E14-SFE0004894.pdf

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Guzelgoz, Sabih
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Characterizing wireless and powerline communication channels with applications to smart grid networks
h [electronic resource] /
by Sabih Guzelgoz.
260
[Tampa, Fla] :
b University of South Florida,
2011.
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Title from PDF of title page.
Document formatted into pages; contains 142 pages.
Includes vita.
502
Disseration
(Ph.D.)--University of South Florida, 2011.
504
Includes bibliographical references.
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Text (Electronic dissertation) in PDF format.
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ABSTRACT: Smart grid aims at improving the efficiency, reliability, security, and quality of service (QoS) of the current electricity grid by exploiting the advances in communication and information technology. In parallel to size of the electricity grid, smart grid communication infrastructure should cover a very large geographical area that may extend from remote generation sites to densely populated residential regions and inside buildings, homes, and electricity-power-system environments. In such an extensive communication network, different communication technologies operating on different communication medium are likely to coexist. Among the communication technologies available, wireless and power line communication (PLC) based solutions are comparatively attractive especially considering cost of the initial investment required for the realization of a communication network with such an immense size. In this dissertation, a detailed investigation of wireless and PLC channel characteristics of the smart grid networks is presented. Among the topics discussed are the time variation characteristics of wireless channels, root-mean-squared (RMS) delay spread and path amplitude statistics of PLC channels, and the impact of impulsive noise on orthogonal frequency division multiplexing (OFDM) systems.
538
Mode of access: World Wide Web.
System requirements: World Wide Web browser and PDF reader.
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Advisor:
Arslan, Huseyin .
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Impulsive Noise
Ofdm
Powerline Communication Channel Characterization
Smart Grid Communication Environments
Wireless Communication Channel Characterization
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Dissertations, Academic
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x Electrical Engineering
Doctoral.
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t USF Electronic Theses and Dissertations.
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u http://digital.lib.usf.edu/?e14.4894



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Iowemuchtomyfriendsandseniors:Dr.MustafaEminSahin,Dr.HishamMah-moud,Dr.SerhanYarkan,Dr.HasariCelebi,Dr.TevkYucek,Dr.IsmailGuvenc,IbrahimDemirdo~gen,HasanBasriCelebi,TayyarGuzel,MuradKhalid,OmarZakaria,Is-mailButun,JamalHaque,SadiaAhmed,AliGorcin,EvrenTerzi,Dr.BahattinKarakaya,Dr.CelalCeken,Dr.BilalBabayi~git,AliRzaEkti,OzgurYurur,Ca~gatayTalay,HazarAk,AlphanSahin,MemhetBahadrCelebi,MuratKarabacak,AhmedH.Mehanna,EmreSeyyal,KosolSon,LokmanAkbay,SalihErdem,SalimErdem,SenerGultekinandMustafaCenkErturk.Ilearnedsomanyvirtuesfromthem.Sincerefriendshiptostartwith,un-selshness,tolerance,andhelpfulness. Mysincereappreciationgoestomyparentsandmyyoungersisterfortheirsacriceandunconditionalsupportaswellasmyparentsinlawandsistersinlaw.Iwillalwaysbeindebtedtothemthroughoutmylife. Last,butbynomeansleast,mydeepestgratitudefrommyheartgoestomywife,Ozden,forherlove,allthesacricesshemade,herrmsupport,hervastpatience,andhersteadyencouragementforalmostfouryearsnow.Finally,IliketoextendmygratitudetomyunbornkidforaddingexcitementtothenalyearofmyPhDprogram.

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LISTOFFIGURESv ABSTRACTviii CHAPTER1INTRODUCTION1 1.1DissertationOutline4 1.1.1Chapter2:WirelessandPLCPropagationChannelCharacteristicsforSmartGridEnvironments5 1.1.2Chapter3:InvestigationofTimeSelectivityofWire-lessChannelsThroughtheUseofRVC6 1.1.3Chapter4:ArticulatingFactorsDeningRMSDelaySpreadinLVPLCNetworks7 1.1.4Chapter5:StatisticalCharacterizationofthePathsinMultipathPLCChannels7 1.1.5Chapter6:HandlingBurstyImpulsiveNoiseinOFDM8 1.1.6OtherWorksDone8 1.1.6.1AnalysisofaMulti-ChannelReceiver:Wire-lessandPLCReception9 1.1.6.2TimeFrequencyAnalysisofNoiseGener-atedbyElectricalLoadsinPLC10 1.1.6.3DemandCharacterizationandEstimationforElectricVehicleChargingStations11 CHAPTER2WIRELESSANDPLCPROPAGATIONCHANNELCHARACTER-ISTICSFORSMARTGRIDENVIRONMENTS13 2.1Introduction13 2.2PropagationMechanism18 2.3WirelessChannelCharacteristics19 2.3.1MultipathCharacteristics22 2.3.1.1TimeDispersion22 2.3.1.2TimeSelectivity23 2.3.1.3AmplitudeStatistics24 2.3.2NoiseCharacteristics24 2.4PLCChannelCharacteristics26 2.4.1MultipathCharacteristics26i

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2.4.1.2TimeSelectivity28 2.4.1.3AmplitudeStatistics28 2.4.2NoiseCharacteristics29 2.5ConcludingRemarks30 CHAPTER3INVESTIGATIONOFTIMESELECTIVITYOFWIRELESSCHAN-NELSTHROUGHTHEUSEOFRVC34 3.1Introduction34 3.2WirelessChannelModel,DopplerSpectrum,andMotionScenarios36 3.2.1WirelessChannelModelandDopplerSpectrum36 3.2.2MotionScenarios37 3.2.2.1MotionofTransmitter/Receiver37 3.2.2.2MotionofSurroundingObjects40 3.3MeasurementSystemandProcedure42 3.4MeasurementResults45 3.4.1ImpactofFrequencyofOperationandSpeed45 3.4.2ImpactofMotionIntensityonDopplerSpectrum48 3.4.3ImpactofAOAStatisticsonDopplerSpectrum48 3.5Discussion50 3.5.1EectiveFactorsonDopplerSpectrum51 3.5.2RealizationofTheoreticalDopplerSpectruminRVCs51 3.6ConcludingRemarks54 CHAPTER4ARTICULATINGFACTORSDEFININGRMSDELAYSPREADINLVPLCNETWORKS56 4.1Introduction56 4.2PLCMultipathChannelModelandRMSDelaySpread59 4.2.1Reection/TransmissionCoecientatBranching60 4.2.2Reection/TransmissionCoecientatTerminationPoints61 4.3ImpactofAttenuationandLoadingonRMSDelaySpread62 4.4ImpactofthePhysicalCharacteristicsofthePLCChannelonRMSDelaySpread70 4.5ConcludingRemarks73 CHAPTER5STATISTICALCHARACTERIZATIONOFTHEPATHSINMUL-TIPATHPLCCHANNELS75 5.1Introduction75 5.2MultipathPropagationandAnalysisoftheFirstArrivingPath77 5.2.1MultipathinPLCChannels77 5.2.2AnalysisoftheFirstArrivingPath78 5.3Discussion89 5.4ConcludingRemarks92ii

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6.1Introduction94 6.2SystemModel97 6.3AnalysisoftheNullingOperationattheReceiver99 6.4OFDMReceiverStagesAfterNulling105 6.4.1SampleReplacementBasedIterativeCancellationTechnique105 6.4.2SuccessiveCancellationTechnique107 6.5NumericalResults108 6.6ConcludingRemarks113 CHAPTER7CONCLUSIONANDFUTUREWORK116 7.1ListofSpecicContributions116 7.2FinalCommentsandFutureWork118 REFERENCES119 ABOUTTHEAUTHOREndPageiii

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Figure1.2Measurementresults:I-dimmerandII-drill.11 Figure2.1Integratingcustomerwithsmartgrid.16 Figure2.2PropagationmechanismsforwirelessandPLCchannels.19 Figure3.1Geometryofmovingreceivercase.38 Figure3.2Dopplerspectrumformovingreceivercase.39 Figure3.3Geometryformovingobjectscase.40 Figure3.4Dopplerspectrumwithmovingobjectscasefordierentvaluesofm.42 Figure3.5Pictorialdescriptionofthemeasurementsetup.43 Figure3.6MappingbetweenfactorsaectingDopplerinphysicalenvi-ronmentandstimuliconditionsforRVCexperiments.46 Figure3.7Dopplerspectrogramofthemeasurements.47 Figure3.8ImpactofoperatingfrequencyandspeedonDopplerspectrum.47 Figure3.9ImpactofmotionintensityonDopplerspectrum.49 Figure3.10ImpactofabsorbersonDopplerspectrumat910MHz.50 Figure3.11Ellipticmotionofascatterer.52 Figure3.12TheoreticalapproximationofclassicalJakes'Dopplerspec-trumwithinRVCs.52 Figure3.13ObtainingJakes'classicalDopplerspectrumwithxedreceiverconguration.54 Figure4.1Reection/Transmissioncoecientsatbranchingandtermination.60 Figure4.2T-networktopology.63v

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Figure4.4PDFoftheRMSdelayspreadofT-networktopologywhennodeCisrandomlyloaded.69 Figure4.5CDFoftheRMSdelayspreadofT-networktopologywhennodeCisrandomlyloaded.69 Figure4.6GraphicalillustrationofthePLCnetworktopologyconsideredinthestudy.72 Figure4.7DependencyofRMSdelayspread(rms)onthenumberofnodes(b)betweentransmitterandreceiverwhenseparationdistancebetweentransmitterandreceiveris150mandbranchlengthsareassumedtobeuniformlydistributedover[10m-30m].72 Figure4.8DependencyofRMSdelayspread(rms)ontheseparationdistance(d)betweentransmitterandreceiverwhennumberofnodesbetweentransmitterandreceiveris4andbranchlengthsareassumedtobeuniformlydistributedover[10m-30m].73 Figure4.9DependencyofRMSdelayspread(rms)onthelengthstatis-ticsofbrancheswhennumberofnodesbetweentransmitterandreceiveris4andseparationdistancebetweentransmitterandreceiveris150m.74 Figure5.1Analysisoftherstarrivingpath.79 Figure5.2Reectionatabranchingnode.80 Figure5.3MeanofYwithdierentvaluesofx.82 Figure5.4VarianceofYwithdierentvaluesofx.83 Figure5.5ResultsofKStestforthevericationofGaussianityassump-tionwithZ0=50andde=U[1,1].86 Figure5.6MeanofYwithZ0=50andde=U[25,25].87 Figure5.7VarianceofYwithZ0=50andde=U[25,25].88 Figure5.8MeanofYwithZ0=50andde=U[25,25]whenthenum-berofbranchesareU[3,xaxis]andthenumberofnodes(x)isassumedtobe10.89 Figure5.9VarianceofYwithZ0=50andde=U[25,25]whenthenumberofbranchesareU[3,xaxis]andthenumberofnodes(x)isassumedtobe10.90vi

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Figure6.2ICIpowercontributionversuscarrierindexforN=64withnormalizedunitypowervalue.102 Figure6.3BERperformanceforN=256andK=25whenreplacementbasediterativedecodingisemployed.110 Figure6.4BERperformanceforN=256andK=25whensuccessivesymboldetectionisemployed.111 Figure6.5BERperformanceforN=256anddierentvaluesofKatSNR=30dB.112 Figure6.6BERperformanceforN=256andK=50whenreplacementbasediterativeandsuccessivesymboldetectiontechniquesareemployedwith3iterations.113 Figure6.7BERperformanceforN=256andK=50whenreplacementbasediterativedecodingwithproposedtransmissionschemeisemployed.114 Figure6.8BERperformanceforN=256andK=50whensuccessivesymboldetectionwithproposedtransmissionschemeisemployed.115 Figure6.9BERperformanceforN=256withdierentvaluesofKandnormalizeddelayspreadvaluesatSNR=30dB.115vii

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Inthisdissertation,adetailedinvestigationofwirelessandPLCchannelcharacteristicsofthesmartgridnetworksispresented.Amongthetopicsdiscussedarethetimevariationcharacteristicsofwirelesschannels,root-mean-squared(RMS)delayspreadandpathampli-tudestatisticsofPLCchannels,andtheimpactofimpulsivenoiseonorthogonalfrequencydivisionmultiplexing(OFDM)systems.viii

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AtransmitsignalgoesthroughvariousdistortionsonitswaytoreceiverinbothwirelessandPLCchannels.Avarietyofparametersisemployedwhilequantifyingthesedistortionsincommunicationchannels.Inwirelesscommunications,theconceptofpathlossisusedtocapturehowthepowerofthetransmitsignalvariesasafunctionofdistance.ItisdenedasthedB(decibel)valueoftheratioofthetransmitpowertothereceivedpower.Presenceoftheobstaclesbetweentransmitterandreceivergivesrisetorandomuctuationsofpathlosscalledshadowingthatisusuallydenedwithlog-Normalprobabilitydensityfunction(PDF)asveriedbymeasurementcampaignsovertheyears.Sincevariationsduetopathlossandshadowingtakeplaceoverrelativelylargedistances,thesetwovariationsaretradi-tionallyreferredtoaslarge-scalepropagationeectsbywirelesscommunicationcommunity.Inaddition,thedrasticchangesinthereceivedsignalpowerforshortdisplacements,whichareontheorderoffewwavelengths,areknowntobeconsequencesofsmall-scaleeects.Theunderlyingreasonbehindthesedrasticchanges,whicharecapturedbythenotionofpathamplitudestatistics,isrelatedtothemultipathphenomenonandtimevariationofthewirelesscommunicationchannel,duetomotioningeneral.Quanticationofthesmallscaleeectsisachievedwithtwodierentparametersthatarecloselyrelatedtomultipathpropagationandtimevariationofthewirelesschannels:delayspreadandDopplerspread.Atransmitsignalcantraveltothereceiverbyfollowingdierentpathsthatmayinvolveavarietyofpropagationmechanismssuchasreection,diraction,andscattering.Thus,multiplereplicasoftheoriginaltransmitsignalarriveatthereceiverwithdierentdelays.Delayspreaddescribestheextentofthetimedispersionofthewirelesschannel.Incon-nectionwiththedelayspreadparameterintimedomain,coherencebandwidth,whichisinverselyproportionaltodelayspread,isusedtodescribethechannelinthefrequencydomainrevealingthechannel'sfrequencyselectivitycharacteristics.Inthisrespect,timedispersionandfrequencyselectivitycharacteristicsofacommunicationchannelareanalo-2

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InPLCdomain,aslightlydierentterminologyisusedfordeningcommunicationchannelcharacteristics.Therelationshipbetweentransmitpowerandreceivedpoweriscapturedthroughtheconceptofattenuation.Similartowirelesschannels,atransmitsig-nalarrivesatthereceiverbyfollowingdierentpathsleadingtotimedispersionthataremainlygovernedbyasinglepropagationmechanism,whichisreectionmostlyasaresultofimpedancemismatchesinthenetworksseenbythetransmitsignalalongitspropagationpath.Delayspreadandcoherencebandwidthareusedtodescribetheextentoftimedisper-sionandfrequencyselectivitycharacteristicsofPLCchannels,respectively.TimevariationisalsoanimportantattributeofPLCchannels.Unlikewirelesschannelsinwhichtimevariationisrelatedtomotioningeneral,timevariationinPLCchannelsisclassiedaslongtermandshorttermvariationsandstemsmainlyfromthevaryingimpedanceconditionsinthepowerlinenetwork(PLN).Longtermvariationisrelatedtothecontinuouslyvary-ingimpedanceconditionsatterminationpointsasthedevicesconnectedtothePLNareswitchedon/o,whereasshorttermtimevariationofthePLCchannelstemsfromthefactthatimpedanceofmostelectricalloadsisdependentonAlternatingCurrent(AC)mainscycle. Besidesdistortionscausedbythefrequencyandtimeselectivitynatureofcommuni-cationchannels,noisecharacteristicsarealsoofparamountimportanceconsideringtheperformanceofcommunicationsystems.Inwirelesscommunicationchannels,noiseisas-sumedtobeadditivewhiteGaussianwithaatpowerspectrummainlyduetomathemat-icaltractability.However,interferencewithimpulsivenaturewhichismostlyreferredto3

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Ascanbeseenfromthedissertationstructure,somechaptersfocussolelyoneitherwirelesschannelorPLCchannel(Chapters3-4-5),whereasdiscussionsinsomeotherchap-4

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Asapartofwirelesscommunicationchannelcharacterizationeorts,radiopropagationcharacteristicsofundergroundminesarediscussedin[6{8].InlinewithPLCchannelchar-

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Scarcityofspectrumandinterferencealongwiththenewconceptsintroducedsuchascognitiveradio(CR)[20]arethemainmotivationsbehindthisstudy.Forinstance,CRsaresupposedtosensethespectrumanddetectwhitespacesbeforecommencingtransmissioninordertomakesurethattheydonotcauseanyharmfulinterferencetoprimaryusers.ConsideringscarcityofavailablewhitespacesandtheabundanceofsecondaryusersforbothwirelessandPLCenvironmentsforfuturecommunicationapplications,thecapabilityofaccessingbothmediumcouldbeofgreatvalueforthecontinuityofreliablecommunica-tion.Incaseofthesuitabilityofbothmediumsforcommunication,CRsmaychangetheirstrategiesandstartusingbothcommunicationchannelsinordertobecomemorerobustto9

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EachdeviceconnectedtothePLNhasauniquenoisestructure.Thisuniquenesscanbeemployedforseveralsmartgridapplications.Forexample,providingstatisticsofthedevicestohouseholdisverycrucialfromtheperspectiveofenergymonitoring.Inthissense,asmartmeterthatisdesignedtoprocessthesenoisesignaturesandmapthemintocorrespondingdevicetypemightbeofgreathelpwhileinformingtheusersabouttheirenergyusestatistics.10

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ArticulationofstatisticalcharacteristicsofpowerdemandattheCSsisbasedonunder-standingtheactivitiesoftheEVsattheCSs.EachEVislikelytooccupyaCSforacertaindurationoftime.EVsmaycontinuouslydrawpowerfromthegridovertheentiredurationoftheirparkingtimeortheymightbeidle(stopdrawingpowerfromthegrid)foracertain11

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Understandingofthesmartnessintheterm\smartgrid"hasbeenrapidlyexpandedbytheindustryfromsmartmeteringthatismorefocusedonadvancedmeteringinfrastructure(AMI)1totruesmartgrid[21].Withthisrecentlyendorseddenition,objectivesofthesmartgridcanbesummarizedasfollows[22]:

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Objectivesofthesmartgridrequirethecollectionofvarioustypesofinformationre-gardingelectricitygeneration,consumption,storage,transmission,anddistributionthroughitscommunicationinfrastructure.Consideringthisrequirement,smartgridcommunicationinfrastructureshouldcoveraverylargegeographicalareathatmayextendfromremotegenerationsitestodenselypopulatedresidentialregionsandinsidebuildings,homes,andelectricity-power-systemenvironments.Indeed,supervisorycontrolanddataacquisition(SCADA)systemshavebeenimplementedtomonitorandcontrolelectricitygridtosomeextentforsometime[23].However,denitionofsmartgridclearlynecessitatesthede-velopmentofamorecomplicatedtwo-waycommunicationarchitecturebeyondcurrentlyemployedrelativelyinsecureSCADAsystemsforalargerscalemonitoringandcontrol. Inordertobetterunderstandthecommunicationneedsofthesmartgrid,itmightbeagoodstrategytonarrowdownthescopeandfocusonlyononeofitsobjectives\integratingcustomersintothegrid"whichreceivesthemostattentionintermsofplanningandinvest-ment.Theunderlyingreasonforcustomerintegrationistomaximizetheeciencyofthedistributionnetworkbyencouragingthecustomertoreacttosometypeofstimulicomingfromtheutility.Theopportunitieswiththecustomerintegrationincludes:1.providingcus-tomerswithnewpricingoptions,2.detectingpoweroutageswithautomaticvericationofrestoration,3.enablingcustomerstorespondtopricingandloadcontrolsignals,4.enablingcustomerstomonitor,control,andschedulelocalenergyconsumptionformaximizingthebenetsregardingcostofelectricityusageandutilizationofthedistributionnetwork. Itisobviousthatcommunicationinabroaderperspectiveliesinthecoreofthecus-tomerintegration.First,acommunicationinfrastructurebetweenhomedevicesand\smartmeter"shouldbesetupsothat\smartmeter"cancollectinformationfromthedevicesandtakeinitiativetoadjustthelocalconsumptionconsideringthecustomerpreferences.Sec-ond,acommunicationlinkbetween\smartmeters"andtheutilityshouldbeestablishedso14

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Wirelessandpowerlinecommunication(PLC)basedsolutionsareverypromisingandattractivecomparedtotheotheroptionsconsideringthecostofinitialinvestmentrequiredforthesmartgridcommunicationinfrastructure[27].Whileaddressingthecommunica-tionneedsofsmartgrid,twostrategiescanbefollowed.Oneoftheapproachesisbasedonintegratingexistingcommunicationstandards(e.g.IEEE802.11,IEEE802.15.1,IEEE

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Inspiteofbeingcosteectivesolutionsforsmartgridapplications,wirelessandPLCenvironmentsareveryharshposinggreatchallengestoreliabilityandperformanceofcom-municationsystems.Inthisrespect,objectiveofthisstudyistoarticulatethechannelcharacteristicsofbothwirelessandPLCchannelsinsmartgridenvironmentsintermsofseveralfactorsincluding: Theremainderofthechapterisorganizedasfollows.Section2.2providesareviewofpropagationmechanismseectiveinwirelessandPLCenvironments.Section2.3givesthedetailsofwirelesscommunicationcharacteristicsofsmartgridenvironments.DetailsregardingPLCchannelsarediscussedinSection2.4.Finally,theconcludingremarksaregiveninSection2.5.

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ThepropagationinPLCchannelsismostlygovernedbyreections.InPLCsys-tems,atransmitsignalpropagatingfromonelocationtoanothersuersfromreectionsatimpedancediscontinuitiesalongitspath.Branchingandimpedanceappearingattheterminationpointsarethemainsourceofimpedancediscontinuityinpowerlinenetworks(PLNs)givingrisetoreections.ThesemechanismsareillustratedinFig.2.2. Duetothepropagationmechanismseectiveinbothenvironments,whenasignalisemittedbyatransmitter,thesignalreceivedatthereceiverconsistsofattenuated,delayed,andphase-shiftedreplicasofthetransmitsignalleadingtotimedispersion.Incommu-nicationscommunity,signicanceoftimedispersionisquantiedbyaparametercalledroot-mean-squared(RMS)delayspread.RMSdelayspreadforbothcommunicationmedi-umsistobediscussedinamoredetailedwayinthesubsequentsections.Besidestimedispersioncharacteristic,bothwirelessandPLCchannelsaretimeselectiveaswell.Mo-bility(orrelativemotionbetweentransmitterandreceiverfromabroaderperspective)isthemainreasonbehindtimeselectivityofwirelesschannels,whereasthereasonfortimeselectivityinPLCchannelsisrelatedtothevaryingimpedanceconditionsinthePLNespe-18

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Figure2.2PropagationmechanismsforwirelessandPLCchannels.2.3WirelessChannelCharacteristics

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whered0isthereferencedistanceinthefareldofthetransmitantenna,nisthepathlossexponent,andXdenotesarealzeromeanGaussianrandomvariable(RV)withaparticularstandarddeviation.Xisreferredtoasshadowingandaccountsfortheimpactoftheterrainproleonthetransmitsignal.Notethatpossessionofknowledgeregardingtwoparameters,whicharenand,whilecharacterizing(2.1)isessential.Bothnandareenvironmentaldependentparametersandmaychangesignicantlydependinguponcommunicationmediumprole.Smartgridcommunicationinfrastructureislikelytobedeployedinavarietyofcommunicationenvironments.Amongthesedeploymentoptionsare: Notethatadistinctionbetweenindoorandelectric-power-systemfacilityhasbeenmadeintheclassicationgivenabove.Thisisduetothefactthatelectric-power-systemenviron-mentshaveverydiscriminativefeaturescomparedtoregularindoorenvironmentssuchasprevalenceofmetallicstructure,dierentnoisecharacteristicsthatmaystemfromcoronaeectorswitchingoperations,hostilityintermsoftemperatureandhumidity,etc.Stem-mingfromthesedierences,furtherdiscussionisbuiltupontheclassicationgivenabove. Mostoftheresultsreportedintheliteratureregardingindoorcommunicationenviron-mentsarebasedonmeasurementscarriedoutataround900MHzand1:9GHz.Pathlossexponent(n)foravarietyofindoorpropagationenvironmentsrangefrom1:2to6[43{46].20

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Thetypicalvaluesforpathlossexponent(n)foroutdoorenvironmentsrangesfrom2:7to6:5dependingupontheenvironmentalcharacteristics[50].Forinstance,recommendedvalueofpathlossexponentbyITUis4forbothurbanandsuburbanareas[49].Itisalsoworthmentioningthatruralareaswithatterrainshouldassumelowervaluesofn.Shadowingforurbanenvironmentsistypically810dB[51].ITUconsidersastandarddeviationvalueof10dBasappropriateforbothurbanandsuburbanareas[49]. Thenumberofstudiesforcharacterizingtheradiopropagationmediumwithinelectric-power-systemenvironmentsisverylimitedintheliterature.Anexperimentalstudyindierentelectric{power{systemenvironmentsincludinga500kVsubstation,anindustrialpowercontrolroom,andanundergroundnetworktransformervaultreportsthatpathlossexponentnvariesfrom1:45to3:55dependinguponline-of-sight(LOS)and(NLOS)conditionsbetweentransmitterandreceiver[52].Shadowingvaluesintheseenvironmentsarefoundtobebetween2:25dBand3:29dB.21

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whereN(t)representsthenumberofresolvablemultipathcomponentsattimet,ar(t)istheamplitudeofther-thmultipathcomponent,r(t)denotesthephase,r(t)representsthearrivaltime,and()istheDiracdeltafunction.2.3.1.1TimeDispersion

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Intheliterature,timedomainsamplesoftheentirenoiseprocess(backgroundnoisecorruptedwithimpulsivenoise)isveryfrequentlyrepresentedbyamixtureofzeromeancomplexGaussianvariableswithdierentvariancesandoccurrenceprobabilitiesasfollows:f(n)=LXl=0pIg(nj2I);(2.3) wherepI'sdenotemodelparameterswhosesumshouldequalunityandg(nj2I)isthePDFofthecomplexGaussianvariablewithzeromeanand2Ivariance.Notethat(2.3)isageneralizationofBernoulli{GaussianandMiddletonClass-Amodelsasnotedin[66].Inspiteofbeingwidelyusedforthepurposeofanalysis,thismodelismemorylessandlacksrepresentingtheburstynatureofimpulsivenoise[67].Inordertoincorporateitsburstynatureintoanalysis,Markovmodeliscommonlyemployed[67,68].EmployingMarkovmodelalongwithapersistenceparameterwhichsigniesmemoryofthechannelmayturnthismemorylessmodelintoaburstymodelformingamorerealisticanalysisplatform.25

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wherefanddcorrespondtofrequencyofthesignalandthedistancecovered,respectively.a0,a1,andkareallcabledependentparametersandaremostlyextractedbyempiricalmeasurements[69].2.4.1MultipathCharacteristics whereandTcorrespondtothereectionandtransmissioncoecientsalongthepropaga-tionpath,respectively,A(f;di)meansthefrequency{and{distancedependentattenuationstemmingfromthephysicalcharacteristicsofthecable,andexp(j2fi)referstothephaseoftheithcomponentduetothetimedelay.KandMrepresentthenumberofreectionandtransmissioncoecientsexperiencedbythepropagatingsignalalongapar-ticularpathdenotedbythesubscripti.Finally,itisworthmentioningthatmultiplicationof'sandT'sin(2.5)isreferredasthereectionfactor(jrijeji)ofaparticularpropaga-tionpath.Notethati,thetimedelay,isrelatedtothespeedofpropagationwithinthecommunicationmedium,powerlinecablesinourconsiderationasfollows:i=dip

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InspiteofconfusionandunclarityinRMSdelayspreadcomputationinPLCliterature,valuesreportedin[73,74]showthatitismostlyontheorderof23swithafewexceptionsashighas56sforafrequencyrangeupto30MHz.Anotherveryextensivestudythatconsidersthesitemeasurementsof120channelsinthe1:830MHzrangerevealsthattheRMSdelayspreadismostlybelow1:31swithonlytwoexceptionsofchannelresponsesthatexhibitahighervalue1:73sand1:81s[75].Similarly,RMSdelayspreadvaluesreportedoverthesamefrequencyrangerevealsthatitissmallerthan0:5sfor99%ofthestudiedchannels[76].Also,asimilarstudyconductedoverafrequencyrangeupto30MHzreportsthat95%ofthechannelshaveanRMSdelayspreadvaluebetween240nsand2:5s[77].Anotherstudywhichconsidersalargerfrequencybandupto100MHzndsoutthat80%ofthechannelsexhibitRMSdelayspreadvaluesbetween0:06sand0:78swithameanvalueof0:413suponconductingextensivemeasurementcampaignsbyobtaining144transferfunctionscollectedfrom7sites[78].Inconclusion,typicalRMSdelayspreadvaluesinLVPLCchannelsareontheorderoffewmicroseconds.27

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Modelsproposedregardingthenoisecategoriesmentionedaboveareallbasedonem-piricalmeasurementcampaigns.Themainapproachundertakenwhilemodelingtheback-groundnoiseisbasedonitsfrequencydomaincharacterization.OneofthemethodstocharacterizethebackgroundnoiseistoexpressitasafunctionoffrequencybyusingitsttedPSD[87].Themajordownsideofthisapproachisthattherandombehaviorofthenoiseprocessisnotconsideredatall.Inordertoincorporateitsrandomnatureintoanal-29

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Asanalnote,noticethatmostoftheprecedingdiscussionsarededicatedtotheLVPLCchannels.However,thisdoesnotnecessarilyimplythatothersegmentsofthePLNcannotbeconsideredforthepurposeofcommunicationinspiteofsomereliabilityrelatedconcerns9[93{95].However,althoughHVpowerlinesserveasacommunicationmediumforvoiceforalongtimedatingbackto1920s[96],theliteraturedeningitschannelcharacteristicsisalmostinexistent.RegardingthecommunicationchannelcharacteristicsofMVchannels,althoughthereisnotmuchstudyintheliterature,somegeneralconclusionscanstillbedrawn.SimilartoLVPLCchannels,MVlinesexhibittimedispersion.RMSdelayspreadvaluesofMVPLCchannelsareontheorderof10s.TimevariationofthechannelisveryweakandtheamplitudestatisticsobeyNakagami-mdistribution[97].Inadditiontothesemultipathrelatedparameters,noisecomponentsofMVpowerlinesareusuallyverysimilartothoseofLVpowerlineswithsomediscriminativefeaturessuchasthedominanceofcoronadischargesinthebackgroundnoise[98].2.5ConcludingRemarks

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Wireless Powerline Highlydependentonthepropagationenvironmentofinterestswithextensiveresultsreportedintheliterature DependentonthecharacteristicsofcableusedinthePLN Timedispersion/Freq.selectivity Governedbyreection,diraction,andscattering Governedbyreectionsmainlyduetoimpedancediscontinuitiesalongthepropagationpath Timeselectivity/Freq.dispersion Mobilityoftransmitter/receiverpairsormotionofsurroundingobjects Impedancevariationsoverbothlongandshortterm PathAmplitudes MostlyassumedRayleighorRiceandependingonNLOS/LOScondition Merelyresemblesshadowingeectinwirelesschannelsandmostlyassumedtoobeylog-NormalPDF Noise MostlyassumedAWGN,presenceofimpulsivenoiseincertainenvironments Morecomplicatednoisestructure:coloredbackgroundnoise,narrowbandnoiseandimpulsivenoiseveryeective sideringthecostofinitialinvestment.Beingcosteectivesolutions,twoapproachesarelikelytoemerge:integrationofalreadyexistingPLCandwirelesstechnologiesintothegridwithsomemodicationsregardingQoS,latency,reliability,powerconsumption,etcordevel-opingnovelcommunicationprotocolsparticularlyaddressingthesmartgridcommunicationneeds.Nomatterwhatapproachistaken,adeepunderstandingofthecommunicationchan-nelcharacteristicsofsmartgridenvironmentsisessential.Inthisstudy,communicationcharacteristicsofbothPLCandwirelessenvironmentswerediscussedindetail.Smartgridwirelessdeploymentoptionswereclassiedroughlyasindoor,outdoorandelectric-power-systemenvironments.SimilarmethodologywasfollowedinPLCenvironmentsaswellbyclassifyingthemasLV,MV,andHV. Amongthecommunicationchannelcharacteristicsdiscussedwerepathlossandattenua-tion,timedispersion,timeselectivity,pathamplitudesandnoisecharacteristicsasoutlined31

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Itisworthmentioningthatsomeaspectsofthesmartgridneedsfurtherinvestigationintermsofcommunicationchannelcharacteristics.Forinstance,amorein-depthunder-standingoftheradiopropagationcharacteristicsinelectric-power-systemenvironmentsisessentialforthedesignofreliablewirelesscommunicationsystemsinthesmartgrid.Simi-larly,mostoftheresearcheortsinPLCchannelsarededicatedtotheLVsideofthePLNandlackofliteratureinMVandHVPLCchannelssuggestsamorecomprehensivelookattheseenvironments.33

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Selectivityisastatisticaltoolthatisusedforcharacterizingwirelesschannels.Formally,selectivityisdenedinbothtimeandfrequencydomains.Timeselectivityisusedtocharacterizetheconsequencesofmotion[99].TimeselectivitymanifestsitselfintransformdomainasaspectralbroadeningwhichisknownasDopplerspread.ImpactofthespreadisgenerallyevaluatedthroughtheobservationofDopplerspectrum. Itisknownthatdierentpropagationenvironmentsandmotionbehaviorsleadtodier-entDopplerspectrumcharacteristics.Inordertoachieveareliablewirelesscommunicationssystem,itisrequiredthatallsortsofpropagationcharacteristicsshouldbewellunderstood.Furthermore,theentirecommunicationsystemmustbeevaluatedundervarioustransmis-sionconditionswhosecharacteristicshavebeenderivedbasedonarduousexperimentaleldtests.Amongthesepropagationcharacteristics,Dopplerphenomenonisoneofthemost34

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TheRVCisaclosedcavitywhichisgenerallyofmetallicstructure.Whenitisexcitedempty,ithasmanywell-behavedpropagationmodeswhichleadtogreatelectromagnetic(EM)eldvariations[100].AstirrerisrotatedtorandomizethemaximaandminimalocationsoftheEMeldmagnitudesgivingrisetoamoreuniformeldmagnitudedistri-butionthroughoutthechamber.RotationofthestirrerinsidetheRVCcausesalsoDopplerspreadinthereceivedsignal.AlthoughtherearenotmanyDopplerrelatedRVCstudiesintheliterature,someresearchcanstillbefoundintheframeworkofabroaderperspective.In[101]whichcanbeconsideredtorelateDopplerdirectlytoRVC,theauthorsderivearelationbetweenthespeedofstirrerandmaximumobservedDopplerfrequency.AnotherDopplerrelatedstudyforRVCscanbefoundin[102]whichcomparestheexperimentalresultswiththeJakesspectrum.Theauthorsclaimthatthereisadiscrepancybetweenthemodelandtheexperimentalresultsstemmingfromthedimensionalassumptionsinsig-nalpropagation.Incontrasttothepreviousstudies,anindirectrelationbetweenDopplerandRVCisestablishedin[103]fromthetimedomainperspective.Similarly,in[104],multiple-inputmultiple-output(MIMO)performanceanalysisfornonisotropicpropagationenvironmentsisperformedinanRVC.However,asconcludedbytheauthors,nonisotropicpropagationenvironmentsneedtobefurtherinvestigatedespeciallyintermsofmotionrelatedparameters. ThestudypresentsthendingsofthemeasurementcampaignswithinanRVCthatareperformedtomakeacompletecharacterizationoftheDopplerbehavior.Theobjectivescanbesummarizedasfollows:

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Theremainderofthechapterisorganizedasfollows.Section3.2givestheanalyti-calbackgroundforwirelesschannelmodelandDopplerspectruminthelightofspecicmotionscenarios.Section3.3providesthedetailsofmeasurementsystemandprocedureemployedinthestudy.Section3.4elaboratestheoutcomesoftheexperimentsconducted.Section3.5discussestheeectivefactorsonDopplerspectrumandtherealizationoftheo-reticalDopplerspectrainRVCssuchasJakes'model.Finally,theconcludingremarksaregiveninSection3.6.3.2WirelessChannelModel,DopplerSpectrum,andMotionScenarios

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In(3.1),theimpactofthemobilitymanifestsitselfinthephaseterm,namelyr(t),foreachtap(delay).Dopplerspreadinthereceivedwaveformsiscausedbytheinstantaneouschangesinr(t)stemmingfromthedierencesinthepathdistancebetweenreceiverandtransmitterantennasoveraverysmalldurationoftime.Inordertocharacterizetheprop-agationchannel,thestatisticalbehaviorofthetaps(delays)in(3.1)overtimeshouldbeinvestigated.Channelcorrelationfunctionisusedasatoolinordertoevaluatethisstatis-ticalbehavior.TransformdomaincounterpartofchannelcorrelationfunctionisknownasDopplerspectrum.SincedierentmotionscenariosleadtodierentDopplerspectra,itisappropriatetoinvestigatethemindividually.Subsequently,thefollowingfundamentalmo-tionscenarioswillbethefocus:motionoftransmitter/receiverandmotionofsurroundingobjects.3.2.2MotionScenarios3.2.2.1MotionofTransmitter/Receiver AreceivermovingwithaparticularspeedofvisconsideredintheanalysisasdepictedinFigure3.1.Althoughthereceivertravelsveryshortdistanceovertheintervaloft,phasesoftheraysarrivingthereceiverfromdierentangleschangedrastically.Theassumptions37

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Forthesakeofsimplicityandeaseofanalysis,milderassumptionscanbeemployedsuchasconstantarrivingraypowerlevels,uniformlydistributedrayarrivalangles,omni-directionalantennapattern,andsoon.NotethatallthesesimpliedassumptionscanbeformallyexpressedbythefollowingzerothorderBesselfunctionoftherstkindwhenthechannelcorrelationfunctionisconsideredfortherthtap:Efh(t;r)h(t+t;r)g=Rh(t)=J0(2fDt);(3.2) Figure3.1Geometryofmovingreceivercase. whereEfgisthestatisticalexpectationoperator,()denotesthecomplexconjugateofitsinput,tisthetimeshiftinthecorrelationoperation,andfDismaximumDopplerfrequency.MaximumDopplerfrequency,namelyfD,isrelatedtothecarrierfrequencyofthetransmitsignalandtothespeedofthemobileas(vfc)=cwherecisthespeedoflight.TheFouriertransformof(3.2)whichcorrespondstoDopplerspectrumisknownasJakes'38

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Whenaparticularreceivervelocityisassumed,graphicalrepresentationoftheDopplerspectrumremindsofthefamousbathtub-likeshapeasdepictedinFigure3.2.NotethatfrequencyaxisisnormalizedbythemaximumDopplerfrequencyfDwherethecarrierfrequencyfcisrepresentedwithf=0.Intheliterature,severalmeasurementsperformedwiththistransmitter-receivercongurationapproximatethisDopplerbehavior[56,105].ItisworthmentioningthattheassumptionsconsideredintheanalysisofJakes'modelareverystrongandnotapplicableinmostofthepropagationenvironments.However,Jakes'Dopplerspectrumisvastlyusedintheliteratureforcomparisonpurposesoftheexperimentaldataorofsomeothertheoreticalmodels[102]. Figure3.2Dopplerspectrumformovingreceivercase.39

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Figure3.3Geometryformovingobjectscase. CorrespondingDopplerspectrumwhichistheFouriertransformof(3.4)canbecomputedas:RH(f)=8>>>><>>>>:2 whereK()impliesthecompleteellipticintegral.Dopplerspectrumindicatedby(3.5)isvalidifalltherayscomeacrossamovingobjectbeforearrivingthereceiver.Thisisnot40

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Theabove-mentionedideacandirectlybeincorporatedintothechannelcorrelationfunctionaswell.Ifafactor,namelym,denotestherayscomingfromthemovingobjectswithvariousvelocitiesthatcanbedenedbyaprobabilitydensityfunction(PDF)and1mtheraysreectedfromstationaryobjects,thechannelcorrelationfunctiontakesthefollowingform[58]:Rh(t)=(1m)+mEfJ20(2fcVt=c)g(3.6) Notethat(3.6)stillincludesastatisticalexpectationtakenoverVwhichistherandomvariablecharacterizingthespeedofsurroundingobjects.Inordertoexemplifythis,consideratypicalresidentialenvironment.Insuchenvironments,mostofthetimemotioniscausedbypedestrianswhosespeedisof3m/s.InordertoemphasizetherandomnessofVandincorporatetheeectofthemotionofotherpossibleobjects,itisreasonabletoassumethatithasaPDFwhichisdistributedover(0;3]m/s.Notethatin(3.6)thisrandomnessisweightedbythefactormwhichiscalledmotionintensity. Motionintensityarticulatesthesignicanceofmotioninaparticularenvironment.ItformsaplatforminwhichDopplerspectrumcharacteristicsofdierentmotionscenarioscanberelatedtoeachother.Forinstance,thescenariogiveninSection3.2.2.1correspondstothecasewheremotionintensityisequaltounity,whereasthescenariogiveninSec-tion3.2.2.2correspondstoamotionintensityfactoroflowerthanunity.Thisreasoningstemsfromthefactthatm=1representsabsolutemotionwhichcanbeinterpretedaseachrayarrivesatthereceiverfromasourceinmotion.Furthermore,thecasewherem=0impliesanabsolutestationaryenvironmentinwhichthereexistsnomotionatall.41

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DierentDopplerspectrumshapesstemmingfromdierentmotionintensityfactorsmaregiveninFigure3.4.WhilederivingtheplotinFigure3.4,thespeedofthesurroundingobjectsareallassumedtobethesame.Itcanbenoticedthatasthemotionintensityoftheoperatingenvironmentdecreasesmeaningthatthelessamountofraysbeingreectedbymovingobjects,thespectrumsignicantlychanges.Recallthatasthemotionintensityapproachestozero,theDopplerspectrumconvergestoaDiracdelta.Thisisveryintuitivesinceitisexpectedthatnospreadisobservedinanabsolutestationaryenvironmentasmentionedearlier. Figure3.4Dopplerspectrumwithmovingobjectscasefordierentvaluesofm. UponintroductiononthenatureofDopplerspreadexaminedwithdierentscenarios,subsequentsectionsdealwithitscharacterizationintheRVCs.3.3MeasurementSystemandProcedure

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Figure3.5Pictorialdescriptionofthemeasurementsetup. InordertoextracttheDopplercharacteristicsofthewirelesspropagationchannelbetweentransmitterandreceiverantennaswithintheRVC,twotonesat910MHzand2410MHzweretransmittedviaAgilentE4438CESGVSG.AgilentE4440APSAseriesVSA43

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whereWdenotesthespanofthebandwidthtobecapturedbythedeviceandfscorre-spondstothedesiredsamplingrate.Inallofthemeasurements,thespanoftheVSAwassettoW=8kHzcorrespondingtofs=10:24kHzofsamplingrate. CapturedwaveformwhichisprovidedbyAgilentE4440APSAseriesVSAasI/Qcom-plexdatasamplesneedstobeprocessedsothattheDopplerspectrumisrevealed.Thepost-processingstagestepsareasfollows:

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TheeectofoperatingfrequencyandthespeedofthestirreronDopplerspectrumcanbeseenbyobservingthespectrogramofthereceivedsignalasshowninFigure3.7,namelythrough(a)-(d).Ifthegureisinvestigatedeitheralongthehorizontalaxisoralongtheverticalaxis,itisclearthatanexpansionoccursinthefrequencyspectrumoftransmittedsignal.Thisexpansionisemphasizedbythedashedrectangularboxesplacedontheright-handsideofeachsubgure.2Notethat,thesizeofeachrectangularboxexpandsbothinthedirectionofoperatingfrequencyandinthedirectionofstirrerspeed.ThisshowsthatanincreaseinoperatingfrequencyorstirrerspeedgivesrisetoanexpansioninDopplerspectrum.Notealsothattheamountofexpansioncausedeitherbytheoperatingfrequencyorbythestirrerspeedevolveslinearly.Thisisnotsurprisingsincetheverywell-knownDopplershiftequation(vfc)=cisalinearfunctionofbothoperatingfrequencyandspeed. Inordertobetterseetheeectofspeed,timefrequencyanalysis(TFA)canbeprojectedontosolelyfrequencydomainyieldingtheDopplerspectrum.Figure3.8(a)and3.8(b)plottheresultsfor910MHzand2410MHzoftwodierentstirrerspeeds,respectively.Ascanbeclearlyseenfromthegures,thetendencyofthecurvesindicatesthattheenergyspreads

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Figure3.7Dopplerspectrogramofthemeasurements. Inlightofthemeasurementresultspresentedinthissection,itisconcludedthattheenvironmentinsideanRVCisseentoyieldaDopplerspectrumthatissimilartothemotionscenariooutlinedin3.2.2.2. (b)f=2410MHzFigure3.8ImpactofoperatingfrequencyandspeedonDopplerspectrum.47

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(b)f=2410MHzFigure3.9ImpactofmotionintensityonDopplerspectrum.thereceiverhavingcontributionsonlyfromsomeparticularanglesisexpectedtoyieldadierentDopplerspectrum(usuallymoreasymmetric)fromthetraditionalones. ItisworthmentioningthatthespeedofthestirrerissettoitshighestvalueduringtheexperimentspresentedinthissubsectionsincethepurposeisonlytoseethechangeintheDopplerspectrumwithregardtotheAOA.Dopplerspectrumwasanalyzedbeforeandaftertheintroductionoftheabsorberssothattheireectcouldbecomparativelyseen.Intheexperiments,absorberswerelocatedaroundthereceiverantennainawaythatitremindsacubicshape.OnlyonesideofthecubicshapewasopeninsidetheRVCallowingthewirelesssignaltoarriveatthereceiverantennafromthisparticularangle. Theresultoftheexperimentat910MHzisshowninFigure3.10.ItisseenthattheDopplerspectrumappearstohaveamoresymmetricstructurepriortoplacingtheab-sorbers.Notethatthegurehasbeenzoomedinsothattheasymmetrycanbeobservedinaclearerway.Introducingtheabsorbersinordertoblockwirelesssignalpropagatingfromcertainanglesdestroyedthesymmetricstructureofthespectrumtosomeextent.Atthispoint,itisessentialtomentionthatuseoftheabsorberstohaveasymmetricDopplerspectrumdoesnotseemtobetheonlysolution.Basedupontheexperienceoftheauthors,itwasseenthatthelocationoftheantennaandthestirrerwithintheRVCplayarole49

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Figure3.10ImpactofabsorbersonDopplerspectrumat910MHz.3.5Discussion

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Figure3.11Ellipticmotionofascatterer. ConsiderthecaseinwhichascatteringobjectismovinginaparticulardirectionasshowninFigure3.12.IfananalysissimilartotheonepresentedinSection3.2.2.2isper-formed,itisseenthatthedelayonaparticularpropagationpathduetothemovementofthereector,andthecorrespondingphasechangebecome2Vtcos=cand4fcVtcos=c,respectively.Assumingthatthereceiverantennaisomnidirectionalandisuniformlydis-tributedover(,],thefollowingchannelcorrelationisobtainedasafunctionoftimeosett:Rh(t)=1 2Zej4fcVtcos=c=J0(4fDt)(3.8) Figure3.12TheoreticalapproximationofclassicalJakes'DopplerspectrumwithinRVCs. NotethatthisisverysimilartothechannelcorrelationfunctionobtainedinJakes'modelgivenby(3.2).However,itisworthmentioningthatthespeedofmobilemustbehalvedinordertoachievethesamemaximumDopplerfrequencyastheclassicalJakes'model.This52

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2Zej4fcVtcos=c=(1m)+mJ0(4fDt)(3.9) Itispracticallyverydiculttodesignanenvironmentwithmequalsonewithxedreceiverandsurroundingobjectsinmotion.However,themotionintensityofthewirelesspropagationenvironmentwithintheRVCcanbeincreasedbyplacingmoremovingobjectsinsideasshowninSection3.4.2. Figure3.13showstheclassicalDopplerspectrumandtheDopplerspectrumwhichisobtainedfromthemodeldepictedinFigure3.12withthesameconstantspeedvalue.Itisseenthatbyintentionallyaligningthedirectionofthemovingobjectswithrespecttothetransmitandreceiverantennas,classicalJakes'spectrummaybeapproximated.However,animpulseatthezerofrequencyisalwaysobservedduetotherayscomingfromstationaryobjects.Thepowerofthisimpulsemaybereducedbyincreasingthemotionintensityoftheenvironment,i.e.introducingmoremovingobjects.ItisalsoseenthatthemaximumDopplerfrequencyobtainedduetothemotionofthesurroundingobjectsistwicetheclassicalJakes'shapewiththesamespeedvalue. ItistheoreticallyshownthatitispossibletoapproximateclassicalJakes'spectrum;however,thepracticalvericationneedssometechnicalcapability.Insummary,itiscon-cludedthattheclassicalJakes'spectrumcanbegeneratedwithinanRVCbyintelligentlyadjustingthemotionpatternaswellasthelocationofthetransmitter-receiverantennapairs.3

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Inthisstudy,DopplerphenomenoncausedbymotionisinvestigatedinRVCsbyelabo-ratingthekeyfactorssuchasoperatingfrequency,speed,AOA.Inaddition,motionintensitywhichcanbeconsideredasaformalgeneralizationofwirelesschannelmobilitycharacter-isticsisintroducedanditsconsequencesarediscussed. Also,averywell-knownJakes'Dopplermodeliscomparedwiththeexperimentalnd-ings.ItisobservedthatthereisasignicantdiscrepancybetweenJakes'modelandthe54

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Althoughitisobviousthattheeldtestsyieldthemostreliableresultsregardingtheperformanceofwirelesscommunicationsystems,concernsincludingcostandtimeconsump-tionwhileperformingthesetestsforcetohavealternativeapproaches.RVCsarepromisingcandidatesinthisaspect.However,themainhurdleforRVCstobeareliablereplacementtoeldtestsliesintheirdesign.Therefore,RVCdesignshouldbeimprovedinasensethatitiscapableofemulatingvariousmotionscenarioswithminormodications.55

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FuturePLCbasedsystemsareenvisionedtoprovideveryhighdataratesrequiringwidebandtosupporthigh{qualitymultimedia.ThepopularityofwidebandPLCespeciallyinlowvoltage(LV)networksforlast{inchapplicationsisgrowing[109,110].Inwidebandcommunicationchannels,multipathinducedinter-symbolinterference(ISI)isoneofthephenomenathatleadstoperformancedegradation.Incommunicationscommunity,signif-icanceofISIisquantiedbyaparametercalledroot-mean-squared(RMS)delayspread.Inanutshell,theRMSdelayspreadindicatesthecapabilityofthecommunicationchannelofsupportinghighdataratecommunicationsbyimplyingtheprobabilityofperformancedegradationwhichmayoccurduetotheISIasaresultofmultipathsignalpropagation.56

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TheaimofthischapteristoinvestigateandexplainstatisticallytheimpactofthesefactorsontheRMSdelayspreadvalueofLVPLCnetworks. Basedonextensivemeasurements,frequency{distancedependentattenuationinLVPLCnetworksisdenedas[69]A(f;d)=exp(a0a1fk)d;(4.1) wherefanddcorrespondtofrequencyofthesignalandthedistancecovered,respectively.a0,a1,andkareallcabledependentparametersandaremostlyextractedbyempiricalmeasurements[69].a0,a1,andkareconsideredtobetimeinvariant,i.e.xedparametersforaPLCnetwork.Hence,attenuationdenedby(4.1)doesnotcauseanytimevariationintheRMSdelayspreadforagiventopology.Unliketherstfactorlistedabove,load-inginLVPLCnetworksistimevarying.Branchesinthenetworkareterminatedwithvariouselectricalloadswithdierentimpedancecharacteristics.Theloadingconditionof57

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Theremainderofthechapterisorganizedasfollows.Section4.2givestheanalyticalbackgroundforthemultipathpropagationmodelinPLCchannelsanddenesRMSdelayspread.Section4.3discusesimpactofattenuationandloadingontheRMSdelayspreadinPLCchannels.Section4.4providesthedetailsontherelationbetweenthephysical58

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whereandTcorrespondtothereectionandtransmissioncoecientsalongtheprop-agationpath,respectively,A(f;di)meansthefrequency{distancedependentattenuationstemmingfromthephysicalcharacteristicsofthecableusedinthenetworkandgivenby(4.1),andexp(j2fi)referstothephaseoftheithcomponentduetothetimede-lay.Finally,KandMrepresentthenumberofreectionandtransmissioncoecientsexperiencedbyapropagatingsignalalongaparticularpathdenotedbythesubscripti.Multiplicationofreection()andtransmission(T)coecientsleadstoaparameterwhichiscalledreectionfactorintheliterature.Reectionfactor,denotedasjrijexp(ji)foracertainpathimpliedbythesubscripti,isusuallybutnotnecessarilyacomplexnumber.ItaccountsforthelossesinicteduponthetransmitsignalduetophysicalcharacteristicsofthePLCenvironment.Itisclearfrom(4.2)thattheaccuratecomputationofthereectionfactors(reectionandtransmissioncoecients)isessentialforatruecharacterizationofthePLCchannel.InPLCsystems,atransmitsignalpropagatingfromonelocationtoanothersuersreectionsatimpedancediscontinuitiesalongitspathtothereceiver.Duetotheseimpedancemismatches,somepartofthesignalisreectedbacktowardsthesource,whereassomeproceedstothedestination.Reectioncoecientarticulatestheamplitude/phaseratiobetweenthereectedsignalandtheincidentsignal,whereastransmissioncoecientT59

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whereZLreferstotheimpedancethatthesignalseesatadiscontinuity.SincebranchingandimpedanceappearingattheterminationpointsarethemainreasonbehindtheimpedancediscontinuityforhomogeneousPLNswhicharetobeconsideredinourstudy,itisworthtakingacloserlookatthecalculationofthereectionandtransmissioncoecientsattheseinstantsasillustratedinFig.4.1. Figure4.1Reection/Transmissioncoecientsatbranchingandtermination.4.2.1Reection/TransmissionCoecientatBranching

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wherenisthetotalnumberofbranchesextendingfromanodeincludingthebranchonwhichtheincidentsignalpropagates.1Byusing(4.3),itcanbeeasilyshownthatreectionandtransmissioncoecientsaregivenby,=ZtotalZ0 nandT=+1=2 whereZDdenotestheimpedanceseenbytheincidentsignalattheterminationpoint.Notethattheincidentwaveisfullyreectedincasetheterminationpointisopenorshortwiththesameamplitudebut180ofphasedierence.Incaseadeviceisconnectedtotheterminationpoint,thenimpedanceofthecorrespondingdevicemustbetakenintoconsid-erationwhilecomputingreection/transmissioncoecients.SignalpassesthroughmanyimpedancediscontinuesandexperiencesmultiplereectionsonitswaytothereceiverinaPLCnetwork.Reectionfactor,thatwaspreviouslymentionedwhileintroducingthemultipathcharacteristicsofPLCchannels,representsthetotaleectofallthesereec-tion/transmissioncoecientsonthepropagatingsignal.

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RMSdelayspreadisderivedfromtheCIRanddenedas:[47]rms=vuut PRj=02jjhjj2 whereRisthenumberofpathsconsideredinthecalculationandusuallydeterminedbythresholdingaswillbeclearintheforthcomingsections.Itisworthmentioningthatdelayoftherstarrivingpath,whichisdenotedas0,isalignedtozerobeforecomputation. Sofar,signalpropagationandmultipathcharacteristicsofPLCchannelsaswellasthecomputationoftheRMSdelayspreadareelaborated.Theseconceptsareimportantinasensethattheyformabasisforourfuturediscussions.Fromthispointon,ourdiscussionwillbeextendedtotheRMSdelayspreadandthefactorsthatcharacterizeitinPLNs.4.3ImpactofAttenuationandLoadingonRMSDelaySpread

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T-networktopologyisdepictedinFig.4.2.ItiscomposedofthreebranchesconnectedtonodeBwiththelengthofd1,d2,andd3.Adenotesthepointwherethesignalisinjectedintothenetwork,andDisthepointwherethesignalisreceived.ConsiderationofthehomogeneousnetworkstructureinwhichallthebrancheshavethesamecharacteristicimpedanceZ0isoneoftheassumptionsmadefortheeaseofanalysis.Inaddition,AandDareassumedtobematchedtoZ0forthesakeofsimplicity,henceBandCaretheonlysourcesofreectioninthetopology. Figure4.2T-networktopology. ReectionandtransmissioncoecientsatnodeB(b,Tb)andC(c,Tc)forthisparticularnetworktopologyaregivenby(4.5)and(4.6)forn=3.NotethatZDin(4.6)referstoimpedanceoftheelectricalloadconnectedtonodeC. FollowingthediscussiononPLCchannelandRMSdelayspreadgiveninSection4.2,itisnowconvenienttoarticulatewhythersttwofactors(attenuationandloading)thatarelistedinthebeginningofthechapterplayaroleintheRMSdelayspreadofPLCchannels.RecallthattheRMSdelayspreadofacommunicationchanneliscomputedbyaligningtherstarrivingpathtozerodelay.Uponthisalignment,thenumberofpathstobeincludedintheRMSdelayspreadcomputation,whichisRascanbeseenin(4.8),isdeterminedbyapplyingathresholdconsideringthemaximumpowervalueinthedelayprole.Withthisthresholdsodetermined,thepathswiththepowervaluesbelowareconsideredtobenoiseandexcludedfromtheanalysis.Withtheexplanationgiven,theimpactofattenuationon63

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Thesecondfactorgiveninthebeginningofthechapter,whichistheloading,determines'sandT'sin(4.2).Therefore,anychangeintheloadingconditionleadstoachangein'sandT'sinthenetworkandresultsinachangeintheRMSdelayspread.Recallalsothateveniftheloadingconditionisnotaltered,thedependencyoftheloadimpedancesontheACmainscycle[80]givesrisetoacyclicchangeintheRMSdelayspreadofPLCchannels.Iftheterm,A(f;d)in(4.2)isignoredinordertoisolateourselvesfromtheeectofattenuationandsolelyfocusontheimpactofloading,(4.2)reducestothefollowingform:H(f)=NXi=0hKYk=1ikMYm=1Timiexp(j2fi);(4.9) IfIFFToperationisappliedtotheCFR,CIRisobtainedasfollows:h()=NXi=0hKYk=1ikMYm=1Timi(ti);(4.10) Notethatthereectionfactorofthedirectpath(A-B-D)iscomposedofonlyonetermwhichisthetransmissioncoecientatB,namelyTb.Thereectionfactorsofotherpathsconsistofc,b,andTb.Baseduponthisobservation,theCIRofT-networktopology64

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ngj1(c)j(j);(4.11) whereRreferstothenumberofreectionsconsideredbetweenBandC. Thegraphicalillustrationoftheamplitudeof(4.11)isgiveninFig.4.3.Ascanbeseen,amplitudeofthesignalcomponentsdecreaseswithincreasingdelay.Thisisduetothefactthatpowerofthesignalreducesasitpassesthroughmorereectionpointsonitswaytothereceivereventhoughtheattenuationeectisnotaccountedfor.Takingtheattenuationintoconsideration,amplitudeofeachcomponentshouldbeevensmaller.Therefore,theRMSdelayspreadvaluesobtainedfromFig.4.3arepessimisticsincetheeectofattenuationespeciallyforlatearrivingpathsisnotaccountedfor.However,thiswillnotaectourconclusionssinceourfocusisontheimpactofloadingratherthanattenuation. Figure4.3GraphicalrepresentationoftheCIRforT-networktopology. Forthepurposeofmathematicaltractability,iftwoofthedelays(0and1)alongthedelayaxisareconsidered(R=1)inFig.4.3,using(4.8)and(4.11)theRMSdelayspreadrmstakesthefollowingform:rms=12njcj

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whereristhedielectricconstantoftheinsulationmaterialandc0isthespeedoflightinvacuum. Referringbackto(4.3),cbeingthereectioncoecientatnodeCdependsontheimpedanceoftheelectricaldeviceZDconnectedtothenetworkwhichisregardedasarandomvariable(RV)inthisstudyforgeneralizationsothatvariousloadingconditionscanbetakenintoaccount.IfCisassumedtobeleftopen(ZD=1),cbecomes1.cbecomes1ifashortcircuitassumption(ZD=0)isconsideredatnodeC.Thesetwoscenarioscorrespondtotwoextremecases.Therefore,itisexpectedthatanyelectricaldeviceconnectedtonodeCyieldsareectioncoecientbetweenthevaluesgeneratedbytheseextremecases,1and1.ThesetwovaluesarealsothemaximumandminimumvaluesofcduringanACcycledurationeveniftheelectricalloadconnectedtonodeCisunchanged. InordertounderstandtheimpactofloadingontheRMSdelayspreadrms,wehavetoderivetheprobabilitydensityfunction(PDF)ofthevariable=6jcj Beforeproceedingwiththestatisticalcharacterizationof,someimportantobservationsshouldbemaderegardingitsbehavior.hasthefollowingcharacteristics:

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Thederivativeofwithrespecttocisgivenbyd dc=5424(c)2 Sinced dc>0for0
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Referringbacktothestatisticsof,severalPDFscanbeoeredinordertocharacterizethestatisticalbehaviorofc.ExtractingthestatisticsofdeviceimpedancesthatarewidelyusedinLVnetworksandbuildingastatisticalmodelwouldbeverydesirable.Sincenosuchastudyisavailableintheliterature,cisassumedtobeuniformlydistributedover[1,1].Byusingthefundamentaltheoremforfunctionsofonerandomvariable[114]andemployingchangeofvariablesY=jcj,thePDFof(4.14)canbeexpressedasfollows:f()=362+(33p 13(4.18) Integrating(4.18)leadstothecumulativedistributionfunctions(CDF)of.CDFcanbecalculatedbychangingthevariablecos()=p 2tanarcsin(2) 2;0<<6 13(4.19) Figures4.4and4.5showthePDFandCDFof.Itisclearlyseenthatanalyticalderivationsandsimulationresultsareingoodagreement.Curvesarealsoseentobeingoodagreementwiththelemmaprovided.Forinstance,pluggingjcj=1into(4.14)forthepurposeofmaximizationyields6=13.Duetothemaximization,mustneverexceed6=13anditisseenfromFig.4.5thatthisobservationissatised.68

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Figure4.5CDFoftheRMSdelayspreadofT-networktopologywhennodeCisrandomlyloaded. ImpactofattenuationandloadingontheRMSdelayspreadisdetailedinthissection.Subsequently,impactofthephysicalcharacteristicsofthePLCoperatingenvironmentwillbeourfocus.69

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ItisobviousthattheanalysisthatweplantoperforminthissectionrequirestheestablishmentofmorecomplicatedPLCnetworksthantheT-networktopologyutilizedinSection4.3.ModelingPLCsystemsandbuildingsimulationtechniquesforthemhavebeenthefocusofseveralstudiesearlierintheliterature.ThemodelwhichconsidersthePLCchannelasamultipathcommunicationenvironmentwasrstintroducedin[69]asmentionedearlier.Baseduponthismultipathconsideration,analyticalcalculationofthemultipathcomponentsbydescribingthePLCchannelviaasetofmatricesisproposedin[115,116].PLCmodelsthatarebasedontreatingthetransmissionlineasatwo-portdeviceareavailableintheliteratureaswell[117,118].Achannelmodelandasimulationplatformalongwiththeresultsofvariouschannelmeasurementcampaignsarediscussedin[79,119].AstatisticalPLCchannelcharacterizationregardingattenuation,multipathrelatedparameters,etc.ispresentedin[78,120].Inouranalysis,thematrixbasedPLCsimulationtechniqueproposedin[115]willbeconsideredasthebasis.However,matricesintroducedin[115]aretobemodiedinawaythatthesimulationmoduleletsuseasilygeneratePLCnetworkswithdierentphysicalcharacteristics.Inlinewiththeproceduredescribedin[115],generatedPLCnetworktopology,whichisillustratedinFig.4.6,is70

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wheretandbcorrespondtothenumberofterminationpointsandbranchingpoints(referredtoasinternalnodesin[115]),respectively.CCisthesubmatrixwhichdescribestheinter-connectionsamongbranchingnodes.CTshowstheconnectionsbetweenbranchingnodesandterminationpoints.Thecorrespondinglengthofeachinterconnectionandimpedancesatterminationpointsarekeptinseparatematrices.InordertoisolateouranalysisfromtheimpactofimpedancevariationthatwasdiscussedinSection4.3andfocussolelyontheimpactofphysicalcharacteristicsoftheenvironment,itisassumedthattheterminationpointsareopencircuit.Inaddition,numberofbranchesextendingfromeachbranchingnodeisconsideredtobeuniformlydistributedover[3,6]inthesimulations.SimilartotheanalysisperformedinSection4.3,transmitterandreceiverarealsoassumedtobematchedtothecharacteristicimpedanceofthehomogeneousPLCnetwork.Impactofphysicalat-tributesisstatisticallyinvestigatedbygenerating20000realizationsofPLCnetworkforeachcasetakenintoconsideration.PLCtopologieswithdierentphysicalattributesaregeneratedbymanipulatingthevaluesoft,b,andthelengthmatrixwhoseelementsarecomposedofthevalueslijshowninFig.4.6.NotethatachangeinthetopologygivesrisetoachangeinthevaluesoftandbwhichresultsinachangeinthedimensionsofthesubmatricesdenotedasCCandCT.Foreachrealization,CIRwascalculatedbytakingtheIFFTofCFRgivenby(4.2).AfterCIRisobtained,proceduredescribedinSection4.2isfollowedwiththethresholdvalueof20dBwhilecomputingtheRMSdelayspread. TheimpactofnumberofnodesbetweentransmitterandreceiverontheRMSdelayspreadcanbeseeninFig.4.7.Whilederivingthisgure,transmitter{receiverseparationdistanceandlengthstatisticsofthebranchesareconsideredtobe150mandU[10m-30m]2,respectively.Upontheanalysisperformed,itisconcludedthatanincreaseinthenumber

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Figure4.7DependencyofRMSdelayspread(rms)onthenumberofnodes(b)betweentransmitterandreceiverwhenseparationdistancebetweentransmitterandreceiveris150mandbranchlengthsareassumedtobeuniformlydistributedover[10m-30m].ofnodeswhilekeepingalltheothereectivephysicalattributesofthePLCnetworkthesamegivesrisetoanincreaseinitsRMSdelayspreadvalue.Thisbehaviorcanberelatedtothemultipathcomponentsarrivingatlargerdelaysasbisincreased.Thisrelationwaspreviouslynoticedin[70]byconsideringsomespecicPLCnetworktopologies.OurndingsverifytheresultsofthisearlierstudybytakingmoregeneralPLCnetworkscenariosintoaccount.Fig.4.8showstheimpactoftransmitter{receiverseparationdistanceonrms.Similartothepreviouscaseanalyzed,increasingseparationdistancebetweentransmitterandreceiverleadstothereceptionofmultipathcomponentsatlargerdelaysleadingtoan72

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ThemultipathcharacteristicsofthePLCcommunicationenvironmenthavebeenthefocusofseveralpublicationsearlierintheliterature.MultipathmodelforPLCchannelsisrstelaboratedin[69].Amatrixbasedalgorithmforthecalculationofmultipathcom-ponentsinPLCnetworksisgivenin[115,121,122].ChannelcharacterizationofindoorPLNswithvariousloadingconditionsisinvestigatedin[70].Similarly,theimpactofloadimpedanceswhichareclassiedashighresistive,lowresistive,andinductive,linelengthandbranchingtothemultipathcharacteristicsofthePLCchannelisanalyzedin[123,124]bystudyingcertainscenarios.PLCchannelmodelsthatarebasedontreatingthetrans-missionlineasatwo-portnetworkareavailableintheliteratureaswell[117,118,125,126].AllofthesestudiespresentedasthepriorartformananalysisplatformforPLCenvironmentswithexactlyknowncharacteristicsleadingtosite-specicinformation.Our75

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Inlinewithourobjective,althoughnotsomanypapersareavailableintheliterature,someotherstudiesaimatmodelingthePLCchannelsstatisticallybasedupontheresultsderivedfrommeasurementcampaigns[78].Patharrivaltimesandamplitudesareinves-tigatedparticularlyfornarrowbandchannelsin[72].TheauthorsapproachisbasedondeningthepatharrivaltimesasNormallydistributed.Thisdenitionforpatharrivaltimesleadstothecharacterizationofpathamplitudesaslog-NormallydistributedalthoughitsrelationtothePLCnetworktopologyisnotarticulated. Asstatedearlier,impedancediscontinuitiesinthePLNsleadtothemultipathprop-agationphenomenon.ImpedanceoftheelectricalloadsandthebranchingarethemaincausesofimpedancediscontinuitiesinPLCnetworks.Thesignicanceoftheimpactoftheimpedancediscontinuityonthetransmitsignalmayonlyberevealedbyhavinganexactknowledgeoftheimpedancesatthecorrespondingdiscontinuitylocations.PossessionofthisinformationisveryunlikelyconsideringthevarietyofelectricalloadswithdierentimpedancecharacteristicsthatcanbeconnectedtothemediumaswellasthedierencesinPLCnetworktopologiesleadingtodierentbranchingstructures.Therefore,consideringthesetwoparametersasthehigh-levelattributesofthePLCcommunicationmediumandapproachingtheproblembyemployingstatisticaltoolsseemtobeappropriate.Asmen-tionedearlier,thiswillhelpusreachmoregeneralconclusionsregardingtheperformanceofcommunicationsystemsbyavoidingnetwork-specicanalysis. Asaresultofthemultipathpropagation,receivedsignalinpowerlinecommunicationsystemsconsistsofthereplicasofthetransmitsignal.Amongthesereceivedreplicas,knowledgeontherstarrivingpathbehaviorisimportantsinceitreachesthereceiverwith76

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IfthetermA(f;d)isignoredinordertosolelyfocusonthecharacteristicsofthephysicaloperatingenvironmentofthePLCsystems,(5.1)reducestothefollowingform:H(f)=NXi=0hKYk=1ikMYm=1Timiexp(j2fi);(5.2) IffastFouriertransform(FFT)operationisappliedtotheCFR,channelimpulsere-sponse(CIR)isobtainedasfollows:h()=NXi=0hKYk=1ikMYm=1Timi(ti);(5.3) wheremultiplicationofandTin(5.3)isreferredasthereectionfactor(jrijeji)ofaparticularpropagationpath.Ascanbeseenclearly,computationofreectionfactorplaysanimportantroleinthecharacterizationofPLCchannels.Withthisobservation,itscharacterizationalongthedirectpath(i=0)isessentialforunderstandingtherstarrivingpath.AmoredetailedlookatthereectionfactorinPLNscanbefoundin[113].5.2.2AnalysisoftheFirstArrivingPath Ascanbeseen,thedirectpropagationpathbetweentransmitterandreceiveroperatingonaPLCsystemconsistsofseveralbranchingnodesthatarerepresentedbytheletternin78

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Notethatthereectionfactoroftherstarrivingpath(jr0jej0)iscomposedofonlythetransmissioncoecients(T0s)experiencedalongthedirectpathstemmingfromtheimpedancediscontinuitiesatthebranchingnodes.So,calculatingT0sissucientinordertocharacterizethereectionfactoroftherstarrivingpath. AbranchingnodeisdepictedinFig.5.2inwhichthecharacteristicimpedanceofthebranchesarelabeledwiththeletterZ0s.Accordingtotransmissionlinetheory,reectionandtransmissioncoecientsatabranchingnodeareexpressedbyconsideringparallelconnectionsofextendedbranchesasfollows[112]:=(Z1==Z2==:::==Zz)Z0 Incasetheimpedanceofallthebranchesareequaltoeachother(Z0),then(5.4)becomes=2z zandT=2 wherezreferstothetotalnumberofbranchesextendingfromaparticularbranchingnode. ReferringbacktoFig.5.1,assumingthatthetransmitterandreceiverarematchedtotheimpedanceofthecorrespondingcharacteristicimpedanceofthecableforthesakeof79

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whereni(i=1;2;:::;x)1isthenumberofpathsextendingfromabranchingnodeincludingthepathonwhichtheincidentsignalpropagates.Notethatthephasetermofthereectionfactoris0forthisparticularcasesincenicannotbeacomplexnumber,i.e.jr0jej0=jr0j. Inlightofthediscussionpresentedinthebeginningofthechapter,ni'sandxcanbeconsideredasthetwoofthehigh-levelattributesofthePLCchannel.Stemmingfromthisfact,jr0jgivenby(5.6)isindeedarandomvariable(RV).OurinitialobservationswillbeontherstandsecondorderstatisticsofthisRV.Ifthenaturallogarithmofbothsidesof(5.6)isconsideredY=ln(jr0j)=xln2xXi=1lnni(5.7) Uponthismathematicalmanipulation,itiseasytoseethatYisanRVwiththefollowingmean,andvariance,2:=xln2xXi=1E[ln(ni)]and2=xXi=1Var[ln(ni)](5.8)

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ba+1lnb! (a1)!+xln2(5.9)2=xVar[ln(n)]=xE[(ln(n))2]xE[(ln(n))]2(5.10) Someimportantobservationscanbemaderegardingand2atthispoint. Proofoftheobservationscanbegivenasfollows.Thederivativeofwithrespecttoxisgivenbyd dx=1 (a1)!+ln2(5.11) Inordertomakesurethatabranchingexistsatabranchingnodeaandbmustbeequaltoorgreaterthan3.Consideringthisfactitiseasytoseethatb! (a1)!1 Reasoningin(5.12)naturallyproposesthat(5.11)mustbenegative.Sinced dx<0fora;b3,isamonotonicallydecreasingfunctionofx.

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(5.13)isequaltothevarianceoftheRVln(n).VarianceofanRVisalwayspositive.Sinced2 MeanandvariancevaluesofYwhichwereobtainedthroughsimulationandanalyticalderivationarepresentedinFigures5.3and5.4ifnisassumedtobeuniformlydistributedover[3,6].Ascanbeseenclearly,themeanvalueofYdecreaseswithincreasingx,whereasitsvarianceincreasesasxisincreasedwhichisingoodagreementwiththeclaimsproposedabove. Figure5.3MeanofYwithdierentvaluesofx. Notethatthedenominatorof(5.6)iscomposedofthemultiplicationofRVs.Multi-plicationofRVscanbeapproximatedwithlog-NormalPDFaccordingtothecentrallimittheoremforproductsofRVs[114].However,eachoftheni'sappearinginthedenominatorcanonlytakediscretevaluescomingfromadiscretedistributionduetothehomogeneousnetworkstructureassumption.Thelog-Normalapproximation,hencetheuseofcentral82

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HavingahomogeneousPLCmediumisphysicallyverydiculteventhoughthesametypeofcableisusedthroughoutthenetworkduetothevarietyoffactorsthataectthecharacteristicimpedance.Ifweweretocontinuewiththehomogeneityassumption,adeviationtermwhichimpliestheminorchangesofimpedancesacrossthebranchingnodescanbeconsideredtobemorepractical.Thisway,theimpedanceofabranchwhichwasassumedtoequalZ0cannowbeassumedtobeZ0+de,wherededenotesthedeviationfromZ0.Similartothepreviouscase,severalassumptionscanbemaderegardingthe83

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whererecallthatTi'sarethetransmissioncoecientsatcorrespondingbranchingnodesandYisanRVcharacterizedwiththeNormalPDF. Priortotheinvestigationoftherstandsecondorderstatisticsofjr0j,KolmogorovS-mirnov(KS)testwillbeperformedinordertoverifytheGaussianityassumptionpresentedin(5.14).Inordertoverifythisassumption,asimulationhasbeenperformedbyassumingZ0anddetobe50andauniformlydistributedRVover[1,1],respectively.InKSgoodness-of-ttest,thefollowingdistancemeasureistakenintoconsiderationD=maxxjF(x)FN(x)j(5.15) whereF(x)andFN(x)aretheCDFoftheempiricaldataandtheCDFofthetheoreticalNormaldistribution,respectively. Inordertoquantifythestatisticsoftheunderlyingprocess,thefollowinghypothesestestwasperformed: and84

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recallthatYisdenedasthelogarithmofthemultiplicationofthecorrespondingtrans-missioncoecientsTi'sasoutlinedby(4.7)and(5.14)Y=ln(jr0j)=ln(xYi=1Ti)(5.16) ResultsoftheKSgoodness-of-tforYareshowninFig.5.5withthesignicancelevelequals0:05.Notethattheverticalandhorizontalaxesrefertothep-valueobtainedfromthetestandthenumberofbranchingnodes(x),respectively.ThevaluesofpshowninFig.5.5wereobtainedbyaveragingtheresultsof100trails,eachwith10000samples. Beingatwo-tailedtest,thefollowingconditionp>=2mustbesatisedinordertoacceptH1.Ascanbeclearlyseenfromthegure,xaslowas7issucientfortheacceptanceofH1. Asmentionedpreviously,theoreticalderivationofthemeanandvarianceofYfornet-workswhosecableimpedanceisdenedasZ0+deisnotasimpletask.However,MonteCarlosimulationscanbeemployedinordertoovercomethisdiculty.Indeed,thissamereasoningcanbeappliedtonetworkswithheterogeneousstructureifthecableimpedancescanbecharacterizedwithaparticularPDF.Thisheterogeneitywillbeintroducedbyma-nipulatingthestatisticsofdeinthisstudybyassumingittobeuniformlydistributedoveralargerrangethanthepreviouscase.Figures5.6and5.7showthemeanandvarianceofY(logarithmofthereectionfactor)whenZ0anddeareassumedtobe50anduni-formlydistributedover[25,25],respectively.ThiscorrespondstoaPLNinwhichthecharacteristicimpedanceofthecablestakessomevaluebetween25and75accordingto85

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Althoughtherstandthesecondorderstatisticscannotbeexpressedinthesamewayasin(5.9)and(5.10),claimspresentedaboveregardingand2stillhold.Resultspresentedin(5.17)and(5.18)carriessignicantimportanceconsideringthesimulationofPLCchannelswithunknownnetworkstructure.IfthePLCcommunicationenvironmentisnotknownexceptforsomehigh-levelattributes,theamplitudeoftherstarrivingpathcanbecharacterizedwiththelog-NormaldistributionasshowninFig.5.5.Themean86

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Intheaboveexample,thesetwoparametersareextractedforaparticularcase;however,thismethodologyalongwiththelog-NormalapproximationmaybeeasilyusedforothercasesinwhichcharacteristicimpedancesassumedierentPDFsaswell.Themoststrikingoutcomeofthislog-Normalapproximationistheavoidanceofnetworkspecicresults.Uponthisapproximation,allnetworkswhoseattributesaredenedwiththeabove-mentionedstatisticscanbeincorporatedintotheperformanceanalysiswhichcanbecarriedoutpriortosystemdeploymentprocess.87

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OurnextobjectivewillbeinvestigatingtherelationbetweenthenumberofbranchesextendingfromabranchingnodeandthemeanandvarianceofY.Thisinvestigationwillbebasedonincreasingthemaximumnumberofbranchthatmayextendoutabranchingnodewhilekeepingthenumberofbranchingnodes(x)xed.Recallfrom(5.9)thatthisnumberisdenotedasb.Theresultsofthesimulationswhenbisvariedfrom6to10areshowninFigures5.8and5.9.Similartox,increaseinbgivesrisetoadecreaseinthemeanandanincreaseinthevarianceofY.ThisproposesthatwhentwodierentPLCenvironmentstructuresareconsideredwiththesamenumberofbranchingnodes(x),theenvironmentinwhichmorebranchesareexpectedtoextendoutfromeachbranchingnodesyieldslowermeanandhighervarianceforthelog-Normalapproximation.88

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UponarticulatingtherelationbetweenattributesofPLCnetworktopologyandstatis-ticsoftherstarrivingpath,statisticsregardingotherpathsaswellastheassumptionsconsideredintheanalysiswillbeclearlypresentedinthesubsequentsection.5.3Discussion

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Sofar,statisticsofthestrongestpathinPLCenvironmenthasbeenthefocalpointofthediscussion.Inadditiontothereceptionoftherstpath,anumberofpathsfromotherreectionpointsisreceivedbythereceiverasindicatedby(5.3).Thelog-Normalityassumptiontodenethestatisticsofthesepathsshouldholdaswellespeciallywhenthe90

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ThenalremarkthatisworthmentioningatthispointisregardingthebandwidthassumptionortimeresolutionoftheCIR.Itmustbenotedthatinouranalysis,theband-widthwasassumedtobeinnitewhichledtotheresolutionofeachandeverymultipathcomponentindividuallyalongthedelayaxisofCIR.Ifthesymboldurationisconsideredtobelimitedwithanitevalue(nitebandwidth),thereceiverobservesthevectorialad-ditionofthemultipathcomponentsthatfallintoonesymbolduration[47].Thenumberofmultipathcomponentsthatarevectoriallyaddedatthereceiverdependsonboththebandwidthandthenetworktopology.Asanextremecase,ifthedelayofthelatestarrivingmultipathcomponent,whichisNin(5.3),issmallcomparedtothedurationofasym-bol,theresultantreceivedsignalisthevectorialcombinationofNmultipathcomponentswhosestatisticsaredenedwithlog-NormalPDFs.Fortunately,somemethodsarealreadypresentintheliteraturetoapproximateadditionofcorrelatedlog-NormalRVsbyanotherlog-NormalRV[127,128].

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MeanandvariancearethetwoparametersthataresucienttocharacterizeaNormal,hencealog-NormalRV.TherelationbetweenthesetwoparametersofYandthehigh-levelattributesofthePLCenvironmentwaselaboratedbyconsideringtherstarrivingpathasacasestudy.Uponinvestigation,followingconclusionswerereached: Asanalnote,ouranalysiswasperformedbyassumingtheavailabilityofinnitebandwidth.However,itwaspointedoutthatndingsconcludedwiththisassumption92

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Consideringthecurrentcommunicationtrend,itisobviousthatrobustnessofOFDMsystemsagainstimpulsiveinterferenceshouldbemaintained.ThereareseveralpublicationsintheliteratureproposingsolutionsformitigatingimpactofimpulsivenoiseonOFDM.Adecisiondirectedimpulsivenoisemitigationtechniqueisproposedin[132].Acompensa-tiontechniquebasedonsomeoperationsperformedinthefrequencydomainisintroducedin[135].Animpulsivenoisecancellationtechniquethatexploitsthepresenceofpilottonesisgivenin[136].Iterativedecodingbasedsolutionsareavailableaswell[137{140].Re-gardlessoftheimpulsivenoisemodelconsidered,itisawell-knownfactthatimpactofimpulsivenoiseonOFDMcouldbedetrimentalonceitspowerexceedsacertainthresh-oldsinceFFToperationatthereceiverspreadsitseectovertheentireOFDMsymbolblock[130].Detectingandblanking(ornulling)thesamplescorruptedwithimpulsivenoiseatthereceiverpriortoFFToperationisoneofthestraightforwardsolutionstodiminishitsadverseimpact[66,andreferencestherein].Althoughthisfactisbroughttotheattentionofthereaderinmostoftheseaforementionedstudies,itsrelationtotheOFDMreceiverandalgorithmperformanceisnotdiscussedanyfurther.Inadditiontothis,theemphasisinmostofthesestudiesisgivenonmemorylessimpulsivenoisemodels. ThischapterdealswiththeanalyticalevaluationandmitigationofburstyimpulsivenoiseeectsonOFDMsignalsundertheinuenceoffrequencyselectivecommunicationchannelassumingthatthereceiverperformsnullingpriortoFFT.Notethatnullingproce-dureimplementedatthereceiverdistortsorthogonalityamongthesubcarriersandgivesrisetointer-carrierinterference(ICI).Inbrevity,harmfulimpactofimpulsivenoiseisavoidedatthecostofICI.FurtherprocessingstagesmayberequiredinordertocopewiththeemergingICIandenhancetheOFDMreceiverperformance.Beforethesestages,theim-95

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Samplereplacementbasediterativetechniqueisoneoftheproposedsolutionsforhan-dlingimpulsivenoiseinOFDM[138{140].Weanalyticallyanalyzethistechniqueinrelationtothenullingoperationforthersttimeintheliterature.Inaddition,wepresentasucces-sivedetectiontechniqueforcompensatingtheimpactofburstyimpulsivenoiseonOFDMsignals.Performanceofthesetechniquesistobearticulatedbyobservingbiterrorrate(BER)guresalongwiththeircomputationalcomplexities.Thekeycontributionsanddistinctionsofthischapteraresummarizedasfollows:

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Thischapterisorganizedasfollows:Section6.2givesthesystemmodel.ImpactofnullingonOFDMsignalsthatsuerfromfrequencyselectivecommunicationchannelisanalyzedinSection6.3.Section6.4.1providesthedetailsofreplacementbasediterativetechnique.SuccessivedetectiontechniqueisintroducedinSection6.4.2.Section6.5presentsthenumericalresults.Finally,theconcludingremarksaregiveninSection6.6.6.2SystemModel whereNisthenumberofsubcarriers,NGisthelengthofcyclicprex(CP),S(k)cor-respondstotheinformation-bearingsymbolonthekthcarrier.ItisassumedthatS(k),k2[0,N-1],arecomplexrandomvariables(RVs)withE[S(k)]=0andE[S(k)S?(m)]=(km).HereE[]istheexpectationoperatorand()denotestheKronecker'sdeltafunction. TimedomainOFDMsymbolpassesthroughcommunicationchannelandsuersfromimpulsivenoisewithburstynature.Receivedsignalsamples,r(n),canbeexpressedasr(n)=h(l;n)?s(n)+n(n);(6.2) whereh(l;n)isthetimevaryingcommunicationchannelimpulseresponse,n(n)correspondstotheimpulsivenoiseprocess,and?referstotheconvolutionprocess.Thesameexpression97

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whereListhenumberofchanneltaps.Samplesthatarecorruptedwiththeimpulsiveinterferenceinthereceivedsignal,r(n),aredetectedandnulledbeforeFFToperationatthereceiversothatimpulsivenoisepowerbeingspreadoverallfrequencydomainsymbolsisavoided.Assumethaty(n)isobtaineduponnullingoperation,y(n)=8><>:r(n)n=2Z0n2Z(6.4) whereZreferstoasetthatholdssampleindexescorruptedwithimpulsivenoise.AsadirectconsequenceoftheIFFToperationatthetransmitter,demodulationatthereceiverisrealizedbyapplyingFFTony(n).SelectinglengthoftheCP,NG,largerthanthemaximumexcessdelayofthecommunicationchannelavoidsISI.Assumingperfecttime98

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Aroughdescriptionofthesystemmodelisgiveninthissectionwithoutgoingintodetailsoftheoperationsperformedatthereceiversideinordertoavoidthedetrimentalimpactofimpulsivenoise.Thesedetailsaretobediscussedsubsequently.6.3AnalysisoftheNullingOperationattheReceiver

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NS(m)H(m)1 IfKconsecutivesamplesstartingwiththesampleindexx0arenulledatthereceiverasgiveninthesystemmodeldescribedinSection6.2,thenitispossibletowritetheobtainedsignaluponnullinginamoreclearexpressionthan(6.7)byusinggeometricseriesexpansion:Y(m)=NK NS(m)H(m)1 sin((km)=N)ej(km)(K1+2x0)=N=NK NS(m)H(m)1 whereI(x)=sin(xK=N) sin(x=N)ejx(K1+2x0)=N. RemarkI:NotethatnullingsomeofthesamplesofthereceivedOFDMsymbolgivesrisetothefollowingtwophenomena:reductioninthepoweroftheusefulsymbolandthelossofsubcarrierorthogonality,henceICIeachweightedwiththeircorrespondingchannelfrequencyresponse(CFR)coecients.Intheanalysisgivenabove,noiseisconsideredtobe100

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NH(m)2 sin((km)=N)2+NK NN0(6.9) Asaspecialcase,forAWGNchannelinwhichallchannelcoecientsareequaltounity,SINRatthemthsubcarrierisgivenbySINRm=NK N2 NN0=NK K+NN0(6.10) RemarkII:AnotherobservationisthattheneighboringcarriersareexpectedtoplaythemajorroleintheICIthataparticularsymbolsuersfromespeciallyforlargevaluesofK=N.ThiscanbeveriedbylookingintoaveragepowerpercarriercontributedtothetotalICIthatcanbecomputedbyaveragingtheinstantaneousICIpowervaluesoverchannelrealizations.So,thecontributioncomingfromkthsubcarriertothemthsubcarriercanbeexpressedas:P(k)=1 sin2((km)=N)usin2((km)K=N) Fig.6.2showstheICIcontributioncomingfromsubcarrierswithinanOFDMsymbolblockforaparticularvalueofm.Ascanbeclearlyseen,contributioncomingfromtheneighboringsubcarriersbecomesmoredominantasKincreases.Forinstance,morethan70%oftotalICIpowerstemsfromtheadjacentsubcarriersforK=25whentotalnumberofsubcarriersNisconsideredtobe64.ItmustbeemphasizedthattheratioK=Nplaysa101

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Figure6.2ICIpowercontributionversuscarrierindexforN=64withnormalizedunitypowervalue. RemarkIII:Employingmatrixrepresentation,(6.8)canbealternativelyexpressedas:Y=HS;(6.12) whereYisanNx1vectorrepresentingthefrequencydomainsymbolsobtaineduponnulling,SdenotestheNx1vectoroffrequencydomaintransmitsymbols,andHisannon{diagonalNxNmatrixaccountingfortheimpactofnullingatthereceiveraswellasthewirelesscommunicationchannelonS.TherstrowofHisgivenbelowasanexample:H(1;:)=NK NH(0)I(1)H(1)I(N1)H(N1)102

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where()yand()Harethepseudoinverseandcomplexconjugateoperators,respectively.IfHisafullrankmatrix,then(6.13)iscorrect. Withthematrixnotationemployedforourcase,HisanoninvertibleandrankdecientmatrixwiththerankequaltoNK,hencedoesnotsatisfy(6.13).InspiteofthefactthatHisrankdecient,eachandeverysymbolS(k),k2[0,N-1],canstillbeuniquelydemodulated. WewillrstshowwhyHisrankdecientandthenexplainwhyeachsymbolisstilluniquelyidentiable.WeadoptAWGNassumptionintheremainderofdiscussioninwhichH(k)=1,k2[0,N-1];however,frequencyselectivechannelcaseisalsoapplicable.Ex-pressing(6.12)inamoreexplicitway:Y=HS=FFHzS;(6.14) whereFistheFouriermatrixandFHzreferstotheinverseFouriermatrixwhoseKrowsarenulledinordertorejectimpulsivenoisepowerintotheOFDMdemodulator.Notethatifnoimpulsivenoiseispresentintheenvironment,FHz=FHmakingHanidentitymatrix.SinceFHzhasKnumberofitsrowsequalto0,ithasNKnonzerosingularvalues,hencearankofNK.ThefollowingequalitymustholdsinceFisafullrankmatrix:Rank(H)=Rank(FFHz)=Rank(FHz)(6.15) ThisprovesthatHisarankdecientmatrix,hencenoninvertiblewitharankvalueofNK.However,thisfactdoesnotimplytheidentiabilityofonlyNKsymbolsinS.LetussplitHintotwomatrices,H1andH2.H1holdsthediagonalvaluesofHinitsdiagonalwithallotherremainingelementsequal0,whereasH2hastheremainingvalues103

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notethatthersttermholdstheinformationregardingthedesiredterm,whereasthesecondtermintheequationreferstotheundesiredterm,i.e.ICI.ICItermin(6.16)whichisseenasasumofRVsisusuallyassumedasGaussianintheliteratureconsideringthevalidityofcentrallimittheoremforlargeclassesofvariablesespeciallyforlargeN.ItisalsoworthmentioningthatGaussianassumptionasadditivenoisecorrespondstotheworstcasescenariofromchannelcapacitystandpoint[144,page337].Withthisassumptionadopted,H2Scanbethoughtofanerrorterm,,denedwithzeromeanGaussianRVwhosevarianceisequaltoK(NK)=N2ascanbeseenfrom(6.10).So,ourproblemturnsintoidentifyingNsymbolsinanAWGNchannelasfollows:Y=H1S+;(6.17) sinceH1isinvertibleandsatisesequalizabilitycondition,eachandeveryS(k),k2[0,N-1]canbeuniquelydemodulatedwithacertainprobabilitythatdependsonthemodulationorderandK.Thisisanimportantobservationconsideringtheapplicabilityofthetechniquesthataretobediscussedsubsequently.Asanalnoteforfrequencyselectivechannel,symbolidentiabilityisstillapplicablegiventheconditionthatH(k)6=0,k2[0,N-1].Obviously,thisconditionisnotrelatedtothenullingoperationandmustbesatisedforanyconventionalOFDMreceiveraspointedoutin[145].Indeed,thisobservationthatrelatesrankdeciencytouniquesymbolidentiabilitywasdiscussedearlierinadierentcontextintheliteratureaswell[146]. ThebottomlineinthisremarkisthatnosymbolislostatthereceiverduetothenullingoperationalthoughnullinggivesrisetotheappearanceofarankdecientchannelmatrixwitharankvalueofNK.InspiteofthefactthatchannelmatrixHhastherankvalueofNK,allsymbolscanstillbeuniquelydemodulated.Althoughzeroforcingequalizercan104

PAGE 116

Inthisrespect,remainderofthesectionisdedicatedtothediscussionoftechniquesthatareusedtotackletheemergingICIasaresultofburstyimpulsivenoiseeect.First,wewillarticulateatechniquenamed\samplereplacementbasediterativecancellationtechnique"thatwaspreviouslyproposedintheliterature(notinthisdetailthough),nextwewilldiscussourproposedscheme.6.4OFDMReceiverStagesAfterNulling6.4.1SampleReplacementBasedIterativeCancellationTechnique

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NS(m)H(m)1 Intheiterativedecodingtechniqueconsidered,ri'saresupposedtocorrespondtosomeparticularsamples(whoseindexesareindicatedbyzi's)ofIFFTofthefrequencydomainsymbolsestimatedfromthenulledreceivedwaveformandconvolvedwiththechannelre-sponse.So,ri=1 Afterpluggingthisinto(6.19),Y(m)becomesY(m)=NK NS(m)H(m)+K N^S(m)H(m)1 NotethattheICItermin(6.21)vanishesforthecase^S(m)=S(m)whichimpliesthatallthesymbolsareestimatedcorrectly.Notealsothat(6.7)isaspecialcaseof(6.21)for^S(m)=0.SimilartotheanalysisperformedinSection6.3,iftheimpulsivenoisehasaburstynatureoccupyingacertainamountofsamplesovertheOFDMsymbol(Ksamplesstartingwiththesampleindexx0),Y(m)intheiterationscanbealternativelyexpressedasY(m)=S(m)H(m)K NE(m)H(m)1

PAGE 118

NH(m)j2 sin((km)=N)j2(6.23) SupposethatY(m)hasthebestSIRandtherstsymboltobedetectedwiththecorrespondingestimatedsymbol^S(m).Aftermakingharddecision,thereceivedvectorYisupdatedasYnew=YoldH^S(6.24)107

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Inordertofurtherimprovetheperformanceofsuccessivetechnique,PICcanbeem-ployedandthenalsymbolvectorwhichholdsthetentativehardsymbolinformationcanbesubtractedfromtheinitialreceivedvectorafterbeingmultipliedwiththecorrespondingcoecientsgivenby(6.8).ThisprocedurecanbeiteratedmorethanonceforenhancingtheBERperformance.ThecomputationalburdenthatisintroducedbythePICprocedurerequiresadditionalO(N2)operationsateachiteration.ThereplacementbasedtechniquedescribedinSection6.4.1canalsobeemployedinsteadofPICforlesscomputationalbur-den.6.5NumericalResults

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Thecomparativeperformanceanalysisofthesetechniquescanbeclearlyseenbyob-servingFig.6.5.Fig.6.5comparestheperformanceofthesetwotechniquesforavarietyofKvaluesataspecicsignal-to-noiseratio(SNR)valueof30dB.Itisclearlyseenthattheperformanceofthetechniquethatisbasedonsuccessivesymboldetectionalwaysout-performstheotherespeciallyasK=Ngoeshigher.AsinglecycleofsuccessivedetectionissucienttokeeptheBERbelow103uptoK40,whereasthesimilarperformanceisobservedwithsamplereplacementbasediterativetechniqueafter3iterationsatK30.Asnotedearlier,thecontributionofneighboringcarrierstotheICIpowerisexpectedtobecomemoredominantasK=Ngoeslarger.Thisbehaviorbringsuptheimportanceofor-deringinthedetectionprocessespeciallyforhighK=Nvalues.Byorderingthesubcarriersandemployingsuccessivedetection,theICIcontributioncomingfromestimatedsymbolsonlowSIRcarriersareseenimmediatelyleadingtoabetterperformancecomparedtothe

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Itshouldalsobekeptinmindthattheperformanceofbothtechniquescannotbesatisfactoryevenafteraparticularnumberofiterationsareperformedduetotheerrorpropagationphenomenon.Inordertoseethis,lookatFig.6.6whichshowstheBERper-formanceofbothdetectiontechniquescomparativelywhenK(henceK=NforxedN)isdoubled.ItisseenfromFig.6.6thatevenafter3iterations3,bothtechniquesdonoteasilyconvergetothelowerbound,noICIcase.NoteagainthatsuccessivedetectionprovidesuswithabetterBERperformance;however,thismaynotbesucientforcertaincom-municationapplications.Inordertoovercomethisconvergenceproblem,ICIthatemergesuponnullingneedstobediminished.So,oneshouldaskwhatmeasuretakenbeforetrans-

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Figure6.6BERperformanceforN=256andK=50whenreplacementbasediterativeandsuccessivesymboldetectiontechniquesareemployedwith3iterations.6.6ConcludingRemarks

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Figure6.9BERperformanceforN=256withdierentvaluesofKandnormalizeddelayspreadvaluesatSNR=30dB.115

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WirelessandPLCchannelcharacteristicsofsmartgridenvironmentswerepresentedinaverydetailedway.Amongthecommunicationchannelcharacteristicsdiscussedwerepathlossandattenuation,timedispersion,timeselectivity,pathamplitudesandnoisecharacteristics. Dopplerspectrumcharacteristicsofwirelesschannelsaswellasthefactorswhichdeneitsbehaviorwereinvestigatedthroughtheuseofanreverberationchamber(RVC).Operatingfrequency,speed,andangleofarrival(AOA)wereamongthefactorsstudied.Inconjunctionwiththesefactors,anewperspectiveofmobilityinwireless116

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Impactofthephysicalattributesandloadingofthepowerlinenetwork(PLN)ontheRMSdelayspreadstatisticsofthecommunicationchannelwasinvestigatedindetail. StatisticsofthepathamplitudesinPLCchannelswerestudiedanditwasshownthatitcanbeconsideredtofollowalog-Normaldistribution.TherelationshipbetweenthephysicalattributesofthePLNandthemeanandvarianceoftheapproximatinglog-Normaldistributionwasarticulated. AdetailedanalysisoftheICIthatemergesuponnullinginOFDMreceiversop-eratinginimpulsivenoiseenvironmentsundertheinuenceoffrequencyselectivechannelwasgiven.AdetailedperformanceanalysisofthesubsequentstagesoftheOFDMreceiveruponnullingwascarriedout.Mathematicalevaluationofthesamplereplacementbasediterativetechniqueinrelationtothenullingoperationwasper-formed.Alternativetothesamplereplacementbasediterativetechnique,successivesymboldetectiontechniquewasappliedalongwithrelevantdiscussions.Incasebothtechniquesfailtoprovidesatisfactoryperformance,anewtransmissionschemethatisbasedonICIreductionwasintroducedattheexpenseofreduceddatarate(orspectralunderutilization).117

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Smartgridinfrastructurecannotbeisolatedfromtheadvancesintheradiotechnol-ogy.Inthisrespect,cognitiveradio(CR)anditsrelationtothesmartgridapplicationsshouldbeestablishedinastrongermanner.Besides,emergenceofelectricvehicles(EVs)andtheircommunicationandnetworkingrequirementsintermsofelectricitybillchargingandtheutilizationasabackupsourceofpowerwhenneededislikelytoleadtoveryexcitingresearchissuesfrommanyaspects.Inaddition,theirimpactonthepowergridshouldbegivenspecialattentionfordevelopingoptimumdemandschedulingandresourcemanagementalgorithms.Therearealsosomeimportantresearchopportunitiesconsideringtheintegrationofcustomerstothesmartgridnetwork.Forinstance,statisticsregardingtheuseofelectricaldevicesisverycrucialforthehouseholdstomonitortheirenergyus-age.Oneofthemosteconomicallyconvenientwaysofcollectingthesestatisticscouldbetoprocessthenoisethatthesedevicesemitintothepowerlineconductors.Communicationandnetworkingrequirementsinalternativegenerationandstoragesitesarelikelytogiverisetogoodresearchopportunities.Eachofthesesiteswillhaveitsuniquecharacteristicsaectingthecommunicationsystemsdeployedindierentways.Asaspecicexample,oneofthequestionsrequiringfurtherinvestigationishowthewirelesscommunicationisaectedbythewindturbinebladesinwindpowergenerationstationsorwhatcouldbethemainsourcesofdataerrorsintheseenvironmentsforvariouscommunicationoptions.Finally,OFDMbeingthemostpopulartechnologyforfuturecommunicationsystemswasconsid-eredinourstudy.Findingsofthisdissertationcanalsobeeasilyextendedtosomeotherpromisingtechnologiessuchassinglecarrierfrequencydomainequalization(SC-FDE).Alloftheseabove-mentionedresearchissuescanleadtoanotherPhDdissertation.118

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