COLLABORATIONBASEDSPECTRUMSHARINGALGORITHMSINCOGNITIVERADIONETWORKSByChowdhurySayeedHyderADISSERTATIONSubmittedtoMichiganStateUniversityinpartialfulllmentoftherequirementsforthedegreeofComputerScience-DoctorofPhilosophy2017ABSTRACTCOLLABORATIONBASEDSPECTRUMSHARINGALGORITHMSINCOGNITIVERADIONETWORKSByChowdhurySayeedHyderRadiospectrumassignmenttowirelessprovidersusingtraditionalxedallocationpolicywillnolongerbeaviabletechniquetomeetthegrowingspectrumdemandofemergingwirelessapplica-tions.Thisisbecausewhiletheavailablepoolofunassignedradiospectrumislow,thespectrumalreadyassignedtoexistingapplicationsisalsooftenunderutilizedintime,frequency,andloca-tion.Withfeaturesliketransmissionexibilityandadaptabilitycognitiveradio(CR)providesausefulmeansofspectrumsharingamonggrowingusersasanalternativetothecurrentxedpol-icy.Thecognitiveradionetwork(CRN),basedonthefunctionalityofCR,consistsoftwotypesofusersŠprimaryusers(PU)andsecondaryusers(SU).Primaryusersarelicenseduserswhohaveexclusiveaccessrightsofaxedspectrumrange.Secondaryusersareunlicenseduserswhoopportunisticallyexploitthespectrumholesornegotiatewithprimaryuserstoearntransmissionaccessrights.TheCRNbasedefcientspectrumsharingalgorithmsworkondifferentformsofcollaborationbetweenthePUsandtheSUs(inter-usercollaboration)andamongtheSUsthemselves(intra-usercollaboration).Inthesensingbasedcollaborationmodel,theSUssenselicensedspectrumandcollaborativelydecideaboutitsavailabilitybasedonthesensingresultswithoutanyinvolvementsfromthePUs.Intherelaybasedcollaborationmodel,theSUscoordinatewiththePUsdirectly,relayprimarypacketsinexchangefortransmissionopportunities,andthusbuildawin-wincooper-ativeframeworktoattainmutualbenets.Intheauctionbasedcollaborationmodel,theSUsbidfortemporaryorpermanentusagerightsofunusedlicensedspectrumbandsthatareputintoauctionforsalebythePUs.Eachofthesecollaborationmodelsfacesdifferentsetsofchallengestowardsachievinghighspectrumutilization.Inthisdissertation,weaddresssomeofthesechallengesandpresentasetofefcientspectrumsharingalgorithmsbasedonthesecollaborationmodels.Therstworkinthisdissertationaddressesthespectrumsensingdatafalsication(SSDF)attackinIEEE802.22wirelessregionalareanetwork(WRAN)underthesensingbasedcollab-orationmodel.Wediscussdifferentstrategiesofmanipulatingsensingreportsbyoneormoremalicioususersandhowthesemanipulationstrategiesmayaffectthespectrumutilization.Tode-fendagainstsuchmaliciousattacks,wepresentanadaptivereputationbasedclusteringalgorithm.ThealgorithmcombinestheclusteringtechniquewithfeedbackbasedreputationadjustmenttopreventindependentandcollaborativeSSDFattacksandquarantinestheattackersfromthedeci-sionmakingprocess.Ournextsetofworkinthisdissertationfallsundertherelaybasedcollaborationmodel.Weinvestigatethefeasibilityofthiscollaborationmodelinthecaseofreal-timeapplications.Wequantifytheimpactofpacketdeadlinesandcooperationoverheadonthesystemperformance.Wediscusstheimpactofinterferencethatmaycausefromsecondarytransmissions.Basedontheanalysis,wedevelopaninterferenceawarereliablecooperativeframeworkwhichimprovesthepacketreceptionrateofbothuserswithlowoverhead.Weextendourinvestigationofthisrelaybasedcollaborationmodelfromsinglehoptomultiplehopsintheformofcooperativerouting.WeformulatetheroutingproblemasanoverlappingcoalitionformationgamewhereeachcoalitionrepresentsaroutingpathbetweenprimarysourceanddestinationconsistingofmultipleSUsasintermediaterelays.TheproposedmodelallowsSUstoparticipateinmorethanonecoalitionsandcreatesmoretransmissionopportunitiesforthemwhileachievingstableroutingpathsforPUs.Ournalsetofworkinthisdissertationdealswiththechallengesintheauctionbasedcollabo-rationmodel.Weconsideranonlinesettingofspectrumauctionswhereparticipationandvaluationofbothbiddersandsellersarestochastic.Weanalyzethebehaviorofbiddersandsellersinsuchsettingsanddeveloptruthfulauctionmechanismswithrespecttobidandtime,improvingspectrumreuse,auctionefciency,andrevenue.Thendingsfromourresearchwillhelptounderstandtheunderlyingchallengesinfuturenetworks,buildabetterspectrumecosystem,andencouragenewspectrumsharingmodelsinwirelessbroadbandcommunications.Tomyparents.vACKNOWLEDGMENTSAllpraisesareduetoAllah,themostbenevolentandmerciful.IwouldliketothankDr.XiaoforgivingmeanopportunitytoworkasoneofherPhDstudents.Fromthebeginning,sheinstructedmetoinvestigateresearchproblemsonmyownwhichhelpedmetounderstandthechallengesintheeldofmyresearch.Shetaughtmehowtopresentideasintowriting,howtoreviewapaper,howtoaddressthecommentsofthereviewer,andsoon.Thisknowledgedenitelyhelpedmetondmylimitations,realizemyweaknesses,andIamgratefultoherforthatvaluableinsight.IwouldalsoliketothankmyotherPhDcommitteemembers-Dr.Mutka,Dr.Esfahanian,Dr.Jeitschko,andDr.Mandrekarfortheirexibilitywiththeschedule,patiencetositthroughhoursofmypresentation,andtheirinputtomakeitbetter.IhavebeenworkingwithDr.Jeitschkoforthelastcoupleofyears.Hisprofoundknowledgeinauctiontheorymadetheinterdisciplinaryresearchsomucheasy,fun,andinteresting.Hebecamemymentor,guide,andafriend.Iwillremainevergratefultohimforhissupportandencour-agementduringthedarkesttimesofmylife.Inthisregard,Ialsowanttoshowmygratitudetothosepeoplewhohavenotdismissedmyconditionslikeothersandgenerouslyextendedtheirhelpthroughcounselingandguidance.HadInotreceivedthatsupport,itcouldhavebeenentirelyadifferentstory.Ialsowanttothankallofmycoauthorswhohavecollaboratedwithmeindifferentprojectsandcontributedwiththeirvaluableinputsandcorrections.IwanttospeciallythankDr.AlimalIslam(Razi)whosementalsupport,domainknowledge,andunyieldingattitudeledtosomegoodnishedprojects.IwanttothankDr.Torngforhisvaluablesuggestionandimportantcontributiontothejointresearchwork.Apartfromthat,Iwanttospeciallythankhimforhissupportasthegraduatedirectorofthedepartment.HealongwithDr.Mckinleywerethetwoteacherswhovishowedhowtomakeagraduateclassfunandinteresting.Despitetheirdifferentteachingstyles,Ienjoyedbothoftheirclassesandwillnothesitatetofollowtheirstyles(ifIeverpursueanacademiccareer).IamalsogratefultothelocalBangladeshiCommunity(Jewelvai&vabi,Kabirvai&vabi,Touqvai&vabi,Jamalvai&vabi,Aftabvai&vabi,Linconvai&vabi,SomaapaandZibi)whoembracedusasoneoftheirownandEastLansingbecamemyhomeawayfromhome.IalsowanttothanktheMSUBangladeshiStudentsAssociation(ABSS)anditsmembersfororganizingcolorfuleventstoremindusourbeautifulcultureeveryyear.Iwasfortunateenoughtogettheopportunitytostudyinthetopmostengineeringuniversity,BangladeshUniversityofEngineeringandTechnology(BUET)inBangladeshatalmostnocost.IamgratefultothehardworkingtaxpayingcommonpeopleofBangladeshwhosecontributiontothenationaleconomymadethispossibleforthousandslikeme.Inthisoccasion,Ialsoremembermyteachersandcolleaguesfrommyundergraduateinstitu-tion-Dr.MasroorAli,Dr.SohelRahman,Dr.AshikurRahman,Dr.MasudHasan,Dr.HumayunKabir,Dr.YusufSarwar,Dr.Atif,Dr.Rifat,Dr.Enamul,andArup.Allofthemhasmadeapositivechangeinmylife.PerhapsIwouldnotbehereifIhadnottheopportunitytomeetmytwounclesataveryearlystageofmylife.My`Boromama'wasahighschoolmathteacherwhotaughtmemathinmyhighschools.My`chotomama',anelectricalengineerbyprofession,wasmysourceofinspirationtoproblemsolvingandthatearlychildhoodexperienceledmetopursuemystudiesincomputerscience.Iremembertheircontributioninmyacademiclifewithrespectandhumility.Iamalsogratefultomytwofriends-SaidulandMasudwhoalwayskeptmefocusedinthebigpicturethroughdifculttimes.Finally,itisbecauseofmyparents,mybrother,andmyfamilyIkeepgoingagainstallodds.Myparent'supbringingtaughtmetoenjoysuccesswithhumility,andembracefailurewithviistrongerdetermination.Mymedicaldoctorbrotherdemonstratedinhisdailylifehowtobecomeacompassionatehumanbeing.IamwhoIambecauseoftheirlove,sacrice,guidance,andprac-tice.MywifeTamannahasbeenatruefriendthroughoutmyPhDyearsandalwaysbelievedinmewhenImyselfwasdoubtful.MylittleangelPriyotaalwaysbroughtsmiletomyfaceevenatthelowestpointofmylife.IthanktheAlmightyforthiswholerollercoasterexperienceandforstrengtheningmybeliefonthissayingfiallthehardshipsandnegativityinlifeisshort-livedandthebeautyandblessingsinlifeiseternal.flviiiTABLEOFCONTENTSLISTOFTABLES.......................................xiiiLISTOFFIGURES......................................xivKEYTOSYMBOLS......................................xviiCHAPTER1.........................................1INTRODUCTION.......................................11.1PresentStatusandCoreproblem...........................11.2SolutionwithCognitiveRadioNetwork.......................21.3CollaborationbasedSpectrumSharing........................31.3.1SensingbasedCollaborationModel.....................41.3.2RelaybasedCollaborationModel......................51.3.3AuctionbasedCollaborationModel.....................61.4Contribution......................................81.5Organization......................................8CHAPTER2.........................................10BACKGROUNDANDRELATEDWORK.........................102.1Background......................................102.1.1SpectrumLicensing..............................102.1.2FCCReformationInitiatives.........................112.1.3SpectrumSensing...............................122.1.4IEEE802.22WRANStandard........................122.1.5RelayingStrategies..............................132.1.6VCGAuctions................................14
2.1.7McAfeeAuction...............................152.2RelatedWork.....................................152.2.1RelatedWorkonSensingbasedCollaborationModel............152.2.2RelatedWorkonRelaybasedCollaborationModel.............172.2.3RelatedWorkonAuctionbasedCollaborationModel............20CHAPTER3.........................................23ARC:ANADAPTIVEREPUTATIONBASEDCLUSTERINGALGORITHMAGAINSTSSDFATTACKINIEEE802.22NETWORKS..............233.1SystemModel.....................................253.1.1NetworkModel................................26
3.1.2TheDecisionRules..............................273.1.3HonestUserModel..............................283.1.4AttackModel.................................293.1.4.1IndependentAttack.........................29ix3.1.4.2CollaborativeAttack........................293.2AlgorithmDesign-AttackersvsBS.........................313.2.1Attackers'Impact...............................313.2.2DesignoftheAlgorithm...........................333.3AdaptiveReputationbasedClustering(ARC)Algorithm..............353.3.1ClusterFormation(ClusteringPhase)....................363.3.2DecisionMaking(VotingPhase).......................373.3.2.1Intra-ClusterVoting........................383.3.2.2Inter-ClusterVoting(FinalDecision)...............383.3.3ReputationAdjustment(UpdatePhase)...................393.4AnalysisofAttackModels..............................393.5PerformanceEvaluation................................463.5.1PerformanceMetrics.............................463.5.2SimulationParameters............................473.5.3IndependentAttack..............................473.5.4CollaborativeAttack.............................493.5.5AdaptiveAttack................................543.6Summary.......................................55CHAPTER4.........................................56INTERFERENCEAWARERELIABLECCRNSFORREAL-TIMEAPPLICATIONS564.1RelaybasedCollaborationModel...........................574.1.1LimitationsofPriorWork...........................584.1.2ProposedApproach..............................584.1.3KeyDesignChallenges............................594.1.4OurContributions...............................614.2SystemModelandProblemFormulation.......................624.2.1Preliminaries.................................624.2.2PUTrafcModel...............................63
4.2.3ChannelModel................................64
4.2.4CooperativeTransmission..........................644.2.5PacketLoss..................................65
4.2.6MDPFormulation...............................664.3AnalysisofaCooperativeTransmissionModel...................684.3.1ActionSet...................................69
4.3.2TransitionProbabilityMatrix.........................714.3.3RewardFunction...............................724.3.3.1CalculationofDa(t)(˙;˙0).....................744.3.3.2CalculationofVa(t)(˙).......................754.3.3.3CalculationofWa(t)(˙)......................774.3.4Comparison..................................804.4Multi-userCooperativeTransmissionModel.....................834.4.1Step1:Pre-screening.............................844.4.2Step2:Negotiation..............................85x4.4.3Step3:DataTransmission..........................874.4.4Step4:CooperationRenewal.........................884.5PerformanceEvaluation................................894.5.1PerformanceMetrics.............................894.5.2SimulationSetup...............................904.5.3SingleUserSetting..............................904.5.4Multi-usersetting...............................914.6Summary.......................................94CHAPTER5.........................................96COOPERATIVEROUTINGINCOGNITIVERADIONETWORKS..........965.1SystemModelandProblemFormalization......................995.1.1SystemModel.................................99
5.1.2Preliminaries.................................1015.1.3Formulation..................................1025.1.3.1RoutingpathConstructionasCoalitionFormation........1025.1.3.2SchedulingasResourceSharing..................1035.1.4PayoffofaPrimaryUser...........................1055.1.5PayoffofaSecondaryPlayer.........................1085.1.6ProblemStatement..............................1095.2CooperativeRoutingProtocol.............................1095.2.1MessageFormat................................1115.2.2CoalitionOfferandPayoffCalculation....................1125.2.3StabilityofCoalitions.............................1145.3PerformanceEvaluation................................1155.3.1Topology...................................116
5.3.2PerformanceComparisonwithPriorWork..................1165.3.3ResultswithVaryingNumberofPUs....................1185.3.4ResultswithVaryingNumberofSUs....................1195.3.5ResultswithAlgorithmParameters......................1195.4Summary.......................................121CHAPTER6.........................................122TRUTHFULONLINESPECTRUMAUCTIONS.....................1226.1OnlineDynamicAuctions...............................1266.1.1TheAuctionEntities.............................1266.1.2AuctionProperties..............................1286.1.3DesignChallenges..............................1286.1.4Illustration...................................1296.2AuctionDesign....................................1326.2.1Prank-I(SameValuationCase).......................1336.2.2Prank-II(SingleAuctionCase).......................1366.2.3Prank-III(DoubleAuctionCase)......................1396.3DistributionAwareAuctionAlgorithms.......................1416.3.1SOADE:OnlineSingleAuctionAlgorithm.................141xi6.3.2AnalysisofSOADE..............................1446.3.3distAware:OnlineDoubleAuctionAlgorithm................1506.3.4AnalysisofdistAware.............................1506.4DistributionFreeOnlineDoubleAuctionAlgorithm.................1536.4.1CandidateScreening(Phase1)........................1546.4.2DebtCalculation(Phase2)..........................1566.4.3CriticalPriceandWinnerSelection(Phase3)................1576.4.4AnalysisofdistFree..............................1596.5PerformanceEvaluation................................1616.5.1PriorityAnalysis...............................1626.5.1.1Prank-II..............................162
6.5.1.2Prank-III.............................1646.5.2AlgorithmPerformance............................1656.5.3SingleAuctionAlgorithm..........................1656.5.3.1ResultsonSettingwithNoSpectrumReusability.........1666.5.3.2ResultsonSettingwithSpectrumReusability...........1686.5.4DoubleAuctionAlgorithms.........................1686.5.4.1ResultsonSettingwithNoSpectrumReusabililty........1706.5.4.2ResultsonSettingwithSpectrumReusability...........1716.6Summary.......................................173CHAPTER7.........................................175CONCLUSION........................................1757.1SummaryofContributions..............................1757.1.1ContributiononSensingbasedCollaborationModel............1757.1.1.1TheSSDFAttackandProposedSolution.............1767.1.1.2PerformanceEvaluation......................1777.1.2ContributiononRelaybasedCollaborationModel..............1787.1.2.1CooperationAlgorithminReal-timeApplications........1787.1.2.2CooperationAlgorithminMulti-hopRouting...........1807.1.3ContributiononAuctionbasedCollaborationModel............1827.1.3.1OnlineSpectrumAuctions.....................1827.1.3.2PerformanceEvaluation......................1847.2FutureWork......................................1857.2.1UniedSolutionsagainstCombinedSSDFandPUEAttacks........1857.2.2PervasiveCommunicationsinCooperativeCognitiveRadioNetworks...1867.2.3TrustandSecurityissuesinCooperativeCognitiveRadioNetworks....1867.2.4Multi-unitOnlineSpectrumAuctions....................1877.2.5CombinatorialSpectrumAuctions......................1887.2.6PreventingBidderCollusioninSpectrumAuctions.............1897.2.7SpectrumAuctionInfrastructure.......................189BIBLIOGRAPHY.......................................191xiiLISTOFTABLESTable4.1:Statetransitionprobabilities.........................71Table5.1:AlgorithmmcRoute:foraPUuseri....................111Table5.2:AlgorithmmcRoute:forSUuserj.....................112Table5.3:Simulationparameters............................116Table6.1:AlgorithmSOADE:SecondaryOnlineAuctioninDynamicEnvironments142Table6.2:AlgorithmdistAware:DistributionAwareOnlineDoubleAuction.....151Table6.3:Symbolsusedinthealgorithm.......................155Table6.4:Functionsusedinthealgorithm.......................155Table6.5:AlgorithmdistFree:CandidateScreening(Phase1)............156Table6.6:AlgorithmdistFree:DebtCalculation(Phase2)..............157Table6.7:AlgorithmdistFree:CriticalPriceDetermination(Phase3)........158xiiiLISTOFFIGURESFigure1.1:Sensingbasedcollaborationmodel.....................4Figure1.2:Relaybasedcollaborationmodel......................5Figure1.3:Auctionbasedcollaborationmodel.....................7Figure3.1:Systemdetectionaccuracywithvaryingattackers.............32Figure3.2:Reputationdistribution...........................34Figure3.3:Blockdiagramofdifferentphasesofthealgorithm.............35Figure3.4:Informationpropagation..........................37Figure3.5:Relationshipsamongattackersandhonestusers..............43Figure3.6:Independentattackwithvaryingnumberofattackers...........48Figure3.7:Independentattackwithvaryingattackingprobability...........48Figure3.8:Independentattackwithvaryingdetectionprobability...........49Figure3.9:Collaborativeattackwithvaryingnumberofattackers...........50Figure3.10:Collaborativeattackwithvaryingattackingprobability..........50Figure3.11:Collaborativeattackwithvaryingdetectionprobability..........51Figure3.12:CollaborativeSubGroupattackwithvaryingnumberofattackers.....52Figure3.13:CollaborativeSubGroupattackwithvaryingattackingprobability.....52Figure3.14:CollaborativeSubGroupattackwithvaryingdetectionprobability.....53Figure3.15:CollaborativeGAMAattackwithvaryingnumberofattackers......53Figure3.16:AdaptivecollaborativeSubgroupattack..................54Figure4.1:Impactofsecondaryinterferenceincooperativecommunication.....60Figure4.2:Matchingpairandactionselection.....................67xivFigure4.3:Cooperationbetweenaprimaryandasecondaryuser...........69Figure4.4:Rewardcomponent.............................76Figure4.5:Comparisonbetweencooperationmodels(packetreceptionrate).....81Figure4.6:Comparisonbetweencooperationmodels(averagepuwaitingtime)...82Figure4.7:Cooperationlifecycleofauser.......................86Figure4.8:Handshakingprotocol............................86Figure4.9:Comparisonbetweenmodelsofasinglepairofprimaryandsecondaryusers.....................................91Figure4.10:Markovthreestatetrafcmodelwithvaryingtransmissiondeadline...92Figure4.11:Markovthreestatetrafcmodelwithvaryingqueuelength........92Figure4.12:Poissontrafcmodelwithvaryingdeadline................93Figure4.13:Poissontrafcmodelwithvaryingqueuelength..............93Figure4.14:Poissontrafcmodelwithvaryingpurate.................94Figure5.1:Networkmodel...............................99Figure5.2:Overlappingcoalitionexample.......................101Figure5.3:Messageformat...............................112Figure5.4:ComparisonbetweenmcRouteandnpRoute[79].............115Figure5.5:ResultswithvaryingPUs..........................118Figure5.6:ResultswithvaryingSUs..........................118Figure5.7:Resultswithvaryingalgorithmparameters.................120Figure6.1:Auctionwithdynamicbidderandsupply..................126Figure6.2:Applyingstaticauctionrules[142]indynamicenvironments.......130Figure6.3:Latearrivalmanipulationbyabidderwhileapplyingstaticauctionrules[142].....................................131xvFigure6.4:LatedeparturemanipulationbyabidderwhileapplyingTopaz[30]....131Figure6.5:Priorityvaluewithvaryingparameters(Prank-II)............163Figure6.6:Priorityvalueswithvaryingparameter(Prank-III)............164Figure6.7:Topazvs.SOADEonsettingwithnoreusability..............167Figure6.8:Topazvs.SOADEonsettingwithspectrumreusability..........169Figure6.9:Performancecomparisononsettingwithnoreusability..........171Figure6.10:Performancecomparisononsettingwithspectrumreusability.......172xviKEYTOSYMBOLSnnumberofsecondaryusersnanumberofmalicioussecondaryusersnhnumberofhonestsecondaryusersmnumberofprimaryusersPsetofprimaryusersSsetofsecondaryuserspprimaryuserssecondaryuserPfaprobabilityoffalsealarminindividualchannelsensingPmdprobabilityofmisdetectionintermsofchannelsenPIprobabilitythatachannelisidlePBprobabilitythatachannelisbusyPhdetectPUdetectionprobabilityofanhonestsecondaryuserPadetectPUdetectionprobabilityofanattackerPdiffHHprobabilitythattwohonestusersdifferPdiffAHprobabilitythatanhonestuserandanattackerdifferPmaattackingprobabilityKL(xjjy)KLDmeasuresbetweendistributionxandydxydistancebetweenxandyQEerrorrateQDfalsedetectionrateQFfalsepositiverateˆireputationofuseriweightfactor01VidecisionofavirtualclusteraboutchannelstatusVdecisionoftheBSaboutchannelstatusnumberofdimensionofsensingreportsperusermaintainedbyBSQgoaltargetsetbyanattackerEpprimarytransmissionpowerEssecondarytransmissionpowerHihypothesisiLqueuelengthPxprobabilityofeventxhichannelgainsetofstatesAsetofactions˚transmissionpolicy˙systemstatediscountfactora(t)actionattimetUa(x;y)utilityofauserafteractionaandmovingfromstatextoyttimeperiodDa(x;y)packetdropprobabilityduetoqueueoverowVa(x;y)successfuldeliveryprobabilityofapacketWa(x;y)successfuldeliveryprobabilityofqueuedpacketsxviiiP(x;y)transitionprobabilityfromstatextoyRdatarateCicoalitioniCScoalitionstructureriresourceofuseriTtotaltimetrafcrateBbandwidthdconvergenceparameterGttransmittergainGrreceivergainRi(Ci)datarateprotofcoalitioniDi(Ci)delayprotofcoalitioni jsellerj'spaymentvivaluationofbidderibibidofasecondaryuserib(h)h-thhighestbidinthesetaiaskofaprimaryuseria(h)h-thlowestaskinthesetoiarrivaltimeofuseridideadlineofuserigilocationofuseriE[ˇ˝(vi)]expectedpayoffofabidderofvalueviwith˝moreperiodstolivexix˝(vi)priorityofabidderiwithvaluationviand˝periodstoliveL˝(vi)losingprobabilityofabidderiwithvaluationviand˝periodstolive˚p
jsales/bidrequestCi(i)coalitionjoinrequestofuseriVjsetofuserintheneighborhoodofuserjFkcumulativedistributionfunctionofusers'lifetimeFncumulativedistributionfunctionofarrivingbiddersFmcumulativedistributionfunctionofsuppliesxxChapter1
Introduction
1.1PresentStatusandCoreproblem
Thecommunicationworldhaswitnessedatremendousadvancementinwirelesstechnologyoverthelastfewdecades.Adiverserangeofwirelessserviceshasbeenofferedstartingfromhealth-careapplicationstovehicularnetworks,fromreal-timesystemmonitoringtoInternetofThings(IoT)applications.Anewsetofwirelesscommunicationdeviceslikesmartphones,tablets,wearabledeviceshavebeenintroducedwithusefulandinterestingfeatures.Asaresult,theusageofwirelessdeviceshasskyrocketed,wirelesscommunicationhasbecomeanintegralpartofourdailylives,andwirelesstrafchasgrownatanexponentialrate.AccordingtoCiscostudy[25],mobiledatatrafchasgrown4000-foldoverthelast10yearswith74%growthinthelastyearonly,andthistrendwillcontinuetoincreaseinfuture.Inthesamestudy,itisexpectedthatmonthlymobiledatatrafcwillbe30.6exabytes(EB)by2020.ThishugetrafchastobecarriedoveraxedrangeofradiospectrumwhoseusageandaccessareregulatedbyFederalCommunicationsCommission(FCC)intheUS.TraditionallytheFCCapprovesdifferentserviceprovidersanexclusivelicenseofaxedspec-trumband.Inthefaceofgrowingtrafcdemand,suchxedallocationcannotmeetfuturedemandwiththeunassignedspectrumbandsonly.Theserviceproviderswithalreadylicensedspectrumarenotutilizingtheirshareveryefcientlyaswell.Forexample,SharedSpectrumCompany(SSC)conductedacitywideexperimentinVienna,VAontheusageofspectrumbetween30MHz1and3GHz[108].Thestudyshowedthatasignicantnumberofspectrumbandswerefihighlyunderutilizedflorfialmostneverused.flSimilarspectrumoccupancystudieshavebeenperformedindifferentcities,andtheresultsareconsistentthroughoutallthesestudies[116][89][11][17].Therefore,thecurrentallocationsystemisprovedtobeinadequate,anditsreformationisaneces-sitytodevelopanefcientspectrumsharingplatform.
1.2SolutionwithCognitiveRadioNetwork
FederalCommunicationsCommission(FCC),thespectrumregulationcommitteeintheUShastakensignicantsteps(seeSec.2.1.2)toaccommodatenewusersandsatisfytheirrequirements.SimilarstepshavebeentakenbyotherspectrumregulationcommitteesinEuropeandAsia[91].Theconceptofcognitiveradio(CR)isintroducedasaviablesolutiontoboththespectrumscarcityproblemandunderutilizationproblembydynamicallysharingspectrumtoendusersaccordingtotheirqualityofservicerequirements.Bydenition,cognitiveradiocanchangeitstransmissionparametersbasedoninteractionwiththeenvironment.Therearetwofeaturesthatmakecognitiveradiouniqueinthenetworkingworld[3]:(1)itscognitivecapabilitytocapturetheinformationfromtheradioenvironmentand(2)itsrecongurabilitytoworkondiversefrequenciesindifferenttransmissionaccesstechnologies.Basedontheusagerights,cognitiveradionetwork(CRN)consistsoftwotypesofusersŠprimaryusers(PU)andsecondaryusers(SU).Primaryusersarebasicallythelicenseholders,andtheyhaveexclusiveaccessrightstouseaxedspectrumband.Ontheotherhand,secondaryuserseitheropportunisticallyexploitfreespectrumornegotiatewithprimaryuserstotransmittheirowndata.Cognitiveradionetworkhasthusbecomeaprominentresearcheldtoaddressthespectrumallocationandsharingproblem.Variousspectrumsharingalgorithmshavebeenproposed2anddevelopedbasedonthecollaborationbetweenPUsandSUsinCRN.Inthisdissertation,wehaveexploredseveralofthesecollaborationmodels.Wehavediscussedtheuniquechallengesassociatedwitheachmodel,anddevelopedefcientspectrumsharingalgorithmsaddressingsomeofthesechallenges.
1.3CollaborationbasedSpectrumSharing
InitialfocusoftheCRNresearchwastondunusedspectrumwithoutinterferingprimaryusers'transmission.Spectrumsensingtechniquesbecamethecenterofresearchtoidentifyprimaryusers'activity,detectunusedspectrum,andopportunisticallyutilizethatspectrumfortransmissionofsecondarypackets.Overtheyearsdifferentsensingtechniquesweredevelopedbytheresearchers(foracomprehensivesummaryofsensingtechniques,readersarereferredtoSec.2.1.3).Whilethesensingtechniquesofferanimmediateopportunitytoutilizeunusedspectrumwithoutanymajorchangeintheexistingprimaryuserarchitectureitalsofacesseveralchallenges.Forexample,determiningsensingdurationandsensingfrequencywhilemaintainingahighsensingaccuracywereamajorconcern.Furtherresearchshowsthatcooperativesensingcanreducethesensingerrorandprovidebetterdetectionandspectrumutilizationthanindependentsensing.Consequently,anIEEEstandard[110]isdevelopedaroundcollaborativesensingtodesignaregionalareanetwork.Thestrictrequirementofspectrumsharingislaterrelaxed,andsecondaryusersareallowedtotransmitaslongastheinterferencecausedfromtheirtransmissiondonotexceedapredenedthreshold.Inthismodel,collaborationbetweenprimary-secondarypairsisestablishedonthebasisofcooperativediversityandmutualneeds.Thesecollaborationmodelsofspectrumsharing,theirimplementationchallenges,andfutureprospectswerediscussedinthe2009NSFworkshop[109].Inparalleltothesetechniques,thereisacontinuousefforttoensureefcientspectrumsharing3Figure1.1:Sensingbasedcollaborationmodelbyimprovingtheexistingspectrumregulationsystem.Awellregulationsystemshouldmotivatetheprimaryuserstosharetheirunusedspectrumtosecondaryusersinexchangeforadditionalrevenue.Thiseffortfromtheresearchersandpolicymakersleadstodesignofvariousinnovativeauctionmechanismswithdynamicnetworksettings.Theseongoingeffortshavebeenrecognizedinthe2013NSFworkshoponwirelessnetworking[13]andwelladaptedbyFCCindesigningfuturespectrumtrading.Wesummarizethesespectrumsharingtechniquesintothefollowingthreecategoriesbasedonthecollaborationbetweentheprimaryandsecondaryusersasfollows[6].1.3.1SensingbasedCollaborationModel
Therstspectrumsharingmodelinvolvescollaborationamongthesecondaryusersonly.Theprimaryusersareunawareoftheexistenceofthesecondaryusers,andthereforesecondarytrans-missionmustnotinterferetheirtransmission.Toavoidinterferencewithprimarytransmissions,thesecondaryusersapplyspectrumsensingtechniques,andtogether,theydecidethepresenceorabsenceofPUactivity.WhentheircollaborativedecisionimpliestheabsenceofPUs,thesec-ondaryuserscansharetheunusedspectrumfortheirowntransmission.Anindustrystandard[110]IEEE802.22isbeingdevelopedforWirelessRegionalAreaNet-work(WRAN)basedonthissensingbasedcollaborationmodel.Fig.1.1showsaWRANconsist-4Figure1.2:Relaybasedcollaborationmodel1ingofonebasestation(BS)andmultiplesecondaryusersasconsumerpremiseequipments(CPE).Inthisstandard,abasestationinstructstheCPEstosensespectrum,andthesecondaryuserssendbacktheirreportstothebasestation.Thebasestationthenmakesadecisionbasedonthesensingreports.However,thiscollaborationamongsecondaryusersalsogivesamalicioususeranoppor-tunitytomanipulatethesystem[15].Anindividualsecondaryusermaysendanincorrectsensingresult,leadthebasestationtoawrongdecision,andusethespectrumforitsownbenets.Thisformofmanipulationisreferredtoas`spectrumsensingdatafalsication'orSSDFattackinIEEE802.22networks.Inourresearchwork,weaddressthisproblemanddevelopadecisionmakingalgorithmthatpreventsSSDFattackandisolatesthemanipulatorsfromthedecisionmaking.1.3.2RelaybasedCollaborationModel
Thisspectrumsharingmodelinvolvesmutualneedbasedcollaborationbetweenprimaryandsec-ondaryusers(seeFig.1.2).Secondaryusersintendtoaccessprimaryspectrumfortheirowntransmissioninexchangeforrelayservicestoprimaryusers.Thisrelaybasedcommunicationreducestheimpactofpathattenuation,multi-pathpropagation,shadowingbyobstaclesandthushelpstostrengthentheprimarysignalatthedestination.PUsandSUsexchangetheircoopera-tioninformationandbuildacollaborativespectrumsharingmodel.Thismodelisalsoknownas1thepictureispartiallytakenfromhttp://famousbloggers.net/quickhaggle.html5cooperativecognitiveradionetwork(CCRN).InthisCCRNmodel,thePUssharetheirlicensedspectrumintemporal,spectral,andspatialdomainiftheSUsofferrelayingservicestoPUtrafc.ThePUsandSUscoordinateandscheduletheircooperativetransmissionsforachievingmutualbenetsbyapplyingdifferentrelayingstrate-gies(seeSec.2.1.5).Sincevideowillbethedominantpartofthefuturetrafc,weinvestigatewhethermutualcooperationhelpstosupportreal-timetrafc.WepresentadetailedanalysisofthecollaborationmodelbetweenPUsandSUsaddressingtheimpactofcooperationoverheadandin-terferenceconstraints.Wedevelopadistributedinterferenceawarereliablecooperationalgorithmthathelpsausertomakecooperationdecisionandtransmitsitsdata.Nextwetakeourinvestigationfromsinglehoptomulti-hopcooperativecommunicationinre-laybasedcollaborationmodel.Weconsidermulti-hopcooperativerelayingtoestablisharoutingpaththroughtheSUsinexchangeoftheirtransmissionopportunities.Weapplytheconceptofanoverlappingcoalitiongametodenetherewardofanindividualuserforparticipatinginacoop-eration.Thesimulationresultsshowthatitincreasestransmissionopportunitiesofthesecondaryuserswhileimprovingtherewardoftheprimaryusersintermsofdatarateandtransmissiondelay.1.3.3AuctionbasedCollaborationModel
Intheauctionbasedcollaborationmodel,theprimaryandsecondaryuserscollaborateviaathirdpartye.g.,FCC[39].ThePUsauctiontheirunusedspectrumforextrarevenuewhereastheSUsbidintheauctiontoacquirenecessaryusagerights.Usuallyatrustedauthority(e.g.,FCC)holdstheauction,administersspectrumallocation,andmanagesthepaymenttransaction.Fig.1.3illustratesdifferentcomponentsofaspectrumauction.RecentinitiativesfromtheFCCstronglyindicatethatspectrumauctionswillplayasignicantroleinrevolutionizingfuturespectrumdistributioningeneralaswellasinmilitaryuse.6Figure1.3:AuctionbasedcollaborationmodelThemajorchallengeinthismodelistoaccommodatediversityinbiddersandsellerswhileensuringintegrityandreliabilityoftheauction.Thelicensedusersmayauctiontheirspectrumintemporalandspatialdomainwithdifferentvalues.Similarly,thesecondaryusersplacetheirbidsaccordingtotheirtransmissionrequirementswhichalsovaryfromuserstousers.Inpresenceofsuchdiversity,anauctionmechanismmustensuretruthfulnessthatcannotbeachievedwithwell-knownVCGmechanism(seeSec.2.1.6).Additionally,spectrumauctionsmustensurereusabilitywhichisdifferentfromtraditionalauctions.Intraditionalauctions,asingleunitofproductissoldtoasinglebidderwhereasinspectrumauctions,thesamespectrumcanbeallocatedtomorethanoneusersaslongastheyarenotinterferingwitheachother.Theseuniquedifferencesmakethetraditionalauctionalgorithmsinapplicabletospectrumauctions.Inthiscontext,wefocusononlineauctionsinparticularwherethenumberofbiddersandspectrumunitsarenotknownaprioriandtheauctioneerneedstomakedecisiononline.ThissettingisinlinewiththePUactivityandspectrumdemandfromtheopportunisticusers.Wealsoconsiderthediversityinbidders'transmissionrequirements.Forexample,adelaytolerantusercanofoaddataatlatertimewhereasaninteractiveuserwantsimmediatespectrumaccess.Weconsiderdiversefeaturesofbiddersandsellersanddesignstrategyproofauctionalgorithmswhicharethenevaluatedintermsofefciencyandrevenue.71.4Contribution
Withthearrivalofnewapplicationsofferingdifferentservices,thefuturenetworkrequirestoaccommodatethespectrumdemandoftheirusers.Inthisdissertation,weaddresssomeofthechallengestowardsaccomplishingthatrequirement.Thehighlightsofourcontributionareasfollows:(i)IEEE802.22[110]isthewirelessstandardforruralbroadbandaccess.SSDFattackisamajorprobleminIEEE802.22networks.OursolutionofthisproblempresentedinChapter3willbehelpfultodevelopasecurecollaborativesensingplatforminIEEE802.22.(ii)Sincethevideotrafcwilldominateinnearfuture,thenetworkshouldbeabletosupportreliablevideotransmissionwithlowinfrastructurecost.OurresultsfromtherelaybasedcollaborationmodelwillbeusefultodevelopareliablenetworkbasedonmutualcooperationbenetsbetweenthePUsandSUs.Theresultsarefurtherextendedfromasinglehopmodeltomulti-hopcollaborationmodel.(iii)Theubiquitousnessofwirelessserviceswillincreasethenumberofconsumerswhowillwanttoaccessnetworksanytimeanywhere.Thediversityintherequirementsoftheseusersandsuppliesneedtobeaddressedonlinetobuildbetterspectrumsharingmodelsaroundit.Ourproposedauctionmechanismspresentedinthisdissertationensureonlinespectrumallocationanddeterminepriceconsideringdiversitiesofboththebuyersandsellers.1.5Organization
Thisdissertationisorganizedintoseveralchapters.InChapter2,werstprovidesomebackgroundinformationrelatedtoourresearch,thenpresentanextensivesummaryofrelatedworkondifferent8collaborationmodels.Eachofthefollowingchaptersaddressesaspecicproblembasedonuserrequirementsandcollaborationmodels.Chapter3addressestheSSDFattackinIEEE802.22networksundersensingbasedcollaborationmodelandpresentsanadaptiveclusteringalgorithmtopreventsuchattacks.Chapter4focusesonthechallengeswithreal-timetrafcandpresentsaninterferenceawarereliablecooperationalgorithminrelaybasedcollaborationmodel.Chapter5exploresthemulti-hoprelaybasedcollaborationmodeltoestablishstableroutingpathsforthePUswhileensuringSUtransmissionopportunities.InChapter6,weanalyzethediversityofbiddersandsellersunderauctionbasedcollaborationmodel.Wedeveloponlinesingleanddoubleauctionalgorithmsthatensuretruthfulness,individualrationality,budgetbalance,andimproveefciencyandrevenue.Finally,Chapter7concludesourworkanddiscussesourfutureresearchdirections.9Chapter2
BackgroundandRelatedWork
Tobetterunderstandtheresearchproblemsandtheproposedsolution,weprovidesomeback-groundinformationaboutsomerelevanttopics.Wealsopresentacomprehensivesummaryofexistingresearchworkonthreecollaborationmodels.
2.1Background
2.1.1SpectrumLicensing
Ineachcountry,spectrumlicensingishandledbyagovernmentauthorizedentitythatregulatesspectrumallocation,usageanddistributionamongtheinterestedproviders.IntheUS,FederalCommunicationCommission(FCC)isresponsibleformanagingandlicensingradiospectrumthroughoutthecountrytoadiverserangeofcommercialandnon-commercialusersincludingpub-licsafetyandemergencyresponseservices[36].Sinceitsformationin1934,theFCCworkswithspecicgoalsofadvocatinginnovationandinvestmentinbroadbandservices,offeringhigh-estandbestspectrumallocationtechniques,andensuringefcientandreliableaccesstoallocatedspectrum.Currently,theFCCcontrolstheallocationofspectrumbetween9KHzand275GHz.BasicallytherearetwowaystheFCCmakesspectrumavailabletowirelessservices-licensedandunlicensed.Thelicensedspectrumassignmentisusuallydonethroughspectrumauctions.Notethatdifferentradiofrequenciesholddifferentpropagationcharacteristicsandaresuitablefordif-10ferentservices.TheFCCholdsauctionforaspecicfrequencybandandselectsthehighestbidderaswinneramongtheinterestedserviceproviders.TheFCCthengrantsthewinnerpermissiontousethatspectrumbandforaspecicorentiregeographicallocation.Forexample,cellularserviceisintherangeof824-849MHzand869-894MHz[107].Intheunlicensedspectrum,usersoperatewithoutanylicense,however,mustcomplywiththetechnicalrequirementsguidedbytheFCC.TheFCCalsograntsexclusiveaccesstospecicspectrumrangetopublicsafetyagenciesandrstresponders.
2.1.2FCCReformationInitiatives
ItisevidentfromthepresentstatisticsandtheCiscotrafcforecast[25]thatitisnotpossibletosatisfythegrowingdemandusingtraditionalspectrumlicensingtechniques.TheFCCadvocatesaninnovativeapproachofspectrumsharingbetweenlegacynetworksandnewusersviadynamicspectrumaccess(DSA).Basedonearlystatistics,theFCCopenstheTVbroadcastchannelsforunlicensedaccesswithanimposedinterferenceconstraint[38][37].Ithasbeenproposedtocreateadatabasewithspectruminformation.In2010,theFCCpresentedtheNationalBroadbandPlan(NBP)whichrecommendsseveralstepstoreformthespectrumpolicytoaddressthespectrumsit-uation[90].Therecommendationsincludetakinginitiativetomake500MHzofspectrumavailableforbroadbandaccess,offeringincentivesandmechanismstorepurposespectrum,andexpandingopportunitiesforinnovativespectrumaccessmodels.Subsequently,theFCChasstartedanincen-tiveauction,rstofitskind,inthemonthofMarchof2016[58].Recently,theFCCisplanningtosharethe3:5GHzspectrumwhichiscurrentlyusedbythegovernmentradarsandxedsatel-lites[26].Athreelayeraccesspolicyhasbeenproposed.Inthisproposal,thelegacynetworkhasthehighestpriorityandoperatesontherstlayer,thesecondlayerprovidesaccessbasedonanincentiveauction,andthethirdlayerisopentousersforunlicensedaccess.112.1.3SpectrumSensing
Anumberofdifferentsensingalgorithmsarepresentedinliterature[101][42][9].Themostcommonsensingtechniqueisenergybaseddetectionduetoitslowcomputationalcostandimple-mentationalcomplexities.ThereceivedsignaliscomparedwithapresetthresholdvaluetodetectthepresenceofPU.ThechallengeofthistechniqueincludestheappropriatethresholdselectionanditsdifferentiationbetweenPUsignalandnoiseunderlowsignal-to-noise(SNR)values.Inthewavelet-basedsensing,knownpatternisusedtodetectPUsignalthatensureshigherreliabilityandfasterconvergencethantheenergydetectionmethod.Anothersensingmethodistoexploitcyclostationaryfeaturesofthereceivedsignals.Cyclostationaryfeaturescanevenbeusedtodis-tinguishamongdifferenttypesoftransmissionsandprimaryusers.WiththeknowledgeofthetechnologyusedinPUtransmission,severalfeaturescanbeextractedfromthereceivedsignalandvariousclassicationmodelcanbeappliedtodetectthePUsignal.Besidesthesesensingmethods,fewothermethodsarepresentedinliterature[133].However,detectionperformanceofanindividualsecondaryuseroftensufferfrommultipathfading,shadowing,receiveruncertaintyissues[4].Collaborativespectrumsensingisfoundtobeaneffectivesolutiontoovercometheselimitations[133].
2.1.4IEEE802.22WRANStandard
TheIEEE802.22standardhasbeenstartedbeingdevelopedin2004[1][29].Itistargetedtoprovidelowpopulationdensityruralareaswithbroadbandaccess.IEEE802.22denesacentral-ized,singlehop,pointtomulti-pointcommunicationstandardforwirelessregionalareanetwork(WRAN).ThebasestationisconnectedtotheInternetthroughabackhaulwhilethecustomerpremiseequipments(CPE)areconnectedtothebasestationthroughvacantTVchannels.The12usersapplycognitiveradiotechniquestoavoidinterferencetobroadcastusers.Thespectrumsensingiscontrolledandcoordinatedbythebasestation.Thebasestationalsohasaninterfacetoaccessthespectrumdatabase.Thenetworkoperatesover54-862MHzandusesOFDMAtechnol-ogy[1].Acompleteproposaldraftanditsamendmentscanbefoundhere[122].2.1.5RelayingStrategies
Inrelaybasedcollaborationmodel,theprimarysourcenodesendspackettoanintermediatesec-ondarynode,andthenintermediatesecondarynodeforwardsittothedestination.Therearegen-erallytwostrategiesusedinrelayingpacketsfromsourcetodestination.Theyareasfollows:(a)AmplifyandForward(AF)[28]:Therelaynodereceivesthesignalatrst,thenampliesit,andnallyrelaysittothedestination.(b)DecodeandForward(DF)[28]:Therelaynodetriestodecodethesignalafteritreceiveditfromthesourceandextracttheintendedmessage.Itthenre-encodesthemessageandtransmitsittothedestination.TheAFstrategyispreferredwhentherelaynodeisclosertothedestination,andtherelaydoesnotneedtousemuchpower.Sincetherelayampliesthenoisyreceivedsignal,thenoiseisalsoampliedanditseffectbecomesmoreseverewhentherelayisfarfromawayfromthedestination.Ontheotherhand,theDFstrategyworksbetteriftherelaynodeisclosertothesource.Itisthenmoreprobablethattherelaynodedecodesthemessagewithoutanyerror.Boththeserelayingstrategiesarestudiedinrelaybasedcollaborationmodel[86][50][23]toexplorethecooperationbenetsoftransmittingprimarypacketsthroughsecondaryusersincognitiveradionetworksunderinter-usercollaborationmodel.Thereisanotherlessknownrelayingstrategycalledcompressand13forward(CF)[28].Inthisstrategy,therelaynodequantizesthereceivedsignal,encodesthesamplesintoanewmessage,andthenforwardsthemessagetothedestination.2.1.6VCGAuctions
Ingeneral,anauctionmechanismshouldhavethefollowingpropertiessuchastruthfulness,in-dividualrationality,andbudgetbalance.Thetruthfulnesspropertyensuresthatabiddercannotincreaseitsprotbymanipulatinganyofitsinformation.Individualrationalitymeansthatanyparticipantintheauctionmustachievenonnegativeprot.Anauctionisbudgetbalancedifthetotalamountpaidtothesellersisnogreaterthanthetotalamountpaidbythebidders.ThedesignofsecondpriceauctionbyVickreyensurestruthfulbiddingofbidders.Accordingtothisauction[72],biddersplacetheirsealedbids.Thehighestbidderwinsbutpaysequaltothesecondhighestbid.ThisconceptisfurthergeneralizedbyVickrey,Clarke,andGroves[138].Intheirproposedsealedbidmulti-unitauction(referredtoas`VCGauction'),biddersbidtheirvaluationsforthedesireditemwithoutknowingthebidinformationofcompetingbidders.Theauctioneerassignsitemsinasociallyoptimalmanner.Eachwinnerischargedtheamountequaltothebidofthelosingbidderwhocouldwinifthewinnerwerenotpresent.Thismechanismisageneralizationofthesecondpriceauctionandisprovedtobeincentivecompatibleandindividualrational.Themechanismisattractivesinceitguaranteestruthfulreportingasthebeststrategyofabidderandabiddercannotincreaseitsprotbymanipulatingitsbid.However,thismecha-nismdoesnotguaranteetruthfulnesswhenthebiddershaveexibledeadlinesandtheirarrivalisdynamic.142.1.7McAfeeAuction
McAfeeinhisseminalpaper[88]designedadominantstrategyforbothbuyersandsellersinastaticdoubleauction.Thisstrategyisusedtodesignatruthfulmechanismforspectrumdoubleauctions[20,143].Accordingtothisstrategy,biddersinthesetTaresortedintonon-increasingorderofbidb1b2:::bn0wheren0denotesthenumberofbiddersintheauction,i.e.,jTj=n0.ThesellersinsetS0aresortedintonon-decreasingorderofaska1a2:::am0wherem0denotesthenumberofsellersintheauction,i.e.,jS0j=m0.Theminimumbidofthebiddersb(n0+1)andthemaximumaskofthesellersa(m0+1)aresetto1and1respectively.Then,hpairsareselectedsuchthat8ih;biaiandb(h+1)<a(h+1).So,thereareh1tradesintheauction,andtheh1highestbidbuyersandtheh1lowestasksellersareselectedaswinners.Ifh=1,nowinnerisselected.Thisimpliesthattheremustbeatleasttwopairsofbiddersandsellerstohaveonesuccessfultrade.Eachwinningbidderi2Tpaystheamountequaltob(h),andeachwinningsellerj2S0ispaidtheamountequaltoa(h).Theauctioneer'sutilityisequalto(h1)(b(h)a(h)).Whilethismechanismworksforstaticsetting,itfailstoensuretruthfulnessinonlinesettingconsistingofbidderswithtransmissiondeadlines.2.2RelatedWork
Wediscusstheexistingresearchworkbasedonthecollaborationmodelsbetweentheprimaryandsecondaryusersinthenetwork.
2.2.1RelatedWorkonSensingbasedCollaborationModel
Earlyresearchoncognitiveradionetworkmostlyaddressestheindependenteffortofsecondaryuserstondspectrumholeswithoutprimaryusers[77][83][100][56][8].Furtherresearch15showedthatcollaborativesensingimprovesthesensingaccuracyandincreasessecondarytrans-missionopportunitiesincomparisontoindependentsensing[133][4][42].Whilecooperativesensingimprovestheaccuracyofprimaryuserdetection,itbringsdifferentformofchallengessuchasSSDFattack.WedividetheexistingsolutionstocombatagainstSSDFattackintothreecategoriesŠreputation-based,dataminingbased,andarticialintelligenceap-proaches.Wangetal.[120]proposedanonionpeelingapproachbasedonBayesianstatisticstoassignsuspicionlevelstoallnodesinthenetwork.Theytesttheirheuristicbasedapproachforfalsealarmattacks,missdetectionattacks,andcombinationsthereof.However,theyassumethatbasestationhaspriorknowledgeabouttheactivitiesofattackers,whichisnotverycommon.Also,Qinetal.[93]proposedatrustbasedmodelanduseaweightedsensingresultaggregationmethodtoremovemaliciousnodesfromthedecisionmakingprocess.Chenetal.[18]presentedahy-bridmethodcalledtheweightedsequentialprobabilityratiotest(WSPRT)thatcombinesanode'sreputationandtheuseofasequentialprobabilityratiotesttoidentifymaliciousorfaultyunits.WSPRTisonlytestedagainstattackersutilizinganalways-falseoralways-freeresponsewhichareunsophisticatedattackstrategiesnotlikelytoreectrealscenarios.Rawatetal.in[7]exploredindependentandcollaborativeSSDFattacksandproposedasimplereputation-basedmethodtoidentifyattackers.TheydeterminedoptimalattackingstrategiesforcollaboratingattackerswheretheBScannotpossiblydiscriminatebetweenhonestandattackingCRs.AmathematicalanalysisofdetectionperformancewascarriedoutusingtheKullback-Leiblerdivergence(KLD).Accord-ingtotheirresults,inpresenceof50%independentattackers,BScannotdifferentiatebetweenthehonestusersandtheattackers.However,forcollaborativeattack,thisratioreducesto35%.AnewapproachbasedonK-neighborhooddistancealgorithmispresentedin[78]todetectindependentmalicioususers.Thisapproachdoesnotneedanypriorknowledgeofattackerdistri-butionandexposesattackersacrossmultiplesensingrounds.However,whenattackerscollaborate,16theycansuccessfullyevadedetection.Furtherworkhasbeendoneby[65]inestablishingamorerobustdecisionalgorithmcorroboratinginformationregardingPUpositioningandpathlosstothesecondaryuser.Theproposedmethoddramaticallyincreasesmisdetectionswhenusingincorrectstaticthresholds.Clancyetal.[27]addressedaseriesofstepstocombatthesensitiveareasinCRbyassuminganoisyenvironment,implementinglevelsofcommonsense,andprogrammaticallyresettinglearnedvaluestoavoidextendedcorruptionfromattackers.Theyofferuptheuseofswarmbehaviorindeterminingaglobaldecisiononwhetherasensedsignalwasactuallygeneratedbyaprimaryuser,alongwithatrust-basedmethod.HowevertheproposalsonhowtheseCRsshouldoperateintheeldarepresentedwithoutdetailsforverication.TheyalsodonotaddresshowtoincorporatethisnewinformationintothecurrentIEEE802.22networks.Besidestheseapproaches,Yuetal.in[132]considereddatafalsicationattacksinadhoccognitivenetworksandusedaconsensusbasedalgorithminspiredfromanimallifetodetectindependentattackersonly.Fewmoreresearchstudieshaveaddressedthespectrumsensingdatafalsicationattacksbyusingsupportvectormachine[35],suspicionlevel[84],incentivebasedapproaches[105],radiopropagationcharacteristics[85],crosslayerinformationandstatisticalanalysis[106].However,noneofthesestudieshaveconsideredtobeeffectiveinthecaseofcollaborativeattackers.2.2.2RelatedWorkonRelaybasedCollaborationModel
Overtheyearsresearchershaveshowngreatinterestindevelopingcooperationframeworksbe-tweentheprimaryandsecondaryusersusinggametheoryapproacheslikeStackelberggame[136][131],[103],[48],noncooperativegames[81],back-pressurealgorithm[67,127]andsoon.Also,initialresearchworkinthiscategorymainlyfocusesonsinglehopcommunication[53,61,62,64,67,76,131,136].Thesinglehopcooperationisconsideredintimedomainorfre-17quencydomainorinboth.Zhangetal.[136]modeledthecooperationasaStackelberggameandanalyticallyfoundtheNashequilibrium.Inthiscooperationmodel,aprimaryuserusesasecondaryuserasarelaytoimproveitsthroughputwhilethesecondaryusercanaccessafractionofthechannelaspaymentforrelayingtheprimarytrafc.Thesamemodelisalsoconsideredin[115],[131],and[103].Accordingtothismodel,timeslotsaredividedintosubslots.Theprimaryuserbroadcastsitspackettoachosensetofsecondaryusersintherstsubslot.Inthenextsubslot,allthesecondaryusersrelayprimarytrafcwhiletheprimaryusertransmitsthepacketdirectly.Inthelastsubslot,secondaryuserstransmittheirtrafc.However,thismodelisdesignedforoneprimarytransmitterandoneprimaryreceiver.Theyassumethattheprimarytransmitterusesapredenedxedtrafcrate.Thefocushereisonmaximizingprimaryuserutilitywhilesecondaryuserutilityisignored.Also,in[103],cooperationbetweenprimaryandsecondaryusersisinvestigatedusingStackelberggame.Cooperationmodelbasedonpacketretransmissionsonlyisanalyzedin[74].Yietal.[131][130]alsostudythecooperationframeworkamonguserswheretheprimaryac-cesspoint(AP)andsecondaryAPsequentiallydecidethestrategyforcooperativerelayselection,slotallocationamongmultipleusers,andspectrumleasingprice.ThesequentialprocessisagainformulatedasaStackelberggame,andauniqueNashequilibriumisfoundusingbackwardinduc-tionanalysis.However,thisworkalsoconsidersaxedtrafcratefortheprimaryusersandnominimumrequirementforthesecondaryusers.Since,weconsidercooperation,secondaryusers'performancecannotbeignored.Authorsin[111]consideraslightlydifferentmodelwherethepri-maryusersgiveupapartoftheirbandwidthforthesecondaryusersexclusivelytotransmittheirtrafcandproposeanoptimizedallocationmechanismtomaximizeprimaryusers'powersavingandsecondaryusers'transmissionrate.Thestudyin[69]considerscooperationbetweenprimaryandsecondaryusersinaprimary18multicastnetwork.Inthiscontext,primaryusersleveragesecondaryusersasrelaysinreturnforpartoftheirtransmissiontimewhichisdistributedamongallsecondaryusersinTDMAfashion.Theauthorsformulateanoptimizationproblemtondthetimeallocationbetweenprimaryandsecondaryuserstoimproveutilityofbothnetworks.Anapproximationalgorithmbasedonlinearprogrammingisproposedtosolvetheproblem.Khaliletal.[67]addedimmediaterewardandlongtermrewardforsecondaryusersinthecooperativemodel.Inthecaseofimmediatereward,theprimaryusersharesthesametimeslotwiththesecondaryuserwhileinthecaseoflongtermreward,thesecondaryuserisguaranteedtogetashareofthespectruminthelongterm.However,likepreviousapproaches,itschedulesonlyonepairofprimaryandsecondaryusersandassumesbothtypesofusershavebackloggedtrafc.Additionally,thealgorithmsacricestheprimaryusers'transmissiontosupportthelongtermtransmissionopportunityforthesecondaryusers.Thisframeworkmaynotbesuitableforpacketswithdeadlineconstraints.Besidesgametheoryapproaches,oneofthecommontoolsusedtoformulateandanalyzethecooperationframeworkisaMarkovdecisionprocess(MDP).Forexample,authorsin[87]consideranetworkconsistingofasingleprimaryuserwithinnitebufferandmultiplesecondaryusersandformulateaconstrainedMDPproblemwiththeaimofmaximizingsecondarytransmissionoppor-tunitieswhileguaranteeingstabilityofthequeueoftheprimaryuser.Theauthorsin[117]derivedastablethroughputregionconsideringasingleprimary-secondaryuserpairwhereasecondaryuser'ssequentialdecisiontocooperateornotisformulatedasaMDPproblemfocusingonthetradeoffbetweengainandcostofcooperation.Afewpapersaddressthedelayissueindifferentsettings.Forexample,Shaeetal.in[98]considereddelaysensitiveprimaryusers,Ashouretal.in[10]analyzedthetradeoffbetweenthroughputanddelay,Elmahdyetal.in[34]studiedniterelayingbuffers,andHyderetal.in[53]presentedananalyticalframeworkfordelayoptimizationincognitiveradionetworks.19Theresearchparadigmisrecentlyshiftedfromsinglehoptomulti-hopcooperativecommu-nication.Intermediaterelaysinacooperativetransmissiontrytoachievethesamegoalasdoestheprimarysource.Forexample,theauthorsin[2,57,68]exploitedtheroutinginformationfordifferentchannelmodelstominimizetheoverallenergyconsumption.InthecontextofCCRN,theintermediaterelaysaresecondaryuserswhomayhavedifferentandcontrastinggoals.Across-layeroptimalschedulingalgorithmwasproposedin[127]forcooperativemulti-hopCRNs.Inthisnetwork,thesecondaryuserscooperatewithprimaryuserstotransmitinamulti-hopfashion,andthesecondaryusersearntransmissionopportunityinreturn.Theanalysiswasdevelopedtoachieveoptimalthroughputfortheprimaryuserswheretheupperboundwasderived.However,theanalysisconsidersaxedroutingpathbetweenapairofprimarysourceanddestinationnodes.Lietal.[79]considersmulti-hopcooperationamongprimaryandsecondaryusersinbothtimeandfrequencydomainandinvestigatesthecooperationopportunityforndingastableroutingpath.Accordingly,theroutingpathconstructionproblemisformulatedasanetworkformationgame,andutilityandpayofffunctionsaredenedaccordingly.Primaryuserssequentiallyconstructrout-ingpathsthroughoneormoresecondaryusers.However,membersoftwoseparateroutingpatharemutuallyexclusivei.e.nosecondaryusercanparticipateinmorethanoneroutingpath,whichlimitstheopportunityofsecondaryuserstoimproveitswinningprobability.Therefore,itisim-portanttostudythecooperationbehaviorconsideringthestrategicindependenceofprimaryandsecondaryusers.
2.2.3RelatedWorkonAuctionbasedCollaborationModel
Spectrumauctionscanbecategorizedinsingle(single-sided)anddouble(double-sided)auctionsorstatic(ofine)andreal-time(online)auctions.Insingleauctions,oneormoresellershaveoneormultiplenumberofspectrumunitsforsalebuttheyhavenotsetminimumpriceperunit.However,20thebiddersmakedifferentbidsforoneormultipleunitsofspectrum.Indoubleauctions,sellersalsosetdifferentsellingpricesfortheirunits.Instaticauctions,thenumberofbiddersandthenumberofsellersarexedandtheauctioneerisawareoftheentireset.Inonlineauctions,theauctioneerdoesnotknowthenumberoffutureparticipantsandtakedecisionon-the-yabouttheallocationandpricing.VERITAS[142]presentsaframeworksothattheauctioneercanapplydifferentallocationalgorithmsaccordingtoitsobjectivefunctionwheretheobjectivecanbeensuringfairnessormax-imizingrevenue.Theproposedauctionmechanismisprovedtobetruthfulandefcient.Senguptaetal.in[96,97]presentsanauctionmechanismwherewirelessserviceproviders(WSP)bidtoacquirespectrum.Theallocationproblemismappedtoaknapsackproblemandwinnerselec-tionandpricingareoptimizedunderbothrstpriceandsecondpricebiddingstrategies.Sunetal.in[113]provedtheexistenceofNashequilibriuminanauctionwhereusersarebiddingforwirelessfadingchannelwithbudgetconstraint.Kongetal.in[71]usesavariationoftheVCGalgorithmtoallocateresourcesinanon-cooperativeOFDMnetworkandensurestruthfulnessofthemechanism.Wuetal.in[123]proposedanauctionalgorithmfocusingonwaitingtimein-steadofauctionrevenue.TheiranalysisprovestheexistenceofauniqueNashequilibriumandthesimulationresultsshowthattheproposedauctionimprovesthewinningprobabilitiesofsecondaryusers.Laterworkcapturesthediversityinsellers'valuationsindoubleauctionsettings.TRUST[143]istherstdoubleauctionmechanismthatensuresspectrumreusabilityandsatisesauctionpropertiessuchastruthfulness.Laterwork([21,22,31,40])ondoubleauctionsconsiderssimilarstaticmodelsandimprovescertainauctionoutcomessuchasrevenueandfairness.Alloftheseaboveresearchconsiderstaticmodelsandpresentofineauctionmechanisms.Recentresearchfocusesononlinespectrumauctionmodels[30,41,63,125,126].Consideringthe21onlinearrivalofusers,theauthorsin[30]proposedanefcientonlinespectrumauctionmecha-nismwithpreemptionwhichpreventsbothbid-basedandtime-basedcheating.However,itdoesnotprovideaperformanceboundonrevenuewithrespecttotheoptimalsolution.Underthesameonlineauctionmodel,Xuetal.[125]proposedTOFU,anotheronlinesemi-truthfulspectrumauc-tionmechanismwithchannelpreemption.Incontrasttoprevioussolutions,TOFUachievesonlysemi-truthfulnesswhereusersmayunderbidtogain.TORA[63],ontheotherhand,considersareverseauctionwherenumberofbiddersisxedthroughouttheauction.LOTUS[20]proposedalocationanddistributionawareonlinedoubleauctionmechanismwheredynamicrequestsfrombiddersaresatisedfromaxedsetofspectrumunits.However,itcannotensuretruthfulnessinthepresenceofdynamicavailabilityofspectrumandbidderswithtransmissiondeadlines.22Chapter3
ARC:anAdaptiveReputationbased
ClusteringAlgorithmagainstSSDFAttack
inIEEE802.22Networks
Astheresearchoncognitiveradiomatured,itwasrealizedthatcooperativesensingbasedcollab-orationmodel1amongsecondaryusersmaydetectthePUpresencemorequicklyandaccuratelythanindependentsensing[4].Thisrealizationwasreectedonthedesignoftherstcognitiveradiobasednetworkstandard,IEEE802.22forwirelessbroadbandaccess(seeSec.2.1.4).Thisstandarddenestheimplementationofopportunisticspectrumsharing(OSS)byoutlininghow/whenwire-lessdevicesareabletoutilizetemporarilyidlebandsinlicensedradiospectrums.Theproposalalsodenesthecellularlikecommunicationinterfacebetweenabasestation(BS),andsecondaryuserscalledconsumerpremiseequipments(CPE).TheBSisresponsibleforcontrollingthespec-trumusageandchannelassignmenttoCPEs.AllCPEsinacellperiodicallymonitorprimaryusersignalsandtheBSleveragesthedistributedsensingpowerofCPEsthroughcontinualspectrum1Theworkpresentedinthischapterhasbeenpublishedintworesearcharticles:(i)ChowdhurySayeedHyder,BrendanGrebur,LiXiao,flDefenseAgainstSpectrumSensingFalsicationAttacksinCognitiveRadioNetworksfl,InternationalConferenceonSecurityandPrivacyinCommunicationNetworks(Securecomm),pp154,London,UK,Sept7-9,2011.(ii)ChowdhurySayeedHyder,BrendanGrebur,LiXiao,MaxEllison,flARC:anAdaptiveReputationbasedClusteringagainstSpectrumSensingDataFalsicationAttacksfl,IEEETransactiononMobileComputing,13(8),pp1707-1719,August2014.23reportsobtainedfromthem.Tocoordinatetheprocess,acentralizedBScollectssensinginformationfromthesecondaryusersattachedtothecell.Eachusersubmitsahypothesisregardingwhetherornottheysuspecttheprimaryuseristransmitting.Asradiowavesareaffectedbyphysicalbarriersorenvironmentalconditions,thedetectionaccuracyofanynodewithinsensingrangeofthePU'ssignalvariesfromtimetotime.Malfunctionsassociatedwiththesensingequipmentmayalsoinuencethenode'sobservedmeasurements.Fromthehypothesessuppliedbythesecondaryusers,theBSmustdecideontheactualstateoftheassociatedspectrum.Onceadecisionismade,thebasestationinformsSUsandrevokespermissionoftheuserscurrentlytransmittingonthatspectrum.Duetoitsuniquecharacteristics,CRNsfacenewsecuritythreatsinadditiontothecommonexistingsecuritychallengesinwirelessnetwork.OnetypicaltypeofattackistheSpectrumSensingDataFalsication(SSDF)attackorByzantineattack.Duringsuchanassault,themalicioususercompromisesoneormoreofthesecondaryusersandmaybeginsendingmodiedsensingreportstotheBS.Inthisway,anattackertriestoinuencetheBSintoproducingawrongdecisionaboutthechannelstatus.Compromisednodesmayworkindependently,ormaycollaboratetoreducespectrumutilizationanddegradeoverallperformanceofthenetwork.Constructingadecision-makingstrategythatmitigatestheimpactofbothindependentandcollaborativeSSDFattackerswillbeinvaluabletotheadvancementofCRN.Bystrengtheningthebasestationagainstmaliciousormalfunctioningusers,theinterferenceproducedfromCRNswillbeminimized,potentiallyexpeditingtheimplementationofsuchnetworkalternatives.Ultimately,bothusersandbusinessescanreapthebenetsofefcientradiospectrumusagethroughCRNs.Existingresearchstudieslike[78],[120],[121]mainlyconsiderindependentmaliciousattack.However,theseapproacheseitherrequirepriorinformationofattackers(e.g.numberofattackers[121],attackers'distribution,attackingstrategy[120]etc.)ordependoncarefulthresholdselection24[78].Tothebestofourknowledge,onlyonework[7]handlesbothindependentandcollaborativeattacksusingareputationbasedmethodandlimitstheerrorrateindecidingchannelstatusandinidentifyingattackers.Althoughtheidenticationrateofattackersofthisapproachishigh,italsomisdetectsalargenumberofhonestusersasattackers.Additionally,thisapproachfailscompletelywhenonlyafewuserscollaborateinSSDFattack,anderrorrate(i.e.numberofincorrectdecisions)increasesalmostlinearlywithnumberofattackers.Inthisregard,weproposeanadaptivereputationbasedclusteringalgorithmtodefendagainstbothindependentandcollaborativeSSDFattacksthatdoesnotrequirepriorinformationaboutthenumberofattackersorattackingstrategies[55][54].Thewholeprocessgoesthroughasequenceofphasestomakeadecision.First,thenodesareclusteredbasedonthesensinghistoryandinitialreputationofnodes.Thechannelstatusisdecidedthroughintra-clusterandinter-clustervoting.Thenaldecisionispropagatedbacktotheclustersandthentotheindividualnodesforadjustingthereputationofthenodes.Wecomparetheperformanceofouralgorithmwiththatofthealgorithmproposedin[7]underdifferentattackingscenarios.OuralgorithmhandlesSSDFattackssignicantlybetterthantheonein[7]andminimizestheerrorindecidingchannelstatus.Ouralgorithmalsoidentiesmostoftheattackerswhilekeepingamuchlowermisdetectionrate.3.1SystemModel
Inthissection,weexplainthetopologyoftheCRnetwork.WealsoconsiderbothindependentandcollaborativeattackingmodelsandexplainthedecisionmechanismoftheBS.253.1.1NetworkModel
WeconsideranIEEE802.22WRANnetworkwheretheBSisthecentralcoordinatorandactsasthefusioncenterthatregulatesthemediumaccessofallnsecondarynodesattachedtoit.Amongthensecondarynodes,nanodesareattackersandnharehonestusers(nanh).Honestusersarecompletelyunawareofthepresenceoftheattackers.Wedonotconsiderthenumberofattackersmorethan50%becauseitisnotproductivetostudyanetworkwhereamajorityofnodesareattackers.TheBSperformsdistributedsensingthroughsecondaryuserstodecideonthechannelstatus.Atthestartofeachtimeperiod,SUsperiodicallysenseachannelandreportitbacktotheBS.TheBStakesthenaldecisionbasedonthereportsandifthechannelisfree,itallocatesthechannelamongtheusers.WeassumethatSUsusethethresholdbasedenergydetectiontechnique[133]forspectrumsensingandthethresholdforprimaryuserdetectionisdenedbytheBS.AllsecondarynodesdecideaboutthePUpresenceindependentlybasedonthedetectiontech-niqueandsendtheirreportstotheBS.AccordingtotheIEEE802.22standards[99],therequiredsensingtimeofanodeis2secandtheprobabilityofafalsealarmshouldbekeptto0:1atmaxi-mum.However,duetothesensingtimeconstraintsandlimitationofdetectiontechniques,itisnotpossibleforSUstodetectPUpresencewith100%accuracy.Wealsoassumethatneithersecondaryusersnorthebasestationhaveanyknowledgeabouttheactualchannelstatus.Ineachtimeslot,honestSUssensethechannel,comparethesensedenergywiththethreshold,anddecideindependentlyaboutthechannelstatus.Finally,theyreporttheirndingstotheBSwithoutanyalteration.Ontheotherhand,thedishonestuserscanbeselshormaliciousbasedontheirintention;botharecommonlyreferredtoas`attackers'.Fromaselshattacker'spointofview,thegoalistomakethebasestationtakeawrongdecisionaboutthechannelstatusso26thatitmayexploitthespectrumopportunitytotransmititsowndata.Onthecontrary,amaliciousattacker'sgoalisnotonlytominimizethespectrumutilization,butalsotodegradethenetworkperformance.Thelatteroneismoreharmfulthantheformersinceitalsoincreasestheinterferencewithprimaryusers.
3.1.2TheDecisionRules
TheBSperformsabinaryhypothesistesttodecideontheactualchannelstatusthatcanbedenedasfollows.H0:Primaryuserisabsent(channelisfree)H1:Primaryuserispresent(channelisbusy)Whenthereisnoattackpreventionmechanism,theBSgenerallyfollowsa'n0outofn'ruletodecideonthechannelstatuswherendenotesthetotalnumberofsecondaryusers.Accordingly,ifeachsecondaryuserisendsitsownindividualhypothesis(Di2f0;1g)tothebasestation,thenaldecisionDcanbedenedasfollows[32].D=8
>
>
>
<
>
>
>
:H1ifPn
i=1Din0H0otherwiseThespecialcase(whenn0=1)isreferredtoasORrule(ifanyofthenodessensethechannelbusy,BSdecidesabusychannel).Thisapproachisveryconservativeinthesensethatonesingleattackerorevenamalfunctioninghonestnodecanreducethespectrumutilization.Thealternativeapproachistodecidedependingonmajorityvoting(e.g.n0=n2).Thisresolvesthespectrum27underutilizationproblembutsignicantlyincreasesthemisdetectionrate.Asaresult,itbecomesvulnerablewhenattackerscollaborativelydecidetheirattackingstrategyaswell.3.1.3HonestUserModel
WeassumethatevenanhonestusercannotdetectPUpresencewith100%accuracy.WedenefalsealarmrateastheprobabilityofsensingthepresenceofaPUwhenitisactuallynottrans-mitting,andwedenemisdetectionrateastheprobabilityofnotsensingaPUwhenitisactuallyoperating.LetusassumethattheprobabilityoffalsealarmandmisdetectionrateofauserarePfaandPmdrespectively.Pfa=Pr(yi=1jH0);Pmd=Pr(yi=0jH1)whereyirepresentsthesensedresultbyuseri.Asexplained,honestusersdonotchangetheirsensingresults.LetusassumethatxirepresentsthereportsenttotheBSbyuseri.Pr(xi=1jyi=1)=1;Pr(xi=0jyi=1)=0;Pr(xi=0jyi=0)=1;Pr(xi=1jyi=0)=0Accordingly,wecancalculatethedetectionprobabilityofanhonestuser,PhdetectusingEqn.3.1.Phdetect=Pr(xi=0jH0)Pr(H0)+Pr(xi=1jH1)Pr(H1)=(1Pfa)PI+(1Pmd)PB(3.1)Here,PIandPBdenotetheactualidleandbusyrateofthechannelrespectively.283.1.4AttackModel
Weconsiderthatattackersdevisetheirplanindependentlyorcollaboratively.Basedontheirat-tackingstrategy,eachattackernodemayalteritssensingresultfrombusytoidleandfromidletobusywithdifferentprobability.Wealsoassumethatbothoftheprobabilitiesarethesame.How-ever,ourresultscanbeeasilyextendedfordifferentprobability.Accordingly,weconsideroneindependentandthreecollaborativeattackingtechniques.Weselectedtheattackingtechniquesconsideringtheeaseofimplementation,impactoftheattack,frequencyofattackandsoon.Therstcollaborativetechniquefinloutofnaflwasalreadyshowntobeeffectivein[7].Thesecondtechniqueisconsideredhereduetoeaseofimplementationanditfollowsanintuitiveattackingmodel.Thethirdtechniqueisconsideredtoexploittheproposeddecisionmechanismused.3.1.4.1IndependentAttack
EachindependentattackerchangesitssensingresultwithprobabilityPmal.Thedetectionproba-bilityofanindividualattacker,PadetectwhileworkingindependentlycanbeexpressedusingEqn.3.2.Padetect=Pr(xa
i=0jH0)Pr(H0)+Pr(xa
i=1jH1)Pr(H1)=[(1Pmal)(1Pfa)+PmalPfa]PI+[(1Pmal)(1Pmd)+PmalPmd]PB(3.2)Similarly,wecanndthefalsealarmprobabilityofanattacker(Pafa).3.1.4.2CollaborativeAttack
InthecaseofacollaborativeSSDFattack,attackersexchangetheirsensinginformationanddecidetheirresponsecollaboratively.First,weconsiderthecollaborationstrategy`nloutofna'attack.29Itisshownin[7]thatonly35%ofattackersusingthisapproachcanblindthedecisionmechanismoftheBS.LetusassumethatPa1detectandPa1fadenotethecommondetectionprobabilityandfalsealarmprobabilityofattackers.Inthiscase,Pa1detectandPa1fawillbe,Pa1detect=naXi=nl(na;i;Padetect);Pa1fa=naXi=nl(na;i;Pafa)(3.3)where,(na;i;k)=nai(k)i(1k)nai:Here,nlisdenedin[7]nl=minna;˘na1+ˇwhere,=lnPfaPhdetectln1Phdetect1PfaThesecondcollaborationtechniqueisinspiredfromthefactthatifamajorityofthenodesaltertheirsensingreports,theBSwilltakeawrongdecision.Accordingly,weconsidertheGoingAgainstMAjority(GAMA)attacktoanalyzetheimpactofcollaborationinwhichallattackerssharetheirtruesensingresultsandthendecidetosendtotheBStheoppositetothemajoritysensingresultwithacertainprobability.Forexample,iftwoattackerssensethechannelidleandoneattackersensesthechannelbusy,allthreeattackersreporttotheBSthatthechannelisbusy.Inthiscase,thecommondetectionprobabilityofattackerswillbePa2detect=naXi=l(na;i;1Phdetect);Pa2fa=naXi=l(na;i;1Pfa)(3.4)wherel=na=2+1.ThethirdcollaborationtechniqueweconsideristheSubGroup(SG)attack.Thereasonwe30selectthisapproachistoinvestigatewhetheritispossibleforattackerstosuccessfullyattackandavoidbeingdetectedsimultaneouslyiftheyattackinsubgroups.Consequently,attackersformsmallgroups,andeachgroupchangestheirsensingresultaccordingtotherstapproach.Finally,onegroupischosenrandomly,andalltheattackersinthatgroupreportthesamesensingresult.Wedidnotconsiderthatattackerscanoverhearthehonestusersanddevisetheirplanaccord-inglysinceitisnoteasytooverhearthesensingreportsfromallusers.Evenifanattackercanreportitssensingreportbasedonthat,itsresponsewillincurasignicantlatencytoreachtotheBSwhichcanbeexploitedtodiscarditfromthedecisionmechanism.Also,thistypeofattackwillbemoreeffectiveiftheBSfollowsanORruleinsteadofmajorityrule[32].3.2AlgorithmDesign-AttackersvsBS
Inthissection,weshowtheimpactofattackersinthedecisionmechanismandexplainthedefensemechanismthattheBSusestodefendagainstdifferentattackingstrategiesindetail.3.2.1Attackers'Impact
Inthissection,weanalyzetheimpactofattackers,bothindependentandcollaborative,inthedecisionmechanismoftheBS.Letusassumethatthebasestationdecidesbasedonamajorityvoting.LetXandYdenotethenumberofhonestusersandmalicioususersthatdetectthechannelstatuscorrectly.Sinceallthehonestusersareindependent,XfollowsabinomialdistributionwithparameternhandPhdetect.Similarly,inthecaseofindependentmaliciousattack,YalsofollowsabinomialdistributionwithparameternaandPadetect.So,PS,theoveralldetectionprobabilityofthesystem,canbecalculatedusingthejointdistributionofdetectionprobabilityofindependenthonestusersandindependent31Figure3.1:Systemdetectionaccuracywithvaryingattackersattackers.Let,k=(na+nh)=2.PS=Pr(X+Y>k)=nhXi=1(nh;i;Phdetect)naXj=ki(na;j;1Padetect)Inthecaseofcollaborativeattack,thedetectionprobabilitydegradesaccordingtotheircollab-orationstrategy.Here,weonlydemonstratetheimpactofaGAMAattackasarepresentativeofcollaborativeattack.Similarly,othervariationsofcollaborativeattackscanbeexplored.LetusconsidertheGAMAattackwhenalltheattackerschangetheirdecisionagainstthemajoritysensingresultwithprobabilityi.e.Pmal=.So,eitherallattackerssendcorrectchannelstatusornoneofthemsendscorrectreport.Forsimplicity,letusassumethatprobabilityofattackis1.So,attackersalwayssendtheoppositeofthemajoritysensingresults.LetPYdenotetheprobabilitythatalltheattackerswillsendcorrectsensingreportinGAMAattack.Thisisequivalenttothecasewhenmajorityattackersfailtosensethecorrectchannelcondition.PY=Pr(Y<na2)=na=21Xj=1(na;j;Phdetect)=Pa2detect32Theoveralldetectionaccuracyofthesystemdependsonthejointdistributionofattackersandhonestusers'detectionprobability.Eqn.3.5representsthecorrectdetectionprobabilityinpresenceofcollaborativeGAMAattackers.PS=PYPr(Xkna)+(1PY)Pr(Xk)=Pa2detectnhXi=kna(nh;i;Phdetect)+(1Pa2detect)nhXi=k(nh;i;Phdetect)(3.5)TheimpactofbothindependentandcollaborativeattackersinthedecisionmakingprocessisshowninFig.3.1.WecalculatethedetectionaccuracyofindependentattackersaccordingtoEqn.3.5.andofcollaborativeattackersaccordingtoEqn.3.5.Weachievedsimilarresultsforothertypeofcollaborativeattacks.Theparametersweconsiderhereareasfollows:PI=0:9,PB=0:1,Pfa=Pmd=0:2.3.2.2DesignoftheAlgorithm
Thedecisionmechanismshouldberobustandcapableofdefendingagainstanyattackingstrategyadoptedbyanynumberofmalicioususers.However,theBSdoesnothaveanyinformationabouttheattackingstrategiesornumberofattackers.TheonlyinformationavailabletotheBSisthesensingreportssentbyusersattachedtoit.So,thedefensemechanismshouldbeabletonullify(oratleastreduce)theimpactofcollaborationofattackers,identifythemandquarantinethemfromtheprocess.Accordingly,wedesignanadaptivereputationbasedclustering(ARC)algorithmtodefendagainstbothindependentandcollaborativeSSDFattacks.Thealgorithmworksagainsttheinten-tionandmotivationofmalicioususersandtriestonullifytheirinuenceonthenaldecision.Toreducetheimpactofattackers,wecreateclusterssothatnodeswithsimilarsensinghistory33Figure3.2:Reputationdistributionwillbeinthesamecluster.Then,eachclusterhasonlyonevotetocastandthechannelstatusisdecidedbasedonmajorityvotingoftheclusters.Theideabehindthisisthatiftheattackersattackfrequently,attackersandhonestnodeswillbeinseparateclustersduetotheirdifferentsensingreports.Also,thecollaborationofattackerswillnothelptoincreasetheerrorratesinceeachclusterhasonlyonevote.Thekeytoattackers'successistoavoidbeinginthesameclusterandtotakecontrolofthemajorityoftheclusters.Tohandletheseissues,weintroducedistanceweightedvotinginaclusterandafeedbackcomponentineachnode'sreputation.Eachnode'svotingweightintheclusterisinverselyproportionaltoitsdistancefromthemedianofthatcluster.Similarly,eachnodegetsreputation,whichisinverselyproportionaltoitsdistancefromthemedianofthatcluster.Bydistributingthereputationbasedondistancefromthemedian,nodesareonlyimpactedrelativetotheirficondenceflofthatgroup.ThereputationassignmenttoeachnodeinasampleclusterisdemonstratedinFig.3.2wherethereputationofeachnodeisshowninsidetheparenthesisofeachnode.Asexplained,thecloseristhenodetothemedian(M),thehigheristhereputationofthenode.Accordingly,themediannode(M)hasthehighestreputation(4)whilethenodefarthestfromthemedian(A)hasthelowestreputation.34Figure3.3:BlockdiagramofdifferentphasesofthealgorithmFurthermore,fromthenextround,nodes'modiedreputationisalsousedforclusteringinadditiontosensinghistory.Inthisway,evenifanattackerandanhonestuserincorrectlyfallinthesamecluster,attackerscannotestablishtheirdecision.Furthermore,astimegoeson,thedistancebetweenanhonestuserandanattackerwillbeampliedduetothejointconsiderationofreputationandsensinghistoryinclusterformation.
3.3AdaptiveReputationbasedClustering(ARC)Algorithm
Theproposedadaptivereputationbasedclustering(ARC)algorithmexecutesasequenceofphasestoreachthenaldecision(Fig.3.3).Inthecollectionphase,theBScollectsthesensingreportsfromallthenodesinitscell.Intheclusteringphase,themodiedversionofthepartitioningaroundmedoids(PAM)algorithmisappliedtocreatekequalsizedvirtualclusters.Inthevotingphase,naldecisionismadebasedonintra-clusteringandinter-clusteringvoting.Thisisfollowedbyanupdatephasewherethenumberofclustersareadjustedandthereputationofallnodesarereevaluated.Next,themajorcomponentsofouralgorithmareexplained.353.3.1ClusterFormation(ClusteringPhase)
Clusteringtechniquesareoftenusedinanomalyidenticationoroutlierdetection.TwooftheprominentclusteringtechniquesareK-meansandK-medoid[66].K-meansdenesaclusterintermsofacentroid,whichisusuallythemeanofthegroupofpoints.ItclusterstheobjectsinawaytominimizethesumofsquaredEuclideandistance.Ontheotherhand,K-medoiddenesaclusterintermsofamedoid,whichisthemostrepresentativeobjectforagroupofobjectsandcanbeappliedtoawiderangeofdata.TheK-medoidalgorithmrequiresonlyaproximitymeasureforapairofobjectsandtriestominimizethetotalerror.WepreferK-medoidtoK-meansalgorithmforclusteringsincetheformerismorerobusttonoiseandoutliersthanthelatterandminimizesasumofpairwisedissimilaritiesinsteadofasumofsquaredEuclideandistances.SeveralalgorithmshavebeenproposedtoimplementK-medoidclustering.WeusetheParti-tioningAroundMedoid(PAM)algorithm[66]toclusternodesbasedontheirsensingreports.Amedoidisthenodeoftheclusterwhoseaveragedissimilaritytoallothernodesinthesameclusterisminimal.Giventhenumberofclustersandsensingreportsfromallthenodesasinput,PAMsequentiallyndsthesamenumberofnodesasmedoidsaroundwhichallothernodesareclusteredinawaysothattheobjectivefunctionisminimized.WemodifyPAMsothateachclusterhasequalnumberofnodes.TheBSmaintainsa+1dimensionalvector(Xi=[ˆi,x1;i,:::x;i])tostoreinformationforeachnodei.Therstentryinthevectorrepresentsthereputationandtheremainingonesrepresentlatestsensingreports.Themostrecent1sensingreportsofeachnodei(fromx2;i,:::x;i)aredirectlyconsideredincalculationwhilethepriorhistoryisalsomaintainedinoneentryx1;iasweightedaverageofprevioussensingreports.So,theeffectofpastsensingreportsdecreasewithtime.Wedonotconsiderlargedimensionofvectorfortworeasons.First,thealgorithmmay36Figure3.4:Informationpropagationsufferasthedimensionincreasessincethedatapointsbecomemoreuniforminhighdimensions.Thisispopularlyknownascurseofdimensionality.Second,higherdimensionsofdataincreasecomputationalcostthatmakesthealgorithmundesirable.
3.3.2DecisionMaking(VotingPhase)
Oneofthekeyfeaturesinouralgorithmishowwereachthenaldecisionandusethatdecisionrecursivelytoupdatetheclustering.TheowchartofinformationpropagationineachtimestepisillustratedinFig.3.4.Asstatedearlier,theBSconsidersthemostrecentsensingreportsofeachnodeinadditiontotheirreputationduringclusterformation.Thereputationscoreisalwaysbetween0and1.WeassumethattheBSisunawareofthelocationofnodesattachedtoit.Allnodesareassigned0:5astheinitialreputationscore.Thedecisionprocessgoesthroughtwosubsteps:intra-clustervotingandinter-clustervoting.373.3.2.1Intra-ClusterVoting
Eachclusternalizesitsdecisionaboutchannelstatusinauniqueway.Onlythelastroundsensingreportofeachnodeintheclusterisconsidered.However,eachresponseisweightedwithanimpactfactorthatisinverselyproportionaltothedistancebetweenthenodeandthemedianofthatcluster.TheimpactfactorofanodejdenotedbyIjisdenedasIj=1d(j;mi)wheremiisthemedianoftheclusteriandd(j;mi)denotesthedistancebetweennodejandmedianmiofthesamecluster.Nodesclosertothemedianhavehigherinuenceindecisionmakingprocessthanthefarones.Accordingly,thevotingViofclusteriisdeterminedbyEqn.3.6.Vi=Pnh=kj=1Ijx;jPnh=kj=1Ij(3.6)Here,kisthenumberofclustersandx;jisthelatestsensingreportfromnodejthattakesvaluefromf0;1g.3.3.2.2Inter-ClusterVoting(FinalDecision)
Aftereachclusternalizesitsdecision,theBSchecksthevalidityofeachclusterandmakesthenaldecisionVonthebasisofmajorityvotingamongthevalidclusters.Iftheaveragereputationofallmembernodesofaclusterisbelowathreshold,theclusterisinvalid;thenthemembersinthatclustercannotvoteandaremarkedasattackers.Theclustervalidationprocessisperformedperiodically.Assumingk0validclusters,V=d2Pk0i=1Vi=k0e.383.3.3ReputationAdjustment(UpdatePhase)
Attheendofeverytimestep,theBSupdatesthereputationofallthenodesaccordingtothealgorithmandifneeded,increasesthenumberofclusters.Thenalresultispropagatedbacktotheclusters,andthentotheindividualnodes.Ifthenaldecisionmatcheswithaclusterdecision,thatclustergetsapositivefeedback;otherwise,itgetsnegativefeedback.Similarly,ifanode'sdecisionmatcheswithitsclusterdecision,itgetspositivefeedbackwhileitreceivesnegativefeedbackforamismatch.Eachnode'sreputationisthenadjustedaccordingtoEqn.3.7.ˆj=ˆj+(Vi;V)Pnh=kj=1(Vi;x;j)IjPnh=kj=1Ij(3.7)whererjdenotesthereputationofnodejand(a;b)isanindicatorfunctionthatreturns1ifaequalsb,anditreturns-1otherwise.Thenalresultisalsousedtoadjustthenumberofclusters.Initially,westartwith5clusterswith5randommedoids.Aftereachvalidationperiod,ifallclusterspassthevalidation(i.e.averagereputationscoreexceedsthreshold,=0:5),weincrementthenumberofclustersandcontinuethesameprocess.Otherwise,weremoveallthenodesintheclusterthatfailsthetest.Afterfewperiods,wegobacktoinitialstateremovingfiattackerfltagandstartthealgorithmfromthebeginning.
3.4AnalysisofAttackModels
Inthissection,weexplainthesignicanceoftheusers'sendingreportsindecisionmaking.Wethenanalyzehowtheattackersexploitthemechanismtotheirownbenetsandhowourproposed39algorithmworksagainsttheattackingstrategies.Tobeginwith,theBSperformsabinaryhypothesistestbasedonthesensingreportssentbythesecondarynodes.ThetestcanbeexpressedasPr(Hjjx1;x2;:::xn)8j2f0;1g.AccordingtotheBayesiantheory,thehypothesistestcanbefurthersimpliedasPr(Hjjx1=j;x2=j;:::;xn=j)=Pr(x1=j;x2=j;:::;xn=jjHj)Pr(Hj)Pr(x1=j;x2=j;:::;xn=j)=Pr(x1=jjHj)Pr(x2=jjHj):::Pr(xn=jjHj)Pr(Hj)Pr(x1=j;x2=j;:::;xn=j):SincetheBSdoesnotknowtheactualchannelstatistics,thetestresultdependsontheprob-abilitiesofsensingreportsofindividualnodes.Accordingly,foranyuseri,wecalculatetheconditionalprobabilitiesPr(xi=jjHj)andPr(xi=jjHj)8j2f0;1gandtheseprobabilitydistributionsdeterminetheaccuracyofthedecisionmechanism.Therefore,weneedtodeterminetheclosenessbetweentheseprobabilitydistributions.WeemploytheKullback-Leiblerdivergence(KLD)toanalyzethedifferenceintheprobabilitydistribution.TheKLDisbeingusedindifferentdetectionscenariosincludingByzantineattacksincognitiveradionetworks[7].Technically,KLDisastatisticalmeasurethatquantiesinbitshowcloseaprobabilitydistributiona=aiistoamodel(orcandidate)distributionq=qi[102].KL(ajjq)=Xiailog2aiqi(3.8)Similarly,wecanexpresstheKLDbetweenthedistributionsPr(xijH0)andPr(xijH1)as(Pr(xijH1)jjPr(xijH0))=Xj2f0;1gPr(xijH1)log2Pr(xijH1)Pr(xijH0):(3.9)40Foranhonestuseri,thedistributionsPr(xijH1)andPr(xijH0)dependonthenode'ssensingaccuracy.(Pr(xijH1)jjPr(xijH0)=Pmdlog2Pmd1Pfa+(1Pmd)log21PmdPfaWhenthereisnoattacker,thefalsealarm(Pfa)andmisdetection(Pmd)probabilitiesaresig-nicantlysmall.Therefore,theKLDvalueislargeandtheBSmostlytakestherightdecisionaboutchannelstatus.However,inthepresenceofattackers,theprobabilitiesaredifferent.Letusassumethatde-notesthefractionofnodesactingasattackersandeachattackerindependentlychangesitssensingreportwithprobabilityPmal.Accordingly,thecollectiveprobabilitydistributioncanbeexpressedasPr(xjHj)=Pr(xa
ijHj)+(1)Pr(xijHj)8j2f0;1g:(3.10)UsingresultsfromEqn.3.8,independentattackerscandisruptthedecisionmechanismif(Pr(xjH1)jjPr(xjH0)=0whichimpliesthefollowingconditionPr(xjH1)=Pr(xjH0):(3.11)Solvingtheaboveequationleadsustondthenecessaryconditionforattackerstobesuccessful.TheconditioncanbestatedasfollowsPmal=12where0;Pmal1:(3.12)41Accordingtothecondition,ifhalfofthenodesindependentlyalwayschange(i.e.withprobability1)theirsensingreport,attackerstakecompletecontrolofthedecisionmechanismofthebasestation.Asattackingprobabilityofindividualnodedecreases,itneedsmoreandmorenodestoactasattackerstoblindthebasestation.Inasimilaranalysisin[7],itisshownthatif=35%,collaborativeattackerscandisruptthedecisionmechanismcompletely.Next,weexplainhowARCpreventsbothindependentandcollaborativeattackersfromdis-ruptingthedecisionmechanism.ARCseparatesattackersfromhonestusersbasedonsensingreportsusinganadaptiveclusteringtechnique.Asaresult,iftwousersfollowthesameprobabilitydistribution,theyendupinthesamecluster.Therefore,inadditiontotheconditionalprobabilities,attackersmustmakesurethattheirsensingreportsarenottoodifferentfromthoseofhonestuserstoavoidbeingdetectedbyARC.Otherwise,attackerswillbeseparatedintothesameclusterandthus,willbedetectedandeliminated.LetPdiffHHdenotetheprobabilitythattwohonestusersdifferintheirsensingreportatanytime.PdiffHH=2[PIPfa(1Pfa)+PBPmd(1Pmd)](3.13)Similarly,letPdiffAHdenotetheprobabilitythatanattackerandanhonestuserdifferintheirsensingreportsatanytime.PdiffAH=2PI(1Pmal)Pfa(1Pfa)+PIPmal(1Pfa)2+P2fa+2PBPmd(1Pmd)(1Pmal)+PBPmalP2md+(1Pmd)2(3.14)Accordingly,iftheattackerswanttobesuccessful,theKLDvalueofthesetwoprobabilitiesshould42(a)case1:dA1H>dA1A2anddA1H>dHH(b)case2:dA1A2>dA1HanddHH>dA1HFigure3.5:Relationshipsamongattackersandhonestusersbeequaltozero.(PdiffHHjjPdiffAH)=PdiffHHlog2PdiffHHPdiffAH=0(3.15)Ontheotherhand,wecanestimatethedistancebetweenanhonestuserandanattackerandbetweentwohonestusersaccordingtothestronglawoflargenumbersfromtheclusteringpointofview.Accordingly,thenormalizeddistancebetweenanytwohonestusersdHHconvergestoPdiffHHwithtime.Similarly,thenormalizeddistancebetweenanhonestuserandanattackerdAHconvergestoPdiffAHwithtime.Itfollowsthatifthesetwoprobabilitiesareequal,thendistancebetweenanhonestuserandanattackerandbetweentwohonestusersareapproximatelyequal.Hence,attackersandhonestuserswillendupinthesameordifferentclusterswithequalprobabilityandcannotbeseparatedbyARC.Withsimilaranalysisin[78],itcanbeshownthatmalicioususerscanavoidthedetectionbysettingproperPmalifthefalsealarmandmisdetectionprobabilitiesaregreaterthanorequalto0:4.However,asthestandardfalsealarmandmisdetectionprobabilityare0:1,wecanconcludethatindependentattackerscannotdefeattheARCinnormalconditions.ThealternativeapproachtodeceiveARCistotakecontrolofthemajorityoftheclusterswhichweexploredinSubGroupattack.Itiseasilyobtainableifattackersoutnumberthehonestusers.43Otherwise,thepossiblewaytomanipulatethedecisionmechanismistospreadoutintodifferentclustersanddominateindecisionmakingofeverycluster(or,majorityoftheclusters)consistently.Accordingly,eachattackergroupworkswithadifferentattackingprobability,andallmembersinagroupreportthesamesensingresulttoinuencetheclusterdecisionintheirfavor.LetusassumethattheattackingprobabilityoftheattackergroupAiisi,andtheprobabilitythattheattackergroupAiandthehonestuserdifferintheirsensingreportsatanytimeisPdiffAiH.Similarly,PdiffAiAjdenotestheprobabilitythatanyattackergroupAiandattackergroupAjdifferintheirsensingreportsatanytime.PdiffAi;Aj=[iPfa+(1i)(1Pfa)][j(1Pfa)+(1j)Pfa]+[i(1Pfa)+(1i)Pfa][jPfa+(1j)(1Pfa)](3.16)Hereforsimplicity,weassumePfa=Pmd.Accordingtothestronglawoflargenumbers,thenormalizeddistancedAiAjbetweenanytwoindependentattackergroupsAiandAjconvergestoPdiffAiAjwithtime.Similarly,thenormalizeddistancebetweenhonestusersandbetweenanyattackergroupandhonestusercanbeestimatedandarerepresentedasdHHanddAiHrespectivelywhichareequivalenttoPdiffHHandPdiffAH.So,theclustersareformedbasedontherelativedistancebetweenhonestusersanddifferentattackergroups.Now,weneedtoanswerthefollowingquestionfromattackers'perspective:WhatshouldbetherelationshipamongdHH,dAiH,anddAiAjtomanipulatetheclusterformationanddeceiveARCcompletely?Inordertoachievethat,differentgroupsofattackersshouldnotbeinthesameclusterandalsoattackersmustpreventclusterformationwithhonestusersonly.Fig.3.5illustratestheclustercharacteristicsfordifferentcases.Case1showstheexpectedclusterformationforanydetectionalgorithmwhereattackersandhonestusersareindifferentclusters.Case2showsthe44expectedformationforattackerswhereeachclusterisformedwithcombinationofattackersandhonestusers.Theattackerswilltrytomaximizetheerrorindecisionmakingwhilesatisfyingtheconditionsofcase2inFig.3.5.Forexample,considerthecaseof3clusters.Theattackerswillbesuccessfulifatleasttwoofthegroupsattackandiftheprobabilityofdifferenceinsensingresultbetweenanygroupofattackerandhonestusersmustbelessthanminimumofthedifferencebetweentwogroupsofattackersandbetweenanytwohonestusers.Furthermore,attackersmustbedominatinginthemajorityofclusterstotakecontrolofthedecisionmechanismthatdependsoninitialseedselectionandnumberofiterationsusedforclusterformation.Hence,themaximizationfunctionforattackerscanbestatedasfollows.max1232
4Xi;j;kij(1k)+Yii3
5suchthat8i;jPdiffAiH<minPdiffHH;PdiffAiAjand1;2;3>0Sincethenodesdonotknowtheactualchannelstatus,itisunlikelythattheattackerscancalculatetheexactvalueofPdiffHH.EveniftheycanestimatePdiffHH(itwillbesignicantlysmall),ndingtheattackingprobabilityfordifferentgroupsofattackerswhilesatisfyingthenecessaryconditioncannotbepossibleinanormalcondition.Fromtheaboveprobabilisticanalysis,wecanconcludethatARCcanwithstandallkindsofnonadaptiveindependentandcollaborativeattackundernormalconditions.453.5PerformanceEvaluation
Inthissection,wediscusstheperformanceresultsofourproposedmethodbyspecicallycom-paringitseffectivenessagainstapreviouslyproposedmethodin[7].Fromthispoint,wewillrefertothisalgorithmasfiRawatmethodflor`R',bythenameoftherstauthorofthework[7].Wecomparethesetwoalgorithmsacrossbothindependentandcollaborativeattacksaswellasvariousprobabilitiesofattackunderarangeofsensingconditions.3.5.1PerformanceMetrics
Inordertoevaluatetheperformanceofouralgorithm,weusethreeperformancemetrics.Firstoneistheprobabilityoferrororerrorrate,denotedasQE.Itdenoteshowmanytimesthebasestationmakesanincorrectdecision.Theloweristheerrorrate,thebetteristhealgorithm.ThesecondmetriciscalledtruedetectionrateorrecallandisdenotedasQD.Itiswidelyusedindataminingapplicationstoevaluatethesuccessfuldetectionofmembersofaclassthatareconsideredmoresignicantthanthedetectionofmembersofotherclasses.Algorithmswithhighervalueofrecallaredesirable.Inourwork,identifyingattackersismoresignicantthanidentifyinghonestusers.ThethirdmetricisfalsepositiverateandisdenotedasQF.Thismetricrepresentshowmanynodesaremisidentiedasattackers.Inthiscase,thelowerthefalsepositiverate,thebetterthealgorithmis.QE=#ofincorrectdecisionT(3.17)QD=#ofattackerstrulyidentied#ofactualattackers(3.18)QF=#ofhonestusersmisidentied#ofnodesidentiedasattackers(3.19)463.5.2SimulationParameters
Weconsiderthatachannel'sidletimefollowsaBernoullidistributionwithparameter0:6.Inotherwords,primaryuserstransmitoverthechannelwithprobability0:4.Ateachtimestep,thechannelstatusisrandomlydrawnfromtheprobabilitydistributionfunction.Foreachtest,themethodsarerunfor80timesteps.Foreachtimestep,themethodsmustproduceanalhypothesis,whichiscomparedagainstactualtransmissionstateoftheprimaryusertodeterminethemethod'serrorrate(QE).Ratesforthecorrectdetectionofattackingnodes(QD)andtheincorrectdetectionofhonestusersasattackers(QF)arealsoreportedattheendofthetest.Eachtestisthenrepeated30timeswithanaverageofthevaluesdisplayedinthegraphs.Atestconsistsofrandomlygeneratedreportsforeachsecondaryuser,adheringtolabeledprobabilitydistributions.Foravalidationtest,weconsider=0:5.Foreachtypeofattack,wetesttheperformanceofthealgorithmwiththreevariations.Theyareasfollows.varyingnumberofattackersvaryingattackingprobabilityvaryingdetectionprobability3.5.3IndependentAttack
Inthenextstep,wecomparetheperformanceofouralgorithmwithreputationbasedmethodin[7]forindependentSSDFattacks.Inthisattack,attackersdonotcollaboratetoexchangetheirreports.Eachattackerworksindependentlytomaximizeitsgoal.Fig.3.6showstheerrorrateoftwoalgorithmswithvaryingnumberofattackers.WekeeptheattackingprobabilityPmal=1.4710152025303540455000.10.20.30.40.50.60.7# of Attackers (out of 100 nodes)QE  Error Rate(R)Error Rate(ARC)(a)ErrorrateQE1015202530354045500.40.50.60.70.80.91# of Attackers (out of 100 nodes)QD  Recall(R)Recall(ARC)(b)RecallQD10152025303540455000.10.20.30.40.50.60.70.8# of Attackers (out of 100 nodes)QF  False Detect(R)False Detect(ARC)(c)FalsePositiverateQFFigure3.6:Independentattackwithvaryingnumberofattackers0.50.60.70.80.9100.050.10.150.20.250.30.350.40.450.5Pmal (35 attackers, 100 total nodes)QE  Error Rate(R)Error Rate(ARC)(a)ErrorrateQE0.50.60.70.80.910.40.50.60.70.80.91Pmal (35 attackers, 100 total nodes)QD  Recall(R)Recall(ARC)(b)RecallQD0.50.60.70.80.9100.10.20.30.40.50.60.70.8Pmal (35 attackers, 100 total nodes)QF  False Detect(R)False Detect(ARC)(c)FalsePositiverateQFFigure3.7:IndependentattackwithvaryingattackingprobabilityAlso,probabilitiesfortrueandfalsedetectionofasignalaresettoPhdetect=0:9andPfa=0:1.AlthoughouralgorithmperformsbetterthanRawatalgorithm,theerrorrateincreaseswiththenumberofattackers.Ontheotherhand,ouralgorithmperformsmoderatelytodetectmaliciousattackerswhiletheiralgorithmconsistentlyidentiesattackerswithhighprecision.However,theiralgorithmeliminatesalargenumberofhonestusersincorrectly.Fig.3.6showsthatabout40%honestusersaremisidentiedasattacker.Ontheotherhand,falsedetectionrateofouralgorithmisalmostnegligible.Althoughthereputationbasedalgorithmperformsbetterindetectingattackersthanouralgorithm,theymisidentiedalargenumberofhonestusersasattackers,whichmakestheiralgorithmlesseffective.Similarly,werunthesimulationforindependentSSDFattackswithvaryingattackingprob-ability.Wevarytheattackingprobabilityfrom0:5to1andplotQE,QD,andQFinFig.3.7480.50.60.70.80.9100.10.20.30.40.50.60.7Pdet (35 attackers, 100 total nodes)QE  Error Rate(R)Error Rate(ARC)(a)ErrorrateQE0.50.60.70.80.910.20.30.40.50.60.70.80.91Pdet (35 attackers, 100 total nodes)QD  Recall(R)Recall(ARC)(b)RecallQD0.50.60.70.80.9100.10.20.30.40.50.60.70.80.91Pdet (35 attackers, 100 total nodes)QF  False Detect(R)False Detect(ARC)(c)FalsePositiverateQFFigure3.8:Independentattackwithvaryingdetectionprobabilityforouralgorithmandreputationbasedalgorithmproposedin[7].Again,ouralgorithmperformsbetterindecisionmaking(Fig.3.7).Errorrateofouralgorithmisalmostnegligiblewhiletheirerrorrateoftheiralgorithmincreasesalmostlinearlywithattackingprobability.Thetrueattackerdetectionrateisalmostthesameforbothalgorithmswhentheattackingprobabilityexceeds0:65.However,theiralgorithmconstantlyeliminates60%ofhonestnodesasattackersforanyattackingprobabilityrangingbetween0:5and1:0.Ontheotherhand,ouralgorithmperformssignicantlybetterandkeepsafalsedetectionrateclosetozero.Next,wevarythedetectionprobabilityofnodesfrom0:5to1:0andplotQE,QDandQFinFig.3.8forouralgorithmandreputationbasedalgorithmproposedin[7].Asusual,theerrorrateofouralgorithmoutperformstheiralgorithm.Also,ouralgorithmperformsbetterintermsofmisidenticationofattackers.However,theiralgorithmidentiesalmostallattackersirrespectiveofthedetectionprobability.Ontheotherhand,ouralgorithmgraduallyincreasesthetruedetectionratewiththeincreaseofdetectionprobability.
3.5.4CollaborativeAttack
Wetestedbothmethods(Rawatmethod[7]andARC)againsteachofthecollaborativebyzantineattacksdiscussedinSection3.1.4.2.Therstsetofsimulation(Fig.3.9)presentstheresultfor4910152025303540455000.10.20.30.40.50.60.7# of Attackers (out of 100 nodes)QE  Error Rate(R)Error Rate(ARC)(a)ErrorrateQE10152025303540455000.10.20.30.40.50.60.70.80.91# of Attackers (out of 100 nodes)QD  Recall(R)Recall(ARC)(b)RecallQD10152025303540455000.10.20.30.40.50.60.70.80.91# of Attackers (out of 100 nodes)QF  False Detect(R)False Detect(ARC)(c)FalsePositiverateQFFigure3.9:Collaborativeattackwithvaryingnumberofattackers0.50.60.70.80.9100.10.20.30.40.50.60.7Pmal (35 attackers, 100 total nodes)QE  Error Rate(R)Error Rate(ARC)(a)ErrorrateQE0.50.60.70.80.9100.10.20.30.40.50.60.7Pmal (35 attackers, 100 total nodes)QD  Recall(R)Recall(ARC)(b)RecallQD0.50.60.70.80.9100.10.20.30.40.50.60.70.80.91Pmal (35 attackers, 100 total nodes)QF  False Detect(R)False Detect(ARC)(c)FalsePositiverateQFFigure3.10:Collaborativeattackwithvaryingattackingprobabilitythecollaborativeattackdenedin[7].Thenumberofmalicioususersrangefrom10to50outof100totalsecondaryusers.Theattackingprobability(Pmal)issetto1.Sensingprobabilitiesforcorrectlydetectingasignalandfalselydetectingasignalweresetto(Phdetect)=0:9and(Pfa)=0:1respectively.ARCoutperformsconsistentlywithrespectto(QE)showingamarkedlydecreasederrorrateuntilroughly50%ofthepopulationbecomesattackers.Oncethepopulationcontainsamajorityofmalicioususers,itisimpossibleforanysensingstrategytosustainanerrorrateunder50%.TheRawatmethodshowsahighQDinitiallybutquicklydiminishesafter20%ofnodesareattackersandbecomescompletelyineffectivewhen1=3ofthepopulationareattackers.Atapproximatelythesameattackerconcentration,ourmethodexceedsandmaintainsamarkedincreaseinidenti-fyingattackers.Conversely,theRawatmethodbeginswithasignicantfalsedetectionrate(QF)500.750.80.850.90.95100.10.20.30.40.50.60.7Pdet (35 attackers, 100 total nodes)QE  Error Rate(R)Error Rate(ARC)(a)ErrorrateQE0.750.80.850.90.95100.10.20.30.40.50.60.70.80.91Pdet (35 attackers, 100 total nodes)QD  Recall(R)Recall(ARC)(b)RecallQD0.750.80.850.90.95100.10.20.30.40.50.60.70.80.91Pdet (35 attackers, 100 total nodes)QF  False Detect(R)False Detect(ARC)(c)FalsePositiverateQFFigure3.11:Collaborativeattackwithvaryingdetectionprobabilitywhileourmethodminimizesthisrateacrosstheentirerangeofattackers.Maintainingalowmisde-tectionrateallowsourmethodtomaximizehonestuserreportsandmitigatetheimpactofattackersevenunderheavyattacks.Asecondsetofmeasurementsobservedtheimpactofcollaboratingmalicioususerswhenvaryingtheirprobabilityofattack.Malicioususerscanutilizethistechniquetoescapedetectionfromhighdimensionalclusteringmethods.InFig.3.10,attackersproduceonaveragelessthan20%errorrateswhiletheRawatmethodsustainssignicanterrors.Regardlessofattackingrate,ourmethodconsistentlyidenties50%oftheattackers.TheRawatmethodexhibitsanunusuallyhighattackermisdetectionrate,whichislikelytoleadtothehigherrorrate.Thenexttestlooksatconsequencesofvariablesensoraccuracy(Fig.3.11).Here,35collab-oratingmalicioususersattackduringeachsensingstep.Bothmethodsbeginwithrelativelyhigherrorrates,asthesensingreportsofhonestusersresemblethatofattackersduetotheinaccuratesensorreadings.Oncesensingerrorsfallbelow65%,ourproposedmethodshowsalinearde-creaseintheHypothesiserrorrate.TheRawatmethodtakessignicantlyhigherdetectionrates(approximately80%)beforeerrorratesbegintodecline.Wealsotestouralgorithminthecaseofsubgroupcollaborativeattacks(Fig.3.12).Weassumethatattackersknowthenumberofclustersandcreateequalnumberofgroupsofattackers.At-5110152025303540455000.10.20.30.40.50.60.70.80.9# of Attackers (out of 100 nodes)QE  Error Rate(R)Error Rate(ARC)(a)ErrorrateQE1015202530354045500.50.550.60.650.70.750.80.850.90.951# of Attackers (out of 100 nodes)QD  Recall(R)Recall(ARC)(b)RecallQD10152025303540455000.10.20.30.40.50.60.70.80.91# of Attackers (out of 100 nodes)QF  False Detect(R)False Detect(ARC)(c)FalsePositiverateQFFigure3.12:CollaborativeSubGroupattackwithvaryingnumberofattackers0.50.60.70.80.9100.050.10.150.20.250.30.350.40.45Pmal (35 attackers, 100 total nodes)QE Error Rate(R)Error Rate(ARC)(a)ErrorrateQE0.50.60.70.80.910.50.550.60.650.70.750.80.850.90.951Pmal (35 attackers, 100 total nodes)QD  Recall(R)Recall(ARC)(b)RecallQD0.50.60.70.80.9100.10.20.30.40.50.60.70.8Pmal (35 attackers, 100 total nodes)QF  False Detect(R)False Detect(ARC)(c)FalsePositiverateQFFigure3.13:CollaborativeSubGroupattackwithvaryingattackingprobabilitytackersareequallydistributedinallsubgroups.Asthenumberofattackerincreases,QEincreasesslightlyinouralgorithmwhileQEreachesalmost40%inthereputationmethod.Asexpected,boththeirtruedetectionandfalsedetectionrateishigh.Ontheotherhand,QDisabout65%andQFisalmostnegligibleinouralgorithm.Similarly,ouralgorithmoutperformsRawatalgorithmintermsoferrorrate,recallandfalsedetectwithvaryingattackingprobability(Fig.3.13)andwithvaryingdetectionprobability(Fig.3.14).WendinterestingresultsforattackerswithGAMAstrategy.Inthecaseofouralgorithm,QEis0andonlyincreaseswhenthenumberofattackersexceeds37.Ontheotherhand,QEincreasesalmostlinearlywiththenumberofattackersinthereputationbasedmethod.Wegetsimilarresultsintrueandfalsedetectionrate.TheresultsareplottedinFig.3.15.Similarly,ouralgorithmoutperformsRawatalgorithmwithvaryingattackingprobabilityandwithvarying520.50.60.70.80.9100.10.20.30.40.50.60.7Pdet (35 attackers, 100 total nodes)QE  Error Rate(R)Error Rate(ARC)(a)ErrorrateQE0.50.60.70.80.910.40.50.60.70.80.91Pdet (35 attackers, 100 total nodes)QD  Recall(R)Recall(ARC)(b)RecallQD0.50.60.70.80.9100.10.20.30.40.50.60.70.80.91Pdet (35 attackers, 100 total nodes)QF  False Detect(R)False Detect(ARC)(c)FalsePositiverateQFFigure3.14:CollaborativeSubGroupattackwithvaryingdetectionprobability10152025303540455000.10.20.30.40.50.60.70.8# of Attackers (out of 100 nodes)QE  Error Rate(R)Error Rate(ARC)(a)ErrorrateQE1015202530354045500.40.50.60.70.80.91# of Attackers (out of 100 nodes)QD  Recall(R)Recall(ARC)(b)RecallQD10152025303540455000.10.20.30.40.50.60.70.80.9# of Attackers (out of 100 nodes)QF  False Detect(R)False Detect(ARC)(c)FalsePositiverateQFFigure3.15:CollaborativeGAMAattackwithvaryingnumberofattackersdetectionprobability.Theresultsarenotshownduetopagelimitation.Interestingly,Rawatalgorithmshowshighererrorratewithhigherdetectionprobabilityinallcases(seeFig.3.8a,3.14a).Thisisbecausetheattackerscontributetothecorrectdecisionmakingbyalteringthesensingresultsinthecaseoflowdetectionprobability.Asdetectionprobabilityincreases,alteringthesensingresulthelpsattackersincreasingerrorrate.Thetruedetectionratealsodecreaseswithhigherdetectionprobabilityforthesamereason.Wealsoexaminedtheclusters'convergencetime.Theclustersbecomestableafter8to10timestepsonaverage.However,ifthestartingdimensionofeachnodegoesbelow20,theclusterperformancedegradessignicantly.Therefore,tostartwith,wemaintainthelatest20sensingreportsofallnodesinoursimulation.Wealsosimulatedanalternativeapproachwhereinsteadofremovingattackernodesfromthedecisionmechanismcompletely,weresettheiridentityandstart53(a)withvaryingnumberofattackers0.50.60.70.80.9100.10.20.30.40.50.60.7Qgoal (35 attackers, 100 total nodes)QE  Error Rate(R)Error Rate(ARC)(b)withvaryingattackinggoalFigure3.16:AdaptivecollaborativeSubgroupattackthealgorithmagain.Theresettimerissetaftertheconvergenceoftheclusters(e.g.after10timesteps).Asaresult,theperformanceresultsdonotchangesignicantly.3.5.5AdaptiveAttack
Sofar,wehaveonlyconsiderednon-adaptiveattack.Inthissection,weconsideranadaptivevariationofbothindependentandcollaborativeattackswhereattackersadaptivelychangestheirstrategiestoreachcertaingoalintermsofattack.Intheindependentadaptiveattackingapproach,eachattackerstartswitharandomattackrate,periodicallycomparesitssuccessratewithitssetgoal,andadjustsitsattackrateaccordingly.WendthatindependentattackerscannotsignicantlyimpactthedecisionmechanismoftheBSinbothapproaches(theerrorratenevergoesabove10%).Inthecaseofadaptivecollaborativeattack,weonlyconsiderthevariationofSubGroupattack.Similartoindependentadaptiveattack,attackerssetacommongoal(Qgoal)ofachievingsuccessintermsofattack.EachsubgroupofattackersstartswithrandomattackingprobabilityPmal,periodicallycheckstheirpresentsuccessrate(QE)withthesetgoalandlinearlyincreases(or,decreases)theirattackingrates(Pmal)toreachtheirtargetsuccessrate.Intherstsimulation54set,wesetQgoal=0:8andvarythenumberofattackers.ThesimulationresultinFig.3.16ashowsthatouralgorithmperformssignicantlybetterthanRawatalgorithmintermsoferrorrate.Thenumberofattackersarevariedupto45sinceboththealgorithmshowsrandombehaviorinthepresenceof50%attackers.Inthesecondsimulation,thenumberofattackersaresetto35andnumberofsubgroupscreatedare5.ThesimulationresultsarepresentedinFig.3.16bwithvaryingattackinggoalforboththealgorithms,anditshowsthatouralgorithmoutperformsRawatalgorithmwithsignicantmargin.
3.6Summary
Inthischapter,wediscussoneofthemajorsecurityproblemsafictingCRNsandproposeareputationbasedclusteringalgorithmtodefendagainsttheseattacks.Weusereputationofnodesinadditiontotheirsensinghistorytoformclustersandthenadjustreputationbasedontheclusteroutput.Thisrecursiveapproachistestedinthepresenceofindependentandcollaborativespectrumsensingdatafalsicationattacks.Withrespecttocurrentapproaches,ouralgorithmsignicantlyreducestheerrorrateinthenaldecisionmakingprocess,thusincreasingspectrumutilization.Thefalsedetectionratebyouralgorithmisalmostnegligiblewhiletrueattackerdetectionrateperformsreasonablywell.However,theinitialnumberofclustersplaysanimportantroleinoverallperformanceofthealgorithm.55Chapter4
InterferenceAwareReliableCCRNsfor
Real-timeApplications
Withgrowingreal-timetrafcandlimitedspectrumresources,thecommunicationsystemmustadoptreliableandefcientspectrumsharingtechniquesforprovidingimprovedservicestoendusers.Relaybasedcollaborationmodelbetweentheprimaryandsecondaryuserswillplayanimportantroleinreshapingandrestructuringthespectrumallocationmechanism.Intheworkpresentedinthischapter1,weproposeanewmethodforconstructingreliablereal-timenetworksystemssuchasreal-timeindustrialautomationmeshnetworks[46]andtime-criticalsensornet-works[24].Suchareal-timenetworkrequirespacketstobedeliveredwithinadeadline.Accord-ingly,wemeasurethereliabilityofthesereal-timenetworksusingpacketreceptionrate.Whenauserinsuchnetworkstransmitsapacket,areceivermayfailtodecodethepacketintimebecauseofatemporarilyunstablelinkduetorandomnoise,fading,andshadowingorcollisionwithotherongoingtransmissions.Waitinguntilsuchalinkisusableagainisnotacceptableinreal-timesys-1Theworkpresentedinthischapterhasbeenpublishedinthreeresearcharticles:(i)ChowdhurySayeedHyder,ABMAlimalIslam,LiXiao,andEricTorng.flInterferenceawareReliableCoop-erativeCognitiveNetworkswithforReal-timeApplicationsfl,inIEEETransactionsonCognitiveCommuni-cationsandNetworks(TCCN),2(1),pp53-67,May2016.(ii)ChowdhurySayeedHyder,ABMAlimAlIslam,LiXiao,flEnhancingReliabilityofReal-timeTrafcviaCooperativeSchedulinginCognitiveRadioNetworksfl,at23rdInternationalSymposiumonQualityofService(IWQoS),pp249-254,Portland,Oregon,USA,June15-16,2015.(iii)ChowdhurySayeedHyder,LiXiao,andMaxEllison,flExploitingCooperationforDelayOptimizationinCognitiveNetworksfl,at9thInternationalConferenceonMobileAdhocandSensorSystems(MASS),pp362-370,LasVegas,Nevada,USA,October8-11,2012.56temsiflinkdowntimecanexceedpacketdeadlines.Evenifthelinkbecomesstable,traditionalretransmissionofdroppedpacketsmaynotdeliverthepacketintimeatthereceiver.Weproposetouserelaybasedcollaborationmodelaspartofthesolutionfordevelopingreli-ablereal-timenetworksystemsleveragingtheexibilityanddiversityofCRNtoovercometran-sientpackettransmissionissues.Forexample,cooperativecommunicationcanmitigatechannelfadingbyexploitingspatialdiversitywhichleadstonewtransmissionpaths[52,57,136].BasedonthetransmissionmodelinCRN,secondaryusersaregrantedchannelaccessbyprimaryusersinreturnfortheirserviceinrelayingprimarypackets.
4.1RelaybasedCollaborationModel
Relaybasedcollaborationmodelisalsoreferredtoascooperativecognitiveradionetwork.TodesignatransmissionmodelinCCRN,weneedtodenethreecomponents.Therstcomponentofthemodelistoselectthecooperativetransmissionstrategy(i.e.howtocooperate).WeusethetwophasepowerdivisionapproachproposedinHanetal.[47]toschedulecooperativetransmissions(explainedinSection4.2.4).Thesecondcomponentofthedesignistodeterminetheconditionforcooperation(i.e.whentocooperate).Thenalcomponentofthedesignistoselectmatchingcooperationpairsandscheduletheirtransmissionsconsideringmutualinterferencebetweenusers.Throughoutthischapter,wediscussthechallengeswefaceindevelopingeachcomponentofthecooperativetransmissionmodel,andhowweaddresstheseissuesintoourproposedmodelfocusingonuniquefeaturesofreal-timetrafc.574.1.1LimitationsofPriorWork
WhiletherehasbeenextensiveresearchinCCRNwherethegoalistooptimizespecicnetworktraitssuchasmaximizingthroughput[70]orminimizingdelay[53]orexploringthetradeoffbe-tweenthem[10],thisresearchisnotapplicabletoreal-timesystemsbecauseofthefollowingreasons.First,existingresearchdoesnotincludepacketdeadlinesintothecooperationmodelandthusignorestheeffectofeachtransmissiondecisiononthesuccessprobabilityofremainingpacketsinthequeue,andfuturepacketsthathavenotyetarrived.Second,thisresearchdoesnotdiscusstheoverheadassociatedwithcooperativetransmission.Forexample,beforeacooperativetransmissiontakesplace,usersneedtoexchangecooperationinformation(e.g.transmissiontime)andselectcooperationpairswhichintroducessignicantoverhead[124].Ignoringthisoverheadmayincreasepacketlossrate.Finally,mostoftheexistingresearchfocusesonasinglecooperat-ingpairofprimaryandsecondaryuserswhichmaynotextendtoamulti-userenvironment.Forexample,allowingasecondaryusertotransmitaspartofcooperationagreementmaychangetheinterferencerelationshipbetweenexistingusers,andifnotproperlyadministered,itmayinterferewithotherongoingtransmissionscausingpacketloss.Furthermore,mostexistingworkassumesinnitequeueswhereasrealsystemshaveonlynitequeues.
4.1.2ProposedApproach
Inthischapter,weproposeanewmethodforconstructingreliablereal-timenetworksystemsbaseduponCCRNthatovercomesthelimitationsofpriorwork.Ourapproachistoformulatethemulti-userreal-timecommunicationsystemwithnitequeuesasaMarkovdecisionprocess(MDP)wherewemodeltheimpactoftransmissiondeadlinesandcooperationoverheadintherewardfunctionsoftheMDPandcontrolmutualinterferencebyregulatingtransmissionpower58ofsecondaryusers.Themodeldecidesbetweendirectandrelaybasedcooperativetransmissionandchoosesthetransmissionpowerofsecondaryusersconsideringthetradeoffbetweenthesuc-cessfulreceptionprobabilityofthecurrentpacketandtheimpactofcooperationoverheadonlaterpackets.Forexample,whilecooperativetransmissionmayincreasethesuccessprobabilityofthecurrentpacket,theassociatedoverheadmayreducethesuccessofremainingpacketsinthequeue.Thus,theMDPrewardfunctionsrepresentthedeadlineconstraintsandhelpausermakeeffectivetransmissiondecisions.WefurtherstudyandanalyzetheMDPofasinglepairofprimaryandsecondaryuserstounderstandthedynamicsofcooperation.Basedonthisanalysis,wedevelopadistributedcooper-ationalgorithmforuseinpracticalsettingstohelpusersmakecooperationdecisionsandscheduletheirtransmissions.Weevaluatetheperformanceoftheproposedalgorithmincomparisonwithanexistingcooperationalgorithm[117].
4.1.3KeyDesignChallenges
Tobuildasuccessfulsystem,wemustaddressthreedesignchallenges.(i)cooperationoverheadvs.transmissiondeadlines:Theprocessofrelayselectionandchannelestimationrequiresexchangeofcontrolinformationamonguserswhichcausessignicantoverheadandimpactstheperformanceofcooperativerelaying[124].Thisoverheadissuebecomesevenmorecriticalinthecaseofreal-timesystemsbecauseoftransmissiondead-lines.Therefore,weneedtoquantifytheoverheadofrelayselectionandincorporateitintotransmissiondecisions.Forexample,acooperativetransmissionmayincreasetheproba-bilityofsuccessfuldeliveryofthecurrentpacketatthecostofdecreasingprobabilityofsuccessfuldeliveryofpacketsinthequeue.So,insteadofdecidingtotransmitsolelybased59(a)nointerference(b)interferenceFigure4.1:Impactofsecondaryinterferenceincooperativecommunicationonthecurrentpacket,wemustalsoconsiderqueuedpackets.WedenetherewardfunctionsoftheMDPwhereeachtransmissiondecisionisevaluatedconsideringitsimpactonboththecurrentpacketandqueuedpackets.(ii)cooperationduration:Anotherdesignissueistodeterminetheoptimumcooperationdura-tionforapairofusers.Cooperationdurationreferstotheamountoftimetwousersengageincooperativetransmissionaccordingtotheiragreement.Whereasfrequentcooperationnegotiationmaygivebetterestimatesofchannelsandmoreup-to-datecooperationoppor-tunities,italsoincreasesoverhead.Ontheotherhand,alongercooperationperiodreducestheoverheadbutmayextendcooperativetransmissionlongerthanneeded.Weaddressthisissuebyintroducingalowoverheadprotocolwherethecooperatingusersassesstheirstatusandextendthecooperationperiodifappropriate.(iii)secondaryinterference:Thethirddesignissueistocontroltheinterferencecausedbysec-ondaryusers'transmissions.Forexample,considerthesimplescenariodepictedinFig.4.1wheretwopairsofprimarytransmitterandreceiver(A,A0)and(B,B0)arecommunicat-ingoverchannel1outoftheinterferencerangeofeachother.IftheprimarytransmitterAcooperateswithasecondaryuser(SU)andrelaysitspacketthroughSU,SU'stransmis-60sionoverchannel1mayinterferewithB0.Asuccessfulmodelmustconsidertheimpactofsecondaryinterferencewhileschedulingcooperativetransmission.Weregulatethetrans-missionpowerofsecondaryusersbasedontheinterferencerelationshipbetweenusersandpresentahandshakingprotocoltoensureinterferencefreedatatransmission.4.1.4OurContributions
Tosummarize,wemakethefollowingkeycontributionsintheworkinthischapter.WeidentifythechallengesassociatedwithdesigningarelaybasedcollaborationmodelinCCRNforreal-timesystems.WeformulatethetransmissionmodelasanMDP.Weconverttheessenceoftransmissiondeadlinesandcooperationoverheadintorewardfunctions.WedenetheactionsetsofMDPbyimposingpowerconstraintsonsecondarytransmissiontocontrolmutualinterferencebetweenusersinthenetwork.Wepresentanextensiveanalysisofthecollaborationmodelofasinglepairofprimaryandsecondaryusersandcompareitsperformancewithanexistingmodel[117].Theanalysisshowsthatthelattermodelleadstopoorreceptionrateduetoignoringcooperationoverheadandtransmissiondeadlinesintheirformulationwhileourproposedmodelprovideshigherpacketreceptionrateandlowwaitingtime.Theanalysisalsorevealstheimpactofvariousnetworkparametersonsystemperformance.Weproposeadistributedcooperationalgorithmwhereprimaryusersnegotiatewithsec-ondaryusersaboutcooperationdurationandtransmissionpower.Ausermakestransmissiondecisionbasedoncooperationgainthatiscalculatedintermsoftransmissionopportunity,transmissionpower,andqueuesize.Wealsopresentahandshakingprotocolforcooperatinguserstoscheduledatatransmissionavoidingmutualinterference.61Finally,weconsiderdifferentprimaryreal-timetrafcmodelstoevaluatetheperformanceoftheproposedcooperationmodelincomparisontoanexistingcooperativetransmissionmodel[117].Thesimulationresultsshowthattheproposedrelaybasedcollaborationmodelachieveshigherpacketreceptionratethanthepriormodelunderdifferentnetworksettings.Wealsoprovideanoverheadanalysisintermsoffrequencyofcooperationnegotiationandcostbenetanalysisintermsofenergyconsumptioninrelaying.4.2SystemModelandProblemFormulation
Inthissection,wedescribenetworksetup,explainthepowerdivisioncooperativetransmissionapproach,andformulatetherelaybasedcollaborationmodel.4.2.1Preliminaries
WeconsideraCRNconsistingofasetofmprimarytransmittersP=fp1;:::;pmg,theircorrespondingmprimaryreceiversP0=fp0
1:::p0
mg,andasetofnsecondarytransmittersS=fs1;:::;sng,andtheircorrespondingnsecondaryreceiversS0=fs0
1:::s0
ng.Each(primaryorsecondary)userhasasingletransceiverradioandcannottransmitandreceivesimultaneously.Sincethecooperationdecisionistakenamongthetransmittersonly,weuseprimarytransmitterandprimaryuser,andsecondarytransmitterandsecondaryuserinterchangeably.Weassumethattheprimarynetworkhasanexclusivelicenseofaxedbandwidthspectrum.Eachprimaryuserisassignedafractionofthisbandwidthwhichisreferredtoasa`channel'.Channelsmaybeoverlapping(similarto802.11)orcompletelydisjointbasedontheallocationalgorithm.Sinceourfocusistoanalyzethecooperationmodel,wewillnotdiscussthechannelallocationalgorithm(pleasesee[95]foralistofchannelselectionalgorithms).Secondarytrans-62mitters,ontheotherhand,dependontheprimaryusersfortheirtransmissionopportunitytotheirrespectivesecondarydestinations.Weassumethataprimaryusercontendsforchannelswithotherprimaryusersinthesamenet-work.Letusdenotethataprimaryuserisassignedachannelbythecontrollerwithprobabilityq.Inotherwords,aprimaryusercannottransmitorengageinanytransmissionactivities(cooperativeornon-cooperative)withprobability1qindependentofitsqueuestatus.Finally,weassumeaprimaryusermayeitherchoosetotransmitdirectlyoragreetocooperativetransmission.EachprimaryandsecondarytransmitterhasanitepriorityqueueQ()oflengthLtostorepackets.Eachpackethasadeadlinet;thepacketmustbedeliveredwithinttimeunitsfromthetimeofitsgeneration.Ifthequeueisfull,thenextpacketgeneratedisdropped.Otherwise,thepacketisaddedattheendofthequeue.Usersinthesystemdonotretransmitpackets.Onceapacketistransmitted,itisremovedfromthequeueevenifisnotsuccessfullyreceivedatthedestination.
4.2.2PUTrafcModel
VarioustrafcmodelsarestudiedtoaccuratelyrepresentPUactivityincognitiveradionetworks[19][94].Markovmodulatedprocessisthemostcommonmodelamongthem.InSec.4.3,weassumethattheprimarytrafcfollowsaBernoullidistributiontokeepouranalysissimple.How-ever,thisanalysiscanbeextendedtoaMarkovmodulatedprocessasmentionedin[117].LaterinSec.4.5,weuseathreestateMarkovchaintorepresentthePUtrafcmodel[49]andevaluatetheproposedcooperationmodelwithsimulation.WealsoconsiderPoissondistributiontorepresentthePUtrafcmodel[134][80]todemonstratetheperformanceoftheproposedcooperationmodelwithadifferenttrafcmodel.634.2.3ChannelModel
WeconsiderthatchannelsexperienceRayleighatfadingwhichimpliesthatthechannelgainre-mainsconstantwithinatimeslotwhereitchangesfromoneslottoanother[104],[33].ChannelgainhiisexpressedasaGaussianrandomvariablewithmean0andvariancediwherediisthenormalizeddistancebetweensenderandreceiverandisthepathlossexponent.Channelexpe-riencesadditivewhiteGaussiannoiseatthereceiverwithmean0andvariance2.SincechannelgainhifollowsaRayleighdistribution,itcanbeshownthati=jhij2followsanexponentialdistributionwithmeand
ii.e.i˘exp(d
i)[47].4.2.4CooperativeTransmission
Forcooperativetransmission,wepreferthepowerdivisionapproachtothetimedivisionap-proach[34,98]becausetheformerapproachprovidesexibilitytocontrolthesecondarytrans-missionpowerandtheprimaryuserdoesnotincuradditionaloverheadforsecondarytransmis-sion.Inthismodel,aprimaryusermayestablisharelaytransmissionpathviaasecondaryuserbyadoptingthepowerdivisiontransmissionapproachproposedin[47]wherecooperativetrans-missionisscheduledintwophases.Intherstphase,aprimaryusertransmitsitspackettoitsdestinationwhichisalsoreceivedbytheparticipatingsecondarytransmitter.Inthesecondphase,thecooperatingsecondarytransmitterregeneratestheprimarysignalandsuperimposesitwithitsowntransmission.Thetransmissionpowerofthesecondarytransmitterisproportionallyallocatedtotheprimarysignalandsecondarysignal,andthecombinedsignalisthentransmittedbythesecondarytransmitter.Theprimaryreceiverdecodesthepacketfromthesetwosignalsreceivedfromdirectandrelayedtransmission.Thejointtransmissiondecisionbetweenaprimarytransmitterpi2Pandasecondarytrans-64mittersj2Scanthusbecharacterizedwith(01),thetransmissionpowerdistributionratio.Primaryuserpirsttransmitsthepackettoitsdestination,anditisalsoreceivedbythesecondaryusersj.ThesecondaryusersjassignstransmissionpowerEtotheprimarysignaland(1)Etothesecondarysignalandtransmitsthecombinedsignal.Additionally,theuserpimayoptfordirecttransmissionwithoutanycooperation,andtheusersjmaytransmitonlywhenthequeueofthepiisempty.Thistransmissiondecisionisrepresentedwith=;.Wemakethefollowingassumptionsregardingthecooperationmodel.First,usersexchangecooperationinformationoveracommoncontrolchannelandcannottransmitwhilenegotiatingcooperationterms.Second,aprimaryusermayparticipateinacooperativetransmissionwithatmostonesecondaryuseratanytime.Theremaybemultiplecooperatingpairsbasedonthenumberofusersandavailabilityofresources(channels).Third,aprimary(orsecondary)useralreadyinvolvedinacooperativetransmissiondoesnotinitiateoracceptanothercooperationrequestuntilthepresentcooperationagreementends(i.e.ongoingtransmissionphasenishes).Forth,allpacketshavethesamelength,anddecodingandregeneratingaprimarypacketatthesecondaryusertakesconstanttime.Finally,theprimarypacketreceivedbyasecondaryuserisimmediatelyrelayedtoitsdestination;therelayedpacketdoesnotexperiencesignicantwaitingtimeinthequeueofthesecondaryuser.
4.2.5PacketLoss
Packetlossmayoccurforthefollowingreasons.First,ifaqueueisfull,anincomingpackettothatqueueisdropped.Second,ifthewaitingtimeofapacketexceedsitsdeadline,thepacketisremovedfromthequeue.Finally,ifareceiverfailstodecodeapacketbyitsdeadlineduetointerference,thepacketislostandiscountedasanunsuccessfultransmission.Ourgoalistodevelopacooperativetransmissionmodelthatreducespacketlosses.654.2.6MDPFormulation
WemodelthejointtransmissiondecisionoftheprimaryandsecondaryusersasaMarkovDecisionProcess(MDP).InanMDP,eachstateisassociatedwithasetofactionsandcorrespondingrewards.Thus,thecooperationmodelisrepresentedwithanMDP(,A,P:(;),U:(;),)whereisanitesetofstates.Eachstatedenotesthepresentnumberofpacketswaitinginthequeueofalltheusersinthenetwork.Thusastate˙2canberepresentedas˙=(ip
1;:::ip
m;js1;:::jsn).Hereip
mandjsndenotethenumberofpacketswaitinginthequeueofaprimaryuserpmandasecondaryusersn.Thenumberofdifferentstatesofthesystemisjj=(L+1)m+nwhereLdenotesthequeuesize.Aisasetofallpossibleactionswhereeachactionrepresentsajointtransmissiondecisionofaprimaryandasecondaryuser.Weexpressanactionas(pi;sj)whichdenotesthedis-tributionofpowerallocationbetweenthesignalsoftheprimaryuser(pi)andthesecondaryuser(sj).Sincecanbeanyvaluebetween0and1,thenumberofpossibleactionsisthe-oreticallyinnite.Weuse=;toexpressthedirecttransmissionapproach.TheactionsetcanthusberepresentedasA=f(pi;sj)=;_(pi;sj)2[0;1];pi2P;sj2Sg.Wedroptheindexin(pi;sj)whenwediscussontransmissionpoweringeneral.Attimet,asubsetofactionsa(t)ˆAischosenasthetransmissiondecisionsofprimaryandsecondaryusersinthenetworksuchthatnotwoactionsofthesetinvolvethesameprimaryuserorthesamesecondaryuserorboth.Pa(t)(˙;˙0)=Pr(˙t+1=˙0j˙t=˙;a(t)=f(;)gˆA)denotesthetransitionprobabil-ityfromstate˙tostate˙0iftheactionseta(t)ˆAistakenattimet.66Figure4.2:MatchingpairandactionselectionUa(t)(˙;˙0)denotestherewardoftransferringfromstate˙to˙0duetotheactionseta(t)attimet.Therewardfunctioniscalculatedintermsofimmediaterewarddiscountedbythefutureopportunitycost.Therewardfunctionalsoincludestheimpactofthechangeinthestatusofthequeue.2[0;1]isadiscountfactorthatbalancestheimportanceofimmediaterewardsversuslongtermrewards.Ourgoalistodeterminetheoptimumpolicy'thatmaximizestheexpectedrewardofthecoop-eratingusersoveralongperiodT.Assumingemptyqueuesofallusersastheinitialsystemstate˙0,weexpresstheobjectivefunctionasfollowsmax'limT!11TE'0
@TXt=0tUa(t)(˙;˙0)j˙0=(0;:::;0)1
A:(4.1)wherea(t)representstheactionstakeninstate˙attimetaccordingtothepolicy'andE'()istheexpectationtakenunderpolicy'.Theobjectivefunctioninvestigatestheimpactofdifferentactionsa2Aonallpairsofprimaryandsecondaryusers(PS)todeterminetheoptimalpolicythatrecommendsoptimumactionatdifferentsystemstate(seeFig.4.2).Ifthepairsaremutuallyindependentintermsofthecho-senactionandtheirimpacts,wecanseparatelycalculatetherewardcomponentforallsuchpair67(pi;sj)PS.WeusetheBellmanequationordynamicprogrammingtosolvetheproblemforapairofprimaryandsecondaryuseranddetermineoptimumactionintheirdifferentstates.Werepeatthesameproceduretocalculatetherewardcomponentforallpossiblepairsintheirdifferentstatesfordifferentactions.Finally,wecanuseweightedbipartitematchingtodeterminetheopti-mumactionandoptimummatchingpairsfromthesetatanygiventimetthatmaximizesreward.Tobetterunderstandtheprocedure,weanalyzetheMDPcooperationmodelofasinglepairofprimaryandsecondaryusersinSec.4.3.However,inpractice,anactionofapairofusersaffectstherewardofanotherpairduetomutualinterferenceandtherewarddependencybetweenpairsmakeitintractabletondadeterministicsolutionattimet.Wethereforedevelopadistributedmulti-usercooperationalgorithm(Sec.4.4)addressingthemutualinterferencebetweenuserswithsimultaneoustransmission.
4.3AnalysisofaCooperativeTransmissionModel
Tounderstandthedynamicsofsystemparametersonourmultiusercooperationmodel,wersttakeacloserlookatthecooperationmodelforthecaseofasinglepairofprimaryandsecondaryusers.Thesinglepairanalysiswillhelpusidentifytheimpactofdifferentsystemparameters;theseresultswillbeusedtodevelopthedistributedalgorithminSec.4.4.Wedepictthenetworkconsistingofaprimarytransmitterp,aprimarydestinationp0,asec-ondarytransmitters,andasecondarydestinations0inFig.4.3.Wedenotethechannelgainbetweenpandp0,pands,pands0,sandp0,andsands0ash1,h2,h3,h4,andh5respectively.BothusershaveanitequeueoflengthL.WedenotethetransmissionpowerofthecooperatingprimaryuserpandsecondaryusersasEpandEs,respectively.Primaryandsecondarypackets'arrivalfollowaBernoullidistributionwithmeanpandsrespectively.Thesamedistribution68Figure4.3:Cooperationbetweenaprimaryandasecondaryuserisusedtomodelprimaryuseractivityin[12][94].WecanextendthisanalysisfromaBernoullidistributiontoaMarkovmodulatedprocess[117].ThistwouserMDPmodelhasatotal(L+1)2states.Eachstate˙2isrepresentedwith˙=(˙p;˙s)where˙pand˙sdenotethenumberofpacketsinprimaryandsecondaryqueuerespectively,and0˙p;˙sL.Weassumethatsystemparametersremainunchangedwhileausercompletesanaction;changesoccuronlyatstatetransitions.Atthebeginningofeachstate,ausertakesatransmissiondecisionfortherstpacketofthequeue.Auser'sdefaulttransmissiondecisioninthemodelistotakethesingleactionavailableinanon-cooperativesystemi.e.directtransmissionwhereptransmitsdirectlytop0andstransmitstos0onlywhentheprimaryqueueisempty(˙p=0).Thesuccessfuldeliveryoftherstpacketandwaitingtimeofthequeuedpacketsdependsonthedirectdatarate,trafcrate,andchannelavail-ability.Whentheusersinthenetworkintendtoexplorecooperativetransmissionopportunities,theyneedtogothroughanegotiationperiod.Whilethiscooperativetransmissionmayimprovethesuccessfuldeliveryoftherstpacket,thenegotiationperiodcontributestoadditionalwaitingtimetoqueuedpacketsthatmayaffecttheirsuccessfuldeliveryatlatertime.4.3.1ActionSet
Thetransmissiondecisionsarerepresentedasactions(p;s)2AinMDP.Sinceweareconsid-eringasinglepairofprimaryandsecondaryusers,tosimplifynotation,wereferto(p;s)as.69Insummary,theactionsareasfollows=;:Thisrepresentsthedefaultnon-cooperativetransmissionapproachwhereptransmitsdirectlytop0andstransmitsonlywhenthequeueofpisempty.Usersexecutethisactionwithnoadditionalcostofcooperationnegotiation.=0:Thisrepresentsthecooperativetransmissiondecisionwherepdefersitstransmissionandletsstransmitwithfulltransmissionpower.Thisactionisprecededbycooperationnegotiation.=1:Thisrepresentsthecooperativetransmissiondecisionwheresrelaystheprimarypacketwithitsfulltransmissionpoweranddoesnotcombines'sowntransmission.Thisactionisalsoprecededbycooperationnegotiation.0<<1:ThisrepresentsthecasewheresallocatesEspowertotheprimarysignaland(1)Espowertoitsownsignal,combinesbothsignals,andthentransmits.Thisactionisalsoprecededbycooperationnegotiation.Atanytimet,pandstakeajointtransmissiondecisiona(t)=,whichmovesthesystemfromastate˙toastate˙0withaprobabilityofPa(t)(˙;˙0)andachievesrewardUa(t)(˙;˙0).Notethat,theoreticallythecooperatinguserscanselectanyvaluebetween0and1fortransmissionpower.However,basedontherelativedistancebetweentransmittersandreceivers,smallchangesintransmissionpowermaynotaffectthesignalstrengthsignicantlyandthusitcanbenarroweddowntoanitenumberofvalues.Foranalysis,weuse=0:65torepresenttheaveragepowerdivisionwithextremevaluesof=0and1.70No.nextstatetransitionprobabilityconditions(1)(i-1,j-1)q(1p)(1s)1i;jL(2)(i-1,j)q(1p)s1i;jL(3)(i,j-1)qp(1s)1i;jL(4)(i+1,j+1)(1q)ps0i;jL1(5)(L,1)(1q)s+qpsi=L;j=0(6)(0,j+1)(1p)si=0Table4.1:Statetransitionprobabilities4.3.2TransitionProbabilityMatrix
Thetransitionprobabilitymatrixrepresentsthetransitionprobabilitiesfromonestatetoanotherstatedependingontheactiontakenbytheusers.Duetopagerestrictionsandtoimprovereadabil-ity,weavoidlistingtheentirematrix.Instead,wepresentalistoftransitionprobabilitiesatstate˙(˙p;˙s)whenanaction(0<<1)istakenfollowedbyashortdescription(seeTable4.1)whereqrepresentsthechannelaccessprobabilityofuserp.Thefollowingstatetransitionoccurs(i)whenbothpandsdecidetotransmitcooperativelyandnonewpacketsarriveatthequeueatthattime.(ii)whenbothpandscooperativelytransmitandonlyanewsecondarypacketarrives.(iii)whenbothpandscooperativelytransmitandonlyanewprimarypacketarrives.(iv)whenpdoesnotgetchannelaccessandbothprimaryandsecondarypacketsarrive.(v)whentheprimaryqueueisfullandthesecondaryqueueisemptyandonlyanewsecondarypacketarrives.(vi)whentheprimaryqueueisemptyandonlyanewsecondarypacketarrives.Similarly,wecanliststatetransitionprobabilitiesforallothercases.714.3.3RewardFunction
TherewardfunctionUa(t)(˙;˙0)denotesthetotalrewardachievedbythecooperatingprimaryandsecondaryuserforactiona(t)whereweweighttherelativeimportanceofthetwouserswithparameter.Ifsuccessfuldeliveryofprimarypacketsismore(less)preferredtothatofsecondarypacketsinthesystem,thevalueofissethigher(smaller)than0:5.Laterinsimulation,weset=0:5consideringbothrewardcomponentswithequalimportance.Weomittheindex(`p'or`s')fromtherewardcomponentwhenitappliesforbothusers.Ua(t)(˙;˙0)=Upa(t)(˙;˙0)+(1)Usa(t)(˙;˙0)(4.2)ThekeychallengeinmodelingtheMDPistoselectanappropriaterewardfunctionthatac-curatelymeasurestheimpactofthechosenactiononthesystemperformanceintermsofpacketloss.Asmentionedearlier,whileacooperativetransmissiondecisionatastatemayincreasetheprobabilityofsuccessfuldeliveryoftherstpacketofthequeueitalsoaddswaitingtimetolaterpackets.Thismaydecreasethesuccessfuldeliveryoflaterpackets.Likewise,adecisiontode-ferpackettransmissionmayincreasethedroppingprobabilityofanincomingpacket.Therefore,givenapairofprimaryandsecondaryuserandthesystemstate˙,therewardfunctionUa(t)(˙;˙0)shouldanswerthefollowingtwoquestionsHowdoestheactiona(t)atstate˙change(increase/decrease)thedropprobabilityofincomingpacketsduetoqueueoverow?Howdoestheactiona(t)atstate˙change(increase/decrease)thesuccessprobabilityofthepacketswaitinginthequeue?Toanswerthesequestions,weconsideranexampleofapairofaprimaryandasecondaryuser72withqueuelength10.Weconsiderthatthesuccessprobabilityofaprimarypacketwith=;,and=1is0:65,and0:9respectively.Assumethatifthetransmissiondecisionreducesthenumberofwaitingpacketsinthequeueby1,thedropprobabilityofanincomingpacketisreducedby0:2.Anycooperativeactionaddswaitingtimeandreducesthesuccessprobabilityofaprimarypacketwithdirecttransmissionby0:05.Weevaluatetheimpactofdirectandcooperativeactionfromtheperspectiveofaprimaryuserwhenthesystemmovesfromastatewith3waitingpacketstoastatewith2waitingpackets.Thetotalimpactofdirecttransmissioncanthusbequantiedassummationof0:2(changeindroppingprobability)and0:65(successprobabilityoftherstpacket).Letusconsideracooperativeactionwith=1.Inthiscase,theimpactofthecooperativeactionis0:2fromthechangeindroppingprobabilityand0:9fromthesuccessprobabilityoftherstpacket.Furthermore,theremaining2packetsinthequeueexperienceadditionalwaitingtimewhichreducestheprobabilityofsuccessfuldeliveryby0:052=0:1.So,thetotalimpactis0:2+0:90:1=1:0.Thenetrewardofusingaction=1over=;is1:00:85=0:15.Basedontheaboveexample,wedenetherewardfunctionUa(t)(˙;˙0)foreachactionthatincludesitsimpacton1)thepacketattheheadofthequeue,2)theremainingpacketsinthequeue,and3)incomingpacketsnotyetinthequeue.BoththerewardfunctionsUpa(t)(˙;˙0)andUsa(t)(˙;˙0)havethreecomponents(seeEqn.4.3)thataremeasuredincomparisonwithdirecttransmission.Therstcomponentmeasuresthechangeinthedropprobabilityofanincomingpacketbecauseofqueueoverowifactiona(t)isappliedinsteadofdirecttransmission.Thiscomponentdependsonboththechosenactiona(t),currentstate˙,andthenextstate˙0.WedenotethisrewardcomponentasDa(t)(˙;˙0)D;(˙;˙0).Thesecondcomponentmeasurestheprobabilityofsuccessfuldeliveryofthepacketatthe73headofthequeueifactiona(t)isappliedinsteadofdirecttransmission.Thesecondcompo-nentdependsonlyontheactiona(t),andcurrentstate˙.WedenotethesecondcomponentasVa(t)(˙)V;(˙).Thethirdcomponentmeasuresthenetchangeinprobabilityofsuccessfuldeliveryofthequeuedpacketsifactiona(t)isappliedatpresentstate˙insteadofdirecttransmission.WedenotethethirdcomponentasWa(t)(˙)W;(˙).Theusersinthecurrentstatedonotknowwhichactions(exceptthedefaultaction)willbeavailableatfuturestates.Therefore,theimpactofcurrentactiononlaterpacketsisevaluatedonthebasisofdirect(default)transmissiondecision.Forasecondaryuser,thesuccessprobabilityofdefaulttransmissiondecisiondoesnotchangeaslongastheprimaryqueueisnotempty.Therefore,thethirdcomponentdoesnotcontributetotherewardfunctionofasecondaryusers.Insummary,weexpresstherewardofanactionatanygivenstateasthedifferencebetweentheimpactofthatactionanddefaultaction.Upa(t)(˙;˙0)=Dpa(t)(˙;˙0)Dp;(˙;˙0)+Vpa(t)(˙)Vp;(˙)+Wpa(t)(˙)Wp;(˙)(4.3)Usa(t)(˙;˙0)=Dsa(t)(˙;˙0)Ds;(˙;˙0)+Vsa(t)(˙)Vs;(˙)(4.4)4.3.3.1CalculationofDa(t)(˙;˙0)TherstcomponentDa(t)(˙;˙0)denotesthechangeinpacketlossprobabilityduetoqueueover-owbecauseoftheactiona(t)andtransitionfromstate˙tostate˙0.Atransmissiondecisionopensupaslotinthequeueforanewpacket.Therefore,eachtransmissiondecisionreducesthefuturepacket'sdroppingprobabilitybeforeitentersthequeue.However,thisreductioninpacketlossprobabilityisnotsameatallstates.74Thepacketlossprobabilityatstate˙isexpressedasPr(Q(t0)=Lj˙)whichdenotestheprobabilityofaqueuebecomingfullattimet0givenitscurrentstate˙attimet.Assumingservicerateremainssame,thisprobabilityisapproximatedbasedonthepacketarrivalrateasfollowsDpa(t)(˙;˙0)=(p)L˙p(p)L˙0p(4.5)Dsa(t)(˙;˙0)=(s)L˙s(s)L˙0s:(4.6)Here,˙pand˙sdenotethenumberofpacketswaitinginthequeueoftheprimaryandsecondaryuseratstate˙.Asthenumberofpacketsincreasesinthequeue,theprobabilitythatthenextpacketwillbedroppedalsoincreases.Accordingtothisfunction,ifanactionandchangeofstateleadtofewerwaitingpackets,theeventisrewarded.Ontheotherhand,asthequeuebecomesfull,thepenaltyincreases.Forexample,consideraprimaryqueueoflength10andmeantrafcarrivalrateof0:7.Wecalculatetherewardcomponentfortwocases-(1)whentheactionleadstoastatewithonelesspacketswaitinginthequeue,(2)whentheactionleadstoastatewithonemorepacketswaitinginthequeue.Fig.4.4showsthetwocomponentsforprimaryuseronly.Theresultshowsthatreducingthenumberofwaitingpacketsismorehighlyrewardedasthequeuegetsfuller.Similarly,increasingthenumberofwaitingpacketsismorehighlypenalizedwhenthequeueisfuller.
4.3.3.2CalculationofVa(t)(˙)Va(t)(˙)denotestheprobabilityofsuccessfuldeliveryofthepacketattheheadofthequeueusingtheselectedtransmissiondecisiona(t)atstate˙.Consideringtransmissiondeadlineandpacketlengthastandlen,wecalculatetheprobabilityofsuccessfuldeliveryofanyarbitrarypacketintermsofthetransmissionrateRofferedbya(t)andwaitingtime!.So,Pr(!+lenRtj!)7524681000.10.20.30.4number of current packetsDa(t)p(sp,sp - 1)  reward component(a)changetoastatewithonelesswaitingpacket02468-0.4-0.3-0.2-0.10number of current packetsDa(t)p(sp,sp + 1)  reward component(b)changetoastatewithonemorewaiting
packetFigure4.4:Rewardcomponent=Pr(Rlent!j!)=Pr(Rg(!)j!)=(R;g(w)).Here,g(!)=lent!isafunctionofwaitingtimethatalsodenotestheminimumdataraterequiredtodeliverapacketsuccessfully;g(!)dependsonthepresentstateoftheuserandandtheselectedtransmissionapproach.NotethatthetransmissionrateRfollowsadistributioninducedbytherandomchannelgainandthetransmissionapproach.Basedontheaboveequation,weexpresswaitingtime,transmissionrate,andpacketreceptionprobabilityintermsofactiona(t)andthepresentsystemstate˙.Wedenotetheaveragewaitingtimeoftherstpacketofprimaryuserpandsecondaryusersatstate˙as!(˙p)and!(˙s)re-spectively.WealsodenotetransmissionrateofprimaryuserpandsecondaryuserswithRpa(t)andRsa(t)andpacketreceptionprobabilitywith(Rpa(t);g(!(˙p))and(Rsa(t);g(!(˙s))respectively.Vpa(t)(˙)=(Rpa(t);g(!(˙p))=PrRpa(t)g(!(˙p)jw=!(˙p))(4.7)Vsa(t)(˙)=(Rsa(t);g(!(˙s))=PrRsa(t)g(!(˙s)jw=!(˙s))(4.8)764.3.3.3CalculationofWa(t)(˙)Thethirdrewardcomponentisapplicabletoonlytheprimaryuser.Weobservethatacooperativetransmissiondecisionofaprimaryusermayincreasethesuccessfulreceptionprobabilityoftherstpacketatthecostofincreasingwaitingtimeoflaterpackets.Thelongerthecooperationnegotiationperiod,thehighertheimpactonremainingpacketswillbe.Therefore,eachcooperationdecisionmustconsiderhowitaffectsthechanceofsuccessfuldeliveryoflaterpacketsincasethereisnocooperationinthenextstateandpacketsaretransmitteddirectlytothedestination.So,thisthirdcomponentincludesthesuccessprobabilityofremainingpacketswithcooperationoverhead.WecanexpressthenetrewardasfollowsWpa(t)(˙)=˙pXi=1hRp;;g(!(i)+s)i:(4.9)Here,sdenotestheadditionalwaitingtimeimposedonlaterpacketsbecauseoftheactiontakenatpresentstate.Next,wecalculateRpand(Rp;g(!(˙p))fordifferentvaluesofa(t)=.Specically,therearefourcasesweneedtoconsider.=;:TheprimaryusersendsthepacketattherateR1andthesecondaryuseropportunis-ticallysendspacketatrateR5thatarecalculatedasfollows:Rp;=R1=log1+Ep12;Rs;=R5=log1+Es52Forthedirecttransmission,thesuccessfulpacketreceptionprobabilityatrespectivedestina-77tionscanbeexpressedas(Rp;;g(!(˙p)))=expd
12Ep2g(!(˙p))1(4.10)(Rs;;g(!(˙s)))=expd
52Es2g(!(˙s))1:(4.11)=0:Inthiscase,pletsstransmits'spacketwhichimpliesthatRp0=0.ThensappliesitsfulltransmissionpowertosenditspacketatrateR5i.e.Rs0=R5.However,allowingstheexclusivetransmissionopportunityincreaseswaitingtimeofp'spacketsinadditiontothenegotiationtimes.Rp0=0;Rs0=R5=log1+Es52Thesuccessfulpacketreceptionprobabilityofaprimaryandasecondaryuseratstate˙canbeexpressedas(Rp0;g(!(˙p)))=0(4.12)(Rs0;g(!(˙s)))=expd
52Es2g(!(˙s))1:(4.13)=1:Theprimaryuserrelaysthroughsecondaryuserandthesecondaryuserappliesitsfulltransmissionpowertorelaytheprimarysignaltoitsdestination.So,theeffectiveprimarytransmissionrateisminimumofthetransmissionratefromprimarysourcetosecondarysource(p!s)andfromsecondarysourcetoprimarydestination(s!p0).Rp1=12minlog1+Ep22;log1+Ep1+Es4278Wecalculate(Rp1;g(!(˙p)))asfollowsRp1;g(!(˙p))=8
>
>
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<
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>
:expd
22Ep22g(!(˙p)1;if24+1d
1d
1d
4exp(yd
4)d
4d
1d
4exp(yd
1);otherwise:(4.14)Here,y=2Ep(22g(!(˙p)1).0<<1:TheprimaryuserrelaysthroughsecondaryuserandthesecondaryuserappliesEstorelaytheprimarysignaltoitsdestinationandapplies(1)Estotransmititsownsignal.So,theeffectiveprimarytransmissionrateisminimumofthetransmissionratefromprimarysourcetosecondarysource(p!s)andfromsecondarysourcetoprimarydestination(s!p0).Rp=12minlog1+Ep22;log1+Ep12+Es4(1)Es4+2Wecalculate0=(21)(1+Es42)4+(21)Es42whichdecidestheeffectivetransmissionrateoftheprimaryuser.Rp;g(!(˙p))=8
>
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<
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:expd
22Ep22g(!(˙p))1if0expd
12Ep22g(!(˙p))1otherwise(4.15)Thesuccessfulpacketreceptionprobabilityofasecondaryuserwillbecalculatedasfollows:(Rs;g(!(˙s)))=exp2(1)Esd
522g(!(˙s))1(4.16)794.3.4Comparison
Inthissection,weevaluatehoweffectivelytheproposedmodel(referredtoas`rtCoop')representsthereal-timesystemrequirements.Ifamodelcapturesthetruecharacteristicsoftheunderlyingsystem,itsselectedactionshouldleadtotheoptimumsystemperformance,inthiscase,higherpacketreceptionrate.Inthisregard,wealsoconsideranexistingmodelpresentedin[117](referredtoas`prCoop')forcomparison.Inthismodel,rewardfunctionsaredenedbasedonthecostofstoringandrelayingaprimarypacket.Weassumethattherearefourdifferentvaluesof(;,0,1,0:65)tochoosefrom.Accordingly,wesolvetheMDPofeachmodelusinglinearprogramming,runthesimulation,andrecorddifferentstatisticse.g.theaveragewaitingtime,packetreceptionrate.Additionally,weincludethedirecttransmissionapproachintheanalysiswhereptransmitsdirectlytop0andstransmitsonlywhentheprimaryqueueisempty.Werefertothedirecttransmissionas`noCoop'.Toanalyzethesimulationresults,wevarydifferentsystemparameterse.g.distancebetweenusers,queuelength,trafcrate.Foreachdifferentconguration,wecollectseveralstatisticse.g.numberoftimesacooperativeactionispreferredoverdirecttransmission,averagewaitingtime!pexperiencedbyp,andcumulativepacketreceptionrateandcomparetheresults.First,wextheprimaryandsecondarytrafcratefollowingaBernoullidistribution,channelaccessprobability(q=0:8),queuesize(L=5).Wevarythedistancebetweenpandsandp0ands0whicharedenotedasd2andd4respectively.Allthedistancesarenormalizedto1.Wemovethesecondaryuseralongthelinebetweentheprimarytransmitterandthedestinationi.e.wesetd2=1d4whilekeepingthedistancebetweenthesecondarytransmitterandthesecondarydestinationxedto0:3.Fig.4.5aand4.6ashowthatrtCoopachieveshighercumulativepacketreceptionrateandloweraverageprimarywaitingtimecomparedtoprCoop.800.30.40.50.60.7lineardistance(d)60708090100PRR (%)noCooprtCoopprCoop(a)Varyingd2=1d40.511.5distance60708090100PRR (%)noCooprtCoopprCoop(b)Varyingd2=d444.555.56qLen60708090100PRR (%)noCooprtCoopprCoop(c)Varyingqueueinglength0.20.40.60.8purate6p5060708090100PRR (%)noCooprtCoopprCoop(d)VaryingpFigure4.5:Comparisonbetweencooperationmodels(packetreceptionrate)810.30.40.50.60.7lineardistance(d)00.20.40.60.8wpunoCooprtCoopprCoop(a)Varyingd2=1d40.511.5distance00.20.40.60.8wpunoCooprtCoopprCoop(b)Varyingd2=d444.555.56qLen00.20.40.60.8wpunoCooprtCoopprCoop(c)Varyingqueueinglength0.20.40.60.8purate6p00.20.40.60.8wpunoCooprtCoopprCoop(d)VaryingpFigure4.6:Comparisonbetweencooperationmodels(averagepuwaitingtime)82Next,weputthesecondaryuserawayfromthelinebetweentheprimarytransmitterandthedestinationandwesetd2=d4andd5=d22.Wealsovarythequeuelength,primarytrafcrate,andsecondarytrafcratewhilekeepingallotherparametersxed.Foreachofthesedifferentcongurations,weplotthepacketreceptionrateandaveragewaitingtimeofaprimarypacketinFig.4.5.TheresultsshowthattheproposedcooperationmodelrtCoopimprovesthepacketrecep-tionratecomparedtoprCoopandnoCoop.WealsorecordtheaveragewaitingtimeencounteredbyprimaryusersandshowtheresultsinFig.4.6.Ingeneral,itshowsthatprCoopincurshigherwaitingtimecomparedtoourproposedmodel.Thisisbecausetheformerapproachdoesnottakeintoconsiderationthecommunicationoverheadassociatedwithcooperationthatleadstowrongtransmissiondecisionandlowpacketreceptionrate.
4.4Multi-userCooperativeTransmissionModel
Thecooperationmodelinmulti-usersettingaddssomeuniquechallengestothesingleusermodel.First,inthesingleuseranalysis,weassumethatchangesoccuratdiscretetimeintervalsandsystemparametersdonotchangeinastate.However,inreality,theinteractionbetweenprimaryandsecondaryusersisasynchronous.Packetsarriveasynchronouslyattheuserandtransmissiontimesmaydifferfromusertouser.Therefore,statetransitionmayoccuratdifferentintervals.Second,weneedtoconsidertheinterferencebetweenprimaryandsecondarytransmissionswhichwasabsentinthesingleuseranalysis.Furthermore,auserhasnoknowledgeofotherusers'trafcandqueuestatus,andhastodecidesolelybasedonitsstateparametersandcooperationoffersreceivedfromitsneighbors.Addressingtheseaboveissues,wepresentadistributedcooperativetransmissionmodelformakingcooperationoffers,negotiatingtermsofcooperation,selectingatransmissionapproach,andnallyschedulingpackettransmission.Weexplainthesestepsofthe83algorithmnext.
4.4.1Step1:Pre-screening
Inthisstep,asecondaryuserconstructsaninterferencemapwhichhelpsittoidentifypotentialprimaryusersthatitcanengageincooperativetransmissions.Weassumethateachsecondaryuserisawareoftheinterferenceconstraintoftheprimarynetworkandknowsthechannelgainbetweenitselfandeveryprimaryreceiverinthenetwork.Asecondaryusermayestimatethechannelqualityandlinkratefromoverhearingthemessageexchangebetweenprimarytransmittersandreceiversandbyapplyingstandardtrainingsequencemethods[43]orbyanalyzingthereceivedpatterns[82].Thus,asecondaryuserdeterminesthemaximumtransmissionpoweritcanuseforeachprimaryuserandbuildstheinterferencemap.LetV(sj)denotethesetofprimaryuserswithintransmissionrangeofsj.TheinterferencemaphasjV(sjjentriesandeachentryrepresentsthemaximumtransmissionpowermax(pi;sj),sjcanuseinrelayingwhilecooperatingwithpi2V(sj).sjcalculatesitsinterferencecontributiontootherongoingtransmissionwhilecooperatingwithpiandndsthemaximumvalueitcanusewithoutinterferinganyofthesetransmissions.Forexample,tocalculatemax(pi;sj)wecalculatemax(pi;sjjpk),themaximumtransmissionpowersjcanuserelayingpi'strafcwithoutinter-feringwithpk'stransmission.Finally,themaximumpowermax(pi;sj)issettotheminimumofthesemaximumvalues.max(pi;sj)=min8k2Pmax(pi;sjjpk)(4.17)Ontheotherhand,aprimaryuserbydefaultoperatesindirecttransmissionmode.Aprimaryusercontinuouslymonitorsitsqueuesizeandpacketlossrate,andifthechangeinpacketloss84exceedsbeyondathresholdp,ittunestocontrolchannel,looksforcooperationopportunity,andentersintothenegotiationstep.
4.4.2Step2:Negotiation
Atthisstep,theinteresteduserstunetothecommoncontrolchannelforsubmittingoracceptingitscooperationoffer.Aprimaryuser'sgoalistondasecondaryuserwhoserelayingwillreducepacketloss.Asecondaryuser'sgoalistoensuretransmissionopportunitywhilespendinglesspowerinrelayingandavoidinginterferencetoothers'transmission.Accordingly,asecondaryuserconsultsitsinterferencemap,initiatesthecooperationprocess,andsendsanoffertooneormoreprimaryusersfromthelist.Acooperationofferfromasecondaryuserincludesthevalueof,anditstransmissionduration.Tostartwith,sjstartswithanofferofthehighesttransmissionpowermax(pi;sj)itcanprovidetopi.Thisinitialofferhelpssjinassessingitsfuturecooperativetransmissionopportunities.ThesubsequentoffersaremodiedusingEqn.4.18.Ifitsofferisaccepted,thevalueoft(pi;sj)ischangedattherateofthechangeinqueue.Ontheotherhand,thevalueoft1(pi;sj)isdoubledinthenextoffer.Here,dQdtdenotesthechangeinthenumberofwaitingpacketswithtime.t(pi;sj)=8
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:mint1(pi;sj)1+dQdt;max(pi;sj)ifsuccessfult1(pi;sj)2otherwise:(4.18)Aprimaryuserwillingtocooperatelooksintothecooperationoffersithasreceived.Foreachsuchpotentialoffer,aprimaryusercalculatesitscooperationgainconsideringitsimpactoncurrentandlaterperiodsincomparisonwithdirecttransmission.So,aprimaryuserpireceivesofferfromitsneighboringsecondaryusersjintheformoftransmissionpowert(pi;sj)andtransmission85Figure4.7:CooperationlifecycleofauserFigure4.8:Handshakingprotocoltimeytj.Foreachofferfromsj,piestimatescooperativechannelgain,calculatestheexpectedrelaytransmissiontimeandcooperationgainGj(i),andcomparesitwithdirecttransmissionap-proach.Bothimmediategainandfutureopportunitiesareconsideredingaincalculationandareweighedbythestateofthequeue.Giventheremainingtimetotransmitapacket(rti),estimateddirecttransmissiontime(dti),andestimatedofferedtransmissiontime(xtj)andtherequestedtransmissiontime(ytj),picalculatesthecooperationgainGj(i)ofacooperationofferfromsjasfollows:
Gj(i)=c1(dtirti)max(rti;dti)+c2(rtixtj)max(rti;xtj)+c3(dtixtj)max(dti;xtj)1QiL+1ytjxtjQiL(4.19)Here,c1,c2,andc3areconstantsthatdenotetherelativeweightfactorofthesesubcomponentswherec1+c2+c3=1.Qidenotesthenumberofpacketswaitinginthequeueofpi.piselectsthesecondaryuserwiththehighestgainforcooperation.Otherwise,itdecidestotransmitdirectly.Inthenalstep,asecondaryusersjreceivesconrmationfromoneormoreprimaryusers.Ifthereismorethanonereply,sjpickstheonethatincreasesitscooperationgaini.e.achieveshigherenergyefciencyandlesspowerconsumptioninrelaying.sjsendsaconrmationmessage86totheselectedprimaryuser,andbothusersstartagreetocooperativetransmission.Sinceprimaryusersoperateasynchronously,ausermayreceivecooperationoffersfromotheruserswhileitisindatatransmissionmode.However,alltheseoffersduringtransmissionmodeareignored.Fig.4.7showsthedifferentphasesofthecooperationlifecycleofatypicaluser.Eachusergoesthroughthisabovenegotiationproceduretomaketransmissiondecisions.4.4.3Step3:DataTransmission
AprimaryuserincooperationagreementwithasecondaryuserfollowsamodiedRTS/CTShandshakingprotocolbeforedatatransmission.InthetraditionalRTS/CTShandshakingprotocol,thesourceandthedestinationsendssmallcontrolpackettoannouncetheirnextdatatransmission.Anyuseroverhearingeitherofthesepacketsbacksoffthetransmissionperiodandtriesagain.Incooperativerelayedtransmission,anadditionaluserinvolvesindatatransmission.Specif-ically,thesecondaryuserreceivesapacketfromtheprimaryuserandthenrelaysthepackettothedestination.Withthetraditionalhandshakingprotocol,asuccessfulpacketdeliveryinvolvesatleasttwohandshakingperiods-therstonefromprimarytransmittertosecondaryuser,andthesecondonefromsecondaryusertoprimaryreceiver.Theprimarypacketneedstobestoredinthesecondaryqueue.Intheproposedhandshakingprotocol,weintroduceanadditionalcontrolpacketRTR(readytorelay)whichwillbesentbythecooperatingsecondaryuser.Thisensuresaprimarypacketspentminimumtimeinasecondaryqueue,andreducestheoverheadofhandshaking.Ac-cordingly,whentwocooperatingusersarereadytotransmit,aprimaryusersendsaRTSpacketincludingthenameofthesecondaryuseritiscooperatingwith.ThecooperatingsecondaryuserthensendsaRTRpacketdenotingtheaddressofboththesenderandreceiver.Finally,theprimaryreceiversendsaCTSpacketwithcooperationduration.Ifeachcooperatinguserinvolvedintheco-operationagreementreceivestheothertwocontrolpackets,itassumesthatthechannelissecured87anddatatransmissionstarts.Anyotheruseroutsidethiscooperationagreementbacksofftheentiredurationwhenitreceivesanyofthosecontrolpackets.Fig.4.8demonstratesahandshakingeventbetweenacooperatingprimaryandsecondaryuser.
4.4.4Step4:CooperationRenewal
Thenalstepofthecycleistodeterminethecooperationduration.Ifthedurationissmall,usershavetofrequentlygothroughnegotiationperiods;theoverheadassociatedwithitmayoutweighthecooperationbenets.Ontheotherhand,whilelongerintervalsreducethecommunicationoverhead,usersmaymisscooperationopportunitieswhichhurtthesystemreliability.So,itisimportantforausertobeabletoadaptthecooperationdurationwithchanginguserandnetworkconditions.Withthisinmind,theproposedmodelallowsacooperatingusertocontinuecooperativetrans-missionwithoutgoingthroughnegotiationperiod.Aprimaryuserkeepsrecordoftherateofchangeinqueuestatusandthechangeinpacketreceptionrate.Ifthisratiodropsbelowathreshold(p),itterminatesthecurrentcooperationperiodandswitchestodirecttransmission.Otherwise,itcontinuestosenditspackettothecooperatingsecondaryuserwithoutadditionalmessageex-change.Similarly,asecondaryuseralsokeepsrecordoftherateofchangeinitsqueuestatusandcooperationgainintermsofenergyconsumption.Iftheratiodropsbelowathreshold(s),thesecondaryuserdoesnotparticipateinhandshaking.Thiswaycommunicationoverheadisreducedwithoutsacricingsignicantcooperationbenets.Thetradeoffiscontrolledbyadjustingtheparameterspands.884.5PerformanceEvaluation
Inthissection,weevaluatetheperformanceoftheproposedcooperationmodelinacognitiveradionetworktosupportreal-timetrafc.
4.5.1PerformanceMetrics
Weusethreemetricstoanalyzetheperformanceofthemodel.Theyareasfollows:packetreceptionrate:Ourprimaryevaluationmetricispacketreceptionrateofthenetwork.Wedene`weightedpacketreceptionrate'or`weightedPRR',PRRasweightedsumofprimaryandsecondarypacketreceptionrate.So,PRR=Pm
i=1PRRi+(1)Pn
j=1PRRj.Here,PRRiandPRRjdenotethepacketreceptionrateofprimaryuserpiandsecondaryusersj.Throughoutoursimulation,weuse=0:5i.e.weconsiderequalprioritytoprimaryandsecondarypackets.cooperationoverheadanalysis:Weintroduceanothermetricthatdeterminestheoverheadcausedfromexchangingmessageduringnegotiationprocedure.Wedene`puoverhead'asthenumberoftimesaprimaryuserengagesincooperationnegotiation(whetheritissuccessfulornot)duringitslifetime.costbenetanalysis:Weperformacostbenetanalysisforsecondaryusersintermsofpowerconsumptioninrelayingprimarytrafc.Wedene`sucostperpacket'asaratioofthetotalpowerspentinrelayedtransmissionandnumberofitspacketsithastransmitted.894.5.2SimulationSetup
Weconsidera150m150msimulationareawheresecondaryusersarerandomlyplacedintheareabetweenprimarysourcesanddestinations.Numberof(primaryandsecondary)usersarevariedbetween1and5.Foreachsetofprimaryandsecondaryusers,wecreate20randomtopologiesandforeachtopology,werunthesimulationoneachtopology20times;eachcaseissimulatedfor1000ms.Ineachtopology,itwasmadesurethateachprimary(secondary)userhasatleastonesecondary(primary)userwithinitstransmissionrange.Allresultsaresummarizedoverthesetopologiesandpresentedwith95%condenceinterval.Eachprimaryuserisassignedachannelofbandwidth20KHz.The(maximum)primaryandsecondarytransmissionpower,Ep=Es=E=100mWandthenoise,N0issetto10e10mW/Hz.Pathlossissetto4andthesizeofthepacket,lenissetto1Kb.Weuseadditiveinterferencemodel[59]tocalculatemutualinterferencebetweenongoingtransmissions.Wecomparetheperformanceoftheproposedmodelintwodifferentusersettingswithtwodifferentprimarytrafcmodel.Intherstsetting,weconsiderasinglepairofprimaryandsec-ondaryuserswhereprimarytrafcfollowsaPoissondistribution.Inthesecondsetting,wecon-sideramulti-usersettingwherenumberofchannelsarelessthantheactiveprimaryusersandtwoprimaryusersmayusethesamechannel.
4.5.3SingleUserSetting
Weselectthepowerdivisionapproachproposedin[47]tocomparetheperformanceofourpro-posedcooperationmodel.Werefertotheproposedcooperationmodelas`rtCoop'andthebasicpowerdivisionapproachin[47]as`prCoop0'.Inthisapproach[47],thepowerdistributionisoptimizedtoreducetheoutageprobabilityoftheprimarysystems.Thisapproachdoesnottake900.811.21.4pu rate00.20.40.60.8weighted PRRrtCoop (lbound)rtCoop (ubound)prCoop0 (lbound)prCoop0 (ubound)(a)weightedPRR0.811.21.4pu rate0.30.40.50.60.70.80.9pu PRRrtCoop (lbound)rtCoop (ubound)prCoop0 (lbound)prCoop0 (ubound)(b)pupacketreceptionrate0.811.21.4pu rate00.20.40.60.8su PRRrtCoop (lbound)rtCoop (ubound)prCoop0 (lbound)prCoop0 (ubound)(c)supacketreceptionrateFigure4.9:Comparisonbetweenmodelsofasinglepairofprimaryandsecondaryusersintoconsiderationtheuser'squeuestatusandfutureopportunities.Thenetworktopologyandsimulationprocedureremainssame.WeconsiderthattheprimarytrafcfollowsaPoissondistribution.Wevarythemeanprimarytrafcratefrom0:75and1:5,andrecordthepacketreceptionrateforeachcases.TheresultisshowninFig.4.9wheretheproposedmodeloutperformsthebasicmodel[47].Thisisbecauseinourproposedapproach,asecondaryuserhasequalrightstoselectcooperationparametersandtakesitsdecisionfromtheperspectiveofreal-timetrafc.4.5.4Multi-usersetting
Tocomparetheperformanceoftheproposedmodelinamulti-usersetting,weconsiderthecoop-erationmodelproposedin[117].Inthismodel,asecondaryuserconsidersthecostofstoringapacketinqueueandspendingpowerinrelayingandsendscooperationofferaccordingly.Apri-maryuserselectsthesecondaryuserthatoffersthehighesttransmissionpower.Uponnegotiation,RTS/CTShandshakingprotocolisusedfordatatransmission.Weconsidertwotrafcmodelstoevaluatetheperformanceoftheproposedmodel.TherstoneisaMarkovmodulatedprocesspresentedin[49]whichhasthreeinternalstatesandtrafcgenerationratevariesbetweenstates.ThesecondtrafcmodelweconsiderhereisaPoissondistribution.Inbothcases,secondary915060708090100Deadline00.20.40.60.8weighted PRRrtCoop (lbound)rtCoop (ubound)prCoop (lbound)prCoop (ubound)(a)weightedPRR5060708090100Deadline1520253035pu overheadrtCoop (lbound)rtCoop (ubound)prCoop (lbound)prCoop (ubound)(b)puoverhead5060708090100Deadline050010001500200025003000su costrtCoop (lbound)rtCoop (ubound)prCoop (lbound)prCoop (ubound)(c)sucostFigure4.10:Markovthreestatetrafcmodelwithvaryingtransmissiondeadline1015202530Queue length00.20.40.60.8weighted PRRrtCoop (lbound)rtCoop (ubound)prCoop (lbound)prCoop (ubound)(a)weightedPRR1015202530Queue length20253035pu overheadrtCoop (lbound)rtCoop (ubound)prCoop (lbound)prCoop (ubound)(b)puoverhead1015202530Queue length05001000150020002500su costrtCoop (lbound)rtCoop (ubound)prCoop (lbound)prCoop (ubound)(c)sucostFigure4.11:Markovthreestatetrafcmodelwithvaryingqueuelengthuser'strafcfollowsaPoissondistribution.Foreachtrafcmodel,werunsimulationwithvaryingtransmissiondeadlineandqueuelengthandanalyzetheperformanceoftheproposedmodel.First,wevarythetransmissiondeadlinewithMarkovthreestatetrafcmodelandplottheresultsinFig.4.10.ThesimulationresultshowsthatrtCoopachieveshigherpacketreceptionratethanprCoop.However,bothapproachesexhibithighpuoverheadbecauseoftherateofchangeinqueuesizeisnotconsistentwhichmakesthecooperationdurationsmallandtriggersfrequentcooperationnegotiation.However,secondaryusersspendlesspowerinrtCoopcomparedtoprCoop.Next,wevarythequeuelengthandplottheperformancemetricsinFig.4.11whichshowssimilartrendaswithvaryingtransmissiondeadline.Next,weconsiderthatprimarytrafcfollowsaPoissondistribution.Themeanvalueoftrafc9220406080100Deadline0.30.40.50.60.7weighted PRRrtCoop (lbound)rtCoop (ubound)prCoop (lbound)prCoop (ubound)(a)weightedPRR20406080100Deadline050100150pu overheadrtCoop (lbound)rtCoop (ubound)prCoop (lbound)prCoop (ubound)(b)puoverhead20406080100Deadline5001000150020002500su costrtCoop (lbound)rtCoop (ubound)prCoop (lbound)prCoop (ubound)(c)sucostFigure4.12:Poissontrafcmodelwithvaryingdeadline1015202530Queue length0.50.520.540.560.580.6weighted PRRrtCoop (lbound)rtCoop (ubound)prCoop (lbound)prCoop (ubound)(a)weightedPRR1015202530Queue length05101520pu overheadrtCoop (lbound)rtCoop (ubound)prCoop (lbound)prCoop (ubound)(b)puoverhead1015202530Queue length5001000150020002500su costrtCoop (lbound)rtCoop (ubound)prCoop (lbound)prCoop (ubound)(c)sucostFigure4.13:Poissontrafcmodelwithvaryingqueuelengthisvariedissetto0:05.AgainwevarythetransmissiondeadlineandplotthreemetricsinFig.4.12.Asdeadlineincreases,thepacketreceptionrateincreases,however,rtCoopensureshigherpacketreceptionrateinallcases.TheproposedmodelalsoachieveslowprimaryoverheadandlesssecondarycostperpacketcomparedtoprCoop.WealsovarythequeuelengthandtheresultsareshowninFig.4.13.Again,theproposedmodeloutperformsprCoop.Next,wevarythemeanvalueofPoissondistributionwhilekeepingeveryotherparameterxed.TheresultsareshowninFig.4.14.Theresultsshowthattheproposedmodelachieveshigherpacketreceptionratewhileensuringlowprimaryoverheadandlowenergyperbitforasecondaryuser.Finally,wevarythenumberofsecondaryusersfrom5to15whilekeepingthenumberofprimaryusersxedto5toanalyzetheimpactofcooperationoverheadonthesystemperformance.930.020.040.060.080.1pu rate (Poisson)0.20.40.6weighted PRRrtCoop (lbound)rtCoop (ubound)prCoop (lbound)prCoop (ubound)(a)weightedPRR0.020.040.060.080.1pu rate (Poisson)0102030405060pu overheadrtCoop (lbound)rtCoop (ubound)prCoop (lbound)prCoop (ubound)(b)puoverhead0.020.040.060.080.1pu rate (Poisson)05001000150020002500su costrtCoop (lbound)rtCoop (ubound)prCoop (lbound)prCoop (ubound)(c)sucostFigure4.14:PoissontrafcmodelwithvaryingpurateThesimulationresultshowsthatthecooperationoverheadintheproposedalgorithmincreasesveryslowlycomparedtotheexistingmodels.Thisisbecauseasecondaryuserintheproposedalgorithmgoesthrougharenewalstepwithalmostnooverheadinsteadoffrequentnegotiationintheexistingalgorithms.
4.6Summary
Inthischapter,wedevelopaninterferenceawarecooperativecognitiveradionetworkforreal-timeapplications.WeformulatethecooperationoptimizationproblemintoanMDPanddeneitsstates,actionsets,transitionmatrix,andrewardfunctionsreectingthetradeoffbetweencoop-erationoverheadandcooperationbenets.Wedenetherewardofaprimaryuserintermsofsuccessfulpacketreceptionprobabilitysubtractedbythecostofcooperationoverhead.Likewise,wedenetherewardofasecondaryuserintermsofsuccessfulpacketreceptionprobabilitywithrespecttotransmissionpowerappliedtorelayedtransmission.Ouranalysisofasinglepairofpri-maryandsecondaryuserspointsoutthefactthatthereisaneffectivecooperationregionintermsofthedistanceamongusers.Inamulti-usercooperationmodel,wedene`cooperationgain'thatrepresentsbenetsofcooperationandselectspairsfortransmissionfollowinganegotiationproce-94dure.ThecooperatingpairsuseamodiedRTS/CTShandshakingprotocolfordatatransmission.Weperformextensivesimulationsunderdifferentnetworksettingswithvaryingdifferentnetworkparametersandcomparetheresultswithanexistingmodel.Theresultshowsthatcooperativetransmissionensureshigherpacketreceptionratethanthepriorcooperationmodel.Weperformacostbenetanalysisthatrepresentsthesecondaryuser'scostintermsofenergyconsumptioninrelayingprimarypacket.Wealsoperformanoverheadanalysiswhichdemonstratestheeffectofcooperationnegotiationonprimaryusers.Theproposedmodelensureslowcontroloverheadandlowenergycostforcooperatingprimaryandsecondaryusersrespectively.95Chapter5
CooperativeRoutinginCognitiveRadio
Networks
AsdiscussedinChapter4,relaybasedcollaborationmodelbringsapowerfulmeanstocombatchannelfading,toachieveimprovednetworkcapacity,andtoprovideefcientspectrumsharingamongprimaryandsecondaryusers.Byexploitingcooperativediversity,aprimaryuser(PU)appointsasecondaryusertorelayitspackets,andimprovesitsthroughput,andasecondaryuser(SU)increaseschannelaccessopportunitiesinreturnforitsservices.Thesuccessinsinglehoprelaymodelmotivatestheresearcherstostudyandexplorethecollaborationmodelinmulti-hopcooperativecommunication.Inthischapter1,westudyandanalyzethemulti-hopcooperativerelayselectionandschedulingproblem.Inamulti-hopcooperationmodel,aprimaryuserintendstoestablishastableroutingpathtoitsdestinationbyselectingmultiplesecondaryusersasintermediaterelays.Asecondaryuser,ontheotherhand,participatesinoneormoreroutingpathstoensureitstransmissionopportunitieswhilelimitingpowerconsumptioninrelaying.Exploitingtimeandspacediversityovermultiplehops,thismodelcanofferaninnovativesolutionforrelayingthegrowing3G=4Gcellulartrafc[128].Theemergingtechnologyofcognitivesensornetworkswithlimitedtransmissionrangeand1Theworkpresentedinthischapterhasbeenpublishedinthefollowingresearcharticle:(i)ChowdhurySayeedHyder,andLiXiao.flCooperativeRoutingviaOverlappingCoalitionFormationGameinCognitiveRadioNetworksfl,inthe10thWorkshoponWirelessMeshandAd-hocNetworking(WiMAN),Waikoloa,Hawaii,USA,Aug4,2016.96longerlifetimeexpectationalsoadvocatesanefcientmechanismforrelayingtrafc[79].Finally,networkmodelrelyingonspectrumsensingtechniquesmaynotprovidesatisfactoryresultsduetoimperfectsensing.Ontheotherhand,cooperationamongprimaryandsecondaryuserseliminatestheunintentionalcollisionwithPUtransmission[127].Althoughmulti-hopcooperativerelayingbringssignicantpromises,weneedtoaddresssev-eraluniquechallengestodesignthecooperationmodelandexploititsfullbenets.Themainchallengeistoquantifythemutualinterestofprimaryandsecondaryusersintopayoffandincor-porateitincooperationdecisionmaking.Forexample,whileasecondaryuserasanintermediaterelaymayofferhigherdatarate,italsointroducesdelayinthesameroutingpath.Therefore,aprimaryuser'spayoffmustreectthetradeoffbetweenachievablethroughputandpathdelay.Ontheotherhand,unlikesinglehoprelaymodel,asecondaryuser'scooperationbenetisdenednotonlybyitsownactionbutalsobytheactionofotherusersintheroutingpath.Therefore,wemusttakeintoconsiderationthecompetitionamongthesecondaryuserstomeettheirrequirements.Asaresult,singlehoprelaybasedresearch([64,67,76,131,136])arenotextensibletomulti-hopscenarios.Inthisregard,fewwork[79,127]addressthemulti-hopcooperativerelayselectionproblemanddesignacooperationmodelfocusingonprimaryusers'interestonly.Forexample,Xueetal.[127]presentaschedulingalgorithmforasingleprimarytransceiverpairwhoseroutingpathconsistsofxedandpredeterminedsecondaryrelaynodes.However,thecompetitionamongmul-tipleprimarysource-destinationpairsisnotaddressedandtheconsiderationofxedroutingpathmakethecooperationmodelimpractical.AlthoughLietal.[79]haveconsideredmultipleprimaryusersintheirwork,themodelbecomesunstablewhenusershavetodealsimultaneousrequests.Furthermore,asecondaryuseractsonlyinresponsetoprimaryusers'specicrequests,andeachonemaycooperatewithatmostoneprimaryuser.Thislimitationpreventsasecondaryuserfrom97exploringitscooperativetransmissionopportunity.Finally,weneedtoensurethestabilityoftheroutingpathandthescalabilityandcomplexityofthecooperationalgorithm.Anunscalablealgo-rithmcausesunstableroutingpaththatleadstocollisionandpacketloss,andthenetworkoutputdegradessignicantly.Therefore,theseproposedframeworkdonotrepresentthetruepotentialofamulti-hopcooperationframework.Inthischapter,weanalyzethemulti-hopcooperationframeworkandpresentmcRoute,amulti-hopcooperation-basedrelayselectionandtransmissionschedulingalgorithmaddressingtheissuesdiscussedabove.Weconsidercoexistingprimaryandsecondaryusersandanalyzeamulti-hopcooperationframeworkbasedonusers'mutualinterests.Inthisframework,weconsiderbothprimaryandsecondaryusersas`active'participantswhichactivelyadoptstrategiestodecidewhenandhowtoacceptcooperationfromotherusersforimprovedsystemperformance.Thiscomplexinteractionandnegotiationprocessisanalyzedusinganoverlappingcoalitionformationgame.Theresultfromthisanalysisisthenusedtodeviseacooperationbasedroutingalgorithmthathandlessi-multaneousroutediscoveryrequestsandensuresstableroutingpathsthroughcoalitionformation.Therefore,ournetworkmodelismoregeneralthanothersandexploitsthefullbenetsofmutualcooperation.Thesalientcontributionsofourworkaresummarizedasfollows.Weformulatethemulti-hoprelayselectionandschedulingproblemasanoverlappingcoali-tionformation(OCF)game.Unlikeexistingapproaches,thismodelinvolvesactivepar-ticipationfrombothprimaryandsecondaryuserswhereonesecondaryusercanjoinmorethanonecoalition.Theuserpayofffunctionsinthegamearedenedreectingtheirmutualinterestoncooperation.WeproposemcRoute,acooperationbasedroutingalgorithmbasedonthepropertiesofthe98Figure5.1:NetworkmodelOCFgame.Eachprimarytransmitterinitiatesaroutediscoveryrequest.Whenasecondaryuserreceivessuchrequests,itcoordinatesbetweenmultiplerequestsandcarefullysetsitscooperationparameterstoshowitsinteresttojoinincoalitions.Afterexchangingmessagesbetweenusers,theroutingpathsareguaranteedtoconvergeandpacketsarescheduledfortransmissionintimedomain.Finally,wedeveloptheproposedjointroutingandschedulingalgorithmandcompareoural-gorithmwithanexistingwork[79]andshowthatouralgorithmperformsbetterthanexistingone.Wealsoanalyzeourproposedalgorithmintermsofvariousperformancemetrics.5.1SystemModelandProblemFormalization
5.1.1SystemModel
WeconsideranOFDMA-basednetworkconsistingofmindependentsource-destinationpairsofprimaryusers(Fig.5.1).ThesetofprimarytransmittersisrepresentedasP=fp1;:::pmgwhilethesetofcorrespondingreceiversisrepresentedasP0=fp0
1;:::p0
mg.WeassumethecoexistenceofanadhocsecondarynetworkwithnsecondarytransmittersinsetS=fs1;:::;sngandtheircorrespondingreceiversinsetS0=fs0
1;:::;s0
ng.Eachuser(primaryandsecondary)isequipped99withtworadiosŒoneisdedicatedfordatatransmissionandtheotheroneisforexchangeofcontrolmessage.Tomakethebestuseofthebandwidthsavailabletotheprimarynetwork,theorthogonalsub-carrierscanbedividedintodatachannelsandcontrolchannels[73][140].Sinceourgoalistoaddressthemulti-hoprelayselectionandroutingpathformationviacooperation,thischannelallocationtechniqueamongtheprimaryuserswillnotbediscussed.Forsimplicity,weassumethateachprimarytransmitterpi2Pisallocatedasubsetofsub-carriers,andtogethertheyarereferredtoas`sub-channel'fordatatransmission[79].Weconsiderthateachsub-channelconsistsofanequalnumberofsub-carriers,therebyachievingequalbandwidth2,B.Eachsecondaryusersi2Scanoperateoveranyofthesub-channelsoftheseprimaryusersbasedontheircooperationagreement.Acommoncontrolchannelisalsoestablishedforexchangingcontrolmessageintimedomainamongtheusers.Weassumethatusersengageincooperativetransmissionandsharetheirresourcesintimedomain[64,67,79]ifitincreasestheirprot.Aprimaryuserisinterestedinexploitingthecoop-erationdiversitytobuildaroutingpaththatprovidesimprovednetworkperformance.Similarly,asecondaryuser'sinterestistoensureenoughtransmissiontimetomeetitsraterequirementwhilespendingaslesspowerinrelayingprimarypacketsaspossible.Thismutualinterestinachievinghigherpayoffdrivestheuserstonegotiatecooperationterms,shareresourcesintimedomain,andbuildsamulti-hopcooperationmodel.Ourgoalhereistodeterminethetermsofcooperationanddesignamulti-hoptransmissionmodelthatmaximizesusers'payoff.Toachievethisgoal,werstformulatetherelayselectionproblemasanoverlappingcoalitionformationgame.Westartwithabriefdescriptiononoverlap-pingcoalitionformationgamefollowedbystepbystepproblemformalization.2Themodelcanbeextendedtouserswithvariablebandwidth.1005.1.2Preliminaries
Overlappingcoalitionformationgameisaspecialtypeofcooperativegamewhereplayerscanparticipateinseveralcoalitions.Thistheoryhasbeenusedtomodelcollaborativespectrumsensingincognitiveradionetworks[119],interferencemanagementinsmallcellnetworks[139],andsoon.InthecontextofrelayselectioninCCRN,weadopttheoverlappingcoalitionformationgametomodelandanalyzethebehavioroftheframework.Wepresentthepropertiesoftheoverlappingcoalitionformationgameinthefollowingdenitions.Figure5.2:OverlappingcoalitionexampleOCFGame:AnOCFgameGwithplayersetN=P[SisgivenbyacharacteristicfunctionU[0;1]m+n7!R,whereU(0m+n)=0.Theroleofthecharacteristicfunctionofacoalitiongamespeciesthevaluationofacoalition[139].CoalitionStructure:AnoverlappingcoalitionstructureoverN,denotedasCS,isdenedasasetCS=fC1;:::;Cmgwheremisthenumberofcoalitions,CjˆNand[m
j=1Cj=N.Thecoalitionscanbeoverlapping,andthus,thesetsmaynotbedisjoint.ResourceVector:AcoalitionCj2CScanalsoberepresentedasaresourcevectorrj.rjisthecumulativeresourcecontributionofeachplayerinthatcoalition.So,rj=[rj1:::rj(m+n)]whererjidenotesthefractionofresourcethatplayeriallocatestocoalitionCj.Ifrji=0,itmeansthatuseridoesnotbelongtocoalitionCj.101AcoalitionstructureCSisalsorepresentedwithanitelistofvectorsCS=(r1;:::;rm)thatsatises(i)rj2[0;1]m+n;and(ii)Pm
j=1rji1foralli2N.PaymentVector:ThecharacteristicfunctionUdenesamappingfromtheresourcevectorrtopaymentvectorUforallcoalitionCj2CS.ThisisrepresentedasU(r;CS)=U=[U1U2:::Um].ThepaymentvectorofanindividualcoalitionCjcanberepresentedasU(Cj;CS)=U(rj;CS)=Uj=[Uj1Uj2:::Ujm+n].Thepaymentofanindividualplayercanberepresentedasasummationofpaymentfromallthecoalitionsithasparticipatedin.Ui(CS)=Pm
j=1Ui(Cj;CS)=Pm
j=1uj
i.5.1.3Formulation
WeformulatethecooperativerelayselectionandschedulingproblemasanOCFgame,G=(N;U)whereN=P[S,andjNj=m+n,andUdenotesthepayofffunctionthatconvertsauser'scontributioninacoalitionintoitsprot.Wepresenttheformulationintotwosteps-routingpathconstructionascoalitionformationandtransmissionschedulingasresourcesharinginanOCFgame.
5.1.3.1RoutingpathConstructionasCoalitionFormation
Inthecontextofcooperativerelaycommunication,aprimaryuserinitiatesasearchfordiscover-ingaroutingpathtoitsdestination.Nodesareaddedtothepathbasedontheirmutualinterest(expressedaspayofffunction).Finally,aroutingpathbetweenaprimarytransmitter(source)andaprimaryreceiver(destination)isestablishedthatincludesoneormoresecondaryusersasinter-mediaterelaynodes(toreceivepacketsfromthepreviousoneandforwardpacketstothenextone102inthepath.)TheconstructionofroutingpathcanbemappedtothecoalitionformationinanOCFgame.Eachprimarytransmitteri2Pstartstheprocess,secondaryusersjointhecoalitionifitincreasestheirpayoff,andacoalitionCi(i.e.apathbetweentheprimarytransmitterandreceiver)isformed.Thus,Cirepresentstheroutingpathstartingwithprimarytransmitteri,followedbyoneormoresecondarytransmittersfromthesetNbasedontheirmutualneeds-constructingamulti-hoproutingpathandcreatingtransmissionopportunitiesrespectively.Thepayoffofacoalitionisdenedasthesummationofthepayoffofallitsmembersearnedfromjoiningthecoalition.AcoalitionstructureCSrepresentsthesetofmsuchcoalitions(i.e.routingpathofmprimaryusers)whereanyofthesecondarytransmittersmayparticipateinmorethanonecoalition.So,CS=fC1;:::;Cmg.Forexample,therearetwocoalitionsformedinFig.5.2.Therstprimarytransmitter-receiverpair(p1;p0
1)formsacoalitionC1withfoursecondaryuserss1,s3,s4,ands5.Thisimpliesthepacketsfromprimaryuserp1followsthispathp1!s1!s3!s4!s5!p0
1.Thesecondprimarytransmitter-receiverpair(p2;p0
2)formsanothercoalitionC2withthreesecondaryuserss2,s3,ands4.Therearetwosecondaryusers(s3,s4)overlappinginboththecoalitions.
5.1.3.2SchedulingasResourceSharing
Thepackettransmissionschedulingcanbemappedtoresourcesharinginthecoalitiongame.Theresourcecontributionofindividualuseri2NisdenotedasriandtheresourcecontributiontoacoalitionCjisdenotedasrjiandri=Pm
j=1rji.TheresourcevectorofacoalitionCjisdenotedasrj=[rj1:::rj(m+n)]wheretherstmentriesrepresentresourcecontributionfromprimaryusersandthenextnentriesrepresentcontributionfromsecondaryusers.ConsideringTtimeslots,eachuserhasmaximumTtimeslotstoshareitwithotherusersinitscoalitionorscheduleitsown103transmission.Aprimaryuseronlycontributestoitsowncoalitionandtheresourcecontributionbyaprimaryuseri2Pisthetotalamountoftimesecondaryusersinitscoalitiontransmittheirownpacketsinitssub-channels.ri=rii=1TTXt=1Xj2Ciij!j0(t)1;8i2P(5.1)Here,jx!y(t)isanindicatorfunctionwhosevaluecanbef0;1g.jx!y(t)=1impliesthatuserxsendspackettouseryattimetincoalitionCjwherex;y2N,0meansnotransmission.Ify=x0,userxsendspacketdirectlytoitscorrespondingdestination.Asecondaryusercontributesitsresourcetomorethanonecoalitions.Theresourcecontribu-tionbyasecondaryuseri2StoacoalitionCjistheamountoftimeitengagesinreceivingandrelayingpacketsoftheprimaryuserj2Pofthatcoalition.rji=1TTXt=12
6
4Xk2Cjji!k(t)+Xq2Cjjq!i(t)3
7
5;8i2S(5.2)Foranyuseri2Nbydenition,ri1.Inordertoscheduleusers'transmissionwithoutinterference,additionalconstraintsmustbesatised.Ingeneral,anyuserx2Ncannotsendtomorethanoneusery2N.Also,itcannotreceivefrommorethanoneusery2N.mXj=1Xy2Cjjx!y(t)1;(x2N)(5.3)mXj=1Xy2Cjjy!x(t)1;(x2N)(5.4)104Also,auserx2Ncannotsendandreceivepacketsimultaneouslyatthesametimeslott.mXj=12
6
4Xy2Cjjx!y(t)+Xy2Cjjy!x(t)3
7
51(5.5)Furthermore,allthescheduledtransmissionsmustbeinterferencefree.So,whileauserinacoalitionisreceivingpacketfromanotheruserinthesamecoalition,allotherinterferinguserstothatreceiverinthesamecoalitioncannotsendanypacket.Otherwise,thereceiverwillexperienceinterference.jx!y(t)+Xz2IyXq2Vzjz!q(t)1(5.6)Here,Iyrepresentsthesetofnodesinterferingtousersy'stransmissionwhileVzrepresentsthesetofnodeswithintransmissionrangeofuserz.Notethat,auser'sinterferencerangeisusuallylongerthanitstransmissionrange.
5.1.4PayoffofaPrimaryUser
Thepayoffofaprimaryuseri2PfromacoalitionCi,Upi(Ci;CS)isdenedintermsofdatarateprot<i(Ci)andpathdelayprotDi(Ci)inEqn.5.7Upi(Ci;CS)=<i(Ci)+(1)Di(Ci)(5.7)Here,theparameterdenesthecharacteristicsofaprimaryuserbasedonhispreferencebetweenthroughputanddelayinpayoffcalculation.Forexample,=1meansthataprimaryuser'sonlyfocusistomaximizethroughputwhile=0meansthattheuserisdelaysensitiveandaimsto105minimizedelay.Thedatarateprot<i(Ci)ofaprimaryuseriincoalitionCiiscalculatedcomparingcooper-ativetransmissionrate3Ri(Ci)withRi(fig).Ri(fig)denotestheeffectivetransmissionratethattheprimaryplayericanachievefromdirecttransmissioni.e.coalitionhasonlyoneplayer.WecancalculateRi(fig)directlyfromEqn.5.10.<i(Ci)=Ri(Ci)Ri(fig)Ri(fig)(5.8)Similarly,thedelayprotDi(Ci)ofaprimaryuseriincoalitionCiiscalculatedasaratioofdelayimprovementcomparedtodelayfromdirecttransmission.Di(Ci)=i(fig)i(Ci)i(fig)(5.9)Westartouranalysiswiththecalculationofdatarate.WeassumethatthechannelexperienceswhiteGaussiannoise,andthesignalqualitydegradesduetopathloss.Theeffectivetransmis-sionrateRijfromnodeitonodejiscalculatedfollowingEqn.5.10[44].Thus,wecalculatetransmissionratebetweenanylinkbetweentwoconsecutivemembersinacoalition.Rij=Blog21+EtxGtGr(d0=d)N0B(5.10)whereEtx,Gt,Gr,andN0denotethetransmissionpowerofnodei,transmittergain,receivergain,andpowerspectraldensityofnoiserespectively.Also,disthedistancebetweennodeiandnodej,d0isthereferencedistancefortheantennafar-eld,andisthepathlossexponent.Theoverallpackettransmissionrateofaprimaryuserfromacoalitionisdenotedastheminimumdata3Ri(Ci)andRi(CS)aresameforaprimaryuseri106rateofanyofthelinksinthatcoalition(sincenodeshavetoreceivethepacketrstandthensendittothenextone,theeffectivetransmissionrateisfactoredby12).Consequently,theeffectivetransmissionrateofaprimaryuseriinacoalitionCiisdenedas,Ri(Ci)=minRi(fig);12min8j;j+12CiRj;j+1(Ci)(5.11)Here,Rj;j+1(Ci)denotesthedataratebetweentwoconsecutivemembersinthecoalitionCi.Next,wepresentthedelayanalysis.Accordingto[14],thedelayindirecttransmission(i(fig))iscalculatedconsideringM=G=1queueingsystembythefollowingequation:i(fig)=i2i(ii)+1i(5.12)Here,iandidenotethepacketarrivalrateandpackettransmissionraterespectivelyandinsteadystate,i<i.Ontheotherhand,thedelayoftheroutingpathisthesummationofeachlinkdelayinthecoalition.i(Ci)=Xj;j+12Cij;j+1(Ci)(5.13)Here,j;j+1(Ci)denotesthedelaybetweentwoconsecutivesecondaryusersinthecoalitionCi.Weperformaqueuinganalysistocalculatethelinkdelayj;j+1(Ci)betweentwoconsecutiveusersinacoalitionCi.ThequeueingsysteminasecondaryusercanbemodeledasanM=G=1queuewithvacationperiod.Accordingtothisqueueingmodelasecondaryuserj2Nactsasarelayforc(cm)primaryusers(i.e.coalitions).TheuserjreceivespacketsfromtheprimaryusersatratesfollowingPoissondistributionwith1,:::,candoffersrelayservicetimesyj;1,:::,yj;crespectively.107Whentherelayedtransmissionisnished,thesecondaryuserstartstransmittingitsownpacketsinthevacationtime(i.e.thebandwidthtimeithasearnedthroughcooperation).Asecondaryuserprecalculatesrequiredvacationtimepercyclebasedonitstransmissionre-quirement.Letusconsiderthatvacationtime˛isarandomvariablewithdistributionF(˛)andnitemean˛andtheservicetimesareindependentrandomvariablesdrawnfromacommondis-tributionHyandnitemeany.UsingCobham'swell-knownformulaforthewaitingtimeofanarbitraryarrivalinthehigherpriorityqueue,wecancalculatethemeandelayj;j+1(Ci)experi-encedbyapacketofaprimaryuserifromonesecondaryuserjtoanothersecondaryuserj+1inthecoalitionCiasfollows[75]j;j+1(Ci)=E(y2)2(1y)+E(˛2)2˛(5.14)Here,=1+:::+c.5.1.5PayoffofaSecondaryPlayer
Thepayoffvalueofasecondaryplayerjisdenedintermsofthefractionoftransmissionperiodearnedinreturnforrelayperiodandpowerconsumptioninrelaying.Asecondaryplayer'spayoffisdeterminedbythefollowingequation:Usj(Ci;CS)=RaPT
t=1ij!j0(t)TPk2Pwj;krkj(5.15)Here,ij!j0(t)denotesthatuserjtransmitstoitsdestinationusingsub-channelsofprimaryuseriincoalitionCiattimet,RadenotesthetransmissionratebetweensecondarytransmitterandsecondaryreceiverwhichcanbecalculatedusingEqn.5.10,rkjdenotesthepacketrelaytimeof108primaryuserk,andwj;kdenotesthetransmissionpowerspentinrelayingtrafcfromprimaryuserkpertimeunit.Asitcanbeseenfromthepayofffunction,asecondaryusercanincreaseitspayoffeitherbyaskingformorebandwidthtimefromtheprimaryuserorspendinglesspowerinrelayingprimarytrafc.
5.1.6ProblemStatement
GiventhesetofprimaryplayersPandsecondaryplayersSandtheircorrespondingresources,thegoalistoallocateresourcesintomcoalitionssuchthatindividualpayoffismaximizedwhilesatisfyingtheroutingandschedulingconstraintsmentionedinEqns.(5.1)-(5.6).Mathematically,wedenetheproblemstatementasfollows:maxrUpi;Usj8i2P;j2S(5.16)suchthatEqns.(5.1)-(5.6)aresatisedTheresultingprotmaximizationproblemcanbesolvedtondstablesolutionsusinglinearprogramming.However,thisproblemisNP-hard.TheproofofthecomplexityreliesonareductionfromawellknownNP-hardprobleme.g.multipleknapsackproblem(MKP)[16].Sinceitisnotpracticaltocoordinatebetweenallusersinalargenetwork,wedevelopadistributedcoalitionformationalgorithminthenextsection.
5.2CooperativeRoutingProtocol
Inthissection,wepresentmcRoute,adistributedcooperativeroutingprotocol.Theroutingpro-tocoldependsonmessageexchangebetweenuserstoconstructstableandprotableroutingpaths.109Therearethreetypesofmessageexchangedbetweenusers.TherstmessageiscoalitionjoinrequestCi(i)thatdenotesacoalitionrequestinitiatedbyprimaryuseri.ThesecondmessageiscoalitionreplyrequestCi(j)whichisaresponsefromsecondaryuserjtotheinitiatingprimaryuseri.Thethirdmessageiscoalitionapproval,Ciwhichconrmssecondaryusersintheselectedroutingpathofprimaryuseri.Next,weexplaintheroutingprotocolfromtheperspectiveofbothaprimaryandasecondaryuser.TheprimaryuseriinitiatesacoalitionjoinrequestCi(i)tosearchforamoreprotablepaththanthedirecttransmission.Accordingly,itincludesbasicparameterse.g.directtransmissionrate,trafcrate,anddirectendtoenddelayinthemessage.Themessageisthensenttoeachuserj2ViwhereVidenotesthesetofsecondaryuserswithinitstransmissionrange.Aprimaryusermovestoawaitstatetoreceivecoalitionofferfromitsneighbors.Ifnoreplyisreceivedwithinapredenedtime,thePUusercontinuestransmittingdirectlytothedestination.Otherwise,theprimaryuserembracesthecoalitionofferthatmaximizesitspayoff.j=argmaxjUpi(Ci(j))(5.17)Finally,theprimaryusersendsacoaltionapprovalCitowardstheselectedsecondaryuserj.Theentireprocessofroutingpathconstructioncontinuesuntiltheparameterdreducesbelowapredenedthreshold(theupdateprocessofdisdiscussedlater).TheprotocolissummarizedinTable5.1.AnSUjreceivingacoalitionjoinrequestCi(i)rstcheckswhetherthedestinationisreach-ableornot.Otherwise,iteitherdropstherequestfromi(ifitisnotinterested)orforwardsittoitsneighbork2Vjandmovestowaitstate.Sinceasecondaryuser'ssuccessdependsonotherusersonroutingpath,itrstselectsthebestproposalfromthecoalitionoffersithasre-110Table5.1:AlgorithmmcRoute:foraPUuseriCi=fig,Upi(Ci)=0initiateacoalitionjoinrequestCi(i)=figrepeatsendCi(i)toeachnodej2VireceivecoalitionreplyCi(j)fromeachnodej2Viselectj=argmaxjUpi(Ci(j))ifUpi(Ci)<Upi(Ci(j))thenselectCi=Ci(j)sendthecoalitionapprovalCitouserjendif
updated,addjasnexthop,andupdatetheroutingtableadvanceroundduntildceivedfromitsneighbors.Itcombinesitsowncooperationtermstotheselectedofferconsideringallotheravailablerequestsfromotherprimaryusers.Weexplaintheparameterselectionmech-anisminSec.5.2.2.Thecombinedofferisthensentintheupstreamdirectionasacoalitionoffercoalitionreply,Ci(j)fromuserj.WhensecondaryuserjreceivescoalitionapprovalCi,itupdatesitsroutingtable,schedulesitspacketfortransmission,andforwardsthepacketinthedownstreamdirection.TheprotocolissummarizedinTable5.2.Wewillfurtherdiscussthemessageformatandtheselectionandmodicationprocessofcoali-tionoffer.
5.2.1MessageFormat
Acoalitionmessagecontainssomeimportantparameterstorepresentthecoalitionoffer.Theparameterscanbeclassiedintothreemaincategories.Thebasiccategorycontainstheinitiatorid(SrcID),thedestinationid(DstID),packettype(pktType),andpacketid(Round).Thesecondcategoryrepresentstheprimaryuser'sinformatione.g.itsdirectdatarate(R0),end-to-enddelay(D0),andthetrafcrate(0).Thethirdcategorycontainsthecooperationofferintheformthat111Table5.2:AlgorithmmcRoute:forSUuserjrepeatforeachcoalitionjoinrequestCi(i)doinitializeCi(j)=fjgifdestinationisnotreachablethenforwardthepacketCi(i)toeachnodek2VjreceivecoalitionreplypacketCi(j)fromeachnodek2Vjselectj=argmaxkUpi(Ci(k))combineCi(j)=Ci(j)[Ci(j)endif
calculateUsj(Ci(j)),Upi(Ci(j))withitsownoffersendcoalitionreplypacketCi(j)inupstreamandmovetowaitstateifcoaltionapprovalCiisreceivedthenforwardthecoalitionapprovalpacketCiindownstreamupdateroutingtableendifendforuntilnomorecoalitionjoinpackethasbeenreceivedFigure5.3:Messageformatisunderstandabletotheprimaryuser.Theeldsinthecoalitionoffercategoryareasfollows:R0:thecooperativedatatransmissionratethroughsecondarypath,D0:thecooperativedelaythroughsecondarypath,andX0:thecumulativetransmissiontimedemandedfromtheprimarytransmitter.5.2.2CoalitionOfferandPayoffCalculation
Whenasecondaryuserj2SreceivescoalitionproposalsfromitsneighborsinresponsetoacoalitionjoinCi(i),itselectsthecooperationofferthatprovidesthemostprotablepathfortheinitiatingprimaryuseri2P.Letusassumethattheoffer,Ci(k)fromuserk2Vjisselected.Theuserjnextselectstwoparametersasitscooperationtermstoaddintothechosencooperation112offerCi(k).Therstparameterdenotesthecycletimeitallocatesforrelayingthecorrespondingprimaryuserandthesecondparameterdenotesthebandwidthtimeitrequestsfromthecoalitionofprimaryuseri.Inordertoselectthesetwoparameters,theusercheckstheoffersitmadetootherprimaryusers.Intherstround,itselectsparametersforeachcoalitionrequestproportionaltothepowercon-sumptioninrelayingthecorrespondingprimarytrafc.Basedonitssuccessatpreviousrounds,asecondaryusereither(i)reducesitsdemandforbandwidthtimewhilerelaytimeremainsun-changed,(ii)requestsmorebandwidthtimewhilerelaytimeisunchanged.(iii)approvesmorerelaytimetotheprimaryuserwiththerequestofthesameunchangedtransmissiontime,or(iv)reducesrelaytimewithunchangedtransmissiontime.Finally,thecooperationofferofasecondaryuserisconvertedtoaformthatisunderstandabletoaprimaryuserthatexpectstheofferintheformofcooperativedatarateandend-to-enddelay(seeFig.5.3).Accordingly,anSUjcalculatestheprimaryuseri'spayoffasfollowsusingEqn.5.11.Ri(Ci(j))=min(Rj;k;Ri(Ci(k))Theintermediatepathdelay(Eqn.5.14)introducedbyasecondaryuserjinacoalitionSiisasfollows:Dj(Ci)=PT
t=1Pm
x=1xj!x(t)+xx!j(t)lenPT
t=1ij!i(t)R(Ci)Di(Ci(j))=Di(Ci(k))+Dj(Ci)Here,lendenotesthelengthofthepacket.Also,thepayoffofasecondaryuserjiscalculated113basedontheresourcesharingwiththeprimaryusersusingEqn.5.15.5.2.3StabilityofCoalitions
Inordertoensurestablecoalitions,wecontrolthesearchforcoalitionbytwoparameters.Apri-maryusermaintainsaconvergenceparameter,d.Thevalueofthisparameterdetermineswhethertheuserwillinitiateanotherroundofroutediscoveryornot.Theinitialvalueoftheparameterissetto1.Aftereachroundd,theusercalculatesthechangeinpayoffovertotalroundsandifthevaluedropslowerthanthethreshold(),theuserstopstheroutediscoveryprocess.Thevalueofisasystemdenedparameter.Theparameterdatrounddiscalculatedasfollows:d=8
>
>
>
<
>
>
>
:jUdj=difd>11otherwise(5.18)whereUddenotesthedifferencebetweenuseri'spayoffatrounddandatroundd1.Asthenumberofroundincreases,ddecreasestoavaluebelowthethresholdandprimaryuserbecomesstablewithitscoalition.Also,eachsecondaryusercannotrequesttransmissiontimelowerthans.Whenasecondaryuser'srequestwithminimumtransmissiontimetoaprimaryuserfails,itstopsparticipatinginthatcoalition.Thus,theusageofdandscontrolstheconvergencespeed,andtheroutingpathsbecomestable.Whenusersareonastableroutingpath,thechannelstatesmaychangethatmayreducethepayoffvaluationofoneormoreusersonthepath.Toavoidcontinuingonalessprotablepath,allparticipantscontinuouslymonitorthepayoffvalue.Ifthepayoffdropssignicantlyfromtheagreedone,theprimaryusermayswitchtodirecttransmissionandinitiatethesearchfortherout-ingpathwhileasecondaryusermayremoveitselffromthepathandsearchforanewopportunity.1145678910# of PUS, # of SUs 30, Tx power 0.100000W02468PU profitmcRoute upper limitmcRoute lower limitnpRoute upper limitnpRoute upper limit(a)averagePUprot5678910# of PUS, # of SUs 30, Tx power 0.100000W0.60.70.80.911.11.21.31.4SU profitmcRoute upper limitmcRoute lower limitnpRoute upper limitnpRoute upper limit(b)averageSUprot5678910# of PUS, # of SUs 30, Tx power 0.100000W051015202530data ratemcRoute upper limitmcRoute lower limitnpRoute upper limitnpRoute upper limit(c)averagedatarate5678910# of PUS, # of SUs 30, Tx power 0.100000W-101234number of roundsmcRoute upper limitmcRoute lower limitnpRoute upper limitnpRoute upper limit(d)numberofroundsFigure5.4:ComparisonbetweenmcRouteandnpRoute[79]5.3PerformanceEvaluation
Inthissection,weanalyzetheperformanceofcoalitionbasedmulti-hopcooperativeroutingalgo-rithm.Wesimulateacognitiveradionetworklocatedinanareaof5000m5000m.Wedeploydifferentnumberofprimarysource-destinationpairs(5to10).Eachprimarysourcenodeisas-signedachannelwith20KHzbandwidth.Thetransmissioncycletimeisnormalizedtooneunitandasecondaryuserrequires1=10thofitscycletimeisforsupportingitsminimumraterequire-ment.Inordertoevaluatetheimpactofcooperationintheroutingpathselection,wevarythe115Table5.3:SimulationparametersParametersValueBandwidth(B)20KHzTransmitterandReceiverGain(Gt;Gr)1PowerspectraldensityofNoise(N0)1010W/HzTransmissionPower(Etx)100mWPathlossexponent()2Basedistance(d0)10m[44]Threshold()0:001Packetlength(len)1024bitsnumberofprimaryusers,secondaryusers,andtransmissionpower.ThesimulationparametersarelistedinTable5.3.
5.3.1Topology
Theprimarysourceanddestinationnodesarerandomlyanduniformlydeployedinthenetworkarea.Secondaryusersarealsorandomlyanduniformlydeployedintheareasothateachuserhasatleastoneneighbor.Wealsomadesurethateachpairofprimarysourceanddestinationnodeisconnected,andthereexistsatleastonepathbetweenprimarysource-destinationpairsthroughsecondaryusers.Foreachsetofinputconguration,wehavegeneratedasmanyas50samplescenariosandthestatisticsarerecordedforeachset.Finally,forstatisticalcondence,wetakeanaverageofresultsofallsetstorepresenttheoutcomeofeachscenario.5.3.2PerformanceComparisonwithPriorWork
Tocomparewithanexistingalgorithm,weimplementamodiedversionofthealgorithmproposedin[79].Wehavechosen[79]over[127]sincethelatteroneassumesxedroutingpath.Unlike[79],inthemodiedversion,asecondaryusermayreceivesimultaneouscoalitionrequestsfrommorethanoneprimaryuser.Asecondaryuserprocessesmultipleconcurrentcooperationrequests,116selectsoneofthemrandomly,andparticipatesinroutingpathofonlyoneprimaryuseratatime.Werefertothisalgorithmas`non-overlappingrouting'inshort`npRoute'.WecalculatePUandSUprot(with95%condenceinterval)withthevaryingnumberofprimaryuserswhilethetransmissionpowerissetto0:1Wandnumberofsecondaryusersissetto30.Fig.5.4aand5.4bshowthattheproposedcooperationalgorithmachieveshigherPUandSUpayoffthanthoseofnpRoute.InmcRoute,PUprotstaysalmostconstantwiththeincreaseinthenumberofPUs.ThisisbecauseeachprimaryuseronaveragecooperateswithsamenumberofsecondaryusersandincreasingnumberofprimaryusersdoesnotincreasetheaveragePUprot.Ontheotherhand,SUprotdecreasesduetoincreasingcompetitionamongthem.WealsoshowinFig.5.4cthatthecooperativedatarateachievedthroughmcRouteishigherthannpRoute.Also,weinvestigateaveragenumberofrounds[119]thatreectsthestabilityandconvergencespeed.Fig.5.4dshowsthatnpRouteconvergestoalocalmaximawhenithandlesmultiplecooperationofferssimultaneously.Ontheotherhand,mcRoutegoesthroughfewmoreroundstoachievehigherdatarateandhigherPUandSUpayoff.Similarly,wealsovarythenumberofsecondaryusersandcalculatePUandSUprot(with95%condenceinterval).mcRoutecreatesmorecooperationopportunityforsecondaryusersthannpRouteandincreasesthenumberofsecondaryusersinvolvedincooperationandtheirprotsaswell.Tobetterunderstandthemulti-hopcooperationbehaviorincognitivenetworks,wefurtherinvestigatethefollowingpropertiesoftheproposedmechanisminadditiontoaveragetoPUandSUprot.First,averagelengthoftheroutingpath(i.e.numberofrelaysoneachpathofPU);italsoindicatestheaverageparticipationofsecondaryusersineachroutingpath.Second,numberofoverlappingsecondaryusers(i.e.numberofSUsinvolvedinmorethanoneroutingpathsofPUsincomparisontototalparticipatingSUs).117# of PUS, # of SUs: 20, Tx power 0.100000 W5678910path length23456max path lengthmin path lengthavg path length(a)pathlengthvs.numberofPUs# of PUS, # of SUs: 20, Tx power 0.100000 W5678910# of SUs24681012overlapping SUsparticipating SUs(b)numberofoverlappingSUsvs.numberofPUsFigure5.5:ResultswithvaryingPUs# of PUS 5, # of SUs, Tx power 0.100000 W1015202530path length23456max lengthmin lengthavg length(a)pathlengthvs.numberofSUs# of PUS 5, # of SUs, Tx power 0.100000 W1015202530# of SUs0246810overlapping SUsparticipating SUs(b)numberofoverlappingSUsvs.numberofSUsFigure5.6:ResultswithvaryingSUs5.3.3ResultswithVaryingNumberofPUs
Werstvarythenumberofprimaryusersfrom5to10pairswhilethenumberofsecondaryusersisxedto20.Figure5.5showstheroutingpathlength,andthenumberoftheoverlappingnodesparticipatinginthecooperation.Althoughthelengthoftheroutingpathdoesnotvarywiththenumberofprimaryusers(Fig.5.5a),thenumberoftheparticipatingandoverlappingsecondaryusersincreasesalmostlinearly(Fig.5.5b).1185.3.4ResultswithVaryingNumberofSUs
Next,weperformthesamesetofexperimentsbutwithvaryingnumberofSUsfrom10to30.Thenumberofprimaryusersisxedto5pairs.Allotherparametersarekeptthesame.TheresultsaredepictedinFig.5.6.Thepathlengthincreaseswithanincreaseinthenumberofsecondaryusers(Fig.5.6a).Asexpected,thenumberofcooperatingSUsincreaseswithvaryingnumberofSUs(Fig.5.6b).Wealsoevaluatetheimpactoftransmissionpoweroncooperationbyvaryingthetransmissionpowerfrom0:1Wto0:5W.5.3.5ResultswithAlgorithmParameters
Weinvestigatetheimpactofchangingtwokeyparametersinrelayselectionandcoalitionforma-tion.TherstparameterdenotesthetradeoffbetweenthroughputanddelayinthepayoffofaprimaryuserinEqn.5.7.Wevarythevalueofbetween0and1andrecordthechangeinuserpayoff,pathlength,andnumberofcooperatingsecondaryusers.TheresultisshowninFig.5.7.Asthevalueofreachesto1,theprimaryuserismoreinterestedinincreasingdatarateandachievablethroughputandignoringthedelaycostintroducedbyrelayingsecondaryusers.There-fore,numberofparticipatingsecondarynodes(Fig.5.7a)andpathlength(Fig.5.7b)increaseswiththeincreaseinvalueof.ThisalsoincreasesPUprotalmostlinearlyandopensmoreop-portunityforsecondaryuserstoincreasetheirpayoff(Fig.5.7c).Next,weselecttoinvestigatethestabilityofthealgorithm.Fig.5.7dshowsthatmoreroundsareneededtoreachstablecoali-tionswithsmallervaluesof.Thus,thesetwoparameterscontrolthecooperationopportunityandconvergencespeedoftheroutingpaths.119# of PUS: 10, # of SUs: 30, Tx power 0.100000 W00.20.40.60.81# of SUs0510152025overlapping SUsparticipating SUs(a)numberofoverlappingSUsvs.# of PUS: 10, # of SUs: 30, Tx power 0.100000 W00.20.40.60.81path length24681012max path lengthmin path lengthavg path length(b)pathlengthvs.00.20.40.60.81# of PUS: 10, # of SUs: 30, Tx power 0.100000 W051015average PU profit1.11.21.31.4average SU profitavg. PU profitavg SU profit(c)protvs.00.0010.01 0.1  1    convergence time33.544.55number of rounds(d)ConvergenceandstabilityFigure5.7:Resultswithvaryingalgorithmparameters1205.4Summary
Inthischapter,weformulatethecooperativeroutingpathformationproblemasanoverlappingcoalitiongamewheresecondaryusersactivelyparticipateinmultipleroutingpaths.APU'spayoffisdenedasacombinationofdatarateprotandpathdelay.AnSU'spayoffisdenedasbitperenergyspentinrelaying.BasedonthepayofffunctionsdenedinanOCFgame,wedeviseadis-tributedmulti-hoproutingandschedulingprotocol.Bothprimaryandsecondaryusersgothroughroundsofexchangingmessagesandnegotiatingoncooperationtermstobuildstableroutingpaths.WecompareouralgorithmwithanexistingworkandthesimulationresultsshowthatourapproachoutperformstheexistingworkintermsofPUandSUprot.Ouralgorithmprovidesstableroutingpathsthatisalsoveriedthroughsimulation.Wehaveconsideredsinglepathroutingbetweeneachprimarysourcedestinationpair.Wewillinvestigatetheimpactofcooperativebehaviorinthecaseofmulti-pathroutingandpossiblecooperationstrategywithsecondaryusersinfuturework.121Chapter6
TruthfulOnlineSpectrumAuctions
Inpreviouschapters,wehavediscussedspectrumsharingtechniquesundersensingandrelaybasedcollaborationmodels.Inthesensingbasedcollaborationmodel,secondaryuserssharetheirsens-ingreportstotakeajointdecisionwithoutprimaryusers'participation.ThesuccessinspectrumutilizationdependsontheaccuracyofPUdetectiontechniquesandtheircollaborativedecision.Intherelaybasedcollaborationmodel,PUsactivelycoordinatewithSUstoimprovetheirsignalper-formancewithcooperativediversity.WhenthePUsareidlewithnopendingtransmissionrequeststheyhavenoincentiveinsharingtheirunusedspectrumwithspectrumhungrysecondaryusers.Inthischapter,weexploreauctionbasedcollaborationmodels1thathaverecentlybeeninvestigatedasameanstoencouragetheseusersintosharingtheirunusedspectrumandearningrevenueinre-turn.RecentinitiativesfromFCCalsoindicatetheprospectofauctionbasedcollaborationmodel.Accordingtothismodel,PUscanselltheirunusedlicensedspectrumunitsintemporal,spectral,and/orspatialdomainsfordifferentdurationswhilethebuyerslikesmallwirelessnetworks,indi-vidualinfrastructurenetworks,orhomenetworkscanbidfortheshareofthespectrum[22].These1Theworkpresentedinthischapterhasbeenpublishedinthreeresearcharticles:(i)ChowdhurySayeedHyder,ThomasD.Jeitschko,andLiXiao.BidandTimeTruthfulOnlineSpectrumAuc-tionswithDynamicUserArrivalandDynamicSpectrumSupply,inthe25thInternationalConferenceonComputerCommunicationandNetworks,Waikoloa,Hawaii,USA,Aug1-3,2016.(ii)ChowdhurySayeedHyder,ThomasD.Jeitschko,andLiXiao.TruthfulOnlineDoubleAuctionswithReal-timeStochasticArrivalofDemandandSupply,inthe25thInternationalConferenceonComputerComminca-tionandNetworks,Waikoloa,Hawaii,USA,Aug1-3,2016.(iii)ChowdhurySayeedHyder,ThomasD.Jeitschko,andLiXiao.Towardsatruthfulonlinespectrumauctionwithdynamicdemandandsupply.inMilitaryCommunicationsConference(MILCOM),pp413Œ418,Tampa,Florida,USA,October26-28,2015.122users'spectrumdemandmayvarydependingontheapplicationtype,usertrafc,andusermobil-ity.Forexample,auserwithdelay-tolerantapplicationscandeferitstransmissionwhereasauserwithdelay-sensitiveapplicationsmayrequireimmediatetransmission.Auctionbasedcollaborationmodelshavebeenstudiedinthecontextofspectrum(re-)allocation,withparticularattentionbeingpaidtotheresultingefciencyofspectrumuse(bothwithinandacrosslocations,becauseforagivengeographicallocation,non-interferinguserscanbeallocatedthesamespectrumtoincreasebothcoverageandcapacity[114]),therevenueorprotgeneratedintheprocessof(re-)allocation[31,129],demandsatisfaction[135,143],andotherperformancemetrics.Similartothesesingleauctionmechanisms,doubleauctionmechanismshavebeende-signedwithauxiliarymotivationsofimprovingefciency,increasingrevenue,etc.[22,31,40,143].Thereareadditionalpracticalconcerns:forinstance,byexploitingtheinherentcharacteristicsofwirelessnetworks,abiddermayoverhearorinterceptthebiddinginformationofcompetitorsandgainanadvantage[138];and,thus,considerableattentionhasbeengiventoassuringthattheauc-tionmechanisminducesparticipantstotruthfullyreporttheirneedsandrequirements,ratherthanhavethemmisrepresenttheirunderlyingsupplyordemandconsiderationsinordertofigameflthesystemandtherebyincreasetheirownbenetsattheexpenseofothers[142].Thisauctionbasedresearchconstitutesasignicantadvancementinthepotentialforeffectivespectrummanagement.However,mostworkfocusesonstatic(oroff-line)settingswithknownnumberofbiddersandsupplies,therebysuppressingtheinherentdynamicaspectsofspectrumavailabilityandspectrumneedsdiscussedattheoutset.Also,existingworkconsidersuserswithnotransmissiondeadlinesandtherefore,theproposedauctionmechanismsareonlybidtruthful.Unfortunately,giventhetransmissionexibilitytheusersmaymanipulatetheoutcomeoftheseauctionsbytweakingtheirdeadlineseveninthecaseofasingleunitdemandperuser(explainedwithexamplesinSec.6.1.4).Anexceptiontothisissomerecentwork(e.g.,TRADE[141],123Topaz[30],andTofu[125])thatconsidersdynamicarrivalofbiddersandaddressesonlinesingleauctionmechanismsbasedontheideaspresentedin[45].Thebiddersintheseauctionsplacetheirbidstocompeteforaxednumberofspectrumunits.However,thesupplyuncertaintyi.e.,thedynamicsinspectrumavailabilityhasnotbeenanalyzedinthesestudies.Ontheotherhand,thestudyin[114]andTORA[63]analyzethesingleauctionmechanismconsideringthedynamicsinspectrumavailabilitywhilethenumberofbiddersisxedthroughouttheauction.TODA[118]presentsadoubleauctionmechanismconsideringstochasticarrivalofuserswithoutconsideringspectrumreusabilitywhichisoneofthedistinctfeaturesofspectrumauction.Amorerecentpaper,LOTUS[20]considersadoubleauctionmodelconsistingofaxednumberofuserswithdynamicdemandandxednumberofspectrum.Althoughthisworkconsidersadoubleauctionwithdynamicuserdemand,thebiddershavenotransmissiondeadlinesandthenumberofsellersisxed.Asaresult,LOTUSfailstosatisfythetruthfulnesspropertywhenitisappliedinanonlinesettingsinceusersmaygainbenetsbylyingabouttheirdeadlines.Incontrast,weinvestigateauctionbasedcollaborationmodelsinwhichbothspectrumavail-abilityanddemandarestochasticthroughouttheauctions,andusers'urgencyfortransmissionisalsorandom.Werstanalyzethisdynamicsettingfromthesingleauctionperspective,discussitschallenges,anddevelopthetruthfulmechanism.Wefurtherextendouranalysistoanonlinedoubleauctionsettingwherebothbiddersandsellersstochasticallyjointheauctionwithdifferentdeadlinesandvaluations.Anonlinedoubleauctionbetterrepresentsthesecondaryspectrummar-ketthanthesingleauctionsincedoubleauctionsaccommodatediversityinsellers'reservepricesandofferexibilitytotheauctiondesign.Inpresenceofsuchdiversity,anauctioneerhastomakeonlinedecisionsonspectrumallocationandpricingwithouttheknowledgeoffutureparticipantsandtheirdemandandsupply.Thisonlinefeaturemakesthespectrumauctioneasilyvulnerabletobidanddeadlinemanipulation.Abidderorsellermaygainbenetoverothersbymisreportingits124arrival,deadline,oritsvaluation.Therefore,themechanismmustbeholdthetruthfulnessproperty.Additionally,themechanismmustsupporttheallocationofsamespectrumunittonon-interferingbidderstoimprovethespectrumutilizationrate.Ourgoalhereisthustoexploresuchdynamicsettingsanddesignonlinemechanismsforbothsingleanddoubleauctionsthatconformtotheserequirements.Summaryofourcontributionsinonlineauctionsettingsis:Westudythespectrumallocationproblemtosecondaryusersinanauctionsettingwhereidlechannelsarrivestochasticallyandthetotalchannelsupplyisunknown;andbidderswithrandomlifetimes(transmissiondeadline)arriveattheauctionstochasticallywiththetotalnumberofbiddersbeingunknown.Weidentifythechallengesassociatedwiththedynamicauctionmodelandshowthevulnerabilitiesofexistingresearchinsuchsettings.Wepresentouranalysisofthisdynamicsettinginthreesteps.Intherststep,allbidders(andsellers)havethesamevaluations.Inthesecondstep,werelaxthisrestrictionandconsiderdiversityinbidders'valuations.Inthethirdstep,wealsoconsiderthesellerswithdifferentvaluations.Ouranalysisoftheseauctionsettingsisbasedonanendogenouspriorityvaluefunctionthatdeterminesthepriorityofabidderateachperiodgivenitsvalueandurgencyfortransmissioniftheauctioneerhasdistributionknowledge.Weprovethatourproposedmechanismadherestotruthfulnessandindividualrationality.Consequently,wepresentthreeauctionalgorithms.Therstalgorithmisderivedbasedonthepriorityfunctiontodevelopadistributionawaretruthfulsingleauctionmechanism.Thesecondalgorithmisalsoderivedbasedonthepriorityfunctionanddevelopadistributionawaretruthfuldoubleauctionmechanism.Finally,wepresentadistributionunawaremech-anismforatruthfuldoubleauction.Weintroduceabid-independent`debtfactor'thatadjuststhepaymentamountofawinnerdependingonthenumberofusersinterferingwithitover125Figure6.1:Auctionwithdynamicbidderandsupplyitslifetime.Theusersgothroughacandidatescreeningphasefollowedbyadebtcalculationphase,andnallywinnersareselectedadheringtopricingrulesinthealgorithm.Finally,wepresentsimulationresultstoanalyzetheperformanceofthesealgorithmsunderdifferentauctionsettings.Weevaluatetheefciencyoftheproposedmechanisms.Wecom-paretheperformanceoftheauctionmechanismswithanoff-linemechanismandexistingworke.g.Topaz[30]intermsofrevenue,demandsatisfaction,andspectrumutilization.6.1OnlineDynamicAuctions
Inthissection,weexplainthedifferentcomponentsoftheauctionmodelandhighlightthedesignchallengestoachieveatruthfulonlineauctionmechanism.
6.1.1TheAuctionEntities
Weconsiderperiodicspectrumauctionswhereusers'arrivalsandspectrumavailabilityoccuronlyatthebeginningofaperiod(seeFig.6.1).Theperiodlengthisxedacrosstime.Thethreeentitiesinvolvedinaspectrumauctionareprimaryusersassellers,secondaryusersasbidders,andanauctioneer.Sellers:Primaryusersputtheirunusedspectrumresourcesforsaleattheauctioninunitsofxedspectrumbandwidth.Thesalesunitsareidentical;however,eachsellerhasitsownvaluation126ofitsspectrumunits.Aspectrumunitremainsattheauctionforsaleforoneperiodonly.Asalesrequestofatypicalsellerjcontainsitsreserveprice,commonlyreferredtoasthe`ask'thatdenotestheminimumpriceasellerwillacceptperspectrumunit.Werepresentasalesrequestwith˚p
j=(aj)whereajdenotesthesellerj'saskforitsspectrumunit.Aseller'sutilityiscalculatedbysubtractingitsvaluefromthepaymentitreceivedattheauc-tion.So,sellerj'sutilityUj=xj( pj-vj)wherexj2f0;1gdenoteswhethersellerjhaswon(xj=1)ornot(xj=0),vjdenotesseller'svaluation,and pjdenotessellerj'spaymentwhenitwinsintheauction.Bidders:Secondaryuserssubmittheirspectrumrequirementsintheformofbidrequests.Abidrequestofabidderiisrepresentedas˚i=(gi;oi;di;bi)wheregidenotesitslocationinfor-mation,oidenotesthetimeofarrivalattheauction,di(oi)denotesthetransmissiondeadline,i.e.,themaximumtimeabidderstaysintheauction,andbidenotesthemaximumvalueabidderiswillingtopayforonespectrumunit.Eachbidderhasunitdemandandhasnoparticularpreferenceoveranyspectrumunitsinceallunitsareidentical.Abidder'slifetimedenotesitstransmissiondeadline,anditisexpressedintermsofnumberofperiodsabiddercanstayintheauctiontowinaspectrumunit.Ifthebiddercannotwinbyitsdeadline,itexitstheauction.Thelifetimeliofabidderiwitharrivaltimeoianddeparturetimediisexpressedasli=dioi+1.Bidderi'sutilityisUi=xi(vi si)wherexi2f0;1gdenoteswhetherbidderihaswon(xi=1)ornot(xi=0),videnotesthebidder'svaluation,and sidenotesbidderi'spaymentwhenitwinstheauction.Auctioneer:Theauctioneerisresponsibleforconductingper-periodauctions.Ateachperiod,theauctioneerappliesanalgorithmtoselectwinnersanddeterminetheirprices.Theauctioneer'sutilityisreferredtoastherevenueitmakesfromtheauctionthatiscalculatedbysubtractingthetotalamountofsellers'paymentfromthetotalamountofbidders'payment.Theauctioneer's127utility,UAisthusdenedas,UA=Pi si-Pj pjwhere sirepresentsthepaymentreceivedfrombidderiand pjdenotesthepaymentmadetosellerj.6.1.2AuctionProperties
Denition1AnonlineauctionmechanismistruthfulifandonlyifnobiddericanimproveitsutilityUibyreportingb0
i6=vi,orfalselyreportingitslocationg0i6=gi,orarrivaltimeo0
i6=oi,ordeadlined0
i6=di,oranycombinationofthemandnosellerjcanimproveitsutilityUjbyreportingitsaska0
j6=vj[30].Denition2Anauctionmechanismisfiexanteweaklyindividualrationalflifallagents'expectedutilityfromthemechanismwhenenteringintotheauctionarenon-negative.Anonlineauctionmechanismisfiexantestronglyindividualrationalfliftheexpectedutilityofallagentswhenen-teringintotheauctionarepositive.Anonlineauctionmechanismisfiexpostweaklyindividualrationalflifallagents'realizedutilityfromthemechanismisnon-negative.Anonlineauctionmechanismisfiexpoststronglyindividualrationalflifallagents'realizedutilityfromthemecha-nismispositive.Thisimpliesthatforanybidderi,Ui0andforanysellerj,Uj0.Denition3Thebudgetbalancereferstonon-negativeutilityoftheauctioneer.Anauctionmech-anismisbudgetbalancedifineachperiodthetotalpaymentsreceivedfromallbuyersisnolessthanthetotalamountspaidtoallsellers.ThisimpliesthattheutilityoftheauctioneerUA0.6.1.3DesignChallenges
Anonlineauctionindynamicenvironmentsposesseveralchallengesindesigningthemechanism.Wepresentthreekeydesignchallengesasfollows:128(a)Onlinedecisionwithdemandandsupplyuncertainty:Theprimarychallengeistotakeanonlinedecisionwithoutknowingtheexactnumberofsupplyandbidderinfutureperiods.Themechanismmusttakeintoconsiderationthetradeoffbetweenpresentopportunityandfutureuncertaintyforefcientspectrumallocation.(b)Spectrumreusability:Unliketraditionalauctions,samesupply(i.e.,spectrum)canbesoldtomultiplenon-interferingbiddersinspectrumauctions.Thisuniquepropertymakesitmorechallengingtoachieveatruthfulmechanism.(c)Timeandbidbasedcheating:Duetotheonlinedemandandsupplynatureofthespec-trumauction,biddersmayreporttheirbids,arrivaltime,anddeadlineuntruthfully,andgainadvantageintheformofincreasedutilities[30].Theauctionmechanismmustprovidesafe-guardagainstanysuchattemptofcheatingfrombidders.6.1.4Illustration
Beforeexplainingourauctiondesign,wedemonstratehowbidderscangainadvantagebymisre-portingtheirinformatione.g.theirarrivaltimesordeadlinesinanonlinedynamicauctionsetting.Usingillustrativeexamples,weshowthatexistingstaticorpartiallydynamicmodelscannotensuretruthfulnessinsuchcases.Forthesakeofsimplicity,wehaveonlyshownbidderswithdifferentvaluationsinthefollowingexamples.Westartwithasimpleexamplewhereeachparticipantreportstruthfully.BiddersA,B,andCarriveattimet1andbid$100,$80,and$50respectively.Oneunitofspectrumalsobecomesavailableatthesametime.Weassumethatallthreebiddersareinterferingtoeachother.Thelifetimeofbiddersis[t1;t4),[t1;t2),[t1;t5)respectively.Weapplystaticauctionrulespresentedin[142]wherethehighestbidderswinandthepriceisdeterminedbythenexthighestlosing129Figure6.2:Applyingstaticauctionrules[142]indynamicenvironmentsbidderinitsneighborhood.Accordingly,bidderAwins,andpays$80.Attimet2,Bleavestheauction,andattimet3,anotherspectrumunitbecomesavailable.So,Cwinsnextandpays$0.Finally,anotherspectrumunitarrivesatt6butremainsunsold.So,theauctionefciencybecomes$150($100+$50),revenuebecomes$80($80+$0),bidders'satisfactionratiobecomes2=3,andspectrumutilizationratebecomes2=3.Fig.6.2demonstratesthearrivalanddepartureofbiddersintheauctionandalsonotesdownthedecisionmadebytheauctioneerateachperiodfollowingrulesin[142].Next,weshowthatabiddercanlieaboutitsarrivaltimeandincreaseitsutilitywhilestaticrules[142]areappliedinanonlinedynamicenvironment.Inthesamepreviousexample,considerbidderAreportsitsarrivaltimeatt3insteadoft1(t3>t1)andthusavoidscompetitionwithhighervaluedbidders.Asaresult,bidderBwinsatt1,pays$50,andleavestheauction.Attimet3,bidderAwinsandpays$50,andthusincreasesitsutilityby$30.Again,thereisnotradeattimet6.So,thebiddersatisfactionratioandspectrumutilizationrateremainunchanged,butefciencyandrevenuebecome$180($100+$80)and$100($50+$50).Fig.6.3demonstratesthisauctionscenario.Fromthisinstance,itisclearthatstaticauctionrulescannotbeappliedtoonlineauctionsindynamicenvironments.Finally,weselectapartiallydynamicmodelTopaz[30]andshowhowabiddermisreportsitsinformationandincreasesitsutilityindynamicenvironments.Inthesameexample,consider130Figure6.3:Latearrivalmanipulationbyabidderwhileapplyingstaticauctionrules[142]Figure6.4:LatedeparturemanipulationbyabidderwhileapplyingTopaz[30]thatbidderAreportsitsdeadlinet7insteadoft4(t4<t7).AccordingtoTopazrules,thepriceisdeterminedattheendofawinner'sdeadlinethatissettotheminimumofthecriticalpriceatanyperiodoveritslifetime.Byreportinglatedeadline,Awinsaspectrumunit,pays$0andincreasesitsutilityto$100.Theauctionrevenuereducesto$0whileallotherparametersremainunchanged.Fig.6.4demonstratesthedecisionmadebytheauctioneerateachperiodfollowingrulesin[30].Therefore,theserulescannotensuretruthfulness.Fromtheabovedemonstration,itisclearthatexistingstaticorpartiallydynamicmodelbasedmechanismscannotensuretruthfulnessinfullydynamicenvironments.Next,wediscussthede-signprinciplesbehindourproposedmechanismandexplainitscomponents.1316.2AuctionDesign
Topreventanyattemptofstrategicmanipulationofinformation(explainedinprevioussection),anauctionmechanismmusttakeintoconsiderationthepossiblewinningopportunityofabidderinfutureperiodsofitslifetime.Asexplainedin[60],biddersinsequentialauctionsbidtheirvaluesfortheobjectdiscountedbythefioptionvaluefloffutureauctions.Similarlyinthiscase,sinceabidderhastheoptionofwinningaspectrumunitinlaterperiodsofitslifetime,abidder'svaluationofaunitatearlierperiodsisdifferentfromitsactualvaluation.Therefore,anauctioneermustconsiderabidder'soptionvalueoffutureperiodswhiledeterminingitsvalueatpresentperiodinordertoassuretruthfulreportingofvalues.Accordingly,wederiveafunction,Prankthattakesintoconsiderationthefioptionvalueflatfutureperiodsandgivenabidder'sinformation,thisfunctiondeterminestherankofabidderofwinningspectrumatanyperiodofitslifetime.Werefertothisrankvalueasits`priority'andtothePrankfunctionas`priorityfunction'.Thispriorityvaluealsorepresentstheamountthebidderiswillingtopayinthatperiod.Anauctioneerusesthepriorityvaluesofbiddersinsteadofitsbidduringspectrumallocation.Thisconsiderationinprioritycalculationpreventsabidderfrommisreportingitsbidandattemptinganykindoftimebasedcheating.WeexpressthepriorityofabidderiofvalueviattimetasafunctionofthefollowingparametersŠthesetofactivebiddersA(t),theauctionstatefromtheviewpointofbidderi,andthesetofdistributioninformationF.i;t=˝(vi)=Prank(A(t);˙i(t);F)(6.1)where˝=dit+1PrankworksonthebasisofthisgenericEqn.6.2whichstatesthatabidder'spriorityvalueat132anyperiodisequaltoitstruevaluationsubtractedbytheexpectedpayofffromremainingperiodsofitslifetime.˝(vi)=vi˝1Xx=10
@˝Yy=x+1Ly(vi)1
AE[ˇx(vi)](6.2)Here,˝(vi)denotesthepriorityvalueofabidderofvalueviwith˝remainingperiodsinitslife-time.Also,E[ˇ˝(vi)]andandL˝(vi)denotebidderi'sexpectedpayoffandthelosingprobabilitywith˝remainingperiodsofitslifetimeli.Next,wewillderivedifferentcomponentsofthepriorityfunction.WeassumethattheauctioneerknowsthedistributionofspectrumavailabilityFm,thedistribu-tionofarrivalofbiddersFn,andthedistributionofbidders'lifetimeFk.Throughoutouranalysis,weassumethatthesupportofdistributionFkisf1;:::;kgˆN,andthesupportofdistributionFmisfm;:::;mgˆN.6.2.1Prank-I(SameValuationCase)
Prank-Iassumesthatallbiddershavethesamevaluation(i.e.8i2A(t)vi=vandsellersdonothaveanysetvaluefortheirunits.So,thepriorityfunctioncanbesimpliedto˝(v)=v˝1Xx=10
@˝Yy=x+1Ly(v)1
AE[ˇx(v)]:(6.3)Here,˝(v)denotesthepriorityvalueofabidderofvaluevwith˝remainingperiodsinitslifetime.Also,E[ˇ˝(v)]andandL˝(v)denotebidderi'sexpectedpayoffandthelosingprobabilitywith˝remainingperiodsofitslifetimeli.Ifabidderiwith˝periodstolivewins,thewinningpriceissetbythepriorityrankofanybidderj2A(t)withyperiodstolivewhereky˝andkdenotesthemaximumlifetimeof133anybidder:E[ˇ˝(v)]=k+1Xy=˝vy(v)Pr si=y(v):(6.4)Here, siisthepricebidderipayswhenitwins.TheprobabilityPr si=y(v)iscalculatedbyconsideringthreepossiblecases.First,ifthetotalnumberofbiddersislessthanthenumberofavailablespectrumunits,thebidderwinsatnocost.ConsideringmunitsofspectrumavailablefollowingdistributionFm,weexpresstheprobabilityofsuchaneventasfollows:Pr( si=0)=Pr0
@m>kXx=1nx1
A=1Fm0
@kXx=1nx1
A+fm0
@kXx=1nx1
A=1Nk(6.5)whereNy=FmPy
x=1nxfmPy
x=1nx.Second,ifthetotalnumberofoldestbidders(bidderswithonlyoneperiodtolive)aremorethanthenumberofsupplyitems,thebidderpaysthehighestvalueandearnszeroutility.So,thepaymentissetbythepriorityrankofabidderj2A(t)with1periodtolive:Pr( si=1(v))=Pr m<1Xx=1nx!=Fm 1Xx=1nx!fm 1Xx=1nx!=N1:(6.6)Apartfromthersttwocases,thewinningpriceissetbyabidderj2A(t)andisgivenby:Pr si=y(v)=Pr0
@y1Xx=1nxm<yXx=1nx1
A="Fm yXx=1nx!fm yXx=1nx!#2
4Fm0
@y1Xx=1nx1
Afm0
@y1Xx=1nx1
A3
5=NyNy1:(6.7)134LettingN0=0,Nk+1=1andcombiningallthreecases,werewritethepdfofthewinningpriceasPr si=y(v)=NyNy1:(6.8)Eqn.6.4canthenbesimpliedtoE[ˇ(˝)]=k+1Xy=˝vy(v)NyNy1=v(1N˝1)k+1Xy=˝y(v)Cy;(6.9)whereCy=NyNy1.Next,wecalculatethelosingprobabilityofabidderiwith˝periodstolive.Thelosingproba-bilitydependsonthepopulationofbidderswhoareolderthanthebidder(i.e.,havefewerperiodstolive).Therearetwocomponents.Therstcomponentdeterminestheprobabilitythatthenum-berofavailablespectrumunitsisstrictlylessthanthenumberofbidderswith˝periodstolivebutgreaterthanthenumberofbidderswith˝1periodstolive.Thesecondcomponentdealswiththecasewhentherearenotenoughunitstoprovideallbidderswith˝periodstolive,andsoeachofthemareequallylikelytowinorlosetheauction.L˝(v)=Pr ˝1Xx=1nx<m<˝Xx=1nx!P˝
x=1nxmn˝+Pr m˝1Xx=1nx!=˝+Fm ˝1Xx=1nx!:(6.10)Here,˝denotesthelosingprobabilityofbidderiwith˝periodstolivewhilethewinningpriceissetbythepriorityrankofabidderjwith˝periodstolive.Summarizingtheaboveequations,
135werewriteEqn.6.3as:˝(v)=v˝1Xy=10
@˝Yx=y+1Lx(v)0
@v1Ny1k+1Xx=yx(v)Cx1
A1
A:(6.11)Finally,bidderi'spriorityrankwith1˝kperiodstoliveisexpressedasaweightedsummationofitspriorityrankindifferentperiodsfromthersttothelastperiod:˝(v)=v2
41˝1Xy=10
@˝Yx=y+1Lx(v)1Ny11
A3
5+˝1Xy=10
@yXz=1˝Yx=z+1Lx(v)1
Ay(v)Cy+kXy=˝0
@˝1Xz=1˝Yx=z+1Lx(v)1
Ay(v)Cy:(6.12)Solvingk1polynomialequations,wedeterminethepriorityrankingbidofabidderiinallkperiods.6.2.2Prank-II(SingleAuctionCase)
Prank-IIassumesthatbiddershavedifferentvaluationsandtheauctioneerisawareofthedis-tributionofvaluationFv.Abidder'struevaluationofasinglespectrumunitisconsideredtobeadiscreterandomvariablefromtherangefv;:::;vgˆNfollowingcdfFv.Weexpressthepriorityofabidderiofvalueviattimetasafunctionoftheseparameters.i;t=˝(vi)=Prank-II(A(t);˙it;Fv;Fm;Fn;Fk)(6.13)where˝=dit+1Here˙it(n;m)denotestheauction`state'concerningtherivalsofuseriattimet,anditisrepresentedbyak-dimensionalmatrixn=[nk;:::;n1]andthenumberofspectrumunits(m)136availableinthatperiod.Here,nxdenotestheexpectednumberofbidderswithxperiodstolivewithintheinterferencerangeofuseri.Notethat,˙itchangesdependingonuserlocationandtherivalbidders'densityinthatarea.Next,wecalculatethesetwosubcomponentsinthepriorityfunction(seeEqn.6.2)-expectedpayoffandlosingprobability.Abidder'sexpectedpayoffatanygivenperiodwillbethesummationofexpectedpayoffconditioningontheavailablespectrumunitsmmultipliedbytheprobabilityoftheavailabilityofthatnumberofunits(fm).E[ˇ˝(vi)]=mXm=mfmE[ˇ˝(vijm)](6.14)Theconditionalexpectedpayoff,E[ˇ˝(vijm)]dependsonthewinner'spaymentwhichcanbeanyvaluebetween0anditspriorityvalueatthatperiod˝(vi)(sincepriceissetbyhighestlosingbidder).Accordingly,weexpressE[ˇ˝(vijm)]intermsoftheprobabilityofallpossibleprices.Pr(X(m)=z)denotestheprobabilitythatmthhighestpriorityvalueisequaltozintheremainingpopulation.E[ˇ˝(vijm)]=˝(vi)Xz=0(viz)Pr( si=z)=˝(vi)Xz=0(viz)PrX(m)=z(6.15)ThepricingprobabilityPrX(m)=zcanbeexpressedasdifferencesbetweencdfsF(m)X(z)andF(m)X(z1).F(m)X(z)denotesthecdfofthehighestpriorityvalueamongtheremainingpopulation.SimplifyingtheresultsinEqn.6.15,weobtainasfollowsE[ˇ˝(vijm)]=(vi˝(vi))F(m)X(˝(vi))+˝(vi)1Xz=0F(m)X(z)(6.16)137Similarly,wecalculatethelosingprobabilityofabidderwith˝remainingperiodsconditioningonthenumberofavailablespectrumunits.L˝(vi)=mXm=mfmL˝(vijm)(6.17)Here,L˝(vijm)denotestheprobabilitythatabidderofvalueviwith˝periodstolivedoesnotwintheauction.Thisprobabilityisequaltotheprobabilitythatthepriceishigherthanthebidder'spriorityvalue˝(vi).L˝(vijm)=1PrX(m)˝(vi)=1F(m)X(˝(vi))(6.18)BothEqns.6.16and6.18dependonthecdfvalue,F(m)X(z)thatdenotesthecdfofthem-thhighestpriorityvalueamongtheremainingpopulationofactivebidders.F(m)X(z)=PrX(m)z=m1Xi=0Pr(N(z)=i)(6.19)Here,Pr(N(z)=i)denotestheprobabilitythatthereareexactlyibiddersinthepopulationwithpriorityvaluegreaterthanz.Sincethepopulationconsistsofbidderswithdifferentremainingperiods,theseibidders(withpriorityvaluegreaterthanorequaltoz)maycomefromanyofthesebiddergroups.Therefore,wetakeallpossiblecombinationsofibidderswithpriorityvaluegreaterthanorequaltozfromthepopulation.Pr(N(z)=i)=f(a)Pr(N1(z)=a1):::PrNk(z)=aksuchthat,kX
j=1aj=i(6.20)Here,f(a)representstheprobabilityofhavingthisexactcombination[a1:::ak]fromkgroups.138PrNj(z)=ajdenotestheprobabilitythatthereareexactlyajbidders(withjremainingperiodsintheirlifetimes)whosepriorityvalueisgreaterthanz.Here,Fj(z)denotesthecdfofpriorityvalueofbidderswithjremainingperiodsoftheirlifetimes.PrNj(z)=aj=njaj1Fj(z)ajFj(z)njaj(6.21)Finally,wecombinetheresultsfromtheseEqns.6.16,6.18,and6.21intoEqn.6.2togetthepriorityvalueofabidderofvalueviwith˝remainingperiodsofitslifetime.BasedonthispriorityfunctionPrank-II,wecalculateprioritiesofbiddersofdifferentvaluesandatdifferentperiodsoftheirlifetimes.ThevaluesarerecordedinaprioritytablePT.6.2.3Prank-III(DoubleAuctionCase)
Inadditiontobidders'valuations,Prank-IIIassumesthataseller'svaluationofasinglespectrumunitisadiscreterandomvariableonfa;:::;agfollowingcdfFawhichisknowntotheauctioneer.Thepriorityofabidderiofvalueviattimetbecomesi;t=˝(vi)=Prank-III(˙it;Fn;Fk;Fv;Fm;Fa)where,˝=dit+1:(6.22)Here˙it(n;m)denotestheauction`state'concerningtherivalsofuseriattimet,anditisrepre-sentedbyak-dimensionalmatrixn=[nk;:::;n1]andthenumberofspectrumunits(m)availableinthatperiod.Here,nxdenotestheexpectednumberofbidderswithxperiodstolivewithintheinterferencerangeofuseri.Notethat,˙itchangesdependingonuserlocationandtherivalbidders'densityinthatarea.139WeusethesameEqn.6.2tocalculatethepriorityofbiddersandsellers.Thepriorityofabidderatthelastperiodofitslifetimeisequaltoitsvalue.Sinceeachsellerlastsonlyoneperiod,thepriorityofasellerisalwaysequaltoitsvalue.Forwinnerselection,wefollowedamodiedapproachproposedbyMcAfee[88].McAfeeproposedatruthfuldoubleauctionmechanismforstaticsettings.PleaseseeSec.2.1.7fordetailalgorithm.ItcanbeshownthatMcAfeerulescannotensuretruthfulnessindynamicsettings.Fromnowon,werefertothismechanismas`MRules(T,S0)'.Asstated,abidder'sutilitydependsonthepriceitpaystotheauctioneer.Abidderiwith˝remainingperiodswinsifthewinningpriceatthatperiodislessthanorequaltoitspriorityvalue˝(vi).So,theexpectedutilityE[ˇ˝(vi)]canbeexpressedasE[ˇ˝(vi)]=˝(vi)Xz=0(viz)Pr( si=z):(6.23)Here,Pr( si=z)denotestheprobabilitythatthebidderi'spaymentisequaltoz.Thewinner'spaymentinagivenperiodisdeterminedaccordingtoMcAfeerules(seeinSec.2.1.7)whichdependsontheorderstatisticsofthedistributionofvaluationsofbiddersandsellers.Therefore,wecalculatetheprobabilityoverallpossiblematchesandtheexpectedsumoftheseprobabilitiesdenestheprobabilityPr( si=z).Letusrepresenttheh-thhighestpriorityvalueandh-thlowestaskasX(h)andY(h)intheauctionrespectively.Pr( si=z)=mXm=mfmmXh=2PrX(h)=zPrY(h)zjmPrY(h+1)>zjm=mXm=mfmmXh=2PrX(h)=zF(h)Y(zjm)1F(h+1)Y(zjm)(6.24)Thersttermfmdenotesthepdfofspectrumavailabilityatanauctionperiod.ThesecondtermPrX(h)=zintheaboveequationdenotesthepdfoftheh-thorderstatisticofbidders'140prioritieswhichcanbecalculatedusingEqn.6.19.ThethirdandforthtermsdependonF(h)Y(zjm)thatdenotestheconditionalcdfoftheh-thlowestorderstatisticofsellers'asks.WecalculatethecdfF(h)Y(zjm)conditioningonthenumberofavailablespectrumunitsasF(h)Y(zjm)=mhX
j=0(1Fa(z))j(Fa(z))mj:(6.25)CombiningEqns.6.24,6.25,6.19,wecalculateprioritiesofabidderatdifferentperiodsofitslifetimeandrecordtheminaprioritytable,PT.6.3DistributionAwareAuctionAlgorithms
Inthissection,wedeviseauctionmechanismbasedonthepriorityfunctionsdiscussedinSec.6.2.Wepresenttwoalgorithmsfocusingonsingleanddoubleauctionsrespectively.6.3.1SOADE:OnlineSingleAuctionAlgorithm
WeexplaintheauctionmechanismSOADE(SecondaryOnlineAuctioninDynamicEnvironments)constructedaroundthepriorityfunctionPrank-II.Ateachperiod,theauctionmechanismcon-sistsoffoursteps.Step1(prescreening):Inthisstep,abidder'sidentityisvalidatedbytheauctioneerbeforeitsentrancetotheauction.Eachbidderisrequiredtoberegisteredofinewithacentralizeddatabasethattheauctioneerhasaccessto.Onsuccessfulregistration,bidderiisassignedanencryptionkeyKi.Anylightweightencodingalgorithme.g.Paillier'shomomorphicencryption[51]canbeusedforthispurpose.Anewbiddersubmitsitsencryptedbidrequesttotheauctioneerwithitscredentialsanduponapprovalfromtheauctioneer,itenterstheauction.141Table6.1:AlgorithmSOADE:SecondaryOnlineAuctioninDynamicEnvironmentsscreenandvalidatenewbidderswithbidrequestsB=;foreachactivebidderi2A(t)dogeti;tfromPTupdateB=B[figendfor
B=sort(B),C=;whileB6=;doi=Top(B)if(ch=NextAvailable(i,Gi(t)))6=0thenassignchtoi,C=C[figendif
B=Bnfigendwhile
whileC6=;doi=Top(C)if(q=NotAllocatedNeigh(i,Gi(t)))=0then i=0else i=q;tendif
C=CnfigsendanencryptedmessageKi(i; i)tobidderiendwhileStep2(ranking):Atthebeginningofeachperiodt,theauctioneerconsidersonlytheactivebidrequestsinA(t)whereA(t)=f˚ijoitdig.NewbiddersareaddedafterprescreeningandtheconictgraphG(t)isupdatedaswell.TheconictgraphG(t)representstheinterferencerelationshipamongtheactivebiddersattimetandGi(t)representthelistofactivebidderswhoarewithintheinterferencerangeofuseriattimet.Gi(t)=fjjG(i;j)=1^i;j2A(t)g(6.26)Notethattheconictgraphisupdatedatthearrivalofnewbidder(also,atthedepartureofawinnerorlosingbidder).Foreachactivebidder,itspriorityvalueisaccessedfromfromthepriority142table,PTwhichispopulatedbasedonthefunctionPrank-II(explainedinSection6.2.2).TheactivebiddersarethenstoredinBinanon-increasingorderoftheirpriorityvalues.Biddersareconsideredforspectrumallocationinthisorder.Step3(allocation):TheallocationprocessstartswithanemptysetC.Foreachbidderi2B,theauctioneerchecksthelistofitsinterferersGi(t)andndsthelowestindexchannelthatisnotassignedtoanyofitsinterferers.Here,Gi(t)denotesthelistofactiveusersinterferingwithbidderi.Ifthereisanunassignedchannelavailable,itassignsthechannelchtouserianditismovedinC.ThefunctionNextAvailable(i,Gi(t))takesuserianditsinterfererlistGi(t)asinput,andreturnsthelowestavailablechannelindex.Step4(pricing):Inthenalstep,thewinningpriceisdeterminedforeachwinner.Eachwinneri2Cpaystheamountequaltothehighestpriorityvalueofabidderj2Gi(t)thathasnotwontheauction.Iftherearemorechannelsthanthenumberofinterferers,theuserwinsatnocost.ThefunctionNotAllocatedNeigh(i,Gi(t))searchesthroughtheneighborlisttondthehighestprioritybidderfromitsneighborhoodGi(t)thathasnotbeenallocatedanychannel.Abidderleavestheauctionimmediatelyifitwinsaspectrumunitorstaysintheauctionuntilitslifetimeexpires.Theauctioneersendsanencryptedmessagetothewinnercontainingthewinneridandpaymentamount.Thewinnerdecryptsthemessage,paystheprice,andusesthespectrum.Anyotheruseroverhearingthemessagecannotdecryptthemessage.Thus,thewinningpriceandwinneridentityarenotrevealedtoall.AllthestepsoftheauctionmechanismissummarizedinTable6.1forconvenience.Example:ToillustratehowthealgorithmworkswesolvetheEqns.forn˘Poisson(2),m˘U[0;2],andk˘U[1;3],anddeterminetheprioritiesofbidders.WereenacttheexamplescenarioinFig.6.2.Attimet1,theeffectivebidofbidderA,B,andCwillbetheirpriorityvalues$58,$80,143and$41respectively.AccordingtoAlgorithmSOADE(Table6.1),bidderBwinsandpays$58.Similarly,theeffectivebidofbidderAandCattimet2are$67and$43.So,bidderAwinsandpays$43.Notethat,bidderBwinsbeforebidderAalthoughB'sactualvalueissmallerthanA's.ThisisbecauseB'spriorityishigherthanA'spriorityatt1.Auctionefciencyis$180($100+$80)andrevenueis$101($58+$43).6.3.2AnalysisofSOADE
WeanalyzethecharacteristicsofthepriorityvaluefunctionPrank-IIandprovetheusefulprop-ertiesoftheauctionmechanism.
Theorem1Thepriorityvalueofbidderiatdifferentperiodsinitslifetimeliismonotonici.e.,li(vi)1(vi).Byconstruction,foranyperiodinitslifetime,abidder'sexpectedpayoffE[ˇ˝(vi)]0.Thepriorityvalueofabidderatanyperiodiscalculatedbysubtractingthecumulativeexpectedpayoffofremainingperiodsfromitstruevaluation,andsinceeachremainingperiodcontributesanon-negativecomponenttothetotal,li(vi)1(vi).Theorem2Thepriorityvaluefunction˝(v)isastrictlynon-decreasingstepfunctionwithcon-caveenvelopewithrespecttov.Letusconsidertwobiddersofvaluev1andv2and˝=1wherevv1<v2v.Weknowthatatthelastperiodofitslifetime,abidder'spriorityisequaltoitstruevaluation.Therefore,1(v1)<1(v2).Next,weconsiderthecaseof˝=2.2(v)=vE[ˇ1(v)]=vvXz=0(vz)Pr( si=z)144Duetotheirdifferentvaluations,theexpectedpayoffatthelastperiodoftheirlifetimewillbedifferent.Giveneverythingremainssame,thehigherthevaluationofabidder,thelesscompetitionitfacesfromtheyoungbidders.Thisimpliesthatabidderwithhighervalue(v2)expectshigherpayoffthanthatofabidderwithlowervalue(v1)atthesameperiod.Asaresult,thepriorityofabidderofvaluev2cannotbelowerthanthatofabidderofvaluev1.So,2(v1)2(v1).Asthevalueincreases,thechangeinpriorityvalueofbiddersattheirsecondlastperiodwithrespecttotheirvaluesdecreases.Bythesameargument,wecangeneralizethestatementfor˝>2.Theorem3TheproposedauctionmechanismSOADEistruthful.Letusconsiderbidderiwithamanipulatedbidrequest(g0i;o0
i;d0
i;v0i),itsremaininglifetimeattimet,˝0=d0
it+1anditspriorityvalueattimetis˝0(vi).Themanipulatorcanlieaboutoneormoreparametersinitsbidrequest.Weprovethatlyingaboutanyofitsinformation(location,arrivaltime,value,anddeadline)doesnotbringanybenettothemanipulator.(a)o0
i>oi:Thismeansthatamanipulatorreportslatearrivaltimeandpretendsnottobeavailablewhenitisactuallyactive.Themanipulatorcannotlearnabouttheauctionstateduringthoseperiodssincethewinnerinformationisencrypted.So,themanipulatorwillnothaveanyaddedadvantageforlaterperiods.Onthecontrary,itwillmissanopportunitytowinspectrumintheskippedperiods.Therefore,reportinglatearrivalwillnotbenetthemanipulator.(b)o0
i<oi:Thepriorityvalueofabidderisalwaysdeterminedbasedonitsvalueanddeparturetime.Therefore,claimingearlyarrivaltimeinbidrequestwillnotchangeitspriority.Also,ifthemanipulatorreportso0
i<oi,itpretendstobeactiveinaperiodwhenitwasnotactuallypresent.So,evenifthemanipulatorisconsideredasawinneratthatperiod,itcannotuse145thespectrumunit.Furthermore,itwillloseanyopportunitytowinitinlaterperiods.So,reportingearlyarrivalwillnotbenetthemanipulator.(c)d0
i>di:Therearepossibletwocaseswhileamanipulatorreportslongerdeadline.Case1:themanipulatorwinstheauctionatd0
it>dii.e.,aftertheactualdeadlinehasexpired.Althoughthemanipulatorwins,ithasnouseofthespectrumunitbutstillhastopay.Thisresultsinnegativeutility.Case2:themanipulatorwinsattdi.Since˝<˝0,accordingtoLemma1,˝(vi)˝0(vi).Ifamanipulatorwinsanauctionwithpriorityvalue˝0(vi),itspaymentpmustbelessthanorequaltoitspriorityvalue.So,therelationshipholdsasfollows:˝(vi)˝0(vi)p.Ifthemanipulatorwins,thetruthfulbidderalsowinsandachievesthesameutility.Therefore,abidderwillnotgainanyadvantagebyreportingd0
i>di.(d)d0
i<di:Whenamanipulatorreportsearlierdeadline(d0
i<di)weneedtoconsiderthreecases.Case1:themanipulatordoesnotwinbyt=d0
i.Althoughitsactualdeadlineisnotover,themanipulatorwillnolongerbeconsideredintheauctionfromthenextperiod.Hadthebidderreporteditsdeadlinetruthfully,itcouldhavewoninlaterperiodsd0
i<tdiandcouldhaveachievedpositiveutility.Case2:themanipulatorwinsattd0
iand si˝(vi).Thisimpliesthatthebidderwouldhavewonifitreporteditsdeadlinetruthfullysincethepaymentisalsolessthanthepriorityvalueofthetruthfulbidderatthatperiod.Case3:thebidderwinsattd0
iand si>˝(vi).AccordingtoLemma1,˝0(vi)146˝(vi).Wecalculatetheexpectedpayoffofthemanipulatedbidderattimet,E[ˇ˝0(vi)]=˝0(vi)Xz=˝(vi)+1(viz)PrX(m)=zviXz=˝(vi)+1(viz)PrX(m)=z(6.27)Thetruthfulbidderwouldnotwintheauctioninthecurrentperiod;however,itsex-pectedpayofffromremainingperiodsofitslifetimeisgreaterthanthatofamanipula-tor.Thetruthfulbidder'sexpectedpayoffatthelastperiodisE[ˇ1(vi)]=viXz=0(viz)PrX(m)=zviXz=˝(vi)+1(viz)Pr(X(m)=z)(6.28)Thus,atruthfulbidder'sexpectedpayoffishigherthanthatofamanipulator.E[ˇ1(vi)]E[ˇ˝0(vi)](6.29)Therefore,amanipulatorwillnotgainanyadvantagebyreportingitsdeadlineincor-rectly.(e)v0i>vi:Withoutlossofgenerality,letusassumethatabidderiwinsanauctionwith˝remainingperiodsofitslifetime.AccordingtoLemma2,thepriorityvalueofamanipulator(˝(v0i))ishigherthanthatofatruthfulbidder(˝(vi))i.e.,˝(v0i)>˝(vi).Threepossiblescenariosmayoccurbasedonwhenthebidderiwinsandhowmuchitpays si.Case1( si˝(vi)):Inthiscase,thetruthfulbidderalsowinsandachievesthesamepayoff.So,thebidderwillnotgainanyadvantagebymisreportingitsvalue.147Case2( si>˝(vi),˝=1):Inthiscase,themanipulatorwinsandpaysmorethanitstruevaluationthatwillresultinnegativepayoff.Case3( si>˝(vi),˝>1):Inthiscase,themanipulatoronlywinsbecauseitoverbidsinthatauctionperiod.Theexpectedpayoffofthemanipulatoratthisperiodis
E[ˇ˝(v0i)]=˝(v0i)Xz=˝(vi)+1(viz)Pr(X(m)=z)viXz=˝(vi)+1(viz)Pr(X(m)=z)(6.30)Ontheotherhand,thetruthfulbidderlosesthecurrentauction;however,itsexpectedpayofffromtheremainingperiodswillbehigherthanthatofthemanipulator.Thetruthfulbidder'sexpectedpayoffatthelastperiodonlyishigherthanthat(seeEqn.6.28).E[ˇ1(vi)]E[ˇ˝(v0i)](6.31)(f)v0i<vi:AccordingtoLemma2,thepriorityvalueofatruthfulbidderishigherthanthevalueofthemanipulatori.e.,˝(v0i)˝(vi).Therefore,ifamanipulatorunderbids,itspriorityvalueatanyperiodofitslifetimewillalwaysbelowerthanorequaltothatofthetruthfulbidder.Thisimpliesthatifabidderwinsbyunderbidding,itcouldhavealsowonbybiddingtruthfully.FromEqn.6.27,6.28,6.30,wendthattheexpectedpayoffofabidderwitheithermanipulatedvalueormanipulateddeadlineissmallerthanthatofatruthfulbidderatthelastperiodofitslifetime.Thisresultalsoholdswhenabiddercombinesanyofthesemanipulatedinformation148(arrivaltime,deadlineandvalue).Basedontheabovediscussion,weconcludethatabidderwillnotbenetbymisreportingitslocation,bid,arrivaltime,anddeadline,andtheproposedmechanismistimeandbidtruthful.
Theorem4TheproposedauctionmechanismSOADEisexantestronglyindividuallyrational.Therearetwoentities(sellersandbidders)intheauction,andwehavetoprovetherationalityforboththeentities.LetuscalculatetheexpectedpayoffE[ˇj]ofsellerj.Theseller'spayoffdependsonthepricerange(between0andvinclusive)abidderpaystowinanauction.E[ˇj]=vXz=0zPr( pj=z)>0Similarly,bidderi'sexpectedpayoffE[ˇ˝(vi)]with˝remainingperiodsinitslifetimecanbecalculatedusingEqn.6.16whichisalsogreaterthan0.Therefore,boththeentitiesintheauctionachievepositiveutility,andthustheproposedmechanismisexantestronglyindividualrational.Theorem5TheproposedauctionmechanismSOADEisexpostweaklyindividuallyrational.Therecanbethreepossibleauctionoutcomesfromtheperspectiveofbidderiwith˝remainingperiodsofitslifetime.First,thebidderdepartswithoutwinningandearnszeroutility.Second,thebidderwinsandpays si.Sincethewinningpriceofabidderisalwayslessthanitspriorityvalueatthatperiodandthehighestpriorityofabidderisequaltoitsvaluationvi, sivi.So,thebidderachievesutilityequaltovi si0.Similarly,itcanbeshownthattheproposedauctionmechanismisexpostindividuallyrationalfromtheperspectiveofaseller.Therefore,boththeentitiesintheauctionachievenon-negativeutility,andthustheproposedmechanismisexpostweaklyindividualrational.1496.3.3distAware:OnlineDoubleAuctionAlgorithm
Thedistributionawareonlinedoubleauctionmechanismworksbasedonthepriorityfunction,Prank-III.Atthebeginningofeachperiod,thepriorityvalueofeachactivebidderistakenfromtheprioritytablePT.Anactivebidderreferstoabidderwithatleastoneperiodtolivethathasnotwonaspectrumunitinearlierperiodsofitslifetime.Sellersonlyhavelifetimesofoneperiod.BiddersaresortedbasedontheirpriorityvalueinlistB0.Foreachbidderi2B0,alistTofactivebiddersinterferingwithiiscreatedusingtheconictgraphG.TheauctioneerappliesMcAfeerulestondthecriticalpriceforbidderiattimet,CP(i;t),whichindicatestheminimumvaluebidderi'spriorityshouldbetowintheauctionatthatperiod.Ifbidderiwins,itpaystheamountequaltothepriorityvalueofh-thbidderini'sneighborhood.TheauctioneerallocatesspectrumusingnextAvailableChannel()whichndsthelowestindexspectrumthathasnotbeenallocatedtoanyofitsinterferingbidders.Similarly,sellers'paymentsaredeterminedaccordingtoMcAfeerules.Notethat,sellersarepaidmultipletimesatdifferentamountsduetospectrumreusability.Thewinnersfrombothbiddersandsellersareremovedfromtheactivebidderlist;thelosingbiddersmoveontothenextperiodwithonelessperiodtolive.TheentirealgorithmispresentedinTable6.2.
6.3.4AnalysisofdistAware
Theorem6Thedistributionawareonlinedoubleauctionmechanismistruthful.Accordingtothedenitionoftruthfulness,weneedtoshowthataparticipantcannotincreaseitsutilitybyreportingincorrectarrivaltime,deadline,and/orbid.Letusdenotethetruebidderi'sbidrequestas˚=(gi;bi;oi;di)anditsutilityasUiwherebi=vi.Letusalsodenotethemanipulatori0anditsbidrequestas˚0=(g0i;b0
i;o0
i;d0
i),itsutilityasU0iandwhereg0i6=gi,b0
i6=bi,a0
i6=ai,150Table6.2:AlgorithmdistAware:DistributionAwareOnlineDoubleAuctionfori2Bdoassignpriorityi;t=PT[vi;dit+1]endfor
sortbiddersaccordingtopriority,B0=sort(B)W=;whileB06=;doi=Top(B0)T=fig[fjjG(i;j)=1^j2Bgndh=MRules(T,S0),CP(i;t)=T(h)ifi;t>CP(i;t)thenj=nextAvailableChannel(i);
W=W[fig; si=CP(i;t),chn(i)=j, pj= pj+aS0(h)endif
B0=B0-figendwhiled0
i6=di.Notethat,ifabidderreportsanincorrectlocation,itwillbeallocatedspectruminthatlocationwhichdoesnothelpthemanipulatortogainbenets.Therefore,amanipulatordoesnotreportincorrectlocation.Wewillshowthatanycombinationofothermanipulatedinformationfromi0doesnotincreaseitsutility.(a)First,weconsiderthecasewhereb0
i<vi.Basedonthepriorityfunction,8t2li,t(b0
i)t(vi)i.e.,atanyperiodtinitslifetime,thepriorityofabidderisnolessthanthatofamanipulator.Therefore,giveneverythingelseremainsthesame,ifamanipulatorwinsatperiodt,thetruebidderalsowinsatthatperiodandthemanipulatordoesnotgainanybenetbyunderbidding.(b)Second,weconsiderthecasewhereb0
i>vi.Ifthemanipulatorwinsatthelastperiodandpays si>vi,itpaysmorethanitsactualvaluationwhichincursnegativeutility.If si<vi,atruebidderalsowinsgiveneverythingremainsthesame.Ifthemanipulatorwinsatanearlierperiod,thereareagaintwopossiblecases.Letusconsiderthatamanipulatorwins151atperiodt.Sincethemanipulatoroverbids,themanipulator'spriorityishigherthanatruebidder'spriority,i.e.,t(b0
i)>t(vi).If si<t(vi),themanipulatordoesnotgainsinceitwouldhavewonbybiddingtruthfully.Ift(b0
i)> si>t(vi),thetruebiddercouldnotwinatt.However,itcanbeshown(Eqn.6.32)thatatruebidder'sexpectedutilityfromitslastperiodonlyishigherthanthatofamanipulatorwhichdiscouragesamanipulatortooverbid.E[ˇt(b0
i)]=t(b0
i)Xz=t(vi)+1(viz)Pr( si=z)viXz=0(viz)Pr( si=z)=E[ˇ1(vi)](6.32)(c)Next,weconsiderthecasewhereamanipulatorinformslatearrival(o0
i>oi)orearlydepar-ture(d0
i<di)whichimpliesshorterdeadline.Inbothcases,amanipulatormisseswinningopportunityeitheratitsearlierperiodsorlaterperiodsofitslifetime.However,byreportinglatearrivalorearlydeparture,amanipulatorimpliesshorterdeadlineforthereportedperi-odsofitslifetime.So,amanipulator'sremainingperiod(˝0)isalwayssmallerthanthatofatruebidder(˝)i.e.,˝0<˝;amanipulator'spriorityis,therefore,higherthanthatofatruebidderi.e.˝(vi)<˝0(vi).If si<˝(vi),manipulatordoesnotgainanybenetsinceitwouldhavealsowonbytruthfullyreportingitstime.If˝0(vi)> si>˝(vi),thetruebiddercouldnotwinatthatperiod.Usingsimilarargument,weshow(Eqn.6.33)thatatruebidder'sexpectedutilityfromitslastperiodonlyishigherthanthatofamanipulatorwhichdiscouragesamanipulatortoreportlatearrivalandearlydeparture.E[ˇ˝0(vi)]=˝0(vi)Xz=˝(vi)+1(viz)Pr( si=z)viXz=0(viz)Pr( si=z)=E[ˇ1(vi)](6.33)152(d)Finally,weconsiderthecasewhereamanipulatorinformsearlyarrival(o0
i<oi)orlatedeparture(d0
i>di)whichimpliesalongerdeadline.Inbothcases,amanipulatormayendupwinningaspectrumunitbeyonditsvalidperiodswhichresultsinnegativeutility.Also,invalidperiods,themanipulator'sprioritywillbelowerthanthatofatruebidder.So,ifamanipulatorwinsatruebidderalsowinsinthesameperiodwhichdiscouragesamanipulatortoreportearlyarrivalandlatedeparture.Usingsimilarapproach,itcanbeshownthatamanipulativesellerdoesnotgainanybenetbyunderbiddingoroverbidding.Theorem7Thedistributionawareonlinedoubleauctionmechanismisindividuallyrational.Byconstruction,asellereitherfailstosellitsspectrumandearnszeroutilityorsellsitsspectrumaccordingtoMcAfeerulewhichguaranteesnon-negativeutility.Ontheotherhand,abiddermayfailtoearnaunitwhichresultsinzeroutility.Otherwise,abiddermaywinatanyperiodofitslifetime,anditspaymentisalwayslessthanorequaltoitspriorityvalueofthatperiod.Sinceabidder'shighestpriorityvalueisequaltoitsactualvaluation,awinningbidderneverpaysmorethanitsvaluation.Thisprovesthatthemechanismisindividuallyrational.Theorem8Thedistributionawareonlinedoubleauctionmechanismisbudgetbalanced.Atanyperiod,allmatchesbetweenbiddersandsellersaredeterminedaccordingtoMcAfeerules.Thisguaranteesthebalancedbudgetpropertyofthemechanism.6.4DistributionFreeOnlineDoubleAuctionAlgorithm
ThealgorithminSec.6.3requiresdistributionknowledgewhichmaynotbeeasilyavailabletoreecttherealauctionscenario.Inthissection,wethereforepresentanauctionmechanismthatrequiresnoknowledgeoftheunderlyingdistributionsofbiddersandsellers.153Inthisalgorithm,abidderwinsatanauctionperiodonlywhenabidder'sbidishigherthanthecriticalpriceofthatperiod.Thecalculationofthecriticalpriceissomewhatdifferentfromthedistributionawarealgorithm.Abidderi'scriticalpriceattimet,CP(i;t)hastwocomponents-onecomponentisderivedaccordingtoMcAfeerules,MP(i;t)andthesecondcomponentiscalculatedbasedonthe`debtfactor',DP(i;t)(willbedescribedlaterinthissection).Bidderi'snalpaymentisdeterminedasthelowestcriticalpriceoverallperiodsofitslifetime.Aseller'scriticalpriceisdeterminedsolelybasedonMcAfeerule. si=mint2[oi;di]CP(i;t)(6.34)Thealgorithmhasthreephases.Inthescreeningphase,thealgorithmidentiesthecandidatesofpotentialwinnersfromthelistofactivebidders(sellers)anddeterminestheminimumamounttheyneedtopay(tobepaid)accordingtoMcAfeerulesdescribedinSec.2.1.7.Inthedebtcalcu-lationphase,thealgorithmcalculatesthedebtfactorofeachcandidateconsideringtheinterferingbiddersthathavewonatpreviousperiodsbuttheirlifetimeshavenotexpiredyet.Inthenalphase,thealgorithmdeterminesthecriticalpriceofthatperiodforeachbidder,selectswinnersfromthelistofactivebiddersandsellersofthisperiod,andifapplicable,changesthepaymentamountofthepreviouswinners.Forconvenience,wesummarizeallsymbolsusedinbothalgorithmsinTable6.3andbrieffunctiondescriptionsareinTable6.4.
6.4.1CandidateScreening(Phase1)
First,theactivebidderlistBissortedbasedontheirbid(fromhightolow)inB0.Thespectrum(orseller)listSisalsosortedbasedontheirask(lowtohigh)inS0.Foreachbidderi2B0,an154Table6.3:SymbolsusedinthealgorithmsymbolsmeaningB,B0unsortedandsortedactivebidderlistS,S0unsortedandsortedactivesellerlistP,P0unsortedandsortedactivependerlistAcandidatebidderlistA0candidatependerlistWwinners'listT(h)thepriorityoftheh-thbidderinthelistTbT(h)thebidoftheh-thbidderinthelistTaS0(h)theaskoftheh-thbidderinthelistS0pp(i;t)denotesintermediateMcAfeepriceofpenderiGConictgraphorInterferencegraphG(i,j)=1ifiandjinterfere,0otherwiseTable6.4:Functionsusedinthealgorithmfunctiondescriptionchn(i)thespectrumunitassignedtobidderiTop(B)returnsthetopelementfromthelistBNextAvailableChannel(i)returnsthespectrumunitwiththelowestaskwhichhasnotbeenassignedtoanyoftheneighborsofbiddericount(i)numberofbiddersinneighborhoodsharingthedebtofpenderi155Table6.5:AlgorithmdistFree:CandidateScreening(Phase1)whileB0is6=;doi=Top(B0)T=fig[fjjG(i;j)=1^j2Bgndh=MRules(T,S0),MP(i;t)=bT(h)ifbi>MP(i;t)thenj=nextAvailableChannel(i)
A=A[fig si=MP(i;t),xi=1,chn(i)=j, pi=aS0(h)endif
B0=B0-figendwhileinterfererlistTiscreatedbasedontheconictgraphG.GiventhelistTandS0attimet,weapplyMcAfeerulestoidentifythewinningpotentialofbidderiandtherstcomponentofitspaymentamount,McAfeepriceMP(i;t).Italsokeepsrecordofthecorrespondingseller'spayment.Ifbidderiisselectedasapotentialwinner,afunctionnextAvailableChannel()ndsthelowestindexchannelavailableforbidderithatisnotallocatedtoanyofitsneighbors.Thus,attheendoftherstphase,eachbidderiseithermovedtothelistAofcandidateofwinnersorremovedfromconsiderationforthecurrentauctionperiod.TherstphaseofthealgorithmdistFreeispresentedinTable6.5.
6.4.2DebtCalculation(Phase2)
Inthesecondphase,wereviewthelistPofpendingwinnersfrompreviousperiodswhoselifetimeshavenotexpiredyet(referredtoas`penders')tocalculatethedebtamountinthecurrentperiod.Accordingly,pendersaresortedinorderoftheirbids(fromhightolow)inP0.Foreachpender,aninterfererlistTisconstructedusingtheconictgraphG.McAfeeruleisappliedtodeterminewhetherthependerwouldwinatthecurrentperiodifithadnotwonbefore.Incaseofwinning,itcalculatesthepriceitwouldhavepaidinthecurrentperiod.Ifthispriceishigherthanits156Table6.6:AlgorithmdistFree:DebtCalculation(Phase2)whileP06=;doi=Top(P0)T=fig[fjjG(i;j)=1^j2Bgndh=MRules(T,S0),MP(i;t)=bT(h)ifMP(i;t)< pithenDP(i;t)= pi-MP(i;t)A0=A0[figendif
pp(i,t)=MP(i;t),P0=P0figendwhilecurrentpayment,nofurtheractionisneeded.Ifthepender'scalculatedpriceislowerthanitscurrentpaymentbuthigherthanthecorrespondingseller'spayment,wesetthecurrentpaymenttothecalculatedprice.Ifthecalculatedpriceislowerthanthecorrespondingseller'spayment,thedifferenceinpaymentisconsideredtobe`debt'andmustbecompensatedbythemechanismtomaintain`budgetbalance'property.ThependerismovedtolistA0fornextphaseanalysis.ThesecondphaseofthealgorithmdistFreeispresentedinTable6.6.6.4.3CriticalPriceandWinnerSelection(Phase3)
Inthenalphase,wecalculatethe`debtfactor'foreachcandidatewinneri2A.Foreachpenderj2A0,wendthebiddersfromAwhoareinitsinterferencerange,andthedebtofpenderjisequallysharedamongitsinterferers.So,thedebtofabidderiattimetisthetotaldebtfactorfromallpendersDP(i;t).IfthecriticalpriceCP(i;t)ofbidderi2Aexceedsitsvaluationbi,iisremovedfromAandthedebtamountisrecalculatedforalltheexistingcandidatebiddersinA.ThisprocesscontinuesuntilallthebiddersinAareremovedorthebiddersinAsettleinsharingdebtswiththependersinA0.Ifallthebiddersareremoved,therewillbenowinnersinthatperiodandthepaymentamountofpenderswillnotchange.Otherwise,thepaymentamountofthependersisupdatedbasedontheircriticalpriceofthatperiod.157Table6.7:AlgorithmdistFree:CriticalPriceDetermination(Phase3)whileisConverged=falseandA6=;doisConverged=true
fori2Adoforj2A0doifG(i,j)=1thenDP(i;t)=DP(i;t)+xiDP(j;t)count(j)endifendfor
if si+DP(i;t)bithenA=Afig,xi=0isConverged=falseendifendforendwhile
fori2A0do si=min si;pp(i;t)+DP(i;t)endfor
fori2Ado si=bs
i+DP(i;t)P=P[figendfor158Finally,ifthelifetimeofanypenderj2Pexpires,itisremovedfromP.ThewinningbiddersatthecurrentperiodwhoselifetimehasnotexpiredyetaremovedfromAtoP.ThenalphaseofthealgorithmdistFreeispresentedinTable6.7.
6.4.4AnalysisofdistFree
Inthissection,weprovideatheoreticalanalysisoftheproposedalgorithmsandshowthatboththesemechanismssatisfyallthreeauctionproperties.
Theorem9Thedistributionfreeonlinedoubleauctionmechanismistruthful.Accordingtothedenitionoftruthfulness,weneedtoshowthataparticipantcannotincreaseitsutilitybyreportingincorrectarrivaltime,deadline,and/orbid.Letusdenotethetruebidderi'sbidrequestas˚=(gi;bi;oi;di)anditsutilityasUiwherebi=vi.Letusalsodenotethemanipulatori0anditsbidrequestas˚0=(g0i;b0
i;o0
i;d0
i),itsutilityasU0iandwhereg0i6=gi,b0
i6=bi,a0
i6=ai,d0
i6=di.Notethat,ifabidderreportsanincorrectlocation,itwillbeallocatedspectruminthatlocationwhichdoesnothelpthemanipulatortogainbenets.Therefore,amanipulatordoesnotreportincorrectlocation.Wewillshowthatanycombinationofothermanipulatedinformationfromi0doesnotincreaseitsutility.(a)First,wesupposethatmanipulatori0underbids,i.e.,b0
i<vitoincreaseitsutility.Sincespectrumisallocatedinnon-decreasingorderoftheirbids,ahighervaluedbidderalwayswinsbeforealowervaluedbiddergiveneverythingelseremainsthesame.Therefore,i0doesnotgainanyadvantagebyunderbidding.(b)Second,weconsiderthecasewhereamanipulatoroverbids,i.e.,b0
i>vi.Letusassumethatamanipulatorwinsatanearlierperiodt,andthetruebidderdoesnotwinatthatperiod.So,159themanipulator'spaymentissetto si0=CP(i0;t)>vi.Inthisalgorithm,abidder'snalpriceisdeterminedastheminimumcriticalpriceofanyperiodoveritslifetime.So,ifthenalprice si0<vi,itimpliesthatthecriticalpriceatalaterperiodt0ofitslifetimeissmallerthanitsvalue,CP(i0;t0)<vi.Giveneverythingelseremainsthesame,thetruebidderiwouldalsowinatthatsameperiodt0andwouldachievethesameutility.Otherwise,themanipulator'snalpricewillbehigherthanitsactualvaluation.Inthatcase,atruebidderdoesnotwinandhaszeroutility,however,themanipulatorendsuppayingmorethanitsvaluationwhichresultsinnegativeutility.(c)Next,weconsiderthati0reportslatearrival(o0
i>oi).Sinceatruebiddergetsmoreopportu-nitytowinanauctionandreduceitspaymentamount,i0doesnotgainanyadvantageoveri.Next,weconsiderthatmanipulatori0reportsearlydeadlined0
i<di.Bysubmittingdeadlineearlierthanitsactualdeadline,amanipulatormaymissanopportunitytoreduceitspay-mentamount.Butitdoesnotgetanyadvantagebyreportingearlydeadlinesincespectrumallocationdoesnottakebidder'sdeadlineintoconsideration.Therefore,reportingearlierdeadlinedoesnothelpamanipulatorinincreasingutilities.Finally,ifamanipulatorreportsearlyarrivalorlatedeparturethemanipulatormayenduppayingwhenitnolongerneedsaspectrumunit.Therefore,amanipulatordoesnotreportearlyarrivalorlatedeparture.Usingasimilarapproach,itcanbeshownthatamanipulativesellerj0cannotgainanyadvantagebysubmittinghigherorloweraskthanitstruevaluationoftheunit.Theorem10Theproposeddistributionfreedoubleauctionmechanismisindividuallyrational.LetusrstconsidertheutilityUiofabidderi.Ifabidderdoesnotwin,itdoesnotpayanythinganditsutility,Ui=0.Therearetwocaseswhenabidderwins.First,abidderwinsatthelastperiodofitslifetime.Inthe3rdpartofthealgorithm,abidderisselectedasawinneronlyifthe160bidder'sbidishigherthanthecriticalpriceatthatperiod.So,Ui0.Second,abidderwinsatanearlyperiodofitslifetime.Inthiscase,thebidderismovedtothependinglist.Apender'snalpaymentissettotheminimumofthecriticalpricesoflaterperiodsinitslifetime.So,insubsequentperiods,thepaymentwillnevergoup.Therefore,Ui0.LetusconsidertheutilityUjofasellerj.Ifasellerdoesnotwin,itisnotpaidanything.So,Uj=0.Ifasellerwins,thepaymentisdecidedaccordingtoMcAfeerulewhichguaranteesthatthewinningsellerispaidnolessthanitsask.
Theorem11Thedistributionfreeonlinedoubleauctionmechanismisbudgetbalanced.Letussupposethatthebidder'slifetimeisonlyoneperiod.Whenbothbiddersandsellersliveforonlyoneperiod,themechanismreducestotheMcAfeemechanismineachperiod.Therefore,themechanismisbudgetbalanced.Whenabidder'slifetimeismorethanoneperiodandwinsatanearlierperiod,itspaymentmaybereducedatlaterperiods;however,aseller'spaymentdoesnotchangeafterwards.Theremaybetwopossiblecases.First,thebidder'spaymentisreducedtonotlowerthanthecorrespondingseller'spayment.Inthatcase,conditionforbalancedbudgetstillholds.Second,thepaymentisreducedtobelowthecorrespondingseller'spayment.However,inthatcase,thedifferenceisequallysharedamongitswinningneighbors(whichisreferredtoas`debtfactor').So,theauctioneer'sutilitywillnotbenegativeandthemechanismisbudgetbalanced.
6.5PerformanceEvaluation
Weorganizethissectionintotwoparts.Intherstpart,weanalyzethepriorityfunctionspresentedinSec.6.2.Specically,weinvestigatehowthepriorityofabidderchangeswiththechangeinthedistributionparametersandexplaintheirproperties.Inthesecondpart,wecomparethe161performanceoftheproposedalgorithmswithanoff-linemechanismwithorwithoutspectrumreusability.
6.5.1PriorityAnalysis
AspresentedinSec.6.2,weconsidertwoversionsofpriorityfunctionŠPrank-IIandPrank-III.Weconsiderdifferentcongurationofauctionenvironmentsbyvaryingbidders'arrivalrateFn,supplyavailabilityFs,bidders'lifetimeFk,biddersvaluationsFv,andsellers'valuationsFa.Foraspeciccongurationoftheauctionenvironment,wesolvethepriorityvaluefunctionstondthepriorityvalueofabidderatdifferentperiodsofitslifetime.Tostartwith,weassumethatthebidders'priorityisequaltotheirvaluationindependentoftheirlifetime.Wesimulatetheauctionfor10000timeperiodsandiftheestimatedpriorityvaluesmatchwiththesimulationoutcome,westopthesimulation,andtheresultsarerecorded.Otherwise,thenextiterationstartswiththeresultofpreviousiterationandcontinuesuntiltheresultconverges.Forstatisticalcondence,theentireprocesswasrepeated10times,andwetakeanaverageoveralltheserunstoconstructtheprioritytable.Notethat,accordingtoStrongLawofLargeNumbers,weusethesamplemeanastheactualmeanforbidders'populationwithdifferentperiodstolive,anduseitinprioritycalculation.Thesameprocessisrepeatedfordifferentauctionconguration,andallsimulationresultsarecalculatedfollowingthisprocess.
6.5.1.1Prank-II
Prank-IIisadistributionawarerankingfunctionthatcalculatesthepriorityofabiddergivenitsvalueandlifetimeinanonlinesingleauctionsetting.WepresentthesimulationresultsofthepriorityvaluefunctionPrank-IIandinvestigatehowthepriorityvalueofabidderchangeswithchangesinbidders'arrivalrate,supplyavailability,andbidders'lifetime(seeFig.6.5).162value v020406080100priority value -(v)20406080100n ~ Poi(2), k ~ U[1,3], m ~ U[0,4], k =1n ~ Poi(2), k ~ U[1,3], m ~ U[0,4], k =2n ~ Poi(2), k ~ U[1,3], m ~ U[0,4], k =3(a)priorityvalueatdifferentperiodsvalue v020406080100priority value -(v)20406080100n ~ Poi(3), k ~ U[1,2], m ~ U[0,2], k =2n ~ Poi(3), k ~ U[1,2], m ~ U[0,4], k =2n ~ Poi(3), k ~ U[1,2], m ~ U[0,6], k =2(b)priorityvaluewithvaryingsupply
ratevalue v020406080100priority value -(v)20406080100n ~ Poi(2), k ~ U[1,3], m ~ U[0,4], k =2n ~ Poi(2), k ~ U[1,3], m ~ U[0,4], k =3n ~ Poi(3), k ~ U[1,3], m ~ U[0,4], k =2n ~ Poi(3), k ~ U[1,3], m ~ U[0,4], k =3(c)priorityvaluewithvaryingbidder
arrivalrateFigure6.5:Priorityvaluewithvaryingparameters(Prank-II)First,weconsideranauctionenvironmentwherenewbiddersarrivefollowingaPoissondistri-butionwithameanvalueof2andlifetimeofthebiddersareuniformlydistributedoverf1;2;3g.Also,numberofavailablespectrumunitsateachperiodisuniformlydistributedoverf0;:::;4gwithameanvalueof2.Fig.6.5ashowsthepriorityvalueofabidderatdifferentperiodsofitslife-timeunderthissetting.Forexample,theprioritiesofabidderofvalue$100are$40,$45,and$100with3,2,and1periodtolive.Asexpected,abidder'spriorityvalueincreasesasitapproachestheendofitslifetime.Next,wesetthebidderarrivalratefollowingaPoissondistributionwithameanvalueof3andthelifetimeofthebiddersareuniformlydistributedoverf1;2;3g.Wevarythesupplyavailabilityratef0;1;2g;f0;:::;4g;f0;:::6gwithmean1,2,and3respectively.Fig.6.5bshowsadecreaseinthepriorityvalueofabidderwithanincreaseinsupplyrate.Thisisbecausemoresupplyperperiodincreaseswinningprobabilityatearlyperiods,andtheexpectedpayofffromremaininglifetimeperiodsincreaseswhichdecreasesthepriorityvalueofthebidder.Third,wevarythemeanvalueofthebidderarrivalratewhilethelifetimeofthebiddersareuniformlydistributedoverf1;2;3g.Weplotthepriorityvalueofabidderwith2and3remainingperiodsofitslifetimeinFig.6.5c.Themeanarrivalrateareconsidered2and3.Theresultshowsthatthepriorityvalueofabidderatthesameperiodincreaseswithanincreaseinthebidderarrival163value v203040506070priorityvalue-(v)10203040506070n ~ Poi(4), k ~ U[1,2], m ~ U[5,7], k =2n ~ Poi(6), k ~ U[1,2], m ~ U[5,7], k =2n ~ Poi(8), k ~ U[1,2], m ~ U[5,7], k =2Figure6.6:Priorityvalueswithvaryingparameter(Prank-III)rate.Thisisbecausewiththearrivalofmorebidders,theauctiongetsmorecompetitive,andthewinningprobabilitydecreases.Thisleadstoadecreaseintheexpectedpayoffwhichisfollowedbyahigherpriorityvalue.
6.5.1.2Prank-III
Prank-IIIisadistributionawarerankingfunctionthatcalculatesthepriorityofabiddergivenitsvalueandlifetimeinanonlinedoubleauctionsetting.Inthissection,weanalyzethepropertiesofPrank-III.Wetakeacloserlookatthepriorityvaluesofabidderatdifferentperiodsofitslifetime.Weconsiderasettingwherebiddershaveeither1or2periodsoflifetime.Weassumethatbidders'arrivalsfollowaPoissondistributionwithmeanvaluevaryingbetween4and8.ThepriorityvaluesofabidderatthesecondtolastperiodareshowninFig.6.6acrossdifferentvaluations.Theresultshowsthatthepriorityvalueofabidderincreaseswiththeincreaseinbidders'arrivalratesandincreaseinbidders'valuations.Thisisbecausepriorityiscalculatedbasedontheexpectedutilityoffutureperiods,andwiththeincreaseinbidders'arrivalrates,abidderhastocompetewithmorebidderswhichreducestheexpectedutilityatfutureperiods.1646.5.2AlgorithmPerformance
Weconsidertwodifferentauctionsettings.Intherstsetting,allbiddersarelocatedinsideeachother'sinterferencerange.Thus,theinterferencerelationshipbetweenusersformsacompletegraph.So,aspectrumunitcannotbeallocatedtomorethanoneuser.Inthesecondsetting,theusersarerandomlydeployed.So,eachusermayexperiencedifferentnumberofinterferersthatmaymakeitpossibletoallocatethesamespectrumunittomorethanoneuser.Therstsettingisreferredtoas`settingwithnoreusability'andthesecondoneisreferredtoas`settingwithreusability'.Foreachsetting,wehaveconsideredthefollowingfourperformancemetricstoevaluatetheperformanceoftheauctionalgorithms(i)spectrumutilizationrate-itdenotestheratiobetweenthenumberofbidderswhowonaspectrumunitandthenumberofspectrumunitsauctionedforsale.(ii)biddersatisfactionrate-itdenotestheratiobetweenthenumberofbidderswhowonaspectrumunitandthenumberofbidderswhoparticipatedintheauction.(iii)averagevalueofwinner-itdenotestheaveragevaluationofawinningbidderwhichisrelatedtotheefciencyoftheauction.(iv)revenueperwinner-itdenotestheaveragepriceawinningbidderpaysforaspectrumunit.6.5.3SingleAuctionAlgorithm
Inthissection,wesimulatedifferentauctionsettingstoverifythepropertiesandanalyzetheper-formanceoftheproposedauctionmechanism.Weassumethatboththebidders'arrivalandspec-trumavailabilityfollowaPoissondistribution[30].Also,thebidders'lifetimefollowsaUniformdistributionwhilethebidders'valuationfollowsaUniformdistributionwithsupportf1;:::;100g.165Tothebestofourknowledge,thisistherstworkaddressingboththedynamicarrivalofbiddersanddynamicspectrumsupply.Forperformancecomparison,weselectTopaz[30]thatsuccessfullyhandlesthedynamicarrivalofbiddersbutconsidersaxednumberofavailablespec-trumunits.Itallocatesspectrumtothebiddersinthenon-decreasingorderoftheirbidswheneveranewbidderarrives.Inordertohandlethedynamicsupply,wealsoinvoketheallocationpro-cedurewhennewspectrumarrivesattheauction.Notethat,Topazisnottruthfulsinceabiddercangainbenetbyreportingalongerdeadline(seeinFig.6.4).Additionally,wehaveconsid-eredanauctionsettingwherespectrumsupplyisxed.Wehavealsoincludedtheresultsfromanoff-linealgorithmwheretheauctioneerhascompleteinformationofbidderarrivalandspectrumsupplyinfutureperiods.Thustheoff-linealgorithmservesasabenchmarksolutiontoanalyzetheperformanceofSOADE.
6.5.3.1ResultsonSettingwithNoSpectrumReusability
Weevaluatetheperformanceoftheproposedsingleauctionalgorithminthesettingwithnospec-trumreusability(denedinSec.6.5.2).Inthissettingwithnoreusability,weassumethatthebiddersarrivefollowingaPoissondistribution,andtheirlifetimeisuniformlydrawnfromthesetf1;2;3g.Wechangethemeanarrivalrateofthebiddersbetween2:0and3:0.WeassumethatsupplyarriveateachperiodfollowingaUniformdistributionfromthesetf0;1;2g.Underthesettingwithnospectrumreusability,Fig.6.7showsthesimulationresultsoffourperformancemetricsofSOADEandTopaz.Inthecaseofspectrumutilizationrate(Fig.6.7a)andthebiddersatisfactionrate(Fig.6.7b),SOADEperformsmarginallybetterthanTopaz.ThisisbecauseinSOADE,abidderwithsmallervalueandshorterlifetimemayhavehigherprioritythanabidderwithlargervalueandlongerlifetimeandwinsoverit.Also,asexpected,thespectrumutilizationrateincreases,andthebiddersatisfactionratedecreaseswiththeincreaseinbidders'1661.522.533.5bidder arrival rate00.20.40.60.81spectrum utilization rateTopazSOADEOff-line(a)spectrumutilizationrate1.522.533.5bidder arrival rate00.10.20.30.40.5bidder satisfaction rateTopazSOADEOff-line(b)biddersatisfactionrate1.522.533.5bidder arrival rate020406080average values of a winnerTopazSOADEOff-line(c)averagevalueofawinner1.522.533.5bidder arrival rate01020304050average price paid by a winnerTopazSOADEOff-line(d)revenueperwinnerFigure6.7:Topazvs.SOADEonsettingwithnoreusabilityarrivalrate.Thenextgure(Fig.6.7c)reectstheauctionefciencyoftheauction.Boththeapproachesshowsimilarresultwheretheaveragevalueincreaseswiththeincreaseinbidders'arrivalrate.Finally,wecomparethewinner'spayment(denotedasauctionrevenue)inFig.6.7d.Theresultshowsthatrevenueincreaseswiththeincreaseinarrivalrateduetothepresenceofmorecompetitorsintheauction.Foraxeduserarrivalrate,SOADEgeneratesmorerevenuethanTopazbutlessthantheoff-linealgorithm.ThisisbecausewinningpriceinSOADEdependsonthepriorityvaluesoftheparticipatingbiddersonthesameauctionperiod.1676.5.3.2ResultsonSettingwithSpectrumReusability
Wealsoevaluatetheperformanceoftheproposedsingleauctionalgorithminthesettingwithspectrumreusability(denedinSec.6.5.2).Underthissettingwithspectrumreusability,weallocatethesamespectrumtomorethanoneusersaslongastheyarenotinterferingeachother.Weconsiderthatnodesarerandomlydistributedwithin250m250marea.Theinterferencerangeofauserissetto50mi.e.,twonodeswillinterfereeachotheriftheyarelessthanorequalto50mapart.Inotherwords,twouserslocated50mapartfromeachothercanusethesamespectrumunitwithoutanyinterference.Asbefore,thebidders'lifetimeisuniformlydrawnfromthesetf1;2;3gwhilethemeanbidders'arrivalrateischangedbetween16and24.Wealsoconsiderthatthespectrumunitisuniformlydrawnfromthesetf0;1;2gwithmean1.ThesimulationresultispresentedinFig.6.8.TheresultshowssimilarpatterntotherstsetupandSOADEgeneratesrevenueclosertothatoftheoff-linealgorithm.Wehavealsoconsideredanauctionenvironmentwithxednumberofspectrumsupplypertimeperiod.WegetsimilarresultswhereSOADEachieveshigherrevenueandhigherbiddersatisfactionratethanthatofTopaz2.Insummarywithxedordynamicspectrumsupply,withorwithoutspectrumreusability,SOADEgeneratesauctionrevenueclosetooff-linerevenueinadditiontoslightlyincreasingspec-trumutilizationrate,biddersatisfactionrate,winners'valuationswhilepreservingtruthfulnessincomparisontoTopaz.
6.5.4DoubleAuctionAlgorithms
Inthissection,weanalyzeandevaluatetheperformanceoftheproposedalgorithmsunderdif-ferentauctionsetting.Forconvenience,werefertothedistributionawareonlinedoubleauction2DuetotheitssimilaritywithFig.6.7,resultsarenotshownhere1681618202224bidder arrival rate024681012spectrum utilization rateTopazSOADEOff-line(a)spectrumutilizationrate1618202224bidder arrival rate00.20.40.6bidder satisfaction rateTopazSOADEOff-line(b)biddersatisfactionrate1618202224bidder arrival rate020406080average values of a winnerTopazSOADEOff-line(c)averagevalueofawinner1618202224bidder arrival rate0102030average price paid by a winnerTopazSOADEOff-line(d)revenueperwinnerFigure6.8:Topazvs.SOADEonsettingwithspectrumreusability169mechanismas`distAware'andthedistributionunawaremechanismas`distFree'.Weconsiderbidders'arrivalfollowsaPoissondistributionandspectrumbecomesavailablefollowingaUniformdistribution[118][30].Inallfollowingsimulations,spectrumavailabil-ityperperiodisuniformlydrawnfromf5;6;7g.Bidders'valuationsareuniformlydrawnfromf21;:::;70gwhilesellers'valuationsareuniformlydrawnfromf1;:::;50g.Foranyauctionset-ting,werunthesimulation5timesandeachtime,thesimulationrunsfor5000timeperiods.Forstatisticalcondence,wetakeanaverageofalltheseruns.Similartosingleauctionperformanceanalysis,weusetwodifferentauctionsettings.
6.5.4.1ResultsonSettingwithNoSpectrumReusabililty
Weevaluatetheperformanceoftheproposeddoubleauctionalgorithminthesettingwithnospectrumreusability(denedinSec.6.5.2).Tothebestofourknowledge,existingresearchcannotensuretruthfulnessinanonlinedynamicsetting.Therefore,wecompareouralgorithmswithanoff-linealgorithm.Notethattheoff-lineauctionbenchmarkisnecessarilycounter-factualinthatitisnotpossibletoimplementitwithoutknowingthefuturerealizationsofthedistributions.However,itservesasagoodbenchmarkinthatitgivesthebestpossibleoutcome.Weconsideranauctionsettingwhereallbiddersareinterferingtoeachother.Bidders'arrivalsfollowaPoissondistributionwithameanvaluevaryingbetween4and6andbidders'lifetimesareuniformlydrawnfromf1;2;3g.Underthesettingwithnospectrumreusability,weobservethatbothdistAwareanddistFreeshowalmostashighbiddersatisfactionrateandspectrumutilizationrateastheoff-lineapproachwhenthemeanarrivalrateofbiddersisclosetothemeannumberofspectrumunits.Wealsoplotthetotalpaymentmadebybidders(Fig.6.9c)andtotalpaymentmadetothesellersrespectively.TheresultsshowthatdistAwaregeneratesrevenueclosertotheoff-lineapproachthandistFree170mean bidder arrival rate (k ~ U[1,3], m ~ U[5,7])456787B0.450.50.550.60.650.7distAwaredistFreeoffline(a)biddersatisfactionratemean bidder arrival rate (k ~ U[1,3], m ~ U[5,7])456787s0.40.450.50.550.60.650.7distAwaredistFreeoffline(b)spectrumutilizationratemean bidder arrival rate (k ~ U[1,3], m ~ U[5,7])45678total payment by bidders per period80100120140160180200distAwaredistFreeoffline(c)bidders'paymentmean bidder arrival rate (k ~ U[1,3], m ~ U[5,7])45678sum values of winning bidders per period120140160180200220240distAwaredistFreeoffline(d)winningbidders'valuationsFigure6.9:Performancecomparisononsettingwithnoreusabilitywithvaryingmeanarrivalrates.Finally,weplotthewinningbidders'valuationsinFig.6.9d.Itshowsthatbothalgorithmsgivealmostthesameresultasintheoff-linealgorithm.6.5.4.2ResultsonSettingwithSpectrumReusability
Likesingleauctions,weinvestigatetheperformanceofthedoubleauctionalgorithmsinthesettingwithspectrumreusability(denedinSec.6.5.2).Underthesettingwithspectrumreusability,thesamespectrumisallocatedtonon-interferingbidders.Weconsiderthenetworkinwhichthesecondaryusersarescatteredrandomlywithinanareaof100m100m.Theinterferencerange171mean bidder arrival rate (k ~ U[1,3], m ~ U[5,7])30405060707B0.540.560.580.60.620.640.660.68distAwaredistFree(a)biddersatisfactionratebidder arrival22.22.42.62.83spectrum utilization rate s0.70.750.80.850.9k ~ U[1,3], m ~ U[0,4](b)spectrumutilizationratemean bidder arrival rate (k ~ U[1,3], m ~ U[5,7])3040506070total payment by bidders per period6008001000120014001600distAwaredistFree(c)bidders'paymentmean bidder arrival rate (k ~ U[1,3], m ~ U[5,7])3040506070total payment to sellers per period400600800100012001400distAwaredistFree(d)paymenttowinningsellersFigure6.10:Performancecomparisononsettingwithspectrumreusabilityofasecondaryuserissetto20m.Twouserslocated20mapartcanusethesamespectrumunitwithoutanyinterference.AninterferencegraphGisconstructedbasedontheuser'stransmissionrange.Inthesimulation,bidders'arrivalsfollowaPoissondistributionwithmeanvaluevaryingbetween32and64,andtheirlifetimesareuniformlydrawnfromf1;2;3g.Underthesettingwithspectrumreusability,werstplotbiddersatisfactionratesinFig.6.10a.Theresultshowsthatwiththeincreaseinbidders'arrivalrates,thewinningrateofbiddersde-creases.However,thedistFreealgorithmachievesthesamesatisfactionrateasthedistAwarealgorithm.Wealsocalculatethewinningprobabilityofabiddergivenitsvalue,referredtoas172Pr(xi=1jvi).Asexpected,thehighervaluedbiddershavehigherprobabilitiestowinandthewinningprobabilitydecreaseswiththedecreaseinbidders'valuations.Also,thedistAwarealgo-rithmshowsaslightincreaseinthewinningprobabilityforhighervaluedbidderscomparedtothedistFreealgorithm.Next,weplotthespectrumutilizationrate(s)intheauctioninFig.6.10b.Thearrivalofmorebiddersintheauctionincreasesspectrumreusability,however,therateofchangeinspectrumutilizationdiminishesathigherarrivalratesofbidders.Wealsocalculatethewinningprobabilityofasellergivenitsvaluationandtheresultshowsthatthelowertheaskofaselleris,themoreitislikelytowin.Fig.6.10cshowstheaveragepaymentabidderpaysaccordingtotheproposedalgorithms,whileFig.6.10dshowsthetheaveragepaymentasellerreceives.Theresultsshowthatbidders'paymentsarelowerinthedistFreealgorithmthaninthedistAwarealgorithmwhilethesellers'paymentsarealmostsameinbothcases.Also,thenumberoftradesincreasesasthebidders'arrivalratesincrease,however,therateofchangeinthenumberoftradesdiminishes.Theauctioneer'sbalanceishigherinthedistAwarealgorithmthaninthedistFreealgorithm.6.6Summary
Inthischapter,weinvestigateonlinesingleanddoubleauctionforspectrumallocationinthedy-namicsecondarymarket.Inthisspectrummarket,bothbiddersandsellersarrivedynamicallywithdifferentlifetimesanddifferentvaluations.Werstpresentanonlinesingleauctionmecha-nismtoallocatetherandomlyavailablespectrumamongthebiddersaccordingtotheirvalueandurgencyoftransmission,suchthatbidderswithhighervaluesandshorterlifetimesofdemandre-ceiveahigherpriority.Byallocatingthesamespectrumunittonon-interferingbidders,weachieve173spectrumreusability.Weformallyprovethatthemechanismisindividuallyrationalforallagentsensuringtruthfulreportingbybothsellersandbidders,includingbidders'valuationsandlifetimereports.Theproposedmechanismissimulatedundervariousdistributionalsettings,andauctionrevenueandbiddersatisfactionratearesignicantlyincreasedcomparedtoexistingwork.Second,wepresenttwoalgorithmsforwinnerselectionandpricedeterminationinanonlinedoubleauc-tionsetting.Therstalgorithmassumesthattheunderlyingdistributionsofarrivalofbiddersandsellersareknowntotheauctioneer.Usingthisinformationinapriorityfunction,theauctioneerdeterminesthewinningopportunityofabidderatdifferentperiodsofitslifetime.ThesecondalgorithmworkswithoutanydistributionknowledgeanddeterminesthecriticalpriceforabidderbasedonMcAfeerulesandactivebiddersinitsneighborhood.Bothmechanismsareprovedtobetruthful,individuallyrational,andbudgetbalanced.Wecomparetheperformanceofthesealgo-rithmswithanoff-linealgorithm.Thesimulationresultsshowthatthesealgorithmsprovidealmostthesamebiddersatisfactionrateandspectrumutilizationratecomparedtotheoff-linemechanismwhenthenumberofbiddersandsuppliesareequalonaverage.Wealsocompareresultsintermsofauctionrevenue,bidders'valuations,andsellers'valuationsandndthatboththesealgorithmsachieveresultsveryclosetotheoff-linemechanism.174Chapter7
Conclusion
Cognitiveradionetworkhasprovidedpromisingmeansofspectrumsharingtoaddressthelimita-tionsofthetraditionalxedallocationsystem.WiththeexibilityandadaptabilityoftheCRN,theprimaryandsecondaryusersadoptvariouscollaborationmodelsforefcientspectrumman-agement.Inthisdissertation,wehaveexploredthreecollaborationmodelsbetweentheprimaryandsecondaryusersŠsensingbased,relaybased,andauctionbased.Wehaveidentiedthechallengesinthesemodelsandaddressedsomeofthesechallengestowardsthedevelopmentofefcientspectrumsharingalgorithms.Wealsoprovidealistofresearchtopicsforourfuturestudy.
7.1SummaryofContributions
Inthissection,wesummarizeourcontributionsonsolvingdifferentproblemsinthreedifferentcollaborationmodels.
7.1.1ContributiononSensingbasedCollaborationModel
Inthesensingbasedcollaborationmodel,secondaryuserssharetheirsensingreportsamongthem-selvestodetectfreechannelswithoutprimaryusers'knowledge.Basedonthismodel,anIEEE802.22standardisdevelopedforwirelessregionalareanetwork.Weaddressawellknownvulner-abilityinsharingsensingreportsinIEEE802.22,proposeapreventionmechanism,andvalidate175itseffectivenessthroughsimulations.
7.1.1.1TheSSDFAttackandProposedSolution
ThereportsharingvulnerabilityinIEEE802.22isreferredtoasspectrumsensingdatafalsication(SSDF)attack.AccordingtotheIEEE802.22guidelines,allSUssendtheirsensingreportstothebasestation,andtheBSmakesadecisionaboutthePUpresencebasedonallthereports.WehaveidentiedthatintheSSDFattack,amalicioussecondaryusermaysendfalsesensingreportstofoolthebasestation.WehaveshownthatamalicioususermayconvincetheBStomakeawrongdecisionaboutthePUpresenceandafterwards,itcanusethefreechannelwithoutsharingitwithothers.Thisattackisproventobeharmfultopromoteeffectivespectrumsharing.TofurtheranalyzetheSSDFattack,wehavediscussedhowamalicioususermayexploitthisvulnerabilityinthenetworkindependentlyandcollaborativelyandmaygainbenetsfromthat.Wehaveconsideredthreedifferenttypesofgroupattacks.Inthersttypeofgroupattack,malicioussecondaryusersformdifferentsubgroups.ThemembersinthesamesubgroupalterreportswiththesameprobabilityandreporttotheBS;howeversubgroupsareindependentandmayopttoaltersensingreportswithdifferentprobability.Inthesecondtypeofgroupattack,themalicioususersfalselyreporttheexactoppositeoftheactualsensingreportofmajorityoftheusers.Thisway,theattackerstrytomaximizetheirchancesofsuccesstomanipulatetheBSwhileavoidingdetectionbytheBS.Inthethirdtypeofgroupattack,malicioususersfollowanadaptiveattackingstrategywhereanattackerchangesitsattackingprobabilitybasedontheoutcomeofitsactionandadaptsaccordingly.Todefendagainstsuchindividualandgroupattacksofmalicioussecondaryusers,wehavepresentedanadaptivereputationbasedclusteringalgorithm,ARC.Inthisalgorithm,theBSkeepsrecordofrecentsensingreportsfromthesecondaryusers.Anumberofvirtualclustersareformed176basedontheirsensingreportsandtheirreputationusingk-medoidclustering.ThedecisionaboutthePUpresenceismadeinatwostepvoting.Intherststep,eachclusterdeterminesitsdecisionaboutthePUpresence.Tocalculatetheclustervote,currentreportofeachmemberoftheclusterisnormalizedbytheinverseofthedistancebetweenthememberandthemedoidofthecluster.Thus,dependingonauser'sdistancefromthemediod,itsvotingcontributionvaries.Auserclosertothemedoidhasmorepowertoinuencethecluster'sdecisionthantheonefarawayfromit.Inthesecondstep,thebasestationtakesamajorityvoteamongtheclusterstomakeanaldecision.Thenaldecisionisthenusedtoadjustthereputationoftheusersinthesameway.Auserclosertothemedoidofitsclusterexperiencesmorechangesinreputationthanauserawayfromthemedoid.Thus,thehonestandmalicioususersareseparatedintheBS,andSSDFattacksinIEEE802.22areprevented.
7.1.1.2PerformanceEvaluation
ToverifytheefcacyoftheproposedalgorithmARC,wehaveusedthreeperformancemetrics-errorrate,recall,andfalsealarmrate.ErrorratedenotesthenumberoftimestheBSmakesawrongdecisioninpercentage.Recalldenotestheratioofnumberofattackersdetectedbytheproposedalgorithmincomparisontotheactualnumberofattackersinthenetwork.Thefalsealarmratedenotesthenumberofhonestuserstaggedasattackersincomparisontothetotalnumberofuserstaggedasattackersinthenetwork.Wehaveperformedsimulationvaryingtheattackingprobability,changingthenumberofattackers,andadoptingdifferentattackingstrategieswiththealgorithmin[8].Thesimulationresultsshowthatourproposedalgorithmlowerstheerrorratethan[8].Italsodetectsmanyoftheattackersintheprocessandthefalsealarmrateisalmostnegligiblecomparedto[8].Theperformanceofourproposedalgorithmcanbeexplainedasfollow.Wheneverthenumberofattackersinthenetworkortheirattackingprobabilityincreases,thevirtual177distancebetweenhonestandmalicioususersisalsoincreased.Thisresultsintwocases.First,thehonestandmalicioususersendupinseparateclusters.Aslongastotalnumberofmalicioususersaresmallerthanthenumberofhonestusers,malicioususerscannottakeovermajorityoftheclustersandtheirinuenceontheBSisreduced.Second,themalicioususerscoexistwiththehonestusersindifferentclusters.Butthevirtualdistancebetweenthehonestandmalicioususersinthesameclusterbecomessignicantlylarge.Therefore,themalicioususerscannotinuencemostofthecluster'svoteandtheerrorratedropssignicantly.Thus,theproposedalgorithmARCneutralizestheharmfulimpactofthemalicioususersontheBSdecision.7.1.2ContributiononRelaybasedCollaborationModel
Inrelaybasedcollaborationmodel,theprimaryuserssharetheirspectrumintimeand/orfre-quencydomaininexchangeforrelayingservicefromthesecondaryusers.Thesecondaryusersactasintermediaterelaysinreturnfortransmissionopportunities.Thus,primaryandsecondaryusersschedulecooperativetransmissionbasedontheirmutualneeds.Weexplorethevalidityandeffectivenessofthismodelinthecaseofreal-timeapplications.Wealsoapplythismodeltoformroutingpathswheresecondaryusersrelayprimarypacketsovermultiplehopsinexchangefortransmissionopportunities.Wedevisecooperationalgorithmsbasedonthismodelforbothcasesanddiscussourndingsfromsimulationresults.
7.1.2.1CooperationAlgorithminReal-timeApplications
Wehaverstanalyzedtherelaybasedcollaborationmodelforreal-timeapplications.Duetothetimeconstraintsinreal-timepacketdelivery,thecooperationoverheadbecomesaseriousissueinthismodel.Thenegotiationphaseforcooperationmayimposehigherdelaytolaterpacketswhichmayhurtthesystemperformance.Wehavealsoidentiedthatsecondarytransmission178maycauseoverwhelminginterferencetoprimarytransmissionifnotproperlyanalyzed.Whenaprimaryuserisinagreementwithasecondaryuser,itallowsthesecondaryusertotransmit.Byallowingsecondarytransmission,theinterferencerelationshipamongusersischanged.Asaresult,theongoingtransmissionofotherprimaryusersmightexperienceinterferencefromthesecondarytransmission.Boththeseissuesarecarefullyhandledinouranalysis.Wehaveincludedtheimpactoftransmissiondeadlines,negotiationoverhead,andsecondaryinterferenceinauser'scooperativetransmissiondecision.Wehaveformulatedthecooperativerelayselectioninreal-timeapplicationsasaMarkovdeci-sionprocess.EachstateintheMDPrepresentsthequeuestatusofthenetworkandeachactionintheMDPrepresentsatransmissiondecision.Basedonthestatetransitionandtheselectedactiontherewardofprimaryandsecondaryuserisdened.Forprimaryusers,wedenetherewardastheprobabilityofsuccessfullydeliveringapacketwhileforsecondaryuserswedenetherewardasthenumberofbitstransmittedforeachunittransmissionpowerspentinrelaying.BasedonourMDPanalysis,wehavepresentedaninterferenceawarecooperationalgorithm.Inthisalgorithm,userstrytoreducetheoverheadbyprolongingthecooperativetransmissionperiodwithoutgoingthroughthenegotiationperiod.Asecondaryuserinitsoffernegotiatesthetransmissionpowertoreducepowerconsumptioninrelayingwithintheoperatingrange.Ontheotherhand,aprimaryuseracceptstheofferthatprovidesbesttransmissiontimeincomparisontodirecttransmission.Onceacooperationissetup,thecooperatinguserscontinuouslymonitorsthechangeinqueuesizeandthepacketdeliveryrate.Ifthestatuschangeexceedsacertainthreshold,bothusersterminatethecooperationandreturntonegotiationperiod.Otherwise,theuserscontinuecooperativetrans-missiononthenegotiatedterms.Thus,relaybasedcollaborationmodelenhancestheperformanceofreal-timeapplications.Ouranalysisrevealsthatthedistancebetweenaprimaryuserandasecondaryuserplaysa179signicantroleonthesuccessofrelaybasedcollaborationmodelinreal-timeapplications.Specif-ically,wefoundthatasecondaryusercanonlycooperatewiththeprimaryuserslocatedwithinacertaindistancefromit.Tofurtherunderstandtheeffectivenessofthecollaborationmodelandstudytheperformanceoftheproposedcooperationalgorithm,wehavefocusedonthreefeatures.Therstperformancemetricwelookintoisthepacketreceptionrate.Thesimulationresultshowsthattheproposedcooperationalgorithmimprovespacketreceptionrateandtransmissionopportu-nitiesofprimaryandsecondaryusersrespectivelythanthealgorithmproposedin[117].Thisisbecauseourproposedalgorithmtakesintoconsiderationtheinterferencecausedfromsecondarytransmission,andasecondaryuseradjustsitstransmissionpowerinrelayingprimarypacketsac-cordingly.ThesecondevaluationmetricweconsiderhereisthePUoverheadwhichdenotesthefrequencyofnegotiationperiodsinscheduledtransmissions.Thesimulationresultsshowthatourproposedalgorithmsignicantlyreducesthefrequencyofnegotiationperiodcomparedto[117].Unlike[117],ouralgorithmavoidsfrequentnegotiationbycontinuinganexistingcollaborationuntilthechangeinpacketreceptionratewithrespecttochangeinqueuedecreases.Thistradeoffalsoreducesthepowercostofsecondaryusersinrelayingprimarypacketswhichisconrmedinthecostbenetanalysis.Thecostbenetanalysisreferstotheamountofpowerconsumptioninrelayingtotransmitonesecondarypacket.
7.1.2.2CooperationAlgorithminMulti-hopRouting
Wehaveextendedouranalysisfromsinglehoptomultiplehopsinrelaybasedcollaborationmodel.Inthismodel,theroutingpathofaprimarysource-destinationpairisestablishedovermultiplesecondaryuserswhereeachsecondaryuserrelaysthepacketsofcooperatingprimaryuserstothenextoneinexchangefortransmissionopportunities.Weidentiedthatsuchmulti-hoprelaybasedcooperativeroutingfacescoupleofnewchallenges.First,unlikesinglehopcommunication,180thesuccessinamulti-hopcommunicationalsodependsonthesharingamongsecondaryusers.Second,themulti-hopcooperationneedstoensureconvergenceoftheroutingpathanditsstability.Wehaveformulatedthemulti-hoprelayselectionproblemasanoverlappingcoalitionforma-tiongamewhereeachcoalitionrepresentstheroutingpathofaprimarysource-destinationpair.Secondaryusersmayparticipateinoneormoreroutingpathsdependingontheopportunitiesandthusmayoverlapinmorethanonecoalition.Theprimaryuserssharetheirbandwidthwiththesecondaryusersparticipatingintheirroutingpaths.Wehavedenedtherewardofprimaryandsecondaryusersastheprimarythroughputintermsofdatarateandpathdelay,andsecondaryopportunitiesintermsofenergyconsumptionrespectively.Wehavepresentedacooperationbasedroutingalgorithm.Inthisalgorithm,aprimaryuserinitiatesthesearchofcooperativeroutingpathtoitsimmediateneighbors.Consequently,thereceivingsecondaryusersforwardtotheirneighborsiftheydonothaveanydirectpathtothenaldestination.Whileasecondaryuserreceivesaroutingproposal,itaddsitsowndemandandreturnstothesource.Finallythesourceprimaryuseracceptsthenewpathorcontinueswiththeexistingpath.Thedecisionofsearchingforroutingpathorcontinuingwiththeexistingoneisdeterminedbasedonsomecarefullytunedcontrolparametersthatensurequickconvergenceofthealgorithmandstabilityoftheroutingpaths.Theproposedcooperativeroutingalgorithmisevaluatedbyvaryingdifferentparametersandsimulationresultsarecomparedwiththealgorithmin[79].Thesimulationresultsshowthattheproposedalgorithmincreasesdatarateofprimaryusersandtransmissionopportunitiesofsec-ondaryusers.Wealsoobservethatthelengthoftheroutingpathremainsalmostsamewhereasthenumberofoverlappingsecondarynodesincreaseswiththeincreaseofnumberofprimaryusersinthenetwork.Thisimpliesthateachroutingpathhasamaximumlengthafterwhichitisnotprotableforbothprimaryandsecondaryusers.Ontheotherhand,thepathlengthincreaseswith181increasingnumberofsecondaryusers.Thisisbecausemoresecondaryuserscreatemoreoppor-tunityforcooperativeroutingpaths.Wealsovarytwoalgorithmparameters.First,wechangetheweightfactorthatcontrolsthetradeoffbetweendatarateprotanddelayprotofaprimaryuser.Astheprimaryprotsinclinetowardsdatarate,thenumberofoverlappingsecondaryusersandpathlengthincreases.Thesecondparametercontrolstheconvergencerateofthealgorithm.Aswesetsmallervalue,theroutingpathstakemoretimetoconverge.Thisisbecauseforasmallervalue,usersintendtoexploremoreopportunitiesforbetterroutingpaths.Thesendingsrevealthattheselectionofparameters'valuesisveryimportantforthesuccessoftheproposedcooperationalgorithm.
7.1.3ContributiononAuctionbasedCollaborationModel
Intheauctionbasedcollaborationmodel,primaryusersleasetheirunusedspectrum(whichwouldhavebeenunutilizedotherwise)tosecondaryusersformonetaryprots.Inthisdissertation,weinvestigateonlinedynamicsecondaryspectrummarkets,designtruthfulmechanisms,andpresentourndingsfromthesimulationofonlineauctions.
7.1.3.1OnlineSpectrumAuctions
Wehaveidentiedseveralmajorchallengestoadoptauctionbasedcollaborationmodelinonlinedynamicspectrummarkets.Therstchallengeinspectrumauctionsistoensuremaximumspec-trumutilizationi.e.thealgorithmshouldbeabletoallocatethesameunittomultiplebiddersaslongastheyarenotinterferingeachother.Thesecondchallengeweneedtoaddressistomakeonlinedecisiononspectrumallocationandpricing.Themechanismmustalsoadheretothedesiredpropertiessuchastruthfulness,individualrationality,andbudgetbalance.Wehaveaddressedtheseproblemsconsideringtwocases.Intherstcase,wehaveconsidered182thatdistributioninformationisknowntotheauctioneer.Abidderwithtransmissiondeadlinewillnotvalueanitemthesamewhenithasanopportunitytowinatlaterperiodsofitslifetime.Inthedistributionawaremechanism,theauctioneerusesthedistributioninformationtocalculatetheamountabidderiswillingtopayatdifferentperiodsofitslifetime.Wehavedenotedthatamountasabidder'spriorityandusedthisamounttorankthatbiddertoconsiderforspectrumallocation.Wehaveapproachedthecalculationinthreesteps.Intherststep,wehavecalculatedthebidders'priorityvaluesofthedynamicsettingwhenallbiddershavethesamevaluationofaspectrumunit.Next,wehaverelaxedthatassumptionwherebiddershavedifferentvaluations.Finally,wehavecalculatedthedynamicauctionsettingwheresellersalsohavedifferentvaluations.Basedonthesepriorityvalues,wedesigntwoonline(bothsingleanddouble)auctionmechanismsthatareprovedtobetruthful,individuallyrational,andbudgetbalanced.Inthesecondcase,wehaveconsideredthatthedistributioninformationisnotknowntotheauctioneer.Wehavepresentedspectrumallocationandpricingalgorithmfortheonlinedoubleauctionsetting.Wehaveappliedbidmonotonicspectrumallocationtosettheorderofbiddersconsideredforspectrum.Todeterminethespectrumpriceforawinningbidder,wehavecalcu-latedthecriticalpriceateachperiodofitslifetimeandthenalpriceissettotheminimumofthosecriticalvalues.Ateachperiod,themechanismexecutesthreesteps.Intherststep,candidatebid-dersareselectedaccordingtothespectrumavailability,interferencerelationshipamongbidders,andtheirbids.Inthesecondstep,debtsforthecurrentperiodiscalculated.Wehavecalculatedthedebtconsideringthewinnerswhohaswonbeforethelifetimeexpiresandthepricetheycouldhavepaidinthecurrentperiod.Inthenalstep,weselectthewinnersfromthecandidatelistinawaysothatthedebtsinthesecondstepcanbecompensatedequallybytheneighboringuserswithoutviolatinganyoftheauctionproperties.1837.1.3.2PerformanceEvaluation
Wehaverunsimulationwithvaryingdistributionparameterstoverifytheaccuracyofthepriorityfunctionsforbothonlinesingleanddoubleauctionsettings.Forbothsettings,theresultsshowthatthepriorityfunctionisastrictlynon-decreasingfunctionwithconcaveenvelopewithrespecttovalue.Theresultsalsoshowthatthepriorityofabidderincreaseswithincreaseinthenumberofarrivalofbiddersanddecreaseinnumberofsuppliesgiveneverythingremainssame.Wehavethusestablishedourobservationaboutthebidders'willingnesstopaythroughsimulationforbothdistributionawareonlinesingleanddoubleauctions.Wehavealsoperformednumericsimulationstotesttheperformanceoftheproposeddistribu-tionaware(bothsingleanddouble)anddistributionfreedoubleauctionalgorithmsbasedonfourdifferentmetricsŠ1)biddersatisfactionratedenotingthepercentageofbiddersthatwinspectrumunits,2)spectrumutilizationratedenotingthepercentageofspectrumunitssoldtobidders,3)av-eragevalueofawinnerdenotingtheaveragevaluationofwinningbidders,and4)averagepriceofawinnerdenotingthepriceawinnerpaysforspectrum.WehavecomparedtheirperformanceswithTopaz[30]andofinealgorithms.Users'densityisalsovariedtoenforcetestswithspectrumreusability.ThesimulationresultsshowthattheproposedonlinesingleanddoublealgorithmshavebetterbiddersatisfactionrateandspectrumutilizationthanTopaz[30].Theauctionefciencyismeasuredintermsofthetotalvaluationofwinningbiddersandtheauctionrevenueismeasuredintermsofwinners'payments.Again,ourproposedalgorithmsachievehigherefciencyandhigherrevenuethanTopaz[30]whileensuringtruthfulness,individualrationality,andbudgetbalance.1847.2FutureWork
Whilewehaveaddressedsomeofthechallengestowardsthedevelopmentofefcientspectrumsharingalgorithmsunderdifferentcollaborationmodels,therearestillsomeopenresearchprob-lemsneededtobesolved.Wepresentalistoftopicsthatwilldirectourfutureresearch.7.2.1UniedSolutionsagainstCombinedSSDFandPUEAttacksInthesensingbasedcollaborationmodel,wehavediscussedtheSSDFattackandpresentedanef-fectivesolutiontothisproblem.Inthisproblem,weassumedthatallsecondaryusersarewithintheinterferencerangeofthesingleprimaryuser.Eachsecondaryuserappliesenergydetectiontech-nique(basedonreceivedsignalstrength)andsendsabinaryreport(yes/no)totheBS.However,theremightbemorethanoneprimaryuserintheareaandbasedontheirlocationandtransmissionpower,thereceivedsignalstrengthmayvaryfromonesecondaryusertoanother.Asaresult,evenhonestsecondaryusersreachwrongconclusionaboutthechannelstatusfollowingenergydetectiontechnique.Ourproposedreputationbasedclusteringalgorithmmayincorrectlyidentifysomehonestsecondaryusersasattackersbecauseoftheirunintentionalfalsereporting.Thiswillincreaseerrorrateandfalsealarmrate.Therefore,thesecondaryusersshouldsubmittheirreceivedsignalstrengthwithlocationinformationtotheBSinsteadofbinaryreportsonly.Additionally,amalicioussecondaryusermayemulatethesignalofaprimaryusertofoolthedetectionmethodofanhonestsecondaryuser.Thisbehaviorisknownas`primaryemulationattack'orPUEattackinshort[5].Inthisattack,amalicioussecondaryuseremulatesaprimarysignalduringthesensingperiod.Allhonestusersdetectthesignal,andfalselyreporttheprimaryuser'spresence.TheBSdecidesthatthechannelisbusyandstopsanysecondarytransmission.Themalicioussecondaryuserscanexploitthatopportunityandexclusivelyusethechannelbythemselves.Themalicious185userscanformgroupstofurthermanipulatethesystem.Therefore,thefutureresearchshouldbedirectedondevelopingauniedsolution[112]thatpreventsbothSSDFandPUEattacks.7.2.2PervasiveCommunicationsinCooperativeCognitiveRadioNetworksWehaveanalyzedtherelaybasedcollaborationmodeltosupportreal-timetrafc.Wehaveex-tendedouranalysisfromsingletomultiplehopsandpresentedacooperationbasedroutingalgo-rithm.Whiletheresearchbroadensourunderstandingonrelaybasedcollaborationmodel,therearestillsomeunresolvedissues.Intheexistingresearch,theimplicitassumptionisthatthesec-ondaryusersalwaysrelayoverthesamespectrumasthecorrespondingprimaryuserstransmit.Thisrequirementlimitsthespectrumsharingopportunitiesinrealscenarioswherethespectrumisalreadycrowded.Instead,asecondaryusermayexploreallavailablespectrumbandstorelaypacketsofprimaryusers.Thispervasivemodeofcommunicationopensmoresharingopportunityamongusersoperatingoverdifferentspectrumbands.Interoperabilityamonguserswithdifferenttechnologiesanddifferentspectrumbandswillbeasignicantadvancementtowardstheconnec-tivityrequirementoffuturenetworks.
7.2.3TrustandSecurityissuesinCooperativeCognitiveRadioNetworksInrelaybasedcollaborationmodel,thesecondaryusereitherampliestheprimarysignalandre-laysit(amplifyandforward)ordecodesthesignal,reconstructsit,andthenrelaysit(decodeandforward).Thelattermethodoffersmoreresistancetomulti-pathfadingthantheformermethod.Inbothcasestheprimaryusersaretrustingsecondaryuserswiththeirpacketinformation.Thiswayofcommunicationmayopenopportunitiestothemalicioussecondaryusers[137].Withthisunre-strictedaccesstoprimarycontents,asecondaryusermaymanipulatethecontentswithmalicious186intent.Thesecondaryuserscanalsoextractcondentialinformationanduseittodevisedifferentspoongandrelayattacks.Sinceprimaryandsecondaryusersmaynotbelongtothesamenet-work,itisimportanttostudythetrustandsecurityissuesinmutualcommunication.Ensuringtheintegrityandcondentialityofthecontentsofprimaryusersinamulti-hopcooperationframeworkisanimportantresearchdirection.
7.2.4Multi-unitOnlineSpectrumAuctions
Basedontheauctionbasedcollaborationmodel,wehavedevelopedtheonlinespectrumalloca-tionmechanisms.Oneofthelimitationsoftheproposedmechanismsisthatthebidderscanbidforsingleunitofspectrumonly.Thisassumptionmaynotbepracticalinrealscenariossincebiddersmayhavedifferentbandwidthrequirements.However,theproposedmechanismscannotbedirectlyextensibletomulti-unitcasesbecauseofthefollowingreason.Asecondaryuserwithmulti-unitdemandmaymanipulatetheauctionmechanismbysettingalowervalueforlaterunits.Thus,asecondaryusermayindirectlyinuencethepricingofitsspectrum.Thisopportunityformanipulationcanbepreventedbyforcingabiddertohavethesamevalueforeachunitirrespectiveofitstotaldemand.Whilethismightworktopreventmanipulation,itisunfairtothehonestbiddersandtheauctionefciencyandrevenueturnoutwillbelow.Therefore,thefutureresearchshouldfocusondesigningmanipulationfreeonlineauctionmechanismssupportingmulti-unitdemandsfrombidders.Thebidders'demandsforspectrummayalsobediverseintermsofduration.Inourpresentwork,secondaryusers'demandofspectrumisforoneperiodonly.Similartomulti-unitdemand,abiddermayaskforspectrumforlongerdurations.Supportinguserswithspectrumdemandofdifferentdurationsinanonlineauctionsettingisalsoachallengingproblem.Forexample,afterreceivingallbidsforthecurrentperiod,ausermaybeallocatedspectrumforcontinuoususage.But187thescenariomaychangeinthenextperiodduetoarrivalofnewbidders,andassigningspectrumtothenewusermayearnmorerevenuethancontinuingwiththepreviousbidder.Inthatcase,themechanismhastopreemptthepreviouslyallocateduser,andthemechanismcannotchargetheuserforpartialusage[30].Thus,itisimportanttoaccommodatesuchuserdemandonlinewhileensuringhighspectrumutilization,auctionefciency,andrevenue.Followingourcurrentresultandrelatedresearchwork,thefutureonlinespectrumauctionswilladdressthediversityinuser'sdemandintermsofspectrumunitsanddurations.
7.2.5CombinatorialSpectrumAuctions
Acombinatorialauctionisonewherebidderssubmitmultiplebidtuplesinsteadforasingleone.Eachtuplemayrequestadifferentnumberofspectrumunitsfordifferentdurationsandausermaysetdifferentmaximumamountheiswillingtopayforeachunit.Wehaveconsideredanauctionsettingwherebidders'submitasinglebidrequest,andavailablespectrumarequantiedinunits.However,users'requirementsareusuallyexpressedintermsofminimumbandwidthandmayhavedifferentpreferences.Forexample,abiddermaywanttopaymoreforspectrumwithbetterpropagationcharacteristics.However,itmightalsoprovoketheuserstohidetheiractualdemandandmanipulatetheauctionmechanismtopayalesseramount.Wealsoneedtodevelopabiddinglanguagetoexpressusers'demandandsellers'supplytotheauctioneerefcientlyandeffectively.Thetransformationofcomplexsupplyanddemandintounderstandableformatanddevisingacombinatorialauctionmechanismwillbeanimportantdirectioninfutureresearch.Also,thecommonassumptionisthatifabidderdoesnotgetitsrequireddemanditsutilityremainszero.Butthisisnotthecasesinceitspacketwillbelostandthislossneedstobeincludedintheanalysis.Thismakesthedesignofcombinatorialauctionmechanismmuchmorechallenging.Ensuringauctionpropertieslikeindividualrationalityand188truthfulnessinacombinatorialauctionmechanismwillconstitutethefutureresearch.7.2.6PreventingBidderCollusioninSpectrumAuctions
Inanyauction,maliciousbiddersmaywanttomanipulatetheoutcomebychangingtheirbidscollaboratively.Thisformofunauthorizednegotiationamongbiddersisknownas`biddercollu-sion'.Traditionallongtermleasingspectrumauctionshavealreadysufferedthenegativeimpactofbiddercollusion[92].Newermodelofspectrumauctionsmayexperiencesimilarnegativeimpactintermsofauctionrevenueandspectrumutilization.Thisvulnerabilitythreatenstheopportunityofsmallbusinessesagainstthebigcorporate.Onlyrecentlyfewstudieslike[144]addressedtheproblemandpresentedanauctionmechanismthatdiscouragebiddersfromlyingabouttheirtruevaluation.However,thisstudyonlyconsidersbidderswithsingleunitdemand.Therefore,itisimportanttounderstandbiddercollusioninthecontextofdynamicsecondarymarket.Theauc-tionmechanismmustbeabletoidentifyanysuchattemptofbiddercollusionandtakenecessaryactionstomaintainfairnessandtruthfulness.
7.2.7SpectrumAuctionInfrastructure
Auctionbasedcollaborationmodelprovidesaneffectivemeansforspectrumsharing.Wehavesuccessfullyanalyzedthepropertiesoftheauctionmechanisminonlinesettings.Differentvari-ationsofspectrumauctionshavebeenproposedbytheresearchersfocusingonauctionrevenue,fairness,andtruthfulreporting.Astheallocationalgorithmsmaturethefutureresearchshoulddirecttobuildaninfrastructureforspectrumauctions.FCChasrecentlyputforwardathreetieredarchitectureplanforspectrumauction[26].Theresearchersneedtoresolvelotsofinfrastructuralandmaintenanceissuesregardingthisplanthathavenotbeenconsideredinliterature.Forexam-189ple,weneedtostandardizethebiddingprotocolforthesecondaryusers.TheresearchersneedtodevelophowtheFCCwillmaintaintheavailablespectruminformationandhowitwillshareitacrossvariouslocations.Ononehanditisdifculttoadoptacentralizedmechanismtotthediversityofbiddersandsellers;ontheotherhand,decentralizedmechanismwouldbeverydif-culttomaintainandkeepasynchronizeddatabase.Therefore,weneedtoconsideralldifferenttradeoffsininfrastructureplanning.Finally,whiletheseapproachesindividuallymayimprovespectrumutilization,itwillbeinter-estingtoseehowtheseapproachescoexistandcomplementeachotherinfuturenetworks.Thiswillalsoopenthepossibilityofapplyingthesesharingtechniquesaltogetherinpractice.Wewillstudyandanalyzetheperformanceofthesesharingtechniquesinthefutureresearch.190BIBLIOGRAPHY191BIBLIOGRAPHY[1]G.ChouinardA.N.Mody.Ieee802.22wirelessregionalareanetworks.IEEE802.22-10/0073r03,June2010.[2]H.Adam,C.Bettstetter,andS.M.Senouci.Multi-hop-awarecooperativerelaying.InVehicularTechnologyConference,2009.VTCSpring2009.IEEE69th,pages1Œ5,April2009.[3]I.F.Akyildiz,Won-YeolLee,andKaushikR.Chowdhury.Crahns:Cognitiveradioadhocnetworks.AdHocNetworks,7(5):810Œ836,2009.[4]IanF.Akyildiz,BrandonF.Lo,andRavikumarBalakrishnan.Cooperativespectrumsensingincognitiveradionetworks:Asurvey.Phys.Commun.,4(1):40Œ62,March2011.[5]A.Alahmadi,M.Abdelhakim,J.Ren,andT.Li.Defenseagainstprimaryuseremulationattacksincognitiveradionetworksusingadvancedencryptionstandard.IEEETransactionsonInformationForensicsandSecurity,9(5):772Œ781,May2014.[6]MohammedAltamaimi.Spectrumsharing:Quantifyingthebenetsofdifferentenforce-mentscenarios,2014.[7]P.Anand,A.S.Rawat,HaoChen,andP.K.Varshney.Collaborativespectrumsensinginthepresenceofbyzantineattacksincognitiveradionetworks.InCommunicationSystemsandNetworks(COMSNETS),2010SecondInternationalConferenceon,pages1Œ9,2010.[8]A.Anandkumar,N.Michael,andA.K.Tang.OpportunisticSpectrumAccesswithMultipleUsers:LearningUnderCompetition.InProc.ofIEEEINFOCOM,SanDeigo,USA,March2010.[9]D.D.Ariananda,M.K.Lakshmanan,andH.Nikookar.Asurveyonspectrumsensingtechniquesforcognitiveradio.InCognitiveRadioandAdvancedSpectrumManagement,2009.CogART2009.SecondInternationalWorkshopon,pages74Œ79,May2009.[10]MahmoudAshour,AmrA.El-Sherif,TamerA.ElBatt,andAmrMohamed.Cognitiveradionetworkswithprobabilisticrelaying:Stablethroughputanddelaytradeoffs.CoRR,abs/1404.6112,2014.[11]D.GunawardenaB.Radunovic,A.ProutiereandPeterKey.Exploitingchanneldiversityinwhitespaces.TechnicalReportMSR-TR-2011-53,MicrosoftResearch,April2011.192[12]A.BanaeiandC.N.Georghiades.Throughputanalysisofarandomizedsensingschemeincell-basedad-hoccognitivenetworks.InCommunications,2009.ICC'09.IEEEInterna-tionalConferenceon,pages1Œ6,June2009.[13]S.BanerjeeandD.O.Wu.Finalreportfromthensfworkshoponfuturedirectionsinwirelessnetworking.Technicalreport,NationalScienceFoundation,November2013.[14]D.BertsekasandR.Gallager.DataNetworks.Prentice-Hall,1987.[15]KaiguiBianandJung-MinflJerryflPark.Securityvulnerabilitiesinieee802.22.InProceed-ingsofthe4thAnnualInternationalConferenceonWirelessInternet,WICON'08,pages9:1Œ9:9,ICST,Brussels,Belgium,Belgium,2008.ICST(InstituteforComputerSciences,Social-InformaticsandTelecommunicationsEngineering).[16]ChandraChekuriandSanjeevKhanna.Aptasforthemultipleknapsackproblem.InPro-ceedingsoftheEleventhAnnualACM-SIAMSymposiumonDiscreteAlgorithms,SODA'00,pages213Œ222,2000.[17]DaweiChen,SixingYin,QianZhang,MingyanLiu,andShufangLi.Miningspectrumusagedata:alarge-scalespectrummeasurementstudy.InProceedingsofthe15thannualinternationalconferenceonMobilecomputingandnetworking,MobiCom'09,pages13Œ24,NewYork,NY,USA,2009.ACM.[18]RuiliangChen,Jung-MinPark,andKaiguiBian.Robustdistributedspectrumsensingincognitiveradionetworks.InINFOCOM2008.The27thConferenceonComputerCommu-nications.IEEE,2008.[19]Y.ChenandH.-S.Oh.Asurveyofmeasurement-basedspectrumoccupancymodelingforcognitiveradios.CommunicationsSurveysTutorials,IEEE,PP(99):1Œ1,2014.[20]YanjiaoChen,PengLin,andQianZhang.Lotus:Location-awareonlinetruthfuldoubleauctionfordynamicspectrumaccess.InDynamicSpectrumAccessNetworks(DYSPAN),2014IEEEInternationalSymposiumon,pages510Œ518,April2014.[21]YanjiaoChen,JinZhang,KaishunWu,andQianZhang.Tames:Atruthfulauctionmecha-nismforheterogeneousspectrumallocation.InINFOCOM,2013ProceedingsIEEE,pages180Œ184,2013.[22]ZhiliChen,HeHuang,YueSun,andLiushengHuang.True-mcsa:Aframeworkfortruthfuldoublemulti-channelspectrumauctions.WirelessCommunicatio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