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Primary User Behavior Estimation and Channel Assignment for Dynamic Spectrum Access in Energy-Constrained Cognitive Radi...

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Title:
Primary User Behavior Estimation and Channel Assignment for Dynamic Spectrum Access in Energy-Constrained Cognitive Radio Sensor Networks
Physical Description:
1 online resource (111 p.)
Language:
english
Creator:
Li, Xiaoyuan
Publisher:
University of Florida
Place of Publication:
Gainesville, Fla.
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Thesis/Dissertation Information

Degree:
Doctorate ( Ph.D.)
Degree Grantor:
University of Florida
Degree Disciplines:
Electrical and Computer Engineering
Committee Chair:
Mcnair, Janise Y
Committee Members:
Wu, Dapeng
Yang, Liuqing
Zhang, Lei

Subjects

Subjects / Keywords:
channel -- cognitive -- environment -- primary -- user
Electrical and Computer Engineering -- Dissertations, Academic -- UF
Genre:
Electrical and Computer Engineering thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract:
Cognitive radio technology improves spectrum utilization by allowing secondary users(SUs) to access the licensed spectrum bands in an opportunistic manner as long as it does not interfere with the activity of the primary users (PUs). This technology may also be used for wireless sensor networks (WSNs) to solve the problem of spectrum scarcity and bursty traffic. With the knowledge of PU behavior, sensors can transmit packets on the channels which are currently not occupied and vacate the bands by the detection of PU signals. In this dissertation, the spectrum sensing and spectrum access problems are investigated in a cognitive radio sensor network (CRSN), in which a cognitive radio is installed in each sensor and it can be tuned to any available channel. Modeling and estimating the PU behavior is critical to implement dynamic spectrum access.We investigate the estimation accuracy of the PU behavior based on the Markov model. The performance of Maximum Likelihood (ML) estimation is evaluated by its distribution. To meet the requirement of estimation accuracy while reducing the unnecessary sensing time, we propose a learning algorithm to dynamically estimate the required length of the sample sequence. Due to the inherent power and resource constraints of sensor networks, energy efficiency is the primary concern for the network design. We investigate the residual energy aware channel assignment problem in a cluster-based multi-channel CRSN. An R-coefficient is developed to estimate the predicted residual energy using sensor information (current residual energy and expected energy consumption) and channel conditions (PU behavior). An Optimization-based channel assignment scheme which maximizes the total residual energy of the network is proposed to reduce energy consumption and prolong the network lifetime. We also consider another important concern for proposing an appropriate opportunistic spectrum access scheme, the total energy consumption needed to successfully transmit a certain amount of information bits. It helps sensors to transmit as much information as possible during their lifetime. We dynamically choose the optimal packet size to minimize energy-per-bit (the ratio of the total energy consumption to the amount of successfully transmitted information bits), which adapts to the time-varying channel states depending on both the behavior of primary users and the activity of sensors. Moreover, we increase the network lifetime by balancing residual energy among sensors.
General Note:
In the series University of Florida Digital Collections.
General Note:
Includes vita.
Bibliography:
Includes bibliographical references.
Source of Description:
Description based on online resource; title from PDF title page.
Source of Description:
This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility:
by Xiaoyuan Li.
Thesis:
Thesis (Ph.D.)--University of Florida, 2013.
Local:
Adviser: Mcnair, Janise Y.

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Applicable rights reserved.
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MISSING IMAGE

Material Information

Title:
Primary User Behavior Estimation and Channel Assignment for Dynamic Spectrum Access in Energy-Constrained Cognitive Radio Sensor Networks
Physical Description:
1 online resource (111 p.)
Language:
english
Creator:
Li, Xiaoyuan
Publisher:
University of Florida
Place of Publication:
Gainesville, Fla.
Publication Date:

Thesis/Dissertation Information

Degree:
Doctorate ( Ph.D.)
Degree Grantor:
University of Florida
Degree Disciplines:
Electrical and Computer Engineering
Committee Chair:
Mcnair, Janise Y
Committee Members:
Wu, Dapeng
Yang, Liuqing
Zhang, Lei

Subjects

Subjects / Keywords:
channel -- cognitive -- environment -- primary -- user
Electrical and Computer Engineering -- Dissertations, Academic -- UF
Genre:
Electrical and Computer Engineering thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract:
Cognitive radio technology improves spectrum utilization by allowing secondary users(SUs) to access the licensed spectrum bands in an opportunistic manner as long as it does not interfere with the activity of the primary users (PUs). This technology may also be used for wireless sensor networks (WSNs) to solve the problem of spectrum scarcity and bursty traffic. With the knowledge of PU behavior, sensors can transmit packets on the channels which are currently not occupied and vacate the bands by the detection of PU signals. In this dissertation, the spectrum sensing and spectrum access problems are investigated in a cognitive radio sensor network (CRSN), in which a cognitive radio is installed in each sensor and it can be tuned to any available channel. Modeling and estimating the PU behavior is critical to implement dynamic spectrum access.We investigate the estimation accuracy of the PU behavior based on the Markov model. The performance of Maximum Likelihood (ML) estimation is evaluated by its distribution. To meet the requirement of estimation accuracy while reducing the unnecessary sensing time, we propose a learning algorithm to dynamically estimate the required length of the sample sequence. Due to the inherent power and resource constraints of sensor networks, energy efficiency is the primary concern for the network design. We investigate the residual energy aware channel assignment problem in a cluster-based multi-channel CRSN. An R-coefficient is developed to estimate the predicted residual energy using sensor information (current residual energy and expected energy consumption) and channel conditions (PU behavior). An Optimization-based channel assignment scheme which maximizes the total residual energy of the network is proposed to reduce energy consumption and prolong the network lifetime. We also consider another important concern for proposing an appropriate opportunistic spectrum access scheme, the total energy consumption needed to successfully transmit a certain amount of information bits. It helps sensors to transmit as much information as possible during their lifetime. We dynamically choose the optimal packet size to minimize energy-per-bit (the ratio of the total energy consumption to the amount of successfully transmitted information bits), which adapts to the time-varying channel states depending on both the behavior of primary users and the activity of sensors. Moreover, we increase the network lifetime by balancing residual energy among sensors.
General Note:
In the series University of Florida Digital Collections.
General Note:
Includes vita.
Bibliography:
Includes bibliographical references.
Source of Description:
Description based on online resource; title from PDF title page.
Source of Description:
This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility:
by Xiaoyuan Li.
Thesis:
Thesis (Ph.D.)--University of Florida, 2013.
Local:
Adviser: Mcnair, Janise Y.

Record Information

Source Institution:
UFRGP
Rights Management:
Applicable rights reserved.
Classification:
lcc - LD1780 2013
System ID:
UFE0045265:00001


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PRIMARYUSERBEHAVIORESTIMATIONANDCHANNELASSIGNMENTFORDYNAMICSPECTRUMACCESSINENERGY-CONSTRAINEDCOGNITIVERADIOSENSORNETWORKSByXIAOYUANLIADISSERTATIONPRESENTEDTOTHEGRADUATESCHOOLOFTHEUNIVERSITYOFFLORIDAINPARTIALFULFILLMENTOFTHEREQUIREMENTSFORTHEDEGREEOFDOCTOROFPHILOSOPHYUNIVERSITYOFFLORIDA2013

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c2013XiaoyuanLi 2

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Tomyfamily 3

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ACKNOWLEDGMENTS Firstandforemost,IwanttoexpressmysincerestgratitudetoDr.JaniseMcNair,forhersupportiveadvice,patienceandkindnessonmygraduatestudies.DrMcNairisarespectable,responsibleandresourcefulprofessorandshehasprovidedmewithvaluableadviceinthewritingofthisthesis.Herkeenandvigorousacademicobservationenlightensmenotonlyinthisthesisbutalsoinmyfuturecareer.IwillextendmythankstomyPhDcommitteemembers.IwouldliketothankDr.LiuqingYangforallthepleasanttalkwithher,Dr.DapengWuforhishelpandencouragement,Dr.ShigangChenforhisprecioussuggestiononmyresearchworkandDr.LeiZhangforhiskindness.Iwouldalsoliketoexpressmyappreciationstothemforreviewingmymanuscriptandgivingcomments.Iwouldalsoliketoshowmygratefulthankstoallmylabmates,whomademyPhDlifecolorfulandmucheasier.IwillgivemyspecialappreciationtoDexiangWang,whoprovidedmanyusefulhelpandsuggestiononmyPhDresearch.IwillalsogivemythankstoXiangMao,forhishelpatthelastphaseofmydissertation.Lastbutnottheleast,mythankswouldgotomybelovedfamily,myhusbandandmyparents,whoseloveandsupportisthemostimportantthingtomeandhelpmemovingforward. 4

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TABLEOFCONTENTS page ACKNOWLEDGMENTS .................................. 4 LISTOFTABLES ...................................... 7 LISTOFFIGURES ..................................... 8 ABSTRACT ......................................... 10 CHAPTER 1INSTRUCTION .................................... 12 1.1CognitiveRadioSensorNetworks ...................... 12 1.2EnergyChallenges ............................... 13 1.3IssuesandContributions ........................... 14 1.3.1PrimaryUserBehaviorEstimation .................. 14 1.3.2ResidualEnergyAwareChannelAssignment ............ 15 1.3.3DynamicSpectrumAccesswithPacketSizeAdaptation ...... 15 1.4Organization .................................. 15 2SYSTEMMODELS ................................. 17 2.1FrameStructureandNetworkmodel ..................... 17 2.1.1SpectrumSensingModel ....................... 17 2.1.2ChannelAssignmentModel ...................... 18 2.2PrimaryUserBehaviorModel ......................... 20 2.3EnergyConsumptionModel .......................... 21 3PRIMARYUSERBEHAVIORESTIMATIONWITHPERFECTSENSING .... 23 3.1OverviewofPUEstimationChallenges .................... 23 3.2RelatedWork .................................. 25 3.3TheDistributionofMaximumLikelihoodEstimator ............. 26 3.3.1DerivationoftheProbabilityMassFunction(PMF) ......... 27 3.3.2UsingNormalDistributiontoApproximatetheRealEstimationDistribution ............................... 31 3.4TheAnalysisoftheEstimationAccuracy ................... 34 3.4.1CondenceInterval ........................... 34 3.4.2TheRequiredLengthoftheSampleSequence ........... 36 3.5TheAdaptationoftheSampleSequenceLength .............. 37 3.6SimulationResults ............................... 40 3.6.1EstimationAccuracyofExactPMF .................. 40 3.6.2EstimationAccuracyofAdaptationAlgorithm ............ 43 3.7Summary .................................... 47 5

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4PRIMARYUSERBEHAVIORESTIMATIONWITHIMPERFECTSENSING .. 49 4.1OverviewofImperfectSensing ........................ 49 4.2RelatedWork .................................. 52 4.3TheHiddenMarkovModelofPUbehavior .................. 52 4.3.1ModelofImperfectSensing ...................... 53 4.3.2StructureofHiddenMarkovModel .................. 54 4.4EstimationofTransitionProbabilitiesUsingHMM .............. 56 4.4.1Probabilityofagivenobservedsequence .............. 56 4.4.2EstimationofHMMModelParametersUsingBaum-WelchAlgorithm 58 4.5TheEstimationAccuracyAnalysisofHMM ................. 62 4.5.1CondenceLeveloftheEstimation .................. 62 4.5.2SelectionofInitialParameters ..................... 65 4.6NumericalResults ............................... 66 4.7Summary .................................... 70 5RESIDUALENERGYAWARECHANNELASSIGNMENTSCHEMES ..... 73 5.1SpectrumSharinginCognitiveRadioSensorNetworks(CRSNs) ..... 73 5.2RelatedWork .................................. 75 5.3R-Coefcient .................................. 76 5.4ChannelAssignment .............................. 78 5.4.1RandomPairing ............................. 78 5.4.2GreedyChannelSearch ........................ 78 5.4.3Optimization-basedChannelAssignment .............. 79 5.5SimulationResults ............................... 81 5.6Summary .................................... 85 6DYNAMICSPECTRUMACCESSWITHPACKETSIZEADAPTATIONANDRESIDUALENERGYBALANCING ......................... 87 6.1DynamicSpectrumAccessandEnergyConsumption ........... 87 6.2RelatedWork .................................. 88 6.3PacketSizeAdaptation ............................ 89 6.4ResidualEnergyBalancingChannelAssignment .............. 91 6.5SimulationResults ............................... 95 6.5.1PerformanceofPacketSizeAdaptation ............... 95 6.5.2ResidualEnergyBalancingChannelAssignment .......... 98 6.5.3Impactsofestimationaccuracy .................... 100 6.6Summary .................................... 100 7CONCLUSIONS ................................... 102 REFERENCES ....................................... 104 BIOGRAPHICALSKETCH ................................ 111 6

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LISTOFTABLES Table page 4-1HMMSymbols .................................... 56 5-1Simulationparametersofresidualenergyawarechannelassignment ...... 82 6-1Simulationparametersofdynamicspectrumaccesswithpacketsizeadaption 96 6-2Theimpactofestimationaccuracyonothermetrics ............... 100 7

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LISTOFFIGURES Figure page 2-1Time-slottedstructureofaframe .......................... 17 2-2Acluster-basedCRSNwithPU .......................... 18 2-3Time-slottedstructureofaframe .......................... 19 2-4Atwo-stateMarkovmodelofPUbehavior ..................... 20 3-1Probabilitydistributionof^p ............................. 32 3-2Thecomparisonofbinomialandnormdistribution ................ 33 3-3Thecomparisonofexactandnormdistribution(p=0.5,q=0.5) ........ 35 3-4Theimpactoftransitionprobabilitiesontherequiredsamplesequencelength 38 3-5Theowchartoftheproposedlearningalgorithm ................ 39 3-6Impactoftransitionprobabilitiesonestimationaccuracyof^p ........... 41 3-7Impactofnumberofsamplesonestimationaccuracy(p=q=0.1) ....... 42 3-8Impactoffalsealarmprobabilityonestimationaccuracy(p=q=0.1) ..... 43 3-9EstimatesofPUbehavioroverframes ....................... 44 3-10Thecomparisonoftheoreticalandestimatedresults ............... 44 3-11Thecondenceleveloftheproposedalgorithm .................. 45 3-12Thecomparisonofthecondencelevelbetweenxedandproposedalgorithm 46 3-13Thecomparisonoftherelativeerrorbetweenxedandproposedalgorithm .. 47 4-1PUbehaviormodelwithimperfectsensing ..................... 51 4-2Two-stateHMMmodel ................................ 54 4-3Theprobabilitydistributionofperfectandimperfectsensing ........... 64 4-4Thecomparisonofcondencelevelbetweenperfectandimperfectsensing .. 67 4-5Theimpactoftransitionprobabilitiesontherequiredsequencelengthforimperfectsensing ........................................ 68 4-6Theimpactoftransitionprobabilitiesontherequiredsequencelengthforperfectsensing ........................................ 69 4-7Theimpactoftransitionprobabilitiesontherequiredsequencelength(p=q) .. 69 8

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4-8Theimpactofinitializationontheestimationaccuracy .............. 71 4-9Impactoffalsealarmprobabilityontheestimationaccuracy ........... 71 5-1PseudocodeofGreedyalgorithm ......................... 79 5-2PseudocodeofOptimization-basedchannelassignment ............ 81 5-3Averagenetworkenergyconsumptionoverframes(numberofframes=50) .. 83 5-4Averagestandarddeviationofsensorresidualenergyoverframes(numberofframes=50) ..................................... 84 5-5Numberofremainingalivesensorsaftereachframe(numberofsensors=30) 84 5-6Averageeffectiveenergyconsumptionoverframes(numberofframes=50) .. 85 6-1ThecomparisonofaccumulativenetworkEPBamongdifferentpacket-sizingschemes ....................................... 96 6-2ThecomparisonofoverallnetworkEPBamongdifferentpacket-sizingschemes 97 6-3Thecomparisonofthevolumeofsuccessfullydeliveredinformationamongdifferentpacket-sizingschemes ........................... 97 6-4Thecomparisonofnetworklifetimeamongdifferentchannelassignmentschemes 99 6-5Theimpactofestimationaccuracyonaccumulativenetworkthroughput .... 99 9

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AbstractofDissertationPresentedtotheGraduateSchooloftheUniversityofFloridainPartialFulllmentoftheRequirementsfortheDegreeofDoctorofPhilosophyPRIMARYUSERBEHAVIORESTIMATIONANDCHANNELASSIGNMENTFORDYNAMICSPECTRUMACCESSINENERGY-CONSTRAINEDCOGNITIVERADIOSENSORNETWORKSByXiaoyuanLiAugust2013Chair:JaniseY.McNairMajor:ElectricalandComputerEngineering Cognitiveradiotechnologyimprovesspectrumutilizationbyallowingsecondaryusers(SUs)toaccessthelicensedspectrumbandsinanopportunisticmanneraslongasitdoesnotinterferewiththeactivityoftheprimaryusers(PUs).Thistechnologymayalsobeusedforwirelesssensornetworks(WSNs)tosolvetheproblemofspectrumscarcityandburstytrafc.WiththeknowledgeofPUbehavior,sensorscantransmitpacketsonthechannelswhicharecurrentlynotoccupiedandvacatethebandsbythedetectionofPUsignals.Inthisdissertation,thespectrumsensingandspectrumaccessproblemsareinvestigatedinacognitiveradiosensornetwork(CRSN),inwhichacognitiveradioisinstalledineachsensoranditcanbetunedtoanyavailablechannel. ModelingandestimatingthePUbehavioriscriticaltoimplementdynamicspectrumaccess.Forperfectsensingwithoutsensingerrors,weinvestigatetheestimationaccuracyofthePUbehaviorbasedontheMarkovmodel.TheperformanceofMaximumLikelihood(ML)estimationisevaluatedbyitsdistribution.Tomeettherequirementofestimationaccuracywhilereducingtheunnecessarysensingtime,weproposealearningalgorithmtodynamicallyestimatetherequiredlengthofthesamplesequence.Fortheimperfectsensingwithsensingerrors,atwo-stateHMMisemployedtomodelPUbehaviorwithimperfectsensing.Baum-Welchalgorithmisusedtoestimatethe 10

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transitionprobabilities.Theestimationaccuracyiscomparedwiththatofperfectsensing. Duetotheinherentpowerandresourceconstraintsofsensornetworks,energyefciencyistheprimaryconcernforthenetworkdesign.Weinvestigatetheresidualenergyawarechannelassignmentprobleminacluster-basedmulti-channelCRSN.AnR-coefcientisdevelopedtoestimatethepredictedresidualenergyusingsensorinformation(currentresidualenergyandexpectedenergyconsumption)andchannelconditions(PUbehavior).AnOptimization-basedchannelassignmentschemewhichmaximizesthetotalresidualenergyofthenetworkisproposedtoreduceenergyconsumptionandprolongthenetworklifetime. Wealsoconsideranotherimportantconcernforproposinganappropriateopportunisticspectrumaccessscheme,thetotalenergyconsumptionneededtosuccessfullytransmitacertainamountofinformationbits.Ithelpssensorstotransmitasmuchinformationaspossibleduringtheirlifetime.Wedynamicallychoosetheoptimalpacketsizetominimizeenergy-per-bit(theratioofthetotalenergyconsumptiontotheamountofsuccessfullytransmittedinformationbits),whichadaptstothetime-varyingchannelstatesdependingonboththebehaviorofprimaryusersandtheactivityofsensors.Moreover,weincreasethenetworklifetimebybalancingresidualenergyamongsensors. 11

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CHAPTER1INSTRUCTION Inthischapter,thebackgroundknowledgeofacognitiveradiosensornetworks(CRSN)isprovided,whichincludesitsdenition,motivationanddesignchallenges.Thentheorganizationofthisdissertationfollows. 1.1CognitiveRadioSensorNetworks Therapidgrowthofwirelessservicesleadstothedemandforasolutiontospectrumscarcityandunder-utilizationofthelicensedbands.Therefore,theFederalCommunicationsCommission(FCC)allowsunlicenseduserstoaccessthetemporarilyunusedspectruminanopportunisticmanner[ 1 ].Cognitiveradiotechnologyenablesdynamicspectrumaccessforthesecondaryuser(SU)bysensingtheusageinformationofthespectrumfromtheradioenvironment.TheSUwithcognitiveradiocanaccessthebestavailablespectrumamongthelicensedbandsaslongasitdoesnotcauseanyinterferencetotheprimaryusers(PUs)withaspeciclicense.Inthisway,thespectrumefciencyofthenetworkwillbeimproved. Cognitiveradiotechnologymayalsobeusedinwirelesssensornetworks(WSNs).ExistingWSNsaretraditionallycharacterizedbyxedspectrumallocationovercrowdedbands[ 2 ].Spectrumscarcityishighlightedbecauseoftheeverincreasingdemandforvariouswirelessnetworks,suchasWiFiandBluetooth.Theevent-drivennatureoftengeneratesburstytrafc,whichincreasestheprobabilityofcollisionandpacketloss.TraditionalWSNslacktheabilityofadjustingitsradiocongurationtothedynamicoperatingenvironment[ 3 ].Cognitiveradioallowsopportunisticspectrumaccesstomultipleavailablechannels,whichgivespotentialadvantagestoWSNsbyincreasingthecommunicationreliabilityandimprovingtheenergyefciency.Recentpapers,suchas[ 2 4 14 ],proposethepromisingapplicationsofCognitiveRadioSensorNetworks(CRSNs).SimilartotraditionalWSNs,aCRSNconsistsofalargenumberoflow-costlow-powersensorswithalimitedbatteryenergy.IntheCRSN,eachsensor 12

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isequippedwithacognitiveradio,whichenablestheadaptationofitsoperatingparameters.AsensorselectsthemostappropriatechannelonceanavailablebandisidentiedandvacatesthebandwhenaPU'stransmissionisdetected.TheintegrationofcognitiveradiocapabilitiesprovidesmanyadvantagestoWSNs.Forexample,therearepotentiallymorebandwidthavailableforsensors.Moreover,biterrorratemaybedecreasedduetotheabilitytoaccessthebestavailablechannel. 1.2EnergyChallenges TherearemanychallengesfordesigningcommunicationandnetworkingprotocolsforaCRSN,suchasadditionalcommunicationandprocessingrequirementswithcognitiveradiocapabilities,transmissionpowercontroltoavoidinterferencewithPUs,multi-hopopportunisticcommunicationsamongdenselydeployedsensors.Aboveall,themostimportantoneistheinherentenergyconstraintofthelow-capabilitysensorswithunrechargeablebatteries. First,sincesensormustcollectspectrumusageinformationtoopportunisticallyaccessthelicensedchannelwhichiscurrentlynotoccupiedbyPUs,theyhavetosensespectrumstondspectrumopportunitiespriortotransmission.Unreliableidenticationofspectrumopportunitiesmayresultinpacketlossandretransmission,whichisawasteoftheenergy.However,additionalenergyconsumptionisimposedbyspectrumsensingandtheexchangeofsensingresults.Adedicatedchannelisdesignatedtoexchangecontroldatasuchasspectrumsensingresultandneighborinformation.Sinceanetwork-widecommonchannelmaynotbepossible,alocalcommoncontrolchannelisneededwithinagivenlocality. Second,sensorshavetoanalyzethesensingresultsandmakeadecisionaboutthebestavailablechannelandthecorrespondingoperatingparameters.Moreover,sincemultiplesensorsmaytrytoaccessthesamespectrum,aspectrumsharingmechanismisneededtocoordinatemultiplesimultaneoustransmissions,whichincludesboththemanagementofcoexistencewithPUsandresourceallocationamongsensors.The 13

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mediumaccesscontrol(MAC)protocolsintraditionalcognitiveradionetworkfocusonQoSperformancesuchasthroughputanddelays,whichdonotmatchtheinherentresourceconstraintofsensors.SpectrumaccessinCRSNshastobecoordinatedtoincreasebothspectrumutilizationandenergyefciency. 1.3IssuesandContributions Inthisdissertation,thespectrumsensingandspectrumaccessproblemsareinvestigatedinaCRSN,inwhichacognitiveradioisinstalledineachsensor.Theradiocanbetunedtoanyavailablechannel.SensorscouldaccessthebestavailablechannelwhichistemporarilyunusedbyanyPUandstopsthetransmissionimmediatelyafterthePUssignalsaredetected. 1.3.1PrimaryUserBehaviorEstimation SincethespectrumaccessofsensorsshouldnotcauseanyinterferencetoPUs,aprecisemodelandestimationofthePUbehaviorisimportanttoenableefcientdynamicspectrumaccess.Inthisdissertation,PUbehaviorismodeledasaMarkovchainanditstransitionprobabilitiesareestimatedusingmaximumlikelihood(ML)estimation.WeinvestigatetheestimationaccuracyofthePUbehaviorandtherelationshipbetweentheaccuracyandtheprocessingoverhead. Themaincontributionsofthisworkareasfollows: 1. Anexpressionfortheprobabilitymassfunction(PMF)oftheMLestimatorisderivedtoevaluatetheaccuracyoftheestimatedtransitionprobabilities.Tothebestofourknowledge,thisistherstworktoanalyzetheperformanceoftheMLestimatorbyderivingitsPMF. 2. WeshowthatthedistributionoftheMLestimatorapproximatelyfollowsthenormaldistribution.Theestimationaccuracyisthereforeanalyzedbythecondenceintervaldenedonthenormaldistribution. 3. AlearningalgorithmwhichiterativelyrenestheestimationresultsisdevelopedforanaccurateestimationofthePUbehavior.ThelengthofthesamplesequencerequiredforagivencondencelevelisdynamicallydeterminedtoadapttothechangingPUbehavior.Itachievestherequirementofestimationaccuracywhilereducingunnecessarysensingtime. 14

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4. Atwo-stateHiddenMarkovmodel(HMM)isutilizedtomodelPUbehaviorandestimatePUstatetransitionprobabilitieswithsensingerror.Therelationshipamongthelengthoftheobservedsequence,therealstatetransitionprobabilities,thefalsealarmandmissdetectionprobabilities,theselectionofinitialparametersandtheaccuracyoftheestimatedvaluesisvalidated. 1.3.2ResidualEnergyAwareChannelAssignment SpectrumaccessofsensorshastobecoordinatedtoincreasespectrumutilizationwhileavoidinginterferencetoPUs.Moreover,collisionsamongsensorshouldalsobereduced.Therefore,thechannelassignmentproblemshouldbeinvestigatedfromtheaspectofenergyconsumptionandnetworklifetime. Themaincontributionsofthisworkareasfollows: 1. AnR-coefcientdeterminedbysensorenergyinformationandPUbehaviorisproposedtorepresentthepredictedresidualenergy. 2. AnOptimization-basedchannelassignmentschemeisproposedwhichmaximizesthetotalresidualenergyofthenetwork.Itleadstobetterperformanceintermsofenergyconsumptionandnetworklifetime. 1.3.3DynamicSpectrumAccesswithPacketSizeAdaptation Theeffectiveenergy,whichistheenergyconsumptionforthesuccessfullytransmitteddataisconsideredforthedynamicspectrumaccess.Ithelpssensorstotransmitasmuchinformationaspossibleduringtheirlifetime. Themaincontributionsofthisworkareasfollows: 1. Apacketsizeadaptationschemefordatapacketsisproposedtoimproveenergyefciencybyminimizingthenetworkenergy-per-bit(EPB),whichisdenedastheratioofthetotalenergyconsumptiontotheamountofsuccessfullytransmittedinformationbitsofthewholenetwork. 2. Afterthepacketsizeisdetermined,thechannelassignmentofCRSNisinvestigatedwiththeobjectiveofresidualenergybalancing. 1.4Organization Therestofthedissertationisorganizedasfollows. 15

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InChapter 2 ,thesystemmodelsusedinthisdissertationaredescribed,whichincludesthenetworkmodel,thetime-slottedframestructure,thePUbehaviormodelandtheenergyconsumptionmodel. InChapter 3 ,theestimationaccuracyofPUbehaviorisstudied.Tomeettherequirementofestimationaccuracywhilereducingtheunnecessarysensingtime,weproposealearningalgorithmwhichrenestheestimationresultsiteratively. InChapter 4 ,atwo-stateHMMisemployedtomodelPUbehaviorwithimperfectsensing.Baum-Welchalgorithmisusedtoestimatethetransitionprobabilities.Theestimationaccuracyiscomparedwiththatofperfectsensing. InChapter 5 ,thechannelassignmentproblemisinvestigatedwiththegoaloftotalnetworkresidualenergymaximization. InChapter 6 ,thedynamicspectrumaccessschemewithpacketsizeadaptationandresidualenergybalancingisproposedtoimproveenergyefciencyandprolongthenetworklifetime. InChapter 7 ,weconcludethecurrentworkanddescribetheworkremainingforthisdissertation. 16

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CHAPTER2SYSTEMMODELS Inthischapter,wedescribethesystemmodelsusedineachwork.Thechapterisorganizedasfollows.Section 2.1 introducesthenetworkmodelandthetime-slottedframestructure.Section 2.1.1 describesthetimestructureusedforspectrumsensing.Section 2.1.2 describesthecluster-basednetworkmodelandthetimestructureforchannelassignment.Section 2.2 introducestheMarkovmodelofPUbehavior.TheenergyconsumptionmodelisintroducedinSection 2.3 2.1FrameStructureandNetworkmodel 2.1.1SpectrumSensingModel Figure2-1. Time-slottedstructureofaframe Thesystemistime-slottedwithKslotsinaframe.ThelengthofaframeisassumedtobeshortenoughsothatthePUbehaviorremainsunchangedwithinthedurationofaframe.Eachframeconsistsofachannelsensingphase,whichtakestherstNslots,andachannelaccessphase,whichcantaketheremainingK-Nslots.TheslottedstructureisshowninFigure 2-1 Inthechannelsensingphase,channeloccupancyaccordingtoaPUismonitoredtoformasamplesequenceoflengthN.ThePUbehaviorisestimatedbasedonthesequence.TheSUtransmitsdatapacketsinthechannelaccessphaseinlightoftheestimationresults. 17

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Thereisaninherenttradeoffintheframestructurebetweenthenumberoftimeslotsforchannelsensingandchannelaccess.Anincreaseinthechannelsensingtimeimprovestheestimationaccuracy.However,italsodecreasesthedatatransmissiontimeinthechannelaccessphase.Inaddition,theenergyconsumptionforchannelsensingandthememorycostforthestorageofsensingresultsshouldbeminimized.Therefore,thelengthofthesamplesequenceshouldbecarefullyselectedtoimprovetheoverallperformance. 2.1.2ChannelAssignmentModel Figure2-2. Acluster-basedCRSNwithPU ThePUnetworkandtheCRSNaregenerallyunrelatedintermsofcommunication.TheycoexistinthesameareaasshowninFigure 2-2 .PUsareeitherstaticormobilenodeswithhightransmissionpower.Sensorsareassumedtobestaticormoveinfrequentlyinsidetherangeofacluster.Theresourceandcapabilityconstraintslimitthespectrumsensingcapabilityofsensors.Moreover,thenetwork-widecommoncontrolchannelwhichplaysanessentialroleingeneralcognitiveradionetworksmaynotbefeasibleinalow-powerlarge-areaCRSN[ 2 ].Therefore,weproposea 18

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cluster-basedmulti-channelCRSN,inwhicheachclusterhasaclusterhead(CH)andaxedlocalcommoncontrolchannel.TheCHisaspecialenergy-richsensornodewithhighcognitiveradiocapabilitiesforspectrumsensingandchannelassignmentamongitsclustermembers(CMs).Thelocalcommoncontrolchannelisintroducedtoexchangecontrolinformationforchannelassignmentandnetworkmaintenance. WeassumethereareMdifferentdatachannelsandonecommoncontrolchannelineachcluster.Ateachtime,adatachannelcanonlybeassignedtoonesensorandasensorcanonlytransmitononedatachannel.CMssenddatapacketstoCHondatachannels.CHcollectsdatafromitsmembersandsendstheprocesseddatatothebasestationviatheclusterheadbackbone.Inthiswork,weonlyconsiderchannelassignmentforintra-clustercommunicationandenergyconsumptionduringdatatransmissionfromCMstoCH.Inter-clusterperformancewillbediscussedinourfuturework.Therefore,theconceptnetworkinthisworkmeanstherangeofacluster. Figure2-3. Time-slottedstructureofaframe Thesystemistime-slottedwithK+1timeslotsinaframe.Eachframeconsistsofachannelassignmentphase,whichtakestherstslot,andadatatransmissionphase,whichcantaketheremainingKslots.TheslottedstructureisshowninFigure 2-3 .CHmonitorsPUactivityoneachchannelperiodicallyandestimatesspectrumavailabilitybasedonPUstatistics.Ineachtimeslot,CMswillbeinoneofthethreestates,listen,transmitorsleep.Inchannelassignmentphase,CMsensorsthatneedtotransmitwakeupandinformCHbysendingalowbit-rateassign requestmessageviathecommon 19

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controlchannel.Thentheyturntolistenstateinthisphaseforassign replymessagesfromCH.ThesesensorsarecalledactivesensorsandtheprobabilityofCMsensorsbeingactiveisdenotedasPactive.Theassign requestmessageincludestheresidualenergyandthelocationinformationoftheCMforcalculationofpredictedresidualenergy,whichwillbeexplainedlater. Afterreceivingalltheassign requestmessages,CHcarriesoutchannelassignment,whichwillbediscussedinChapter 5 andChapter 6 .ThenCHbroadcaststheas-sign replymessageswithchannelassignmentresults.IfaCMdoesnotgetassignedtoanychannel,itwillturntosleepstatetosavepower.CMwhogetsassignedtunesitsradiotvothedesignatedchannelandstartstotransmittheeventdatatoCHindatatransmissionphase.However,itwillstopthetransmissionimmediatelyafterdetectingPUsignalsonthesamechannelandtheongoingtransmittedpacketwillbedropped.Whenitstopsornishestransmission,itturnstosleepandwakesupwhenanothertransmissionisrequired. 2.2PrimaryUserBehaviorModel ThePUbehaviorismodeledinatwo-stateMarkovchain,wherethepresenceandabsenceofPUsignalsarerepresentedasbusyandidlestates,respectively,asshowninFigure 2-4 Figure2-4. Atwo-stateMarkovmodelofPUbehavior Letpdenotetheprobabilitythatthechannelstatechangesfromidletobusy.Symmetrically,letqdenotetheprobabilitythatthechannelstatechangesfrombusyto 20

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idle.TheprobabilitythatthechannelisidleandbusycanbeobtainedbyderivingthesteadystateprobabilitiesforthemodelshowninFigure 2-4 8>>>>><>>>>>:Pidle=q p+qPbusy=p p+q(2) ThePUbehavioristhereforedeterminedbythetransitionprobabilities.TheSUmakesthedecisiononchannelselectionbysearchingforthebestavailablechannelbasedontheseparameters.Thedetailswillbediscussedinthefollowingchapters. 2.3EnergyConsumptionModel Inthisdissertation,sinceCHisassumedtoberichinenergy,weonlyconsiderCMs'energyconsumptionforbothcontrolmessageexchangeanddatatransmission.ThereareNsensorsdeployedinaclusterandeachsensorcarriesanon-rechargeablebatterywiththesameinitialenergyEin.Thecommunicationchannelcanbeconsideredasachannelfollowingasimplepathlossmodel,wherefadingandmultipatheffectsareignored[ 15 ].TheenergyconsumedindatatransmissionisEcir+"d,whereEciriscircuitenergyconsumptionand"istheamplierenergyrequiredatthereceiver,bothofwhicharemeasuredperbit.disthedistancebetweenCMandCHandisthepathlosscoefcientdependingonthepathcharacteristics.Inthiswork,afreespacemodelisconsideredforsignaldegradation,inwhichisequalto2. Therefore,ifsensoricontinuouslytransmitsforlslots,thetotalenergyconsumptioniscalculatedasfollows. Etri(l)=(Ecir+"d2i)BTl(2) WhereBisthetransmissionrateinbit=sandTisthelengthofaslotperiodinsecond.EcirisinnJ=bit."isinpJ=bit=m2. 21

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SinceCMsreceivethebroadcastmessagesfromCH,energyconsumedforthereceptionalsoneedstobeconsideredanditisdenotedby Ervi(l)=EcirBTl(2) 22

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CHAPTER3PRIMARYUSERBEHAVIORESTIMATIONWITHPERFECTSENSING Inthischapter,weinvestigatetheestimationaccuracyofthePUbehaviorbasedontheMarkovmodel.MaximumLikelihood(ML)estimationisemployedtoestimatethetransitionprobabilitiesoftheMarkovmodelbasedonthesamplesequenceofPUidle/busystates.AnapproximatedistributionoftheMLestimatorisderivedtoevaluatetheestimationaccuracyspeciedbythecondencelevel.Tomeettherequirementofestimationaccuracywhilereducingtheunnecessarysensingtime,weproposealearningalgorithmwhichrenestheestimationresultsiteratively.ItdynamicallyestimatestherequiredlengthofthesamplesequencewhichisadaptivetothechangingPUbehavior. Thischapterisorganizedasfollows.Section 3.1 introducesanoverviewofthePUestimationproblems.Section 3.2 introducestherecentstudiesrelatedtoPUbehavior.Section 3.3 introducestheMLestimator,followedbythederivationofitsPMFandtheapproximationofitsnormaldistribution.TheanalysisoftheestimationaccuracyandtherequiredlengthofthesamplesequencearediscussedinSection 3.4 .TheestimationalgorithmwithadaptivelengthofthesamplesequenceisproposedinSection 3.5 .Section 3.6 providesthenumericalresults.Section 3.7 concludesthischapter. 3.1OverviewofPUEstimationChallenges Akeyfunctionalityofcognitiveradiodevicesistosensetheradioenvironmentbeforetheyaccessthelicensedspectrum.ThespectrumsensingresultisusedtounderstandhowthePUsusethespectrum.Therefore,accuratespectrumsensingisimportantforSUstoavoidanyinterferencetoPUs.Unreliableidenticationofspectrumavailabilitywouldresultincollisions,packetlossesandunnecessarydelays,whichdegradestheoverallperformance.AprecisemodelandestimationofthePUbehavioristhusneededforpredictionofthefuturechannelstatestohelpimprovespectrumutilization. 23

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ThePUbehaviorhasbeenassumedtofollowtheMarkovmodelinrecentstudies[ 16 22 ].ThechanneloccupancyofPUatanytimeslotisconsideredasastate,whichcanbeeitherbusyoridle.TheMarkovmodelprovidestheinformationforthepredictionoffuturestatesbasedonthecurrentobservations.IfthePUbehaviorisknown,theSUcouldmaketheappropriatedecisiononchannelaccessandproactivelyvacatethechannelevenbeforedetectinganysignalfromthePU.However,thereareseveralchallengesimposedbythismethodology. First,inacognitiveradionetwork,anSUmaynotknowthePUbehaviorinadvance.Itkeepssensingthechanneloverconsecutivetimeperiodsandstoresallthechannelstatestoformasamplesequence.ThenthetransitionprobabilitiesoftheMarkovmodelforthePUbehaviorareestimatedbasedonthesamplesequence.Withoutknowingthemodelparameters,theSUmaycauseharmfulinterferencetoPUsandtheperformanceoftheSUitselfmayalsobegreatlyaffected. Second,thesamplesequenceshouldbelongenoughtoachievecertainprecisionoftheestimation.However,boththeenergywastedforperformingspectrumsensingandthememoryusedforstoringthesamplesareexpectedtobekeptaslowaspossiblefortheSU.Moreover,theSUcannottransmitdatapacketswhenitsensesthechannel.Thetimewastedonthechannelsensingshouldbereducedtoimprovechannelutilization. Third,thePUbehaviormayvaryovertimeduetothechangingPUtrafcdensity[ 22 23 ].Thus,thePUbehaviorestimatehastobeupdatedaccordingly.Moreover,therequirednumberofstatesinthesamplesequenceneededforanaccurateestimationofthemodelmayalsodiffergreatly.TheSUshouldperformthechannelestimationusinganonlinealgorithmwiththevariedlengthofthesamplesequencetoreduceunnecessarysensingtime. Duetotheaboveconcerns,apreciseestimatorofthePUbehaviorisneededtoenableefcientdynamicspectrumaccessofSUs.Maximumlikelihood(ML)estimation 24

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[ 24 ]iscommonlyusedtoestimatethestatetransitionprobabilitiesoftheMarkovmodel.TheaccuracyoftheMLestimationhastobeenforcedfortheSUtoobtainaproperknowledgeofthePUbehaviorbeforeaccessingthespectrum.Inthiswork,theexactdistributionoftheMLestimatorisderivedtoanalyzetherelationshipamongthelengthofthesamplesequence,thestatetransitionprobabilitiesandtheaccuracyoftheestimates.WeshowthatthedistributionoftheMLestimatorapproximatelyfollowsthenormaldistribution.Theestimationaccuracyisthereforeanalyzedbythecondenceintervaldenedonthenormaldistribution.Therequiredlengthofthesamplesequencecanthereforebedeterminedforanygivenaccuracyrequirement.AlearningalgorithmwhichiterativelyrenestheestimationresultsisdevelopedforanaccurateestimationofthePUbehavior.ThelengthofthesamplesequenceisdynamicallydeterminedtoadapttothechangingPUbehavior. 3.2RelatedWork Inmostoftherecentstudiesoncognitiveradionetworks,thechanneloccupancyofPUshasbeenconsideredasatwo-stateMarkovmodel[ 16 22 ].In[ 16 20 21 ],thetransitionprobabilitiesareassumedtobeknowntotheSU.However,inrealapplications,itisverydifcultforanSUtoobtaintheseparametersinadvance.IthastoestimatethePUbehaviorbasedonthecurrentobservations.In[ 19 ],thechannelusagepatternofPUsisassumedtobestatic,whichisalsonotpracticalinachangingradioenvironment.TheSUhastoobtainnewsamplesandre-estimatethetransitionprobabilitiesaccordingtovariationsofthePUbehavior.MLestimation[ 24 ]isusedforestimatingthetransitionprobabilitiesoftheMarkovchainin[ 17 ]and[ 18 ].Thetransitionprobabilitiesaredeterminedbymaximizingtheprobabilityofthecurrentobservations.However,theperformanceanalysisoftheMLestimationisnotconsideredandhowtodecidetherequirednumberofsamplesisnotmentionedin[ 17 ]and[ 18 ].Tothebestofourknowledge,ourworkistherstworktoestimatethelengthofthesamplesequencerequiredforanygivenaccuracyrequirementoftheMLestimatorusingitsdistribution. 25

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3.3TheDistributionofMaximumLikelihoodEstimator Thetwo-stateMarkovchainisusedtomodelthePUbehaviorinthiswork,asdescribedinChapter 2 ,Section 2.2 .Inrealapplications,thetransitionprobabilitiesinEquation( 2 )maynotbeknownaprioriandtheyneedtobeestimatedbasedontheobservationsofthePUbehavior.ThestatesoftheNmostrecentslotsonthechannelformasamplesequencedenotedbyS=fs1,s2,,sNg.Itisabinarysequencewith0and1representingidleandbusystate,respectively.UsingMLestimation[ 24 ],theestimatorsoftransitionprobabilitiespandqarederivedasfollows: 8>>>>><>>>>>:^p=n01 n0^q=n10 n1,(3) where^pand^qdenotestheestimatedvalueofpandq,respectively.nij(i,j2f0,1g)representsthenumberofstatetransitionsfromstateitostatej.ni(i2f0,1g)denotesthenumberofalltransitionsfromstatei. Notethatn01andn0shouldsatisfy: n01min(n0,N)]TJ /F4 11.955 Tf 11.95 0 Td[(n0),(3) whereNisthenumberofstatesinthesamplesequence. Proof:Basedonthedenitionsofn01andn0,n01n0.Thenumberofalltransitionsfromstate1isn1=n10+n11.n0+n1isequaltothenumberoftotaltransitionsN)]TJ /F3 11.955 Tf 11.96 0 Td[(1. Assumen01>N)]TJ /F4 11.955 Tf 11.96 0 Td[(n0,wehave n01+n0>N,n01+n0>n0+n1+1,n01>n1+1(3) 26

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Thenumberoftheoccurrencesofstate1isequalton1ifthelaststateisstate0orn1+1otherwise.Becauseeach0!1transitioninvolvesastate1,n01cannotbegreaterthann1+1.ThiscontradictstheconstraintinEquation( 3 ).Similarly,n10min(n1,N)]TJ /F4 11.955 Tf 11.96 0 Td[(n1). 3.3.1DerivationoftheProbabilityMassFunction(PMF) ThePMFoftheMLestimatorisderivedtoevaluateitsperformanceinthissection.DenotePr(^p=x)astheprobabilitythatptakesvaluexanditiscalculatedasfollows.DenotePr(^q=x)astheprobabilitythatqtakesonvaluexanditcouldbederivedsimilarly. TheobservedsequencewithNstatesamplesisS=fs1,s2,,sNgandhencethetotalnumberofallpossiblesequencesis2N.Itiscomputationallyoverwhelmingtoenumerateeachsequenceandcalculateitscorrespondingtransitionprobabilityestimate.Instead,wesearchforananalyticalwaytocalculatePr(^p=x)bygroupingallthesequencesthatleadtothesamex,whichistheratioofn01ton0.Thatmeansxisthesameforallsequenceswithinthecorrespondinggroup.Then,thePMFcanbeobtainedbysummingalltheindividualoccurrenceprobabilityvaluesofthesequenceswithinthatgroup.Forexample,Pr(^p=0.5)=Pmin(n0,n)]TJ /F7 7.97 Tf 6.59 0 Td[(n0)k=1Pr(^p=k 2k)wherePr(^p=k 2k)representstheprobabilityofoccurrenceofallsequenceswithn01=kandn0=2k. TheprobabilityPr(^p=x)withthegivenn01andn0isderivedasfollows.Denoteaparametersetby=(s1,sN,n0,n01),inwhichs1representstherststateoftheobservedsequence,sNrepresentsthelaststate,n0andn01denotesthenumberoftransitionsstartingwith0andthenumberoftransitionsfrom0to1,respectively.DeneQ()asafunctionoftheparameterset,whichrepresentstheindividualoccurrenceprobabilityofthesequenceswithagiven.Ntotal()representsthetotalnumberofsequenceswiththesame.T()representsthetotaloccurrenceprobabilityofthesequenceswiththegivenanditiscalculatedby: T()=Q()Ntotal(),(3) 27

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Intheaboveequation,Q()with=(1,0,n0,n01)iscalculatedby: Q()=Pbusypn01qn01+1(1)]TJ /F4 11.955 Tf 11.96 0 Td[(p)n0)]TJ /F7 7.97 Tf 6.59 0 Td[(n01(1)]TJ /F4 11.955 Tf 11.96 0 Td[(q)N)]TJ /F7 7.97 Tf 6.58 0 Td[(n0)]TJ /F7 7.97 Tf 6.58 0 Td[(n01)]TJ /F11 7.97 Tf 6.58 0 Td[(2.(3) Notethatinthiscase,therelationshipofN,n0,n01mustsatisfythefollowingconstraints: n01min(n0,N)]TJ /F4 11.955 Tf 11.96 0 Td[(n0)]TJ /F3 11.955 Tf 11.96 0 Td[(2).(3) TheproofisskippedasitissimilartotheproofofEquation( 3 ). NextwewilldescribethecalculationofthenumberofsequenceswiththesameindividualoccurrenceprobabilityQ().Becausethesequenceendswithstate0,thetotalnumberofstates0isn0+1.Denotethenumberofstates0beforethelaststate1bym.Thereforetherearen0+1)]TJ /F4 11.955 Tf 11.96 0 Td[(m(mn0)consecutivezerosattheend.Anexampleofthestatesequenceisshownasfollows: Sj=f1z }| {001z }| {001z }| {00110000g.(3) Thenumberofgroupsz }| {001isn01andthenumberofzerosineachz }| {001isintherangeof[1,m)]TJ /F3 11.955 Tf 11.95 0 Td[((n01)]TJ /F3 11.955 Tf 11.96 0 Td[(1)]. Themzerosshouldbeallocatedton01z }| {001groupsandthenumberofallocationsiscalculatedby Nalloc()=m)]TJ /F11 7.97 Tf 6.58 0 Td[((n01)]TJ /F11 7.97 Tf 6.59 0 Td[(1)Xl=10B@m)]TJ /F4 11.955 Tf 11.95 0 Td[(ln01)]TJ /F3 11.955 Tf 11.96 0 Td[(21CA=0B@m)]TJ /F3 11.955 Tf 11.96 0 Td[(1n01)]TJ /F3 11.955 Tf 11.95 0 Td[(11CA.(3) 28

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Then,foreachallocation,thenumberofplacementsofz }| {001inthestatesequenceis Ncomb()=0B@N)]TJ /F4 11.955 Tf 11.95 0 Td[(n0)]TJ /F3 11.955 Tf 11.95 0 Td[(2n011CA.(3) NotethataccordingtotheconstraintinEquation( 3 ),n01isguaranteedtobelessthanorequaltoN)]TJ /F4 11.955 Tf 11.95 0 Td[(n0)]TJ /F3 11.955 Tf 11.95 0 Td[(2. Sincem2[n01,n0],thetotalnumberofthesequenceswiththesameoccurrenceprobabilityQ()iscalculatedby Ntotal()=n0Xm=n01Nalloc()Ncomb()=n0Xm=n010B@m)]TJ /F3 11.955 Tf 11.96 0 Td[(1n01)]TJ /F3 11.955 Tf 11.95 0 Td[(11CA0B@N)]TJ /F4 11.955 Tf 11.95 0 Td[(n0)]TJ /F3 11.955 Tf 11.95 0 Td[(2n011CA=0B@n0n011CA0B@N)]TJ /F4 11.955 Tf 11.95 0 Td[(n0)]TJ /F3 11.955 Tf 11.95 0 Td[(2n011CA.(3) Therefore,T()with=(1,0,n0,n01)canbeobtainedbyEquation( 3 ). T(0,0,n0,n01),T(0,1,n0,n01),T(1,1,n0,n01)couldbederivedinasimilarway. Notethatifn01=N)]TJ /F4 11.955 Tf 12.57 0 Td[(n0)]TJ /F3 11.955 Tf 12.58 0 Td[(1,thestatesequencewith(s1,sN)=(1,0)doesnotexist.Moreover,ifn01=N)]TJ /F4 11.955 Tf 12.53 0 Td[(n0,thesequencewith(s1,sN)=(0,0),(s1,sN)=(1,0)and(s1,sN)=(1,1)doesnotexist.n01cannotbegreaterthanN)]TJ /F4 11.955 Tf 12.21 0 Td[(n0accordingtotheconstraintinEquation( 3 ).Inthisway,thecompleteexpressionfortheoccurrence 29

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probabilityofallthesequenceswiththesamen0andn01isobtainedby z(n0,n01)=8>>>>>>>>>>>>>>>>>>>><>>>>>>>>>>>>>>>>>>>>:X(s1,sN)2f00,01,10,11gT(s1,sN,n0,n01),1n01N)]TJ /F4 11.955 Tf 11.95 0 Td[(n0)]TJ /F3 11.955 Tf 11.95 0 Td[(2X(s1,sN)2f00,01,11gT(s1,sN,n0,n01),n01=N)]TJ /F4 11.955 Tf 11.96 0 Td[(n0)]TJ /F3 11.955 Tf 11.96 0 Td[(1T(0,1,n0,n01),n01=N)]TJ /F4 11.955 Tf 11.96 0 Td[(n0(3) Thefollowingisanotherwayofderivingtheexpressionofz(n0,n01),whichismoreefcient.InthecalculationofNtotal,therstandthelaststatearebothconsideredwiththeparameterset.However,itcanbeseenfromtheabovedescriptionthatonlysNaffectsthevalueofNtotal.Ifweassumea0!0transitionwhensN=0and1!1transitionwhensN=1,thenn0(thenumberofalltransitionsfromstate0)isthenumberofstates0inthesequenceandn1isthenumberofstates1.Inthisway,theeffectofsNcanbeignoredandNtotalisdeterminedonlybyn0andn01.FindingNtotal(n0,n01),whichistheapproximatenumberofsequenceswiththegivenn0andn01isalsoacombinatoricsproblem. First,withn0states0,weselectn01ofthemtoformthetransitionfromstate0tostate1.Then,N)]TJ /F4 11.955 Tf 12.7 0 Td[(n0)]TJ /F4 11.955 Tf 12.7 0 Td[(n01states1arelefttoinsertintothesequence.Sincetherearealreadyn01transitionsfromstate0tostate1,theremainingstates1canonlybeinsertedafteranyofthen01states1oratthebeginningofthesequence,whicharen01+1possiblepositionsintotal.Thisisessentiallythestarsandbarsproblemofcombinatorialmathematics[ 25 ]withN)]TJ /F4 11.955 Tf 12.51 0 Td[(n0)]TJ /F4 11.955 Tf 12.51 0 Td[(n01starsandn01+1bars.Sothetotalnumberis: 30

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Ntotal(n0,n01)=0B@n0n011CA0B@N)]TJ /F4 11.955 Tf 11.95 0 Td[(n0n011CA.(3) Q()isderivedinthesamewayasEquation( 3 ).Therefore,z(n0,n01)isexpressedby: z(n0,n01)=8>>>>>>>>>>>>>>>>>>>><>>>>>>>>>>>>>>>>>>>>:Ntotal(n0,n01)X(s1,sn)2f00,01,10,11gQ(s1,sn,n0,n01),0n01n)]TJ /F4 11.955 Tf 11.96 0 Td[(n0)]TJ /F3 11.955 Tf 11.96 0 Td[(2Ntotal(n0,n01)X(s1,sn)2f00,01,11gQ(s1,sn,n0,n01),n01=n)]TJ /F4 11.955 Tf 11.95 0 Td[(n0)]TJ /F3 11.955 Tf 11.95 0 Td[(1Ntotal(n0,n01)Q(0,1,n0,n01),n01=n)]TJ /F4 11.955 Tf 11.95 0 Td[(n0.(3) Denex=n01 n0,thePMFof^pisexpressedasfollows. Prob(^p=x)=X(n0,n01)2(n01 n0=x)z(n0,n01)(3) Aspecialcaseisn0=0.Inthiscase,thestatesequenceconsistsofN)]TJ /F3 11.955 Tf 12.1 0 Td[(1numberofconsecutive1withthelaststateunknownanditsprobabilityisPbusy(1)]TJ /F4 11.955 Tf 12.34 0 Td[(q)N)]TJ /F11 7.97 Tf 6.59 0 Td[(2.Theestimateofthetransitionprobability^pisdened1. ThePMFof^pwhenp=0.5,q=0.5isshowninFigure 3-1 3.3.2UsingNormalDistributiontoApproximatetheRealEstimationDistribution Sincethetimespentonexactdistributionevaluationispolynomiallycontingentonthelengthofthesamplesequence,itbecomescomputationallycumbersometoresolvetherealestimationdistributionwhentherequiresamplesequencegetslarge.Instead,accordingtoourobservationonthesimilarityoftherealestimationdistributiontothe 31

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Figure3-1. Probabilitydistributionof^p normaldistribution,wechoosetotakeanapproximationapproachtosimplifysuchdistributionevaluation.Inwhatfollows,onlytheestimationof^pisdiscussedandthedistributionof^qcanbederivedsimilarly. AccordingtoEquation( 3 ),^p=n01 n0,wherebothn01andn0arerandomvariablesandundetermined.However,whenNislargeenough,theprobabilitythatasampleisinstate0isstationaryanditiscalculatedbyEquation( 2 ).Therefore,givenpandq,thenumberofstates0inthesamplesequenceisdeterminedbyn0=NPidle.Theproblemofderivingthedistributionof^pisthusconvertedtoderivingthedistributionofn01,whichisdiscussedasfollows. Thesetofstates0canbeconsideredasn0independentBernoullitrials.Foreachstate0,itgeneratesatransitiontostate1withtheprobabilityp.Theprobabilityofgettingexactlyktransitionsfromstate0tostate1inthesen0trialsisobtainedbythe 32

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probabilitymassfunctionofabinomialdistribution. Prob(n01=k)=0B@n0k1CApk(1)]TJ /F4 11.955 Tf 11.96 0 Td[(p)(n0)]TJ /F7 7.97 Tf 6.58 0 Td[(k)(3) Sincen01isabinomiallydistributedrandomvariable,theexpectedvalueisn0pandthevarianceisn0p(1)]TJ /F4 11.955 Tf 11.95 0 Td[(p).Itisdenotedbyn01B(n0p,n0p(1)]TJ /F4 11.955 Tf 11.95 0 Td[(p)). Ifn0islargeenough,acloseapproximationtothebinomialdistributionof^n01isgivenbythenormaldistribution[ 26 ]: n01Norm(n0p,n0p(1)]TJ /F4 11.955 Tf 11.95 0 Td[(p))(3) Figure3-2. Thecomparisonofbinomialandnormdistribution Figure 3-2 showsacomparisonofthebinomialdistributionandnormaldistributionwhenn01=100andp=0.5. Asuitablecontinuitycorrectionhastobeappliedtotheaboveapproximation[ 27 ].Forexample,ifXhasabinomialdistributionandYhasanormaldistribution,andbothofthemhavethesameexpectedvalueandvariance,then P(Xx)=P(X
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Theadditionof0.5isthecontinuitycorrection;theuncorrectednormalapproximationgivesconsiderablylessaccurateresults.Thisequationwillbeusedlaterfortheanalysisoftheestimationaccuracy. AccordingtotheMLestimatorinEquation( 3 ),^p=n01 n0.Sincen0isdetermined,^pisalsoapproximatelynormallydistributedwiththemeanpandthevariancep(1)]TJ /F4 11.955 Tf 11.96 0 Td[(p) n0. ^pNorm(p,p(1)]TJ /F4 11.955 Tf 11.96 0 Td[(p) n0)(3) TheapproximatenormaldistributioniscomparedwiththeexactdistributioninFigure 3-3 .Thecurveofexactdistributionreectsthesummationofprobabilitymassfunctionwithineach0.025subspaceintheintervalof[0,1].Fornormaldistribution,weplottheprobabilityonthemid-pointvalueofeachsubspacefordemonstration.Itisnotedthatasthelengthofthesamplesequence(N)increases,thetwodistributionsbecomemoreclosetoeachother.ThismeanswhenNisverylarge,thenormaldistributionprovidesagoodapproximationoftheexactdistribution. 3.4TheAnalysisoftheEstimationAccuracy 3.4.1CondenceInterval OurgoalistoachievetheestimationaccuracyoftheMLestimatorwiththeminimumnumberofsamples.Inthischapter,theestimationaccuracyisevaluatedintermsofthecondenceinterval.Acondenceintervalisspeciedwithtwoparameters:acondencelevel1)]TJ /F9 11.955 Tf 13.19 0 Td[(andanerrorbound.Theaccuracyrequirementoftheestimatorisdenedastheprobabilitythatthetruevalueofthetransitionprobabilitypisintheinterval[^p)]TJ /F9 11.955 Tf 11.96 0 Td[(^p,^p+^p]isatleast1)]TJ /F9 11.955 Tf 11.95 0 Td[(: Prob(^p)]TJ /F9 11.955 Tf 11.95 0 Td[(^pp^p+^p)1)]TJ /F9 11.955 Tf 11.95 0 Td[(,0<,<1.(3) Weintroducehowtousethecontinuitycorrectiontocalculatetheprobabilityoftheabovedenitionasfollows.DenetworandomvariablesXandY,XB(,), 34

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Figure3-3. Thecomparisonofexactandnormdistribution(p=0.5,q=0.5) YNorm(,).Thecondenceintervalofinthebinomialdistributionis [X)]TJ /F9 11.955 Tf 11.96 0 Td[(X,X+X].(3) Supposewehave Prob()]TJ /F4 11.955 Tf 9.3 0 Td[(XX)]TJ /F9 11.955 Tf 11.96 0 Td[( X)=1)]TJ /F9 11.955 Tf 11.95 0 Td[(.(3) AccordingtothecontinuitycorrectioninEquation( 3 ),therelationshipbetweenthecumulativedistributionofXandYis 1)]TJ /F9 11.955 Tf 13.15 8.09 Td[( 2=Prob(X)]TJ /F9 11.955 Tf 11.95 0 Td[( X)=Prob(Y)]TJ /F9 11.955 Tf 11.95 0 Td[( X+0.5)=(X+0.5),(3) 35

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where(.)standsforthestandardnormalcumulativedistributionfunction.Therefore,X+0.5isthe1)]TJ /F9 11.955 Tf 12.81 0 Td[(percentileforthestandardnormaldistribution.Forexample,when1)]TJ /F9 11.955 Tf 11.95 0 Td[(=95%,X+0.5=1.96,X=1.46. Therefore,thecondenceintervalof^pis [^p)]TJ /F8 11.955 Tf 11.95 22.1 Td[(s p(1)]TJ /F4 11.955 Tf 11.96 0 Td[(p) n0X,^p+s p(1)]TJ /F4 11.955 Tf 11.95 0 Td[(p) n0X].(3) 3.4.2TheRequiredLengthoftheSampleSequence Inthissection,therelationshipamongthelengthofthesamplesequence,thePUbehaviorspeciedbythetransitionprobabilitiesandthecorrespondingestimationaccuracyisstudiedusingtheanalysisofthecondenceinterval. ThedenitionofthecondenceintervalinEquation( 3 )canberewrittenas Prob(p)]TJ /F9 11.955 Tf 23.59 8.09 Td[( 1+p^pp)]TJ /F9 11.955 Tf 23.59 8.09 Td[( 1)]TJ /F9 11.955 Tf 11.96 0 Td[(p)1)]TJ /F9 11.955 Tf 11.95 0 Td[(.(3) Since 1)]TJ /F9 11.955 Tf 11.96 0 Td[(p 1+p,theabovecondencelevelcanbeguaranteedifthefollowinginequalityholds: Prob(p)]TJ /F9 11.955 Tf 23.59 8.09 Td[( 1+p^pp)]TJ /F9 11.955 Tf 23.59 8.09 Td[( 1+p)1)]TJ /F9 11.955 Tf 11.95 0 Td[(.(3) Similarly,theprobabilityinEquation( 3 )canberewrittenas Prob(p)]TJ /F8 11.955 Tf 11.96 22.1 Td[(s p(1)]TJ /F4 11.955 Tf 11.96 0 Td[(p) n0X^pp+s p(1)]TJ /F4 11.955 Tf 11.96 0 Td[(p) n0X).(3) Therefore,thefollowingconditionhastobesatisedforthecondencelevelof1)]TJ /F9 11.955 Tf 11.96 0 Td[(: s p(1)]TJ /F4 11.955 Tf 11.96 0 Td[(p) n0Xp 1+.(3) Itcanberewrittenas: n0X2(1 +1)2(1 p)]TJ /F3 11.955 Tf 11.96 0 Td[(1).(3) 36

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IfthelengthofthesamplesequenceNislargeenough,n0=NPidle=q p+q.Therefore,thelengthofthesamplesequencewithacondencelevelofp,whichisdenotedbyNp,iscalculatedby Np=n0(p q+1)X2(1 +1)2(1 p)]TJ /F3 11.955 Tf 11.95 0 Td[(1)(p q+1).(3) Similarly,fortheestimationofq,ifandaregiven,therequirednumberofstates1inthesamplesequenceisderivedasfollows. n1X2(1 +1)2(1 q)]TJ /F3 11.955 Tf 11.95 0 Td[(1).(3) Sincen1=NPbusy=p p+q,thelengthofthesamplesequencewithacondencelevelofq,whichisdenotedbyNq,iscalculatedby Nq=n1(q p+1)X2(1 +1)2(1 q)]TJ /F3 11.955 Tf 11.95 0 Td[(1)(q p+1).(3) Given1)]TJ /F9 11.955 Tf 11.68 0 Td[(and,inordertoguaranteethenumberofstates0(n0)andthenumberofstates1(n1)satisfyEquation( 3 )andEquation( 3 ),respectively,theminimumrequiredlengthofthesamplesequenceNis Nmin=max(Np,Nq).(3) Hencewetheoreticallycomputetheminimumlengthofsamplesequencerequiredforthegiventransitionprobabilitiesandacertaincondencelevelspeciedby1)]TJ /F9 11.955 Tf 12 0 Td[(and.Figure 3-4 isa3DgraphoftherelationshipbetweenNandp,qwhen1)]TJ /F9 11.955 Tf 12.35 0 Td[(=95%and=0.1.Itshowsthattherequiredlengthofsamplesequenceincreasesasthetransitionprobabilitiesdecreases. 3.5TheAdaptationoftheSampleSequenceLength TherequiredlengthofthesamplesequencediffersgreatlyaccordingtovariedtransitionprobabilitiesasinFigure 3-4 .SincethePUbehaviorspeciedbythetransitionprobabilitiesoftheMarkovmodelvariesovertime,thelengthofthesamplesequence 37

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Figure3-4. Theimpactoftransitionprobabilitiesontherequiredsamplesequencelength shouldbeselecteddynamicallyovereachframe.AccordingtoFigure 3-4 ,whenthetransitionprobabilitiesdecreases,thelengthofthesamplesequenceshouldbeincreasedforabetterestimationaccuracy.Ontheotherhand,thelengthofthesequencecanbereducedwiththeincreasedtransitionprobabilities.Tothisend,analgorithmwhichestimatesthetransitionprobabilitiesofthesamplesequencewiththerequiredlengthshouldbeconductedatthebeginningofeachframetoadapttothechangingPUbehavior. SincethetransitionprobabilitiesofPUbehaviorarenotknownbytheSUinadvance,Equation( 3 )cannotbeexploiteddirectlytoderivetherequirednumberofstatesinthesequence.Therefore,wedevelopalearningalgorithmwhichinitializestheprocesswithacoarseestimateofthetransitionprobabilitiesfortheMarkovmodelandthenlearnsthemodeliterativelyuntilagivenaccuracyrequirementissatised. 38

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Suppose^p0and^q0astheestimateofpandqfromthepreviousframe.Theestimationaccuracyrequirementisspeciedbythecondencelevel1)]TJ /F9 11.955 Tf 12.87 0 Td[(andtheerrorbound.Intherststep,therequiredlengthofthesamplesequencehastobedetermined.^p0and^q0areusedastheinitializedestimatesandtheysubstituteforpandqinEquation( 3 )andEquation( 3 ).Therefore,therequiredlengthofthesamplesequenceforanaccurateestimationbasedon^p0and^q0iscalculatedbyEquation( 3 )andEquation( 3 ),respectively.TherequirednumberofsamplesfortherstiterationN1isderivedbyEquation( 3 ).Inthesecondstep,thechanneloccupancystateismonitoredforN1consecutiveslotstoformasamplesequence.Equation( 3 )isusedtogeneratetheestimate^p1and^q1.Theprocessstopsiftheterminationconditionismet.Otherwise,itreturnstotherststepwith^p1and^q1substitutingforpandq.Inthisway,thelearningalgorithmupdatestheestimationresultaftereachiteration. Figure3-5. Theowchartoftheproposedlearningalgorithm Animportantfunctionalityoftheiterativelearningalgorithmistodeterminewhethertheterminationconditionissatised.Itisdiscussedasfollows.Let^pi)]TJ /F11 7.97 Tf 6.59 0 Td[(1and^qi)]TJ /F11 7.97 Tf 6.59 0 Td[(1be 39

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thesubstituteforpandqattheithiteration,respectively.TherequiredlengthofthesequenceisdenotedasNi.Theestimationresultsare^piand^qi.Thecondenceintervalof^piis [^pi)]TJ /F8 11.955 Tf 11.96 22.11 Td[(s ^pi)]TJ /F11 7.97 Tf 6.59 0 Td[(1(1)]TJ /F3 11.955 Tf 12.1 0 Td[(^pi)]TJ /F11 7.97 Tf 6.58 0 Td[(1) n0X,^pi+s ^pi)]TJ /F11 7.97 Tf 6.58 0 Td[(1(1)]TJ /F3 11.955 Tf 12.1 0 Td[(^pi)]TJ /F11 7.97 Tf 6.58 0 Td[(1) n0X].(3) Tomeettherequirementofthecondencelevel,thenumberofstates0inthesamplesequence(n0)shouldsatisfy: s ^pi)]TJ /F11 7.97 Tf 6.58 0 Td[(1(1)]TJ /F3 11.955 Tf 12.1 0 Td[(^pi)]TJ /F11 7.97 Tf 6.58 0 Td[(1) n0X^pi.(3) Similarly,thenumberofstates1(n1)shouldsatisfy: s ^qi)]TJ /F11 7.97 Tf 6.58 0 Td[(1(1)]TJ /F3 11.955 Tf 12.2 0 Td[(^qi)]TJ /F11 7.97 Tf 6.58 0 Td[(1) n1X^qi.(3) Theiterativeprocessterminateswhenbothconditionsaresatised.TheoveralloperationoftheproposedlearningalgorithmissummarizedinFigure 3-5 .Inthisway,thelengthofthesamplesequenceadaptstothechangingPUbehaviorsothattheestimationaccuracycanbeachievedwhiletheunnecessarysensingslotsarereduced. 3.6SimulationResults 3.6.1EstimationAccuracyofExactPMF Theestimationaccuracyisevaluatedbythestandarddeviation,whichisdeterminedbybothrealtransitionprobabilitiesandthenumberofsamples.TheimpactofthetransitionprobabilitiesonthestandarddeviationisdepictedinFigure 5-4 .Thisisatheoreticalresultontherelationshipamongthestandarddeviationof^pandrealvaluesofp,q,whenN=50and100,respectively.Itisnotedthatpandqhavedifferentimpactsonthestandarddeviationof^p.Foraxedq,thestandarddeviationof^ptakesonsmallvalueswhenpstaysclosetoitstwoextremepoints(0and1).Thisisbecausewhenpmovestowards0.5,thePMFof^phasitsleft-sidelobeandright-sidelobemoreevenlyandfreelydistributedtowardsitslowend(0)andhighend(1),asshownin 40

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Figure3-6. Impactoftransitionprobabilitiesonestimationaccuracyof^p Figure 3-1 .Thisrendersahighstandarddeviationcomparedwithpmovingtowardseitherlowendorhighendof[0,1],duetothespatialrestrictionplacedonthelatterPMF.Thereforethestandarddeviationhasitsmaximumvalueatp=0.5ifqisxed.Foraxedp,thestandarddeviationdecreasesmonotonouslyasqincreases.SincePidle=q p+q=1)]TJ /F7 7.97 Tf 18.91 5.04 Td[(p p+q,biggerqrendershigherprobabilityfortheMarkovmodeltostayintheidlestate.Asaresult,abiggern0isexpectedandsoisamoreaccurate^p. InFigure 3-7 ,thecurvewiththecircleillustratestheimpactofthenumberofsamplesontheestimationaccuracywhenp=0.1,q=0.1.Itisshownthatasthenumberofsamplesincreases,thestandarddeviationdecreasesmonotonously.Thereforetherequirednumberofsamplesforanaccurateestimationcouldbeobtainedifthetransitionprobabilitiesandthestandarddeviationaregiven.Eventhoughtherealtransitionprobabilitiesarenotknowninadvance,theestimatedtransitionprobabilitiesfromtheprevioustimeframecanbeusedtosubstitutetherealvaluessincePU 41

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Figure3-7. Impactofnumberofsamplesonestimationaccuracy(p=q=0.1) behaviorisverylikelytobesimilaroverconsecutiveframesformanyapplications[ 22 ]. Longetal.[ 28 ]alsoanalyzetherelationshipbetweentheestimationaccuracyandthenumberofsamples.AnapproximatenormaldistributionisderivedfortheMLestimator.Figure 3-7 comparesthestandarddeviationoftheexactdistributionandtheapproximatenormaldistribution.Itcanbeseenthatthereisavisibledifferencebetweenthetwodistributionswhenthenumberofsamplesislessthan100.Sincethenormaldistributionhassmallerstandarddeviation,itresultsinderivationoflessnumberofsamplesthanwhatistheoreticallyrequiredforapreciseestimation.Therefore,theapproximatedistributionisnotaccuratefortheestimationwithasmallnumberofsamples,anditislessapplicabletotheSUwithlowcapability. TheaccuracyoftheestimatedtransitionprobabilitiesinthisletterisinvestigatedundertheassumptionthatallthePUstatesareaccuratelydetected.SincethePUdetectionmaybeaffectedduetointerference/noise,theestimationaccuracyneeds 42

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Figure3-8. Impactoffalsealarmprobabilityonestimationaccuracy(p=q=0.1) tobeexaminedundertheerrordetection.Thefalsealarmprobabilityisintroducedtospecifyhowtheinterference/noiseaffectsthePUdetection.Figure 3-8 showstheimpactofthefalsealarmprobabilityonthestandarddeviationoftheestimation.Itisshownthattheestimationaccuracydecreasesasthefalsealarmprobabilityincreases.However,thereisonlyaslightdifferencebetweeneachcurve,whichmeanstheproposedapproachforanalyzingtheestimationaccuracyisstillapplicablewhenthefalsealarmprobabilitystaysbelow10)]TJ /F11 7.97 Tf 6.58 0 Td[(2. 3.6.2EstimationAccuracyofAdaptationAlgorithm Theperformanceofproposedalgorithmisevaluatedthroughnumericalresults.Someparametersusedinthesimulationareasfollows:Thelengthofaframeis200msandeachslotlasts20s,thereforethereare10000slotsinaframe[ 22 ];ThePUbehavioraccordingtothetransitionprobabilitieschangesevery200frames;Theaccuracyrequirementintermsofthecondencelevelisgivenas1)]TJ /F9 11.955 Tf 12.73 0 Td[(=0.95and=0.1. 43

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Figure3-9. EstimatesofPUbehavioroverframes Figure3-10. Thecomparisonoftheoreticalandestimatedresults 44

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Figure3-11. Thecondenceleveloftheproposedalgorithm Figure 3-9 showshowwelltheproposedalgorithmestimatesthePUbehavior.Theinitialvalueoftheestimatedtransitionprobabilitiesisgivenas^p0=^q0=0.5.Thisgureshowsthattheestimatedtransitionprobabilitiesuctuatearoundtherealvalues.ItdemonstratesthattheproposedalgorithmwelltracksthevariationofthePUbehavior. TheminimumrequiredlengthofthesamplesequenceisobtainedbyEquation( 3 ).Intheproposedlearningalgorithm,theestimatedvaluesofpandqfromthepreviousframesubstitutesfortherealtransitionprobabilitiesinEquation( 3 )andEquation( 3 ).Figure 3-10 showsthattherequiredlengthofthesamplesequenceusingtheestimatedtransitionprobabilitiesisveryclosetotheminimumlengthfromtheoreticalanalysisusingrealvalues. Figure 3-11 showsthecondenceleveloftheproposedlearningalgorithmwhentheaccuracyrequirementis1)]TJ /F9 11.955 Tf 12.37 0 Td[(=0.95and=0.1.Thecondenceleveliscalculatedastheratioofthenumberofframesinwhichthecondenceintervalincludesthetrue 45

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Figure3-12. Thecomparisonofthecondencelevelbetweenxedandproposedalgorithm valuetothetotalnumberofframes.Itshowsthattheestimationresultsoftheproposedalgorithmareveryclosetotheexpectedvalue. Theproposedlearningalgorithmwhichusesadaptivelengthofthesamplesequenceiscomparedwiththemethodusingthexedsequencelengthoverframes.Weonlyshowtheresultsfortheestimationofpandtheresultsforqhavethesimilartrend.Figure 3-12 showsthecomparisonintermsofthecondencelevel.Thecondenceleveliscalculatedastheratioofthenumberofframesinwhichthecondenceintervalincludesthetruevaluetothetotalnumberofframes.Accordingtothisgure,if1)]TJ /F9 11.955 Tf 12.76 0 Td[(=0.95,theproposedadaptivealgorithmonaveragerequires570samplesforsensingperframeandachievesthesamecondencelevelasthexedmethodwith771samples.Ifthexedmethoduses570samplesineachframe,itonlyreachesthecondencelevelof0.919whiletheadaptivealgorithmachieves0.948.When1)]TJ /F9 11.955 Tf 11.96 0 Td[(=0.9,theproposedalgorithmrequires366samplesperframeandachievesthesamecondencelevelasthexedmethodwith429samples.Ifthexedmethod 46

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Figure3-13. Thecomparisonoftherelativeerrorbetweenxedandproposedalgorithm uses366samplesineachframe,itonlyreachesthecondencelevelof0.866whiletheproposedalgorithmachieves0.886. AnothercomparisonbasedontherelativeerrorcanbeobservedinFigure 3-13 .Therelativeerrorisdenedas=1 RRXr=1(pr)]TJ /F3 11.955 Tf 14.08 0 Td[(^pr)2 pr.ThisgureshowsthesimilarresultsasinFigure 3-12 .Therefore,theproposedadaptivealgorithmneedslesssamplespereachframetoreachthesameestimationaccuracyinastatisticalsense.Itisalsoshownthattheproposedadaptivealgorithmoutperformsthexedalgorithmintermsofthecondencelevelwhenthenumberofsamplesisthesame. 3.7Summary ThischapterinvestigatestheestimationaccuracyoftheMLestimatorforthePUMarkovmodelincognitiveradionetworks.AnapproximatenormaldistributionoftheMLestimatorisderivedtoanalyzeitscondencelevel.WeshowthattherequiredlengthofthesamplesequencediffersgreatlyforthevariedPUbehavior.AlearningalgorithmwhichiterativelylearnstheMarkovmodelisproposedwithadaptivelengthofthesamplesequence. 47

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Theproposedlearningalgorithmwhichusesadaptivelengthofthesamplesequenceiscomparedwiththemethodusingthexedsequencelengthoverframes.Numericalresultsshowthattheproposedadaptivealgorithmneedslesssamplespereachframetoreachthesameestimationaccuracyinastatisticalsense.Itisalsoshownthattheproposedadaptivealgorithmoutperformsthexedalgorithmintermsofthecondencelevelwhenthenumberofsamplesisthesame.Therefore,theproposedestimationalgorithmachievestherequirementoftheestimationaccuracywhilereducingunnecessarysensingslots. 48

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CHAPTER4PRIMARYUSERBEHAVIORESTIMATIONWITHIMPERFECTSENSING TheestimationaccuracyofPUbehaviordependsontheresultofspectrumsensing.Inthelastchapter,sensingresultisassumedtobeperfectwithoutsensingerrors.Theproblemofimperfectsensingneedstobestudiedforrealapplications.Atwo-stateHiddenMarkovmodel(HMM)isutilizedtomodelPUbehaviorandestimatePUstatetransitionprobabilitieswithsensingerror.ThetransitionprobabilitiesareestimatedbytheBaum-Welchalgorithm.Theestimationaccuracyisevaluatedintermsofthecondencelevel,byutilizingtheprobabilitydistributionoftheestimator.Simulationresultsshowhowtheestimationaccuracyisaffectedbythelengthofthesamplesequence,therealstatetransitionprobabilities,theselectionoftheinitialparameterandthelevelofsensingerror. Thischapterisorganizedasfollows.Section 4.1 introducesanoverviewofPUbehaviorestimationwithimperfectsensingandproposesHMMasthemodelforestimation.Section 4.2 introducestherecentstudiesrelatedtoimperfectsensingproblems.Section 4.4 introducestheHMM-basedPUbehaviormodel.TheBaum-WelchalgorithmoftransitionprobabilityestimationisdescribedinSection 4.5 .Section 4.6 providesthenumericalresultsfortheevaluationoftheestimationaccuracyandthecomparisonofperfectandimperfectsensing.Section 4.7 concludesthischapter. 4.1OverviewofImperfectSensing Incognitiveradionetworks,spectrumsensingisoneofthemostimportantfunctionalities,asmentionedinChapter 3 .TheaccurateestimationofPUbehaviorimprovesthespectrumutilizationandpreventstheharmfulinterferenceofSUstoPUs.SUskeepsensingthechannelforconsecutiveperiodsandanalyzethereceivedsignalstodecidewhetherPUsareactiveornot.However,theremaybetheundesiredinterferencesignal,suchassystemnoise,onthesamechannel,whichgreatlyaffectsthedecisionofSUs.ThismayresultineitherfalsealarmormissdetectionofaPU 49

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signal.Asaconsequence,thespectrummaybeunder-utilizedortheremaybecollisionsofPUandSUtransmission. Energydetectioniscommonlyusedforspectrumsensingbecauseofitslowcomplexity[ 1 ].Itevaluatesthereceivedenergyinagivenspectrumandcomparesitwithapredenedthreshold.Thechannelisconsideredbusyiftheenergyvalueisabovethegiventhresholdandidleifitisbelowthethreshold.ThereceivedenergyincludesthePUsignalenergyandthenoiseenergy.Althoughitissimpletoimplement,ithasseveralweaknesses.Forexample,thevalueofthenoiseenergyiscriticalfordeterminingthesensingthreshold,whichsignicantlyaffectsthesensingperformance.Inaccurateestimationofpossiblychangingenvironmentnoisemaycausesensingerrors,whichleadstoadegradationofestimationaccuracyofPUbehavior.Moreover,itdoesnotconsiderthedependencyofcurrentstateonthepreviousstate. Inshort,withoutknowingthenoiselevel,itisdifculttoobtainthecorrectstateofPUbehavior.However,therearethreefactsbyexploringtheproblemoftheimperfectsensing. First,althoughthetruestatesofMarkovprocessrepresentingPUbehaviorcannotbedirectlyseenbyanSU,theoutputgeneratedbyeachstatecanbeobserved.TheSUmeasuresthereceivedenergyoverconsecutivetimeperiodsandstorestheoutputsamplestoformanobservedsequence.ThenitconjecturesthePUstatebasedonthesequence. Second,eachsampleoftheobservedsequencedependsonthetruestatewithcertainfalsealarmandmissdetectionprobabilities,i.e.,acertainprobabilitydistribution.Theobservedsamplesareindependentfromeachothersinceeachobservationareonlydeterminedbythetruestateinthesameslot. Third,thefalsealarmandmissdetectionprobabilitiescausedbytheenvironmentnoisemaynotchangefrequently,whichmeanstheyusuallystaythesameduringanobservationperiod. 50

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TheMarkovprocesscanbeillustratedinFigure 4-1 ,whereSirepresentsithsampleofstatesequence,Onrepresentsthesampleofnthsampleoftheobservedsequence,Arepresentsstatetransitionprobabilities,Brepresentstheobservationprobabilitydistribution. Figure4-1. PUbehaviormodelwithimperfectsensing TheMarkovprocessisdeterminedbythecurrentstateandthestatetransitionprobabilities.OnlyOncanbeobservedanditisrelatedtothestatesoftheMarkovprocessbytheobservationprobabilitydistributionB.SincetheobservedsequencegivessomeinformationaboutthestatesequencebyPUbehavior,aHiddenMarkovmodel(HMM)couldbeintroducedtosolvetheproblemofimperfectsensing. InthisHMM,boththestatespaceofthehiddenvariables,formedbyPUbehavior,andtheobservedsequencegeneratedbythePUstate,arediscrete.TheHMMhastwotypesofparameters,transitionprobabilitiesandobservationprobabilities.Thetransitionprobabilitiesdeterminehowthehiddenstateatthecurrentslotisrelatedtothehiddenstateatthepreviousslot.Inaddition,foreachofthepossiblestates,theobservationprobabilitygovernstheoutputvariableataparticulartimegiventhestateofthehiddenvariableatthattime.Thenatureoftheoutputvariablesdeterminesthesizeofthisset. Inthischapter,atwo-stateHMMisemployedtomodelPUbehavior,wherethepresenceandabsenceofPUsignalsarerepresentedasbusyandidlestates,respectively.AsinChapter 3 ,thetransitionprobabilitiesofthehiddenstatesareestimatedfortheSUtopredictthefuturePUbehaviorandbasedonthePUbehavior 51

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determinewhethertotransmitpacketsonthechannel.TheestimationisbasedonsamplesoftheobservedsequenceinsteadoftheonsamplesofPUstatesequencedirectly.TheestimationaccuracyhastobeenforcedtogetaproperknowledgeofPUbehavior.Estimationaccuracyisevaluatedintermsofthecondencelevel,byutilizingtheprobabilitydistributionoftheestimator.Weevaluatetherelationshipamongthelengthoftheobservedsequence,therealstatetransitionprobabilities,thefalsealarmandmissdetectionprobabilities,theselectionofinitialparametersandtheaccuracyoftheestimatedvalues. 4.2RelatedWork TheconceptofHMMhasbeenwidelyusedtospeechandimagerecognition[ 29 ].AsurveyofHMMcanbefoundin[ 30 ].Itrecentlyhasattractedtheattentionofresearchincognitiveradionetworks.Real-timemeasurementswereusedtovalidatetheMarkovexistenceofPUbehaviorin[ 31 ]andtheHMMisusedtopredictthetruechannelstates.In[ 32 33 ],theblindspectrumsensingexploitstheHMMbasedonclassicationofmultipleinterferers.In[ 34 35 ],anHMM-basedspectrumsensingmethodisproposedbasedonquickestdetection.SequencedetectionalgorithmsareproposedforspectrumsensingforHMM-basedPUbehaviorin[ 36 ]. TheHMMparametersareestimatedusingtheBaum-Welchalgorithm[ 30 37 ]forcognitiveradionetworksin[ 38 41 ].However,theestimationaccuracyisnotdiscussedandhowtodecidetherequirednumberofsamplesisnotmentioned.Moreover,theselectionofinitialparametersisnotstudiedinthesepapers.Tothebestofourknowledge,ourworkistherstworktoevaluatetheestimationaccuracyofBaum-WelchalgorithmforHMMestimationincognitiveradionetworks. 4.3TheHiddenMarkovModelofPUbehavior AsdescribedinChapter 2.1.1 ,theSUkeepssensingthechannelforconsecutivetimeslotsinthechannelsensingphase.TheobservedresultsformasamplesequenceoflengthN.ThetransitionprobabilityofPUbehaviorisestimatedbasedonthe 52

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observedsequence.TheSUtransmitsdatapacketsinthechannelaccessphaseinlightoftheestimationresults. 4.3.1ModelofImperfectSensing Foreachsensingslot,theSUhastodeterminewhetherthePUisactiveornot.ThePUbehaviorandsystemnoiseareassumedtoremainunchangedwithinthedurationofaframe.LetBdenotethebandwidthofthefrequencychannel,Tdenotethesensingslotduration.TheSUtakesBTbasebandcomplexsignalsamplesonthechannel.Ify(n,m)denotesthemthsignalsampletakenatthenthslot,x(n,m)denotesPUsignals,w(n,m)denotesinterferencesignalssuchaswhitenoise,y(n,m)canberepresentedas: y(n,m)=8>>>><>>>>:x(n,m)+w(n,m),PUpresentatnthslotw(n,m),PUabsentatnthslot.(4) TheteststatisticisaveragereceivedenergyoftheBTsamplesatthenthsensingslot,whichcanbecalculatedas: en=1 BBTXm=1jy(n,i)j2.(4) TheSUdistinguishesthetwosensingresultsbycomparingenwiththethreshold, On=8>>>><>>>>:1,en0,en<.(4) ThefalsealarmprobabilityPfistheprobabilitythatOn=1giventhatPUsignalisabsent.Ontheotherhand,themissdetectionprobabilityPmistheprobabilitythatOn=0giventhatPUsignalispresent. 53

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Figure4-2. Two-stateHMMmodel 4.3.2StructureofHiddenMarkovModel TheHMMmodelingofPUbehaviorwithimperfectsensingresultsisillustratedFigure 4-2 .ThepresenceandabsenceofPUsignalsarerepresentedasbusyandidlestates,respectively.TheHMMmodelcouldbeviewedasadiscrete-timebivariaterandomprocessf(Sn,On),n=1,2,,Ng.fSngisabinarysequencewith0and1representingidleandbusystate,respectively.ItisthehiddenprocesswhichcannotbeseenbySUs.Itisdenedas: Sn=8>>>><>>>>:1,PUpresentatnthslot0,PUabsentatnthslot.(4) TheelementofstatetransitionprobabilitymatrixAisrepresentedas: ai,j=Prob(Sn+1=jjSn=i).(4) Specically,pistheprobabilitythatthestateatthe(n+1)thslotis1giventhestateatthenthslotis0.qistheprobabilitythatthestateatthe(n+1)thslotis0giventhestateatthenthslotis1.Theycanberepresentedas: 54

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8>>>><>>>>:p=a01q=a10.(4) ThenthestatetransitionprobabilitymatrixAisgivenas: A=2641)]TJ /F4 11.955 Tf 11.95 0 Td[(ppq1)]TJ /F4 11.955 Tf 11.96 0 Td[(q375.(4) fOngisalsoabinarysequencewith0and1representingthedecisionofPUactivity.ItistheobservedprocessfromwhichtheSUsestimatethetransitionprobabilitiesofPUbehavior.EachOnisconditionallydependentonthecorrespondingSnwithprobability bi(y)=Prob(On=yjSn=i).(4) ThenthefalsealarmprobabilityPfandmissdetectionprobabilityPmcanberepresentedas: 8>>>><>>>>:Pf=b0(1)Pm=b1(0).(4) Moreover,bytheassumptionmadeinSection 4.3.1 ,PfandPmareindependentofnandremainthesamewithinaframe.TheobservationmatrixBisdenedas B=2641)]TJ /F4 11.955 Tf 11.95 0 Td[(PfPfPm1)]TJ /F4 11.955 Tf 11.95 0 Td[(Pm375.(4) TheHMMofimperfectsensingisdeterminedandcharacterizedbytheparameterset=(,A,B),whereistheinitialstateprobabilitymatrix=[Pidle,Pbusy].Thetwoprobabilitiesrepresentsthatthechannelisidleandbusyattherstsensingslot.ThemathematicalsymbolsforthismodelissummarizedinTable 4-1 55

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Table4-1. HMMSymbols SymbolDenition NLengthofthesamplesequenceSnStateofPUatthenthsensingslotOnObservationofthechannelatthenthsensingslotiInitialprobabilityofstateiPidleInitialprobabilityofstate0PbusyInitialprobabilityofstate1Initialstateprobabilitymatrixai,jTransitionprobabilityofPUfromstateitostatejpTransitionprobabilityofPUfromstate0tostate1qTransitionprobabilityofPUfromstate0tostate1AStatetransitionprobabilitymatrixbi(y)ObservationprobabilityfromstateitoobservationyPfObservationprobabilityfromstate0toobservation1PmObservationprobabilityfromstate1toobservation0BObservationprobabilitymatrixHMMmodelparameterset=(,A,B) 4.4EstimationofTransitionProbabilitiesUsingHMM TheparametersoftheHMMareestimatedusingtheobservedsequence.GiventheobservedsequenceO=fO1,O2,,sNg,theoptimalvalueoftheestimationisaparameterset^optwhichmaximizestheprobabilityofcurrentobservedsequence. Itisdenotedas: ^opt=argmaxProb(Oj)(4) Inthiswork,wewillrstcalculatetheprobabilityoftheobservedsequencegiveneachpossiblestatesequence.Sincethecalculationisgenerallyinfeasiblefor2Npossiblestatesequences,theestimationofHMMmodelparametersisconductedbasedonadynamicprogrammingalgorithm,whichiscalledBaum-Welchalgorithm. 4.4.1Probabilityofagivenobservedsequence WewanttondouttheprobabilityofagivenobservedsequenceO.LetS=fS1,S2,,SNgbeacertainstatesequence.TheconditionalprobabilityofObasedonSiscalculatedas: 56

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Prob(OjS,)=bS1(O1)bS2(O2)bSN(ON).(4) Theoccurrenceprobabilityofthestatesequenceiscalculatedas: Prob(Sj)=S1aS1,S2aS2,S3aSN)]TJ /F12 5.978 Tf 5.76 0 Td[(1,SN.(4) TheexpressionfortheoccurrenceprobabilityoftheobservedsequenceOisobtainedbysummingupallpossiblestatesequences, Prob(Oj)=XSProb(O,Sj)=XSProb(OjS,)Prob(Sj)=XSS1bS1(O1)aS1,S2bS2(O2)aSN)]TJ /F12 5.978 Tf 5.76 0 Td[(1,SNbSN(ON).(4) Inthistwo-stateHMM,theexpressioncouldbemorespecicbasedonitsuniquecharacteristics.Letnij(i,j2f0,1g)representsthenumberofstatetransitionsfromstateitostatej.ni(i2f0,1g)denotesthenumberofalltransitionsfromstatei. RecallthatinSection 3.3.1 ,theindividualoccurrenceprobabilityofastatesequenceisdependentonaparameterset=(S1,SN,n0,n01).Ifweassumea0!0transitionwhenSN=0and1!1transitionwhenSN=1,thenn0(thenumberofalltransitionsfromstate0)isthenumberofstates0inthesequenceandN)]TJ /F4 11.955 Tf 12.48 0 Td[(n0isthenumberofstates1.Inthisway,theeffectofSNcanbeignoredandthisprobabilityofthestatesequenceisdeterminedonlybyn0andn01.Specically,thereisn01transitionsfromstate0tostate1,n0)]TJ /F4 11.955 Tf 12.55 0 Td[(n01transitionsfromstate0tostate0,n10transitionsfromstate1tostate0andN)]TJ /F4 11.955 Tf 11.96 0 Td[(n0)]TJ /F4 11.955 Tf 11.96 0 Td[(n01transitionsfromstate1tostate1. Giventherealtransitionprobabilitiespandq,Prob(Sj)iscalculatedby: Prob(Sj)=S1pn01qn01(1)]TJ /F4 11.955 Tf 11.95 0 Td[(p)n0)]TJ /F7 7.97 Tf 6.58 0 Td[(n01(1)]TJ /F4 11.955 Tf 11.95 0 Td[(q)N)]TJ /F7 7.97 Tf 6.58 0 Td[(n0)]TJ /F7 7.97 Tf 6.59 0 Td[(n01.(4) 57

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Notethatinthiscase,therelationshipofN,n0,n01mustsatisfythefollowingconstraints: n01min(n0,N)]TJ /F4 11.955 Tf 11.95 0 Td[(n0).(4) TheproofissimilartotheproofofEquation( 3 ). Letmi(i2f0,1g)denotethenumberofobservationi.Supposeoutofm0observations0,thenumberof0semittedbystates0inthestatesequenceisL.ThenthereisLemissionsfromstate0toobservation1,n0)]TJ /F4 11.955 Tf 12.84 0 Td[(Lemissionsfromstate0toobservation0,m0)]TJ /F4 11.955 Tf 12.45 0 Td[(Lemissionsfromstate1toobservation0andN)]TJ /F4 11.955 Tf 12.44 0 Td[(n0)]TJ /F3 11.955 Tf 12.44 0 Td[((m0)]TJ /F4 11.955 Tf 12.44 0 Td[(L)emissionsfromstate1toobservation1.Apparently,Lmin(n0,m0). ThentheconditionalprobabilityofObasedonSwithagivenn0iscalculatedby: Prob(OjS,)=PfL(1)]TJ /F4 11.955 Tf 11.96 0 Td[(Pf)n0)]TJ /F7 7.97 Tf 6.59 0 Td[(LPmm0)]TJ /F7 7.97 Tf 6.58 0 Td[(L(1)]TJ /F4 11.955 Tf 11.95 0 Td[(Pm)N)]TJ /F7 7.97 Tf 6.59 0 Td[(n0)]TJ /F11 7.97 Tf 6.58 0 Td[((m0)]TJ /F7 7.97 Tf 6.59 0 Td[(L).(4) BecauseScantakeoneofpossible2Nvaluesateachstep,itbecomescomputationallyoverwhelmingtoenumerateeachstatesequenceandcalculateitscorrespondingjointprobabilitywiththegivenobservedsequence.TheBaum-Welchalgorithm,whichisaspecialcaseofageneralizedexpectationmaximization(EM)algorithm,isusedtoiterativelyestimatetheparameterset[ 42 ]. 4.4.2EstimationofHMMModelParametersUsingBaum-WelchAlgorithm Buam-WelchalgorithmcalculatesmaximumlikelihoodestimatesforthemodelparametersofanHMM,whenthetrainingsamplesareonlygivenbyobservations.Itmakesuseofbothforwardandbackwardalgorithm. Forwardalgorithm Denei(n)istheprobabilityofobtainingthepartialobservationsequence,O1,O2,,On,andSnisstatei(i=0,1).Itisdenotedas: i(n)=Prob(O1,O2,,On,Sn=ij).(4) 58

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Itcanbecalculatedrecursivelyasfollows. i(1)=bi(O1),i=0,1i(n)=Xj=0,1j(n)]TJ /F3 11.955 Tf 11.95 0 Td[(1)aj,ibi(On),i=f0,1g,n2[2,N](4) ThereforetheoccurrenceprobabilityoftheobservedsequenceOiscomputedby: Prob(Oj)=Xi=0,1i(n).(4) Backwardalgorithm Denei(n)istheprobabilityofobtainingthepartialobservationsequence,On+1,On+2,,ON,giventhatSnisstatei(i=0,1).Itisdenotedas: i(n)=Prob(On+1,On+2,,ON,jSn=i,).(4) Itcanbecalculatedrecursivelyasfollows. i(N)=1,i=0,1i(n)=Xj=0,1j(n+1)ai,jbj(On+1),i=f0,1g,n2[1,N)]TJ /F3 11.955 Tf 11.95 0 Td[(1](4) ThereforetheoccurrenceprobabilityofOiscomputedby: Prob(Oj)=Xi=0,1i(1).(4) Baum-Welchalgorithm 59

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i(n)andi(n)areusedinBaum-WelchalgorithmtocalculatetheprobabilitythatSnisstatei(i=0,1),giventheobservedsequenceisO.Itisobtainedby: i(n)=Prob(Sn=ijO,)=i(n)i(n) Xi=0,1i(n)i(n)(4) TheprobabilitythatSnisstatei(i=0,1)andSn+1isstatej(j=0,1)giventheobservedsequenceisOisobtainedby: i,j(n)=Prob(Sn=i,Sn+1=jjO,)=i(n)ai,ji(n+1)bj(On+1) Xi=0,1Xj=0,1i(n)ai,ji(n+1)bj(On+1)(4) Usingthesetwoexpressions,theexpectednumberoftransitionsfromstateitostatejcanberepresentedasN)]TJ /F11 7.97 Tf 6.58 0 Td[(1Xn=1i,j(n).Inthesameway,theexpectednumberoftotaltransitionsfromstateicanberepresentedasN)]TJ /F11 7.97 Tf 6.59 0 Td[(1Xn=1i(n).Moreover,theexpectednumberofemissionsfromstateitoobservationycabberepresentedasXn2f1,2,,N)]TJ /F11 7.97 Tf 6.58 0 Td[(1g,On=yi(n).Thenthemodelparameterset=(,A,B)isestimatedasfollows. 1.Theinitialstateprobabilitymatrix^: ^0=^Pidle=0(1)^1=^Pbusy=1(1)(4) 2.Thetransitionprobabilitymatrix^A: 60

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^a0,1=^p=N)]TJ /F11 7.97 Tf 6.59 0 Td[(1Xn=10,1(n) N)]TJ /F11 7.97 Tf 6.59 0 Td[(1Xn=10(n)^a1,0=^q=N)]TJ /F11 7.97 Tf 6.59 0 Td[(1Xn=11,0(n) N)]TJ /F11 7.97 Tf 6.58 0 Td[(1Xn=11(n)(4) 3.Theobservationprobabilitymatrix^B: ^b0(1)=^Pf=Xn2f1,2,,N)]TJ /F11 7.97 Tf 6.58 0 Td[(1g,On=10(n) N)]TJ /F11 7.97 Tf 6.59 0 Td[(1Xn=10(n)^b1(0)=^Pm=Xn2f1,2,,N)]TJ /F11 7.97 Tf 6.58 0 Td[(1g,On=01(n) N)]TJ /F11 7.97 Tf 6.58 0 Td[(1Xn=11(n)(4) SincetherealmodelparametersetisnotknownbytheSUinadvance,theaboveequationscannotbeuseddirectlytoperformtheestimation.Therefore,atrainingalgorithmhastobeusedtoupdatethemodelparameter.Itinitializestheprocesswithacoarseestimateofandthentrainsthemodeliterativelyuntilaterminationcriteriaissatised. GiventheobservedsequenceO,thealgorithmisconductedasfollows. 1.InitializetheHMMmodelparametersetas^0=(^0,^A0,^B0).ThencalculatetheprobabilityofthegivenobservedsequenceOProb(Oj^0)bytheforwardorbackwardalgorithm. 2.Computei,j(n)andi(n)using^. 61

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3.Updatethemodelparameterset^1=(^1,^A1,^B1)bytheresultsofStep2.ThencalculateProb(Oj^1). 4.IfProb(Oj^1))]TJ /F4 11.955 Tf 12.58 0 Td[(Prob(Oj^0)>,whereisapredenedthreshold,then^0isapparentlynottheparametersetthatmaximizescurrentobservation.ThenitreturnstoStep1with^1substitutingfor^0. Inthisway,thetrainingalgorithmupdatestheestimationresultaftereachiteration.TheprocesswillterminateifProb(Oj^1)doesnotincreasebyorafterapre-setmaximumnumberofiterations.Thenityieldsthenalestimationofthemodelparameterset^opt. 4.5TheEstimationAccuracyAnalysisofHMM SinceaprecisemodelandestimationofPUbehaviorisveryimportanttoimproveutilizationandavoidharmfulinterferencetoPUs,theestimationaccuracyhastobeenforcedfortheSU.AsdescribedinChapter 3 ,thelengthofthesamplesequenceplaysanimportantpartontheestimationaccuracy.Itshouldbelongenoughtoachievecertainprecisionoftheestimation.However,theenergywastedforspectrumsensingandthememoryusedforstoringthesamplesareexpectedtobekeptaslowaspossibleforthelow-capableSUs.Therefore,ourgoalisselectingthelengthofsamplesequencetoachievetheestimationaccuracywhilereducingunnecessarysensingslot.Inthischapter,weareonlyconcernedabouttheestimationaccuracyoftransitionprobabilitymatrixforimperfectsensing.Thencomparingitwiththeestimationaccuracyforperfectsensing,wecanobservetheimpactofsystemnoiseontheestimationresults.Inwhatfollows,onlytheestimationof^pisdiscussedandtheestimationof^qcanbederivedsimilarly. 4.5.1CondenceLeveloftheEstimation AsinChapter 3 ,derivingtheprobabilitydistributionisastraightforwardwaytoevaluatetheperformanceoftheHMMestimator.DenoteProb(^p=x)astheprobabilitythatptakesonvaluex.GiventheobservedsequencewithNobservationsisO= 62

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fO1,O2,,ONg,twoparametersneedtobecalculatedforcomputingProb(^p=x).OneistheprobabilityofcurrentobservedsequenceProb(Oj).ThisisobtainedbyEquation( 4 )orEquation( 4 ).Theotherparameteristheestimatedvalueof^p=xbasedonthecurrentobservedsequenceO.However,sinceitusesBaul-Welchalgorithm,whichisconductedbyiterativelytrainingthemodel,xcannotbecomputed.Therefore,withoutknowingx,wecannotgroupallthesequencesthatleadtothesamexasinSection 3.3.1 forperfectsensing.Theexactprobabilitydistributioncannotbecomputedinapolynomialtime.Theonlywaytocalculateitistogeneratethetwoparametersforall2Npossiblesequences.BecauseenumeratingallpossiblesequencesbecomescomputationallyinfeasiblewhenNgetslarge,werandomlygenerateacertainnumberofobservedsequencesbasedonHMMandcalculateitscorrespondingProb(Oj)and^p.Whenthenumberofsequencesislargeenough,theresultscouldapproximatelyrepresenttheprobabilitydistributionofHMM. Figure 4-3 showstheapproximateprobabilitydistributionofHMMforimperfectsensingcomparedwiththeprobabilitydistributionofMLestimatorforperfectsensing.ThefalsealarmprobabilityPfandthemissdetectionprobabilityPmarebothsetto0.1.Thenumberofobservedsequenceis1000.Fromthisgure,wecanseethatwhenNisincreased,thePMFconcentratestowardstherealtransitionprobabilityvalue,whichindicatesamoreaccurateestimation.WecanalsoseethattheprobabilitydistributionforperfectsensingismoreconcentratedthanthatofHMMforimperfectsensing,whichveriestheimpactofsensingerrorsontheestimationaccuracy. Amorespecicindicationoftheestimationaccuracyisrepresentedbythecondencelevel.Itcanbeobtainedusingtheprobabilitydistribution.ThesameasinChapter 3 ,theaccuracyrequirementoftheestimatorisdenedastheprobabilitythatthetruevalueofthetransitionprobabilitypisinthecondenceinterval[^p)]TJ /F9 11.955 Tf 12.2 0 Td[(^p,^p+^p]isatleast1)]TJ /F9 11.955 Tf 12.92 0 Td[(,where1)]TJ /F9 11.955 Tf 12.91 0 Td[(isthecondencelevelandistheerrorbound.Itis 63

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Figure4-3. Theprobabilitydistributionofperfectandimperfectsensing representedas: Prob(^p)]TJ /F9 11.955 Tf 11.95 0 Td[(^pp^p+^p)1)]TJ /F9 11.955 Tf 11.95 0 Td[(,0<,<1.(4) Itcanberewrittenas: Prob(p)]TJ /F9 11.955 Tf 23.59 8.08 Td[( 1+p^pp)]TJ /F9 11.955 Tf 23.59 8.08 Td[( 1)]TJ /F9 11.955 Tf 11.96 0 Td[(p)1)]TJ /F9 11.955 Tf 11.95 0 Td[(.(4) GiventheHMMmodelparameters,theprobabilitythat^pfallsintotheinterval[p)]TJ /F9 11.955 Tf 23.77 8.09 Td[( 1+p,p)]TJ /F9 11.955 Tf 23.77 8.09 Td[( 1)]TJ /F9 11.955 Tf 11.95 0 Td[(p]isdeterminedonlybythelengthofthesamplesequence.Thiscanbecalculatedbysummingoveralltheprobabilitieswithintheinterval,usingtheapproximateprobabilitydistribution.Therefore,theminimumsamplesequencelengthshouldbeselectedwhichsatisestheconditioninEquation 4 .Therelationshipamongthelengthofthesamplesequence,thePUbehaviorspeciedbythetransition 64

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probabilitiesandthecorrespondingestimationaccuracywillbeevaluatedusingsimulationinSection 4.6 4.5.2SelectionofInitialParameters RecallthatinBaum-Welchalgorithm,therststepistoinitializethemodelparameters.SincetheBaum-Welchalgorithmisalocallyiterativemethod[ 43 ],thenalestimatedvaluesofHMMandthenumberofiterationsdependsignicantlyontheinitialmodel.TheBaum-Welchalgorithmisguaranteedtoconvergetoone^ofHMMthatlocallymaximizestheprobabilityofthecurrentobservations.Itiswellknownthatiftheinitialparametersarenotchosenproperly,itmayconvergetoalocaloptimumandleadtoinaccurateestimates,whichmaybesignicantlyworsethantheglobaloptimum[ 44 45 ]. AlthoughHMMshavebeenemployedinmanyapplications,afrequentproblemisselectingorestimatinginitialvaluesfortheparametersofthemodel[ 29 46 ].TheinitializationofthemainparametersofHMMsisstudiedformanyapplications,suchastheapplicationofclusteringalgorithms[ 44 47 52 ],GaussianMixtureModels[ 53 57 ]andtheuseofrandomvalues[ 29 44 45 58 59 ].However,thereisnotacommonconsensusconcerningtheuseofanycriteriontoselectthetechniquetobeused.Thecharacteristicsofthescenarioshavetobeutilizedfortheinitialization. Forthespectrumsensing,therearetwofeatureswhichcanbeutilizedfortheselectionofinitialtransitionprobabilities. 1.ThereareonlytwostatesforPUbehavior.Ifweassumeaperfectsensing,basedonthestatesequence,thetransitionprobabilitiescanbeestimatedbytheMLestimatorusingEquation 3 2.Foranimperfectsensing,thefalsealarmandmissdetectionprobabilitiesareusuallykeptaslowaspossiblethroughanumberoftechnique[ 60 65 ]becauseoftherequirementofthecognitiveradionetworks.Itmeanstheobservedsequencecan 65

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stillbeconsideredasanapproximationofthehiddenstatesequenceforacoarseevaluation. Baseonthesetwofeatures,theinitialguessoftransitionprobabilitiescanbeestimatedbyassumingtheobservedsequenceO=fO1,O2,,ONgrepresentsthestatesequenceS=fS1,S2,,SNg. Letmxy(x,y2f0,1g)representsthenumberoftransitionsfromobservationxtoobservationy.mx(x2f0,1g)denotesthenumberofalltransitionsfromobservationx,theinitialguessofthestatetransitionprobabilitiesaregivenby: 8>>>>><>>>>>:^p=m01 m0^q=m10 m1.(4) Theaboveisacoarseestimationofthestatetransitionprobabilities,whichcanbeusedasaninitialguessoftheBaum-Welchalgorithm.Thecomplexityoftheestimatorislow,whichisapplicableforlow-capableSUs.ThentheBaum-Welchalgorithmwillconvergetolocaloptimumaroundthisvalue,whichisusuallyagoodestimationoftheparameters. Theeffectsofanimproperinitializationontheestimationaccuracywillbeillustratedthroughsimulations,whichcanvalidatethesignicanceoftheinitialparameterselection.Wewillalsoshowtheestimationaccuracyusingourapproachtoselecttheinitialguessofstatetransitionprobabilities. 4.6NumericalResults TheperformanceoftheBaum-WelchalgorithmforHMMisevaluatedthroughnumericalresults.Inthesimulation,theaccuracyrequirementintermsofthecondencelevelisgivenas1)]TJ /F9 11.955 Tf 12.58 0 Td[(=0.9and=0.1.1000observedsequencesaregeneratedusingHMMasthesampleset.Eachsequencegeneratesanestimateofthetransitionprobability.Themetricrepresentingtheestimationaccuracyisthecondencelevel, 66

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Figure4-4. Thecomparisonofcondencelevelbetweenperfectandimperfectsensing whichiscalculatedastheratioofthenumberofsequenceswheretheconditioninEquation( 4 )issatisedtothetotalnumberofsequences.Inthefollowinggures,onlytheestimationresultsofpareevaluated. Figure 4-4 showsthecondencelevelof^pforbothperfectsensingandimperfectsensingusingHMMforestimationwithregardtodifferencelengthofsequences,whenp=q=0.5.Forimperfectsensing,sensingerrorisspeciedbyPf=Pm=0.1.ThesamplesequencelengthNchangesfrom300to1000.Thisgureshowsthattheestimationaccuracyintermsofcondencelevelincreaseswhenthelengthofthesamplesequenceincreases.Theestimationaccuracyofimperfectsensingislowerthanthatofperfectsensingbecauseofthesensingerrors. Thesamplesequencelengthhastobecarefullyselectedtoachievetheestimationaccuracyrequirementwhilereducingunnecessarysensingslots.Figure 4-5 isthe3Dgraphshowingtheminimumlengthofsamplesequencerequiredtoachievetherequirementofestimationaccuracywithregardtodifferentpandqcombinations.The 67

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Figure4-5. Theimpactoftransitionprobabilitiesontherequiredsequencelengthforimperfectsensing accuracyrequirementisspeciedby1)]TJ /F9 11.955 Tf 12.64 0 Td[(=0.9and=0.1.Wecanseethattherequiredlengthofsamplesequenceincreasesasthetransitionprobabilitiesdecreases.Italsoshowsthattherequiredlengthissymmetricforpandqbecauseweneedtosatisfythecondencelevelforbothofthem.Whenpislargerthanq,thebottleneckgoestothecondencelevelofq.Symmetrically,whilethebottleneckisthecondencelevelofpifqislargerthanp.ComparedwiththerequiredsamplesequencelengthforperfectsensinginFigure 4-6 ,theimpactofimperfectsensingcanbeseenbytheincreasedlengthofthesamplesequencerequiredforthesamepandqcombination. Inordertounderstandtheimpactofimperfectsensinginamorestraightforwardway,Figure 4-7 showstherequiredsamplesequencelengthwithp=qforperfectsensingandimperfectsensing.Inthissimulation,pissettothesamevalueasqwhichchangesfrom0.1to0.9.Fromthisgure,wecanseethattheimperfectsensingrequireslongersequencetoachievethesamecondencelevelasthatofperfectsensing.Buttheyshowsimilartrendthatwhentherealtransitionprobabilityincreases,therequiredlengthdecreases. 68

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Figure4-6. Theimpactoftransitionprobabilitiesontherequiredsequencelengthforperfectsensing Figure4-7. Theimpactoftransitionprobabilitiesontherequiredsequencelength(p=q) 69

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TheimpactofanimproperinitializationontheestimationaccuracyisillustratedinFigure 4-8 ,whichshowsthesignicanceoftheinitialparameterselection.Thesimulationisconductedwhenwhenp=q=0.5.ThecurverepresentsthecondenceleveloftheBaum-Welchalgorithmusingaxedvaluefrom0.1to0.9astheinitialparameterforall1000sequences.Thevalueofthehorizontallinewithsquaresrepresentsthecondenceleveloftheestimationusingadifferentrandomvaluein(0,1)foreachobservedsequence.Thevalueofthehorizontallinewithstarsisthecondenceleveloftheestimationwith^p0=m01 m0foreachsequence.Itisshownthattheestimationaccuracyusingthevaluewhichisveryclosetotherealpastheinitialvalueisbetterthanusinganyotherinitialvalues.However,itisdifculttoguesstherealpattherststep.Thesimulationshowsthattheestimationusingourapproachtoselecttheinitialstatetransitionprobabilitiesperformsbetterthanusingmostoftheotherxedvalues.Ourapproachisalsomuchbetterthanthatusesrandomselectedvaluesforeachsequence.ThesimulationresultshighlightthesignicanceofproperlyselectingtheinitialmodelparameterspriortotheBaum-Welchalgorithm. Figure 4-9 presentstheimpactofthefalsealarmprobabilityonthecondencelevelof^pfordifferentlengthofsamplesequence.Itisshownthatthecondenceleveldecreasesasthefalsealarmprobabilityincreases,whichvalidatestheimpactoflevelofsensingerrorsontheestimationaccuracy.Italsoprovidesanotherinsightoftheimpactofsamplesequencelengthontheestimationaccuracy.Thecondencelevelincreasesasthesamplesequencelengthincreases. 4.7Summary Inthischapter,atwo-stateHMMisemployedtomodelPUbehaviorwithimperfectsensing.TheestimationoftransitionprobabilitiesisbasedonsamplesoftheobservedsequenceinsteadoftheonsamplesofPUstatesequencedirectly.Estimationaccuracyisevaluatedintermsofthecondencelevel,byutilizingtheprobabilitydistributionoftheestimator.Simulationresultsvalidatetherelationshipamongthelengthoftheobserved 70

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Figure4-8. Theimpactofinitializationontheestimationaccuracy Figure4-9. Impactoffalsealarmprobabilityontheestimationaccuracy 71

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sequence,therealstatetransitionprobabilities,thefalsealarmandmissdetectionprobabilities,theselectionofinitialparametersandtheaccuracyoftheestimatedvalues. 72

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CHAPTER5RESIDUALENERGYAWARECHANNELASSIGNMENTSCHEMES Inthischapter,weinvestigatethechannelassignmentprobleminacluster-basedmulti-channelCRSN,asdescribedinChapter 2 ,Section 2.1.2 .Duetotheinherentpowerandresourceconstraintsofsensornetworks,energyefciencyistheprimaryconcernfornetworkdesign.AnR-coefcientisdevelopedtoestimatethepredictedresidualenergyusingsensorinformation(currentresidualenergyandexpectedenergyconsumption)andchannelconditions(primaryuserbehavior).Weexaminethreechannelassignmentapproaches:Randompairing,GreedychannelsearchandOptimization-basedchannelassignment.ThelasttwoexploitR-coefcienttoobtainaresidualenergyawarechannelassignmentsolution.SimulationresultsshowthatR-coefcient-basedapproachesleadtobetterperformanceintermsofenergyconsumptionandresidualenergybalance.Optimization-basedchannelassignmentoutperformstheothertwoapproacheswithrespecttonetworklifetime. Thischapterisorganizedasfollows.Section 5.1 introducesthechallengesandourmotivation.WereviewtherelatedworkandcompareitwithourstudyinSection 5.2 .InSection 5.3 ,weproposeanR-coefcientasthemetricforchannelassignment.Section 5.4 describesthreedifferentchannelassignmentapproaches.Simulationresultsareprovidedin 5.5 andsummariesaremadeinSection 5.6 5.1SpectrumSharinginCognitiveRadioSensorNetworks(CRSNs) InCRSNs,asensorselectsthemostappropriatechannelonceanavailablebandisidentiedandvacatesthebandwhenaPU'stransmissionisdetected.Sincemultiplesensorsmaytrytoaccessthesamespectrum,aspectrumsharingmechanismisneededtocoordinatemultiplesimultaneoustransmissions,whichincludesboththemanagementofcoexistencewithPUsandresourceallocationamongsensors. Thereisalargeamountofworkintheliteratureondynamicspectrumsharingandchannelassignmentproblem[ 1 66 ],suchasthemulti-carriermodulationtechnology 73

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andtheuseofcommoncontrolchannelforspectrumrelatedinformationexchange.Mostofthestudiesconcentrateonsensingchannelavailabilitytoimprovespectrumutilization,modelingPUactivitytoavoidcollisionoranalyzingQoSperformancesuchasdelayandthroughput.However,onlyafewofthecurrentstudiesforchannelassignmentincognitiveradionetworksconsiderenergyconsumptionproblem,whichisthecriticalconcernforenergy-constrainedWSNs.Reducingenergyconsumptionhelpsnon-rechargeablesensorstooperateforalongertime.Whenacertainnumberofsensorsdie,thenetworkwillbeconsiderednonfunctional.Thetimedurationfromsensordeploymenttotheinstantofnetworknonfunctioniscallednetworklifetime[ 67 ].Sensorsshouldconsumetheenergyatthesamepaceinordertomaximizenetworklifetime.Therefore,energyconsumptionandresidualenergybalancearebothcriticalinWSNdesign.TherearesomerelatedstudiesaboutenergyefciencyinordinaryWSNs.In[ 15 ],arealisticpowerconsumptionmodelforWSNdevicesisproposedtoderivetheconditionsforminimumpowerconsumptionindatatransmissions.In[ 67 ],residualenergyinformationandchannelstateinformationareconsideredforlifetime-maximizingMACprotocols.ForCRSNs,theprimaryconcernishowtoreduceenergyconsumptionandprolongthenetworklifetimewithanappropriatedynamicspectrumallocationscheme. Inthischapter,weconsideracluster-basedmulti-channelCRSN.Thechannelassignmentproblemisinvestigatedfromtheaspectofenergyconsumptionandnetworklifetime.AnR-coefcientdeterminedbysensorenergyinformationandPUbehaviorisproposedtorepresentthepredictedresidualenergy.WetrytobalanceresidualenergyforeachsensorwithchannelassignmentbasedonR-coefcient.Threechannelassignmentapproachesareprovided:Randompairing,GreedychannelsearchandOptimization-basedchannelassignment. 74

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5.2RelatedWork Therearemanyexistingworksstudyingchannelassignmentproblemsincognitiveradionetworks.In[ 68 ],OSA-MACprotocolbasedonIEEE802.11DCFmodelisproposedforopportunisticspectrumaccess.Itprovidesbothuniformlyrandomchannelselectionandspectrumopportunity-basedchannelselection.However,itdoesnotconsiderthestatechangeofPUbehavior,whichisstudiedinourwork.In[ 20 ],theauthorsevaluatesthedatalinklayerQoSperformanceofcognitiveusers,suchasaveragethroughputandpacketlossrate.ItmodelsPUbehaviorasatwo-stateMarkovChain.However,itassumesthatifthechannelisnotusedbyPUsatthebeginningofatimeframe,itremainsunoccupiedduringthetransmissionofcognitiveusers.Inourstudy,aPUmaytakeoverthechannelatanytimeevenbeforeacognitivetransmissionnishes.Inthiscase,thecognitiveuserwillstopthetransmissionimmediatelywhenaPUtransmissionisdetected.Ourgoalistoassignthecognitiveusertothechannelwiththeleastprobabilityofinterruption. Asfaraswehaveseen,therearefewpapersfocusingontheenergyconsumptionandnetworklifetimeforchannelassignmentincognitiveradionetworks.In[ 69 ],anoptimizationmodelforenergy-efcientspectrumaccessisformulatedtominimizetheenergyperbitforeachsingleuser.However,thisnetworkmodelonconsidersandignoresPUbehavior.Also,thechannelselectiondecisionismadeindividuallywithoutconsideringcollisionstoothercognitiveusersandtheenergyconsumptionbasedonthewholenetwork.In[ 8 ],thechannelselectionproblembasedonPUbehaviorandenergyconsumptionisformulatedasamulti-armedbanditproblem.PUbehaviorisalsomodeledasatwo-stateMarkovChain.Butstill,thecognitiveusermakesdecisionsonlybaseditsownobservationanditdoesnotconsiderothercognitiveusers.Inourwork,weconsidertheenergyconsumptionandresidualenergybalancewithrespecttothenetworkperformanceandournalgoalistoprolongthenetworklifetime.Tothebest 75

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ofourknowledge,wearethersttoconsidernetwork-wideresidualenergybalanceforchannelassignmentproblemsincognitiveradionetworks. 5.3R-Coefcient Inthischapter,weusethenetworkmodelandtimeframestructuredescribedinChapter 2 ,Section 2.1.2 .Asmentionedpreviously,whenasensorhasdatatosend,itwakesupandtransmitsanassign requestmessage.WhenCHreceivestheassign requestmessagesfromalltheactivesensors,CHbeginstoprocessthechannelassignmentbasedonthesensorinformationandPU'sstateoneachavailablechannel.Ourprimaryconcerninthisprocessisenergyconsumptionindatatransmission.Basedonourenergyconsumptionmodel,weknowthattransmissionenergyforthesensorisdependentonthelengthoftransmitteddata,whichinourdesignisthenumberofthetransmissionslots. Fordatapackettransmission,werefertotheframestructureinFigure 2-3 ,whereacompletedatatransmissiontakesupLslots.SensorsaccessidlechannelsaccordingtothechannelassignmentdecisionfromtheCH.IfachannelisassignedtoaCMthatneedstotransmit,theCMwillstarttransmissioninthecomingdataslot.SupposethatCMiattemptstotransmitapacketwiththelengthofLslotsonchannelj.IfCMicansuccessfullytransmitthewholepacket,theenergyconsumptionisEtri(L),asinEquation( 2 ).AccordingtotheMarkovmodel,theprobabilitythatasensorcansuccessfullytransmitapacketonchanneljisequaltotheprobabilitythatthechannelremainsintheidlestateforLconsecutivetimeslotsasfollows: Psuccessj=P(idlefornextLslotsjidleintheinitialslot)=(1)]TJ /F4 11.955 Tf 11.96 0 Td[(pj)L.(5) IftheCMonlytransmitsforl
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Plj=(1)]TJ /F4 11.955 Tf 11.95 0 Td[(pj)l)]TJ /F11 7.97 Tf 6.59 0 Td[(1pj1lL.(5) Basedontheaboveequations,theexpectedenergyconsumptionforCMitransmittingonchanneljisderivedasfollows: Edataij=LXl=1Etri(l)Plj+Etri(L)Psuccessj.(5) Ourgoalistoreducethetotalenergyconsumptionwhileatthesametimebalanceresidualenergyofeachsensorinordertomaximizethenetworklifetime.Accordingtothisobjective,weproposeanR-coefcienttorepresentthepredictedResidualenergy.IfsensoritransmitsonchanneljwithcurrentresidualenergyRci,thepredictedresidualenergyisdenotedas Rij=Rci)]TJ /F3 11.955 Tf 13.26 2.66 Td[(Edataij(5) ThevalueofRijdescribesthestatisticallyexpectedresidualenergyofsensoritotransmitonchannelj.Itisanestimatedvalueforpredictionofthepossibleresidualenergyanddependsonthecurrentresidualenergyofsensori,thedistancefromsensoritoCH,andPUstatisticsonchannelj.Wetrytond(i,j)pairwithRijaslargeaspossiblewhencarryingoutchannelassignment. FromthedenitionofRij,wecanseethatpotentially,sensoriwillselectthechannelwithminimumexpectedenergyconsumption.Thereforetheactualenergyconsumptionwillbereducedwithagreaterprobabilityandtheresidualenergyaftertransmissionforeachactivesensorwillberaised.Also,channeljwillbeassignedtothesensorwithlargerresidualenergy.Orequivalently,asensorwithlargerresidualenergyismorelikelytoundertakethetaskoftransmission.Inthisway,theresidualenergyforeachactivesensorcanbekeptaboutthesamelevel.Inotherwords,theresidualenergywillbebalancedacrossallsensorsintheclusterusingthisR-coefcient. 77

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Fairnessamongsensorsisnotguaranteedinthiswork.However,itcanbeimprovedwithsimplemodications.Forexample,inthecasethatasensorhasapackettotransmitbutcouldnotgetthroughforacertainnumberoftimeframes,itwillinformCHandbeassignedwithhigherpriority.Thisproblemwillbestudiedmoreinourfuturework. 5.4ChannelAssignment Nextwewilldescribethreechannelassignmentapproaches.Webrieyintroducerandompairing,whichisasimpleandcommonlyusedmethod.ThenbasedontheR-coefcient,weproposeGreedychannelsearchandoptimization-basedchannelassignment. 5.4.1RandomPairing AssumethatthereareNactivesensorsandMavailablechannelsinthecurrentframe.TheCHpicksupsensorirandomlywithprobability1 N,selectschanneljwithprobability1 Mandthenmakesiandjasapair.Inthisway,channeljisassignedtosensori.Sensoriismarkedassignedsensorandchanneljismarkedassignedchannel.ThenNisupdatedasthenumberofremainingactivesensorsandMisupdatedasthenumberofremainingavailablechannels.Thesameprocedurecontinuesuntileitheralltheactivesensorsgetassignedortherearenomoreavailablechannels.Thisrandompairingissimpletoimplement.However,itdoesnotconsideranyinformationeitherfromthesensorenergyorfromthePUbehavior. 5.4.2GreedyChannelSearch WhentheenergyconsumptionandtheresidualenergyareconsideredforCRSN,itwouldbemoreefcienttoexploitourR-coefcientbyallowingsensoritoaccesschanneljwiththelargestRvalue.Inthisapproach,wecomeupwithtwo-stepGreedyallocation.Intherststep,foreachactivesensor,wendthelargestR-coefcientvalueoveralltheavailablechannels.Inthesecondstep,wesearchovertheselargestvalues,themaximumR-coefcientisobtained.Thenthecorrespondingchanneljwill 78

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beassignedtothecorrespondingsensori.Sensoriandchanneljaremarkedassignedrespectively.Itcontinuesfortheremainingsensorsandchannelsuntileveryactivesensorisassignedoreveryavailablechannelisused.Usingthistwo-stepGreedyallocationduringeachiterationforunassignedsensorsandunassignedchannels,wecanalwaysndan(i,j)pairwiththemaximumvalueofremainingR-coefcient. ThepseudocodeofthisapproachisillustratedinFigure 5-1 Set[R]NM=Rcoefcientmatrix; fornodei=1toNdo ifiisactiveandnotassignedthen forchannelj=1toMdo ifjisavailableandnotassignedthen ifrij=Maxof[R]then Assignjtoi; Markiandjasassigned; update[R]withrij=0; endif endif endfor endif endfor Figure5-1. PseudocodeofGreedyalgorithm 5.4.3Optimization-basedChannelAssignment Withrespecttothenetworkperformanceforthecluster,thenetwork-wideresidualenergyiscriticaltoprolongthenetworklifetime.GreedychannelsearchalwayssearchesforthemaximumvalueofR-coefcientineachsingleiteration.Itcannotguaranteethatthetotalresidualenergyofallsensorsinthenetworkismaximizedafterthisframe.IfwemaximizethesumofR-coefcientforeach(i,j)pairwhencarryingoutchannelassignment,thetotalactualresidualenergyofthewholeclusterafterdatatransmissionwillbekeptasmuchaspossible. 79

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SupposethatthereareNactivesensorsandMavailablechannels.Thedecisionvariablexijrepresentstheassignmentofsensoritochannelj,takingvalue1ifassignedand0otherwise.NXi=1MXj=1Rijxijisourobjectivefunction. MaximizeNXi=1MXj=1RijxijsubjecttoCase1:N>MMXj=1xij1,NXi=1xij=1Case2:NM,thoseMavailablechannelsareassignedtoMselectedsensorswithaone-to-onematching.N)]TJ /F4 11.955 Tf 12.91 0 Td[(Mremainingsensorswillbenotbeabletotransmitinthisframe.IfN
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Thisoptimizationmodelcanbemaderathermoreexibletodifferentcases.IfN>M,thenN)]TJ /F4 11.955 Tf 12.54 0 Td[(Mdummychannelsareinvented,perhapscalledsittingstilldoingnothing,withR-coefcientof0forthesensorsassignedtothem.Inthisway,theconstraintsinCase1becometwoequations.ThentheassignmentproblemcanbesolvedinthesamewayasinCase3andstillgivethebestsolutiontotheproblem.SimilartrickscanbeplayedwhenNmthen Addn-mdummychannels; Constraints=ConstraintsofCase1; else ifn
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isgovernedbyanindependentprobabilityPActive.AllthreechannelassignmentapproachesareappliedinthesimulationonthesamesetofsensoractivityandPUbehavior.TABLE 5-1 showsalltheparametersusedinthesimulation. Table5-1. Simulationparametersofresidualenergyawarechannelassignment ParametersValue Numberofsensors(N)25/30/35/40/45/50/55Numberofchannels(M)10Sensoractiveprobability(Pactive)0.5Channeltransitionprobability(Pidle!busy)0.15-0.35Channeltransitionprobability(Pbusy!idle)0.65-0.85Numberofslotsineachframe(K+1)10Numberofframes(F)50/250Slotperiod(ts)0.001secondSensordatatransmissionrate(R)1Mbits/secondSensorpacketsize(L)6slotsSensorinitialenergy(Ein)1000mJEnergyconsumptionforchannelassignment(Ec)1mJRFcircuitenergyconsumption(Ecir)5mJ/slotAmplierenergyrequiredatCH(")0.001mJ/slot/m2DistancebetweensensorandCH(d)Uniformlydistributedbetween50m-100m Figure 5-3 showsaveragenetworkenergyconsumptionoverframesforthreeapproachesinnetworksofdifferentnumbersofsensors.ItisobservedthatthereisabiggapbetweenRandompairingandothertwoapproaches,whichindicatesthatagreatamountofenergycanbesavedthroughGreedychannelsearchandOptimization-basedchannelassignment.RecallthatwhenR-coefcientisconsidered,asensorismorelikelytoaccessthechannelwithlowenergyconsumptiondemand.Therefore,totalenergyconsumptionofthenetworkismuchlowerforthetwoR-coefcient-basedchannelassignmentapproaches.Besides,Optimization-basedchannelassignmentperformsslightlybetterthanGreedychannelsearch,whichveriesthemeaningoftheoptimalsolutiontotheoptimizationmodel. Figure 5-4 showsthecomparisonofthreeapproachesbasedonaveragestandarddeviationofsensorresidualenergyoverframesrelatedtothenumberofsensors,which 82

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Figure5-3. Averagenetworkenergyconsumptionoverframes(numberofframes=50) indicatesresidualenergybalanceofthesensors.ThedifferenceamongcurvesissimilartoFigure 5-3 .TheobjectiveofusingR-coefcientistosuppresslow-energysensorsbutencouragehigh-energysensorstoaccessthechannels,whichresultsinabalancedresidualenergydistribution.ThisleadstothebiggapbetweenRandompairingandothertwoR-coefcient-basedapproaches. Figure 5-5 showsthenumberofalivesensorsaftereachframe,whichrepresentsnetworklifetime.UsingtheR-coefcientasthemetricinchannelassignmenthelpsbalancetheresidualenergiesofthesensors,whichleadstoabetterchancetoextendnetworklifetime.TheOptimization-basedchannelassignmentperformsbetterthanGreedychannelsearchwithregardtonetworklifetime.ThisisbecauseGreedyapproachtriestomaximizetheexpectedresidualenergyforasinglesensor-channelpairwhileOptimizationmethodreachestheoptimalsolutionofmaximizingthetotalpredictedresidualenergyfortheentirenetwork. 83

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Figure5-4. Averagestandarddeviationofsensorresidualenergyoverframes(numberofframes=50) Figure5-5. Numberofremainingalivesensorsaftereachframe(numberofsensors=30) 84

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Figure 5-6 showsthecomparisonbetweenOSA-MAC[ 68 ]andouroptimizationmethodintermsofeffectiveenergyconsumptionsdenedasthetotalenergyconsumptionofthenetworkdividedbythetotaltransmissionslots.ForOSA-MAC,wesimulatetheirspectrumopportunity-basedchannelselection,inwhichtheselectionapproachtakestheprobabilitiesofspectrumavailabilityaccordingtoPUbehavior.PUbehaviorisassumednottochangeduringthepackettransmissionofcognitiveusersandthecollisionamongcognitiveusersisreducedbybackofftime.Inourwork,theMarkovmodelofPUbehaviormakesitmorerealisticandtheone-to-onematchingbetweensensorsandchannelsaddressesthecollisionproblem.Hence,ourapproachcanachievebetterenergyefciency. Figure5-6. Averageeffectiveenergyconsumptionoverframes(numberofframes=50) 5.6Summary Inthischapter,westudythechannelassignmentprobleminacluster-basedmulti-channelCRSNwithconsiderationofenergyconsumption,residualenergybalancingandnetworklifetime.AnR-coefcientisproposedaccordingtothepredicted 85

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residualenergy.BasedontheR-coefcient,Greedychannelsearchisproposedtoconsecutivelymaximizetheexpectedresidualenergyforeachsinglesensor-channelpair,andanoptimizationmodelisproposedtomaximizethetotalexpectedresidualenergyinordertoimprovethenetwork-wideperformance.ThesimulationresultsshowevidentimprovementcomingfromtheR-coefcientbasedchannelassignmentonbothenergyconsumptionandresidualenergybalance.TheOptimization-basedchannelassignmentoutperformsGreedychannelsearchinnetworklifetime.Besides,thecomparisonwithOSA-MACshowsthattheoptimizationassignmenthasbetterperformanceintermsofeffectiveenergyconsumption. 86

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CHAPTER6DYNAMICSPECTRUMACCESSWITHPACKETSIZEADAPTATIONANDRESIDUALENERGYBALANCING Inthischapter,theeffectiveenergyisconsidered,whichistheenergyconsumptionforthesuccessfullytransmitteddata.Wedemonstrateanimprovementintheenergyefciencyandthenetworklifetimebypacketsizeadaptationandresidualenergybalancing.Thisisachievedbyinvestigatingthedynamicspectrumaccessissueswithtwomethods.Therstemploysapacketsizeadaptation:avariablesizetoadaptthetime-varyingchannelstates,toimprovetheenergyefciencyinthenetwork.Thesecondmethodexploitsanawarenessoftheresidualenergyinthechannelassignment.Thishelpstobalancetheresidualenergytoprolongthenetworklifetime,comparedtotherandompairingapproach. Thischapterisorganizedasfollows.Section 6.1 providestheintroductionoftheproblem.TherelatedworkisreviewedinSection 6.2 .Section 6.3 introducesthepacketsizeadaptationscheme,whichimprovesenergyutilization.Section 6.4 andtheresidualenergybalancingchannelassignment.Section 6.5 providessimulationresultsandanalysis.Section 6.6 summarizesthischapter. 6.1DynamicSpectrumAccessandEnergyConsumption Inthelastchapter,wefocusonreducingenergyconsumptionandprolongingnetworklifetime.Thisisachievedbymaximizingtotalresidualenergyofthewholenetwork.SincetheongoingtransmissionofasensorstopswhenaPUsignalisdetected,thepacketisdroppedandtheenergyiswasted.Evenifthetotalresidualenergyismaximized,theamountofpacketswhichcanbesuccessfullytransmittedmaybeverysmall.Moreover,transmittingtheassign requestmessageandreceivingtheassign requestmessagealsoconsumesenergy.Inthischapter,weconsiderenergyefciency,anotherimportantconcernforproposinganappropriateopportunisticspectrumaccessscheme.Weminimizethetotalenergyconsumptionneededtosuccessfullytransmitacertainamountofinformationbits.Ithelpssensorstotransmit 87

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asmuchinformationaspossibleduringtheirlifetime.Wearealsoconcernedaboutthenetworklifetime,whichisintroducedinChapter 5 .Theaveragewastedenergy,whichisdenedasthetotalunusedenergyinthenetworkwhenitdies,shouldbereducedtoprolongthenetworklifetime[ 67 ].Thus,theresidualenergyofallthesensorsinthenetworkneedtobekeptaroundthesamelevelwithabalancingschemesothatthewastedenergyisminimizedwhentherstsensordies.Inthisway,thenetworklifetimeismaximized. Inthischapter,weinvestigatetheintra-clustercommunicationofacluster-basedCRSN.Withrespecttothetime-varyingchannelconditionsdependingonthePUbehavior,thepacketsizeisadjustedtoimproveenergyefciencyofthenetwork.Afterthepacketsizeisdetermined,thechannelassignmentofCRSNisinvestigatedwiththeobjectiveofprolongingthenetworklifetime.ResidualenergyisbalancedforeachsensorwithchannelassignmentbasedonsensorenergyinformationandPUbehavior. 6.2RelatedWork Thereweremanyexistingworksstudyingdynamicspectrumaccessproblemsincognitiveradionetworks[ 1 16 18 21 28 34 66 71 73 ].However,allthesepapersfocusedonQoSperformance,suchasthroughputandpacketlossrate,withouttheconsiderationoftheenergyefciencyandnetworklifetimeforspectrumaccessincognitiveradionetworks.In[ 71 ],effectivecapacityofcognitiveradiochannelswasstudiedunderQoSconstraintsandchanneluncertainty,inwhichthetransmitterisunawareofthechannelfadingcoefcients.In[ 21 ],aframe-basedopportunisticspectrumschedulingschemewasimplementedtomaximizetheaggregatethroughputofallsecondaryusers. TherewerealsomanystudiesaddressingtheenergyconstraintsinWSNs.In[ 74 ],alinkadaptationmechanismwithanadaptiveframesizewasproposedattheMAClayertoimproveenergyefciency.In[ 75 ],anoptimized-MACprotocolwithhighenergyefciencywasproposedbyadjustingthesensordutycyclebasedonthenetworktrafc. 88

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However,thesestudieswerebasedonordinaryWSNsandtheydidnotneedtoaddressthedynamicspectrumaccessinacognitiveradionetwork.In[ 7 ],anoptimizationmodelforenergy-efcientspectrumaccessinCRSNswasformulatedtominimizetheenergyperbitforeachsingleuser.EachSUmadethedecisionofchannelindividuallyandapowercontrolmechanismisusedtoreducetheinterferenceamongSUs.However,itdidnotneedtoconsidertheimpactsofPUbehavior. 6.3PacketSizeAdaptation Asshowninthelastchapter,theprobabilityofsuccessfullytransmittingapacketcanbecalculatedby: Psuccessj=P(idlefornextLslotsjidleintheinitialslot)=(1)]TJ /F4 11.955 Tf 11.96 0 Td[(pj)L.(6) Weobservethatasthepacketsizeincreases,theprobabilitythatthepacketcansuccessfullygettransmittedisdecreased.TheenergyiswastedifthepacketcollideswithPUpackets.Ontheotherhand,ifthepacketsizereduces,theratioofenergyconsumptionintheaccesscontrolslotofFigure 2-3 totheenergyconsumptioninthedatatransmissionslotsincreases,whichalsoreducesenergyefciency.Takingintoaccountthistradeoff,theremayexistanoptimalpacketsizeleadingtothebestenergyefciency.Inthiswork,themetricenergy-per-bit(EPB)isemployedtodenotetheratiobetweenthetotalenergyconsumptionandtheamountofdatasuccessfullytransmitted.AsintroducedinChapter 1 ,protocoldesignforWSNsiseffectiveonanetworkbasisratherthanonanindividualbasis,sotheobjectiveistominimizetheEPBforthewholenetwork. SinceboththePUbehaviorandsensoractivityaretime-varyinginnature,theadaptationofthepacketsizeisconsideredforeveryframe.AsmentionedinChapter 2 ,Section 2.1.2 ,whenaCMhasdatatosend,itwakesupandtransmitsanac-cess requestmessage.WhentheCHreceivestheaccess requestmessagesfrom 89

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alltheactiveCMs,itbeginstodeterminethepacketsizeforthedatatransmissionofthecurrentframebasedonthePUbehaviorandsensoractivity. Thetotalenergyconsumptioninthenetworkiscomposedoftwoparts:(1)theenergyconsumedintheaccesscontrolslot,whichincludestransmissionenergyforaccess requestpacketsandreceivingenergyforthebroadcastaccess replypacketand(2)theenergyconsumedinthedatatransmissionslots.Inthiswork,thestartopologyisappliedwithanequaldistancedbetweeneachCMandtheCH.Letthesizeofaccess requestpacketandaccess replypacketbeK1andK2bits,respectively.Theenergyconsumedintheaccesscontrolslotiscalculatedby: Econtrol=(Ecir+"d2)K1+EcirK2.(6) Fordatatransmission,theexpectedenergyconsumptionforCMitransmittingonchanneljiscalculatedbyEquation( 6 ), Edataij=LXl=1Etri(l)Plj+Etri(L)Psuccessj.(6) SincethedistancebetweeneachCMandtheCHisthesame,thevalueofEdataijisnotrelatedtotheindexianditcanbewrittenasEdataj. AccordingtoEquation( 6 ),theprobabilityofasuccessfultransmissionisonlydependentonthePUbehaviorofeachchannel.Therefore,theexpectedamountofthesuccessfullytransmitteddatabitsonchanneljis: .Kdataj=PsuccessjBTL.(6) IfthenumberofactiveCMsismorethanthenumberofavailablechannels,alltheavailablechannelscouldbeusedfordatatransmission.Inthiscase,wewritethepredictednetworkEPBasthefollowingequation: 90

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EPB=EcontrolNacitve+MXj=1Edataj MXj=1Kdataj,(6) whereNacitveisthenumberofactiveCMs. IfthenumberofactiveCMsislessthanthenumberofavailablechannels,thechannelswithlesspjareselectedinordertoreducetheprobabilityofcollisionswithPUsduringthedatatransmission.Thisisbecausewithlesspj,thesechannelsaremorelikelytostayinstateidleiftheyaresensedidleintheinitialslot.ThenumberoftheselectedavailablechannelsisNactive. IftheminimumpacketsizeisLminandthemaximumpacketsizeisLmax,whichdependsonspecicnetworkparameterconstraintsonpacketsize,theoptimalpacketsizeintermsofnumberofslotsisobtainedby Lopt=argminL2[Lmin,Lmax]EPB(6) SinceactiveCMsandavailablechannelsaretime-varying,thepacketsizeshouldbeadaptivelychangedtominimizethenetworkEPBforthecurrentframe.TheCHkeepstrackingthechangesofchannelconditionsbyestimatingstatetransitionprobabilitiesandusethisinformationtogetherwiththeaccess requestmessagesfromCMstomakedecisionsonthepacketsizeatthebeginningofeachframe. 6.4ResidualEnergyBalancingChannelAssignment AftertheCHdecidestheoptimalpacketsize,itbeginstoconductthechannelassignmentbasedontheinformationaboutboththechannelconditionsandtheactiveCMs'residualenergy.TheprimarygoalinthisprocessistobalancetheresidualenergyamongalltheCMsinthenetworkinordertomaximizethenetworklifetime.WealsousetheR-coefcientintroducedinChapter 5 ,Section 5.3 torepresentthepredictedResidualenergy.Inthischapter,sincetheenergyconsumedforcontrolinformationis 91

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considered,theexpressionoftheR-coefcientisdifferent.ifIfanactiveCMisassignedtochannelj,thetotalexpectedenergyconsumptioninthecurrentframeis: Ej=Econtrol+Edataj,(6) WhereEcontrolandEdatajiscalculatedbyEquation( 6 )andEquation( 6 ),respectively.WithcurrentresidualenergyRci,thepredictedresidualenergyisobtainedby: Rij=Rci)]TJ /F3 11.955 Tf 13.26 2.65 Td[(Ej.(6) ItisanestimatedvalueforpredictionofthepossibleresidualenergyanddependsonboththecurrentresidualenergyofCMiandPUstatisticsonchannelj.Inthischapter,thebasicideaforassigningchanneljtoCMiistond(i,j)pairswiththevaluesofRijclosetoeachother.Inthisway,theresidualenergyofeachactiveCMcouldbemaintainedatthesamelevelafterthedatatransmissioninthecurrentframe.Therefore,theobjectiveistondtheminimumofthevariancefortheR-coefcientofeachCM. SupposethatthereareseveralactiveCMsandavailablechannels.AccordingtoSection 6.3 ,ifthenumberofactiveCMsislessthanthenumberofavailablechannels,thechannelswithlesspjareselectedfortheassignment.Thesechannelsbecomecandidatechannels.Also,ifthenumberofactiveCMsisgreaterthanthenumberofavailablechannels,thesensorswithlargerresidualenergyareselectedascandidateCMs.Therefore,thenumberofcandidatechannelsisequaltothenumberofcandidateCMs.ThisnumberisdenotedasN.ThedecisionvariablexijrepresentstheassignmentofCMitochannelj,takingvalue1ifassignedand0otherwise. TheaveragevalueoftheR-coefcientsforagivenchannelassignmentisdenedas 92

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R=NXi=1NXj=1Rijxij N.(6) Thevarianceminimizationmodelisdevelopedasfollows: MinimizeNXi=1NXj=1(Rij)]TJ /F25 10.909 Tf 12.15 2.42 Td[(R)2xij NsubjecttoNXj=1xij=1,NXi=1xij=1.(6) NotethatallthecandidateCMsandcandidatechannelswillbeassigned.Thetotalcurrentresidualenergyandthetotalexpectedenergyconsumptionremainthesameforanyassignment,whichmakesthetotalexpectedresidualenergy(R-coefcients)aconstant.Therefore,Risalsoaconstant.Thismeansthattheoptimizationmodelisanintegerlinearprogram(ILP).TheconstraintsindicatethateachcandidateCMcanonlybeassignedtoonechannelandeachcandidatechannelcanonlybeusedbyoneCM.TheconstraintmatrixAconsistsofn2columnsand2nrows. A=266666666664100010............001III377777777775(6) 1isan-rowvectorofallonesandIisannnidentitymatrix.ThedeterminantofeverysquaresubmatrixformedfromAhasvalue-1,0,or+1.ItmeansthatAistotallyunimodular[?].Applyingthispropertytotheoptimizationmodel,anoptimalbasic 93

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feasiblesolutionwithxij=0or1replacedbyxij0willbeallintegers.Therefore,thesolutiontothelinearprogram(LP)isactuallythesolutiontotheILP. ThesimplexalgorithmisapopularalgorithmforLP.However,itisnotveryefcientandsometimesmayhaveexponentialtimecomplexity.Basedonthecharacteristicsofthisproblem,anefcientalgorithmcanbeusedtominimizethevariance.ThebasicideaistomaketheCMswithlargerresidualenergyselectthechannelswithlargerexpectedenergyconsumption.ThecurrentresidualenergyofallcandidateCMsisdenotedbyRi=(R1,R2,...,RN).TheexpectedenergyconsumptionforaCMtransmittingonchanneljisEj=(E1,E2,...,EN).BothRiandEjaresortedinadescendingorder.ThenCMiwiththelargestRiisassignedtochanneljwiththelargestEj,andmarkCMiandchanneljasassigned.ThesameprocedurecontinuesfortheremainingCMsandchannelsuntileverycandidateCMisassignedandeverycandidatechannelisused.TheresidualenergyofCMsafterdatatransmissionisexpectedtohavetheminimumvariance. Thefollowingistoprovethattheproposedalgorithmgivestheoptimalsolution. Thepair(Ri,Ej)denotesthatCMiisassignedtochannelj.Foragivenassignment,ifthereexisttwopairs:(R1,E2)and(R2,E1)withR1>R2andE1>E2,thevarianceisdecreasedbyswitchingthetwopairsto(R1,E1)and(R2,E2). Proof:Denotethevariancefortheassignmentwith(R1,E1)(R2,E2)andtheassignmentwith(R1,E2)(R2,E1)asVar1andVar2,respectively.SincetheassignmentofotherCMsandchannelsisnotchanged,thedifferenceofthevarianceisdeterminedbytheassignmentofCM1andCM2.AssumeVar1>Var2,accordingtoEq.(??),wehave (R1)]TJ /F4 11.955 Tf 11.96 0 Td[(E1)]TJ /F3 11.955 Tf 13.31 2.66 Td[(R)2+(R2)]TJ /F4 11.955 Tf 11.96 0 Td[(E2)]TJ /F3 11.955 Tf 13.31 2.66 Td[(R)2>(R1)]TJ /F4 11.955 Tf 11.95 0 Td[(E2)]TJ /F3 11.955 Tf 13.32 2.66 Td[(R)2+(R2)]TJ /F4 11.955 Tf 11.95 0 Td[(E1)]TJ /F3 11.955 Tf 13.32 2.66 Td[(R)2.(6) Fromthisequation,weget (R1)]TJ /F4 11.955 Tf 11.95 0 Td[(R2)(E1)]TJ /F4 11.955 Tf 11.95 0 Td[(E2)<0.(6) 94

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ThiscontradictswiththefactthatR1>R2andE1>E2.ThereforeVar1>Var2,whichindicatesthevarianceisdecreasedbytheswitch. Basedontheaboveanalysis,foranygivenassignment,wecanalwaystakeacertainnumberofswitchestoreachtheresultoftheproposedalgorithm.Aseachswitchincreasesthevariance,theproposedalgorithmproducestheminimumvariance.Theswitchingprocedureisasfollows:SupposethereareNcandidateCMswithR1>R2>...>RNandNcandidatechannelswithE1>E2>...>EN.Fortheproposedalgorithm,thechannelsassignedtoR1,R2,...,RNshouldbeE1,E2,...,EN,respectively.Foranyotherassignments,ifE1isnotassignedtoR1,wecanrstswitchtwopairs(R1,Ej)and(Ri,E1)to(R1,E1)and(Ri,Ej).Asdescribedabove,thisswitchreducesthevariance.AfterE1isassignedtoR1,anotherswitchistakensothatE2canbeassignedtoR2,whichalsoreducesthevariance.ThesameprocessisdonefortheremainingCMsandchannels,afterwhichtheassignmentisthesameastheresultoftheproposedalgorithmandhastheminimalvariance.Therefore,theproposedalgorithmprovidestheoptimalsolutiontotheoptimizationmodel. Inthisway,theresidualenergyofCMsafterdatatransmissionisexpectedtohavetheminimumvariance.ThetotalunusedenergywhentherstCMdiesisreducedandhencethenetworklifetimeisprolonged,asdescribedinChapter 5 ,Section 5.1 6.5SimulationResults WeconductthesimulationwithinaclusterofCRSN.PUbehavioroneachchannelisrepresentedas(idle/busy)state,whichisdescribedinChapter 2 ,Section 2.2 .TheprobabilitythataCMhasapackettotransmitisPActive.TABLE 6-1 showsalltheparametersusedinthesimulation. 6.5.1PerformanceofPacketSizeAdaptation Theproposedpacketsizeadaptationscheme,asdescribedinSection 6.3 ,isexaminedbycomparingwiththexedpacketsize.Figure 6-1 plotstheaccumulativenetworkenergyefciencyacrossthewholesimulationdurationforthepacketsize 95

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Table6-1. Simulationparametersofdynamicspectrumaccesswithpacketsizeadaption ParametersValue Numberofsensors(N)30Numberofchannels(M)20Sensoractiveprobability(Pactive)0.3Channeltransitionprobability(Pidle!busy)(0,1)Channeltransitionprobability(Pbusy!idle)(0,1)Slotduration(ts)0.002secondDatatransmissionrate(B)40kbpsCMcontrolpacketsize(L)4bytesCHbroadcastpacketsize(L)25bytesCMdatapacketsize(L)[25,128]bytesSensorinitialenergy(Ein)1JRFcircuitenergyconsumption(Ecir)50nJ/bitAmplierenergyrequiredatCH(")100PJ/bit/m2DistancebetweensensorandCH(d)25monaverage Figure6-1. ThecomparisonofaccumulativenetworkEPBamongdifferentpacket-sizingschemes 96

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Figure6-2. ThecomparisonofoverallnetworkEPBamongdifferentpacket-sizingschemes Figure6-3. Thecomparisonofthevolumeofsuccessfullydeliveredinformationamongdifferentpacket-sizingschemes 97

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adaptationschemeandthexedpacket-sizingschemes.ThenetworkenergyefciencyischaracterizedintermsofEPB.WeobservethattheproposedpacketsizeadaptationschemeachievesthebestenergyefciencyinsuccessfulinformationdeliverybykeepingitsEPBatthelowestlevelamongallpacket-sizingschemes.Moredirectcomparisonamongthepacket-sizingschemescanbeobservedinFigure 6-2 andFigure 6-3 ,whichprovidemoreinsightsontheimpactsofpacketsizesontheoverallnetworkEPBandtheoverallvolumeofsuccessfullydeliveredinformationbits.Usingadaptivepacketsize,theEPBis0.431mJ/bitandthenumberoftransmittedinformationis66.95Mb.Forthexedpacketsizingscheme,theEPBvaluerstdecreasesasthepacketsizeincreases,andthenitkeepsincreasing.Thereversetrendexitsintermsofthetransmitteddata.Notethattheoptimalpacketsizeofthexedschemeis50bytes,forwhichtheEPBis0.437mJ/bitandthenumberoftransmittedinformationis66.87Mb.Itisstillworsethantheperformanceofadaptivepacketsize.Sincethepacketsizeadaptationschemedynamicallytracksthechannelbehaviorandcalculatesthenewpacketsizeaccordingly,itisabletoachieveabetterenergyefciencythananyxedframe-sizingschemes. 6.5.2ResidualEnergyBalancingChannelAssignment Theotherresultofinterestisthenetworkresidualenergybalance.Wecomparethebalance-awarechannelassignmentdiscussedinSection 6.4 withtherandompairingschemeinwhichthematchbetweenthesensorsandthechannelsisinapurelyrandomfashion.WealsocomparetheproposedalgorithmwiththeGreedyalgorithmwhichalwayssearchesforthepairwiththemaximumRij.TheresultsshowninFigure 6-4 veriesthedesigngoalofresidualenergybalancingchannelassignmentinthatthedeathofsensorsisdistributedinanarrowtimeperiodcomparedwiththeotherchannelassignmentschemes.Thisisdesirablebecausethetotalunusedenergyisreducedwhenthenetworkdies. 98

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Figure6-4. Thecomparisonofnetworklifetimeamongdifferentchannelassignmentschemes Figure6-5. Theimpactofestimationaccuracyonaccumulativenetworkthroughput 99

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Table6-2. Theimpactofestimationaccuracyonothermetrics Numberofsamples EPB(mJ/bit) Transmitteddata(Mb) Real 0.433 12.25 20 0.469 9.90 40 0.448 11.25 60 0.441 11.71 80 0.439 11.89 100 0.436 11.95 6.5.3Impactsofestimationaccuracy Followingthediscussionoftransitionprobabilityestimationinthetwo-stateMarkovmodelinChapter 3 ,weareinterestedinevaluatingtheimpactofestimationaccuracyonthenetworkenergyefciency.Fig. 6-5 plotstheaccumulativenetworkthroughputacrossthewholesimulationdurationviaapplyingdifferentnumbersofsamples(n).Theaccumulativenetworkthroughputisdenedbythetotalnumberofsuccessfullydeliveredbitsdividedbytheelapsedsimulationtime.Theaccumulativethroughputcurveledbyapplyingtherealtransitionprobabilityservesasanupperboundforthepurposeofcomparison.Aswecanobserve,thenetworkthroughputincreasesasthenumberofsampleincreases,whichshowstherelationshipbetweenestimationaccuracyofthePUbehaviorandthenetworkenergyperformance.ThisrelationisillustratedinmoredetailsinTable 6-2 wheretheoverallnetworkEPBandsuccessfullydeliveredinformationbitsareshown. 6.6Summary Wehavedemonstratedtheuseofthepacketsizeadaptationschemeandtheresidualenergybalancingchannelassignmentapproachinacluster-basedmulti-channelCRSNwiththeconcernofenergyconstraints.ThepacketsizeadaptationisemployedtoexploitthecurrentinformationfrombothPUbehaviorandsensoractivitytominimizeenergy-per-bit,therebyimprovingtheenergyefciencyduringthelifetimeofsensors.TheresidualenergybalancingchannelassignmentreliesontheR-coefcienttobalancetheresidualenergyamongthenetworks,whichhelpstoprolongthenetwork 100

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lifetime.Additionally,wehaveevaluatedtheimpactofPUbehaviorestimationonthenetworkenergyefciency.Itisdemonstratedthattheperformancewiththeestimatedvaluesgetsclosertotheperformancewiththepriorknowntransitionprobabilitiesasthenumberofsamplesincreases. 101

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CHAPTER7CONCLUSIONS Cognitiveradiotechnologyimprovesspectrumutilizationbyallowingsecondaryusers(SUs)toaccessthelicensedspectrumbandsinanopportunisticmanneraslongasitdoesnotinterferewiththeactivityoftheprimaryusers(PUs).CRSNhasbeenproposedasapromisingapplicationinrecentstudieswhere.acognitiveradioisinstalledineachsensoranditcanbetunedtoanyavailablechannel.Inthisdissertation,thespectrumsensingandspectrumaccessproblemsareinvestigatedfortheCRSN.Duetotheinherentpowerandresourceconstraintsofsensornetworks,energyefciencyistheprimaryconcernforthenetworkdesign. Forspectrumsensing,MLestimationisusedfortheMarkovmodelofPUbehavior.ThePMFoftheMLestimatorisderivedtoevaluatetheaccuracyoftheestimatedtransitionprobabilities.Itsapproximatenormaldistributionisalsoderivedtoanalyzeitscondencelevel.WeshowthattherequiredlengthofthesamplesequencediffersgreatlyforthevariedPUbehavior.AlearningalgorithmwhichiterativelylearnstheMarkovmodelisproposedwithadaptivelengthofthesamplesequence.Numericalresultsshowthattheproposedestimationalgorithmachievestherequirementoftheestimationaccuracywhilereducingunnecessarysensingslots.Fortheimperfectsensingwithsensingerrors,atwo-stateHMMisemployedtomodelPUbehaviorwithimperfectsensing.Baum-Welchalgorithmisusedtoestimatethetransitionprobabilities.Theestimationaccuracyiscomparedwiththatofperfectsensing. Weinvestigatethedynamicspectrumaccessprobleminacluster-basedmulti-channelCRSN.ThetotalresidualenergybasedontheR-coefcientismaximizedtoreduceenergyconsumptionandprolongthenetworklifetime. Anotherimportantconcernisthetotalenergyconsumptionneededtosuccessfullytransmitacertainamountofinformationbits.Weemploythepacketsizeadaptationto 102

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exploitthecurrentinformationfrombothPUbehaviorandsensoractivitytominimizeEPB,therebyimprovingtheenergyefciencyduringthelifetimeofsensors. Inordertofurtherextendthiswork,thefollowingproblemscanbestudied: 1.Intheprimaryuserbehaviorestimationwork,moreterminationconditionsandinitialprobabilityestimationmethodscanbeexploredtofurtherimproveitsaccuracy.Anotherinterestingdirectioncanbetheenhancementofimperfectionsensing:sincetheBaum-Welchalgorithmislocallyoptimized,theinitialvalueisveryimportant,somorestudiescanbedonetoimprovetheaccuracyofitsestimation.Itwillalsobegreatifwecanndagloballyoptimizedalgorithmtoavoidthisproblem. 2.WeestimatethetransitionprobabilitiesofPUbehaviorwithoutknowingthefalsealarmandmissdetectionprobabilities.Ifthefalsealarmandmissdetectionprobabilitiesareknowninprior,adifferentmodelmaybeneededfortheestimation.TheestimationaccuracycanbeanalyzedtocomparewiththecurrentHMMmodel. 2.Inthedynamicspectrumaccesswork,weonlydiscussintra-clusterchannelassignment,sothiscanbeextendedtoincludeinterclusterperformance.Also,thethroughputimpactcanbestudiedusingmoresophisticatedmathematicsmodels. 103

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BIOGRAPHICALSKETCH XiaoyuanLireceivedherbachelor'sdegreeinCommunicationsEngineeringfromtheSchoolofCommunicationandInformationEngineering,inUniversityofElectronicScienceandTechnologyofChina,Chengdu,Sichuan,China,in2007.ShereceivedherMaster'sdegreeandPhDdegreeinDepartmentofElectricalandComputerEngineering,inUniversityofFlorida,Gainesville,Florida,USA,in2009and2013,respectively. 111