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Environment, channel, and interference awareness for next generation wireless networks

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Title:
Environment, channel, and interference awareness for next generation wireless networks
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English
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Yarkan, Serhan
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University of South Florida
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Subjects / Keywords:
Cellular networks
Cognitive radio
Line-of-sight identification
Vertical handoff
Dissertations, Academic -- Electrical Engineering -- Doctoral -- USF   ( lcsh )
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non-fiction   ( marcgt )

Notes

Abstract:
ABSTRACT: Wireless communication systems have evolved substantially over the last two decades. The explosive growth of the wireless communications market is expected to continue in the future, as the demand for all types of wireless services is increasing. Beside providing higher data rates, next generation wireless networks (NGWN) are expected to have advanced capabilities such as interoperability, efficient spectrum utilization along with a wide variety of applications over different domains (e.g., public safety and military, aeronautical networks, femtocells, and so on) to the mobile users while serving as many users as possible. However, these advanced capabilities and services must be achieved under the constraint of limited available resources such as electromagnetic spectrum and power. In addition, NGWNs (and nodes within) need to modify themselves under rapidly changing conditions such as wireless propagation channel characteristics, traffic load, and so on. Moreover, NGWNs are expected to optimize their parameters by evaluating their experiences in the past. All of these characteristics imply that NGWNs should be equipped with cognitive capabilities including sensing, awareness, adaptation and responding to changing conditions along with learning about the past experiences. In this dissertation, environment, channel, and interference awareness are investigated in detail for NGWN. Methods for being aware of environment, channel, and interference are provided along with some possible ways of adapting several design parameters of NGWNs. In addition, cross-layer optimization issues are addressed from the perspective of both recently emerging technology called cognitive radio (CR) and NGWN.
Thesis:
Dissertation (Ph.D.)--University of South Florida, 2009.
Bibliography:
Includes bibliographical references.
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Statement of Responsibility:
by Serhan Yarkan.
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Title from PDF of title page.
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Document formatted into pages; contains 146 pages.
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Includes vita.

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ABSTRACT: Wireless communication systems have evolved substantially over the last two decades. The explosive growth of the wireless communications market is expected to continue in the future, as the demand for all types of wireless services is increasing. Beside providing higher data rates, next generation wireless networks (NGWN) are expected to have advanced capabilities such as interoperability, efficient spectrum utilization along with a wide variety of applications over different domains (e.g., public safety and military, aeronautical networks, femtocells, and so on) to the mobile users while serving as many users as possible. However, these advanced capabilities and services must be achieved under the constraint of limited available resources such as electromagnetic spectrum and power. In addition, NGWNs (and nodes within) need to modify themselves under rapidly changing conditions such as wireless propagation channel characteristics, traffic load, and so on. Moreover, NGWNs are expected to optimize their parameters by evaluating their experiences in the past. All of these characteristics imply that NGWNs should be equipped with cognitive capabilities including sensing, awareness, adaptation and responding to changing conditions along with learning about the past experiences. In this dissertation, environment, channel, and interference awareness are investigated in detail for NGWN. Methods for being aware of environment, channel, and interference are provided along with some possible ways of adapting several design parameters of NGWNs. In addition, cross-layer optimization issues are addressed from the perspective of both recently emerging technology called cognitive radio (CR) and NGWN.
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Vertical handoff
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IwouldliketoextendmyspecialthankstoDr.KoonHooTeoatMitsubishiElectricResearchLaboratories(MERL)whosupportedmyresearchnanciallyforthemajorityofmyPh.D.duration.Also,IwouldliketothankDr.AmineMaarefforhisprecioushelpandtimeduringmytimeatMERLandthereafter.IamalsogratefultomycolleaguesatUSFandtoallmyfriendsatWirelessCommunicationsandSignalProcessing(WCSP)groupwhoseeachandeverymembercontributedalottometechnically.However,Iwouldliketorecognizeinaspecialway,Dr.HasariCelebi,AliGorcin,Dr._IsmailGuvenc,Dr.HishamAbdelazizMahmoud,MustafaEminSahin,andDr.TevkYucekwho,duringmostofmytimeatUSF,helpedmeineveryaspect. SpecialthanksgotoTurkishcommunityinTampa.IwouldliketomentionSalihErdem,SalimErdem,AkifUzuner,SenerGultekin,_IsmailButun,AliEmreErcelebi,AliRzaEkti,OzgurYururfortheircontinuoussupport.AlthoughnotresidinginTampa,IwouldliketoextendmythanksalsotoDr.HalimZaimwhoprovidedmewithhissupportandtoDr.CelalCekenwithwhomIhadopportunitytomeetandsharemanygreatthingsinashortperiodoftime. Lastbutbynomeansleast,Iwouldliketoexpressmydeepestgratitudetomyfamilytowhomthisworkisdedicated.Iwillbeforeverindebtedtomyparents,mygrandparents,andmysister.Withouttheirimmensesacrice,theirunconditionalsupport,andtheirprofoundwisdomIwouldnotbeheretoday:::

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LISTOFFIGURESv LISTOFACRONYMSviii ABSTRACTxii CHAPTER1INTRODUCTION1 1.1DissertationOutline3 1.1.1Chapter2:EnvironmentAwarenessTowardImprovedWire-lessSystemDesignforNGWN5 1.1.2Chapter3:ChannelAwarenessforNextGenerationWire-lessNetworks5 1.1.3Chapter4:IdenticationofLOSinTime{Varying,Fre-quencySelectiveRadioChannels6 1.1.4Chapter5:RealTimeMeasurementsforAdaptiveandCRSystems6 1.1.5Chapter6:IdenticationofShadowedFastFadingInterfer-enceinCellularMobileRadioSystems6 1.1.6Chapter7:UpperandLowerBoundsonSubcarrierColli-sionforInter{cellInterferenceSchedulerinOFDMA{BasedSystems:VoiceTrac6 1.1.7Chapter8:InterferenceAwareVerticalHandoDecisionAlgorithmforQualityofServiceSupportinWirelessHet-erogeneousNetworks7 1.1.8OtherWorksDone8 CHAPTER2ENVIRONMENTAWARENESSTOWARDIMPROVEDWIRELESSSYS-TEMDESIGN9 2.1Introduction9 2.2WirelessChannelParameters11 2.3ClassicationofPropagationEnvironments14 2.4KnowledgeSpace,EnvironmentalCharacterization,andAdaptation15 2.5CognitiveRadioNetworksandLocationAwareness21 2.6Conclusion23 CHAPTER3CHANNELAWARENESSFORNEXTGENERATIONWIRELESSNET-WORKS25 3.1Introduction25 3.2ChannelParameters27 3.2.1ChannelSelectivityMeasurement28 3.2.2ChannelQuality(linkquality)Measurement34 3.3OtherParameters38i

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CHAPTER4IDENTIFICATIONOFLOSINTIME{VARYING,FREQUENCYSELEC-TIVERADIOCHANNELS45 4.1Introduction45 4.2TheProposedApproach48 4.2.1TheChannelModel48 4.2.2BoundforKParameter50 4.2.3LOSIdentication57 4.3NumericalResults58 4.4ConcludingRemarks67 CHAPTER5PARAMETERSAFFECTINGINTERFERENCEINNEXTGENERATIONWIRELESSNETWORKS68 5.1Introduction68 5.2ParametersAectingInterference69 CHAPTER6IDENTIFICATIONOFSHADOWEDFASTFADINGINTERFERENCEINCELLULARMOBILERADIOSYSTEMS74 6.1Introduction74 6.2StatementoftheProblemandSignalModel74 6.2.1StatementoftheProblem74 6.2.2SignalModelfor()75 6.3Analyses76 6.3.1Noise{only(Interference{free)Case76 6.3.2Interference{onlyCase77 6.3.3Interference{NoiseCoexistence78 6.4ProposedMethod78 6.5NumericalResults79 6.6ConcludingRemarks81 CHAPTER7PERFORMANCEBOUNDSFORSCHEDULERSINOFDMA{BASEDSYS-TEMS:VOICETRAFFIC83 7.1Introduction83 7.2SystemModelandBasicAssumptions85 7.3UpperandLowerBoundofExpectedNumberofCollisions88 7.4MESandItsPerformance93 7.4.1MESandItsPerformanceinthePresenceofPerfectKnowledge93 7.4.2PerformanceofMESinthePresenceofImperfectKnowl-edge[GeneralizedCase]94 7.5ImpactsofSchedulingPeriodandGeneralizedBound95 7.5.1CompressionEect95 7.5.2SaturationEect96 7.6NumericalResults98 7.7ConcludingRemarks100 CHAPTER8INTERFERENCEAWAREVERTICALHANDOFFFORNGWNS104 8.1Introduction104 8.2RelatedWorks107 8.3TheProposedModelsandAlgorithmsforVerticalHando108 8.3.1SmartTerminalProcessModel108 8.3.2ProposedHandoDecisionAlgorithm111ii

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8.4NumericalResultsandDiscussions116 8.4.1Assumptions116 8.4.2SimulationsandPerformanceAnalysis120 8.5Conclusions125 CHAPTER9CONCLUSIONANDFUTUREWORK127 9.1ListofSpecicContributions127 9.2ConcludingRemarksandFutureDirections128 REFERENCES130 APPENDICES141 AppendixA142 AppendixB144 AppendixC146 ABOUTTHEAUTHOREndPageiii

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Table2.2Somecrucialwirelesstransmissionparameters,theireects,andre-latedadaptationoptions14 Table2.3Frequentlyusedenvironmentalclassicationsforwirelesspropagationwithsomerelatedparameters17 Table3.1DimensionsFofchannelselectivityandtheirimportancewithsampleapplications29 Table4.1Generalparametersetforthesimulations59 Table7.1Symbollist103iv

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Figure1.2Theconceptualrelationshipsbetweentheelementsalongwiththerelevantnotionsstudiedinthisdissertation.4 Figure2.1ConceptualmodelofCRinconnectionwiththetraditionalprotocolstackandalocationsensor.10 Figure2.2TheowoftheenvironmentalclassicationalgorithmforCR.16 Figure3.1Illustrationofsomeoftheeectsofradiochannel.27 Figure3.2AconceptualmodelofCRincludingexternalsensingcapabilitiestoimproveestimationsandtoattainglobaladaptationalongwithob-servableandadjustableparametersacrosstheprotocolstack.35 Figure4.1Illustrationoftheconceptof\underlyingprocess"anditsrelationshipwithCIR.52 Figure4.2DierentDopplerspectrathatareencounteredindierentenviron-mentsfor900MHzcarrierfrequencyandamobilespeedof22m/s.59 Figure4.3Squared{envelopeoftheautocorrelationsofrstandsecondtapforcommonparametersK0=10,v=20m/s,andthesetofAoAf(0)0g.60 Figure4.4Squared{envelopeoftheautocorrelationsoftherstandsecondtapforcommonparameters(0)0==5,K0=10,andthesetoffvg.61 Figure4.5Squared{envelopeoftheautocorrelationsoftherstandsecondtapforcommonparameters(0)0==5,v=20m/s,andthesetoffK0g.62 Figure4.6Theprobabilityofjhs(t1)j2
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Figure4.11ProbabilityofdetectionversusvforSNR=10dB,NSLOT=500,andK0=10.66 Figure4.12ProbabilityofdetectionversusSNRforNSLOT=500,K0=10,andv=20m=s.66 Figure6.1Anillustrationofpointsandnotionsusedintheproposedmethod.79 Figure6.2Thechangeofmwithrespectto2=2N.81 Figure6.3PDresultswithrespectto2=2N.82 Figure7.1Twotypicaltwo{celllayoutsinwhichcellsareassumedtooperateunderFROregimealongwiththe\interior/celledge"distinction.86 Figure7.2AnexamplePMFforF=1000,F1=F2=Fz=100.91 Figure7.3IllustrationofhowMESorganizesitsresourcesofastackformandhowitperformsunderincomingarrivals.94 Figure7.4AnexampleplotofbothupperandlowerboundsforF=1000,F1=F2=100,andaxedtracloadinC2withr2=0:5.99 Figure7.5PerformanceofMESfors=1delineatedbythecorrespondingupperandlowerbounds.100 Figure7.6PerformanceofMESunderdierentknowledgeacquisitionscenariosfors2[0;1],F=1000,F1=F2=100,andaxedtracloadinC2withr2=0:5.101 Figure7.7PerformanceofMESunderthreedierentschedulingperiodswhichareobtainedbyn=2;4;8fors=0:4,F=1000,F1=F2=100,andaxedtracloadr2=0:2.102 Figure8.1TheSMTcross{layerprocessmodel.109 Figure8.2Sequencediagramoftheproposedhandodecisionalgorithm.110 Figure8.3Blockdiagramoftheproposedfuzzylogic-basedhandosystem.111 Figure8.4Fuzzymembershipfunctionfortwodierentdatarates(DR).112 Figure8.5Fuzzymembershipfunctionfortwodierentinterferencerates(IR).113 Figure8.6FuzzymembershipfunctionsfortwodierentRSSIs(RS).114 Figure8.7Examplefuzzyrules.114 Figure8.8ProposedprocessmodelforAPs.116 Figure8.9Verticalhandoexamplewithhigherinterferencerate(referredasScenario1).117vi

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Figure8.11APCVoutputoftheproposedhandodecisionalgorithmforvoicetransferapplicationinScenario1.121 Figure8.12NumberofhandosversusHRforScenario1.122 Figure8.13APCVoutputoftheproposedhandodecisionalgorithmforvoicetransferapplicationinScenario2.123 Figure8.14NumberofhandosversusHRforScenario2.123 Figure8.15RSSI{basedperformanceevaluationchart.124 Figure8.16EEDresults(SMT1-APs)fordierentapplicationtracs.126vii

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However,theseadvancedcapabilitiesandservicesmustbeachievedundertheconstraintoflimitedavailableresourcessuchaselectromagneticspectrumandpower.Inaddition,NGWNs(andnodeswithin)needtomodifythemselvesunderrapidlychangingconditionssuchaswirelesspropagationchannelcharacteristics,tracload,andsoon.Moreover,NGWNsareexpectedtooptimizetheirparametersbyevaluatingtheirexperiencesinthepast.AllofthesecharacteristicsimplythatNGWNsshouldbeequippedwithcognitivecapabilitiesincludingsensing,awareness,adaptationandrespondingtochangingconditionsalongwithlearningaboutthepastexperiences. Inthisdissertation,environment,channel,andinterferenceawarenessareinvestigatedindetailforNGWN.Methodsforbeingawareofenvironment,channel,andinterferenceareprovidedalongwithsomepossiblewaysofadaptingseveraldesignparametersofNGWNs.Inaddition,cross{layeroptimizationissuesareaddressedfromtheperspectiveofbothrecentlyemergingtechnologycalledcognitiveradio(CR)andNGWN.xii

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However,theseadvancedcapabilitiesandservicesmustbeachievedundertheconstraintoflimitedavailableresourcessuchaselectromagneticspectrumandpower.Inaddition,NGWNsneedtomodifythemselvesunderrapidlychangingconditionssuchaswirelesspropagationenvironmentcharacteristics,tracload,andsoon.Moreover,NGWNsareexpectedtooptimizetheirparametersbyevaluatingtheirexperiencesinthepast.AllofthesecharacteristicsimplythatNGWNsshouldbeequippedwithcognitivecapabilitiesincludingsensing,awareness,adaptationandrespondingtochangingconditionsalongwithlearningaboutthepastexperiences.Itisimportanttostatethatarecentlyemergingtechnologycalledcognitiveradio(CR)isconsideredtopossessthesameadvancedcapabilitiespointingoutaconvergenceofcapabilitiesforfuturewirelesscommunicationssystems.Suchaconvergenceisnotacoincidence,becausetheevolutionofwirelesscommunicationshasalwaysbeentowardasystemthatpossessescomprehensiveadaptationandoptimizationcapabilities.Hence,awirelesscommunicationssystemequippedwithadvancedcognitivecapabilitiescanbeconsideredtobethecommonpurposeofallfuturesystemdesigns.Figure1.1illustratesthisconvergencealongwithdesiredobjectivesandsomesampleapplications. Amongtheaforementionedcapabilities,awarenesshasaspecialplacebecauseitinterpretsthedata/informationfedbysensingandconvertsintoknowledgeforadaptationandforpossiblelearningpurposes.Inotherwords,awarenessestablishesthelinkbetweenobservablequantitiesandavailable1

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Whenawirelesssignalistransmitted,itisalteredbythewirelesschannelandreachesatreceiverafterbeingexposedtoseveralotherimpairmentssuchasnoiseandinterference.Theimpactofwirelesschannelonthesignaltransmitteddependsonseveralcharacteristicsofphysicalpropagationenvironmentsuchasitstopographicalstructure,havingline{of{sight(LOS),andsoon.Notethatenvironment,channel,andotherambientimpairmentssuchasinterferenceandnoiseareconceptswhichcannotbedirectlycontrolledbyradiossinceallofthemresidebetweenthetransmitterandreceiverPHYlayers.Therefore,inNGWNs,beingawareoftheoperatingenvironment,ofwireless2

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Inthisdissertation,environment,channel,andinterferenceawarenessareinvestigatedindetailforNGWN.Methodsforbeingawareofenvironment,channel,andinterferenceareprovidedalongwithsomepossiblewaysofadaptingseveraldesignparametersofNGWNs.SincethereisanobviousconvergenceinthecharacteristicsofNGWNandofrecentlyemergingtechnologyCRintermsofawareness,CRperspectiveisalsoinvestigatedindetail.1.1DissertationOutline TheconceptualrelationshipbetweentheseelementsaregiveninFigure1.2.Itisworthmention-ingthateventhoughthephysicalimpactofbothwirelesschannelandinterferencetakesplaceinthepropagationenvironment,eachindividualelementhasitsownuniqueconceptualcharacteristicsandproperties.Manyofthepropagationcharacteristicsofwirelesschannelaredeterminedbythephysicalenvironment.However,forthesamephysicalpropagationenvironment,wirelesschanneltreatssignalsdierentlydependingonthetransmittedwaveforms.Forinstance,multipathchar-acteristicsofaphysicalpropagationenvironmentforultra{wideband(UWB)systemsdierfromthosefornarrow{bandsystemsbecauseofthedierenceintimeresolutionsoftransmittedwave-forms.Thesameargumentholdsforinterferingsignalsaswellsincedierentinterferingwaveformsyielddierenteects.Forinstance,aninterferingsignalofadierenttypefromthatofthedesiredsignalcanbeinterpretedeitheraswide{bandinterference(WBI)orasnarrow{bandinterference3

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Consideringthefactthatwirelesscommunicationstakesplaceinphysicalpropagationenvi-ronment,rsttheenvironmentawarenessisinvestigatedinChapter2.Therelationshipbetweenwirelesschannelparametersandphysicalenvironmentsalongwithvastlyusedpropagationenviron-mentclassesinwirelesscommunityarediscussed.Severalwaysofbeingawareofenvironmentandoftheirpossibleusearealsoprovided.AconceptualmodelbothforNGWNsandforCRisgivenalongwithanenvironment/locationawarenessalgorithminwhichenvironmentalclassesintroducedwithinthesamechapterareexploited. Second,channelawarenessisinvestigatedindetailinChapter3,sincethetransmitter{receiverpairisconnectedtoeachotherviathewirelesschannel.Criticalwirelesschannelparametersareidentiedandlistedindetailalongwithseveralmeasurementmethods.Inaddition,anewmethodonidentifyingandbeingawareofoneofthecriticalwirelesschannelparameters,namelyLOS,isgiveninChapter4. Receivedsignalaccommodatestheimpactnotonlyofthewirelesschannel,butalsoofotherdisturbancessuchasinterferenceandnoisepresentinthepropagationenvironment.Therefore,subsequently,interferenceawarenessisinvestigatedanditsuseisexemplied.InChapter5thefun-4

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Intheremainderofthischapter,amoredetailedoutlineofthefollowingchaptersinthisdisser-tationareintroduced.1.1.1Chapter2:EnvironmentAwarenessTowardImprovedWirelessSystemDesignforNGWN

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IntheframeofenvironmentalclassicationdiscussedinChapter2.3,radiopropagationchar-acteristicsinextremeenvironmentssuchasundergroundminesareinvestigatedin[14{17].AsmentionedinChapter3,timeselectivitycausedbymotioninthepropagationenvironmentmustbeunderstoodverywellintermsofchannelawarenessforNGWN.Anexperimentalstudyrelatedtocharacterizingtheimpactofmotioninwirelesschannelsisestablishedaswell[18].Similarly,electromagneticspectrumaspectofwirelesschannelisstudiedfromtheperspectiveofopportunisticspectrumusageconceptwhichisbelievedtobeoneofthekeyconceptsinNGWNs[19].Inthelightofinterferenceawarenessconcept,reportingperiodforinterferencestatusisalsoexaminedinordertooptimizetheover{the{airsignalinginNGWNs[20].8

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Inspiteofthisvastvarietyofwirelessandotherapplicationsembeddedinasingledevice,itisstrikingthatthefunctions,whichhavetheabilitytoprovideextremelyimportantinformationtoeachother,operateindependently.Thislackofcooperationstemsfromthefactthatthereisnounitwhichcancontrol,coordinate,andinterpretthedataobtainedfromdierentfunctions.However,withtheemergenceofcognitiveradio(CR),thislackofcooperationcanberemoved. Asanemergingtechnology,CRreceivessignicantattentionfrombothacademiaandindustry.Nevertheless,thereisnoformaldenitionofCRonwhicheverybodyagrees.However,distinctfeaturesofCR,whicharesensing,beingawareof,learning,andadaptingtoitssurroundingenvi-ronment[21],allowustodescribeitcoarsely.Builtonsoftware{denedradio(SDR),CRisabletoemploythesefeaturesinitsadaptationcyclewiththeaidofseveralsensors(e.g.GPS,light,andtemperaturesensors)andtoolsusedinarticialintelligence(AI)applications(e.g.neuralnetworks,hiddenMarkovmodels(HMM),geneticalgorithms).Naturally,theadaptationcyclerequiresacom-9

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Eachformofthesmall{scaleeectsintroducesadierentaspectofthewirelesschannel.Delayspreadisusedtodescribethetimedispersionofthechannel.Inconnectionwithcoherenceband-width,itisrelatedtothefrequencyselectivityofthechannel.Typicalvaluesofdelayspreadof

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Dopplerspreadisthemeasureofthebroadeningofthesignalinfrequencydomainduetotemporalvariationofthechannel.ThetemporalvariationofthechannelisquantiedbycoherencetimeanditisinverselyproportionaltotheDopplerspread.Thus,thelargertheDopplerspread,thenarrowerthecoherencetimeinterval,andthefasterthechannelchanges.Itisalsoknownthattheslowerthemobile,thenarrowertheDopplerspectrum.Therefore,itiseasilydeducedthatfortheenvironmentsinwhichthemobilityislimited(e.g.insidethebuildings),theDopplerspectrumismorelikelytobenarrow.Conversely,fortheenvironmentsinwhichthemobilityisnotlimited(e.g.ruralareas),itisexpectedthattheDopplerspectrumiswide. Forangularspread,theeectofmultipathsisexaminedfromtheperspectiveoftheiranglesofarrival.Theamountofspreadingisdirectlyrelatedtotheamountofscatteringintheenvironment.Thericherthescatteringenvironmentis,themorethespreadisexperiencedintheangledomain.Besides,thelargertheangularspreadis,thelowerthecorrelationbecomesbetweenantennael-ements.Forindoorcommunications,onemightanticipatethattheangularspreadislargerthanthatforoutdoorbecauseofthepresenceofnumerousscatterers.Withthesamereasoning,itispossibletonddierentangularspreadbehaviorswithindierentscenariosamongoutdoorradioenvironmentsub{classes.Forinstance,inanenvironmentwhichisidentiedasopenruralarea,theangularspreadisexpectedtobenarrowerthanthatinanareawhichisidentiedasurban. Theimpactofenvironmentalcharacteristicsonsmall{scaleparametersdiscussedupuntilthispointispresentedinTable2.1. Apartfromsmall{scaleparameters;therearesomecrucialparametersforfurtherdescriptionofthewirelesschannel.Inalmosteverywirelessradiotechnologystandard,therelevantchannelmodelsareclassiedbasedonaveryimportantdistinction:beinginline{of{sight(LOS)ornon{line{of{sight(NLOS).Itisknownthatforeverykindofradiotransmission,LOSchannelsdierfromNLOSchannelsbecauseofthepresenceofthedirectpath.Thisfactalongwithseveralother12

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Description Illustration Delayspreadcharacteristicsdependonphysicalenvironment.Somestandardsclassifytheenvironmentsandassignex-plicitstatisticalpowerdelayprole(PDP)foreachofthem.Inthegurenextcell,thefourmajorcategoriesofPDPsfortyp-icalurban,badurban,ruralarea,andhillyterraininEuropeanCo{operationintheeldofScienticandTechnicalre-search(COST)231(andeveninCOST259)isshown[24].Ineachcategory,thecorrespondingPDPhassomedistinctfeaturessuchasnumberofclustersandarrivaltimesbesideacommonproperty,whichisexponentiallydecayingpower. Dopplerspread Dopplerspreadcharacteristicsdierfromeachotherfordierentpropagationen-vironments.AccordingtoInternationalTelecommunicationUnion{Radiocom-munications(ITU{R)model,foroutdoor,classicalJakes'typeDopplerspectrumisrecommended,whereasforindoor,atDopplerspectrumisrecommended[25]. Angularspread Dependingontherichnessofthescatter-ersinanenvironment,anglesofarrivalofmultipathcomponentsvary[22]. eectssometimesrequiresaspecialdesignstructureinwirelesscommunicationsystemssuchasin10{66GHzportionofthephysicallayerpartofIEEE802:16. Noisealsomustbetakenintoaccountinrealisticwirelesschannelmodels,sinceitsimpactonthecommunicationsystemsisobvious[26].Generally,becauseofitsmathematicaltractability,noiseisassumedwhiteandchosenasGaussiandistributed,whichhasaatpowerspectrum.However,ithasbeenreportedthatoces,factories,andhospitalshaveimpulsivenoiseratherthanwhiteandGaussiandistributed[27]aswellassomeoutdoorenvironments,duetoman{madenoisesources.13

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Eect Howtouse RSS Linkadaptationviaadaptivecoding/modulation Hando(handover) Channelallocation Interferencemanagement Simpledistant{basedpowercontrolalgorithm DelaySpread Frequencyselectivity Numberofequalizertapsforsinglecarriersystems Numberofpilotsandspacingformulticarriersys-tems fastFouriertransform(FFT)sizeformulticarriersystems Carrierspacingformulticarriersystems Adaptivelteringforchannelestimation Cyclicprexlengthformulticarriersystems Dopplerspread Timeselectivity Channeltrackerstepsize Interleavingschemes Handomanagement Frequencyallocation Angularspread Spatialselectivity Beamforming Smartantenna Adaptivemulti{inputmulti{output(MIMO) Interferencemanagement Frequencyallocation LOS/NLOS Overallchannelbehavior Transmissionfrequency Poweradjustment Noise Capacity Transmissionfrequency Linkadaptation(Adaptivecoding/modulation) Furthermore,itisshownthatmaximalratiocombining,equalgaincombining,andselectiondiversityarenoteectiveinimpulsivenoiseenvironments[28].Hence,beingawareofthetypeofthenoiseisofcrucialimportanceinadjustingsomeofthesystemparameterssuchascodingrequirements[27]. Aforementionedpropagationrelatedparameters,theireects,andadaptationoptions(incaseofhavingaprioriknowledgeaboutthem)aretabulatedinTable2.2.2.3ClassicationofPropagationEnvironments

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Consideringthefactthat(I)isfasterandcanprovidesolutionsforgeneralscenarioscomparedto(II),(I)ismoreappropriateforCRatthisstage.However,employing(I)requiresaCRtohavethetopographicalinformationaboutthegeographicalarea.Someofthebasictopographicaldatabasessuchasdigitalelevationmodels(DEM)(i.e.digitalrepresentationsoftopographicsurfaces,whichareusedfordeterminingpropertiesofterrainintermsofelevationatanypoint,slope,aspectandex-tractingfeaturesofit,suchaspeaksandpitsandotherlandforms)havealreadybeenusedinwirelesscommunicationsforsimilarpurposessuchascheckingwhetherLOSexistsbetweenatransmitter{receiverpair[23].DEMsareeasytobeprocesseddigitaldatawhichcangivesomehintstoaCRabouttheattributesofthesurroundingenvironmentviaspatialinterpolationmethods(SIM).Also,aGeographicalInformationSystem(GIS)providescomprehensivetopographicalinformationwhichcanbequeriedbyGPS.Thus,whenthecognitiveengineisprovidedwithasortoftopographicalinformationsuchasDEMorGIS,itcanrecognizethepatternoftheaerialinformation,locatetheappropriateclass,andmatchthemostappropriatestatisticsoutofitsmemory.InFigure2.2,theowoftheenvironmentalclassicationalgorithmisshown.2.4KnowledgeSpace,EnvironmentalCharacterization,andAdaptation InChapter2.2,ithasbeenexplainedthatradiopropagationbehavesdierentlyineachtypeofenvironment.Establishingauniversalmodel,whichworksineverykindofenvironment,isextremelydicultbecauseofthenatureofradiopropagation.AsintroducedinChapter2.3,astochasticapproachsimpliesthemodelingprocesswiththeaidofsometoolssuchasdelaypowerspectra,amplitudedistribution,andcorrelationfunction.Itisalsoknownthatthesetoolscanbedescribed15

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Inadditiontorepresentingthedatainahierarchicalway,CRalsogetsinformationfromvarioussources(asshowninFigure2.1)suchassensors,protocollayers,externaldevices,andevenitsownhardware.Eventhoughthepiecesofinformationobtainedarecomingfromindependentsources,someofthemcanberelated.ConsiderthecaseinwhichCRhaslightandtemperaturesensoralongwithGPS.Ifacontextualconnectioncanbeestablishedbetweenthebitsofinformationprovided16

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Subcl.I Subcl.II Characteristics OUTDOOR 0:5{2s High High 0:3{2s High 0:3{2s High 0:08-0:14s High 0:08-0:14s High 2:8{5:2s High 0:26{1:25s High 0:11{0:2s High High 10{100ns Low 10{100ns Low 30{60ns Low 100{200ns Low 100{200ns Low Upto300ns Low 17

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InorderforaCRtorepresentthedatainahierarchicalandcontextualform,the\KRS"concepthasbeenputforward[21].AKRSrepresentstheuniverseofaCRandconsistsofnumeroussubspacessuchasspace,time,user,theradioitself,spectrum,network,andtheirsubspacessuchasenvironment,airinterfaces,protocollayers,andsoon.ItisverydiculttodocumentallpossiblesubspacesintheuniverseofCR.Althoughthislooksdiscouraging,fortunately,aKRScanbeexpandedwhenitisnecessary.Withthesamereasoning,{eventhoughitisnotfavorablesincearadio,whichisabletointerpretasmanythingsaspossible,isdesired{whenitisneeded(forinstance,duetoinsucientmemory,thenecessityofdeletionofsomesubspacessuchasoldstandardswhichhaveneverbeenused),itcanbeshrunkaswell.Asamatteroffact,thisexibilityisarequirement,sinceaCRisconsideredtohaveadynamiclibrarythatcanbeupdatedeasilywhenenvironments,policies,needs,etc.change. SolelytheconstructionofKRSwillnotbeenoughforaCRtoexploitlocationawareness.BesideKRS,atoolforprocessingKRSmustbepresentaswell.RKRLhasbeenproposedllingthegapinprocessingKRS[21].Therefore,RKRLcanbedenedas\aformalstructurethathelpsCRtoprocessthehierarchicalandcontextualconstruction,whichisKRS." RKRLconsistsofstatementsandeachstatementformsaspecialstructurecalled\frame."Framesexpresstherelationshipbetweentheircontentsinaparticularcontext.TheontologicalstructureoftheuniverseofaCR,thehardwareinaCR,andtheenvironmentinwhichaCRoperatesareonlyafewexamplesthatcanbedenedanddescribedbytheframestructure.Forinstance,theontologicalstructureoftheuniverseofaCRmightbeoftheform:18

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wherehidenotesacontextualsetthatmightcontainseveralsubsets;representsthesetofevery-thing;Idenotesoneofthesubsetsofitssuperset. Followingthesamepatternin(2.1),CRcanrepresentthe\space"indetailas: ...IhSpaceiIfhPositioni;hTemperaturei;:::g: ...IhRadioiIhSensorsiIfhGPSi;hHeati;hLighti;:::g: Notethat,thishierarchicalrepresentationquantieswhataCRcanbeaware.Forexample,aCR,whichsolelyhasGPS,willshrinkitshSensorsisubsetanddeneitbyonlyfhGPSig. Oncethehierarchicalstructureisformed,attachingthecorrespondingcontextstothesourcescanbeinvestigated.Forexample,thecontextofasensor,sayGPS,canbedenedinthefollowing19

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Ascanbeseen,CRisabletorecognizeeachpieceofinformationfedbyeachsensorwiththeaidofthecontext.Furthermore,CRcanevenndtheconnectionwithotherhSpaceiand/orhTimeirelatedentitiesinitsuniversebyjustlookingatthecontextofthesensorofinterest.Forinstance,thedomainsofbothhGPSiandhHeati(i.e.thelefthandsideof7!)containhSpaceiandhTimeitogether.Therefore,itisdeducedthathGPSiandhHeatiproducerelatedinformation.Notethatoncethecontextsandrulesareestablished,asinProlog,{whichisalogicprogramminglanguage,{inRKRL,thereasoningdependssolelyonqueryingtherelationship.Thus,withtheaidofRKRL,CRcanndeverycontextthatisrelatedtoanotheroneinitsKRS. InChapter2.3,ithasbeendiscussedthatenvironmentalclassicationcarriesacrucialimpor-tanceforCR.HavingaclassicationsuchasinTable2.3inhand,representingtheclassicationisstraightforwardbyfollowingthepatternin(2.1).Asanexample,CRcanexpress\openruralarea,"whichwillbeasubsetofhEnvironmenti,asfollows: ...IhOUTDOORiIhRuraliIhOpeni:

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...IhRuraliIhPathLossModeliIhHata0sModeli; Asanalstep,aftermatchingoperation,itissucientforCRonlytoreadthevaluesfromstatisticalmodel\frame"andapplythemtorelevanttransmissionparametersaccordingly.SomeoftheoptionsthatCRcanadaptafteradjustingitsparametersinconnectionwiththepropagationcharacteristicsoftheenvironmentarepresentedinTable2.2.2.5CognitiveRadioNetworksandLocationAwareness

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Becausesomeoftheadaptationoptionsmentionedherehavealreadybeenusedbythecon-temporarywirelesscommunicationsystems,itisappropriatetodiscussthedierencesbetweenCRandcontemporarywirelesscommunicationsystems.Inordertostressthedierences,howcon-temporarywirelesscommunicationsystemsquantifyimportantpropagationcharacteristicscanbereviewed.Incontemporarywirelesscommunicationsystems,path{lossismeasuredfromthesamplesofreceivedsignalstrength(RSS).BasedontheRSSmeasuredandathresholdvalue,thelinkqual-ityisevaluatedandadaptationisestablished.Inordertoestimatethedelayspread,contemporarycommunicationsystemsemploychannelfrequencycorrelationestimatesaswellaslevelcrossingrate22

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Eventhoughcurrentwirelesscommunicationsystemsareabletomeasurethemajorpropagationparametersanduseitforadaptation,theydonothaveanyotheroptionexceptforthereceivedsignal,whichcanbecalledas\internalsensing."However,CRsystemsarenotlimitedtointernalsensing,since,{asdiscussedinChapter2,{therearenewsensingcapabilitiesemerging.Therefore,CRsystemsarecapableoftakingadvantageoftheserecentlyemergingsensingopportunitiestobetterestimatethepropagationparameterswiththeaidofcognitiveengine,whichleadstoimprovementinoverallsystemperformance.Besides,theserecentlyemergingsensingopportunitiescanprovideCRswithnovelawarenessandadaptationoptionsthatcannotbeachievedbyinternalsensing.Forinstance,beingawareoftheuserisoneoftheprominentawarenessandadaptationoptions,whichincludestheuser'sidentity,perception,andpreferencesaswellasthecharacteristicsoftheuser'ssurroundingenvironment(e.g.physicallocation,illumination,ambientacousticnoise,andsoon).Theinformationthatisobtainedbythissortofsensingcanbeveryusefultoimprovethenetworkandserviceperformance[21].However,theuseofthistypeofinformationisonlypossiblewhenthesensingdataisprocessedbyRKRL.CognitiveenginecannotdeterminethecontextofthesensingdataunlessRKRLformsit,asdiscussedinChapter2.4. Onemustkeepinmindthatthetraditionalstrictlylayeredprotocolarchitecturecausesthecontemporarywirelessdevices(andthereforethesystems)toperforminasub{optimalrange.Ontheotherhand,thepresenceofcognitiveenginealongwithexternalsensingcapabilitiesallowsCRsystemstoachievecross{layeradaptationandoptimizationasshowninFigure2.1.CRsystemsareabletoperformintheoptimumrangebyincorporatingthebitsofinformationcomingfromexternalsensingintothecognitioncyclewiththeaidofRKRL,asexplainedbefore.2.6Conclusion

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Consideringtheescalatingdemandinuseofwirelesscommunicationsalongwiththefactthatradiospectrumisnite,astraightforwardconclusion,whichiscalledas\spectrumscarcity,"canbedrawn.Contrarytothiscommonreasoning,recentmeasurementsrevealedthatradiospectrumisactuallyunderutilizedratherthanbeingscarce.CRthatisbasedonsoftware{denedradio(SDR)isbroughtforwardtoremedythisunderutilizationproblem.ThroughcognitioncycleandSDR,CRiscapableofpushingthetraditionalandlimitedadaptationconcepttowardstheglobaladaptationbyintroducingmulti{dimensionalawareness,sensing,andlearningfromitsexperiencestoreason,plan,anddecidefutureactionstomeetuserneeds.Eventhoughthereisnoconsensusontheformal25

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Includingcontemporarycommunicationsystems,itisnotdiculttoseethataglobaladaptationcoveringtheentireprotocolstackhasnotbeenachievedyet.Thisstemsfromthearchitectureoftheprotocolstack,whichisbasedonstrictlydenedindividuallayers.Furthermore,aglobaladaptationrequiresallofthelayerstobeexaminedinacombinedwayleadingtoamulti{dimensionalproblem.However,CRcannotcometruewithouthavingsuchaglobaladaptationwhichcomesattheexpenseofverychallengingtrade{osintermsofcontendinggoalsdenedinlayers.Hence,byitsverydenition,beingawareofthesituation,environment,andmanyotheraforementionedissueswillcompelCRtondacompromisebetweenmanycontendingobjectives.Moreover,itisimportanttonotethatCRisalsoresponsibleforobservingtheconsequencesofitsactionstobeabletoimprovethequalityofitsdecisionsinthefuturethroughitslearningability.Althoughthecontemporarystrictlylayeredprotocolstructuresolvessomeoftheproblemstosomeextent,aconceptualmodelofCRisrequired. Inthischapter,someoftheimportantparametersforenablingtheadaptiveradioandCRsystemswillbediscussedalongwithmeasurementandestimationtechniquesincludingrelevantchallengesandsomesampleapplications.Desireduser'sradiochannelparameterswillbestudiedindetail.Thechannelparameterswillbegroupedundertwocategories,namely,channelselectivitymeasurementsandchannelqualitymeasurements.Interferenceparameters,whichcouldhavealsobeeninterpretedaspartofthechannelparameters,willbetreatedseparately,sinceforCR,thedenitionofinterferenceincludesconceptsbeyondwhathasbeeninterpretedinthepast.Inadditiontothechannelandinterferenceparameters,manyotherparametersthatcanbeusefulforCRwillbediscussedundertheconceptofexternalsensing.Basedonthetraditionalchannelparametermeasurementsalongwithexternallyobtainedones,aconceptualmodelofCRispresented,aswell.26

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Dependingonthetransmissionbandwidth(orsymbolduration)andthetypeofenvironmentinwhichthecommunicationtakesplace,multipathcancausevariousproblems.Whentherelativedelaysaresmallcomparedtothetransmittedsymbolperiod,dierent\images"ofthesamesymbolarriveatthesametime,addingeitherconstructivelyordestructively.Theoveralleectisarandomfadingchannelresponse.Whentherelativepathdelaysareontheorderofasymbolperiodormore,thenimagesofdierentsymbolsarriveatthesametimecausinginter{symbolinterference(ISI). Inaddition,inwirelessmobileradiosystemsmobility,whichincludesthemobilityofthetrans-mitter,thereceiver,andthescatteringobjectswithinthepropagationenvironment,causesthechannelresponsetochangerapidlyintimeleadingtospectralbroadening,whichisalsoreferred27

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Finally,theinterferenceconditionsinwirelesssystemschangerapidly.Manyofthewirelesscommunicationsystemsareinterferencelimited,aectingtheperformance,capacity,range,datarate,andsoon.Sincetheradiochannelsofthedesiredandinterferingusersarehighlyrandom,andthestatisticalcharacteristicsofthechannelareenvironmentdependent,theeectofinterferencealsovariesintime,frequency,andspace.Aswillbediscussedsubsequently,behaviorofinterferenceisalsoinuencedbysomeothernotionssuchastractypeandmobilitypatternswithinthepropagationenvironment. Inthefollowingsections,theimportantmeasurementsrelatedtotheradiochannelwillbedis-cussed.First,channelselectivitymeasuresindierentdimensionswillbereviewed.Then,variouschannelqualitymeasureswillbestudiedindetail.3.2.1ChannelSelectivityMeasurement Therstphenomenonisknownastimeselectivitymeasure/Dopplerspread.Dopplershiftisthefrequencyshiftexperiencedbytheradiosignalwhenthereisarelativemotioninthepropagationenvironment,andDopplerspreadisameasureofthespectralbroadeningcausedbythetemporalrateofchangeofthemobileradiochannel.Therefore,time{selectivefadingandDopplerspreadaredirectlyrelated.Thecoherencetimeofthechannelcanbeusedforcharacterizingthetimevariationofthetime{selectivechannel.Itrepresentsthestatisticalmeasureofthetimewindowoverwhichthetwosignalcomponentshavestrongcorrelation,anditisinverselyproportionaltotheDopplerspread. InCR,Dopplerspreadinformationcanbeusedforimprovingperformanceorreducecomplexity.Forexample,inchannelestimationalgorithms,whetherusingchanneltrackersorchannelinterpo-28

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SampleApplications Illustrations TIME Receiveroptimization(suchaschannelesti-mation),adaptationoftransmitterandsys-temparameters(suchasinterleavinglength,channelandcellas-signment,hand{ooptimization) Adaptiveequalizerde-sign,adaptivereceiverdesign,adaptivecyclicprexdesignforOFDMsystems,andsoon Adaptivemulti{antennasystemdesign Intelligentinterfer-encecancellationandavoidancemechanisms lators,insteadofxingthetrackerorinterpolationparametersfortheworstcaseDopplerspreadvalue(ascommonlydoneinpractice),theparameterscanbeoptimizedadaptivelybasedontheDopplerspreadinformation[31{33].Similarly,Dopplerinformationcouldbeusedforcontrollingthereceiverorthetransmitteradaptivelyunderdierentmobilespeedsasinvariablecodingandinterleavingschemes[34].1Also,radionetworkcontrolalgorithms,suchashand{o,cellassignment,

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Dopplerspreadestimationhasbeenstudiedforseveralapplicationsinwirelessmobileradiosystems.Correlationandvariationofchannelestimates[41]aswellascorrelation[42,43]andvariationofthesignalenvelopehavebeenusedextensively[35,40].MultipleantennascanalsobeexploitedforDopplerspreadestimation[44],wherealinearrelationbetweentheswitchingrateoftheantennabranchesandDopplerfrequencycanbeobtained. AlthoughtheestimationoftheDopplerspreadinformationisveryusefulforadaptivesystems,onemightwonderiftheestimationprocessbringsaheavyburdenontothesystem.Ifweconsidercontemporarywirelessreceivers,weseethatmostofthemarealreadyaccessorizedwithchannelestimationability.AlthoughtheDopplerspreadestimationrequiresadditionaleortafterthechannelestimationprocess,thegaintobeobtainedinthelongtermisencouraging.However,consideringthedesireofhavingamobiledeviceassmallaspossiblesuchasacellphone,theuseofmultipleantennasforthispurposebecomesquestionable. Delayspreadisoneofthemostcommonlyusedparametersthatdescribesthetimedispersivenessofthechannel,anditisrelatedtofrequencyselectivity.Frequencyselectivitycanbedescribedintermsofcoherencebandwidth,whichisameasureofrangeoffrequenciesoverwhichthetwofrequencycomponentshaveastrongcorrelation.Thecoherencebandwidthisinverselyproportionaltothedelayspread[23,45]. Suchastimeselectivity,theinformationaboutfrequencyselectivityofthechannelcanbeveryusefulforimprovingtheperformanceofalltypesofadaptivewirelessradiosystemsincludingCR.Forexample,inatimedivisionmultipleaccess(TDMA)basedGlobalSystemforMobile(GSM),thenumberofchanneltapsneededforequalizationmightvarydependingonthedispersionofthechannel.Insteadofxingthenumberofequalizertapsfortheworstcasecondition,theycanbechangedadaptively,allowingsimplerreceiverswithreducedbatteryconsumptionandimprovedperformance[46,47].Dispersionestimationcanalsobeusedforotherpartsoftransmittersandreceivers.Forexample,inchannelestimationusingchannelinterpolators,insteadofxingtheinterpolationparametersfortheworstexpectedchanneldispersion,theparameterscanbechangedadaptivelydependingonthedispersioninformation[48].30

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Characterizationofthefrequencyselectivityoftheradiochannelisstudiedextensivelyusinglevelcrossingrate(LCR)ofthechannelinfrequencydomain[50{52].FrequencydomainLCRgivestheaveragenumberofcrossingsperHzatwhichthemeasuredamplitudecrossesathresholdlevel.AnanalyticalexpressionbetweenLCRandthetimedomainparameterscorrespondingtoaspecicmultipathPDPcanbeeasilyobtained.LCRisverysensitivetonoise,whichincreasesthenumberoflevelcrossingandseverelydeterioratestheperformanceoftheLCRmeasurement.Filteringthechannelfrequencyresponsereducesthenoiseeect,butndingtheappropriatelterparametersis31

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Anglespreadisameasureofhowmultipathsignalsarearriving(ordeparting)withrespecttothemeanarrival(departure)angle.Therefore,anglespreadreferstothespreadofanglesofarrival(ordeparture)ofthemultipathsatthereceiving(transmitting)antennaarray[54].Anglespreadisrelatedtothespatialselectivityofthechannel,whichismeasuredbycoherencedistance.Suchascoherencetimeandfrequency,coherencedistanceprovidesthemeasureofthemaximumspatialseparationoverwhichthesignalamplitudeshavestrongcorrelation,anditisinverselyproportionaltoangularspread,i.e.thelargertheanglespread,theshorterthecoherencedistance.Foragivenreceiverantennaspacing,largeanglespreadleadstoweakerantennacorrelationsbetweenthesignalsreceivedbydierentantennaelements.Notethatalthoughtheangularspreadisdescribedindependentoftheotherchannelselectivityvaluesforthesakeofsimplicity,inreality,theangleofarrivalcanberelatedtothepathdelay.Themultipathcomponentsthatarearrivingtothereceiverearlier(withshorterdelays)areexpectedhavesimilarangleofarrivals(loweranglespreadvalues). Comparedtotimeandfrequencyselectivity,spatialselectivityhasnotbeenstudiedwidelyinthepast.However,recently,therehasbeenasignicantamountofworkinmulti{antennasystems.Withthewidespreadapplicationofmulti{antennasystems,itisexpectedthattheneedforunderstandingspatialselectivityandrelatedparameterestimationtechniqueswillgainmomentum.Spatialselectivitywillespeciallybeusefulwhentherequirementforplacingantennasclosetoeachotherincreases,asinthecaseofmultipleantennasinmobileunits. Spatialcorrelationbetweenmultipleantennaelementsisrelatedtothespatialselectivity,antennadistance,mutualcouplingbetweenantennaelements,antennapatternsandsoon[55,56].Spatialcorrelationhassignicanteectsonmulti{antennasystems.Fullcapacityandperformancegainsofmulti{antennasystemscanonlybeachievedwithlowantennacorrelationvalues.However,whenthisisnotpossible,maximumcapacitycanbeachievedbyemployingecientadaptationtechniques.Adaptivepowerallocationisonewaytoexploittheknowledgeofthespatialcorrelationtoimprovetheperformanceofmulti{antennasystems[57].Similarly,adaptivemodulationandcoding,whichemploydierentmodulationandcodingschemesacrossmulti{antennaelementsdependingonthechannelcorrelation,arepossible[58,59].Dierentantennasystemssuchasmulti{inputmulti{32

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Researchersneedtoexplorewaystoadaptivelyaccessalldimensionsassociatedwiththeelectro-magneticspectrum.Thethreefundamentaldimensionsofthechannelselectivity(time,frequency,andangle)arewellunderstoodinthewirelesscommunity(seeTable3.1).Thereareotherpossi-bledimensionsthatcanbeconsideredaspartofchannelselectivity.Eventhoughtheymightnotbedirectlyassociatedwiththeactualwirelessmedium,itispossibletoconsiderthemwithinthiscontext.Power,polarization,interference,andcodingaresomeofthesedimensionsthatarereallypartofthesignalspaceratherthantheactualchannelspace.However,theyhavestrongtieswiththechannelspace. Codeselectivity,likepseudonoise(PN)codesindirect{sequencespread{spectrum(DSSS)ortimehoppingcodesinultra{wideband(UWB)orfrequencyhopping(FH)codesinFHsystems,couldbeastrongmeasureforadaptivesystemdesignforfutureCRsystems.Manyofthewirelesssystemsareinterferencelimited.Therefore,thecapacityisdeterminedbyhowmuchinterferencethesystemcantolerate.Forexample,theselfinterference(suchasISI)whichiscausedbythenon{zeroauto-correlationsidelobes,andmulti{accessinterference(MAI)duetothenon{zerocross{correlationsaremajorinterferencesourcesthatarerelatedtothecodedesign.Theeectofinterferenceandnear{farproblemcanbeminimizedbyemployingpowercontrol[62].Alternatively,decreasingsidelobesoftheauto{andcross{correlationalsoreducesinterferenceandincreasesspectraleciency.Therefore,itisdesirabletohavesequenceswithidealauto{andcross{correlationproperties.How-ever,itisproventhat\perfect"sequencesdonotexists.Also,itiswellknownthatthereisatrade{obetweenobtaininggoodauto{andcross{correlationproperties,(i.e.,smallerISI)leadstolargerMAIorvice-versa.Inaddition,thenumberofpossiblecodes(andhencethecapacity)canbeincreasedbyallowingsomecorrelation(orinterference)incodedomain.Beingawareofthatthenumberofcodesthathavegoodcorrelationpropertiesislimited,byallowingsomecorrelationadaptivelydependingontheothersystem,channel,andtransceiverparameters,theoverallcapacityofthesystemcanbeincreased.Thecorrelationpropertiescanalsobechangedadaptivelytoprovidedesiredpropertiesoverazonedependingonotherchannelselectivityparameters. Interferenceselectivitycanbeconsideredhowtheinterferingsources(suchasco{channelinter-ference(CCI)andadjacentchannelinterference(ACI))areaectingthedesiredsignalindierentdimensionsofelectrospace.Forexample,interferencecanbeastrongnarrowbandinterferenceor33

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Themeasurementscanbeperformedatvariouspointsofareceiverorprotocolstack,dependingonthecomplexity,reliability,anddelayrequirements.Therearetrade{osinachievingthesere-quirementssimultaneously.Figure3.2showsasimpleexamplewheresomeofthesemeasurementscantakeplace.Inthefollowingsections,thesemeasurementswillbediscussedbriey. Thereceivedsignalstrength(RSS)estimationprovidesasimpleindicationofthefadingandpathloss,andprovidestheinformationabouthowstrongthesignalisatthereceiverfrontend.IftheRSSexceedsathreshold,thenthelinkisconsideredas\good."Measuringthesignalstrengthoftheavailableradiochannelscanbeusedasapartofthescanningandintelligentroamingprocessincellularsystems.Also,otheradaptationalgorithms,suchaspowercontrolandhand{ocanusethisinformation.TheRSSmeasurementissimplydonebyreadingsamplesfromachannelandaveraging34

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Therearemanyadaptationschemeswherethesemeasurementscanbeexploited.Linkadaptation(adaptivemodulationandcoding,rateadaptation,andsoforth),adaptivechannelassignment,powercontrol,adaptivechannelestimation,andadaptivedemodulationareonlyafewfromcountlessapplications[63,65{67]. SIRestimationcanbeemployedbyestimatingthesignalpowerandtheinterferencepowersep-arately,andthenbytakingtheratioofthesetwo.Inmanynewgenerationwirelesscommunicationsystems,coherentdetection,whichrequiresestimationofchannelparameters,isused.Thesechannelparameterestimatescanalsobeusedtocalculatethesignalpower.Thetraining(orpilot)sequencescanbeusedtoobtaintheestimateofSIR.Insteadofusingatrainingsequence,thedatasymbolscanalsobeusedforthispurpose.Forexample,in[63,68],whereSNRinformationisusedasachannelqualityindicatorforrateadaptation,thecumulativeEuclideanmetriccorrespondingtothedecodedtrellispathisexploitedforchannelqualityinformation.ThereareseveralotherSNRmeasurementtechniquesavailableintheliterature,whichcanbefoundin[69,andreferencestherein]. Notethatsincebothchannelofthedesiredsignalandconditionsoftheinterfererchangerapidly,dependingontheapplication,bothshort{andlong{termestimateswouldbedesirable.Long{termestimatesprovideinformationonlong{termfadingstatisticsduetoshadowingandlog{normalfadingaswellasaverageinterferenceconditions.Short{termmeasurements,ontheotherhand,providemeasurementsofinstantaneouschannelandinterferenceconditions.Applicationssuchasadaptivechannelassignmentandhand{opreferlong{termstatistics,whereasapplicationssuchasadaptivedemodulationandadaptiveinterferencecancellationprefershort{termstatistics. Forsomeapplications,adirectmeasureofthechannelqualityfromchannelestimateswouldbesucientforadaptation.Asmentionedabove,channelestimatesonlyprovideinformationaboutthepowerofthedesiredsignal.ItisamuchmorereliableestimatethanRSSinformation,asitdoesnotincludetheothersortsofimpairmentaspartofthedesiredsignalpower.However,itis36

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Channelestimationforwirelesscommunicationsystemshasaveryrichhistory.Signicantamountofworkhasbeendoneforvarioussystems.Forthedetailsofchannelestimationforwirelesscommunicationsystems,thereadersmayreferto[70,71,andreferencestherein]. Channelqualitymeasurementscanalsobebasedonpost{processingofthedata(afterdemod-ulationanddecoding).BER,symbol{error{rate(SER),FER,andcyclicredundancycheck(CRC)informationaresomeoftheexamplesofthemeasurementsfallinginthiscategory.CRCindicatesthequalityofaframe,whichcanbecalculatedusingparitycheckbitsthroughtheuseofaknowncyclicgeneratorpolynomial.FERcanbeobtainedbyaveragingtheCRCinformationoveranumberofframes.InordertocalculatetheBER,thereceiverneedstoknowtheactualtransmittedbits,whichisnotpossibleinpractice.Instead,BERcanbecalculatedbycomparingthebitsbeforeandafterthedecoder.Assumingthatthedecodercorrectsthebiterrorsthatappearbeforedecoding,thisdierencecanberelatedtoBER.Notethatthecomparisonmakessenseonlyiftheframeiserror{free(goodframe),whichisobtainedfromtheCRCinformation. Althoughtheseestimatesprovideexcellentlinkqualitymeasures,reliableestimatesoftheseparametersrequireobservationsoveralargenumberofframes.Especially,forlowBERandFERmeasurements,extremelylongtransmissionintervalswillbeneeded.Therefore,forsomeapplicationsthesemeasuresmightnotbeappropriate.Notealsothatthesemeasurementsprovideinformationabouttheactualoperatingconditionofthereceiver.Forexample,foragivenRSSorSINRmeasure,twodierentreceiverswhichhavedierentperformanceswillhavedierentBERorFERmeasure-ments.Therefore,BERandFERmeasurementsalsoprovideinformationonthereceivercapabilityaswellasthelinkquality. Measuresafterspeechorvideodecoding:Thespeechandvideoquality,thedelaysondatareception,andnetworkcongestionaresomeoftheparametersthatarerelatedtouser'sperception.Essentially,thesearetheultimatequalitymeasuresthatneedtobeusedforadaptivealgorithms.However,theseparametersarenoteasytomeasure,andinmanycases,measurementsinreal{timemightnotbepossible.Ontheotherhand,thesemeasuresareoftenrelatedtotheothermeasuresmentionedintheprevioussubsections.Forexample,speechqualityforagivenspeechcodercanberelatedtoFERofaspecicsystemundercertainassumptions[72].However,asdiscussedin[72],someframeerrorscausemoreaudibledamagethanothers.Therefore,itisstilldesiredtond37

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Perceptualspeechqualitymeasurementshavebeenstudiedinthepast.Bothsubjectiveandobjectivemeasurementsareavailable[73].Subjectivemeasurementsareobtainedfromagroupofpeoplewhoratethequalityofthespeechafterlisteningtotheoriginalandreceivedspeech.Then,ameanopinionscore(MOS)isobtainedfromthesefeedbacks.Althoughthesemeasurementsreecttheexacthumanperceptionthatisdesiredforadaptation,theyarenotsuitableforadaptationpurposesasthemeasurementsarenotobtainedinreal{time.Ontheotherhand,theobjectivemeasurementscanbeimplementedatthereceiverinreal{time[74].However,thesemeasurementsrequiresampleoftheoriginalspeechatthereceivertocomparethereceivedvoicewiththeundis-tortedoriginalvoice.Therefore,theyarenotapplicableformanyscenarioseither.3.3OtherParameters Inthissequel,wemuststatethattherearesometypesofmeasurementsthatcanbecountedinbothinternalandexternalsensing.Forinstance,estimationofthelocationofamobiledevicecanbeestablishedthroughbasestationsdependingoninternalsensingparameterssuchasRSS.Onthe38

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OneoftheprominentadaptationparametersofCRisthecharacteristicsoftheenvironment,whichcanbeobtainedthroughexternalsensing.Itisknownthatthewirelesschannelishighlydependentontheenvironment.Environmentaldependencymanifestsitselfintermsofpreviouslydiscussedstatisticalparametersofthewirelesschannel.Underdierentgeographicalenvironments,delayspreadstatisticschangedrasticallysuchasinhillyterrainareaandruralarea.Also,someoftheenvironmentsinherentlyhavelessmobilityascomparedtotheothers,whichdeterminesthecrucialfactorforDopplerspread.Itisnotverylikelytohaveuserswithveryhighspeedmobilityinanindoorenvironment.Onthecontrary,inruralareas,themobilityoftheuserscanbemuchmorethanthatinindoor.Similarly,anglespreadhighlydependsonthesurroundingenvironmentofthewirelessdeviceinconnectionwiththenumberofscatterersaround.Consideringthattherearenumerousstatisticalmodelsrelatedtoalmosteverysortofenvironmentintheliterature,CRcantakeadvantageofthesemodelsbychoosingtheonewhichtsthebest.However,selectingthebestmodelincludesamajorchallenge:classicationofthepropagationenvironment.Thischallengestemsfromthefollowingtwofacts:(I)Obtainingthetopographicalcharacteristicsofthesurroundingenvironmentand(II)absenceoftheformaldescriptionsoftheenvironmentspresentedintheliterature.(I)canbeovercomethroughtheuseofdigitalelevationmodels(DEM)(andrecentlyGeographicalInformationSystem(GIS))ofthegeographicalareaofinterest.Theseareeasytobeprocesseddataandwhencombinedwithspatialinterpolationmethods,theycanprovideCRwithsomehintsaboutthetopographiccharacteristicsofitssurroundingenvironment. In(I),CRfacesasortofpatternrecognitionproblem.Because,CRneedstomatchthecharac-teristicsoftheenvironmentwiththeenvironmentalclassication.Unfortunately,thereisnotanyformaldenitionforpropagationenvironmentsintheliterature.However,therearesomepropertiespeculiartoeachenvironmenttosomeextent.Forinstance,asstatedin[75],distinguishingindoorfromoutdoorispossible,throughlightandtemperature.Similarly,foroutdoorenvironments,thetopographicalcharacteristicsofahillyterraincanbeusedtodistinguishitfromruralarea. Anotherchallengehiddeninboth(I)and(II)istorepresenttherawdataobtainedthroughexternalsensingandtoclassifytheminaformalwayformatchingoperation,respectively.ThisisestablishedwiththeaidofaspecialdescriptivelanguagethatallowsCRtorepresententireuniversethroughsemantics[75].Withtheaidofthislanguage,CRisabletonotonlydeductinformationin39

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SinceCRcanrepresenttherawdataandcharacteristicsinasemanticway,byusingitsformaltoolssuchasneuralnetworkandhiddenMarkovmodels,thecharacteristicsoftheenvironmentcanbeselectedappropriately[1].Inthissequel,itmustbementionedthat,theadditionalsensingcapabilitiescomeattheexpenseofadditionalhardwareandprocessing,whichalsomeanspowerconsumptionaswell.Besides,thetoolswithwhichCRisequippedandcognitioncyclebringadditionalburdenontothesystemintermsofdelay,powerconsumption,andoverhead. Asanalremark,wecanstatethatitispossibleforCRtocombineinternalandexternalsensingtoimprovethereliabilityoftheestimates.Inlightofthesepiecesofinformation,aconceptualmodelofCRincludingexternalsensingcapabilitiesisshowninFigure3.2. Inaccordancewiththediscussionabove,someoftheimportantmeasurementsforfutureCRapplicationsarebrieydiscussedbelow:

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TheLOSmeasurementcanbeobtainedfromthereceivedsignalbylookingattherst{orderchannelstatisticsandndingthelikelihoodofwhetherthesestatisticsttheLOSorNLOSchannel[79,80]aswellasexaminingthesecond{orderstatisticsofthechannel[5,6].Also,thisinformationcanbeobtainedbyusingadditionalsensingcapabilitiesthatarediscussedabove.Asmentionedearlier,theestimationofLOS/NLOSneedsagreatdealofresearch. Notethattheparametersthataremeasuredindierentlayerscanaecttheadaptationpa-rametersacrossseverallayers.Thiscanbeconsideredpartofthecross{layeradaptation.Forexample,physicallayerestimatedparametersareoftenrelatedtotheadaptationparametersinphysical,mediumaccesscontrol(MAC),andotherlayersoftheprotocolstack.Therefore,thenetworklayermeasurementsdiscussedaboveshouldnotbeperceivedasthemeasurementstoimproveonlythenetworkperformance.Theycanalsobeusedtoimprovetheperformanceacrossmanylayers. Notealsothat,oftenoneparameter,sayaboutthechannel,canaectmorethanoneadap-tationparameter.Forexample,SNR(orlinkquality)measurecanbeusedforadaptingthemodulation,coding,transmittedpower,orotheradaptationparameterssuchasthepacketdelayinnetworkinglayer.Therefore,severaladaptationparametersshouldnotbechangedindependentlybasedonthe(single)qualitymeasure,asthechangeofoneadaptationparam-etermighteectthemeasuredvalue.Hence,theadaptationofthesystemparametersshouldbedoneinaglobalmannerbyconsideringtherelationamongthem,leadingtothecross{layer41

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Anotherimportantissuerelatedtothenetworkmeasurementsistheawarenessoftheuser'sterminalaboutthepossiblenetworksandotherwirelessterminalsaroundit.Thisisverycriticalformanyapplications,especiallyforemergency,disasterrelief,andrescueoperations.Thetransmissionofotherpossibledevicescanbeobservedbysensingthespectrum,extractingthedatafromtheotheruserstransmission,processingit,comparingitwithsomeaprioriinformation(suchasstandardinformation),andmakingadecisionabouttheexistenceofapossiblenetwork.Currently,high{endsignalanalyzersdesignedbymeasurementcompaniesarecapableofdoingthiskindofmeasurements,but,withextremelyexpensive,powerhungry,andbulkymeasurementdevices.However,thegoalistoimplementsuchcapabilitiesinwirelessterminalswithreasonablehardwareandsignalprocessingcomplexities.Hence,thisareaneedsasignicantamountofresearch,aswell.

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Inmanywirelessstandards,someoftheparametersdiscussedherearemeasuredbythenet-workterminals.Forinstance,receivedsignalstrengthindicator(RSSI),CPICHEc/No,andCPICHRCSParesomeoftheitemstobemeasuredbyuserequipments(UE)inUniversalMobileTelecom-municationsSystem(UMTS),whereasEc/Ioisoneoftheparameterstobemeasuredin1EV-DO.InWorldwideInteroperabilityforMicrowaveAccess(WiMAX),carrier{to{interference{plus{noiseratio(CINR)/SINRismeasuredforthesamepurposebymobilestations(MS).InThirdGenerationLongTermEvolution(3GLTE),referencesymbolreceivedpower(RSRP)ismeasuredbyUEsasacounterpartofRSSImeasurementsinsomeotherstandards[81,andreferencestherein].Also,SINRsortofmeasurementsareavailablein3GLTEforthepurposeofnetworkmanagement[9].Therecent802:11kstandarddenessomeradioresourcemeasurementparameterstofacilitatenetworkman-agementandperformanceenhancement.Severalparametersarelistedanddenedasmandatoryandoptionalradiomeasurementswithinallofthesestandards.However,thesedenedparametersarestillverylimited,andonlyaimedforaspecicstandard,eventhoughthelistismoreenhancedcomparedtotheotherearlierstandards[82,andreferencestherein].Itisexpectedthataswirelessstandardsevolvefurther,someotherparametersthatneedtobemeasuredwillemergeandsuchlistsneedtobeextendedaccordingly. Inparalleltothesemeasurementparametersandrelationsbetweenthem,relevantchallengesfromtheperspectiveofadaptiveradiosystemspushestheresearchtowardstherealizationofCR.Inthisaspect,thereisastrongurgeinthewirelesscommunitytowardthecooperativesensingthatfacilitatesnodeswhichhaveCRcapabilities[83].Forinstance,CRcapabilitynodesareemployedin[84]inordertoestablishcognitivesensingtasks.Furthermore,in[85],theevaluationofthepiecesofinformationgatheredthroughsensingoperationisestablishedbythemanagernodes(peculiar43

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RangingandpositioningaretwoprominentexamplesofwirelesscommunicationapplicationsonwhichLOShassignicanteects.Currently,therearenumerousrangingandpositioningapplicationssuchasenhanced911emergencycallingsystems(E{911)[92],criminaltracking,andlostpatientlocators[93].Inrangingandpositioningapplications,itisextremelyimportanttoknowthestatusofthemultipathsreceivedatthereceiver.AssumethatthereisLOSbetweentransmitterandreceiver45

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Inconjunctionwithrangingandpositioning,knowledgeofbeinginLOSorNLOScanbeusedinadjustingsomeparametersofwirelessnetworksaswell.Forinstance,somespecictypesofnetworkssuchasad{hocnetworks,needthegeometriccharacteristicsoftheenvironmenttoimprovetheircommunicationperformances.Duetotheirdynamicstructures,determiningtherangesbetweennetworknodesasaccuratelyaspossibleisextremelyimportanttooptimizetheroutingscheme.Thisisknownas\locationawareness"[96]. SinceidenticationofLOSprovideswirelessnetworkswithsomesortofawareness,itisworthmentioningarecentlyemergingtechnologywhichdependsheavilyon\awareness":cognitiveradio.Cognitiveradioisdenedasanadaptiveradiosystemthatcansense,beawareofitssurroundingenvironment,andchangethetransmissionparametersaccordingtoitsobservationsandpast\expe-riences"[97].Havingthesecapabilitiesinhand,acognitivedevicethatcanidentifytheLOSstatusofthetransmissioncaneasilyswitchtoahigherordermodulation,oreventoahigherfrequencybandtoobtainmoredatarate[5].Inparalleltotransmissionparametersadaptationforcognitiveradio[1],cognitivepositioningsystemsalsobenetfromLOSstatusofthetransmissionintermsofaccuracyadaptationthattheyprovide[98]. DuetomutuallyexclusiverelationshipbetweenLOSandNLOS,theidenticationprocedureisgenerallyregardedasacompositehypothesistestinwhichToAinformationandrangingmeasure-mentsareemployed[80,95,99,100].ConsideringthatfadingchannelamplitudesofnarrowbandsystemsexhibitRiceandistributionunderLOStransmission,thecomparisonofthetheoreticaldis-tributionwiththeobservedonegivesanideaaboutLOS/NLOSstatusofthetransmission[101].46

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Inthischapter,amethodisproposedtoidentifyLOSfortime{varying,frequencyselectiveradiochannelsforcoherentreceivers.Giventhatchannelanddelayacquisitionestimationareprovidedbymeansofcoherentreceptionalgorithms[103{107],LOSidenticationisperformedbycomparingsecond{orderstatisticalcharacteristicsofunderlyingprocessesinchanneltaps.AssumingthattheLOSpathisinthersttap,acomparisonisestablishedviacoherencetimeandbyinvestigatingtherelationshipbetweenunderlyingprocessesformingthechanneltaps.Thecontributionsofthischaptercanbelistedasfollows:1. ItisshownthatinthepresenceofLOS,foratime{varying,frequencyselectiveradiochannel,thereisalowerboundofKforwhichtheautocorrelationcoecientofthersttapalwaysgreaterthanthoseofsubsequenttapswhentheyreachtheircoherencetime,2. Basedonthepropositionabove,aLOSidenticationmethodisproposedandevaluatedunderpracticalscenarios.

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whereListhetotalnumberofmultipaths,hk(t)denotesthecomplex,time-varyingpathgaincorrespondingtok{thmultipath,()istheDiracdeltafunction,denotesthedelayaxis,andk(t)denotesthepatharrivaltimes[23].Atatimeinstantt,k{thchanneltapgainhk(t)isobtainedbysumofadiusecomponentandaspecularcomponentasfollows[33]:hk(t)=sk(t)+dk(t)(4.2) wheresk(t)=skej(!Dcos((k)0)t+(k)0)(4.3a)dk(t)=dk1 In(4.3a),skdenotesthemagnitudeofthespecularcomponent,j=p 1,!DisthemaximumDopplerfrequencyinradian,(k)0istheangle{of{arrival(AoA),and(k)0isthephaseshiftforsk(t).2

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Forthesakeofcompleteness,thecharacteristicsofpatharrivaltimes,namelyk(t),canbeinvestigated.Sincemultipatheectiscausedbyobjectsinthesurroundingenvironment,itcanbeconcludedthatpatharrivaltimesareaectedbythelocationsoftheseobjects.Assumingthatthesurroundingobjectswithinanenvironmentarerandomlylocated,thepatharrivalstatisticscanbeconsideredasPoissonprocessassuggestedin[108].However,theassumptionthatallowsforrandomlylocatedobjectsmightnotbevalidforurbanenvironments,sincetheresidentialareasandbuildingsinurbanenvironmentshavesomesortofgeometricstructuresratherthanrandom,irregularstructures.Hence,patharrivaltimesneedtobemodeledinadierentmannerinorderforthemodeltoberealistic.Oneoftheverywell{knownmodelsforpatharrivaltimesisknownasmodiedPoissonprocess[109].Notethat,0(t)isdeterministicratherthanrandominLOScases,duetothedistance{delayrelationshipinrangingandpositioningapplicationsmentionedearlierinChapter4.1. Whentheautocorrelationfunctionof(4.2)isconsideredassumingthatuncorrelatedscatteringissatised(i.e.,uncorrelatedattenuationandphaseshiftwithpathsofdierentdelaysexist)andthespecularanddiusedcomponentsareindependent,theautocorrelationofk{thtapcanbecalculatedas:Rhk(t)=Efhk(t)hk(t+t)g=Ef(sk(t)+dk(t))(sk(t+t)+dk(t+t))g=Rsk(t)+Rdk(t)(4.4) whereEfgistheexpectedvalueoperatorand()representsthecomplexconjugateofitsargument.Forthesakeofbrevity,autocorrelationcoecientscanbeusedinanalysisinsteadofautocorrelation

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foranyrandomprocessx(t).Sincethespecularanddiusedcomponentsarepreviouslyassumedtobeindependentofeachother,then,(4.4)canbere{organizedintermsofautocorrelationcoecientsasfollows:hk(t)=Rhk(t) whereKk=2sk=2dk,whichdenesthepowerratiobetweenspecularanddiusedcomponentsandisknownasRiceanfactor.Intherestofthechapter,thesubscriptkisdroppedfromKkforthesakeofbrevity.Hence,fromthispointonwhenKisused,itmustbeunderstoodthattheRiceanfactorfork{thtapisreferredunlessotherwisestated.4.2.2BoundforKParameter K+12jsk(t)j2+2K<(sk(t)dk(t)) (K+1)2+1 where<()denotestherealpartofitsargument. In(4.7),jsk(t)j2becomesunityinconnectionwith(4.3a)and(4.5).Aftersomemathematicalmanipulations(4.7)canbere{writteninthefollowingforminordertohaveaneasieranalysisinfurthersteps:jhk(t)j2=K K+12+2Kjdk(t)jcos!Dcos((k)0)t+(t)

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PeculiartoLOSscenarios,rstbinincludestheLOScomponentbesidesomeotherpathswhichformthediusedcomponentdenedin(4.3b).Therefore,inLOSscenarios,h0correspondstothetap(k=0)thatcontainsLOScomponent.Whenthetapsareconsideredforkwhichdenedasthesetofsubsequenttapsi.e.,k=fkjk>0g,theLOScomponentwillnotbepresentanymore.However,somemeasurementsshowthatfork,theremaystillbearelativelyweakerspecularcomponentcomparedtothersttap[110].Nevertheless,aswillbeexplainedinthesubsequentsections,havingsuchacomponentcausestohavedierentunderlyingprocessesforthesubsequenttapsk;but,itcanstillbetreatedwiththemethodproposed.Despiteitisoutsidethescopeofthischapter,itisworthmentioningtheimpactofUWBtransmissionontheconceptofunderlyingprocessas51

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Beforeproceedingintothefurtherdetailsofthemethodproposed,itisappropriatetogivethedenitionofcoherencetimeofachannel.52

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thesameineachtap,Case2): dierentineachtap(orinsomeofthetapsasillustratedinFigure4.1). Infact,Case1)isaspecialcaseofCase2).Inordertoseethisrelationship,assumethatoneofthesubsequenttapskreachesitscoherencetimeatt1,thatisjhk(t1)j=0:5.Letthedierencebetweentheautocorrelationcoecientsofunderlyingprocesses,namelyjd0(t1)jandjdk(t1)j,bedenedintermsofe(t1)inageneralwayasfollows:jd0(t1)j=jdk(t1)je(t1)(4.9) In(4.9),notethatCase2)isidenticaltoCase1)fore(t1)=0.Notealsothatsince0jx(t1)j1foranyrandomprocessx(t),Denition1requirese(t1)2[0;0:5)inlightof(4.9).Therefore,provingsolelyCase2)willbesucienttoinvestigateProposition1.However,duetothesignof53

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Notethatin(4.10),e(t1)isconsideredasanadditiveterm.Onemightaskwhye(t1)ismodeledasanadditiveterminsteadofamultiplicativeterm.Thereareanalyticalreasonsfore(t1)tobechosenasadditive.Firstandforemost,multiplicationisaspecialcaseofmultipleaddition.Second,ife(t1)weretobechosenasamultiplicativeterm,theresultwouldnotchange;however,becauseofthescalingfactorthedomainofe(t1)wouldbedierent.Bearinginmindthatjd0(t1)jandjdk(t1)jaredenedas0jd0(t1)j;jdk(t1)j1,andjd0(t1)j=e(t1)jdk(t1)j;itcanbeconcludedthate(t1)2[0;2]becauseofDenition1(jdk(t1)j=0:5).Notethattheinterval[0;1)correspondstoCase2A)sincejd0(t1)jjdk(t1)j.Clearly,Case1),whichisaspecialcaseofCase2),occurswhene(t1)=1. Now,onecanproceedtoinvestigatethetwopossiblesituationsin(4.10)alongwiththecorre-spondingproofsforCase2).Therefore,rstthesquared{envelopeofautocorrelationcoecientsofh0andhkmustbecalculated:jh0(t)j2=K0 (K0+1)2+1 Now,itwillbeshownthatthereisalowerboundaryofK0(Kfactorforthersttap)forwhichh0alwayshasahigherautocorrelationcoecientvaluecomparedtothoseofthesubsequenttaps(hk)whentheyreachtheircoherencetime.ProofofProposition1forCase2A).

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(K0+1)2+jdk(t1)je(t1) (K0+1)2+e2(t1)2e(t1)K0cos(f(t1))e(t1) (K0+1)2(4.12) If(4.12)isre{written,then:jh0(t1)j2=K20+e2(t1)+0:25 (K0+1)2| {z }>08K0;t1+K0cos(f(t1))(12e(t1))e(t1) (K0+1)2(4.13) Recallthatitisassumedthatk{thtapreachesitscoherencetimeatt1(i.e.,jdk(t1)j=0:5).Inthiscase,thelowestvalueof(4.13)forthatspecict1isobtainedif!Dcos((0)0)t1+(t1)=(2l+1)(4.14) issatisedwherel2Z+,sincee(t1)2(0;0:5)andthersttermin(4.13)ispositiveforallt1andK0values.4Therefore,itcanbere{organizedasfollowsyielding:jh0(t1)j2=K20K0+0:25 (K0+1)2+e2(t1)+2e(t1)K0e(t1) (K0+1)2=(K00:5)2 (K0+1)2(4.15) Ifachangeofvariableisappliedwith(K00:5)=u,then:jh0(t1)j2=u+e(t1) 22| {z }M1(4.16)

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20:5
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In(4.22),because(0)0andvaretwoindependentparameters,itisveryunlikelythattheworstcasescenariotakesitsplaceinpracticalcases.AswillbeshowninChapter4.3,theconditionK0>3canberelaxedformostofthepracticalcases.However,itrequiresfurtherinvestigationstoseehowmuchrelaxationcanbeallowedinK0.4.2.3LOSIdentication whereTdenotesthestatusofthetransmissionandzdenotesthethreshold.Notethat,iftheautocorrelationcoecientsareknown,inotherwords,iftheycanperfectlybeestimated,(4.23)candetectLOSforK0>3withz=0asshownin(4.21).However,inpracticalcases,receiverdealswithlimitednumberofchannelsamples.Moreover,thesesamplesmighthaveerrorsduetothechannelestimationprocess.Limitednumberofsampleswithpossibleerrorsforcesthereceivertouseestimationsinsteadoftheactualautocorrelationcoecients.Hence,anon{zerothresholdzisrequiredinpracticalcases.AnumericalmethodisappliedinChapter4.3inordertoobtainapropervalueforz. Inthissequel,twoissuesmustbeinvestigatedregardingtheidenticationprocedure.First,onemightwanttoknowwhathappenswhencoherencetimeisreachedatdierenttimeshifts.Moreformally,oneneedstoknowwhethertheidenticationholdsifjhk(t2)j=0:5wheret1
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CommonparameterswhichareusedinsimulationsaregiveninTable4.1.Notethat,inTable4.1,theAoAsareonlychosenfromtheinterval[0;=2].Thisisduetothefactthatcos()isanevenfunctionandtherearetwonestedcos()functionsin(4.8).Thefollowingmainparametersubset

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(b)GAUS1typeDopplerspectrum. (c)GAUS2typeDopplerspectrum. MobileSpeed(v):f1;3;10;20gm/s ChannelSamplingFrequency(fs):1KHz AoA(0)0:f0;=10;=5;=2gradian Forthecategory(i),rstCase1)isconsidered.InCase1),theunderlyingprocessesareassumedtobethesame,thatis,ofJakes'typeinbothrstandsecondtaps.Theresultsarepresentedin59

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(b)(0)0==10 (c)(0)0==5 (d)(0)0==2 InordertoevaluatetheimpactofK0,Figure4.5canbeinvestigated.Itisseenthatthedierencebetweenjh0(t1)j2andjhk(t1)j2isverysignicantinFigure4.5(b),Figure4.5(c),andFigure4.5(d),asexpectedbecauseofProposition1.However,thisdierenceisinsignicantinFigure4.5(a)comparedtothecaseswhereK0>3. Similartof(0)0gandfK0gsets,Figure4.4canbeinvestigatedtodeterminetheimpactofsetfvguponthemethodproposed.InFigure4.4(a),itisseenthatwhenspeedofthemobileisclosetozero,thedierencebetweenjh0(t1)j2andjhk(t1)j2isnotsignicant.However,asvincreases,thedierencebetweenjh0(t1)j2andjhk(t1)j2increasesdrasticallyascanbeseeninFigure4.4(b),60

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(b)v=3m/s (c)v=10m/s (d)v=20m/s(NotethatthisplotisthesameasFigure4.3(c)) Inthissequel,itwillbeusefultoseethecaseswhenK02(0;3).Inordertoinvestigatethis,Case1)isconsideredalongwith(I),sinceitisverywidelyusedinwirelessmobileradiochannelmodels.Inthesesimulations,alltheparametersettingsandsetsaremaintainedexceptforK0.InadditiontotheonepresentedinTable4.1,twomorevalues,namelyKnew=f0:5;2g,areaddedtobetterseetheimpactwhenK0<3.AscanbeseenfromFigure4.6,assoonasthepowerofspecular61

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(b)K0=3 (c)K0=5 (d)K0=10(NotethatthisplotisthesameasFigure4.3(c)) Upuntilthispoint,Case1)isconsideredinsimulations.However,asdiscussedearlier,underlyingprocessineachchannelmightbedierent.InordertotestthemethodproposedforCase2)62

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(b)K0=1 (c)K0=2Figure4.6Theprobabilityofjhs(t1)j2
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AsstatedinChapter4.2.3,duetophysicallimitations,receiversuseestimationsofautocor-relationcoecientsbytakinglimitednumberofslots(samples)intoconsideration.Therefore,theidenticationprocessisestablishedviaanon{negativethresholdz.Itmustbestatedthatzdependsmainlyonnumberofslots,K0,speed(v),andSNR.Therefore,itisverydicult,ifnotimpossible,toobtainaclosed{formsolutiontotheproblemofselectionz.Inthischapter,zvaluesareobtainedusingnumericalevaluationbykeepingthefalsealarmrate,namelyPrLOSj(T=NLOS),at0:05foreachspecicnumberofslotsandvvaluealongwiththeassumptionofperfectchannelestima-tionwherePr(XjY)denotestheprobabilityofeventX,giveneventY.AsshowninFigure4.8,desiredzvaluesformasurfacewhosevaluedecreaseswiththeincreaseofnumberofslotsandv.Thethresholdzcanbeadjustedaccordinglyincasethereceiverknowsthenumberofobservationslotsand/orv.Inthesimulationsofcategory(ii),aswillbediscussedsubsequently,forcomparisonpurposes,fsis1:5KHz.Thenumberofslotsinthegeneralparametersubsetischosenas500andvisassumedtobeunknown.BasedontheresultsshowninFigure4.8,theminimumofzvalues,namelyz=0:1,ischosenasthethresholdandperformanceofthemethodproposedisevaluatedbasedonthisvalue. Incategory(ii),thechannelestimationerrorsareintroducedintotheidenticationprocess.Inordertotesttheperformanceofthemethodproposed,least{squareschannelestimationisem-ployedbykeepingSNR=10dBalongwiththecommonparametersubset.TheresultsareshowninFigure4.9{4.12.ItisseenfromFigure4.9thatasNSLOTincreases,thedetectionrateincreases,sincetheestimationoftheautocorrelationcoecientsbecomesmorereliable.Thedetectionrate64

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Figure4.9Probabilityofdetectionversusnumberofslots(NSLOT)forK0=10,v=20m=s,andSNR=10dB.becomesunityforNSLOT400.InFigure4.10,theimpactofK0valuecanbeobserved.Forthegeneralparametersubset,evenlowerK0valuescanbedetected.Inordertoinvestigatetheimpactofv,Figure4.11canbeexamined.InaccordancewiththediscussionabouttheresultspresentedinFigure4.4,whenv!0,thedierencebetweentheestimatesoftheautocorrelationcoecientsofthetapscannotbedistinguished;therefore,thedetectionrateisdegraded.Figure4.12showstheimpactofSNRonchannelestimationandthereforeidenticationprocess.Forthevaluesgivenintheparametersubset,itisseenthatevenforrelativelylowSNRvalues,theproposedmethodperformswell. Althoughthemethodproposedisbasedontheautocorrelationcoecientestimatesofthechan-neltaps,itsperformanceinidenticationofLOScanbecomparedwiththoseofwhichconsiderpracticalcasessuchaspresentedin[102].Accordingto[102],themethodbasedonthecomparison65

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Figure4.11ProbabilityofdetectionversusvforSNR=10dB,NSLOT=500,andK0=10. Figure4.12ProbabilityofdetectionversusSNRforNSLOT=500,K0=10,andv=20m=s.ofdistributionofthechannelamplitudesreachesthecertaintyaboutidenticationofLOSafterNSLOT=880underarelativelyfastfadingchannelwithv=22:22m/sandK035:45(15:5dB).WiththesamevandK031:62(15dB),againin[102],themodiedversionofthepreviousalgo-rithmreachesthecertaintyafterNSLOT=500.ThemethodproposedreachesthecertaintyabouttheidenticationatNSLOT=300foraweakerspecularcomponent(K0=10dB)andalowerspeedvalue(v=20m/s)viacalculatingtheautocorrelationcoecientsandathresholdvaluez,asshowninFigure4.9.Moreover,insimulations,itisshownthatforsuchhighervvalues,theidentication66

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EventhoughthischapterassumesthatMk1,itdoesnotrequireMk!1.However,whenUWBchannelsareconsidered,duetoincreasedtimeresolution(orequivalentlyverylargetransmissionbandwidth),numberofresolvablepathsincreases,whichmightremovetheconceptofunderlyingprocessbyhavingMk=0.Inthesecases,theproposedmethodmightnotbesucienttoanalyzeLOSwiththewaythatismentionedpreviouslyandillustratedinFigure4.1.Nonetheless,itispossibletotakeadvantageofincreasedtimeresolutionbyconsideringthefrequencyresolutionofeachpathonebyone[112,113].Itisreportedin[112,113]that,withaverynetimeresolutionasinUWBtransmission,\pathhistory"canbeextractedfromthefrequencydependenceofeachpath.SincetheLOSpathdoesnothavefrequencydependence[113],\pathhistory"canbeusedinidentifyingLOSinUWBcasesaswell.67

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Inwhatfollows,parametersaectinginterferencewillbeintroducedanddiscussed.68

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Fromtheperspectiveoftraditionalprotocolstack,therearesomefactorsthataectCCIbutcannotbepopulatedinanyofthelayers,sincetheycannotbemeasured(therefore,controlled)inreal{timeinanadaptivemanner.Weatherandseasonalvariationswouldbeoneofthemostinteresting\non{layerfactors"inuencinginterferencefallingintothiscategory.Duetothepresenceofhighpressureairsometimes,signalscanbereectedtothedistancestowhichtheyarenotintended[114,115].1Sincethesignaloverthesamechannelisabletoreachtheotherterminal,CCIoccurs. Althoughcellularsystemsaredeployedaccordingtothetheoreticalmodelssuchastheuseofhexagonalshapecells,inpracticalcases,coverageandpropagationarenotasregularasinthetheory.Sincecoverageandpropagationisgovernedbythephysicalenvironment(localtopographycanresultinlargeattenuationchangesoverquiteshortdistances),namelytopographicalandevendemographicalcharacteristics,andthetracdistributiondependsalsoonthesamefactors[116,117],\indirectly",itcanbeconcludedthatCCIisaectedbyphysicalenvironmentaswell.However,itisverydiculttomodeltheseeects,sincetheyaremathematicallyintractable.Statisticallyspeaking,onecanstillobservemoresevereinurbanareasduetolargenumberofbasestationsandmobiles[77,andreferencestherein].Inindoorenvironments,dependingontheuseofdevices,CCIismorelikelytooccur,sincetherearemanydevices(e.g.,microwaveovens,telephonehandsets,andsoon)operatingonthesimilarbands.Especiallyinindoorenvironments,inconjunctionwithpropagationchannelproperties,non{line{of{sight(NLOS)casesexperiencemoresevereinterferencecomparedtoline{of{sight(LOS)cases[118].Manypossiblecombinationsofthepropagationeects

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Incellularsystems,sectorizationisestablishedbyreplacingomni{directionalantennaswithnar-rowerbeamwidthantennas(e.g.,six{sectorantennasof60orthree{sectorantennasof120open-ings),thecapacityincreasesandCCIisreduced[23,120{122]. Beamformingmethodsperformspatiallteringbyplacingcomparativelysharpnullsinthedirec-tionoftheinterferingmobilestations,whichisagainrelatedtotheimpactofantennas.Therefore,theinterferencelevelcanbereducedsignicantly[123{125]Ifbeamformingisquantiedbythedirectivityratio,saydand0d1,itisreportedthatCCIisminimizedwhend=1.However,therelationshipbetweentheCCIreductionanddisnotlinear.Resultsaregenerallybasedonsimulations[123].Yet,itispossibletoseetheimpactofbeamformingonCCIwhenfree{spaceisofinterestwithPrx=Ptxd Similartoantennaradiationpatterns,intheliterature,itisalsoreportedthatthepolarizationaectsCCI[126].PolarizationcanbeusedasatooltoreduceCCIrelyingonamethodknownascrosspolarizationdiscrimination(XPD).BecauseofXPD,whenahorizontallypolarizedantennareceivesaco{channelsignalsentfromaverticallypolarizedantenna(andtheotherwayaround),theeectivesignalstrengthisreducedbyseveraldecibels.ItisalsoreportedthattheamountofXPDisreducedifthesignalundergoesextensivescattering.Hence,thisrelationshipissomehowconnectedtosurroundingphysicalenvironmentaswell. Incontrasttonon{layerparameters,therearemanyparametersthatcanbepopulatedintheprotocolstack.InconjunctionwiththediscussioninChapter3.2.2,interferencepowerisoneofthefundamentalmeasurementitemsfallingintophysicallayer.WiththeemergenceofCR,thetermin-terferencepowergainsadditionalconceptswhichhavenotexistedbeforeinpreviouscommunicationsystemssuchas\interferencetemperature"and\primaryuser."Interferencetemperatureisasortofmeasureofradiofrequency(RF)powerthatincludespowerofambientnoiseandotherinterferingsignalsperunitbandwidthforareceiverantenna.Primaryuserscanbedenedastheuserswhohavethehigherpriorityorlegacyrightsontheusageofaspecicpartofthespectrum.Ontheotherhand,secondaryusersaredenedasthosewho(havelowerpriority)exploitthisspectruminsuchawaythattheydonotcauseinterferencetotheprimaryusers.Therefore,secondaryusersneedtohavethecapabilitiesofCRs,suchassensingthespectrumreliablytocheckwhetheritisbeingused70

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Inthisstudy,ananalyticalmethodthatidentiesinterferenceisproposed.Duetothefactthatfastfadingandshadowingprocessesareindependentofeachotherandevolveondierentscales,ametricbasedonthesecond{orderstatisticsofthecompoundprocessisdenedandadecisionmechanismisprovided.proposedmethod(PM)isalsocomparedwiththeconventionalEDapproachandresultsarepresented.6.2StatementoftheProblemandSignalModel6.2.1StatementoftheProblem

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whereD(t)andU(t)denotethedesiredandundesiredparts,respectively;whereas(t)istheinterferingsignalandn(t)istheambientbackgroundnoisewhichisassumedtobeofzero{meanwhiteGaussiannoise(WGN)form.Inordertoextractthedesiredpartfromthereceivedsignal,receiversgenerallyinvokeanestimationprocessinwhichtrainingsequences,orpilotsymbols,orpilotchannelsareused.Sincetheestimationmightbeimperfect,awidelyemployederrormodelforlinearestimatorsintheliteratureisadoptedforthedesiredpartasD(t)=bD(t)+e(t),wherebD(t)istheestimationitselfande(t)istheestimationerrormodeledwithanindependentzero{meancomplexWGNprocess[135,andreferencestherein].Inthiscase,onecanwriteN(t)=n(t)+e(t),whereN(t)isassumedtobeofcomplexadditivewhiteGaussiannoise(AWGN)formsincethesumoftwoindependentAWGNsisalsoofAWGNform.Thus,r(t)canberepresentedwith:r(t)=bD(t)+(t)+N(t)z }| {n(t)+e(t)| {z }bU(t):(6.2) BysubtractingbD(t)fromr(t)asoutputoftheestimation,theestimatedversionoftheundesiredpartisyieldedvia(6.2):bU(t)=r(t)bD(t)=(t)+N(t):(6.3) Hence,thepurposeistoidentifythepresence/absenceofinterferencebylookingatthestochasticcharacteristicsofbU(t)whichincludestheinterferingsignalitself,ambientnoise,anderrorscausedbyimperfectestimation.16.2.2SignalModelfor() Whenawidebandwirelesssignalistransmitted,itundergoesthefollowingthreeeects:(E1)pathloss,(E2)shadowing,and(E3)frequency{selectivefading.2Alloftheseeectsoccurondierentscalesofantennadisplacement.Frequency{selectivefadingoccursmorefrequentlycomparedto

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Pathlossandshadowingcanbothbecapturedbythefollowingsingleprocess[137,138]:s(t)=e((t)+g(t));(6.4) where(t)ispathlossvaryingoverlongerperiodsoftime;isthestandarddeviationoflog{normalshadowing,andg(t)isareal{valuedunitnormalprocessN(0;1)[138].Measurementsalsoshowthatg()isspatiallycorrelatedofanexponentiallydecayingform[139]:Rg(k)=Efg(n)g(n+k)g=2g(jktjv=d);(6.5) wherendenotesdiscretetimesamples;Efgisthestatisticalexpectation;tisthesamplingperiod;visspeed,anddisthedecorrelationdistanceatwhichtheexponentiallydecayingg()dropsbelow0:5.Hence,interferencecanberepresentedwithacompoundprocessincludingpathloss,shadowing,andfrequencyselectivefadingas:(t)=m(t)s(t):(6.6)6.3Analyses6.3.1Noise{only(Interference{free)Case

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whereListhetotalnumberofsamplestakenintoaccount.Notethat(6.7)isastraightlineatnon{zerolags(jkj>0).6.3.2Interference{onlyCase Assumingthatktisrelativelyshortinwhichpathlossremainsconstant(i.e.,(t)=(t+kt)=),(6.8)becomes:ln(I(t+kt))=+2[ln(jm(t+kt)j)+g(t+kt)];(6.9) where=2.Recallthatm(t)andg(t)(therefore,theirfunctions)aremutuallyindependent.Aftersomemathematicalmanipulations,theautocorrelationof(6.9)isfoundtobe:Rln(I)(kt)=2+4Eflnjm(t)jg+42Rg(kt)+Rlnjmj(kt):(6.10) Therearebothdeterministic(constant)andstochastictermsin(6.10).Todistinguishinterference{onlycasefromnoise{onlycase,onecanfocusonthestochasticpartof(6.10)byassuming=0.Inthiscase,theACCsof(6.10)canbewrittenas:ln(I)(kt)= where=2=2M,2Misthevarianceofln(jm(t)j),andM()=Rlnjmj()=2M.NoticethatM()diminishesrapidlywhen1<(i.e.,whenshadowingvarianceislarge),whichcausesg()to77

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ThreearbitrarypointsonACCsofln(jbU(t)j2)aresucienttotestitsstraightness.Forthesakeofbrevity,rstletX(t)=ln(jbU(t)j2)andX()representtheACCsofX(t).LetithpointbedenotedwiththepairP(i)(ti;X(ti)),wherei=1;2;3,satisfyingt1
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wheremisthenormalizednon{zerodeviationthresholdthatisselectedaccordingtodesiredType{IandType{IIerrorrates.6.5NumericalResults

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InFigure6.2,itisseeninbothenvironmentsthatas2=2Nincreases,mincreasestoo.ThisisbecausetheshadowingcorrelationofinterferencebecomesdominantandrevealsitselfinACCsbycausingDtoexpand(i.e.,bydeviatingfromthenoise{likebehavior).Onceinterferencebecomesthedominantpart,furtherincreaseininterferencepowerdoesnotaectthesecond{orderstatisticsmuch;therefore,Ddoesnotexpandfurtherandmconverges.Also,asthespeedincreases,mincreasesaswell.ThisstemsfromthefactthathighervvaluescausetheACCsofthetransformedprocesstodeviatefasterfromthoseofthestraightline.SinceACCsaremainlygovernedbytheexponentialdecayofg()duetoshadowingasshownin(6.11),X(t)valueisreachedataveryearlyt2comparedtotN;therefore,agreatermvalueisobtained. InFigure6.3,PMiscomparedwithconventionalEDbasedonprobabilityofdetection(i.e.,PD=1eII)resultswhenm=0:05.Insimulationstheintegrationsizeissetto15sampleandbackgroundnoisevariance2nisassumedtobeknownfortheED.ItisseenthatPMperformsalwaysbetterthanEDwheninterferenceisnotdominant.Wheninterferencebeginstodominate(around0dB),PMoutperformsED.Nonetheless,PMcannotreachthedesiredPDimmediatelyinthisregion,becauseitstillsuersfromthecombinedimpactofbackgroundnoiseandestimationerrorswhichdonotallowDtoexpand.However,PMreachesthedesiredPDaround5dBandbeyondforallspeedvaluesinbothenvironments.WhenPMreachesthedesiredPD,EDstilllagsbehindduetointensefading(i.e.,largeandfrequency{selectivity)andtomobilityasinvestigatedandpresentedin[134,140,141].

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Tractypeplaysacrucialroleonbehaviorofinterference.Therefore,ICImanagementisinves-tigatedintheliteraturebyconsideringdierenttypesoftracundervariousconditions.CombinedeectofpropagationandvoicetypetraconCCIandperformanceofdynamicchannelalloca-tionfororthogonalfrequencydivisionmultipleaccess(OFDMA){basedcellularsystemsareinvesti-gatedin[149].In[150],performanceanalysisofdierentschedulerschemesforICIcoordinationinOFDMA{basednetworksisgivenunderelastictrac.In[151],ICIisinvestigatedfromtheperspec-tiveofbothstreamingandelastictracunderdierentfrequencyreuseschemesthroughtheuse83

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AlthoughtherearemanystudiesintheliteratureregardingdierentICIconditionsfordierenttractypes,tothebestknowledgeofauthors,thereisnoanalyticalstudywhichconnectssched-ulerswithaparticulartypeoftracbyprovidingtheoreticalperformancelimitsalongwiththefactorsinuencingthem.PerformancelimitsandfactorsinuencingthemarekeypointstodevelopbetterschedulersforICImanagementprocessinNGWNs.Inthischapter,performancelimitsonICIschedulersinOFDMA{basedsystemsarederivedforvoicetracbasedonpilotcellapproachunderFROregimeandfactorsaectingthemareinvestigated.Thecontributionsofthischapteristhreefold.First,itisformallyshownthattheknowledgeabouttheresourcereservationofneigh-boringcellplaysacrucialroleonupperandlowerboundsforICIschedulers.Moreconcretely,itisshownthattheoreticalupperboundcorrespondstothecasesthataredrivenbytheabsenceofknowledge(absoluteuncertainty),whereaslowerboundcorrespondstothecasesthataredrivenbythepresenceofperfectknowledge(absolutecertainty). Second,MinimumExpectednumberofcollisionScheduler(minimumEfKgscheduler(MES))isdevelopedbyexploitingtheresultsofboundanalysis.Itisshownthat,incaseoneofthecellscanacquireknowledgeaboutthereservedresourcesofneighboringcell,MEScanbeimplementedbyorganizingresourcesofastackforminarandommanner.WiththeaidofMES,boundexpressionsareextendedbyappropriatelyquantifyingabsoluteuncertaintyandcertaintyconditionsinsuchawaythattheamountofknowledgeacquiredisalsoincluded. Third,consideringthepracticalcaseswhichimposerestrictionsonschedulersintermsofcompu-tationalpowerandtimealongwithpersistentschedulingschemesproposedforvoicetrac,impacts84

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Thischapterisorganizedasfollows.Chapter7.2providesthedetailsofthesystemmodelalongwiththebasicassumptionsnecessaryfortheanalysis.Chapter7.3givestheupperandlowerboundsontheexpectednumberofcollisionsforgeneralcases.BasedontheresultsinChapter7.3,MESisdevelopedandknowledgeacquisitionisembeddedintotheanalysisinChapter7.4.Chapter7.5discussestheeectsoftheprolongedschedulingperiodonperformance.NumericalresultsalongwithrelevantdiscussionsarepresentedinChapter7.6.Finally,keyndingsaresummarizedandfuturedirectionsareprovidedinChapter7.7.7.2SystemModelandBasicAssumptions AlloftheUEsincellsareassumedtocarryvoicetracwhosesamplescomefromanegativeexponentiallydecayingprobabilitydensityfunction(PDF)withadecayingrateofHwhichisthereciprocaloftheaverageholdingtimeH.Stemmingfromgeneralcharacteristicsofvoicetrac,

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Throughouttheanalysisnohando(handover)isassumedtotakeplaceinordertomakesureofthestabilityofanalysis.However,purebirthprocessforarrivals(i.e.,Poissonprocess)isconsideredforeachCcwithanaveragearrivalrateof(c)A.Inaddition,ifnoresourceisfoundforanyarrivalduringTc,thenthatarrivalisassumedtobeblocked.IfanyuserreleasesanyoftheresourcesduringTc,itisassumedthatthoseresourcescannotbeassigneduntilthenextschedulingtime. SchedulingperiodTccarriesagreatimportanceforICImanagementprocess.Therefore,furtherdetailsofTcareessentialforanalysis.LetTcbedenedintermsofH.Thisisareasonableapproach,sinceHistheonlyparameterinhandprovidinginformationaboutthedurationofresourceuse.LetTcbeexpressedintermsofnumberofschedulingoperationsasTc=H=!c.Notethat!cwith!c2Z+providesabetterperspectivefortheschedulingproblemduetothefollowingtworeasons:First,manycommunicationsystemsarebasedondiscretecharacteristics.Forinstance,mostofthedenitionsinThirdGenerationLongTermEvolution(3GLTE),whichisanOFDMA{basedsystem,arebuiltonanotioncalledtransmissiontimeinterval(TTI),whichisofdiscretenature.Second,schedulingprocessitselfisofdiscretenature:foragiven\unitperiodoftime"eitherschedulingisperformedornot.Thus,!c2Z+providesasuitableapproachfortheanalysis.BoundsarederivedforthepilotcellundertheassumptionthatT1=1T,whichcorrespondstomaximumnumberofschedulingoperationwhereTdenotestheminimumperiodoftimeinwhichonlyoneschedulingoperationcanbeperformed.Becausepurebirthprocessisassumed,systemkeepsevolvingthroughoutT1duetothearrivals.TracloadisusedforquantifyingevolutionofthesystemduringanyschedulingperiodTandexpressedas:rc=(c)AT In(7.1),itisclearthatrc2(0;1)for1Fc.However,caseswhere1
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Intheabsenceofknowledge,bothcellsareassumedtoreservetheirresourcesamongFrandomly.Therefore,probabilitymassfunction(PMF)ofnumberofcollisionsisrequiredinordertocontinuetheanalysis.5Proposition7.3.1(PMFofNumberofCollisions). SincePMFisinhand,anystatisticsdesiredcanbederived.Aswillbeshownsubsequently,(7.2)actuallycontainsthefollowingtwoimportantproperties:(a)expectednumberofcollisionsand(b)breakingpointofcollisions.Itisclearthat(a)isrelatedtotheupperboundandcalculatedbythestatisticalexpectationoperator(i.e.,EfKg).Ergo,noextraexplanationisrequiredhere.Asopposedto(a),(b)isrelatedtothelowerboundandneedsmoredetailedinvestigation.First,(a)isanalyzedwiththefollowing.Corollary7.3.1(ExpectedNumberofCollisionsof(7.2)). ObservethatCorollary7.3.1providesaconstantvalueforexpectednumberofcollisionsbydisregardingtheevolutionofthesystem.However,collisiondoesnotoccurunlessreservedresourcesareassigned.ThisrequiresCorollary7.3.1tobeextendedintermsoftracloadsasfollows:

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Incontrasttoupperbound,lowerboundneedstobeconsideredinthepresenceofknowledgeduetothefollowingreasoning:Denition2explicitlystatesthatnumberofcollisionscannotbelowerthanzero.Therefore,zerocollisionisaveryimportantcharacteristicoflowerbound.However,itcannotbeachievedunlessoneofthecellsisawareofthereservationofitsneighbor,becausecellssupposethatreservationsetsarechosenrandomlyamongFintheabsenceofknowledge,asassumedinProposition7.3.1.WiththesametokeninFootnote3,C1canachievezerocollisionifandonlyifitattainstheperfectknowledgeaboutthereservedsetofC2(orviceversa). Inthissequel,thePMFin(7.2)shouldberelatedwithzerocollisionnotioninaformalway.Inordertoachievethis,rstthefollowingmathematicaltoolisdened.Denition3(BreakingPoint). Denition3andCorollary7.3.3arefollowedbytheidenticationofuniqueregionsin(7.2).Denition4(VulnerableandSecureZone).

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ThediscussionrelatedtoFigure7.2pointsoutthatthereisastrongconnectionbetweenL(orequivalently)andzerocollisions.Inordertoelucidatethisconnection,considertwoidenticalsystemsoneofwhosedesignmightregardEfKgaszerofor1,whereasthatofotheronemighttreatEfKgaszerofor2where16=2.Forthesetwosystems,1and2valuesarethedesign91

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Considerhowbreakingpointevolvesintermsofincreasingcertaintylevel,(i.e.,L!1).Beforeproceedingfurther,rstrecallthatDenition3stipulatesPr(Kk)L
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whererL1isthebendingtracloadofpilotcellandexpressedas:rL1=Hk andXdenotestheconstantpartofUwhenpilotcellapproachisemployedandgivenbyX=r2S:7.4MESandItsPerformance

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In(7.9),itisindicatedthatthebehaviorofLmightbechangedbyintroducingknowledgeacquisitionintothesystemwhenr1rL1,whereasitdoesnotchangewhenrL1
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ObservethatUforr12(0;1]isthesameasUnewforr0120;1=n2,whichistheevidenceofcompressioneectatarateofn.7.5.2SaturationEect whereSmin=min(nX;S).Toproceedfurther,lettheremainingr0121=n2;1intervalbede-composedintothefollowingtwosubintervals:r0121=n2;1=nandr012(1=n;1].BecauseC1canstillacceptnewarrivalswithin1=n2;1=nandr2isassumedtobeconstant,EfKgincreaseswiththesamerate,thatisnmin(nr2S;S),duetothesamereasonsprovidedfor(7.11).Whenthelastsubinterval(1=n;1]isconsidered,1

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Compressionandsaturationeectscanbecombinedtogeneralizetheboundexpressions.From(7.4)and(7.9a),itisclearthattheonlydierencebetweenupperandlowerboundistheknowledgeacquisitionwhereupperboundrepresentstheabsenceofknowledge.Aswillbeshownsubsequently,knowledgeacquisitionallowsonetounifythelowerandupperbounds,whereasprolongedschedulingperiodallows(7.9)tobegeneralized.Since(7.8)isalreadydenedintermsoftracload,Lcanbeexpressedintermsofsandnwiththeaidof(7.9)asfollows:L0=8>>>><>>>>:nSmin(1s)r01;0>><>>>:n(1s)Sminr01;0
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Tobeginwith,upperandlowerboundsareplottedinFigure7.4forr2=0:5.Ascanbeseen,upperboundisaslantwhoseslopeisr2F2z=F,whereaslowerboundobeys(7.13)fors=n=1withrL1=0:9. InordertoseehowMESbehavesunderdierentscenarios,knowledgeacquisitionregimeisemployedinsimulationswhiletheprevioussettingsaremaintained.TheperformanceofMESfors=1isgiveninFigure7.5.Asdescribedearlier,s=1allowsMEStoavoidcollisionbyformingitsassignmentsetasastack.Theimpactofandcorrespondingkisseenwhen0:8r1
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Upuntilnow,T1=Tisconsidered.InordertoseetheimpactofTnew,theperformanceofMESisplottedinFigure7.7forn=2;4;8withr2=0:2ands=0:4.InFigure7.7,boththecompressionandsaturationeectsareclearlyseenwhiler01!0.InordertoexemplifyhowboundsdelineateMES,n=4ischosen.Asstatedin(7.13a),lowerboundfollowsaslantwhoseslopeisn(1s)Smin=19:2for0
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Althoughvoiceisstillconsideredtobethemostdominanttractype,Internetdrawssignicantattentionaswell.ExhibitingverydierenttraccharacteristicsrendersInternetachallengingissueforICImanagement.InvestigatingtheperformanceboundsofschedulersforInternettracisof100

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Symbol Explanation Interior/celledgedistinctionoperator F(I)c PrfEg ProbabilityofKtakingthevaluek EfKg Hk r01 103

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Eventhoughheterogeneousnetworkstructureisaverybigconcernbyitself,terminalswithinthenetworksbringaboutsomeotherissuesforthenextgenerationwirelessnet-works.Inthisregard,itcanbesaidthatthenextgenerationwirelessnetworksneedtoincludeterminalsthatareableto:(I)beawareoftheexistenceofheterogeneousnet-worksaroundand(II)manageseamlesstransitionsbetweenexistingnetworkswhennecessary.Considering(I)and(II)together,onecandeducethatrecentlyemergingtechnologycalledcognitiveradio(CR)canbearemedyforboth,sinceCRsareabletobeawareof,learnabout,andadapttothechangingconditionsinradioenvironment[1].Here,notethattheterm\radioenvironment"hasmanyaspectssuchasphysicalpropagationenvironment,radiofrequencyspectrum,availablenetworksandterminalsaround,andsoon.Becausetheseaspectsarehighlydynamic,capabilitiesofCRsbecomecrucialfromtheperspectiveofbothindividualterminalsandnetworksincludingthem.AlongwithCR,cooperativenetworksconceptshouldalsobeconsideredinthecontextofnextgenerationwirelesssystems.Thecooperativenetworksconceptassumesthatallofthewirelesstechnologiessuchascellularnetworks,wirelesslocal/metropolitanareanet-works,wirelesspersonalareanetworks,shortrangecommunications,anddigitalvideo/audiobroadcastingcancoexistinaheterogeneouswireless-104

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Inadditiontotheconsiderationsrelatedtothecapabilitiesofbothterminalsandnet-works,nextgenerationwirelessnetworksshouldalsoprovidehighdataratetransmissiondespitetheirheterogeneoustopologyandcomplexstructure.Moreover,theyaredesiredtoperformasclosetowirednetworksaspossibleoverwirelessmediumintermsofcosteciencyandofsupportinghighlysophisticatedservicesthatimplyseamlesstransmissionofdierenttractypessuchasvoice,data,andvideo. Handoisdescribedasaprocessoftransferringanongoingcallordatasessionfromoneaccesspointtoanotherinwirelessnetworks.Whenalloftheaforementionedaspectsarecontemplated,itisnotdiculttoconcludethathandowillbeoneofthevitalmechanismsfornextgenerationwirelessnetworks.Traditionalhandoprocess,whichiscalledhorizontalhando,takesplacetoprovideanuninterruptedservicewhenausermovesbetweentwoadjacentcells.Generally,horizontalhandoprocessisinitializedwhenthelinkqualityconditionparameterssuchasreceivedsignalstrengthindicator(RSSI),signal{to{noiseratio(SNR),andsoondropbelowaspeciedhandothreshold.Becausethenextgenerationwirelesssystemsinvolveaheterogeneoustopology,traditionalhandomechanismswillnotbesucient.Therefore,anewtypeofhando,whichisknownas\verticalhando,"isintroduced.VerticalhandoisdenedasaprocesswhichtransfersauserconnectionfromonetechnologytoanothersuchasatransferfromGlobalSystemforMobile(GSM)towirelesslocalareanetwork(WLAN)ortoWorldwideInteroperabilityforMicrowaveAccess(WiMAX).Verticalhandorequiresmoreintelligentalgorithmswhichevaluatemoreparameterssuchasinterferencepower,monetarycost,QoS,remainingenergy,andsooninadditiontoalreadyexistinglinkqualityconditionquantiers.Amongalloftheparameters,interferencemustbetreatedinaseparateplace,sinceeverywirelesssystemisinterferencelimited.Intraditionalcellular-basedsystems,harmfulimpactofinterferenceistriedtoavoid/minimizebyreusingtheavailablefrequenciesindistantcells,whichiscalled\frequencyreuse."Intheliterature,frequencyreuseisquantiedbyafactorcalled"frequencyreusefactor"whichrepresentsthedistinctnumberoffrequencysets(orequivalently,numberofcells)inacluster.Inthisregard,minimumfrequencyreusefactorcanbeoneanditiscalled\frequencyreuseofone(FRO)"oruniversalfrequencyreuse.FROimpliesthateachcellisallowedtousetheentirespectrumavailable.Althoughfrequencyreuseisaveryeectivemethodincombatinginterference,itcomesattheexpenseofinecientspectrumusageand105

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Inthelightofdiscussionsgivenabove,itisclearthatinterference,datarate,andmobilitycon-stitutethethreeprominentaspectsofthenextgenerationwirelessnetworks.Inthisstudy,anewsmartmobileterminal(SMT)isproposed.TheproposedSMTisassumedtohavecognitivecapa-bilitiessuchassensingtheenvironmentperiodicallyforavailableradioaccesstechnologys(RAT),evaluatingtheirworkingconditionsusingitsfuzzylogicbasedalgorithm,triggeringhandoprocessifnecessary,anddecidingthebestaccesspoint(AP)tocampon.Thedecisionisbasedoninterfer-encerate,datarate,andRSSIduetothefollowingreasons:Interferenceratequantieshowseveretheambientco{channelinterference(CCI)powerlevel,dataratetakesintoaccounttheavailabletransmissionrateforapplicationscarriedout,whereasRSSIroughlyhelpstoevaluatethemobil-ity.TheproposedSMTismodeledandsimulatedusingOPNETModelerSoftwareforperformanceevaluation.Besides,thefuzzylogicbasedhandoalgorithmincorporatedinSMTisimplementedinMATLABSoftware.Thecontributionsofthischaptercanbesummarizedasfollows: Theremainderofthepaperisorganizedasfollows:Chapter8.2presentsrelatedworkstotheverticalhandointheliterature.Chapter8.3providestheproposedmodelsforSMT,hando,andbasestation(BS).Chapter8.4includesexampleheterogeneousnetworkscenarioswhichhaveover-106

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Anovelfuzzylogic{basedhandodecisionalgorithmforthemobilesubsystemoftacticalcom-municationssystemsisintroducedin[4].Handodecisionmetricsusedin[4]are:RSSI,theratiooftheusedcapacitytothetotalcapacityfortheaccesspoints,andrelativedirectionsandspeedsofthemobilestoAPs.TheauthorscomparetheiralgorithmwiththeRSSI{basedhandodeci-sionalgorithmaswell.Notethatin[4,Eq.(3)],ambientinterferencepowerisembeddedintotheparameterofcapacity,ratherthanbeingusedasadirectinputtothedecisionprocess. In[5],theauthorpresentsareviewontheproposedverticalhandomanagement,andfocusesonthedecisionmakingalgorithmsinverticalhando.Thearticle[6]presentsatutorialonthedesignandperformanceissuesforverticalhandoinanenvisionedmulti{networkfourth{generationenvironment.In[7],theauthorsgiveafuzzylogicbasedverticalhandoschemeinvolvingsomekeyparametersandthesolutionofthewirelessnetworkselectionproblemusingafuzzymultipleattributedecisionmaking(FMADM)algorithm. Itisconsideredthatadaptationiscrucialfornextgenerationwirelessnetworksfromeveryaspect,suchashandomanagementandscheduling,sinceFROseemstobeoneofthestrongestdeploymentcandidates[8-10].Becauseinterferenceisaverydynamicphenomenon,successoftheadaptationofnextgenerationwirelessnetworksdependsonbeingawareofthefactorsaectingit[11,12].Therefore,thetraditionalfuzzy-basedalgorithmsmightnotbeabletomeettherequirementsofNGWNunlesstheytakeintoaccountinterferenceintheirdecisionprocedures.Tothebestknowledgeofauthors,noneofthefuzzy{basedhandoalgorithmsconsidersambientinterferencepowerlevelasadirectinputtotheirdecisionmechanisms.107

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Figure8.1outlinesthestatetransitiondiagramoftheSMTprocessmodel.TheprocessstartswiththeInitstate.Thisstateperformsadelayuntiltheotherprocessesinthesimulationareinitializedandloadsthecontrolvariables.ThentheprocessenterstheSpectrumScanandHandoDecisionstateswhichareresponsibleforscanningtheenvironmentforavailableAPsandmanagingtheentirehandoprocessexploitingtheproposedfuzzylogic{basedhandoalgorithms.TheWiFiModeandGSMModestatesstandforWiFiandGSMfunctionalities,respectively. Duringthespectrumsensingphase,SMTlistenstowirelessmediumforanyhandobroadcastpacketwhichmightbesentbypotentialAPsforaspeciedtimespan.AlloftheGSMAPshaveabroadcastcontrolchannel(BCCH)whichistherstchannelofallocatedspectrumandisusedforbroadcastingnetworkinformationperiodicallyforpossiblehandoprocessinadditiontoitsotherfunctions.ThedetailedinformationaboutGSMtechnologycanbefoundin[13].TheWiFiAPsbroadcastahandoinformationpacketperiodicallyforthispurposeaswell.Duringthelisteningperiod,theSMTchangesitsworkingparameterssuchasfrequency,modulation,datarate,andbandwidthinordertoadapttoanypossibleAPandtoreceivehandobroadcastpacket.108

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WhenanyAPisavailable,SMTreceivesthehandobroadcastpacketandextractsthenetworkworkingparameters.Ittheninvokesfuzzy{basedhandodecisionalgorithmwhichtakestheseparametersasinputs;processesthem;andproducesanoutputcalledaccesspointcandidacyvalue(APCV).APCVisgenerallydenedbyarealnumberinordertoquantifythestrengthofthecandidacyleveloftheAPfound.Forinstance,APCVcanbedesignedtovarybetweenoneandtenwhereonedenotestheweakest,whereastenrepresentsthestrongestcandidacylevelofquantication.Subsequently,alltheaforementionednetworkparametersalongwithAPCVarestoredinthehandodecisiontable(HDT)forfurtheruse. Allofthesestepsarerepeateduntilthescanprocessisterminated.Ineachturn,SMTlistenstotheenvironmentforpotentialAPs,receivesthehandobroadcastpacketoftheAPfound,calculatestheAPCVusingitsadaptivefuzzyinferencesystem,andstoresallthepiecesofinformationrequiredintheHDT. ThesequencediagramoftheproposedhandodecisionalgorithmisoutlinedinFigure8.2.Thisschemaisrepeatedinevery10sthroughoutthesimulationruntime.109

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Assoonasthescanprocessiscompleted,APCVofeachavailableAPiscomparedwiththatofcurrentAPs.Ifthedierencebetweenthecomparedvaluesisequaltoorgreaterthanthehandoresolution(HR),thatisavaluedeterminedbyuser,thenthesecondcondition,i.e.,mobilespeed,isevaluated.Themobilespeed10km/hisselectedasathresholdvalue.Anyspeedvaluebelowthisthresholdisregardedaswalkingspeedandinthiscase,eitheranyGSMorWiFiAPcanbe110

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Verticalhandodecisionalgorithmshouldinitializehandoprocessconsideringavail-ablenet-workinterfaces(linkcapacity,powerconsumption,linkcost,andsoon),systeminformation(re-mainingbattery),anduser/applicationrequirements(cost,QoSparameters,andsoon).TheblockdiagramoftheproposedhandodecisionsystemisgiveninFigure8.3.111

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Thealgorithmcombinestheuser/applicationrequirementsandnetworkcapabilities,andpro-ducesanoutputwhichisutilizedtomakehandodecisionandtochoosethebestcandidateAP.1Intheproposedhandosystem,therearethreeinputs(datarate,interferencerate,andRSSI)forfuzzyinferencesystem.MembershipfunctionsoftheseinputsaregiveninFigure8.4,Figure8.5,andFigure8.6,respectively.Inthegures,thehorizontalaxisindicatesthecrispvaluesoftheafore-mentionedhandoparameters,whereastheverticalaxis(i.e.,values)standsforthemembershipvalueofrelatedparameter.Thecrispinputsareconvertedintothefuzzyvariablebymeansofthesemembershipfunctions.Trimandtrapezoidshapesarechosenasfuzzymembershipfunctionsduetotheircapabilityofachievingbetterperformanceespeciallyinrealtimeapplications. Thedatarate(DR)inputhastheabilitytochangeitsstructureaccordingtotheapplicationrequirementsaswell.Forinstance,iftheDRrequirementofanapplicationis9:6Kbps(GSMdatatransfer),thenthemembershipfunctionissimilartotheonegiveninFigure8.4.Ontheotherhand,whentheapplicationneedsmorebandwidth,e.g.,25Kbps(GPRSClass6trac),thenitdynamicallychangesitsstructuretoadaptthenewworkingconditionasseenfromFigure8.4. TheinterferencerateparameterisalsoobtainedbyeachAPandsenttotheSMTinordertobeconsideredinhandodecisionprocess.Intheproposedalgorithm,interferenceratereferstoaspecialfuzzylogicvariablewhosevalueisdeterminedbytheambientCCIpowerlevel.InGSM,

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TheRSSIinputofthefuzzysystemhasalsotheabilitytochangeitsstructureaccordingtothenetworkrequirements.TheRSSImembershipfunctionforGSMandWiFinetworksaredierentasshowninFigure8.6. Asstatedearlier,accordingtotheinputsofavailableAPsthefuzzyinferencesystemproducesanoutputvaluebetweenoneandtenwhichdescribesthecandidacylevelofrelatedAP.Anyhandoinitializationprocessisdecideduponthisvalue.Oneofthemostcrucialpartsofthisstudyisthenewadaptivefuzzyinferencesystemwhichisdevelopedinordertomakehandodecision.Afuzzylogicsystemconsistsofthreemainparts:Fuzzier,InferenceEngine,andDefuzzier.Fuzzierconvertsacrispinputintoafuzzyvariablewherephysicalquantitiesarerepresentedbylinguisticvariableswith113

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Figure8.7Examplefuzzyrules.appropriatemembershipfunctions.TheselinguisticvariablesarethenusedinrulebaseofFuzzyInferenceEngine.Sincetherearethreeinputvariableseachhasthreelevels(i.e.,low,medium,andhigh),thereare27rulesusedforproducinganewsetoffuzzylinguisticvariables.SomeofthefuzzyrulesintherulebasearetabulatedinFigure8.7.Forinstance,Rule1correspondstothefollowingIF-THENstructure:ifthepotentialAPsupportslowdatarate,itisinabadinterferencecondition,anditsRSSIisweak,thentheAPCVoftheAPis1,whichmeansitisnotastrongcandidate.Ontheotherhand,Rule21outputsagreaterAPCVvalue,i.e.,10,whichimpliestheAPscandidacylevelisquitehigh. DefuzzierisresponsibleforconvertingthisfuzzyengineoutputintoanumbercalledAPCV.Theoutputofthefuzzysystem,APCV,isthencombinedwiththemobilespeedparametertomakehandodecision.114

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whereDRisdatarate,IRisinterferencerate,andRSisRSSIvalueofavailableAP.Threedimen-sionalfuzzypatternvector(outputoffuzzierandinputofinferenceengine)forcandidateaccesspoints:PVF=[DR1;IR2;RS3](8.2) Sinceproductinferenceruleisutilizedinthefuzzyinferenceenginethen,foranewpatternvector,contributionofeachruleinthefuzzyrulebaseis:Cr=3Yi=1Fi(Pi);(8.3) whereFi(Pi)isthemembershipvalueofthePiforfuzzysetFi,andobtainedfromtheafore-mentionedmembershipfunctions.Thereare27rulesintheproposedsystemandacenteraveragedefuzzierisused.Hence,theoutputofthedefuzzier(i.e.,APCV)becomes:Ma=27Pl=1ylCr whereylistheoutputoftherulel.8.3.3GSMBaseStation Asintheformerprocessmodel,theprocessstartswiththeinitstateaswell,thenenterstheidlestate,andwaitsthereuntilaspecicinterruptarrives.ThefromRxstatemachinedelivers115

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Inthissequel,onemightwonderabouttheimpactoftracloadsofAPspresentintheenvi-ronmentontheperformanceofthemethodproposed.Inbothofthescenariosconsideredinthisstudy,itisassumedthatoneoftheGSMbasestationscanprovidelessdataratecomparedtotheother.Thisassumptionisactuallythecommonconsequenceofthefollowingtwoitems:Either(I)applicationsoftheuserofinterestrequiredierentbandwidths,suchas9.6Kbpsforvoiceapplica-tionand25Kbpsfordatatransmission,or(II)regardlessoftheapplicationrequirementsoftheuserofinterest,GSMbasestationscanoerdierentdataratesforanewcomerduetotheirdierenttracloads.Inotherwords,oneoftheGSMbasestationscanoerlessdatarate,becauseitcannotoerhigherdatarateduetoitshightracloadpresent.Fromthispointofview,resultsforthescenariosconsideredinthisstudyalreadyincludetheimpactoftracloadsofAPspresentintheenvironment. Diameteroftheclusterwhichconstructstheoverallnetworktopologyischosentobefourkilo-meters.Thesimulationwasrunfor3600secondsandotherrelevantparametersaregivenin[13]. Inadditiontothescenarioassumptionsgivenabove,duetoitsimportance,interferenceassump-tionsneedtobeexplainedfurtherforthesakeofcompleteness.Consideringthefactthatdynamicconditionofthemobileradiopropagationenvironmentchangesveryrapidly,thereceivedsignalatareceivercanbedenedformobileradiosbythefollowingtwoprocesses:r(t)=m(t)s(t)(8.5)118

PAGE 134

wherem(t)isthefastfading(i.e.,short{termmultipathfading)componentands(t)isthelocalmean(i.e.,long-termshadowfading)ofthereceivedsignal[17,18].Generally,m(t)ands(t)areidentiedintermsofprobabilitydistributions,sincebotharerandomprocesses.Intheliterature,RayleighandRicedistributionsarefrequentlyassignedtheenvelopeoffornon-line-of-sight(NLOS)andline-of-sight(LOS)cases,respectively.Fieldmeasurementsrevealthatshadowingprocessfollowsalog-normaldistributionwithastandarddeviationwhichisdened,again,inlinearscale[18].Hence,thefollowingformalmodelisadoptedforrepresentings(t):s(t)=e(g(t))(8.6)119

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Inregardtoshadowingprocesss(t),empiricalstudiesshowthatthereisacorrelationinshad-owingwithrespecttodistancebetweentwopointsinthespace.Spatialcorrelationofshadowingisreportedtobeofanexponentiallydecayingform[20].Consideringpracticalpurposes,thereareseveralmodelsproposedintheliterature.Forinstance,[21]denesthenormalizedrelationshipbetweenshadowinganditsspatialcorrelationas:(d)=ed dln2(8.7) whered=5mforindoorandd=20mforoutdoorenvironmentsexemplifyingpracticalscenarios.8.4.2SimulationsandPerformanceAnalysis TherstperformancesimulationsetfocusesonthecaseinwhichSMT1movesalongwiththetrajectoryasillustratedinFigure8.9andFigure8.10ofaspeciedspeed.Thesimulationoftheexamplescenarioshasbeenrunfordierentapplicationsandworkingconditions,i.e.,voicetransferanddatatransfer(9:6Kb/sand25Kb/s),inordertoevaluatetheperformanceoftheproposedapproachcomparatively.Theperformancemetricsexaminedare;APCVofeachavailableAP,numberofhando(s),andaverageend-to-end(EED)delaybetweenSMT1andAPs. Figure8.11illustratestheoutputsofadaptivefuzzylogic{basedhandodecisionalgorithmforavoicetransferapplicationinScenario1.APCVofeachavailableAPiscomputedonceinevery10sduringthespectrumsensingprocessbytheproposedfuzzylogicbasedalgorithmemployedin

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Figure8.12presentsthenumberofhandosasafunctionofHRvalueforScenario1.Asexpected,thenumberofhandosincreaseswhenSMThasalowerHRvalue.Hence,thelowertheHR,thehigherthenumberofhandos.InordertodetermineanoptimumHRvalue,userpreferences,applicationrequirements,and/ornetworkconditionsneedtobetakenintoaccount. Figure8.13illustratestheoutputsofadaptivefuzzylogic{basedhandodecisionalgorithmforScenario2alongwiththesameprocedurecarriedoutinScenario1.NotethatinScenario2,the121

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Figure8.14presentsthenumberofhandosasafunctionofHRvalueforScenario2.ThenumberofhandoincreaseswhenSMThasalowerHRvalue,asinScenario1.AscomparedtotheonegiveninFigure8.12,thenumberofhandoisquitelessinFigure8.14asexpected,sinceGSM1haslowerinterferenceratesmostofthetimesduringthesimulation. Inordertoevaluatetheperformanceofourproposedalgorithmscomparatively,Figure8.15canbeexamined.Figure8.15illustratesthemeasuredGSMandWiFiRSSIresultsasafunction122

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Figure8.14NumberofhandosversusHRforScenario2.123

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InFigure8.16,averageEEDresults(betweenSMT1andAPs)ofdierentapplicationtracsarepresentedasafunctionofthesimulationruntime.TheEEDresultsareobtainedforScenario2whichrepresentsthebetterinterferencerateconditions.NotethatalthoughallofthesettingsusedforScenario2arethesameasthoseforScenario1,themobilitybehaviorofMTsinScenario124

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Whenthedatatransferapplicationwith25Kb/sisrunningonSMT1,aconictbetweendataandinterferenceratearises.Ontheonehand,GSM1observesalowerinterferenceratecomparedtoGSM2.Ontheotherhand,GSM2canprovideahigherDRcomparedtoGSM1.ResultsshowthatGSM2APisselectedafterthedecreaseinDRoeredbyWiFiat300softhesimulationruntime.ThisstemsfromthefactthatfuzzylogicsystemweightsthedataandinterferencerateinputsdierentlybecauseofQoSrequirementsoftheapplicationrunningonSMT1.AscanbeseenfromFigure8.16,theaveragedelayforthisapplicationislowerthanthosefortheotherapplications,sinceGPRSClass6tractypecanbeassigneduptofourslots.8.5Conclusions

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Simulationresultsshowthattheproposedfuzzylogic-basedverticalhandodecisionalgorithmisabletodeterminethemostappropriateaccessnetworkunderdierentdynamicworkingconditions.Moreover,thisstudyrevealsthatinterferenceplaysacrucialroleinmakingverticalhandoforNGWN.126

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Inthisframework,alistofspeciccontributionsindierentchaptersofthisdissertationisgivenbelow.Inwhatfollows,possibleextensionsofthisstudyalongwithfuturedirectionswillbediscussedtoo.9.1ListofSpecicContributions

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S.YarkanandH.Arslan,\ExploitingLocationAwarenesstowardImprovedWirelessSystemDesigninCognitiveRadio,"IEEECommunicationsMagazine,vol.46,no.1,pp.128{136,Jan.2008.[2] H.ArslanandS.Yarkan,CognitiveRadio,SoftwareDenedRadio,andAdaptiveWirelessSystems(SignalsandCommunicationTechnology).Springer,2007,ch.EnablingCognitiveRadioThroughSensing,Awareness,andQuantication.[3] S.YarkanandH.Arslan,\Exploitinglocationawarenesstowardsimprovedwirelesssystemdesignincognitiveradio,"PatentFiled,2006,uSFRef.No.07A006PR.[4] H.ArslanandS.Yarkan,\RealTimeMeasurementsforAdaptiveandCognitiveRadioSys-tems,"EURASIPJournalonWirelessCommunicationsandNetworking,vol.2009,pp.1{15,2009,doi:10.1155/2009/202909.[5] S.YarkanandH.Arslan,\IdenticationofLOSandNLOSforwirelesstransmission,"inPro-ceedingsofIEEECognitiveRadioOrientedWirelessNetworksandCommunications,CROWN-COM2006,vol.1,no.1,MykonosIsland,Greece,June07{11,2006,pp.1{6.[6] ||,\IdenticationofLOSintime{varying,frequencyselectiveradiochannels,"EURASIPJournalonWirelessCommunicationsandNetworking,no.4,pp.1{14,2008.[7] S.Yarkan,A.Maaref,K.H.Teo,andH.Arslan,\ImpactofMobilityontheBehaviorofInterferenceinCellularWirelessNetworks,"inProc.IEEEGlobalCommunicationsConference(GLOBECOM2008),NewOrleans,LosAngeles,U.S.A.,Nov.30Dec.4,2008.[8] K.H.Teo,S.Yarkan,H.Arslan,andA.Maaref,\Methodformanaginginterferenceinamobilenetwork,"PatentFiled,2009,MERL{2029.[9] S.Yarkan,H.Arslan,andK.H.Teo,\IdenticationofShadowedFastFadingInterferenceinCellularMobileRadioSystems,"IEEECommunicationsLetters,2009,underreview.[10] K.H.Teo,S.Yarkan,andH.Arslan,\Methodfordecidingwhetheramobileterminalresideininterferencezoneforfrequencydivisionduplexwirelesscommunicationsystems,"PatentFiled,2009,MERL{2048.[11] S.Yarkan,K.H.Teo,H.Arslan,andJ.Zhang,\UpperandLowerBoundsonSubcarrierColli-sionforInter{cellInterferenceSchedulerinOFDMA{BasedSystems:VoiceTrac,"PhysicalCommunication,2009,underreview.[12] K.H.Teo,S.Yarkan,andH.Arslan,\Methodforschedulingresourcetoreduceinter-cellinterferenceforvoicecommunicationinofdmanetworks,"PatentFiled,2009,MERL{2137.[13] C.Ceken,S.Yarkan,andH.Arslan,\InterferenceAwareVerticalHandoDecisionAlgorithmforQualityofServiceSupportinWirelessHeterogeneousNetworks,"ComputerNetworks,no.10.1016/j.comnet.2009.09.018,2009,toappear.130

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S.YarkanandH.Arslan,\StatisticalWirelessChannelPropagationCharacteristicsinUn-dergroundMinesat900MHz,"inProceedingsofIEEEMilitaryCommunicationsConference,MILCOM2007,Orlando,Florida,U.S.A.,Oct.29{31,2007.[15] S.Yarkan,S.Guzelgoz,H.Arslan,andR.R.Murphy,\UndergroundMineCommunications:ASurvey,"IEEECommunicationsSurveys&Tutorials,vol.11,no.3,pp.125{142,3rdQuarter2009.[16] S.Yarkan,S.Guzelgoz,andH.Arslan,\WirelessChannelPropagationCharacteristicsinUn-dergroundMines:AStatisticalAnalysisandARadioControlledRobotExperiment,"inProc.ThesecondIEEEInternationalConferenceonWirelessCommunicationsinUndergroundandConnedAreas(ICWCUCA),Val{d'Or,Canada,Aug.25{27,2008,acceptedforpublication.[17] ||,\StatisticalWirelessChannelPropagationCharacteristicsinUndergroundMinesat900MHz:AComparativeAnalysisWithIndoorChannels,"IEEETransactionsoninstrumentandMeasurement,2009,underreview.[18] S.Guzelgoz,S.Yarkan,andH.Arslan,\InvestigationofTimeSelectivityofWirelessChannelsthroughtheUseofRVC,"PhysicalCommunication,2009,underrevision.[19] S.YarkanandH.Arslan,\BinaryTimeSeriesApproachtoSpectrumPredictionforCognitiveRadio,"inProc.66thIEEEVehicularTechnologyConference,[VTC2007{Fall],Baltimore,Maryland,U.S.A.,Sep.30{Oct.3,2007,pp.1563{1567.[20] S.Yarkan,H.Arslan,andK.H.Teo,\OnShadowedFrequency-SelectiveInterferenceandReportingPeriodforBroadbandWirelessCommunicationNetworks,"IEEETransactionsonWirelessCommunications,2009,underreview.[21] J.MitolaIII,\Cognitiveradioanintegratedagentarchitectureforsoftwaredenedradio,"Ph.D.dissertation,KTHRoyalInstituteofTechnology,Stockholm,Sweden,May8,2000.[Online].Available: http://www.it.kth.se/jmitola/Mitola Dissertation8 Integrated.pdf [22] H.Arslan,SignalProcessingforMobileCommunicationsHandbook,M.Ibnkahla,Ed.BocaRa-ton,FL:CRC.CRCPress,2004,ch.28,AdaptationTechniquesandtheEnablingParameterEstimationAlgorithmsforWirelessCommunicationSystems,pp.28{1{28{26.[23] T.S.Rappaport,WirelessCommunications:PrinciplesandPractice,2nded.,ser.PrenticeHallCommunicationsEngineeringandemergingTechnologiesSeries.NewJersey,U.S.A.:Prentice{Hall,Inc.,2002.[24] A.Committee,\231:Digitalmobileradiotowardsfuturegenerationsystems{nalreport,"EuropeanCommunities,Tech.Rep.,1999.[25] ITU{R,\GuidelinesforevaluationofradiotransmissiontechnologiesforIMT{2000,"ITU{R,Tech.Rep.RecommendationITU{RM.1225,1997.[26] C.E.Shannon,\TheMathematicalTheoryofCommunication,"TheBellSystemTechnicalJournal,vol.27,pp.379{423;623{656,July,October,1948.[27] K.L.Blackard,T.S.Rappaport,andC.W.Bostian,\Measurementsandmodelsofradiofrequencyimpulsivenoiseforindoorwirelesscommunications,"IEEEJournalonSelectedAreasinCommunications,vol.11,no.7,pp.991{1001,Sep.1993.[28] R.S.Blum,R.J.Kozick,andB.M.Sadler,\AnAdaptiveSpatialDiversityReceiverforNon{GaussianInterferenceandNoise,"IEEETransactionsonSignalProcessing,vol.47,no.8,pp.2100{2111,Aug.1999.131

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T.K.Sarkar,Z.Ji,K.Kim,A.Medouri,andM.Salazar-Palma,\Asurveyofvariouspropaga-tionmodelsformobilecommunication,"IEEEAntennasandPropagationMagazine,vol.45,no.3,pp.51{82,Jun.2003.[30] W.R.BraunandU.Dersch,\Aphysicalmobileradiochannelmodel,"IEEETransactionsonVehicularTechnology,vol.40,no.2,pp.472{482,May1991.[31] H.Arslan,L.Krasny,D.Koilpillai,andS.Channakeshu,\Dopplerspreadestimationforwirelessmobileradiosystems,"inProc.IEEEWCNCConf.,vol.3,Chicago,IL,Sep.2000,pp.1075{1079.[32] M.Sakamoto,J.Huoponen,andI.Niva,\AdaptivechannelestimationwithvelocityestimatorforW-CDMAreceiver,"inProc.IEEEVeh.Technol.Conf.,vol.3,Tokyo,Japan,May2000,pp.2024{2028.[33] C.TepedelenliogluandG.B.Giannakis,\Onvelocityestimationandcorrelationpropertiesofnarrow{bandmobilecommunicationchannels,"IEEETransactionsonVehicularTechnology,vol.50,no.4,pp.1039{1052,Jul.2001.[34] D.MottierandD.Castelain,\AdopplerestimationforUMTS-FDDbasedonchannelpowerstatistics,"inProc.IEEEVeh.Technol.Conf.,vol.5,Amsterdam,Netherland,Sep.1999,pp.3052{3056.[35] L.Wang,M.Silventoinen,andZ.Honkasalo,\AnewalgorithmforestimatingmobilespeedattheTDMA-basedcellularsystem,"inProc.IEEEVeh.Technol.Conf.,vol.2,Atlanta,GA,May1996,pp.1145{1149.[36] C.Xiao,K.Mann,andJ.Olivier,\MobilespeedestimationforTDMA-basedhierarchicalcellularsystems,"inProc.IEEEVeh.Technol.Conf.,vol.2,Amsterdam,TheNetherlands,Sep.1999,pp.2456{2460.[37] W.C.Y.Lee,MobileCommunicationsEngineering.NewYork:McGraw-HillInt.,1982.[38] M.AustinandG.Stuber,\Eigen-baseddopplerestimationfordierentiallycoherentCPM,"IEEETrans.Veh.Technol.,vol.43,pp.781{785,Mar.1994.[39] G.Pollini,\Trendsinhandoverdesign,"IEEECommun.Mag.,vol.34,no.3,pp.82{90,Mar.1996.[40] J.H.A.Sampath,\Estimationofmaximumdopplerfrequencyforhandodecisions,"inProc.IEEEVeh.Technol.Conf.,Secaucus,NJ,May1993,pp.859{862.[41] L.Lindbom,\Adaptiveequalizationforfadingmobileradiochannels,"Licentiatethesis,Tech-nologyDepartment,UppasalaUniversity,Uppasala,Sweden,1992.[42] M.Morelli,U.Mengali,andG.Vitetta,\Furtherresultsincarrierfrequencyestimationfortransmissionsoveratfadingchannels,"IEEECommun.Lett.,vol.2,pp.327{330,Dec.1998.[43] L.Krasny,H.Arslan,D.Koilpillai,andS.Channakeshu,\Dopplerspreadestimationinmobileradiosystems,"inProc.IEEEWCNCConf.,vol.5,no.5,May2001,pp.197{199.[44] K.Kawabata,T.Nakamura,andE.Fukuda,\Estimatingvelocityusingdiversityreception,"inProc.IEEEVeh.Technol.Conf.,vol.1,Stockholm,Sweden,Jun.1994,pp.371{374.[45] H.ArslanandT.Yucek,\Delayspreadestimationforwirelesscommunicationsystems,"inProc.TheEighthIEEEsymposiumoncomputersandcommunications(ISCC'2003),Antalya,Turkiye,Jul.2003,pp.282{287.132

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M.C.Wells,\Super{ResolutionBroadNullBeamformingforCo{channelInterferenceCan-cellationinMobileRadioNetworks,"IEEProceedings{Communications,vol.143,no.5,pp.304{310,Oct.1996.[125] P.D.KaraminasandA.Manikas,\Super{ResolutionBroadNullBeamformingforCo{channelInterferenceCancellationinMobileRadioNetworks,"IEEETransactionsonVehicularTech-nology,vol.49,no.3,pp.689{697,May2000.[126] L.Matabishi,\TheoreticalImplementationofAntennaPolarizationtoImprovetheReduc-tionofCo{channelInterferenceinMobileCellularSystems,"inProc.IEEEInternationalSymposiumonMicrowave,Antenna,PropagationandEMCTechnologiesforWirelessCom-munications(MAPE2005),vol.1,Beijing,China,Aug.8{12,2005,pp.431{433.[127] R.Menon,A.B.MacKenzie,R.M.Buehrer,andJ.H.Reed,\AGame{TheoreticFrameworkforInterferenceAvoidanceinAdhocNetworks,"inProc.IEEEGlobalTelecommunicationsConference(GLOBECOM'06),vol.1,SanFrancisco,California,U.S.A.,Nov.27{Dec.1,2006,pp.1{6.[128] T.WeissandF.K.Jondral,\Spectrumpooling:aninnovativestrategyfortheenhancementofspectrumeciency,"IEEECommunicationsMagazine,vol.42,no.3,pp.S8{14,Mar.2004.[129] Y.-D.YaoandA.U.H.Sheikh,\InvestigationsintoCo{channelInterferenceinMicrocellularMobileRadioSystems,"IEEETransactionsonVehicularTechnology,vol.41,no.2,pp.114{123,May1992.[130] B.C.JonesandD.J.Skellern,\AnIntegratedPropagation{MobilityInterferenceModelforMicrocellNetworkCoveragePrediction,"WirelessPersonalCommunications,vol.5,pp.223{258,1997.[131] Huaewi,\FurtherAnalysisofSoftFrequencyReuseScheme,"3GPPTSGRAN,London,U.K.,AgendaItem10.2.1R1{050841,Aug.29{Sep.2,2005,WG1#42,Discussion&Decision.[132] Ericsson,\AdditionalRSRPreportingtriggerforICIC,"3GPPTSGRAN,Shenzhen,China.,AgendaItem6.3.3R1{0801536,Mar.31{Apr.04,2008,WG1#52bis,Discussionanddecision.[133] Ericsson,\PhysicalLayerMeasurementPeriodofUEMeasurements,"3GPPTSGRAN,SophiaAntipolis,France,AgendaItem4.6R4{070407,Apr.2{4,2007,WG4#42bis,Dis-cussion.[134] A.GhasemiandE.S.Sousa,\Opportunisticspectrumaccessinfadingchannelsthroughcollaborativesensing,"JournalofCommunications,vol.2,no.2,p.71,Mar.2007.[135] Y.MaandJ.Jin,\EectofChannelEstimationErrorsonM{QAMWithMRCandEGCinNakagamiFadingChannels,"IEEETransactionsonVehicularTechnology,vol.56,no.3,pp.1239{1250,May2007.[136] S.A.AbbasandA.U.Sheikh,\AGeometricTheoryofNakagamiFadingMultipathMo-bileRadioChannelwithPhysicalInterpretations,"inProc.IEEE46thVehicularTechnologyConference,vol.2,Atlanta,Georgia,U.S.A.,Apr.28{May1,1996,pp.637{641.[137] M.Patzold,U.Killat,andF.Laue,\ADeterministicDigitalSimulationModelforSuzukiPro-cesseswithApplicationtoaShadowedRayleighLandMobileRadioChannel,"IEEETrans-actionsonVehicularTechnology,vol.45,no.2,pp.318{331,May1996.[138] X.CaiandG.B.Giannakis,\ATwo{DimensionalChannelSimulationModelforShadowingProcesses,"IEEETransactionsonVehicularTechnology,vol.52,no.6,pp.1558{1567,Nov.2003.138

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X.Kai,T.Xiaofeng,W.Ying,andZ.Ping,\Inter{cellpacketschedulinginofdmawirelessnetwork,"inProc.IEEE65thVehicularTechnologyConference(VTC2007{Spring),Dublin,Ireland,Apr.22{25,2007,pp.3115{3119.[155] T.Kwon,H.Lee,S.Choi,J.Kim,D.-H.Cho,S.Cho,S.Yun,W.-H.Park,andK.Kim,\Designandimplementationofasimulatorbasedonacross-layerprotocolbetweenMACandPHYlayersinaWiBroCompatibleIEEE802.16eOFDMAsystem,"IEEECommunicationsMagazine,vol.43,no.12,pp.136{146,Dec.2005.[156] A.Fernekeb,A.Klein,B.Wegmann,andK.Dietrich,\InuenceofTracModelsandSchedul-ingontheSystemCapacityofPacket{SwitchedMobileRadioNetworks,"inProc.15thISTMobileandCommunicationsSummit,Mykonos,Greece,Jun.2006,pp.1{5.[157] H.Lei,X.Zhang,andY.Wang,\Real{TimeTracSchedulingAlgorithmforMIMO{OFDMASystems,"inProc.IEEEInternationalConferenceonCommunications(ICC'08),Beijing,China,May19{23,2008,pp.4511{4515.[158] D.Jiang,H.Wang,E.Malkamaki,andE.Tuomaala,\PrincipleandPerformanceofSemi{PersistentSchedulingforVoIPinLTESystem,"inProc.Intl.Conf.onWirelessComm.,Networking&MobileComp.,Shangai,China,Sep.21{25,2007,pp.2861{2864.[159] 3GPP,\LTEphysicallayerframeworkforperformanceverication,"3rdGenerationPartner-shipProject(3GPP),St.Louis,Michigan,U.S.A.,TSGRANWG1Meeting#48R1{070674,Feb.12{16,2007,Decision.140

PAGE 157

AmongK1selections,thenumberofselectionsthatyieldsexactlykcollisionsisgivenby: Thisstemsfromthefactthat,ifmin(F1;F2)oftheresourcesarereservedamongF,thenremainingnumberofresourcesintheneighboringcellthatmightcausecollisionissimplyFmin(F1;F2).AmongFmin(F1;F2)resources,ifexactlykresourcesarecolliding,thenkresourcescanbeconsideredasreserved(sincetheyarecolliding,theywillbeintheselectionsanyway).Thisimpliesthat,remainingselections(numberofresources)arereducedtomax(F1;F2)k.Hence,thetotalnumberofselectionsamongthissetisexpressedbyK2.Thenumberofallpossibledierentorderingsforkresourcescausingcollisionsamongmin(F1;F2)isK3=min(F1;F2)k:Sincetheprobabilityspace,namelyKS,isknownandthenumberofallpossibleselectionsaredened,thedesiredprobabilitymassfunction(PMF)canbeobtainedby:142

PAGE 158

whichistheequivalentof(7.2)andthiscompletestheproof. 143

PAGE 159

Ifallofthecommontermsinthesummationareregrouped,thenitreads:EfKg=Mmin(FMmin)! Whenthedenominatorsinthesummationareequalizedwithappropriatecoecients,(B.2)becomes: {z }A1Mmin1Yq=k(FMmaxMmin+q+1)| {z }A2:(B.3) In(B.3),foragivenk,considersumofrstandlasttermsofproductsA1andA2,respectively(i.e.,j=2andq=Mmin1).Ifachangeofvariableisappliedforthiscasewithsumofthesetwoterms144

PAGE 160

Finally,onecanexpandallofthefactorialsandproductsandsimplify(B.4)furtherto:EfKg=MminMmax whichconformswith(7.3)inCorollary7.3.1andcompletestheproof. 145

PAGE 161

Therefore,foranygivenLsatisfyingL2[Pr(K=0);1),therealwaysexistsauniquepair(k;k+1)inPcorrespondingtokandthiscompletestheproof.