedtomodelthevacancyoflicensedbandsasaseriesofrandomvariables,characterizedthemulti-hopCRNswithapairof(,)parametersandminimizedtheusageoflicensedspectrumtosupportCRsessionswithraterequirementsatcertaincondencelevels.However,thereremainsalackofstudytoincorporatethesemulti-hoptransmissionconcernsintothedesignofspectrumtradingsystems. Inthiswork,wearetryingtobridgethegapbetweenthesetwoactiveresearchareasinmulti-hopCRNs.Withtheproposedspectrumtradingsystem,spectrumclouds,wehaveacomprehensivestudyontheoptimalspectrumtradingproblemconsideringmultiplefactorsincludingthecompetitionamongCRsessions,theavailabilityofspectrum,linkscheduling,owrouting,etc.Ourworkeffectivelyextendstheper-userbasedspectrumtradingintothesessionbasedspectrumtradingandmakesthosemicroeconomicsinspiredspectrumtradingmechanismspracticallyapplicableinmulti-hopCRNs. 5.3NetworkModel 5.3.1SystemArchitectureforSpectrumClouds Weconsidertheproposedspectrumtradingsysteminmulti-hopCRNs,spectrumclouds,consistingoftheSSP,agroupofSUs,asetofCRmeshroutersandacollectionofavailablelicensedspectrumbands4withunequalsizeofbandwidthsasshownin 3Inthischapter,frequencyschedulingreferstotheschedulinginfrequencydomainormeansfrequencybandallocation,andlinkschedulingreferstotheschedulingintimedomain.4Takingtheleast-utilizedspectrumbandsintroducedin[ 43 ]forexample,wefoundthatthebandwidthbetween[1240,1300]MHz(allocatedtoamateurradio)is60MHz,whilebandwidthbetween[1525,1710]MHz(allocatedtomobilesatellites,GPSsystems,andmeteorologicalapplications)is185MHz. 113

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ASystemarchitectureforspectrumclouds. BAschematicforcomparisonbetweentraditionalspec-trumtradingmechanismsandspectrumclouds. Figure5-1. Anovelarchitectureforspectrumtradinginmulti-hopCRNs. Fig. 5-1A .TheSSPisanindependentwirelessserviceprovider(e.g.,abasestationoranaccesspoint)withitsownspectrum,i.e.,theSSP'sbasicbands(potentiallycongestedalready),andisabletocollectivelyharvesttheavailablelicensedbands.TheSSPhasalsodeployedsomeCRmeshroutersatlowcosttofacilitatetheaccessingofSUs.SUsarejustend-usersnotsubscribedtoprimaryservices.NospecicrequirementsareimposedontheSUs'communicationdevices.Theycouldbeanydevicesusinganyaccessingtechnologies(e.g.laptopsordesktopcomputersusingWi-Fi,cellphonesusingGSM/GPRS,smartphonesusing3G/4G/NxtGaccessingtechnology,etc.).SUscanaccesstothebasicbandsownedbytheSSP,buttheycannotbetunedtotheharvestedlicensedfrequency.TheCRmeshroutersdeployedbytheSSPhaveCRcapabilityandareequippedwithmultipleCRradios. Underspectrumclouds'architecture,themobileSUsreporttheironlinetrafcrequests,whichincludesource/destination,raterequirementsandcorresponding 114

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biddingvaluesoftheSUs'sessions,totheirnearbyCRmeshroutersviabasicbands.ThexedCRmeshrouterscollecttheserequestsfromdifferentend-usersandreportthemtotheSSP.Dependingonthebiddingvalues,raterequirementsandtheavailablespectrumresources,theSSPmakesdecisionsontheaccessing/denialoftheSUs'sessions,andjointlyconductslinkschedulingandowroutingamongCRmeshroutersforSUs'trafcdelivery.FollowingtheguidanceoftheSSP,theCRmeshroutersformunicastCRcommunicationsessionsanddeliverpacketsusingboththeleftoverbasicbandsandharvestedbandsasshowninFig. 5-1A Intraditionalspectrumtradingsystems,thespectrumbandstosell/lease/auctionareknowntoeverySU.Duetobroadcastingnatureofwirelesstransmissions,theSUmayalsoknowhispotentialcompetitorsandoverheartheirbids,sothatmanyschemesareproposedtoensurethatthespectrumtradingisnotmanipulatedinmulti-hopCRNs[ 124 135 ].Bycontrast,inspectrumclouds,theSUhasnoideaaboutthespecicspectrumallocationacrossthewholesession(i.e.,fromthesourcetothedestination).EvenifaSUoverhearsthebidsofotherSUs,itisnothelpfulsincetheSUisnotsurewhoarehiscompetitorsforspectrumusage.Besides,spectrumcloudscansupportsessionbasedspectrumtradinginmulti-hopCRNs,whereastheothersystemscanonlysupportsingle-hopspectrumtradingasshowninFig. 5-1B 5.3.2NetworkConguration SupposethereareN=f1,2,,n,,NgCRmeshrouters,eachCRmeshrouterhasH=f1,2,,h,,Hgradiointerfaces,andtheseCRmeshroutersformasetofLunicastcommunicationsessionsaccordingtoSUs'requests.Eachsessionhasaraterequirementandacorrespondingbiddingvalue.Denotethesource/destinationCRrouterofsessionl2L=f1,2,,l,,Lgbysr(l)/dt(l),andlet(r(l),b(l))betheraterequirement-biddingvaluepairforsessionl2L.AssumetheSUs'usageofbasicbandsinthemulti-hopCRNsisaprioriinformation.TheCRroutersareabletousetherestofbasicspectrumownedbytheSSP.TheCRroutersarealsoallowed 115

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tocommunicatewitheachotherbyopportunisticallyaccessingtothelicensedbandswhentheprimaryservicesarenotactive,buttheymustevacuatefromthesebandsimmediatelywhenprimaryservicesbecomeactive.ConsideringthegeographicallocationoftheCRrouters,theavailablespectrumbandsatoneCRroutermaybedifferentfromanotheroneinthenetwork.Toputitinamathematicalway,letM=f1,2,,m,MgbethebandsetincludingtheavailablebasicbandsandlicensedbandswithdifferentbandwidthsW=fW1,W2,,Wm,,WMgforcommunications,andMiMrepresentthesetofavailablebandsatCRrouteri2N.MimaybedifferentfromMj,wherejisnotequaltoi,andj2N,i.e.,possiblyMi6=Mj. 5.3.3OtherRelatedModelsinMulti-hopCRNs 5.3.3.1Transmissionrangeandinterferencerange SupposeallCRmeshroutersusethesamepowerPfortransmission.Thepowerpropagationgain[ 23 33 43 ]is gij=d)]TJ /F6 7.97 Tf 8 0 Td[(ij, (5) whereisthepathlossfactor,isanantennarelatedconstant,anddijisthedistancebetweenCRroutersiandj.Weassumethatthedatatransmissionissuccessfulonlyifthereceivedpoweratthereceiverexceedsthereceiversensitivity,i.e.,athresholdPT.Meanwhile,weassumeinterferencebecomesnon-negligibleonlyifitisoverathresholdofPIatthereceiver.Thus,thetransmissionrangeforaCRrouterisRT=(P=PT)1=,whichcomesfrom(RT))]TJ /F6 7.97 Tf 6.59 0 Td[(P=PT.Similarly,basedontheinterferencethresholdPI(PIRTsincePI
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interferencerangeisproperlyset,theprotocolmodelcanbeaccuratelytransformedintothephysicalmodelasillustratedin[ 109 ]. 5.3.3.2Linkcapacityandachievabledatarate AccordingtoShannon-Hartleytheorem,ifCRrouterisendsdatatoCRrouterjonlink(i,j)withbandm,thecapacityoflink(i,j)withbandmis cmij=Wmlog21+gijP (5) whereistheambientGaussiannoisepoweratCRmeshrouterj5.Dependingondifferentmodulationschemes,theachievabledatarateisactuallydeterminedbytheSNRatthereceiverandreceiversensitivity[ 16 131 ].However,inmostofexistingliterature[ 43 61 88 103 104 ],theachievabledatarateisapproximatedby( 5 ),eventhoughthisdataratecanneverbeachievedinpractical.Inthischapter,wefollowthesameapproximation.Notethatthisapproximationwillnotaffectthetheoreticalanalysisorperformancecomparisoninthiswork. 5.3.3.3Uncertainspectrumsupply 5.4OptimalSpectrumTradingunderCross-layerConstraintsinMulti-hopCRNs Weexploitbinaryvalue(l)todenotethesuccess/failureofspectrumtradingforsessionl,i.e., (l)=8><>:1,sessionlisaccessedbytheSSP;0,sessionlisdeniedbytheSSP. (5) 5Notethatthedenominatorinsidethelogfunctioncontainsonly.Thisisbecauseofoneofourinterferenceconstraints,i.e.,whenCRrouteriistransmittingtoCRrouterjonbandm,thenalltheotherneighborsofrouterjwithinitsinterferencerangeareprohibitedfromusingthisband.Wewilladdresstheinterferenceconstraintsindetailsinthefollowingsection. 117

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Tomakethedecisionofaccessing/denyingasessionl2L,theSSPmustconsiderboththeraterequirementandbiddingvalueofsessionl.Besides,toeffectivelyutilizetheleftoverbasicspectrumandtheharvestedlicensedspectrum,itisnecessaryfortheSSPtoscheduledatatransmissionamongdifferentCRmeshroutersunderjointspectrumassignment,linkschedulingandowroutingconstraints.Intherestofthissection,werstextendtheconictgraph[ 10 131 ]tocharacterizetheinterferencerelationshipamongCRlinksinspectrumclouds.Then,basedontheextendedconictgraph,wemathematicallydescribelinkschedulingandowroutingconstraintsandformulatethespectrumtradingintotherevenuemaximizationproblemoftheSSPundermultipleconstraints.Byrelaxingtheintegralvariables,wesolvetheoptimizationproblemandprovideanupper-boundoftheSSP'srevenue. 5.4.1ExtendedConictGraph,CliquesandIndependentSets 5.4.1.1Constructionof3-dimensionalconictgraph RegardingtheavailabilityofspectrumbandsandradiosatCRmeshrouters,weintroducea3-DconictgraphtocharacterizetheinterferencerelationshipamongCRlinksinspectrumclouds.Followingthedenitionsin[ 61 ],weinterpretaCRNasathree-dimensionalresourcespace,withdimensionsdenedbylinks,thesetofavailablebandsandthesetofavailableradios.Ina3-DconictgraphG(V,E),eachvertexcorrespondstoal ink-b and-r adio(LBR)tuple,i.e., link-band-radio:((i,j),m,(u,v)), wherei2N,m2MiTMj,j2Tmi,u2Hiandv2Hj.Here,TmiisthesetofCRmeshrouterswithinCRrouteri'stransmissionrange.TheLBRtupleindicatesthattheCRrouteritransmitsdatatoCRrouterjonbandm,whereradiointerfacesuandvareusedatsendingCRrouterandreceivingCRrouter,respectively.BasedonthedenitionofLBRtuples,wecanenumerateallcombinationsofCRmeshrouters,the 118

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AToytopologyinspectrumclouds. B3-Dconictgraph. Figure5-2. Conictrelationshiprepresentedby3-DconictgraphinCRNs. vacantbandsandtheavailableradios,whichcanpotentiallyenableCRcommunicationlinks. Differentfrommulti-radiomulti-channelnetworks[ 61 ],theavailabilityofbandsandradios(i.e.,theleftoverradiosaftercollectingSUs'trafc)ateachCRrouterinCRNsmaybedifferent,i.e.,fori,j2N,maybeMi6=MjandHi6=Hj.Similartotheinterferenceconditionsin[ 43 61 88 ],twoLBRtuplesaredenedtointerferewitheachotherifeitherofthefollowingconditionsistrue:(i)iftwodifferentLBRtuplesareusingthesameband,thereceivingCRrouterofonetupleisintheinterferencerangeofthetransmittingCRrouterintheothertuple;(ii)twodifferentLBRtupleshavethesameradiosatoneortwoCRrouters. Notethattherstconditionnotonlyrepresentsco-bandinterferencebutalsoinherentlycoversthefollowingtwocases:anyCRroutercannottransmittomultipleroutersonthesameband;anyCRroutercannotusethesamebandforconcurrenttransmissionandreception,duetoself-interferenceatthephysicallayer.Meanwhile,thesecondconditionrepresentstheradiointerfaceconicts,i.e.,asingleradiocannotsupportmultipletransmissions(eithertransmittingorreceiving)simultaneously.Accordingtotheseconditions,weconnecttwoverticesinVwithanundirectededgeinG(V,E),iftheircorrespondingLBRtuplesinterferewitheachother. Forillustrativepurposes,wetakeasimpleexampletoshowhowtoconstructa3-Dconictgraph.InthistoyCRNs,weassumetherearefourCRrouterswithCR 119

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transceivers,i.e.,A,B,CandD,andtwobands,i.e.,band1andband2.Dependingonthegeographiclocations,thesetofcurrentlyavailablebandsandradiosatoneCRroutermaybedifferentfromthatatanotherCRrouter.Forexample,thecurrentlyavailablebandandradiosetsforAareMA=f1gandHA=f1g,andthebandandradiosetsforBareMB=f1,2gandHB=f1,2g.Furthermore,weused()torepresentEuclideandistanceandsupposethatd(A,B)=d(B,C)=d(C,D)=d(D,E)=RT=0.5RI.Giventheaboveassumptions,wecanestablishthecorresponding3-DconictgraphasdepictedinFig. 5-2B .Here,eachvertexcorrespondstoanLBRtuple,forexample,vertex((A,B),1,(1,1))correspondstoLBRtuple((A,B),1,(1,1)).Notethatthereisedgebetweenvertices((A,B),1,(1,1))and((B,C),1,(2,1))because(A,B)isincidentto(B,C)overband1.Thereisanedgebetweenvertices((A,B),1,(1,1))and((B,C),2,(1,1))becausetheysharearadioincommonatCRrouterB.Similaranalysisappliestotheotherverticesintheconictgraphaswell. 5.4.1.2Threedimensionalindependentsetsandconictcliques Givena3-DconictgraphG=(V,E)representingspectrumclouds,wedescribetheimpactofvertexi2Vonvertexj2Vasfollows, wij=8><>:1,ifthereisanedgebetweenvertexiandj0,ifthereisnoedgebetweenvertexiandj, (5) wheretwoverticescorrespondtotwoLBRtuples,respectively. ProvidedthatthereisavertexsetIVandanLBRtuplei2IsatisfyingPj2I,i6=jwij<1,thetransmissionatLBRtupleiwillbesuccessfulevenifalltheotherLBRtuplesinthesetIaretransmittingatthesametime.Ifanyi2Isatisestheconditionabove,wecanschedulethetransmissionsoveralltheseLBRtuplesinItobeactivesimultaneously.Suchavertex/LBRtuplesetIiscalleda3-Dindependentset.IfaddinganyonemoreLBRtupleintoa3-DindependentsetIresultsinanon-independentone,Iisdenedasamaximal3-Dindependentset.Besides,if 120

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thereexistsavertex/LBRtuplesetZVandanytwovertexesiandjinZsatisfyingwij6=0(i.e.,LBRtuplesiandjcannotbescheduledtotransmitsuccessfullyatthesametime.),Ziscalleda3-Dconictclique.IfZisnolongera3-DconictcliqueafteraddinganyonemoreLBRtuple,Zisdenedasamaximal3-Dconictclique. 5.4.2CRLinkSchedulingandFlowRoutingConstraints 5.4.2.1CRlinkschedulingconstraints Linkschedulingcanbeconductedintimedomain,infrequencydomainorinbothofthem[ 43 88 ].Inthischapter,weonlyfocusontimebasedlinkscheduling. Giventhe3-DconictgraphG=(V,E)constructedfromthespectrumclouds,supposewecanlistallmaximal3-Dindependentsets6asI=fI1,I2,,Iq,,IQg,whereQisjIj,andIqVfor1qQ.Atanytime,atmostonemaximal3-DindependentsetcanbeactivetotransmitpacketsforallLBRtuplesinthatset.Letq0denotethetimesharescheduledtothemaximal3-DindependentsetIq,and X1qQq1,q0(1qQ). (5) Letrmij(Iq)bethedatarateforCRlink(i,j)overbandm,wherermij(Iq)=0ifLBRtuple((i,j),m,(u,v))62Iq;otherwise,rmij(Iq)istheachievabledatarateforCRlink(i,j)overbandm,whichcanbecalculatedfrom( 5 ).Therefore,byexploitingthe3-DmaximalindependentsetIq,theowratethatlink(i,j)cansupportoverbandminthetimeshareqisqrmij(Iq).Letfij(l)representtheowrateofthesessionloverlink(i,j),wherei2N,l2Landj2Sm2MiTmi.Then,thetradingCRsessionsarefeasibleatlink 6ItisaNP-completeproblemtondallmaximalindependentsetsinG[ 15 29 61 ],whichwillbefurtheraddressedlaterinthischapter.Inthissubsection,wemaketheassumptionwecouldndallthemaximalindependentsetsjustfortheconvenienceofourtheoreticalanalysis. 121

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(i,j)ifthereexistsascheduleofthemaximal3-Dindependentsetssatisfying sr(l)6=j,dt(l)6=iXl2Lfij(l)(l)jIjXq=1qXm2MiTMjrmij(Iq)mij. (5) 5.4.2.2Bandwidthrequiredat Beforewere-formulatetheproblem,wemustquantifythebandwidthrequiredforOSAwhenthevacancyofthelicensedbandisuncertainandmodeledasarandomvariable.Thus,weleverageparametertodenebandwidthrequiredatforOSA.Inspiredbythemathematicalexpressionofvalueatrisk(VaR)in[ 39 ],weuseX(w)todenotebandwidthrequiredatanddeneitasfollows. 8>><>>:HW()=ZhW(w)dw,2RX(W)=inff:HW()g,2[0,1].(5) From( 5 ),wendthattheavailablebandwidthofthelicensedbandwidthintegrationforOSAislessthanX(W)atcondencelevel. 5.4.2.3CRroutingconstraints Asforrouting,theSSPwillhelpthesourceCRmeshroutertondtheavailablepathsandemployanumberofrelayCRmeshrouterstoforwardthedatapacketstowarditsdestinationCRmeshrouter.Itisobviousthatthereshouldbemorethanonepathinvolvedindatadeliverysincemulti-pathrouting7ismoreexibletoroutethetrafcfromasourceroutertoitsdestination.Similartothemodelingin[ 43 88 ],wemathematicallypresentroutingconstraintsasfollows. 7ThemultipleradiosofCRroutersallowformulti-pathrouting. 122

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Tosimplifythenotation,letTi=Sm2MiTmi.IfCRmeshrouteriisthesourcerouterofsessionl,i.e.,i=sr(l),then Xj2Tifji(l)=0. (5) Xj2Tifij(l)(l)=r(l)(l), (5) where(l)2f0,1gindicateswhethersessionlisacceptedbytheSSP(i.e.,sessionlwinstheopportunityfordatatransmissionviaspectrumtrading)ornot. IfCRmeshrouteriisanintermediaterelayrouterofsessionl,i.e.,i6=sr(l)andi6=dt(l),then j6=sr(l)Xj2Tifij(l)(l)=p6=dt(l)Xp2Tifpi(l)(l). (5) IfCRmeshrouteriisthedestinationrouterofsessionl,i.e.,i=dt(l),then Xj2Tifji(l)(l)=r(l)(l). (5) Notethatif( 6 ),( 5 )and( 6 )aresatised,itcanbeeasilyveriedthat( 6 )mustbesatised.Asaresult,itissufcienttolistonly( 6 ),( 5 )and( 6 )asCRroutingconstraintsinspectrumclouds. 5.4.3OptimalSpectrumTradingunderMultipleConstraints Inordertooptimallytradespectrumresourcesanddeterminetheaccess/denialofcertainCRsessions,theSSPmustconsidertheraterequirementsandbiddingvaluesofCRsessions,thecompetitionamongdifferentCRsessions,theavailabilityofbands(includingtheSSP'sleftoverspectrumandtheharvestedspectrum)andtheefcientutilizationofspectrumresources.Thus,theSSPseeksforafeasiblesolutiontotradingtheavailablefrequencybands,assigningthesebandstoCRmeshrouters,schedulingbandsforCRtransmissionandreceptionandroutingthoseCRowsso 123

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thattherevenueoftheSSPismaximizedandradiospectrumresourcesareefcientlyutilizedinmulti-hopCRNs. Withtheproposedtradingsystem,spectrumclouds,theoptimalspectrumtradingproblemundermultipleconstraintsinmulti-hopCRNscanbeformulatedasfollows. MaximizeXl2Lb(l)(l) s.t.:Xj2Tifji(l)=0(l2L,i=sr(l)) (5) Xj2Tifij(l)(l)=r(l)(l)(l2L,i=sr(l)) (5) j6=sr(l)Xj2Tifij(l)(l)=p6=dt(l)Xp2Tifpi(l)(l)(l2L,i2N,i6=sr(l),dt(l)) (5) sr(l)6=j,dt(l)6=iXl2Lfij(l)(l)jIjXq=1qXXm2MiTMjrmij(Iq)mij(i2N,j2Ti,m2Mi\MjandIq2I) (5) jIjXq=1q1,q0(Iq2I) (5) fij(l)0(l2L,i2N,i6=dt(l),j2Ti,j6=sr(l)) (5) (l)2f0,1g(l2L), (5) where(l),fij(l)andqareoptimizationvariables,andr(l)isdeterministicvaluewhensessionlisgiven.Here,( 6 ),( 6 )and( 6 )specifytheroutingconstraintsinspectrumclouds.( 6 )and( 6 )indicatethattheowratesoverlink(i,j)cannotexceedthecapacityofthisCRlink,whichisobtainedfromtheCRlinkschedulingasillustratedinSec. 5.4.2 .NotethatIincludesallindependentsetsinCRNs.Givenallthe 124

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maximal3-Dindependentsets8inG(V,E),wendthattheformulatedoptimizationisamixed-integerlinearprogramming(MILP)problem,whichisNP-hardtosolveasprovedin[ 29 94 ]. 5.5TheUpperBoundfortheSessionBasedSpectrumTradingOptimization Thecomplexityoftheoptimizationabovearisesfromtwoparts:(i)identifyingallthemaximalindependentsetsand(ii)xingthebinary(l)variables.Tondallthemaximalindependentsets/cliquesitselfisNP-complete,butitisnotauniqueprobleminspectrumclouds.Ithasbeenwellinvestigatedinpriormulti-hopwirelessnetworksandmanyapproximationalgorithmshavebeenproposedinexistingliterature[ 61 62 131 ].Forexample,oneofthetypicalapproachesistoemployK(0KjIj)maximalindependentsets(oranumberofmaximalconictcliques)forapproximationinsteadofndingoutallthemaximalindependentsetsinG(V,E). Ontheotherhand,(l)variableswillbeinvolvedaslongastheSSPconductsthesessionbasedspectrumtradinginmulti-hopCRNs.Givenallthemaximalindependentsets,werelaxthebinaryrequirementon(l)andreplaceitwith0(l)1toreducethecomplexityforthecross-layeroptimization.Duetotheenlargedoptimizationspace(causedbyrelaxationon(l)),thesolutiontothisrelaxedoptimizationproblemyieldsanupperboundfortheSSP'srevenuemaximizationproblem.Althoughtheupperboundmaynotbeachievedbyafeasiblesolution,itcanplayasabenchmarktoevaluatethequalityoffeasiblesolutions. 5.6ABiddingValue-RateRequirementRatioBasedHeuristicAlgorithmforSpectrumTrading Inordertondfeasiblesolutions,inthissection,weproposeab iddingv alue-r ater equirementr atio(BVR3)basedheuristicalgorithmfortheSSP'srevenuemaximization 8Thatisageneralassumptionusedinexistingliterature[ 10 61 114 115 131 ]forobtainingthroughputboundsorperformancecomparison. 125

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problem.Accordingtothebiddingvaluesandraterequirementsofcandidatetradingsessions,wemaketheSSPclassifythoseCRsessionsintodifferentcategoriesintermsofdecreasingaccesspossibility.Then,wesequentiallyxthe(l)-variablesindifferentsetsandgiveaheuristicsolution,whichisalsoalowerboundfortheoriginalMILPproblem. 5.6.1TheBVR3BasedRelax-and-FixAlgorithm ThekeytosimplifyingtheNP-hardoptimization,xingowrouting(i.e.,fij(l)-variables)andlinkscheduling(i.e.,q-variables),andattainingafeasiblesolutionisthedeterminationofthebinaryvaluesforthe(l)-variables[ 43 88 ].Althoughwecanemploytheclassicalbranch-and-boundapproachtodetermine(l)-variables,thenumberofiterationsinvolvedinthatalgorithmgrowsexponentiallywithjLj.Toreducethecomplexity,weproposeaBVR3basedrelax-and-xalgorithm[ 94 ].Theintuitionbehindtheproposedalgorithmisthatgiventheleftoverbasicspectrumandtheharvestedspectrum,theSSPwouldliketotakethebestuseofspectrumresourcestomakeasmuchrevenueaspossible.ThatcanberoughlyinterpretedastheSSPpreferstoaccesstheCRsessionwithlargebiddingvalueandsmallraterequirementsinspectrumclouds.ThedetailedprocedureoftheheuristicalgorithmfortheSSP'srevenuemaximizationispresentedasfollows. BasedonbiddingvaluesandraterequirementsofcandidateCRsessions,werstsortalltheCRsessionsintermsofb(l) r(l)andpartitionthesesessionsintoSdisjointsessionsetsL1,L2,,LSintheorderofdecreasingBVR3,whereSs2SLs=LandS=f1,2,,Sg.TheBVR3ofthesessioninLiislargerthanthatofthesessioninLj,ifiislessthanj(8i,j2S). Then,wecreateauxiliarysessionsetsbychoosingsubsetsAswithAsSSu=s+1Lufors2f1,2,,S)]TJ /F7 11.955 Tf 12.16 0 Td[(1g.Forexample,inthespectrumtradingproblem,L1mayincludethe(l)-variablesassociatedwithcandidatetradingsessionsinf1,2,,l1g,L2maybe 126

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associatedwithsessionsinfl1+1,l1+2,,l2g,andsoon,whereasA1wouldincludethe(l)-variablesassociatedwithsessionsinfl1+1,l1+2,,a1g,andsoon. Byleveragingpartitionedsessionsets(i.e.,Ls)andauxiliarysessionsets(i.e.,As),wesequentiallysolvejSjr elaxed-MILPs(R-MILPs)(denotedbyR-MILPswith1sjSj),determinethe-variablesinLs(s2S)andndaheuristicsolutiontotheoriginalMILPproblem.Specically,intherstR-MILP,R-MILP1,weonlyimposethebinaryrequirementonthe(l)-variablesforsessionlinL1[A1andrelaxtheintegralityrestrictiononalltheother(l)-variablesforsessionlinL.Thus,wehave R-MILP1MaximizeXl2Lb(l)(l) s.t.:( 6)-221()]TJ /F7 11.955 Tf 21.25 0 Td[(16 ),( 6)-222()]TJ /F7 11.955 Tf 21.26 0 Td[(17 ),( 6)-222()]TJ /F7 11.955 Tf 21.25 0 Td[(18 ),( 6)-222()]TJ /F7 11.955 Tf 21.26 0 Td[(20 ),( 6)-222()]TJ /F7 11.955 Tf 21.25 0 Td[(21 ),( 5)-221()]TJ /F7 11.955 Tf 21.25 0 Td[(17 )(l)2f0,1g(8l2L1[A1)(l)2[0,1](8l2Ln(L1[A1)) Letf^1(1),,^1(l),,^1(L)gbeanoptimalsolutiontoR-MILP1.Wecanxthe(l)-variablesinL1attheircorrespondingbinaryvalues,i.e.,(l)=^1(l)2f0,1gforalll2L1.Then,wemovetoR-MILP2. InthesubsequentR-MILPs(for2sS),wesequentiallyxthebinaryvaluesofthe(l)-variablesforsessionsinLs)]TJ /F4 7.97 Tf 6.58 0 Td[(1fromthesolutiontoR-MILPs)]TJ /F4 7.97 Tf 6.59 0 Td[(1.Afterthat,wefurtheraddthebinaryrestrictionforthe(l)-variablesinLs[As,andwehave R-MILPsMaximizeXl2Lb(l)(l) 127

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s.t.:( 6)-221()]TJ /F7 11.955 Tf 21.25 0 Td[(16 ),( 6)-222()]TJ /F7 11.955 Tf 21.26 0 Td[(17 ),( 6)-222()]TJ /F7 11.955 Tf 21.25 0 Td[(18 ),( 6)-222()]TJ /F7 11.955 Tf 21.26 0 Td[(20 ),( 6)-222()]TJ /F7 11.955 Tf 21.25 0 Td[(21 ),( 5)-221()]TJ /F7 11.955 Tf 21.25 0 Td[(17 )(l)=^s)]TJ /F4 7.97 Tf 6.58 0 Td[(1(l)(8l2L1[[Ls)]TJ /F4 7.97 Tf 6.59 0 Td[(1)(l)2f0,1g(8l2Ls[As)(l)2[0,1](8l2Ln(L1[[Ls[As)). EitherR-MILPsisinfeasibleforcertains2Sandtheheuristicalgorithmhasfailed,orelsetheproposedBVR3basedrelax-and-xalgorithmprovidesafeasiblesolution(i.e.,thesolutiontoR-MILPjSj)totheoriginalMILPproblem.TheprocedureoftheproposedheuristicalgorithmissummarizedinAlg. 4 Algorithm4TheBVR3basedrelax-and-xalgorithm 1: SortalltheCRsessionsintermsofBVR3,i.e.,b(l) r(l). 2: PartitionallthesesessionsintoSdisjointsessionsets,denotedbyLs(s2S=f1,2,,SgandLsL). 3: CreateauxiliarysessionsetsAsSSu=s+1Lu. 4: Sets=1andrelaxbinaryrequirementon(l)-variables. 5: foralls2Sdo 6: Imposebinaryrequirementonthe(l)-variablesforsessionl2Ls[As. 7: UsingLsandAs,solvetherelaxedR-MILPs. 8: ifR-MILPshasafeasiblesolutionthen 9: Determinethe-variablesinLs. 10: s=s+1.continue 11: else 12: Returnthereisnofeasiblesolution. 13: endif 14: endfor 15: OutputthesolutiontoR-MILPjSjasafeasiblesolutiontotheoriginalMILP. Forillustrativepurposes,wetakeamulti-hopCRNconsistingof7candidatetradingCRsessionsasanexample.WesortthesesessionsbyBVR3anddividetheminto4disjointsessionsets,i.e.,jSj=4.WeconducttheBVR3basedrelax-and-xalgorithmwiththefollowingsetsLsandAs:L1=f1,2g,L2=A1=f3,4g,L3=A2=f5,6g,andL4=A3=f7g.Theiterationsoftheheuristicalgorithmareasfollows. 128

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IntherstR-MILP1,the(l)-variablesassociatedwithsessionsinf1,,4g(i.e.,inL1[A1)arerestrictedtobebinaryvalues,theother(l)-variablesbeingrelaxed. FromthesolutiontoR-MILP1,wecanxthe(l)-variablescorrespondingtothesessionsinf1,2g(i.e.,inL1).Withthedetermined(l)-variablesforsessionsinL1,wecontinuetosolveR-MILP2wherethe(l)-variablesassociatedwithsessionsinf3,,6g(i.e.,inL2[A2)arenowintegerand(l)-variablesinf7g(i.e.,inLn(L1[L2[A2))arerelaxed. FromthesolutiontoR-MILP2,wecanadditionallyxthe(l)-variablescorrespondingtothesessionsinf3,4g(i.e.,inL2).Similarly,wecansolveR-MILP3wherethe(l)-variablesassociatedwithsessionsinf5,6,7g(i.e.,inL3[A3)arenowbinaryandthereareno(l)-variablestorelaxbecauseLn(L1[L2[L3[A3)=. BasedontheoptimalsolutiontoR-MILP3,wecaneasilydeterminethevalueof(l)inf7ganddeterminewhetherthereisfeasiblesolutiontotheoriginalMILP. ThebasicideaoftheBVR3basedrelax-and-xalgorithmisexplicitlyexplainedintheexample.Ateachiteration,wesolveaR-MILPsprobleminvolvingLs[Assessionsandtoavoidbeingtoomyopicwethenonlyxthe(l)-variablescorrespondingtosessionsinLs.TheauxiliarysessionsetsAssmooththeheuristicsolutionbycreatingsomeoverlapbetweensuccessivesessionsets. DifferentfromtheupperboundobtainedinSec. 5.5 ,theproposedBVR3basedrelax-and-xalgorithmyieldsalowerboundtotheoptimalspectrumtradingproblemformulatedinSec. 5.4.3 ,providedthatthereexistfeasiblesolutions. 5.6.2ACoarse-GrainedRelax-and-FixHeuristicAlgorithm FollowingthesameprocedureinSec. 5.5 ,werstrelaxtheoriginalMILPintoLPandndtheoptimalsolutiontotherelaxedLP,inwhich(l)'svalueisin[0,1].Byemployingathreshold0.5<1,wecoarselysetthe(l)-variablesexceedingto1andtheother(l)-variablesto0.Denotethevalueof(l)inthissolutionas~(l)2f0,1g.Inaddition,wekeepthesamedecompositionofsessionsetsastheBVR3basedrelax-and-xalgorithm,i.e.,LsandAsfors2S. Then,ateachsteps(s2S),all(l)-variablesarexedattheir~(l)valuesinthebestsolutionfoundsofar(orinthelastsolutionencountered),exceptthe(l)-variables 129

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inthesetLs[Aswhicharerestrictedtobinaryvalues.Therefore,theproblemsolvedatstepsis R-MILPsMaximizeXl2Lb(l)(l) s.t.:( 6)-221()]TJ /F7 11.955 Tf 21.25 0 Td[(16 ),( 6)-222()]TJ /F7 11.955 Tf 21.26 0 Td[(17 ),( 6)-222()]TJ /F7 11.955 Tf 21.25 0 Td[(18 ),( 6)-222()]TJ /F7 11.955 Tf 21.26 0 Td[(20 ),( 6)-222()]TJ /F7 11.955 Tf 21.25 0 Td[(21 ),( 5)-221()]TJ /F7 11.955 Tf 21.25 0 Td[(17 )(l)=~(l)(8l2Ln(Ls[As))(l)2f0,1g(8l2Ls[As). Ifabettersolutionisfound,~(l)isupdatedandthexingprocedurecontinues.ComparedwiththeBVR3basedrelax-and-xalgorithm,differentstepss(s2S)incoarse-grainedrelax-and-xheuristicareindependentofoneanother,andanysubsetofScanbeperformedinanyorder. 5.7PerformanceEvaluation 5.7.1SimulationSetup Weconsideraspectrumcloudsinmulti-hopCRNsconsistingofaSSP,jNj=36CRmeshroutersandjLj=18candidatetradingsessions,eachofwhichhasarandomraterequirementwithin[10,30]Mb/s.Thebiddingvaluesofthesesessionsarewithin[100,300].AllCRmeshroutersusethesamepowerP=10Wfortransmission.ConsideringtheAWGNchannel,weassumethenoisepoweris10)]TJ /F4 7.97 Tf 6.58 0 Td[(10Watallrouters.Moreover,supposethepathlossfactor=4,theantennaparameter=3.90625,thereceiversensitivityPT=100=10)]TJ /F4 7.97 Tf 6.58 0 Td[(8WandtheinterferencethresholdPT=6.2510)]TJ /F4 7.97 Tf 6.59 0 Td[(10W.AccordingtotheillustrationinSec. 5.3.3 ,wecancalculatethetransmissionrangeRTandtheinterferencerangeRI,whichareequalto250mand500m,respectively.Forillustrativepurposes,weassumeallthebandshaveidenticalbandwidth,whichissettobe10MHz,i.e.,Wm=10MHzforallm2M.Besides,forthesimplicityofcomputation,wesetK=3104,i.e.,ifthetotalnumberofthemaximalindependentsetsinG(V,E) 130

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ARevenueupperbounds:jHj=2,3and4. BRevenueupperboundandlowerbounds:jHj=4. CRevenueupperboundandlowerbounds:jHj=3. DRevenueupperboundandlowerbounds:jHj=2. Figure5-3. ImpactofthenumberofavailablebandsjMjandradiointerfacesjHjonspectrumtradinginmulti-hopCRNs:gridtopology. islessthanorequalto3104,weemployallthemaximalindependentsetsforthesolution;otherwise,weemploy3104maximalindependentsetsforapproximation. Basedonthesimulationsettingsabove,weconductsimulationstostudytheoptimalspectrumtradingprobleminspectrumcloudswiththefollowingtwotopologies:i)agridtopology,where36CRmeshroutersaredistributedwithin10001000m2areaandtheareaisdividedinto25squarecellsin200200m2;ii)arandomtopology,where36CRmeshroutersarerandomlydeployedina10001000m2areaformingaconnectednetwork.NotethatweemployCPLEX[ 79 ]tosolvetherelaxedoptimizationproblemstoobtaintheupperboundandlowerboundsoftheSSP'srevenue. 131

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ARevenueupperbounds:jHj=2,3and4. BRevenueupperboundandlowerbounds:jHj=4. CRevenueupperboundandlowerbounds:jHj=3. DRevenueupperboundandlowerbounds:jHj=2. Figure5-4. ImpactofthenumberofavailablebandsjMjandradiointerfacesjHjonspectrumtradinginmulti-hopCRNs:randomtopology. 5.7.2ResultsandAnalysis InFig. 5-3 andFig. 5-4 ,wecomparetheupperboundoftheSSP'srevenuewiththelowerboundsdeterminedbytheheuristicB VR3basedr elax-and-f ixalgorithm(denotedbyBRFingures)andthec oarse-grainedr elax-and-f ixalgorithm(denotedbyCRFingures)atdifferentnumberofavailablebands(i.e.,jMj)andradios(i.e.,jHj)inmulti-hopCRNs.Werelaxthe(l)-variablesandemployK=3104maximalindependentsetstosolvetheproblemasillustratedinSec. 5.5 ,whichalsoyieldsthe 132

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ARatiooftheupperboundtothelowerbounddeter-minedbytheBVR3basedrelax-and-xalgorithm:gridtopology. BRatiooftheupperboundtothelowerbounddeter-minedbythecoarse-grainedrelax-and-xalgorithm:gridtopology. CRatiooftheupperboundtothelowerboundde-terminedbytheBVR3basedrelax-and-xalgorithm:randomtopology. DRatiooftheupperboundtothelowerbounddeter-minedbythecoarse-grainedrelax-and-xalgorithm:randomtopology. Figure5-5. RatiooftheupperboundtolowerboundsdeterminedbytheproposedalgorithmsatjHj=3andjMj=9. 133

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upperbound.Todevelopthelowerbounds,weequallydividethe18candidatetradingsessionsinto6sessionsets(i.e.,jSj=6andeachsethas3sessions)fortheBVR3basedrelax-and-xalgorithm,andset=0.7forthecoarse-grainedrelax-and-xalgorithmasshowninSec. 6.6 .GiventhenumberofavailablebandsjMjinCRNsandradiosjHjatCRrouters,weemploy50datasetsthatcanproducefeasiblesolutionsandtaketheaveragevalueasaresult.Foreachdataset,were-generateavailablebandsMiatCRrouteri,sr(l)/dt(l)and(r(l),b(l))pairofsessionl,andtherandomnetworktopology(wekeepthesamegridtopologyforeachdataset),whichfollowstheguidelineofsimulationsetup. FromtheresultsshowninFig. 5-3 andFig. 5-4 ,fourobservationscanbemadeinorder.First,theupperboundisclosetothelowerboundsobtainedfromtheproposedBVR3basedrelax-and-xalgorithmandthecoarse-grainedrelax-and-xalgorithm,nomatterhowmanyavailablebandsandradiosarethereinthespectrumclouds.Wewillfurtherpresenttheratiooftheupperboundtolowerboundswith50datasetsinFig. 5-5 ,analyzethestatisticalresultsandshowtheclosenessbetweenthosebounds.Second,asthenumberofavailablebandsandthenumberofCRmeshrouter'sradiosincrease,theSSP'srevenueincreasesaswell.ThereasonisthatmorebandsandradiosavailablecreatemoreLBRtuples,sothatmoreCRlinksinspectrumcloudsmaybeactivatedfortransmissionsimultaneouslyandmoreopportunitiescanbeleveragedforspectrumtradinginCRNs.However,theincrementoftheSSP'srevenuebasicallystopswhenjMjisover9forjHj=2caseinbothgridtopologyandrandomtopology,whichleadstothethirdobservation.Thatis,theCRmeshrouterhastoequipareasonablenumberofradiostoutilizealltheavailablebandsefciently(atleast3radiosforoursimulationscenarios).ThisobservationalsogivesagoodsuggestiononthedesignanddeploymentofCRmeshroutersforspectrumcloudsinpractice.Fourth,theperformanceofthegridtopologygenerallyoutperformsthatoftherandomtopologyintermsoftheSSP'srevenue.Theperformancegapstemsfromthe 134

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differencesintopologicalstructure.Forthegridtopology,eachCRlinkhasthesametopologicalinformationifweignorethebordereffect.TheperformanceimprovementofspectrumtradingismainlydeterminedbythenumberofradiosandtheavailablebandsatdifferentCRrouters.Bycontrast,therandomtopologyisnon-uniformedtopology.Theperformanceimprovementofspectrumtradingisnotonlyhinderedbythenumberofbandsandradios,butalsobottleneckedbythecriticalcliquesintherandomtopology. Figure 5-5 presentstheratiooftheupperboundtothelowerboundsobtainedfromtheproposedheuristicalgorithmsinbothgridtopologyandrandomtopology,wherejHj=3andjMj=9.AsshowninFig. 5-5A andFig. 5-5B ,theratiooftheupperboundtolowerboundinthegridtopologyisnearto1with50differentdatasets,wherethelowerboundsaredeterminedbytheBVR3basedrelax-and-xalgorithmandthecoarse-grainedrelax-and-xalgorithm,respectively.Specically,theaverageratiooftheupperboundtotheBVR3basedlowerboundforallthedatasetsis1.0826,andthestandarddeviationis0.0632;theaverageratiooftheupperboundtothecoarse-grainedbasedlowerboundforallthedatasetsis1.1122,andthestandarddeviationis0.1031.Similaranalysisappliestotherandomtopologyaswell.AsshowninFig. 5-5C andFig. 5-5D ,theaverageratiooftheupperboundtotheBVR3basedlowerboundforallthedatasetsis1.1611,andthestandarddeviationis0.1387;theaverageratiooftheupperboundtothecoarse-grainedbasedlowerboundforallthedatasetsis1.2113,andthestandarddeviationis0.1595.Allthesestatisticalresultsindicatethatthesolutionsfoundbytheheuristicalgorithmsmustbeclosetotheoptimum,sincetheoptimalsolutionliesbetweentheupperboundandthelowerbound. GiventhespecicdatasetatjHj=3andjMj=9,Table 5-1(a) andTable 5-1(b) presentthetradingstatusofthe18candidatesessionsw.r.t.BVR3valuesinthe 135

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gridtopologyandtherandomtopology,respectively.Theresults9demonstratethatunlikeper-userbasedspectrumtradinginCRNs,itisnotnecessaryfortheSSPtoaccommodatetheCRsessionswithhighBVR3valuesinordertomaximizetheSSP'srevenue.Someothercriticalfactorsmayalsoaffecttheresultsofthesessionbasedspectrumtradinginmulti-hopCRNs,e.g.,thelocationofsource/destinationCRroutersofasession,theinterferenceasessionincurstotheexistingows,etc.Asshownintheformulation,theproposedspectrumcloudsgivesacomprehensiveconsiderationonthosefactors.ThedatainTable 5-1 furtherverifythisstatementandexplicitlyshowtheadvantagesofourdesignovertheper-userbasedspectrumtradingsystemsinmulti-hopCRNs. 5.8ChapterSummary Inthischapter,wehaveproposedanovelspectrumtradingsystem,i.e.,spectrumclouds,andpresentedatheoreticalstudyontheoptimalsessionbasedspectrumtradingproblemundermultiplecross-layerconstraintsinmulti-hopCRNs.Weintroduceanewserviceprovider,SSP,andlettheSSPprovidecoverageinCRNswithlow-costCRmeshroutersinordertofacilitatetheaccessingofSUswithoutCRcapability.Consideringthespecialfeaturesofsessionbasedspectrumtrading,weexploitthe3-D(link-band-radio)conictgraphtocharacterizetheconictsamongCRlinksandmathematicallydescribethecompetitionsamongcandidatetradingsessionsinspectrumclouds.Giventheraterequirementsandbiddingvaluesofcandidatetradingsessions,weformulatetheoptimalspectrumtradingintotheSSP'srevenuemaximizationproblemundertheavailabilityofspectrum,linkschedulingandowroutingconstraintsinmulti-hopCRNs.SincetheformulatedproblemisNP-hardtosolve,wederiveanupperboundfortheoptimizationbyrelaxingtheintegervariables. 9WeexploittheproposedBVR3basedrelax-and-xalgorithmtoderivetheseresultsinboththegridtopologyandtherandomtopology. 136

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Table5-1. Spectrumtradingstatusofthecandidatesessionsw.r.t.thedescendingBVR3valuesinmulti-hopCRNs. (a)Gridtopologywith3radiosand9bands. S-IndexBVR3Val.Status S-IndexBVR3Val.Status 124.171p 1015.629223.222p 1114.878p322.411p 1214.627420.489p 1313.462520.014p 1412.239619.074p 159.876p718.475 168.358817.462p 176.908916.081 184.912 (b)Randomtopologywith3radiosand9bands. S-IndexBVR3Val.Status S-IndexBVR3Val.Status 123.188p 1011.672p221.556p 1110.479320.139p 129.002420.101p 138.857518.525p 146.971616.271 155.223714.771p 164.713814.365 174.674913.213 183.737 Furthermore,weproposeheuristicalgorithmsforfeasiblesolutions(lowboundsaswell).Throughsimulations,weshowthat:i)theproposedsessionbasedspectrumtradinghassuperioradvantagesovertheper-userbasedoneinmulti-hopCRNs;ii)thesolutionsattainedbytheproposedheuristicalgorithmsarenear-optimalunderdifferentdatasetsinboththegridtopologyandtherandomone. 137

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CHAPTER6COOPERATIVECOMMUNICATIONAWARELINKSCHEDULINGFORCOGNITIVEVEHICULARAD-HOCNETWORKS 6.1ChapterOverview Withthematurityofroadinfrastructureandtheincreasingnumberofmotorists,highwaytravelinghasbecomeapartoflifeforpeopleinUSandmanyothercountries.VariousbroadbandvehicularcommunicationapplicationsinVehicularAd-hocNetworks(VANETs),whichcanentertainpassengersandmakelongjourneysenjoyable,areenvisionedtobeprevalentinthenearfuture.However,proliferationofvehicularapplicationsbeyondsafetyrequiresadditionalradioresourcestosupport,whichmakesthealreadycrowedlicensedspectrumevenworse.Meanwhile,forallthesepassenger-orientedapplications[ 44 47 116 ],nomattervehicle-to-vehicle(V2V)communicationbasedapplications(e.g.,networkgamingamongpassengersindifferentcars,letransfers,virtualmeetingsamongcoworkers,etc.)orvehicle-to-roadside(V2R)communicationbasedones(e.g.,webbrowsing,cooperativedownloading,onlinevideo,etc.),themostcriticalandessentialrequirementisthedatatransmissionwithhighend-to-endthroughput,whichisalsoachallengingtaskinVANETs. InviewoftheradiospectrumdemandsfromVANETs,FederalCommunicationsCommission(FCC)openstheunder-utilizedlicensedTVspectrum(i.e.,theUHFtelevisionfrequencyspanningover470-806MHz)[ 1 ]andallowstheopportunisticaccessingofunlicensedusers.Byexploitingcognitiveradio(CR)technology,thevehicles/nodes(thewordsvehicles/nodeswillbeusedinthischapterinterchangeably)aswellastheroadsideunit(RSU)inVANETscansensethevacantspectrumandopportunisticallyusetheselicensedbandstemporally/geographically,when/whereprimaryservicesarenotactive.WecallsuchaVANETwithCRcapability[ 77 116 ]asacognitiveVANET(C-VANET). Ontheotherhand,byemployingmultipleantennas,e.g.,multiple-inputandmultiple-output(MIMO),spatialdiversityhasbeenshowntobeeffectiveinloweringbit 138

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AAthree-nodeschematicforcoopera-tivecommunications. BAschematicfortheinterferenceincurredbycooperativecommunications. Figure6-1. Illustrativetoytopologiesforcooperativecommunications. errorrate,enhancingpowerefciencyandimprovingthroughputinVANETs.However,equippingawirelessnodewithmultipleantennasmaynotalwaysbepractical.Toachievespatialdiversitywithoutrequiringmultipletransceiverantennasonthesamenode,theso-calledcooperativecommunicationshasbeenintroducedin[ 58 59 ].Theideaofcooperativecommunicationscanbebestillustratedbyathree-nodeexample[ 58 59 ]showninFig. 6-1A .Inthissub-gure,nodeitransmitstonodejviaone-hop,andnoderactsasacooperativerelaynode.Cooperativetransmissionfromitojisdoneonaframe-by-framebasis.Withineachframe,therearetwotimeslots[ 16 17 44 59 103 ].Inthersttimeslot(solidlines),imakesatransmissiontodestinationj.Duetothebroadcastnatureofwirelesstransmissions,transmissionbyiisalsooverheardbyrelaynoder.Inthesecondtimeslot(dashlines),rforwardsthedataitoverheardinthersttimeslottoj.Thus,undercooperativecommunications,eachnodeisequippedwithonlyasingleantennaandreliesontheantennasofneighboringcooperativenodestoachievespatialdiversity. Ifthecooperativerelaynodeisappropriatelyselected,cooperativecommunicationscaneffectivelyincreasethelinkcapacity[ 103 104 ].However,ifwetaketime-framebasedlinkschedulingintoconsideration,cooperativecommunicationsisnotnecessarilyhelpfultoimprovingtheend-to-endthroughput.TakethetoytopologyshowninFig. 6-1B asanexample.Ifnodeidirectlytransmitspacketstonodej,link(i,j)willhaveno 139

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interferencewithlink(u,v),sothattheycanbescheduledtotransmitsimultaneously.Bycontrast,if(i,j)employsrforcooperativecommunications,(i,j)willconictwith(u,v)sincethetransmissionsofcooperativerelayrcastinterferenceonthereceivingnodevof(u,v).Asaresult,(i,j)and(u,v)cannotbescheduledtotransmitsimultaneously,whichmaydecreasetheend-to-endthroughputfromsrtodt.Intermsofthroughput,thebenetbroughtbycooperativecommunicationsmaybeoffset,orevenoverwhelmedbythelossofopportunitiesforschedulingmorelinkstotransmitatthesametime.Basedonthatobservation,thereappearseveralinterestingquestionsforthethroughputmaximizationprobleminC-VANETs:Whenlinkschedulingisconsidered,doesthereexistanoptimalapproachtomaximizethebenetbroughtbycooperativecommunicationsintermsoftheend-to-endthroughput?Doestheavailabilityoflicensedbandshaveanyimpactontransmissionmodeselection(i.e.,directtransmissionsorcooperativecommunications)aswellasthethroughput?Canwendasimpleandfeasiblewaytosolvethisprobleminpractice? Toaddresstheseissues,inthischapter,weproposeacooperativecommunicationawarelinkschedulingscheme,withtheobjectiveofmaximizingthethroughputforasessioninC-VANETs.WelettheRSUschedulethemulti-hopdatatransmissionsamongvehiclesonhighwaysbysendingsmall-sizecontrolmessages.Jointlyconsideringavailabilityoflicensedspectrum,transmissionmodesandlinkscheduling,wemathematicallyformulatethethroughputmaximizationproblem,near-optimallysolveitbylinearprogramming,andprovideasimpleheuristicalgorithmtogivefeasibleresults.Oursalientcontributionsaresummarizedasfollows. Regardingthefeaturesofcooperativecommunications,wenovellyextendalinkusingcooperativecommunicationsintoacooperativelink.Tokeepnotationconsistent,weleverageadummycooperativerelayandextendalinkusingdirecttransmissionsintoagenerallink. Inspiredbythelinkconictgraphinpriorwork[ 10 61 114 115 131 ],weproposea3-dimensional(3-D)cooperativeconictgraphtodescribetheinterferencerelationshipamongtheextendedlinksinC-VANETs.Similartothemethodology 140

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usedin[ 61 114 115 ],weinterpreteachvertexinthegraphasabasicresourcepointforschedulingandrepresenteachresourcepointwithanextendedlink-bandpair.Basedontheseextendedlink-bandpairs,weestablishthe3-Dcooperativeconictgraphandre-denethecooperativeindependentsetsandconictcliques. Withthehelpof3-Dcooperativeconictgraph,theRSUcanmathematicallyformulatethethroughputmaximizationproblemundermultipleconstraints(i.e.,availabilityofbands,selectionoftransmissionmodesandlinkscheduling).GivenallcooperativeindependentsetsinC-VANETs,theRSUcanrelaxtheintegervariablesintheformulation,solvetheoptimizationproblembylinearprogrammingandobtaintheoptimalend-to-endthroughputbetweenthesourceanddestinationnodes. SinceitisNP-completetondallthecooperativeindependentsetsinC-VANETs[ 30 61 114 115 131 ],weemployanumberofmaximalcooperativeconictcliquesanddevelopaheuristicpruningalgorithmtoapproximatetheoptimalend-to-endthroughput.WelettheRSUselectthebandandtransmissionmodefortheextendedlink-bandpairsinthosecliques,prunethepairsnotselectedandupdatecliquetransmissiontimeuntilthelargestcliquetransmissiontimeamongallcliquescannotbefurtherdecreased.Thethroughputisestimatedasthereciprocalofthelargestcliquetransmissiontime. Bycarryingoutnumericalsimulations,wedemonstratetheimpactofthenumberofavailablebandsandthedistancebetweensourceanddestinationnodesontheperformanceofthroughputinC-VANETs.Wealsoshowthati)theCRcapabilitycreatesmoreopportunitiesforusingcooperativecommunications;ii)theperformanceofcooperativecommunicationawarelinkschedulingisbetterthanthatpurelyrelyingononetransmissionmode;iii)theproposedpruningalgorithmisclosetotheoptimaloneintermsofend-to-endthroughputinC-VANETs. Therestofthischapterisorganizedasfollows.WereviewrelatedworkonthroughputmaximizationinSection 6.2 .InSection 6.3 ,weintroducethesettingsandrelatedmodelsinC-VANETs.InSection 6.4 ,wedescribethe3-Dcooperativeconictgraphandpresenttheconceptofcooperativeindependentsetsandconictcliques.InSection 6.5 ,wemathematicallyformulatethethroughputmaximizationprobleminC-VANETsandnear-optimallysolveitbylinearprogramming.InSection 6.6 ,wedevelopaheuristicpruningalgorithmforcooperativecommunicationawarelinkscheduling.Finally,weconductsimulationsandanalyzetheperformanceresultsinSection 6.7 ,anddrawconcludingremarksinSection 6.8 141

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Figure6-2. Networksettingsandtheend-to-endtrafcdeliverywithtwodifferenttransmissionmodesinC-VANETs. 6.2RelatedWork Throughputmaximizationundercross-layerconstraints(e.g.,owrouting,linkscheduling,etc.)hasbeenextensivelystudiedinexistingliterature.Jainetal.in[ 45 ]studiedtheimpactofinterferenceonperformanceofmulti-hopwirelessnetworkbasedonanNP-completeoptimizationproblem.ZhaiandFangin[ 131 ]investigatedthepathcapacityofagivenpathconsideringlinkschedulingandleveragedtheinterferencecliquetransmissiontimetodesignaroutingmetricforhighthroughputpathselectioninsingle-radiosingle-channel(SR-SC)networks.Formulti-radiomulti-channel(MR-MC)networks,Lietal.in[ 61 ]proposedamulti-dimensional(i.e.,radio-link-channel)conictgraphandexploitedittosolvetheoptimalpathcapacityproblembylinearprogramming. DifferentfromthemobiledevicewithasingleradioinSR-SCnetworksortheonewithmultipleradiosinMR-MCnetworks,theCRdevicehasonlyoneradiobuttheradioisasoftwaredenedone[ 1 3 73 ],whichissupposedtoswitchfrequenciesacrossawidespectrumrange[ 14 97 110 ].InCRresearchcommunity,therehavebeensomeeffortsdevotedtocross-layeroptimizationaswell.Tangetal.in[ 114 ]studiedthejointspectrumallocationandlinkschedulingproblemswiththeobjectivesofmaximizingthroughputandachievingcertainfairnessinmulti-hopCRnetworks.Houetal.in[ 43 ]investigatedthejointfrequencyschedulingandroutingproblemwiththe 142

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objectiveofminimizingthenetwork-widespectrumresourceandpresentedacentralizedalgorithmforspectrumsharinginmulti-hopCRnetworks.Consideringtheuncertainspectrumsupply,Panetal.in[ 88 ]proposedtomodelthevacancyoflicensedbandsasaseriesofrandomvariables,characterizedmulti-hopCRnetworkswithapairof(,)parametersandminimizedtheusageoflicensedspectrumtosupportCRsessionswithraterequirementsatcertaincondencelevels.Unfortunately,thereisstillalackofcross-layerthroughputmaximizationdesigns,whichcaneffectivelyunifytheCRcapabilityofwirelessdevicesandcooperativecommunicationsamongthosedevices. Asforcooperativecommunications,researcheffortsmainlyfocusoninformationtheoreticandcommunicationtheoryproblems.Liuetal.in[ 66 ]andLanemanin[ 58 ]providedanexcellentsurveyofmainresultsonrelatedtopics.Thecommonthemeformostresearchinthiseldistooptimizephysicallayerperformancemeasures(i.e.,biterrorrate,powerefciencyandlinkoutageprobability)fromageneralsystemperspective,withoutmuchconcernabouttheimpactofcooperativecommunicationsonnetworkperformance.Forexample,Host-MadsenandZhangin[ 40 ]andKrameretal.in[ 54 ]investigatedtheachievableratesanddiversitygainsofseveralcooperativeschemeswithagivensourceanddestinationpair.BasedoncascadedNakagamifading[ 121 ],whichprovidesarealisticdescriptionofanintervehicularchannel,Ilhanetal.in[ 44 ]studiedcooperativediversityinVANETs,andproposedarelay-assistedschemetooptimizethepowerallocationforintervehicularcommunications.Somepioneeringeffortsonnetworkingandcross-layerdesignsofcooperativecommunicationsincludemediumaccesscontrolprotocolstoleveragecooperation[ 67 ],cooperativerouting[ 16 56 104 ],optimalnetwork-widecooperativerelayselection[ 103 ],networkcodedcooperativecommunications[ 105 133 ]andcross-layerroutingusingcooperativecommunicationsinVANETs[ 17 ].However,linkschedulingwithajointconsiderationofcooperativecommunicationsandopportunisticspectrumaccessinginVANETsisasubstantiallyunexploredarea. 143

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Pagadaraietal.in[ 80 ]quantitativelyandqualitativelymeasuredandcharacterizedthevacantTVspectrum(470-806MHz)alonginterstatehighway(I-90)inMassachusetts,whichfurtherpavesthewayfortheresearchinC-VANETs.Inthiswork,wearetryingtogiveacomprehensivestudyontheend-to-endthroughputmaximizationinC-VANETs,wheretransmissionmodeselection,availabilityofspectrumandlinkschedulingarealltakenintoconsideration. 6.3NetworkModel 6.3.1NetworkSettingofC-VANETs Weconsideramulti-hopC-VANETs[ 77 116 ]consistingofmultiplevehiclesoperatingondifferentvacantlicensedfrequencybandsandaRSU(e.g.,abasestation(BS),agateway,anaccesspoint(AP),etc.)whoservesthisgroupofnodesN=f1,2,,n,,Ngon(oneway)highwaysasshowninFig. 6-2 .Letsr/dtdenotethesource/destinationnodeforasessioninC-VANETs.Ourobjectiveistomaximizeend-to-endthroughputofthissession.Byexchangingsmall-sizecontrolmessageswiththevehicles,theRSU1canschedulethetransmissionsoflarge-sizedatapacketsformulti-hopV2VcommunicationsorV2Rcommunications[ 77 ].Theschedulingperiodissettoconsideringthevehiclesmerginginto/exitingfromthehighwayaswellastheavailabilityoflicensedbands.SupposethatthesetoflicensedspectrumbandsB=f1,2,,b,,Bghavetheidenticalbandwidth,wherethesizeofthebandwidthisequaltoW.Bothdirecttransmissionsandcooperativecommunicationscanbeusedforpacketsdelivery.Todistinguishtwotypesofrelaynodes[ 104 ]inC-VANETs,wecallarelaynodeusedforcooperativecommunicationspurposeasacooperativerelayandarelaynodeusedformulti-hoprelayinginthetraditionalsenseasmulti-hop 1TheRSUcanalsobeinterpretedasagroupofassociatedRSUsconnectedbythebackbonenetwork,ifthelengthofthepathislong. 144

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relay2.ConsideringtheconceptofcooperativecommunicationsaswellastheinherenthardwarelimitationofCRdevices,wealsoassumethateachnodehasonlyoneradio,buttheradiocanbetunedintoanyavailablefrequencybandforpacketdelivery. Eachnodei2Nemployscertainspectrumsensingtechniques(e.g.,[ 51 60 ])toidentifyasetofavailablelicensedbands,whicharenotoccupiedbyprimaryservices.Dependingonthegeographicallocationsofnodes,theavailablebandsatonenodemaybedifferentfromanotheroneinC-VANETsasshowninFig. 6-2 .Toputitinamathematicalway,letBiBrepresentthesetofavailablelicensedbandsatCRnodei2N.BimaybedifferentfromBj,wherejisnotequaltoi,andj2N,i.e.,possiblyBi6=Bj. Foralink(i,j)usingcooperativerelayr,weassumethetransmissionfromitojandthetransmissionfromrtojusethesameband.Thus,wehaveB(i,r,j)=B(i,j)=BiTBj.Besides,thetimeshare3assignedbytheRSUwillbemeasuredintimeframes,andeachtimeframewillbeequallydividedintotwotimeslotsforthetransmissionfromitojandthatfromrtoj,ifcooperativecommunicationsisemployed. 6.3.2TransmissionModes Inthissubsection,wegiveexpressionsforachievabledatarateunderdifferenttransmissionmodes.Forcooperativecommunications,weconsiderbothAFandDFmodes[ 59 103 ]. 2Notethatacooperativerelayoperatesatthephysicallayerwhileamulti-hoprelayoperatesatthenetworklayer.3Inthischapter,timeperiodreferstotheschedulingperiod,i.e.,;timesharereferstotheactivetimescheduledforanindependentset,i.e.,m,asillustratedinSec. 6.5.2 ;timeframereferstothebasicunitoftimeforlinkscheduling;timeslotreferstothetwotimeslotsdenedincooperativecommunications[ 59 103 ]. 145

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6.3.2.1Amplify-and-forward(AF) Underthistransmissionmode,cooperativerelayrreceives,ampliesandforwardsthesignalfromnodeitonodej[ 59 103 104 ].Lethij,hir,hrjcapturetheeffectsofpath-loss,shadowingandfadingbetweennodesiandj,iandr,andrandj,respectively.Denotezjandzrthezero-meanbackgroundnoiseatnodesjandr,withvariance2jand2r,respectively.Besides,denotePiandPrthetransmissionpowersatnodesiandr,respectively.Sincetheresultsarevalidforallthebands,weomitthebandnotationsinthissubsection. Followingthesamenotationsin[ 58 59 103 104 ],theachievabledatarateunderAFcanbeexpressedas4 CAF(i,r,j)=WIAF(i,r,j), (6) whereIAF(i,r,j)=1 2log21+SNRij+SNRirSNRrj SNRir+SNRrj+1,SNRij=Pi 2jjhijj2,SNRir=Pi 2rjhirj2,SNRrj=Pr 2jjhrjj2,andWistheavailablebandwidthatnodesiandr. 6.3.2.2Decode-and-forward(DF) Underthistransmissionmode,relaynoderdecodesandestimatesthereceivedsignalfromnodeiinthersttimeslot,andthentransmitstheestimateddatatonodejinthesecondtimeslot[ 58 59 103 ].Asin[ 58 59 103 104 ],theachievabledatarateunderDFtransmissionmodeisgivenas CDF(i,r,j)=WIDF(i,r,j), (6) 4Dependingondifferentmodulationschemes,theachievabledatarateisactuallydeterminedbytheSNRatthereceiverandreceiversensitivity[ 16 131 ].However,inmostofexistingliterature[ 43 61 88 103 104 ],theachievabledatarateisapproximatedbythelinkcapacityobtainedfromShannon-Hartleytheorem,eventhoughthecapacitycannotbeachievedinpractice.Notethatthisapproximationwillnotaffectthetheoreticalanalysisaswellasperformancecomparisoninthiswork. 146

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where IDF(i,r,j)=1 2minflog2(1+SNRir),log2(1+SNRij+SNRrj)g. NotethatIAF()andIDF()areincreasingfunctionsofPiandPr,respectively.Thissuggeststhat,inordertoachievethemaximaldatarateundereithermode,bothnodeiandnodershouldtransmitatthemaximumpower.Inthischapter,weletPi=Pr=P. 6.3.2.3Directtransmission Whencooperativecommunicationsisnotused,theachievabledataratefromnodeitonodejis CDTx(i,j)=Wlog2(1+SNRij). (6) Basedontheaboveresults,wehavetwoobservations.First,comparingCAF(orCDF)toCDTx,itishardtosaythatcooperativecommunicationisalwaysbetterthanthedirecttransmission.Infact,apoorchoiceofrelaynodecouldmaketheachievabledatarateundercooperativecommunicationsbelowerthanthatunderdirecttransmissions[ 103 ].Second,althoughAFandDFaredifferentmechanisms,thecapacitiesforbothofthemhavethesameform,i.e.,afunctionofSNRij,SNRir,andSNRrj.Therefore,acooperativecommunicationawarelinkschedulingalgorithmdesignedforAFcanbereadilyextendedforDF.Therefore,itissufcienttofocusononeofthem,wherewechooseAFinthischapter. 6.3.3Transmission/InterferenceRange Theinterferenceinwirelessnetworkscanbedenedaccordingtotheprotocolmodelorthephysicalmodel[ 37 ].Inprotocolmodel[ 37 131 ],therewillbeaxedtransmissionrangeandaxedinterferencerange,wheretheinterferencerangeistypically1.5to3timesofthetransmissionrange.Thesetworangesmayvarywiththefrequencybands.LetTbidenotethesetofneighboringnodeswithinnodei's 147

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transmissionrangeoverlicensedbandb2Bi.Foralink(i,j)usingrforcooperativecommunicationsoverbandb,wehaver6=jandr2Tb(i,j)=TbiTTbj.Ontheotherhand,theconictrelationshipbetweentwolinksoverthesamebandcanbedeterminedbythespeciedinterferencerange.Theprotocolmodelisadoptedbymostoftheexistingwork[ 43 61 88 114 131 ],bywhichtheinterferenceoveranetworkcanbeabstractedintoaconictgraph.WealsoexploittheprotocolmodeltocharacterizetheinterferencerelationshipamongthelinksinC-VANETs,andextendtheconictgraphinto3-Dcooperativeconictgraphconsideringthefeaturesofcooperativecommunications.Thedetailswillbepresentedinthefollowingsection. 6.4CooperativeConictGraph,ConictCliquesandIndependentSetsinC-VANETs Inthissection,werstextendthelinksinC-VANETsintocooperativelinks/generallinkswithrespectto(w.r.t.)thespecialfeaturesofcooperativecommunications.Then,weestablisha3-Dcooperativeconictgraphtodescribetheinterferencerelationshipamongtheseextendedlinks.Besides,wealsore-deneindependentsetsandconictcliques[ 10 131 ]toshowwhichlinkscanbeactivatedatthesametimeandwhichlinkscannot,whencooperativecommunicationsisinvolvedinC-VANETs. 6.4.1ExtendingLinksintoCooperative/GeneralLinks Foralink(i,j),ifnoderisthebestcooperativerelayforit,wecalculatetheachievabledatarateforcooperativecommunications(i.e.,CAF(i,r,j))asillustratedin( 6 ).IfCAF(i,r,j)>CDTx(i,j),wecanextendlink(i,j)into(i,r,j)anddene(i,r,j)asacooperativelink.Tokeepthelinknotationconsistent,weexploit(i,,j)todenotealinkusingdirecttransmissions,whereisadummycooperativerelay,anddene(i,,j)asagenerallink.ThesameprocedurecanbedoneforeachlinkintheC-VANET.DeneRb(i,j)=fgSTb(i,j).Then,wecanextendeachlink(i,j)intotheformof(i,r,j)overbandb,wherer2Rb(i,j).Notethatforalinkqualiedtobeacooperativelink,theRSUcanchoosetouseitasacooperativelinkoragenerallink,whenthe 148

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RSUconsiderstheinterferencerelationshipamongdifferentlinksandschedulesthetransmissionsovertheselinks. 6.4.2Establishingthe3-DCooperativeConictGraph Regardingtheavailabilityoflicensedbandsandthefeaturesofcooperativecommunications,weintroducea3-DcooperativeconictgraphtocharacterizetheinterferencerelationshipamongmultiplelinksinC-VANETs. Specically,ina3-DcooperativeconictgraphG(V,E),eachvertexcorrespondstoanextendedlink-bandpair,whereaextendedlink-bandpairisdenedas((i,r,j),b).Thelink-bandpairindicatesthattheextendedlink(i,r,j)operatesonavailablelicensedbandb.Notethatitincludesthegenerallinkwhenthecooperativerelayr=,andincludesthecooperativelinkwhenthecooperativerelayr6=.Italsoincludescooperativecommunicationsinsingle-radiosingle-channelnetworksasaspecialcasewhenthenumberofavailablelicensedbandsjBj=1. Twoextendedlink-bandpairsaredenedtointerferewitheachother,ifanyofthefollowingconditionsistrue: Condition1:Twodifferentextendedlink-bandpairshavenodesincommon. Condition2:Ifthetwoextendedlink-bandpairsareusingthesameband,theirtransmissionsinterferewitheachotherwheneitherthereceivingnodeorthecooperativerelaynodeofonepairisintheinterferencerangeofeitherthetransmittingnodeorthecooperativerelaynodeintheotherpair. Basedontheseconditions,weconnecttwoverticesinVwithanundirectededgeinG(V,E),iftheircorrespondinglink-bandpairsinterferewitheachother. Forillustrativepurpose,wetakeasimpleexampletoshowhowtoconstructa3-Dcooperativeconictgraph.AsthetoyC-VANETshowninFig. 6-3A ,weassumetherearesixvehicleswithCRtransceivers,i.e.,A,B,C,D,EandF,andtwolicensedbands,i.e.,band1andband2.ThereisapathwithnodeAasthesourceandnodeEasthedestination.Forlink(A,B),weassumeCAF(A,F,B)>CDTx(A,B).Thus,theRSUcanemploynodeFasacooperativerelayandformacooperativelink(A,F,B). 149

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Forlink(B,C),weassumeCAF(B,F,C)
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AToytopologyinC-VANETs. B3-Dcooperativeconictgraph. Figure6-3. Conictrelationshiprepresentedby3-Dcooperativeconictgraph. ((B,,C),2),((C,,D),1)and((D,,E),1).Bycontrast,ifthegenerallink-bandpair((A,,B),1)isadopted,itwillconictwith((B,,C),1),((B,,C),2)and((C,,D),1).ThereasonisthatwemustconsiderboththenodeswithintheinterferencerangeofthetransmittingnodeAandthenodeswithintheinterferencerangeofthecooperativerelayingnodeF,whenthiscooperativelink-bandpairisscheduledfortransmissions. 6.4.3CooperativeIndependentSetsandConictCliques Givena3-DcooperativeconictgraphG=(V,E)representingC-VANETs,wedescribetheimpactofvertexu2Vonvertexv2Vasfollows, wuv=8><>:1,(ifthereisanedgebetweenuandv)0,(ifthereisnoedgebetweenuandv), wherethetwoverticescorrespondtotwolink-bandpairs. Providedthatthereisavertex/extendedlink-bandsetIVandanextendedlink-bandu2IsatisfyingPv2I,u6=vwuv<1,thetransmissionatlink-bandpairuwillbesuccessfulevenifalltheotherlink-bandpairsbelongingtothesetIaretransmittingatthesametime.Ifanyu2Isatisestheconditionabove,wecanschedulethetransmissionsoveralltheseextendedlink-bandpairsinItobeactivesimultaneously.Suchavertex/extendedlink-bandpairsetIiscalledacooperativeindependentset.Ifaddinganyonemoreextendedlink-bandpairintoacooperativeindependentsetI 151

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resultsinanon-independentone,Iisdenedasamaximalcooperativeindependentset.Besides,ifthereexistsavertex/extendedlink-bandpairsetZVinGandanytwoextendedlink-bandpairsuandvinZsatisfyingwuv6=0(i.e.,vertexuandvcannotbescheduledtotransmitsuccessfullyatthesametime.),Ziscalledacooperativeconictclique.IfZisnolongeracooperativeconictcliqueafteraddinganyonemoreextendedlink-bandpair,Zisdenedasamaximalcooperativeconictclique. 6.5OptimalCooperativeCommunicationAwareLinkSchedulingforHighEnd-to-EndThroughput Afterweconstructthe3-Dcooperativeconictgraph,inthissection,werstdiscussthepossiblecollisionsofrelayselectionw.r.t.linkschedulinginC-VANETs.Then,weaddresshowtocalculatethepathcapacityanddescribeowroutingconstraintsforthesingle-radiobasednodes.Accordingtothecross-layerconstraints,wemathematicallyformulatethethroughputmaximizationprobleminC-VANETsandnear-optimallysolveitbylinearprogramming. 6.5.1CollisionsofRelaySelectionw.r.t.LinkScheduling Beforewediscusscooperativecommunicationawarelinkscheduling,weneedtoclarifytwoissuesrelatedtothecollisionsofrelayselectionw.r.t.linkscheduling.Asintroducedin[ 104 ],twokindsofrelayselectioncollisionsmayhappenwhencooperativecommunicationsisincorporatedintomulti-hopwirelessnetworks.Therstoneisthecollisionbetweencooperativerelayselectionandmulti-hoprelayselection(i.e.,anodeischosenbothasacooperativerelayandamulti-hoprelay),asshowninCase1and2inFig. 6-4 ;thesecondoneisthecollisionamongdifferentlinksforcooperativerelayselection(i.e.,differentlinkschoosethesamenodeascooperativerelay),asshowninCase3inFig. 6-4 152

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Ifthereisonlyonebandavailableinthenetwork,itcaneasilybeprovedthattherelayselectioncollisionscanneverhappenw.r.t.linkscheduling5.However,iftherearemultiplebandsavailableinthenetwork(e.g.inC-VANETs),bothcollisionsexistasshowninFig. 6-4 .Fortunately,the3-DcooperativeconictgraphcanperfectlydescribealltherelayselectioncollisionsinC-VANETs(e.g.,allthreecasesinFig. 6-4 satisfyinginterferenceCondition1),sothattheRSUcanexploitittoconductthecooperativecommunicationawarelinkscheduling.NotethatanodeinC-VANETscanalternateitsrolebetweencooperativerelayandmulti-hoprelayatdifferenttimeshares,whichisdifferentfromthenode'sxedrolein[ 104 ]. 6.5.2PathCapacitywithLinkSchedulingConsideration ForagivenpathP,wecanestablishthe3-DcooperativeconictgraphGP=(VP,EP)followingthesameapproachillustratedinSec. 6.4.2 .Then,wecanlistallindependentsetsasIP=fI1,I2,,Im,,IMg,whereMisjIPj,andImVPfor1mM.AlthoughitisaNP-completeproblemtondallindependentsets[ 15 30 61 ],somebrute-forcealgorithmcannishitinpolynomialtimeifthenumberofextendedlink-bandpairsinVPisnotlarge[ 131 ]. Atanytime,atmostoneindependentsetcanbeactivatedtotransmitpacketsforalllink-bandpairsinthatset.Letm0denotethetimesharescheduledtoindependentsetIm,and X1mMm1,m0(1mM). (6) Letrb(i,r,j)(Im)bethedataratefortheextendedlink(i,r,j)overbandb,whererb(i,r,j)(Im)=0iflink-bandpair((i,r,j),b)62Im.Otherwise,if(i,r,j)isacooperativelink 5Thehintisthatforanytwolinkshavingrelayselectioncollision,thesetwolinksinherentlyinterferewitheachotherifthereisonlyonebandavailable.Theycannotbescheduledtotransmitsimultaneously. 153

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Figure6-4. Possiblecasesforrelayselectioncollisionsw.r.t.linkscheduling. and((i,r,j),b)2Im,rb(i,r,j)(Im)istheachievabledataratefor(i,r,j)overbandbwhencooperativecommunicationsisleveraged.UnderAFtransmissionmode,rb(i,r,j)(Im)canbecalculatedfrom( 6 );if(i,r,j)isagenerallinkand((i,r,j),b)2Im,rb(i,r,j)(Im)istheachievabledataratefor(i,r,j)overbandbusingdirecttransmissions,whichcanbecalculatedasillustratedin( 6 ). ByexploitingtheindependentsetIm,theowratethatanextendedlink(i,r,j)cansupportoverbandbinthetimesharemismrb(i,r,j)(Im).Letsrepresenttheaggregatedtrafcdemands.ConsideringtheavailabilityoflicensedbandsinC-VANETs,thetrafcisfeasibleattheextendedlink(i,r,j)ifthereexistsascheduleoftheindependentsetssatisfying ss(i,r,j)=jIPjXm=1mjB(i,r,j)jXb=1rb(i,r,j)(Im). (6) Tomaximizetheend-to-endthroughputofP,wemustconsiderthetrafctravelingthroughalllinksalongthegivenpathfromthesourcetothedestination,i.e., CP=maxmin(i,r,j)2Ps(i,r,j). (6) Letsedenotemin(i,r,j)2Ps(i,r,j),whereeisthebottleneckextendedlinkalongPfortheend-to-endthroughput.Takinglinkschedulingintoconsideration,wecanformulatethepathcapacityproblemasfollows, Maximizese 154

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s.t.:jIPjXm=1m1 (6) sejIPjXm=1mjB(i,r,j)jXb=1rb(i,r,j)(Im) (6) m0,1mjIPj,1bjB(i,r,j)j,se0. (6) AsintroducedinSec. 6.3.1 ,thetimeisdividedintotimeperiodswiththedurationof.Eachtimeperiodisfurtherpartitionedintoasetoftimeslotsindexedbym(1mM),sothatthem-thtimeslothasalengthofm.Inthem-thtimeslot,alltheextendedlink-bandpairsinthesetImwillbescheduledtotransmit.Theend-to-endthroughputofPisdeterminedbythethroughputofthebottleneckextendedlink,i.e.,se.So,duringeachtimeperiodoflength,thepathcapacityofPis se=1 jIPjXm=1mjB(i,r,j)jXb=1rbe(Im)=jIPjXm=1mjB(i,r,j)jXb=1rbe(Im). (6) 6.5.3FlowRoutingConstraintsinC-VANETs Asforrouting,theRSUwillhelpthesourcenodetondtheavailablepathstothedestinationnodefordatadelivery.Similartothemodelingin[ 88 ],wemathematicallypresentthoseroutingconstraintsasfollows. Letfb(i,r,j)representtheowrateoftheextendedlink(i,r,j)overbandb,wherei2N,j2Tbi,r2Rb(i,j)andr6=j.Ifnodeiisthesourcenode,i.e.,i=sr,then Xb2B(j,r,i)r6=i,r2Rb(j,i)Xj2Tbifb(j,r,i)=0. (6) Regardingthesingle-radiorequirementofcooperativecommunicationsandtheinherentsingle-radioconstraintofCRdevices,wefocusontheunicastandsingle-pathroutingproblem.Thus,wehave Xb2B(i,r,j)r6=j,r2Rb(i,j)Xj2Tbifb(i,r,j)b(i,r,j)=s, (6) 155

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whereb(i,r,j)indicatesthattheextendedlink(i,r,j)canonlyhaveanonzeroowatatimeduetothesingle-radioconstraint,i.e., Xb2B(i,r,j)r6=j,r2Rb(i,j)Xj2Tbib(i,r,j)1,b(i,r,j)2f0,1g. (6) Ifnodeiisanintermediatemulti-hoprelaynode(notacooperativerelaynode),i.e.,i6=srandi6=dt,then Xb2B(i,r,j)r6=j,r2Rb(i,j)Xj2Tbifb(i,r,j)b(i,r,j)=Xb2B(j,q,i)q6=i,q2Rb(j,i)Xj2Tbifb(j,q,i)b(j,q,i). (6) Ifnodeiisthedestinationnode,i.e.,i=dt,then Xb2B(j,r,i)r6=i,r2Rb(j,i)Xj2Tbifb(j,r,i)b(j,r,i)=s. (6) Notethatif( 6 ),( 6 ),( 6 )and( 6 )canbesatised,( 6 )isautomaticallysatised.Therefore,itissufcienttolistonly( 6 ),( 6 ),( 6 )and( 6 )assingle-radiobasedroutingconstraints. 6.5.4MaximizingtheThroughputunderMultipleConstraints Tomaximizetheend-to-endthroughputbetweenthesourcenodeandthedestinationnode,theRSUneedstondafeasiblesolutiontojointlyassigningtheavailablefrequencybands,conductingcooperativecommunicationawarelinkschedulingbands,androutingthetrafcfortransmissionandreceptioninmulti-hopC-VANETs.Thus,theend-to-endthroughputmaximizationproblemundermultipleconstraintsinC-VANETscanbeformulatedasfollows. Maximizes 156

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s.t.:Xb2B(j,r,i)r6=i,r2Rb(j,i)Xj2Tbifb(j,r,i)=0(i=sr) (6) Xb2B(i,r,j)r6=j,r2Rb(i,j)Xj2Tbifb(i,r,j)b(i,r,j)=s(i=sr) (6) Xb2B(i,r,j)r6=j,r2Rb(i,j)Xj2Tbifb(i,r,j)b(i,r,j)=Xb2B(j,q,i)q6=i,q2Rb(j,i)Xj2Tbifb(j,q,i)b(j,q,i)(i2Nnfsr,dtg) (6) Xb2B(i,r,j)r6=j,r2Rb(i,j)Xj2Tbib(i,r,j)1,b(i,r,j)2f0,1g (6) 0jB(i,r,j)jXb=1fb(i,r,j)jIjXm=1mjB(i,r,j)jXb=1rb(i,r,j)(Im)(i2N,j2Tbi,r2Rb(i,j),b2B(i,r,j)andIm2I) (6) jIjXm=1m1,m0(1mjIj), (6) where( 6 ),( 6 ),( 6 )and( 6 )specifythatthereisatmostoneoutgoinglinkfromeachnodewithanonzeroow,andthatthereisapathselectedbytheRSUbetweenthesourceandthedestination;( 6 )and( 6 )indicatethattheowrateoftrafcover(i,r,j)cannotexceedthecapacityofthisextendedlink,whichisobtainedfromthecooperativecommunicationawarelinkschedulingasillustratedinSec. 6.5.2 NotethatIincludesallindependentsetsinC-VANETs.Givenallindependentsets6inthenetwork,wendthattheformulatedoptimizationisamixed-integerlinear 6Thatisageneralassumptionusedinexistingliterature[ 10 61 114 115 131 ]forobtainingthroughputboundsorperformancecomparison,wherebothlinkschedulingandowroutingareconsidered. 157

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programmingproblemsinceijonlyhasbinaryvalues.Itcannear-optimallybesolvedinpolynomialtimebysometypicalalgorithms(e.g.,sequentialxingalgorithm[ 43 88 ],branchandbound[ 94 ],etc.)orsoftwares(e.g.,CPLEX[ 79 131 ],LINDO,etc.),providedthatallthecooperativeindependentsetscanbefoundinG(V,E). 6.6AHeuristicPruningAlgorithmforCooperativeCommunicationAwareScheduling Asweknow,tondallcooperativeindependentsetsinG(V,E)isNP-complete[ 10 45 61 115 131 ].Comparedwithcomplexpathselectioninotherwirelessnetworks,itismuchmoresimpleinC-VANETsbecausethereareonlyafewpathsbetweenthesourceanddestinationnodesduetothelimitedspatialredundancyandxeddirectionofhighways7.However,evenforagivenpath,itistoocomplexfortheRSUtondallcooperativeindependentsetsalongthepath,ifthenumberofextendedlinksorthenumberofavailablelicensedbandsalongthepathislarge.Insteadofusingcooperativeindependentsets,inthissection,weemployanumberofmaximalcooperativecliquesandproposea7-steppruningalgorithmtoapproximatethemaximalthroughputforasessioninC-VANETs. 6.6.1AnIterativeLink-bandPairPruningAlgorithm ThedetailedprocedureoftheproposedpruningalgorithmforcooperativecommunicationawarelinkschedulinginC-VANETsispresentedasfollows. Step1:Establishingthe3-Dcooperativeconictgraph GivenacandidatepathP,werstsetupacorresponding3-DcooperativeconictgraphGP(VP,EP)asillustratedinSec. 6.4.2 Step2:Searchingforthemaximalconictcliques 7In[ 17 ],DingandLeungevenemploystringtopologytoinvestigatethecross-layerroutingprobleminVANETs. 158

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Withtheestablished3-DcooperativeconictgraphofthegivenpathP,wetrytondallthemaximalcooperativeconictcliquesinGP(VP,EP)andformthesetZconsistingofthemaximalcooperativeconictcliques.IfPinvolveswithtoomanyextendedlinksoravailablebands,anditisimpossibletondallthemaximalcliques,wecanemployKmaximalcliquesforapproximationwhenKislargeenough. Step3:Calculatingtheconictcliquetransmissiontime Then,welettheRSUemploythemaximalcooperativeconictcliquestoestimatethebenchmarkpathcapacityforthepathP.Similartotheillustrationin[ 10 131 ],wedenethecooperativeconictcliquetransmissiontimeTZforacooperativeconictcliqueZas TZ=X((i,r,j),b)2ZT((i,r,j),b) (6) whereT((i,r,j),b)isthetransmissiontimeforoneunitoftrafcovertheextendedlink(i,r,j)usingtheavailablelicensedbandb.Specically,T((i,r,j),b)canbewrittenas T((i,r,j),b)=1 rb(i,r,j)(Z), (6) whererb(i,r,j)(Z)isequaltotheachievabledatarateoflink(i,r,j)overbandb,if((i,r,j),b)2Z).Otherwise,rb(i,r,j)(Z)=1. Step4:Sortingthemaximalcooperativeconictcliques ForZ2Z,wesortthemaximalcooperativeconictcliquesintermsofthecooperativeconictcliquetransmissiontimeTZ.LetTPbethemaximumvalueofthetransmissiontimeforallcooperativeconictcliques.TPcanbewrittenas TP=maxZ2ZTZ. (6) Consideringanextendedlink-bandpair((i,r,j),b)in^Z=argmaxZ2Z(TZ)andoneunitoftrafcsuccessfullydeliveredfromthesourcetothedestination,ittakestimeTPtotravelthroughalltheextendedlink-bandpairsin^Z,and((i,r,j),b)cannotbe 159

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scheduledtodoanyothertransmissionduringTP.Thatindicatesthatthethroughputattheextendedlink-bandpair((i,r,j),b)islessthanorequalto1 TP.Sincetheend-to-endthroughputcannotbelargerthanthethroughputofanylinkalongthepath,thebenchmarkpathcapacityCPcanbeestimatedas8 CP=1 TP (6) Step5:Selectingtheoptimalbandforthehighthroughput Iftherearemultipleavailablelicensedbandsforanextendedlinktoaccess,oneofthemmustbechosenduetothesingle-radioconstraint.Onbehalfofsuchanextendedlink,theRSUwillselecttheoptimalbandforitsaccessinginordertoimprovetheend-to-endthroughput. From( 6 ),( 6 )and( 6 ),wendthatifthesizeof^Zshrinks,thethroughputofthepathmayincrease.Itisobviousthatifsomeoftheco-bandinterferencebetweentheextendedlinkscanbemitigated,thesizeof^Zcanbeeffectivelyreduced.Asweknow,theCRdevicescanbetunedintodifferentfrequenciesandallowtheextendedlinkstooperateondifferentbands.ThisspecialCRfeaturewillhelptoreduceco-bandinterferencebetweentheextendedlinkssothattheend-to-endthroughputmaybeimproved.Followingthisthread,weconducttheoptimalbandselectionasfollows. First,foranextendedlink(i,r,j)withmultipleaccessingbands,werandomlyselectanextendedlink-bandpair((i,r,j),b)in^Zandtemporarilydeleteother((i,r,j),)pairsaswellastheconictedgesassociatedwith((i,r,j),).Then,wendthemaximalcooperativeconictcliqueintheleftovergraphcutfrom^ZandcalculatethecliquetransmissiontimeT((i,r,j),b)^Zasin( 6 ).Forb2B(i,r,j),thesameprocessisconducted 8Actually,thebenchmarkpathcapacityCPshouldbeupper-boundedby1 TP,i.e.,CP1 TP.Theequalsignholdsiftherearenooddcycles[ 15 ]inGPasillustratedin[ 131 ].Inthischapter,wejustconsiderthegeneralpathswithoutoddcycles. 160

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AOnlyonelicensedbandavailableinC-VANETs(withoutbandselection). BTwolicensedbandsavailableinC-VANETs(withbandselection). Figure6-5. Twoillustrativeexamplesfortheproposedpruningalgorithmwithagivenpath:(a)onelicensedbandavailable;(b)twolicensedbandsavailable. andthevaluesofcliquetransmissiontimearestored.Afterthat,weupdateT^Zas T^Z=minfT((i,r,j),1)^Z,T((i,r,j),2)^Z,,T((i,r,j),jB(i,r,j)j)^Zg. (6) WeidentifythebandreachingthevalueofT^Z,putthatbandinto(i,r,j)'susageandprunealltheother((i,r,j),)pairsaswellastheconictedgesassociatedwith((i,r,j),). Thesameprocedureaboveisrepeatedbyalltheextendedlink-bandpairsin^Zoneafteranother,andtheT^Ziscontinuouslyupdated. Ifalltheavailablelicensedbandsareidenticaltoanextendedlinkintermsofbandcondition(i.e.,bandwidth,thepropagationgain,etc.),itwillbemuchmoresimpletoselecttheoptimalbandforthisextendedlink.Asforsuchanextendedlink,wejustneedtokeeptheextendedlink-bandpairwiththeleastconictedgesandeliminatethe 161

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otherlink-bandpairsassociatedwiththisextendedlink.Meanwhile,wealsoprunethecorrespondingconictedgesandupdateT^Zbasedontheleftovergraphcutfrom^Z. Step6:Pruningthecooperative/generallink-bandpairs Afterthebandselectionforanextendedlink,itisnecessarytodeterminewhichtypeoftransmission(i.e.,cooperativecommunicationsordirecttransmission)shouldbeusedbythisextendedlink.In^Z,theremaybetwocoupledlink-bandpairsextendedfromthesamelink(i,j):agenerallink-bandpair((i,,j),u)andacooperativelink-bandpair((i,r,j),v),(r2R(i,j)andr6=),whereuandvaretheavailablebandsselectedfor(i,,j)and(i,r,j)inStep5,respectively. From( 6 ),( 6 ),( 6 ),( 6 )and( 6 ),wecaneasilycalculatethetransmissiontimefortheclique^Znf((i,,j),u)gand^Znf((i,r,j),v)g,i.e.,T^Znf((i,,j),u)gandT^Znf((i,r,j),v)g,respectively.WecompareT^Znf((i,,j),u)gandT^Znf((i,r,j),v)gandmakethedecisionofpruningthecooperative/generallink-bandpairsasfollows IfT^Znf((i,,j),u)g>T^Znf((i,r,j),v)g,theRSUwillkeepthegenerallink-bandpair((i,,j),u)andprunethecooperativelink-bandpair((i,r,j),v)aswellastheconictedgesassociatedwith((i,r,j),v).Thatis,theRSUchoosesthedirecttransmissioninsteadofcooperativecommunicationsforthelink(i,j).Inaddition,theRSUwillupdateT^ZbysettingT^Z=T^Znf((i,r,j),u)g. IfT^Znf((i,,j),u)gT^Znf((i,r,j),v)g,theRSUwillkeepthecooperativelink-bandpair((i,r,j),v)andprunethegenerallink-bandpair((i,,j),u)aswellastheconictedgesassociatedwith((i,,j),u).Thatis,theRSUchoosescooperativecommunicationsinsteadofthedirecttransmissionforthelink(i,j).Inaddition,theRSUwillupdateT^ZbysettingT^Z=T^Znf((i,,j),u)g. Thesameprocedureisrepeatedbyanytwocoupledextendedlink-bandpairsin^Zassociatedwiththesamelink,andtheT^Ziscontinuouslyupdated. Step7:Iteratingtheprocedureandestimatingthethroughput JumpbacktoStep4,resortthemaximalcooperativeconictcliquesintermsofthecooperativeconictcliquetransmissiontime(withtheupdatedT^Z),ndnew^Zanditeratethefollowingstepswiththisclique.Iterationscontinueuntil^TPcannotbedecreasedfurther.Then,theRSUcansetTP=TP=T^Zandestimatethethroughput 162

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ofPasCP=1 TP.Similarly,theRSUcanmaximizethethroughputoftheotherpathsviacooperativecommunicationawarelinkscheduling,andselecttheonewiththehighestend-to-endthroughput. 6.6.2IllustrativeExamplesfortheProposedPruningAlgorithm Wetaketwoexamplestofurtherillustratetheproposedpruningalgorithm.ThenetworktopologiesofthetwoexamplesarethesameastheoneshowninFig. 6-3A .Thedistancebetweennodesandthetransmission/interferencerangeassumptionsarealsothesame,buttheassumptionsaboutbandavailabilityaredifferent.Fortherstexample,weassumethereisonlyonelicensedbandavailableforeachlinkinthenetwork.Forthesecondone,weassumetheavailablebandsetforeachlinkisthesameasshowninFig. 6-3A ,andthetwobandsareidenticaltotheextendedlinksintermsofbandcondition.Besides,forbothexamples,weassumethecooperativerelayFisoptimallyselected[ 103 ]andr1(A,F,B)>r1(A,,B),whichindicatesthatT((A,F,B),1)
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overT^Znf((A,,B),1)g=2T+T((A,F,B),1)andthatoverT^Znf((A,F,B),1)g=3T.SinceT((A,F,B),1)
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Figure6-6. Comparisonbetweencooperativecommunicationsanddirecttransmissionsforathree-nodeschematic. pruningalgorithm(i.e.,PruningCC/Dtxw/CR),theoptimalthroughputconsideringbandselectionunderdifferenttransmissionmodes(i.e.,OptimalCCw/CRandOptimalDtxw/CR)andthesingle-bandbasedoptimalthroughputunderdifferenttransmissionmodes(i.e.,OptimalCCw/oCRandOptimalDtxw/oCR)[ 131 ].Notethatgiventheindependentsets,wecanemployCPLEX[ 79 ]tosolvetheoptimizationproblemsandobtainnear-optimalresults.Besides,wedemonstratetheimpactofthenumberofavailablelicensedbandsonthethroughputinC-VANETsandpresenttheresultsinFig. 6-7 .Forthesessionsfromthesourcenodetoalltheothernodesalongthehighway,wealsoconductsimulationstoevaluatetheimpactofdistancewithdifferentthroughputmaximizationalgorithmsandshowthecorrespondingresultsinFig. 6-8 InFig. 6-6 ,wecomparetwotransmissionmodesintermsoflinkcapacity.Here,weassumethetransmitter,thecooperativerelayandthereceiverareonthesamelane,andthedistancebetweenthetransmitterandthereceiveris250m.Wendthatcooperativecommunicationsisnotnecessarilybetterthandirecttransmissionsintermsoflinkcapacity,andthebenetbroughtbycooperativecommunicationshighlydependsonthelocationofthecooperativerelay. Figure 6-7 demonstratestheimpactofthenumberofavailablelicensedbandsontheend-to-endthroughputinC-VANETs.FromtheresultsshowninFig. 6-7A andFig. 6-7B ,fourobservationscanbemadeinorder.First,OptimalCC/Dtxw/CRandtheheuristicpruningalgorithmoutperformtheotheralgorithmsintermsofend-to-endthroughput.Itisnotsurprisingbecausebothofthemhaveajointconsiderationof 165

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transmissionmodeselectionandthebandselection,whenthetransmissionsarescheduled.Inaddition,thethroughputobtainedfromtheproposedpruningalgorithmisclosetothatfromtheoptimalone.Second,consideringlinkscheduling,cooperativecommunicationsmayincurextrainterferenceandhindertheend-to-endthroughput,especiallywhenthenumberofavailablebandsislimited.Third,theCRcapabilityofthenodescreatesmoreopportunitiestousecooperativecommunicationsandthereforeimprovethethroughput.AsforthosealgorithmsconsideringtheCRcapabilityofnodes,theend-to-endthroughputincreasesasthenumberofavailablebandsincreases.Thereasonisthatmorelicensedbandsavailablegivemoreopportunitiesfornodes'accessing,sothatmorecooperativelinkscanbeutilizedwithoutincurringadditionalinterferenceandmorelinkscanbeactivatedfortransmissionsimultaneously.Theincrementofthroughputstopswhenthenumberofavailablebandsislargeenough,i.e.,thethroughputcannotbefurtherincreasedsincebothcooperativecommunicationsandlinkschedulingarefullyexploited.Fourth,thedeviationofvehiclespeedleadstoperformancedegradationoflinkscheduling.Thatisbecausespeedingup/slowingdownmayresultincertainchangesofnetworktopology(e.g.,overtaking)inC-VANETs. Figure 6-8 showstheimpactofdistancebetweenthesourceanddestinationnodesonthethroughputinC-VANETs.Forthesimplicityofcomputingindependentsets[ 61 ],weassumethereare2licensedbandsavailableinthenetwork.ExceptfortheobservationswealreadyhavemadeinFig. 6-7 ,wendthatthelongerdistancethepathspans,themorelikelythethroughputisaffectedbythebandselection,transmissionmodeselectionandlinkscheduling.Forashort-distancepathwhichincludesonlyafewlinks,cooperativecommunicationsisalwayspreferredsincethereisnolinkschedulinginvolved.Bycontrast,along-distancepathincludesmorelinks,whichimpliesthatmorelinkscouldbescheduledtotransmitatthesametime.Thus,theend-to-endthroughputmaximizationofsuchapathdependsmoreonbandselection,transmissionmodeselectionandlinkscheduling. 166

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AScenario1:vehiclespeedis75mph. BScenario2:vehiclespeedfollowsGaussiandistribu-tionwithameanof75mphandastandarddeviationof10mph. Figure6-7. Impactofthenumberofavailablelicensedbandsontheend-to-endthroughputinC-VANETs. 167

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AScenario1:vehiclespeedis75mph. BScenario2:vehiclespeedfollowsGaussiandistribu-tionwithameanof75mphandastandarddeviationof10mph. Figure6-8. Impactofdistancebetweenthesourceanddestinationnodesontheend-to-endthroughputinC-VANETs. 168

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6.8ChapterSummary Inthischapter,wehavestudiedthethroughputmaximizationprobleminC-VANETsundermultipleconstraints(i.e.,CRdevices'inherentsingle-radioconstraint,theavailabilityoflicensedspectrum,transmissionmodeselectionandlinkscheduling).Consideringthespecialfeaturesofcooperativecommunications,werstextendthelinksandclassifythemintocooperativelinks/generallinks.Then,dependingontheavailablebandsatdifferentextendedlinks,wedeneextendedlink-bandpairsandforma3-Dcooperativeconictgraphtodescribetheconictrelationshipamongthosepairs.Afterthat,wemathematicallyformulatetheend-to-endthroughputmaximizationproblem.GivenallcooperativeindependentsetsinC-VANETs,wecanrelaxtheformulatedoptimizationproblemandnear-optimallysolveitbylinearprogramming.DuetotheNP-completenessofndingallindependentsets,weprovideaheuristicpruningalgorithmforthecooperativecommunicationawarelinkschedulingaswell.Bynumericalsimulations,wedemonstratethat:i)theCRcapabilitycreatesmoreopportunitiesforusingcooperativecommunications;ii)theperformanceoflinkschedulingwithappropriatelyselectedtransmissionmodeisbetterthanthatpurelyrelyingononetransmissionmode(eithercooperativecommunicationsordirecttransmissions). 169

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CHAPTER7PURGINGTHEBACK-ROOMDEALING:SECURESPECTRUMAUCTIONLEVERAGINGPAILLIERCRYPTOSYSTEM 7.1ChapterOverview Duringthelastdecade,thedilemmabetweentherapidgrowthofwirelessservicesandthelimitedradiospectrumhasshovedthexedspectrumallocationofFederalCommunicationsCommission(FCC)offtheedge,andpouredoutnumerousnewtechniques,whichallowtheopportunisticaccesstotheunder-utilizedspectrumbands[ 1 3 20 73 ].Inspiredbythemechanismsinmicroeconomics[ 84 100 132 ],auctionseemstobeoneofthemostpromisingsolutionstotheproblemofvacantspectrumallocationtothepotentialunlicensedusers[ 48 124 135 136 ]. Ingeneral,conventionalauctionscanbeclassiedintoseveralcategoriesbydifferentcriteria[ 52 55 ],i.e.,openorsealedauctionbythebiddingmanner,rstpriceauction,secondarypriceauction,Vickeryauction[ 117 ],orVickrey-Clarke-Groves(VCG)auction(alsoknownasGeneralizedVickreyAuction,i.e.,GVA)bythepricingmanner,andsingleitemorcombinatorialauctionbythenumberofauctionedgoods[ 13 118 ].Accordingtotherequirements,theseauctionmechanismscanbeappliedtodifferentscenarios.Forinstance,themostwidelyusedauctioneer-favoredauction,Englishauction[ 52 55 ],isanopenrstpriceauction,wherethebidderwiththehighestbidwinstheauctionandpaysatthepriceofhisbid.Thiskindofopenauctionenablestheauctioneertomaximizehismonetarygains,butitisnotstrategy-proof.InEnglishauction,eachbidderhastostrategizedelicatelytowin,whichinevitablyleadstogreatcomplexityandalongauctiontime.Onthecontrary,thesealedsecondarypriceauctioncanmakesurethebidderssubmittheirbidswithtrueevaluationvaluesandsavetheauctiontime.However,itoftenresultsinunsatisfactoryrevenuefortheauctioneer.Equivalenttosealedsecondarypriceauctionforsingleitemauction,VCGauctionhasbeenprovedtobeincentivecompatible,Paretoefcient,andindividualrational[ 55 ].Undercertainassumptions,VCGauctionistheonlymechanismthatcansatisfyallthe 170

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abovethreepropertieswhilemaximizingtheexpectedrevenueoftheauctioneer[ 36 ].Withrespecttothesecurityissues,therehasbeenconsiderableworkondesigningelectronicauctionwithdifferentfeatures,suchasfairness[ 92 123 ],condentiality,anonymityandsoon[ 7 ]. Despitethedesirablecharacteristics,traditionalauctioncannotbehammeredintothespectrumauctiondesigndirectly.Unlikecommongoodsinconventionalauctions,spectrumisreusableamongbidderssubjecttothespatialinterferenceconstraints,i.e.,biddersgeographicallyfarapartcanusethesamefrequencysimultaneouslywhilebiddersincloseproximitycannot.Eventhoughinterferenceisonlyalocaleffect,thespatialreuseoffrequencymakestheproblemofndingtheoptimalspectrumallocationNP-complete[ 25 45 ],whichfailsalltheoptimalallocationbasedconventionalauctionmechanisms[ 135 ].Besides,theseuniquepropertiesofspectrumbutterytheeffectofthelocalback-roomdealing(i.e.,untruthfulbidding,collusionamongthebidders,fraudsoftheauctioneer,andbid-riggingbetweenbiddersandauctioneer)tothewholenetworkwithinthecoverageoftheauctioneer.Therefore,thetaskofdesigningasecurespectrumauctionishighlychallengingbutimperative. Todealwiththemutualinterferencebetweenneighboringbidders,Gandhietal.[ 25 ]hasproposedtheconictgraphandageneralframeworkforwirelessspectrumauctions.Basedontheseconcepts,atruthfullybiddingspectrumauction,VERITAS,isaddressedbyZhouetal.in[ 135 ].Thenotionofcriticalneighbor/valueisproposedandemployedtoguaranteetheauctionstrategy-proof.However,thebiddersinVERITASmustberisk-seeking[ 99 ].Otherwise,ifthebiddersareonlygreedy,butstillrationalandriskneutral,biddersdonothaveincentivetobidarbitrarilyhighorlowwiththeconcernofoverpaymentorlosinginanauction[ 36 ].Inthesealedsecondaryprice/VCGauction,ifariskneutralbidderhasnoinformationaboutthebidsoftheotherbidders,thedominantstrategyforhimistobidwithhistrueevaluationvalues[ 50 55 ].Zhouetal.[ 135 ]alsoprovideanefcientallocationalgorithm,whichassignsbidderswith 171

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spectrumbandssequentiallyfromthebidderwiththehighestbidtotheonewiththelowestbidbyconsideringthecomplexheterogeneousinterferenceconstraints.However,thevalidityofthisalgorithmischallengedbyaspecialscenarioin[ 124 ].Wuetal.in[ 124 ]showthatitisnotalwaysrighttoallocatethespectrumbandstothebidderwiththehighestbidincasethatthesumoftheneighboringbidsismuchhigherthanthehighestbid.Inaddition,thecollusionamongthebiddersisdescribedin[ 124 ].Asapossiblesolution,theygroupthenodeswithnegligibleinterferencetogetherasvirtualbidders,trimthemulti-winnerspectrumauction[ 124 ]intoatraditionalsingle-winnerauction,andthensplitthepaymentorrevenueamongtheparticipatingbiddersusinggametheory.However,itshouldbenotedthattheissueofgrouppartitionitselfisNP-completeintermsofthespatialreuse[ 45 ]. Asidefromtruthfullybiddingandcollusionamongthebidders,asecurespectrumauctiondesignshouldalsotakethefraudsoftheinsincereauctioneer(i.e.,theauctioneeroverchargesthewinningbidderswiththeforgedprice)andthebid-riggingbetweenthebiddersandtheauctioneer(i.e.,theauctioneercolludeswithgreedybidderstomanipulatetheauction)intoconsideration1.Acombinationofinterferenceconsiderationandcryptographictechniquesallowsustoprovideanovelsecurespectrumauctionscheme,THEMIS2,topurgethesepossibleback-roomdealing.Themajorcontributionsoftheproposedauctionarelistedasfollows: 1Inthischapter,greedybiddersandinsincereauctioneeraredifferentfrommaliciousattackers,thoughallofthemmayimpairtheperformanceofthespectrumauction.Greedybiddersandinsincereauctioneerarerationalbecausetheydonotattempttoattackothersonsacricingtheirownprots.Maliciousattackersalwaystrytodegradetheperformanceoftheauctionevenwithhugecost.Inaddition,thefraudandbig-riggingareformallydenedinSec. 7.2.2 .2THEMISisanancientGreekgoddesswhoisablind-foldedladyholdingaswordandasetofscalesasshowninFig. 7-1 .THEMISisworld-widelyreferredasthesymboloftruthandjustice. 172

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1. THEMISsupportsspectrumbandswithdiversecharacteristicsotherthanthebandsonlywithuniformcharacteristicsinpreviousworks[ 25 124 135 ]. 2. THEMISprovidesaneffectiveproceduretoauctionthespectrumbandswithconsiderationoftheinterferenceconstraints.TocountertheNP-completenessofspectrumallocationinviewofthefrequencyreuse,THEMISdividesthewholenetworkintosmallsubnetworksaccordingtothenumberofbiddersandauctionsthespectrumbandsinsubnetworksonebyone.Meanwhile,eachbiddermaintainsalocalconict-table,andabidderisabletoupdatehisconict-tableandbroadcastthespectrumoccupancyinformationtohisneighborswhendetectingchangesoftheenvironment. 3. THEMISleveragesPailliercryptosystem[ 81 83 ]tomaskthebiddingvaluesofeachbidderwithavectorofciphertexts,whichenablestheauctioneertondthemaximumvalue,randomizethebids,andchargethebidderssecurely.Inthisway,theauctioneercouldcomputeandrevealtheresultsofspectrumauction,whiletheactualbiddingvaluesofthebiddersarekeptsecretfromtheotherbiddersandevenfromtheauctioneerhimself. 4. THEMISsecuresthespectrumauctioneffectivelyagainsttheback-roomdealingwithlimitedcommunicationandcomputationalcomplexity.OursimulationresultsshowthatTHEMISachievessimilarperformancecomparedwithexistinginsecureauctiondesignsintermsofspectrumutilization,therevenueoftheauctioneer,andbidders'satisfactorydegree. Theremainderofthechapterisorganizedasfollows.InSection 7.2 ,systemmodelisoutlinedanddesignchallengesaredescribed.VCGauctionandPailliercryptosystemareintroducedasthefundamentalsinSection 7.3 .InSection 7.4 ,theprocedureandencryptiondesignofTHEMISareillustrated.TheperformanceanalysisispresentedinSection 7.5 .Finally,concludingremarksaredrawninSection 7.6 7.2SystemModel 7.2.1Overview Weconsideratypicalspectrumauctionsetting,whereoneauctioneerauctionshisunutilizedspectrumbandsS=f1,2,...,sgtoN=f1,2,...,ngnodes/bidderslocatedinthegeographicregion.TheavailableSspectrumbandsaresupposedtohavedifferentcharacteristicstodifferentnodes(inthesequel,weusethewordsnodesandbiddersinterchangeably)intermsofthefrequencyoftheavailableband,thesegmenttypeof 173

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Figure7-1. Systemarchitecture,conictgraph,andsecurespectrumauctionmemo. theband(i.e.,contiguoussegmentordiscontinuousone),thelocationofthebidders,etc.[ 75 76 125 ],sothatbiddersmaysubmitdifferentbidsfordifferentcombinationsofthespectrumbands.Consideringthefrequencyreuse[ 25 45 ],i.e.,adjacentnodesmustnotusethesamebandssimultaneouslywhilegeographicallywell-separatedonescan,werepresenttheinterferencerelationshipamongbiddersbyaconictgraph,whichcanbeconstructedfromeitherphysicalmodel[ 8 ]orprotocolmodel[ 37 ]asdescribedin[ 25 124 135 136 ].AsshowninFig. 7-1 ,theedgesstandformutualinterferencebetweencorrespondingnodes.Moreover,weassumethatspectrumauctionstakeplaceperiodically3,thebiddersarestaticineachperiod,andthereisacommonchannel4fornecessaryinformationexchangesbetweentheauctioneerandbidders. 3Theauctionperiodshouldnotbetoolong(e.g.,monthsoryears)tomakedynamicspectrumallocationinfeasible,anditshouldnotbetooshort(e.g.,secondsorminutes)toincuroverwhelmingoverheadinspectrumtrading.Thetypicaldurationishoursordaysasshownin[ 31 ].Intherestofchapter,weassumethatallthespectrumauctionsareofxedduration,sothatthetimeparameterisnotincluded,andweonlyneedtofocusonaspecicperiodforthedesignofsecurespectrumauction.4Itislikethecommoncontrolchannel(CCC)proposedin[ 1 ],orthecommonpilotchannel(CPC)in[ 93 ] 174

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Themainnotationsanddenitionsrelatedtothespectrumauctionaresummarizedasfollows. BidderSet(N)N=f1,2,...,ngrepresentsthesetofnbidders. SpectrumBandSet(S)S=f1,2,...,sgisthesetofsavailablespectrumbands. AllocationSet(NS)NS=f:S!NgdenotesthesetofallocationsofspectrumbandsStobiddersN.Forinstance,forN=f1,2gandS=f1g,NS=f1=(f1g,fg),2=(fg,f1g)g,e.g.,(f1g,fg)denotesthatspectrumband1isallocatedtobidder1andnothingtobidder2. BiddingValues(bi)biindicatesthebiddingvaluesofnodeiforcertainallocationset,e.g.,forNS=f1=(f1g,fg),2=(fg,f1g)g,b1=(1,0)andb2=(0,2)indicatethatnode1bids1fortheallocation1and0for2,andnode2bids2fortheallocation2and0for1. EvaluationValues(vi)virepresentsthetrueevaluationvaluesofnodeiforcertainallocationset.Incasethattheauctionisincentivecompatible,viequalstobi. ChargingPrice(pi)piisthepricechargedbytheauctioneerforallocatingthespectrumbandstowinningbidderi.Thischargingpricemightbedifferentamongbidders,andthechargingmechanismsaredifferentovervariousallocationsaswell. Bidder'sUtility(ui)uistandsforthebudgetbalanceofbidderi.Itisdenedasui()=vi())]TJ /F5 11.955 Tf 11.96 0 Td[(piforthespecicallocation. Auctioneer'sRevenue(R)Rdenotesthemonetarygainsoftheauctioneer.ItissimplyexpressedasR=Pn1pi. 7.2.2DesignChallenges Toprecludethethreatsfromuntruthfulspectrumauctionbidders,sealedsecondarypriceauctionorVCGauctionseemstobethemostfavoritechoice,asmentionedintheintroduction.However,basedontrustableauctioneer,thistypeofauctionisvulnerabletothefraudsoftheauctioneerandnotbid-riggingresistant. Denition7.1. Afraudisadeceptionmadebytheinsincereauctioneer.Theauctioneercommitsfraudsbyoverchargingthewinningbidderswiththeforgedpriceforhis 175

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AFraudsoftheinsincereauctioneer BBid-riggingbetweentheauctioneerandthebidders Figure7-2. Challengestosecurespectrumauctiondesign personalmonetarygain,whichdamagestheutilityofthecorrespondingwinnersinthespectrumauction. Denition7.2. Bid-rigginginthespectrumauctionisaformofcollusionbetweentheauctioneerandthebidders,whereinsincereauctioneerconspireswithgreedybidderstoillegallyxtheprice,sharethespoils,andmanipulatetheauctions. Tobespecic,wetakethescenarioshowninFig. 7-2 forexample,whereonlyonespectrumbandisavailableforauction5.InFig. 7-2 (a),thewinningbid(i.e.,thehighestbid)is7andthechargingprice(i.e.thesecondhighestbid)shouldbe6forthewinnerC.However,byfabricatingadummybidclosetothehighestbidat6.9,theinsincereauctioneercanobtainhigherrevenue.Sincetheauctionissealedandnobiddersareabletocheckthebidsofothersduringtheauction,theauctioneermayabusehisunsupervisedauthoritybycarryingoutfrauds,whichwouldnotbeexposedbythebiddersunlessthewinningbidderscanverifyeachbidfromtheirinterferingneighborslaterafterthespectrumauction. 5VCGisequivalenttothesealedsecondarypriceauctioninthesenseofsinglespectrumbandauction. 176

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InFig. 7-2 (b),weshowanexampleofbid-riggingbetweentheauctioneerandthebidders.SupposenodeAisagreedybidderwhocancolludewiththeauctioneer.Sinceallthebiddingvaluesareopentotheauctioneerforappropriatelysortingthebidsandallocatingthebands,theauctioneercanconspirewithAbyrevealingthewinningbidofCtoA.NodeAmaybidfarmorethanhistrueevaluationvaluesothattheauctioneerisabletochargemorefromwinnerC,andsharesthespoilswithA.Inthisway,noawscanbefoundbythewinners,eveniftheytakethetroubleinverifyingeachbidaftertheauction. Therefore,topurgethesepotentialback-roomdealing,anidealspectrumauctionshouldallowtheauctioneertomaketheappropriatedecisionofallocatingspectrumbandsandpublishonlytheresultsoftheauction,i.e.,winnersandtheirpayments,whilethebiddingvaluesmustbekeptsecretevenfromtheauctioneer. 7.3Preliminaries Inthissection,weintroduceVCGauctionanddescribethepropertiesofPailliercryptosystemasthefundamentalsforourproposedTHEMISauction. 7.3.1VCGAuction Asoneofthemostwidelyusedauctionschemes,VCGauctionisprovedtobeindividualrational,Paretoefcient,andincentivecompatible[ 117 ].InVCG,thedominantstrategyforabiddertowintheauctionandmaximizehisutilityistodeclarehistrueevaluationvaluesregardlessofthebiddingactionsoftheotherbidders.DetailsofVCGauctionareasfollows.TodistinguishfromthenotationsinTHEMIS,wesubstituteS=f1,2,3,...,sgwithG=f1,2,3,...,ggforillustrativepurposesinthissubsection. Bidding: Eachbidderisubmitshissealedbiddingvectorbiforallthepossibleallocations2NG. Allocation: 177

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TheauctioneerselectsaParetoefcientallocation2NGbasedonthetruthfulbiddingvalues.Thatis =argmax2NGXibi(). (7) Then,thegoodsareassignedaccordingto. Charging: Assumeiisanallocationwithoutnodeisatisfyingthefollowinginequality Xj6=ibj(i)Xj6=ibj(). (7) Then,thepaymentofbidderiisdenedas pi=Xj6=ibj(i))]TJ /F14 11.955 Tf 11.95 11.36 Td[(Xj6=ibj(). (7) So,theutilityofbidderiisui()=vi())]TJ /F5 11.955 Tf 11.95 0 Td[(pi.Itcanalsobeexpressedas ui()=vi())]TJ /F14 11.955 Tf 11.95 9.69 Td[()]TJ 7.47 1.67 Td[(Xj6=ibj(i))]TJ /F14 11.955 Tf 11.96 11.36 Td[(Xj6=ibj()=vi()+Xj6=ibj())]TJ /F14 11.955 Tf 11.95 11.36 Td[(Xj6=ibj(i), (7) wherethelasttermisdeterminedindependentlyofbidderi'sbiddingvalues,sothatbiddericanmaximizehisutilitybymaximizingthetwotermswithinthesquarebracket.Since Xibi()Xibi(),82NG, (7) tomaximizehisutility,thedominantstrategyofbidderiistosubmitbi()=vi(),i.e.,tobidwithhistrueevaluationvalues. EventhoughVCGauctionhasseveralgoodproperties,itcannotbedirectlyextendedtospectrumauctionbecauseofthefollowingtwoissues: 178

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1. VCGrequiresthesolutiontotheoptimalallocation,whichisNP-completeinspectrumauctionw.r.t.thespatialreuse. 2. VCGisvulnerabletothefraudsoftheinsincereauctioneerandthebid-riggingbetweenthebiddersandtheauctioneer. 7.3.2PaillierCryptosystem Inordertothwarttheback-roomdealingandallocatethespectrumbands,biddingvaluesshouldbekeptsecret.Ontheotherhand,theauctioneerhastondthemaximumbidandchargethecorrespondingbidder.Therefore,acryptosystemisinneedforspectrumauction,whichenablestheauctioneertoproperlyexecutetheauctionandrevealnothingmorethantheresultantpaymentsandallocationofspectrumbands. Pailliercryptosystemissuchaprobabilistic6asymmetricpublickeyencryptionsystemthatsatisestheserequirements.ThespecialfeaturesofPailliercryptosystemincludeshomomorphicaddition,indistinguishability,andself-blinding[ 32 81 82 ]: Homomorphicaddition.GivenEisthePaillier'sencryptionofamessageM,E()isadditivehomomorphic,i.e.,E(M1+M2)=E(M1)E(M2). Indistinguishability.E()isconsideredindistinguishableifthesameplaintextMisencryptedtwice,thesetwociphertextsaretotallydifferent,andnoonecansucceedindistinguishingthecorrespondingoriginalplaintextswithaprobabilitysignicantlygreaterthan1=2(i.e.,randomguessing)unlesshedecryptstheciphertexts. Self-blinding.Anyciphertextcanbepubliclychangedintoanotheronewithoutaffectingtheplaintext,whichmeansadifferentrandomizedciphertextE"(M)canbecomputedfromtheciphertextE(M)withoutknowingeitherthedecryptionkeyortheoriginalplaintext. ThesedesiredpropertiesofPailliercryptosystemareessentialforoursecurespectrumauctiondesignasdescribedinSection 7.4.2 6Thetermprobabilisticencryptionistypicallyusedinreferencetopublickeyencryptionalgorithms.Probabilisticencryptionusestherandomnessinanencryptionalgorithm,sothatwhenencryptingthesameplaintextforseveraltimes,itwillyielddifferentciphertexts. 179

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7.4AuctionDesignofTHEMIS SincespatialreuseofspectrumbandsmakesndingtheoptimalspectrumallocationNP-complete[ 45 135 ],researchersresorttogreedyalgorithmsforpossiblesolutions[ 124 135 ].Inordertosortthebiddersfortheallocationofspectrumbands,theauctioneerhastoknowtheglobalinformationofbidsintheseschemes,renderingthemvulnerabletofraudsandbid-rigging. Inordertodealwiththeback-roomdealing,theproposedTHEMISleveragesPailliercryptosystemtoencryptthebiddingvaluesandenabletheauctioneertochargethewinnerswithoutleakinganyinformationaboutthebiddingvalues.Inparallelwiththeencryptiondesign,THEMISalsoprovidesasupportingconict-table-drivenauctionproceduretoimplementthespectrumauction.Thus,inthissection,werstdescribetheimplementationprocedureofTHEMIStogiveanoverallimpression.Then,wedwellontheencryptiondesigndetailsoftheproposedauction. 7.4.1THEMIS:SpectrumAuctionProcedure Similartothetable-drivenroutingalgorithms,wealloweachbiddertomaintainalocalconict-tablereectingtheinterferenceconstraints.Thelocalconict-tablecanbeconstructedbasedontheconict-matrixderivedfromtheconictgraphasdemonstratedin[ 124 ].Abidderneedstoupdatehisbidsifanyofhisneighboringnodesintheconict-tablewinsspectrumbandsorthenumberofavailablebandsforauctionwithhisinterferencerangehaschanged. Consideringspatialreuse,thewholenetworkisdividedintosmallsubnetworksbasedontheinterferencerangeandthelocationofthebidders,i.e.,subnetworkiconsistsofallthenodeswithinthecircleareacenteredatthelocationofbidderiwiththeradiusofbidderi'sinterferencerange.Auctionisexecutedinonesubnetworkafteranotheruntileachnodehasbeenthecenter.Thespectrumbandallocationandpricechargedforthewinningbiddersdependbothontheresultsofthesubnetworkauctions 180

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andonthelocationofthewinningbidders(especiallyforthenodesinthecrossingareaofdifferentsubnetworks)whentakingtheinterferenceconstraintsintoaccount. ThedetailedprocedureofTHEMISispresentedasfollows. Step1.Preparation: LetN=f1,2,,i,,ngbethesetofnbidders,S=f1,2,,j,,sgbethesetofsspectrumbands,andNS=f:S!Ngbethesetofpossibleallocationsofspectrumbandstobidders.Eachbiddersetsuptwotables,aconict-tableforstoringthenodescausingmutualinterferenceandaprice-chargedtableforstoringaseriesofchargingpricesforthespectrumbandshewon.Biddersllintheconict-tablewithcurrentinterferingneighborsandinitializetheprice-chargedtablewithzeros.Foranybidderi,heencloseshisidentity,locationinformationandhisownbiddingvaluesbiforNSallocationsintohisbid,wheretheidentityandlocationinformationofbidderiarepublictotheauctioneerforsubnetworkdivision,allocatingspectrumbandsandchargingprices,butbiisencryptedusingPailliercryptosystem(Howtoencryptbiiselaboratedinthenextsubsection).Then,bidderssubmittheirbidstotheauctioneer. Step2.Start-up: DuetotheNP-completenessofspectrumallocation,thereisnooptimalchoicefortheauctioneertostartthesubnetworkspectrumauctionswithadesignatedbidderinordertomaximizehisrevenue.Therefore,theauctioneercaninitiatethesubnetworkauctionswitharandomlychosenbidder,saynodei,wherebidderiisregardedasthecenterofthecurrentsubnetwork,andhisinterferencerangeissettobetheradiusofthesubnetwork. Step3.BidderIndexing: TheauctioneersortsthebidderswithinthesubnetworkaccordingtotheirEuclideandistancesfromthecenteri.Theclosertothecenter,thesmallerindexthebidderislabeled.TheauctioneerstorestheindexinformationinadistancevectorD,whoseelementdjdenotesthej-thnodeawayfromthecenteriintermsofdistance. 181

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Step4.SubnetworkAuction: Afterindexingthebidders,theauctioneercollectsthebidsandcarriesoutthesecurespectrumauctionwithinthesubnetworkusingPailliercryptosystem.Theresultsofthesubnetworkauction,i.e.,thesetofwinnersandthesetofcorrespondingchargingprices,arepublished.DetailsofencryptiondesignforthesecuresubnetworkspectrumauctionareelaboratedinSection 7.4.2 Step5.Allocation&Payment: Determinedbybothsubnetworkauctionresultsandlocationofthewinners,theallocationofspectrumbandsandthepaymentaredifferentinthefollowingthreecases: Case1:Ifthecurrentcenter,bidderi,isnotoneofthewinners,theauctioneerneedstochecktheelementsinthewinnersetW,choosethewinningbidderwiththesmallestindextobethenextcenter,andsethisinterferencerangeastheradiusofthenextsubnetwork.Accordingtotheresultsofcurrentsubnetworkauction,allthewinningbiddersstorethespectrumbandstheywonandthecorrespondingchargingpricesintotheirprice-chargedtables.Afterthat,currentcenter,bidderi,isdeletedfromtheconict-tablesofhisneighbors.Thesubnetworkspectrumauctioncenteredatnodeiends,andtheauctiongoestoBidderIndexingofthenextcenterforthenextsubnetworkauction. Case2:Ifthecenter,bidderi,istheonlywinneroftheauction,andheischargedatpifortheallocation,hewillcomparethecurrentchargingpricepiwiththepreviouschargingprices,P,storedinhisprice-chargedtableandpaythehighestoneofallthepricesfortheallocation.Thatistosay,thepaymentforthecenternodeiismax(P)7.Then,thecenternodeupdateshisspectrumoccupancyinformationandhisneighborseliminatehimfromtheirconict-tables.Afterthat,theauctioneersetsthenodewiththesmallestindexasthenextcenter.TheauctiongoestoBidderIndexingforthenextsubnetworkauction. Case3:Providedthattherearemorewinnersthanthecurrentcenteri,theprocessisthesameasinCase2,exceptthattheauctioneerwouldrathertakethenodewiththesmallestindexinthewinningsetWasthenextcenterfortheconsiderationofcomputationalefciency. TheoverallspectrumauctionprocedureofTHEMISissummarizedinAlg. 5 7Payingmax(P)istoguaranteethecenter,bidderi,tobeatothercompetitorsintheprevioussubnetworkauctions,whereiisnotthecenter. 182

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Algorithm5THEMIS-SpectrumAllocationProcedure 1: i=randomch(N) 2: whileN!=do 3: setupthesubnetworkcenteredati 4: D=sortedNbydistancetoi 5: auctionSsecurelywithinthesubnetwork 6: ifi=2Wthen 7: N=Nnfig 8: i=min(D) 9: continue 10: else 11: allocate(i,,max(P)) 12: N=Nnfig 13: W=Wnfig 14: ifW==then 15: i=min(D) 16: continue 17: else 18: i=min(D\W) 19: endif 20: endif 21: endwhile 7.4.2THEMIS:SecureSpectrumAuctionDesign Now,theonlyproblemleftishowtosecurelycarryoutthespectrumauctionineachsubnetwork.SinceVCGauctionhasbeenprovedtobeincentive-compatiblefromthebidderside,wecanmodifyitwithcryptographictoolstopreventtheinsincerebehaviorsfromtheauctioneersideandapplyitintospectrumauctionsofthesubnetworks.Assumingtheonlyinformationthattheauctioneercanexploitisthesubnetworkauctionwinnersandtheircorrespondingpayments,thereisnowayforhimtoconductanyfraudsorbid-riggingtomanipulatethemarket.So,intheencryptiondesignpartofTHEMIS,weelaborateonhowtorepresentthebiddingvalues,howtoentitletheauctioneertoselectthemaximumfromtheencryptedbids,howtorevealthechargingpricesforthewinners,andhowtoestablishthesubnetworkauctionresistanttoback-roomdealing. 183

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7.4.2.1Representationofbiddingvalues BiddingValueEncryption. WeusePailliercryptosystem[ 81 83 ]tomaskthebiddingvalues.Assumingk(1kq)isthebiddingvalueforthespectrumallocation(i.e.,k=b()),kcanberepresentedbyavectore(k)ofciphertexts e(k)=(e1,,eq)=(E(x),,E(x)| {z }k,E(0),,E(0)| {z }q)]TJ /F12 7.97 Tf 6.59 0 Td[(k), (7) whereE(0)andE(x)accountforthePaillierencryptionof0andthecommonpublicelementx(x6=0),respectively.Here,qisanumberlargeenoughtocoverallthepossiblebiddingvaluesfortheallocationofavailablespectrumbands.Forinstance,assumingq=3andk=2forgivenspectrumallocation,e(k)=e(2)=)]TJ /F15 11.955 Tf 5.48 -9.68 Td[(E(x),E(x),E(0). Becauseoftheself-blindingpropertyofE,kcannotbedeterminedwithoutdecryptingeachelementinthevectore(k). MaximumBidSelection. Themaximumofencryptedbiddingvalue,e(ki)=(e1i,...,eqi),canbefoundwithoutleakinginformationaboutanyotherbiddingvalue,e(kj)=(e1j,...,eqj),j6=i,asfollows.Letusconsidertheproductofallthebiddingvectorsforcertainspectrumallocation, Yie(ki)=(Yie1i,,Yieqi). (7) DuetothehomomorphicadditionofPailliercryptosystem,thej-thcomponentofthevectorabovecanbedenotedas yj=Yieji=Ec(j)(x)=E(c(j)x), (7) wherec(j)=jfijjkigjindicatesthenumberofvaluesthatareequaltoorgreaterthanj. 184

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Itisobviousthatc(j)monotonicallydecreaseswhenjincreases,whichgivesussomehintstosolvingthemaximumvalueselectionproblem.Tondthemaximumofthesebiddingvalues,wedecryptyjandcheckwhetherdecryptionE)]TJ /F4 7.97 Tf 6.58 0 Td[(1(yj)isequalto0ornotfromj=qdowntoj=1untilwendthelargestjsubjecttoE)]TJ /F4 7.97 Tf 6.58 0 Td[(1(yj)6=0.Thisjisequaltomaxfkig,i.e.,themaximumofthebiddingvalueforthespectrumallocation. BidRandomization. Wecanmaketheauctioneerrandomizetheelementsinthebiddingvaluevectororaddconstantstoencryptedvectore(k)=(e1,...,eq)withoutdecryptinge(k)norlearningk.Shiftinge(k)byaconstantrandrandomizingtherestofelements,wehave e"(k+r)=(E(x),,E(x)| {z }r,e"1,,e"q)]TJ /F12 7.97 Tf 6.58 0 Td[(r), (7) wheree"jisarandomizedversionofciphertextej.Noinformationabouttheconstantrcanbeobtainedfrome(k)aswellase"(k+r)w.r.t.self-blindingpropertyofPailliercryptosystem.Moreover,itshouldbenotedthatduringrandomizingandconstantaddingoperations,neithere(k)isdecryptednorkisexposed.Thatistosay,ifwecomparee(k)ande(k+r),wecannotgureouttheamountoftheshiftwithoutdecryptingbothofthem. 7.4.2.2Securesubnetworkspectrumauction RepresentingbidsbyencryptedvectorsbasedonPailliercryptosystem,wecaneasilyndthemaximumofthegivenbidsandrandomizethebiddingvalueswithoutknowingthesevaluesthemselves,whichpavesthewaytothesecurecomputationoftheVCGbasedspectrumauctioninthesubnetwork. Forthesimplicityofdescription,weuseE(f)todenotetheencryptedvectorofbiddingvalues,wherefisafunctionfromNStothevectorofbiddingvalues.Theproposedsecuresubnetworkspectrumauctionisasfollows. InitialPhase: 185

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Theauctioneer8generateshisprivateandpublickeyofPailliercryptosystem,andpublishesthepublickeyandpublicelementx(x6=0)overthecommonchannel. BiddingPhase: Step1:EachbidderzdecideshisvectorofbiddingvaluesbzforNS.SincethesubnetworkspectrumauctionisVCGbased,bz(),82NS,isalsothetrueevaluationvalueofbidderzfortheallocation. Step2:Theauctioneercreates(n+1)representingvectorsE=E(O),E1=E(O),,En=E(O),wherethesizeofvectorEisequaltojNSj,andtheinitialO()isalwaysequalto0. Step3:EachbidderzaddshisencryptedbiddingvaluevectorbztotherepresentingvectorsE,E1,,Ez)]TJ /F4 7.97 Tf 6.59 0 Td[(1,Ez+1,,Enexceptthez-threpresentingvectorEztokeepbzsecret.Whenallbiddershavenishedthisprocess,theauctioneerobtains E=Yie)]TJ /F5 11.955 Tf 5.48 -9.68 Td[(bi(1),Yie)]TJ /F5 11.955 Tf 5.48 -9.68 Td[(bi(2),,Yie)]TJ /F5 11.955 Tf 5.48 -9.68 Td[(bi(jNSj). (7) AccordingtothehomomorphicadditionpropertyofPailliercryptosystem,theequationabovecanberewrittenas E=e)]TJ 7.48 1.67 Td[(Xibi(1),e)]TJ 7.47 1.67 Td[(Xibi(2),,e)]TJ 7.48 1.67 Td[(Xibi(jNSj)=E(Xibi). (7) Similarly,theauctioneeralsohas Ez=E(Xi6=zbi)z=1,2,,n. (7) 8Infact,theauctioneershouldbeimplementedbypluralserverstopreventtheauctioneerfromlearningthebiddingvalues.Indeed,thedecryptiontondthemaximumcombinationofthebidsandtheadditionofrandommaskconstantrinthefollowingdesignareperformedinadistributedmannerbytheseservers.Forthedetailsofhowtosharethesecretinformationamongtheseservers,pleasereferto[ 90 128 ]. 186

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OpeningPhase: The5-stepopeningphaseofsubnetworkauctionconsistsoftwoparts:allocationselectionandchargingpricecalculation. I.AllocationSelection Step1:TheauctioneerderivesE(Pibi+R)fromEbyaddingarandomconstantfunctionR()=rtomaskthevalues.WithE(Pibi+R),theauctioneercanndmaskedmaximumsumvalueofthebids m=max2NS(Xibi()+R())=max2NS(Xibi())+r. (7) Tobemorespecic,theauctioneertakestheproductoftheencryptedelementsinEtoobtainQjNSjj=1e(Pni=1bi(j)+r),andmakesuseofMaximumBidSelectiontodeterminethemaximumelementofQjNSjj=1e(Pni=1bi(j)+r),whosevalueism=max2NS(Pibi()+R()). Step2:Theauctioneerthendecryptsthem-thelementofeveryvectore(Pibi()+R())inE,i.e.,foranyallocation2NS,andndsoutwhetherthedecryptionisequaltoxorequalto0.Ifitisequaltoxatallocation2NS,theauctioneerregardsastheallocationthatmaximizesPibi,thesumofallbiddingvalues.Theallocationistheresultofthesubnetworkauction.Correspondingly,thewinnersetisdeterminedby. II.ChargingPriceCalculation TheauctioneerthencomputesthechargingpricepzofbidderzasshowninStep3toStep5. Step3:Theauctioneerderivese(Pi6=zbi()+r")fromtheelemente(Pi6=zbi())ofEzbyaddingarandomconstantr"tomaskthevalue.Then,theauctioneerdecryptsandndsoutthemaskedvalueof(Pi6=zbi()+r"). Step4:TheauctioneerderivesE(Pi6=zbi+R")fromEzbyaddingrandomconstantfunctionR"()=r"tomaskthevalues.SimilartoStep1,theauctioneer 187

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takestheproductofthePaillierencryptedelementsinE(Pi6=zbi+R"),andemploysMaximumBidSelectiontondoutthemaskedmaximum,max2NS(Pi6=zbi()+r").Bythedenitionofx,max2NS(Pi6=zbi()+r")isequalto(Pi6=zbi(z)+r"). Step5:Afterthat,theauctioneercalculatesthechargingpricebysubtractingthesemaskedvalues. pz=Xi6=zbi(z)+r")]TJ /F14 11.955 Tf 11.96 13.27 Td[(Xi6=zbi()+r". (7) Inconsistentwiththeallocation,bidderzshouldbechargedwithpzforspectrumbandshewoninthissubnetworkauction. 7.4.3THEMIS:AnExample TomakebetterunderstandingoftheproposedTHEMIS,weillustrateitwithanexample,whereS=f1,2gandN=f1,2,3,4g,inasimpliedtopologyreectingthetypicalinterferenceconstraintsasdepictedinFig. 7-3 (a). InTHEMIS,theoverallnetworkinFig. 7-3 (a)canbesubstitutedwithfoursubnetworksbasedonthenumberofthenodesandtheirmutualinterference.SinceSubnetwork3 andSubnetwork4 aresymmetricwiththesamebiddingnodesandavailablespectrumresource,theycanbecombinedintoonesubnetwork.Hence,thenetworkcanbedecomposedintothreesubnetworksandthespectrumauctionisexecutedinthesesubnetworksconsecutivelyliketheabstractstatemachineasshowninFig. 7-3 (b). AsforSubnetwork1 ,node1hasnoconictswithnode3and4butnode2.Thecompetitionforspectrumbandsisbetweennode1and2.Therefore,thesetofbiddersisN=f1,2g,andthesetofavailablespectrumbandsisS=f1,2g.So, NS1 =f1=(f1,2g,fg),2=(f1g,f2g),3=(f2g,f1g),4=(fg,f1,2g)g,where,e.g.,2=(f1g,f2g)indicatesthatspectrumband1isallocatedtobidder1andband2tobidder2.Assumethetruthfulbiddingvaluesb1andb2ofbidder1and2are 188

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AThetopologyoftheexample. BSubnetworkdecompositionforspectrumauctions. Figure7-3. AnillustrativeexampleforTHEMIS. b1=(3,2,2,0)andb2=(0,0,2,3),respectively.Then,weobtain b1+b2=(3,2,4,3). TheauctioneercreatesE,E1,andE2=E(O)=(e(0),e(0),e(0),e(0)).Then,biddersusePailliercryptosystemtoencrypttheirbids.Bidder1addshisbiddingvaluestoE,E2andbidder2addshisvaluestoE,E1,i.e., E=(e(3),e(2),e(4),e(3)),E1=(e(0),e(0),e(2),e(3)),E2=(e(3),e(2),e(2),e(0)). First,theauctioneershouldndtheallocationofspectrumbandsinSubnetwork1 TheauctioneeraddsrandomconstantfunctionR()=r=2toE,whichleadsto E(Xibi+R)=(e(3+2),e(2+2),e(4+2),e(3+2)). 189

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TheauctioneertakestheproductofallelementsinE(Pibi+R),)]TJ /F9 11.955 Tf 5.48 -9.69 Td[(e(3+2)e(4+2)e(2+2)e(3+2),whichcanalsobeinterpretedas )]TJ /F15 11.955 Tf 5.48 -9.69 Td[(E(4x),E(4x),E(4x),E(4x),E(3x),E(x),E(0),,E(0)| {z }q)]TJ /F4 7.97 Tf 6.59 0 Td[((4+2). Then,theauctioneerdecryptsthisvectortondmax2NS1 (Pi=1,2bi()+r)=4+2.Afterthat,theauctioneerdecryptsthe(4+2)-thelementofe(3+2),e(2+2),e(4+2),e(3+2)todetermine=3. Next,theauctioneershouldcalculatethechargingpricesforthewinnersinSubnetwork1 Theauctioneeraddsrandomconstantr"=1tothe3-rdelemente(2)ofE1toyield e(Xi6=1bi()+r")=e(2+1), anddecryptse(2+1)tond)]TJ 7.47 -.71 Td[(Pi6=1bi()+r"=b2(3)+r"=2+1. Then,theauctioneeraddsrandomconstantfunctionR"()=r"=1toE1toyield E(Xi6=1(bi)+R")=(e(0+1),e(0+1),e(2+1),e(3+1)), takestheproductof)]TJ /F9 11.955 Tf 5.47 -9.68 Td[(e(0+1)e(2+1)e(0+1)e(3+1),andthendecryptsthistondmax)]TJ 7.47 -.71 Td[(Pi6=1(bi)+R"=)]TJ 7.47 -.71 Td[(Pi6=1bi(1)+r"=b2(4)+r"=3+1. AccordingtoStep5inopeningphaseofthesubnetworkspectrumauction,p1=b2(4))]TJ /F5 11.955 Tf 12.41 0 Td[(b2(3).Thus,theauctioneercalculatesp1=(b2(4)+r"))]TJ /F7 11.955 Tf 12.41 0 Td[((b2(3)+r")=(3+1))]TJ /F7 11.955 Tf 12.23 0 Td[((2+1)=3)]TJ /F7 11.955 Tf 12.22 0 Td[(2=1.Theauctioneercanalsocomputep2=3)]TJ /F7 11.955 Tf 12.22 0 Td[(2=1inthesameway.Consequently,intermsofspectrumauctioninSubnetwork1 ,spectrumband2isallocatedtobidder1atthepriceof1,andspectrumband1isallocatedtobidder2atthepriceof1. However,thespectrumallocationofbidder2isdeterminednotonlybytheinterferencebetweennode2and1,butalsobytheinterferencebetweennode2 190

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andnode3,aswellasnode4.So,whetheravailablespectrumband1shouldbeallocatedtobidder2andhowmuchthechargingpriceiscannotbedetermineduntiltheauctioneernishestheauctioninSubnetwork2 centeredatnode2.BeforetheauctioninSubnetwork2 starts,bidder1shouldupdatehisbidinformation,i.e.,broadcastinghisspectrumoccupancyandlocationinformationtohisneighborstonotifythemwhichbandsaretakenwithinhisinterferencerange. Asaresult,thenodeswithinSubnetwork2 areonlyabletobidfortheleftspectrumband1subjecttotheinterferenceconstraints.Inthisway,bidder1andhisinterferencetobidder2canbeignored,sothatnode1canbedeletedbothfromtheconict-tableofbidder2andfromthebidderlistofauctioninSubnetwork2 asshowninFig. 7-3 (b). Meanwhile,nodesinSubnetwork2 havetorenewtheirbidsfortheavailablespectrumband1.Hence,thesetofthebiddersinSubnetwork2 isN=f2,3,4g,thespectrumbandsetisS=f1g,andtheallocationsetcanberepresentedas NS2 =f1=(f1g,fg,fg),2=(fg,f1g,fg),3=(fg,fg,f1g)g.SimilartoauctioninSubnetwork1 ,e.g.,2=(fg,f1g,fg)standsforallocatingavailablespectrumband1tobidder3andnospectrumbandstobidder2orbidder4.Supposethebiddingvaluesb2,b3andb4ofbidder2,3,and4areb2=(3,0,0),b3=(0,2,0),andb4=(0,0,1),respectively.Thesumofthebiddersis(b2+b3+b4)=(3,2,1). First,theauctioneermakesE,E2,E3,andE4=(e(0),e(0),e(0)).Bidder2addshisbidstoE,E3,andE4,bidder3addshisbidtoE,E2,andE4,andbidder4addshisbidtoE,E2andE3,whichleadsto E=(e(3),e(2),e(1)),E2=(e(0),e(2),e(1)),E3=(e(3),e(0),e(1)),E4=(e(3),e(2),e(0)). 191

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Table7-1. Thecomparisonofdifferentspectrumauctiondesigns. S-AuctionSpatialR-NeutralTruthfulBid-riggingFraudsDesignsReuseAttractionbiddingResistantResistant VERITASXXMWXXXTHEMISXXXXX Then,theauctioneeraddsrandomconstantfunctionR()toE,takestheproductofelementsinEanddecryptsthistondmax2NS2 (Pi=2,3,4bi()+R()).Afterthat,theauctioneerdecryptsthecorrespondingmax-thelementof)]TJ /F9 11.955 Tf 5.48 -9.68 Td[(e(3+R()),e(2+R()),e(1+R())tond=1. Then,theauctioneeraddsrandomconstantR"()=r"=2tothe1-stcomponente(0)ofE2toobtaine(Pi=3,4bi()+r")=e(0+2),anddecryptse(0+2)tond)]TJ 7.47 -.72 Td[(Pi=3,4bi()+r"=b3(1)+b4(1)+r"=0+2. TheauctioneeraddsrandomconstantfunctionR"()=r"=2toE2toyield E(Xi=3,4bi+R")=(e(0+2),e(2+2),e(1+2)). Theauctioneertakestheproductof)]TJ /F9 11.955 Tf 5.48 -9.68 Td[(e(0+2)e(2+2)e(1+2),anddecryptsthisvectortondmax(Pi=3,4bi+R")=Pi6=2bi(2)+r"=b3(2)+b4(2)+r"=2+2. Finally,theauctioneercalculatesp2=[b3(2)+b4(2)+r"])]TJ /F7 11.955 Tf 11.03 0 Td[([b3(1)+b4(1)+r"]=(2+2))]TJ /F7 11.955 Tf 12.03 0 Td[((0+2)=2)]TJ /F7 11.955 Tf 12.03 0 Td[(0=2.ForSubnetwork2 ,spectrumband1isallocatedtobidder2,andspectrumband2isnotvacant.Furthermore,sincenode2liesinthecrossingareaofSubnetwork1 andSubnetwork2 ,hispaymentforthespectrumband1shouldbep2=maxfp(2,1 ),p(2,2 )g=maxf1,2g=2. InSubnetwork3 ,alltheseprocessesarerepeated,andnode3and4arechargedinthesamemanners. 7.5SimulationandAnalysis Comparedwithtwoexistingspectrumauctionschemes,VERITAS[ 135 ]andtheMulti-Winnerspectrumauction(M-W)[ 124 ],THEMISbeatstwounsolvedchallenges 192

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ofsecurespectrumauctiondesign,i.e.,thefraudsoftheinsincereauctioneerandthebid-riggingbetweenbiddersandauctioneer.LeveragingsubnetworkdivisionandPailliercryptosystemencryptedsubnetworkauction,theproposedTHEMISisresistanttothesetwoback-roomdealing,whileitsupportsspatialreuse,attractsriskneutralbidders,andguaranteesstrategy-proofbiddingaslistedinTableI. Inthissection,wealsoshowthatTHEMISachievessimilarperformancetoVERITASandM-Wintermsofspectrumutilization,auctioneer'srevenue,andbidders'satisfactorydegree.Besides,wecarryoutthesecurityanalysisofTHEMISanddemonstratetheefciencyoftheproposedspectrumauctionbyevaluatingitscommunicationandcomputationalcomplexity. 7.5.1PerformanceComparison 7.5.1.1Simulationsetup Weassumethespectrumauctionhostedbytheauctioneerisdeployedina1*1squarearea,wherenodesareuniformlydistributedandconnected[ 6 112 127 ].Supposethewirelessmutualinterferenceissimplydistance-based,andanytwobidderswithin0.1distanceconictwitheachotherandcannotbeallocatedwiththesamespectrumbands.Thebiddingvaluesofdifferentbiddersoverdifferentbandsaresupposedtobei.i.drandomvariablesuniformlydistributedover(0,10].Tobesimple,weleteachbidderrequestonlyonespectrumband. WeusethefollowingthreeperformancemetricstocompareTHEMISwithVERITASandM-W. SpectrumUtilization:Itisthesumofallocatedspectrumbandsofallthewinningbidders,whichisthesameasthedenitionin[ 135 ]. Auctioneer'sRevenue:Itisthesumofpaymentsofallthewinningbidders,asdenedinSection 7.2 Bidders'Satisfaction:ItisdenedastheratioofPi2WuitoPi2Nvi,whichdenotesthepercentageofbidders'potentialmonetarygainsrealized. 193

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ASpectrumUtilization BRevenueoftheAuctioneer CBidders'Satisfaction Figure7-4. PerformancecomparisonofTHEMIS,VERITASandM-W 194

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7.5.1.2Resultsandanalysis WhenwecomparetheperformanceofTHEMISwiththatofVERITASorM-W,weassumealltheauctionsarecollusion-free,andtherearenotanyfraudsorbid-rigging.InFig. 7-4 ,weplotthespectrumutilization,auctioneer'srevenue,andbidder'ssatisfactionofthethreeauctiondesignswith200biddersand300bidders,respectively. InFig. 7-4 (a),asthenumberofspectrumbandsincreases,thespectrumutilizationalsoincreasesuntilitsaturates(i.e.,everybidderisallocatedaband)inallthesethreeauctions.ItisnotsurprisingthattheperformanceresultsofTHEMIS,VERITASandM-Warethesameintermsofspectrumutilization,becausetheymainlydifferintheirpricechargingdesignsifallthepossibleback-roomdealingcouldbeneglected. InFig. 7-4 (b),wendthatTHEMISandM-Warealmostthesameintermsoftheauctioneer'srevenue,andTHEMISisslightlyhigherthanM-Watonlyafewpoints.ItmakessensebecauseTHEMISoriginatesfromtheVCGauctionandM-Wisbasedonsecondarypriceauction,whileVCGisequivalenttosecondarypriceauctionprovidedthatthegoodisasingleitem[ 55 ].Therefore,theperformanceresultsofTHEMISandM-Warequitesimilarinoursimulations.ThebumpofTHEMISoverM-Wisfromthepaymentsforthewinningbidderslocatedinthecrossingarea,asweillustratedinSection 7.4.1 .Inaddition,VERITASischaracterizedbychargingthewinnerswiththeircriticalneighborprices[ 135 ],whichmakeitperformalittlebitbetterthantheothertwoschemesintheauctioneer'srevenue. Ontheotherhand,inFig. 7-4 (c),VERITASloseshisadvantagescorrespondingly,andTHEMISandM-Woutperformitinbidders'satisfactorydegree.Actually,theauctioneer'srevenueandbidders'satisfactorydegreearejusttwocomplementaryevaluationmetrics. Fromthecomparisonandanalysisabove,weshowthatTHEMISsacricesnothinginperformancewhenguaranteeingthespectrumauctionsecure. 195

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Table7-2. Thecommunicationcomplexity patternroundvolume thebidder$theauctioneerO(nlogn)O)]TJ /F5 11.955 Tf 5.48 -9.68 Td[(nlogn(logn)sqlognthebidder$neighborbiddersO(logn)O(logn) Table7-3. Thecomputationalcomplexity computationalcomplexity thebidderO)]TJ /F5 11.955 Tf 5.48 -9.68 Td[(nlogn(logn)sqlogntheauctioneerO)]TJ /F5 11.955 Tf 5.48 -9.69 Td[(anlogn(logn)sqlogn 7.5.2SecurityAnalysis BeforepresentingoursecurityanalysisofTHEMIS,wemustre-emphasizeandclarifytwopropertiesofPailliercryptosystem.First,duetotheindistinguishabilityofthisencryption,noinformationaboutthevaluekcanbeleakedoutfromitsrepresentatione(k)withoutdecryptingeachelement.Second,self-blindingpropertymakesitimpossibletondamappingfunctionfrome(k)toe"(k+r),whererisarandomnumber. Topreventaninsincereauctioneerfromlearningthebidsandmanipulatingtheauctionbyfrauds,weembodiestheauctioneerbymultipleservers9inTHEMIS.Thedecryptiontodeterminethemaximumoftruthfulbiddingvaluesandtheadditionofrandommaskconstantrarebothperformedinadistributedmannerbytheseservers,sothatnoinsincereauctioneercandecrypttolearnaboutthebidsorlearnrandommaskconstantrillegally.Hence,THEMIScankeepbidscondentialexcepttheresultsoftheauction,i.e.,thewinnersandtheircorrespondingpayments. Asidesfromthefrauds,thebid-riggingbetweenthebiddersandtheauctioneerbecomesmeaninglessbecausetheauctioneerhimselfknowsnothingmorethanthe 9Thekeysfordecryptingbiddingvaluesaresharedbythepluralserversbyusingsecretsharingtechnique.Alotofsecretsharingorgroupdecriptionmechanismscanbeemployedtoeffectivelypreventthedistributedserversfromcolludingwitheachothertorevealthebids.Pleasereferto[ 91 101 ]forthedetailsaboutsecretsharingdesigns. 196

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winnersandtheirpaymentsinTHEMIS.Evenifacertainbiddercolludeswitheachofserverscomposingtheauctioneer,heisnotabletondoutanyinformationaboutthebidsiftheauctioniscarriedoutinadistributedmannerbytheseservers. Obviously,THEMISsatisesthefairnessrequirementsofthespectrumauctionbecauseittreatsallthebiddersequally,selectsthebidderwiththehighestbidtowinthespectrumbandineachsubnetwork,andmakesthemultiplewinningbidderspaybypredenedrule.Besides,THEMISalsoguaranteesthecondentialityandanonymityofthespectrumauctioninthesensethatitleaksoutnomoreinformationthanthewinningbiddersandcorrespondingpricechargedduringboththebiddingphaseandopeningphase. 7.5.3EfciencyAnalysis ThecommunicationandcomputationalcomplexityofTHEMISaredeterminedbyseveralfactors,namely,thenumberofbiddersn,thenumberofavailablespectrumbandss,thenumberofpossiblebiddingvaluesq,andthenumberofserversacomposingtheauctioneer.Here,weassumethenetworkintheauctionareaisconnected,whichimpliesthatthenodedensityofthesubnetworksisontheorderofO(logn)[ 127 ]. Table 7-2 showsthecommunicationpattern,theorderofcommunicationroundsandthecommunicationvolumeperbidderinTHEMIS.Thecommunicationcomplexityfromthebiddertotheauctioneerislinearintermsofthenumberofpossiblebiddingvaluesq,soitmayincuraheavycostforalargerangeofbiddingvalues.However,thisisinevitablecostforpurgingtheback-roomdealing.Meanwhile,thecommunicationcomplexityarecloselyrelatedtos.Sincespectrumisscareresourceandtheavailablebandscannotbearbitrarilylarge,smayonlyimposelimitedcommunicationcost.Comparedwithconventionalsecureauctiondesigns[ 113 129 130 ],thereisalsoadditionalcommunicationcomplexityincurredbythesubnetworkdecomposition.But 197

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thisoverheadisavoidablewhenwetakefrequencyreuseintoconsiderationinspectrumauctions. Table 7-3 showsthecomputationalcomplexityfortheauctioneerandabidderinTHEMIS.Similartothecommunicationcost,thecomplexityofeachbidderandtheauctioneerisrelatedtothesubnetworkcomposition,linearintermsofthenumberofpossiblebiddingvaluesqandexponentialintermsofavailablespectrumbandss,whichareinevitablebutlimited. 7.6ChapterSummary Inthischapter,wehaveincorporatedcryptographictechniqueintothespectrumauctiondesignandproposedTHEMIS,asecurespectrumauctionschemeleveragingPailliercryptosystemtopurgetheback-roomdealing.Consideringspectrumreuse,wehavedividedthewholenetworkintosmallsubnetworksandallowedthebidderstomaintainandupdatetheirconict-tables,whichfacilitatethespectrumallocation.THEMISmasksthebiddingvaluesofabidderwithavectorofPaillierciphertexts,whoseadditivehomomorphicpropertyenablestheauctioneertondthemaximumbidandcalculatethechargingpricessecurelyinthesubnetworkauction,whiletheactualbiddingvaluesarekeptsecret.Inthiscase,fraudsandbid-riggingbecomesimpossible,andmanipulationoftheauctionisimplausible.WehavealsoshownthatTHEMISisasecurespectrumauctionwithlimitedcommunicationandcomputationalcomplexity,andisasgoodasotherinsecurespectrumauctionschemesintermsofspectrumutilization,theauctioneer'srevenue,andbidders'satisfaction. 198

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CHAPTER8CONCLUSION Inthisdissertation,wehavestudiedseveralchallengingandfundamentalissuesrelatedtothearchitecture,modelinganddesignofmulti-hopCRNs.Themaincontributionsofthisdissertationcanbesummarizedasfollows. ConsideringtheuncertainspectrumsupplyfromthePSPs,werstintroduceanintuitivemethod,theXloss,toquantifytheriskforSUsatagivencondentlevel.SincetheXlosstheoreticallyunderestimatesthepotentialriskforOSAandmathematicallylacksofsubadditivity,wefurtherproposetheexpectedXloss,amoresuitableriskmeasurementforOSAwithdesiredproperties.BasedonthesimpliedexpectedXloss,weformulatetheSSP'sband-mixselectionfortrafcsplittingintoanoptimizationproblemandsolveitbylinearprogramming.Bynumericalsimulations,weshowthatcomparedwiththeXlossbasedband-mixselectionforOSA,theexpectedXlossbasedselectionnotonlyprovidesmuchmoreaccurateefcientOSAcurvesatdifferentcondencelevels,butalsogivesmuchbetterperformanceintermsofspectrumutilization,SUs'satisfactionandtheSSP'sprot,especiallywhenthedistributionoftheprimaryserviceshasafattail. Withthosemetrics,wehaveproposedanovelarchitectureofCRNsforspectrumharvestingandsharing,andpresentedatheoreticalstudyonthejointfrequencyschedulingandroutingprobleminmulti-hopCRNsunderuncertainspectrumsupply.Werstintroduceanewserviceprovider,SSP,andlettheSSPprovidecoverageinCRNswithlow-costCRmeshroutersinordertofacilitatetheaccessingofSUswithoutCRcapability.Enlightenedbythestatisticsofspectrumutilization,wethenmodelthevacancyofanavailablebandwitharandomvariablesatisfyingcertainstatisticaldistribution.Afterthat,weelaborateonschedulingandinterferenceconstraintsaswellasroutingconstraintsw.r.t.theunpredictableactivitiesofprimaryservices.Furthermore,wecharacterizethenetworkwithapairof(,)parameters,andpresent 199

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amathematicalformulationwiththegoalofminimizingtherequirednetwork-widespectrumresourceata(,)levelforasetofCRsessionswithraterequirements.SincetheformulatedoptimizationproblemisNP-hard,wederivealowerboundfortheobjectivebyrelaxingtheintegervariables.Furthermore,weproposeacoarse-grainedxingalgorithmforafeasiblesolution.Throughsimulations,weshowthatthesolutionattainedbytheproposedalgorithmisnear-optimaltotheformulatedNP-hardproblematany(,)level;meanwhile,the(,)basedsolutionisbetterthanexpectedbandwidthbasedoneintermsofblockingratioandspectrumutilization. Undertheproposednetworkarchitecture,wehavestudiedthepathselectionprobleminmulti-hopCRNsunderowrouting,linkschedulingandCRsource'sbudgetconstraints.ConsideringtheinherentsingleradioconstraintofCRdevicesandthefeaturesofspectrumtrading,weproposea4-DconictgraphtodescribetheconictrelationsamongCRlinks.Afterthat,wemathematicallyformulatethepathselectionproblemundermultipleconstraintsintoanoptimizationproblemwiththeobjectiveofmaximizingtheend-to-endthroughputfortheCRsession.Givenallindependentsetsin4-Dconictgraph,wecanrelaxtheformulatedoptimizationproblemandsolveitbylinearprogramming.RegardingtheNP-hardnessofndingallindependentsets,weprovideaheuristicalgorithmaswell,whichlayersthe4-Dconictgraphandexploitsthemaximumlocalcliquestoapproximatelyselectthepathwiththehighestthroughput.Bysimulations,wedemonstratehowtheCRsource'sbudget,thenumberofavailablebandsanddistancefromCRsourceaffecttheperformanceofpathselectionintermsofpathcapacity.Wealsocomparetheheuristicpathselectionalgorithmwiththeoptimaloneandshowthatthethroughputobtainedfromtheheuristicalgorithmisclosetothatobtainedfromtheoptimaloneinmulti-hopCRNs. Asanextensionofpathselectioninmulti-hopCRNs,wehaveproposedanovelspectrumtradingsystem,i.e.,spectrumclouds,andpresentedatheoreticalstudyontheoptimalsessionbasedspectrumtradingproblemundermultiplecross-layerconstraints 200

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inmulti-hopCRNs.Consideringthespecialfeaturesofsessionbasedspectrumtrading,weexploitthe3-D(link-band-radio)conictgraphtocharacterizetheconictsamongCRlinksandmathematicallydescribethecompetitionsamongcandidatetradingsessionsinspectrumclouds.Giventheraterequirementsandbiddingvaluesofcandidatetradingsessions,weformulatetheoptimalspectrumtradingintotheSSP'srevenuemaximizationproblemundertheavailabilityofspectrum,linkschedulingandowroutingconstraintsinmulti-hopCRNs.SincetheformulatedproblemisNP-hardtosolve,wederiveanupperboundfortheoptimizationbyrelaxingtheintegervariables.Furthermore,weproposeheuristicalgorithmsforfeasiblesolutions(lowboundsaswell).Throughsimulations,weshowthat:i)theproposedsessionbasedspectrumtradinghassuperioradvantagesovertheper-userbasedoneinmulti-hopCRNs;ii)thesolutionsattainedbytheproposedheuristicalgorithmsarenear-optimalunderdifferentdatasetsinboththegridtopologyandtherandomone. WehavealsostudiedthethroughputmaximizationprobleminC-VANETsundermultipleconstraints(i.e.,CRdevices'inherentsingle-radioconstraint,theavailabilityoflicensedspectrum,transmissionmodeselectionandlinkscheduling).Consideringthespecialfeaturesofcooperativecommunications,werstextendthelinksandclassifythemintocooperativelinks/generallinks.Then,dependingontheavailablebandsatdifferentextendedlinks,wedeneextendedlink-bandpairsandforma3-Dcooperativeconictgraphtodescribetheconictrelationshipamongthosepairs.Afterthat,wemathematicallyformulatetheend-to-endthroughputmaximizationproblem.GivenallcooperativeindependentsetsinC-VANETs,wecanrelaxtheformulatedoptimizationproblemandnear-optimallysolveitbylinearprogramming.DuetotheNP-completenessofndingallindependentsets,weprovideaheuristicpruningalgorithmforthecooperativecommunicationawarelinkschedulingaswell.Bynumericalsimulations,wedemonstratethat:i)theCRcapabilitycreatesmoreopportunitiesforusingcooperativecommunications;ii)theperformanceoflinkschedulingwith 201

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appropriatelyselectedtransmissionmodeisbetterthanthatpurelyrelyingononetransmissionmode(eithercooperativecommunicationsordirecttransmissions). Asforthesecurityissuesinmulti-hopCRNs,wehaveincorporatedcryptographictechniqueintothespectrumauctiondesignandproposedTHEMIS,asecurespectrumauctionschemeleveragingPailliercryptosystemtopurgetheback-roomdealing.Consideringspectrumreuse,wehavedividedthewholenetworkintosmallsubnetworksandallowedthebidderstomaintainandupdatetheirconict-tables,whichfacilitatethespectrumallocation.THEMISmasksthebiddingvaluesofabidderwithavectorofPaillierciphertexts,whoseadditivehomomorphicpropertyenablestheauctioneertondthemaximumbidandcalculatethechargingpricessecurelyinthesubnetworkauction,whiletheactualbiddingvaluesarekeptsecret.Inthiscase,fraudsandbid-riggingbecomesimpossible,andmanipulationoftheauctionisimplausible.WehavealsoshownthatTHEMISisasecurespectrumauctionwithlimitedcommunicationandcomputationalcomplexity,andisasgoodasotherinsecurespectrumauctionschemesintermsofspectrumutilization,theauctioneer'srevenue,andbidders'satisfaction. 202

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BIOGRAPHICALSKETCH MiaoPanwasbornin1981inDalian,Liaoning,China.MiaogrewupinDalianandgraduatedfromtheNO.8MiddleSchoolinthesummerof1999.Followinghighschool,MiaoenrolledatDalianUniversityofTechnology(DUT)inDalian,Chinainthefallof1999.HereceivedhisB.E.inelectricalandinformationengineeringandB.A.inEnglishfromDUTin2004.Afterthat,MiaoenrolledatBeijingUniversityofPostsandTelecommunications(BUPT)inBeijing,Chinainthefallof2004,andreceivedhisM.E.degreesinelectricalandcomputerengineeringfromBUPTin2007.MiaoenrolledinthePh.D.programintheDepartmentofElectricalandComputerEngineeringattheUniversityofFloridainthefallof2007,asarecipientoftheUniversityofFlorida'sAlumniFellowship.HereceivedhisPh.D.degreeinelectricalandcomputerengineeringfromtheUniversityofFloridainthesummerof2012.Hisresearchinterestsareintheareasofnetworkprotocoldesign,networkperformanceanalysis,andnetworksecurityguarantee,particularlyforcognitiveradionetworks.Hehaspublishedover30papersinprestigiousjournalsincludingIEEE/ACMTransactionsonNetworking,IEEEJournalonSelectedAreasinCommunications,andIEEETransactionsonMobileComputing,orintopnetworkingconferencessuchasIEEEINFOCOM,andIEEEIPDPS.HealsohasbeenselectedseveraltimesasarecipientofthetravelgrantfromtheNationalScienceFoundation(NSF).MiaoisastudentmemberofIEEE. 215