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Noise and multipath characteristics of power line communication channels

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Title:
Noise and multipath characteristics of power line communication channels
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Celebi, Hasan
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University of South Florida
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Subjects / Keywords:
Power line communication
Noise
Cyclostationarity
Multipath
Impedance
Attenuation
Dissertations, Academic -- Electrical Engineering -- Masters -- USF   ( lcsh )
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non-fiction   ( marcgt )

Notes

Abstract:
ABSTRACT: With the recent developments in technology, information and communication technologies (ICTs) are becoming more widespread and one of the basic building blocks of every humans life. The increasing demand in broadband communication calls for new technologies. Power line communication (PLC) is one of the potential candidates for next generation ICTs. Although communication through power lines has been investigated for a long time, PLC systems were never taken into account seriously because of its harsh communication medium. However, with the development of more robust data transmission schemes, communication over the power lines is becoming a strong alternative technology because of the existence of the infrastructure and the ubiquity of the network. In order to establish reliable communication systems operating on power line networks (PLNs), characteristics of power line channels have to be investigated very carefully. Unpredictable characteristics of PLNs seriously affect the performance of communication systems. Similar to the other communication channels, PLC environment is affected by noise, attenuation, and multipath type of channel distortions. The level of noise in PLNs is much higher than any other type of communication networks. Furthermore, the frequency dependent attenuation characteristics of power lines and multipath stemming from impedance mismatches are the other distortion factors which have to be investigated in order to establish a reliable PLC system. In this thesis, we focus on modeling of noise, frequency dependent attenuation, and multipath characteristics of power line channels within the frequency range between 30kHz and 30MHz.
Thesis:
Thesis (M.S.E.E.)--University of South Florida, 2010.
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Includes bibliographical references.
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by Hasan Celebi.
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Noise and multipath characteristics of power line communication channels
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ABSTRACT: With the recent developments in technology, information and communication technologies (ICTs) are becoming more widespread and one of the basic building blocks of every humans life. The increasing demand in broadband communication calls for new technologies. Power line communication (PLC) is one of the potential candidates for next generation ICTs. Although communication through power lines has been investigated for a long time, PLC systems were never taken into account seriously because of its harsh communication medium. However, with the development of more robust data transmission schemes, communication over the power lines is becoming a strong alternative technology because of the existence of the infrastructure and the ubiquity of the network. In order to establish reliable communication systems operating on power line networks (PLNs), characteristics of power line channels have to be investigated very carefully. Unpredictable characteristics of PLNs seriously affect the performance of communication systems. Similar to the other communication channels, PLC environment is affected by noise, attenuation, and multipath type of channel distortions. The level of noise in PLNs is much higher than any other type of communication networks. Furthermore, the frequency dependent attenuation characteristics of power lines and multipath stemming from impedance mismatches are the other distortion factors which have to be investigated in order to establish a reliable PLC system. In this thesis, we focus on modeling of noise, frequency dependent attenuation, and multipath characteristics of power line channels within the frequency range between 30kHz and 30MHz.
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Impedance
Attenuation
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IwishtothankDr.ChrisFerekidesandDr.ParisWileyforservinginmycommitteeandforoeringtheirvaluablefeedback.Ihopetobeabletobenetfromtheirprofoundknowledgeandexperienceinthefuture,aswell. IowemuchtomyfriendsSabihGuzelgoz,_IbrahimDemirdo~gen,EvrenTerzi,AliGorcin,OzgurYurur,M.BahadrCelebi,AlphanSahin,MuratKarabacak,M.CenkErturk,HazarAk,Dr.BilalBabayi~git,Dr.MustafaEminSahin,MuradKhalid,_IsmailButun,andSadiaAhmed.Wesharedsomanythingswiththem.Theyalsotaughtmesomanyvirtues.Sincerefriendshiptostartwith,unselshness,tolerance,andhelpfulness.Iamgratefultothemformakingmeabetterperson. IalsowouldliketothankTayyarGuzelandDr.MuratEratforhelpfuldiscussionsandTUBITAK-UEKAEforprovidingthemeasurementequipment. MysincereappreciationgoestomyparentsandmysistersTu~gbaandEmineforalwaysencouragingmeforpursuinghigherdegrees.Itisnotpossibletothankthemenough,butIwantthemtoknowthatIwillbegratefultothemthroughoutmylife. Last,butbynomeansleast,mydeepestgratitudegoestomyancee,Rabia,forherlove,allthesacricesshemade,herrmsupport,hervastpatience,andhersteadyencour-agement.Iwanttothankherfrommyheartforeverythingshehasbeendoing.

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LISTOFFIGURESiv ABSTRACTvii CHAPTER1INTRODUCTION1 1.1AdvantagesofPLCSystems1 1.2PLCSystems2 1.3StandardizationofPLCSystems4 1.4PLCChannel4 1.5OutlineofThesis5 CHAPTER2NOISEINPLCCHANNELS7 2.1MeasurementSetup9 2.1.1AnechoicChamber10 2.1.2PowerLineFilter10 2.1.3LISN10 2.1.4TransientLimiter12 2.1.5SpectrumAnalyzer12 2.2NoiseModelandMeasurementDataProcessing12 2.2.1NoiseModel13 2.2.2MeasurementDataProcessing16 CHAPTER3SIMULATINGTHEPLCNOISE35 3.1BackgroundNoise36 3.2NarrowbandNoise36 3.3ImpulsiveNoise37 3.3.1PeriodicImpulsiveNoise38 3.3.2AperiodicImpulsiveNoise39 CHAPTER4MULTIPATHEFFECTINPLCCHANNELS41 4.1MultipathPhenomenoninPower-LineChannel41 4.2TransmissionoverPower-LineChannel43 4.2.1ReectionandTransmissionCoecients43 4.2.2ReectionFactor45 4.2.3TNetworkStructure45 4.3AttenuationAnalysis48i

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5.1MappingNetworkTopology50 5.2PathSelection52 5.3ReectionCoecients53 5.4SimulationResults55 5.4.1EectofPhysicalTopologyonPLCChannels56 5.4.1.1LengthBetweenTransmitterandReceiver57 5.4.1.2LengthofBranch58 5.4.1.3LoadImpedance60 5.4.1.4NumberofBranchings62 5.5ChannelCharacterization64 5.5.1PLNwithTwoBranches66 5.5.2PLNwithFourBranches67 5.5.3PLNwithSixBranches69 5.6StatisticalAnalysis70 CHAPTER6CONCLUSIONANDFUTUREWORK78 REFERENCES81 APPENDICES85 AppendixACalculationofReectionandTransmissionCoecients86ii

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Table4.1MultipathcomponentsforTnetwork47 Table5.1MultipathcomponentsforTnetwork57 Table5.2Channelparametersforthenetworkwithtwobranches66 Table5.3Channelparametersforthenetworkwithfourbranches67 Table5.4Channelparametersforthenetworkwithsixbranches69iii

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Figure2.1NoisetypesobservedinPLCsystems8 Figure2.2Pictorialdescriptionofthemeasurementsetup9 Figure2.3BlockdiagramofLISN11 Figure2.4Noiselevelsoftwooutletsoneinsideandtheotheroutsidetheanechoicchamber13 Figure2.5Autocorrelationoftheabsolutevalueofthenoisegeneratedbyalightdimmer15 Figure2.6Processingofthecaptureddata15 Figure2.7MaximumpowerofchangeforeachfrequencyoveranACcycle20 Figure2.8TFAofbackgroundnoisecapturedfromoutsideofthemea-surementsetup22 Figure2.9TFAofbackgroundnoiseinanechoicchamber23 Figure2.10TFAofcomputertower24 Figure2.11TFAofdimmer25 Figure2.12TFAofdrill26 Figure2.13TFAofvacuumcleaner27 Figure2.14TFAofaTVset28 Figure2.15TFAofLCDmonitor29 Figure2.16TFAofCRTmonitor30 Figure2.17TFAofuorescent31 Figure2.18TFAofalaptopcharger32 Figure2.19TFAofwashingmachine33iv

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Figure3.1NoisetypesobservedinPLCsystems35 Figure3.2GeneratingthecoloredGaussianbackgroundnoise36 Figure3.3PSDofnoiseshapinglter37 Figure3.4Realizationofrealpartofanimpulsenoise39 Figure3.5Realizationofimaginarypartofanimpulsenoise40 Figure3.6SimulatedPLCnoise40 Figure4.1ExampleofanindoorPLNwiththedirectionalsegmentsshownandnumbered.42 Figure4.2MultipathpropagationinTnetwork.46 Figure4.3Multi-corecablewithcopperconductor48 Figure4.4Attenuationproleof100mcable49 Figure5.1ImpulseresponseofthechannelbetweenAandD55 Figure5.2FrequencyresponseandphasedetailsofthechannelbetweennodeAandD56 Figure5.3Impulseandfrequencyresponsefordierentdistancesbetweentransmitterandreceiver;(I)25m,(II)50m,(III)100m,and(IV)200m58 Figure5.4Impulseandfrequencyresponsefordierentlengthsofbranch;(I)5m,(II)10m,(III)15m,and(IV)20m59 Figure5.5Channelfrequencyresponsesfordierentloadimpedanceval-ues;(I)5,(II)10,(III)25,and(IV)5060 Figure5.6Channelfrequencyresponsesfordierentloadimpedanceval-ues;(I)200,(II)50,(III)1k,and(IV)50k61 Figure5.7Tnetworkwithmultiplebranchingsdistributedfromsinglenode62 Figure5.8Impulseandfrequencyresponseformultiplebranchescon-nectedatthesinglenode;(I)twobranches,(II)threebranches,(III)vebranches,and(IV)tenbranches63 Figure5.9GraphicalillustrationofthenPLCnetworktopologyconsid-eredinthissection66v

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Figure5.11SimulatedpowerdelayprolesforthePLNwithfourbranchesandallterminatedin(I)characteristicimpedance,(II)250,(II)2500,and(IV)opencircuit68 Figure5.12SimulatedpowerdelayprolesforthePLNwithfourbranchesandallterminatedin(I)characteristicimpedance,(II)250,(II)2500,and(IV)opencircuit69 Figure5.13GraphicalillustrationofthenPLCnetworktopologyconsid-eredinthissection71 Figure5.14DependencyofRMSdelayspread()andmaximumexcessdelay()onthenumberofbranchingpointskbetweenTxandRx74 Figure5.15DependencyofRMSdelayspread()andmaximumexcessdelay()onthedistancebetweenTxandRx75 Figure5.16DependencyofRMSdelayspread()andmaximumexcessdelay()onthelengthstatisticsofbranches76 FigureA.1Terminatedlosslesstransmissionline86 FigureA.2Transmissionlinefeedingalineofdierentcharacteristicimpedance87vi

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Inordertoestablishreliablecommunicationsystemsoperatingonpowerlinenetworks(PLNs),characteristicsofpowerlinechannelshavetobeinvestigatedverycarefully.Unpre-dictablecharacteristicsofPLNsseriouslyaecttheperformanceofcommunicationsystems.Similartotheothercommunicationchannels,PLCenvironmentisaectedbynoise,attenu-ation,andmultipathtypeofchanneldistortions.ThelevelofnoiseinPLNsismuchhigherthananyothertypeofcommunicationnetworks.Furthermore,thefrequencydependentattenuationcharacteristicsofpowerlinesandmultipathstemmingfromimpedancemis-matchesaretheotherdistortionfactorswhichhavetobeinvestigatedinordertoestablishareliablePLCsystem.vii

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InordertoconnectthePLCtransceiverstothemainsline,couplingcircuitsareused.Thesecircuitsareoneofthemust-haveequipmentforPLCsystems.Thecouplingcir-cuitplacedbetweenthetransceiverandmainslinetoblockthe501Hzor60Hz2frequencycurrentsinordertoprotectthesystemfromthemainslinevoltage.

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PLCsystemsarealsovibrantlymarketingtheirimportance,becausein-expensiveandeasier-to-usesystems.ThereareseveralindoorandoutdoorapplicationsforPLCsystems.Indoorpowerlineapplicationscanbelistedasfollows[3{6]: communicationbetweenelectricalhomedevicesandAMIforsmarthomeappli-cations,2. communicationfromhousetothecentralaccessunitforsmartgridsystems.

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ToregulateallthereleasedstandardsthroughouttheworldandpublishaninternationaltechnicalstandardforPLCsystems,IEEEfoundedanewworkinggroup(WG)in2005namelyIEEEP1901WG[11].ThisWGisamergeofPanasonicandHomePlugPowerlineAlliancemembers.ThescopeoftheP1901WGistodevelopaninternationalstandardforhigh-speedcommunicationdevicesthroughACelectricpowerlinesusingfrequenciesbelow100MHz.Thegoalistoreachdataratesupto100Mbps[12].1.4PLCChannel

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Thesefactorsdeterminethequalityofthechannel.Thequalityismostlyaparameterofthenoiselevelatthereceiverandtheattenuationoftheelectricalsignalatdierentfrequencies.Thehigherthenoiselevel,theharderitistodetectthereceivedsignal.Ifthesignalgetsattenuatedonitswaytothereceiveritcouldalsomakethedecisionharderbecausethesignalgetsmorehiddenbythenoise,whichisexpressedassignal-to-noiseratio(SNR)levelofthesignal.SNRisameasuretoquantifyhowmuchasignalhasbeencorruptedbynoiseandcalculatedas SNRdB=10log10Psignal Aratiohigherthan0dBindicatesmoresignalpowerthannoisepower. Multipatheectofthechannelistheotherdisturbancewhiletransmittingdataoverthechannel.Multipathphenomenoncanbeexplainedasthetransmittedsignalreachingthereceivingcircuitbytwoormorepathswithdierentdelays.1.5OutlineofThesis

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InChapter2,noiseinPLCchannelsisinvestigated3.AsimulationmodelforPLCchannelsisintroducedinChapter3.MultipathandattenuationcharacteristicsofPLCchannelsareanalyzedinChapter4.InChapter5,eectsofdierentPLNtopologiesonPLCchannelsarediscussed.4.ConclusionsandfuturestudiesaresummarizedinChapter6.

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Themainsourcesoftheimpulsivenoisearevariouselectricaldevicesconnectedtothepowerlinenetwork.ImpulsivenoiseneedstobecharacterizedverycarefullysinceitplaysanimportantroleintheperformanceandreliabilityofthePLCsystems.Somestudiesin-vestigatingtheimpulsivenoisecharacteristicsofPLCchannelareavailableintheliterature.Noisecharacteristicsofpowerlinenetworksinvariousbuildingsareinvestigatedin[17{20]byperformingmeasurementsatdierentpoweroutlets.Itisworthmentioningthatun-derstandingtheimpulsivenoisecharacteristicsofelectricaldevicesindividuallyisessentialfromthecommunicationaspect.Inthisrespect,someresultsonnoisecharacteristicsofdierentelectricalappliancesarepresentedin[21,22]aswell.Inthisstudy,aparticularmeasurementsetupisestablishedinordertoinvestigatethenoisecharacteristicsofvariouselectricaldevices.Themeasurementsetupisdesignedinawaythatitsignicantlyreduces8

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9

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anechoicchamber2. powerlinelter3. lineimpedancestabilizationnetwork(LISN)4. transientlimiter5. AgilentE4440APSAseriesspectrumanalyzer2.1.1AnechoicChamber

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BlockdiagramofLISNisdepictedinFig.2.3.LISNsare\Pi-type"ltersandtheyareverypowerfulelectricalnoiselters.ALISNmainlyconsistsoftwocapacitorsandoneinductorasitisshowninFig.2.3.Whenthepowercomesfromthemainsline,capacitorC1oersverylowreactancetohighfrequencycomponentsofthereceivednoiseandveryhighreactancetolowfrequencycomponents.Consequently,noiseathigherfrequenciesthan50Hzarerejectedandonlythelowfrequencycomponentsarekept.SinceinductorLactsasashortcircuitforlowfrequencycomponentsandopencircuitforhigherfrequencies,allthecomponentsthatbelongtohigherfrequenciesareltered.Asaresult,onlythelowfrequencycomponentsofthemainslinewillreachtoDUT.WhentheDUTisturnedon,thehigherfrequencycomponentsseenatpointxwillallbelongtoDUTandtheywillbepreventedtogobacktopowerlinebytheinductorL.CapacitorC2willactasthesameascapacitorC1acts.ItwilltransmitthehigherfrequencycomponentsofDUTwhileitblocksthecomponentsbelongtolowerfrequenciessuchasthemainslinevoltage.Asaresult,withthehelpoftheresistanceR2,higherfrequencycomponentsofthenoise,which11

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Throughoutthemeasurementcampaigns,allthesemeasurementequipmentitemizedaboveaswellastheDUTsexceptforthespectrumanalyzerareplacedinsidetheanechoicchamber.Inaddition,noisedataisobtainedbypluggingeachDUTindividuallyintoanoutletwithintheanechoicchambernotallowinganyotherdevicetosharethesameoutletatthetimeofthemeasurement. Inordertoevaluatetheeectivenessofthemeasurementsetupbeforestartingtheexper-iments,noiseleveloftwooutlets,oneinsideandtheotheroutsidetheanechoicchamber,arecompared.AsdepictedinFig.2.4,aremarkablechangeisobserved.Itisclearlyseenthatthenarrowbandnoiseandthenoiseduetotheelectricalloadsconnectedtothepowerlinenetworkarerejectedsuccessfully.Formostofthefrequencies,morethan20dBsuppressionofnoiseisachieved.2.2NoiseModelandMeasurementDataProcessing

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TheconditionssetaboveindicatethatthemeanandcorrelationpropertiesoftheprocessdonotchangeattheintegermultiplesofaperiodT.InPLCsystems,TcorrespondstohalforoneACcycleperiod,T0. InordertoverifythecyclostationarityofthenoiseandshowthatnoiseinPLCchan-nelsisrepeatingitselfwithaperiodofTorT=2,asimpleanalysisisperformedononeofthedevicesmeasuredbythemeasurementsetup.TheanalysisisbasedonobservingautocorrelationoftheabsolutevalueofthecapturednoisewaveformoveradurationthatisamultipleoftheACcycledurationT0.Theresultoftheanalysis,showninFig.2.5,conrmsthecyclostationarymodel.Notethattheautocorrelationoftheprocessisdenedasfollows:R(t+;t)=Efn(t)n(t+)g(2.3) whereEfgisthestatisticalexpectationoperator,()denotesthecomplexconjugateofitsinput,isthetimeshiftinthecorrelationoperation. Consequently,theinstantaneousPSDofnoisecanbecalculatedbytakingtheforwardfastFouriertransform(FFT)operationoftheautocorrelationofthesignal Itcanbeseenthat,theinstantaneousPSDistimedependentandperiodicaswell.Inordertoeliminatethetimedependencyof(2.4)andrevealtheaveragePSDofacyclosta-tionaryprocess,anaveragingoverthedurationofT0mustbeperformed.TheaveragePSDofacyclostationaryprocessisgivenby14

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Figure2.6Processingofthecaptureddata

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AssumethatthedurationofthecaptureddataequalstheMmultipleofT0andeachsectionwiththedurationofT0isdividedintoKpieces.NotethatthetotaldurationoftherecordeddataequalsMT0.LetNMK(k;m)denotethediscretedatasamplesfallingintothekthpiecewithinthemthACcycle:NKM(k;m)=n(kT0fs wherekandmarethefactorsthatassumevaluesfrom0toK1andfrom0toM1,respectively.fsisthesamplingfrequencyofthemeasurementequipmentthatcapturesthenoisedata,(x:y)impliestheinclusionofdiscretedatasamplesfromstartpositionxtilly.Iftheperiodogramof(2.6)isaveragedbyconsideringeachofthepiecesfallingintothesamephaseoftheACcycle,thefollowingexpressionisobtained:SNKM(k;m)=PK1m=0K T0fsjFFT(NMK(k;m))j2 whereFFT()correspondstoforwardFFToperation.NotethatthetimeresolutionoftheTFAisequaltoT0

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ColumnaoftheguresdemonstratestheTFAofthenoisegeneratedbytheelectricaldevices.Theprocesswhilederivingthissubgureisformulatedin(2.7)andillustratedinFig.2.6.NotethatthepowerlevelsinTFAguresforeachdevicearerepresentedwithdierentcolorcodes.ColumnbisthedemonstrationofthetimeaverageofinstantaneousPSDasdenedin(2.5).Asimilaroperationwasperformedalongthefrequencyaxisaswellinordertoseethenoisepowerevolutionoverthedurationofmainscycle.Theoutcomeofthisoperationisplottedincolumnc. Columna,b,andcshowthateachdeviceexhibituniquecharacteristicsfromtheper-spectiveofbothtimeandfrequency.Inordertoquantifytheconcentrationofthepoweroverfrequency,thebandwidthofthenoiseinjectedintothepowerlinenetworkiscomputedbyconsideringthefrequenciesatwhicha10dBdecreasefromthemaximumpowervalueisobserved.Inaddition,ifthenoiseoorisderivedfromFig.2.4,someimportantconclusionsregardingthenoisecharacteristicsofthedevicesinfrequencydomain(columnb)canbeoutlinedas

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Timedomaincharacteristics(columnc)ofthedevicesareanalyzedaswell.Theobser-vationscanbelistedas

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Inasimilarproceduredenedin[25],thecyclostationarybehaviorofthenoisegener-atedbyelectricaldeviceshasbeenquantiedbyconsideringtwoparameters,namelypeakexcursionandmaximumrateofchangeoftheinstantaneousPSDwhicharedenotedasPeandRc,respectively.PeindicatesthemaximumpowerchangevalueduringoneACcycleamongallthefrequencies,andRcrevealsthemaximumpowerchangeinTrsecondalongthesamefrequencyaxisinoneACcycle.PeandRcareformulatedasfollows:

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(b)Figure2.7MaximumpowerofchangeforeachfrequencyoveranACcycle ResultsforthemeasuredelectricaldevicesaretabulatedinTable2.1.Ascanbeclearlyseen,computertoweranddrillarethemostsignicantnoisesources.20

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Measureddevice Computertower 61:26 17:43 Dimmer 45:61 36:83 Drill 59:66 37:03 Vacuumcleaner 42:49 21:92 TVset 42:13 4:95 LCDmonitor 30:32 21:68 CRTmonitor 28:75 15:45 Fluorescent 24:30 7:98 Laptopcharger 23:47 21:12 Washingmachine 40:81 26:72 Inordertohaveabetterunderstandingofthesignicanceofdevices,themaximumrateofchangeforeachfrequencyhasbeenplottedinFig.2.7(a)and2.7(b). Finally,inordertoseethePLCnoisewhentwoormoredevicesarepluggedintoPLNatthesametime,TVsetanddimmerareplacedtogetherintothemeasurementsetupandnoisegeneratedbydevicesisrecordedandcomputed.theTFAanalysisisshowninFig.2.20.TFAsofTVanddimmernoiseareshownseperatelyinFig.2.14andFig.2.11,respectively.AscanbeseeninFig.2.20,whenthesetwodevicesareconnectedtogether,theystillgeneratetheirnoiseindependentlyfromeachother.Impulsesgeneratedbydimmerarelocatedat6:3msand16:3ms,whileTViscontinuouslygeneratingitsnoise,whichprovestheadditiveeectofnoiseinPLC.21

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BackgroundnoiseofPLCchannelscanbeassumedastheadditionofcoloredbackgroundnoiseandnarrowbandnoisecoupledtohepowerlinecables[30].Theadditioninfrequencydomaincanbestatedasnbg(f)=ncG(f)+nnb(f)(3.1) wherenbg(f),ncG(f),andnnb(f)representthetotalbackgroundnoise,thecoloredback-groundnoisewhichisacoloredGaussiannoise,andnarrowbandnoise,respectively.Thetotalbackgroundnoisenbg(f)remainsstationaryforverylongtimes,e.g.forseveralmin-utesorevenhours[17,31]. AmongallthenoisesourcesdepictedinFig.3.1, Figure3.1NoisetypesobservedinPLCsystems35

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arethemostimportantnoisesourcesinPLCchannels,becausetheiroveralldurationsareinmicrosecondslevelwhichmakethemhighlytimevaryingandtheycausemostoftheerrorsatdatatransmission[14,28,32]. Proposedpowerlinenoisetakesallthenoisesourcesunderconsiderationandgenerateseachnoisetypeindividually.3.1BackgroundNoise ThespectralshapeofcoloredGaussianbackgroundnoiseisobtainedfromthemea-surements.SincethescopeofthismeasurementwastodeterminethecoloredGaussianbackgroundnoiseofPLCchannels,torejectthenarrowbandnoisefromPLN,anechoicchamberwasused.ThenoiseshapinglterHn(f)isdepictedinFig.3.3.3.2NarrowbandNoise

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whereNrepresentsthetotalnumberofnarrowbandinterferers,andAk(t),fk,and'kdescribetheamplitude,centralfrequencyandphaseofthereceivednarrrowbandnoise,respectively.Totalnumberofinterferersandtheircentralfrequenciescanbeextractedbyempiricalmeasurementsandphase'kofeachnoisesourcecanbeselectedrandomlybetween[0;2].3.3ImpulsiveNoise

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whereNDisthenumberofdampedsinusoidsthatformtheimpulse,Akrepresentstheamplitudeofthekthsinusoid,fkdenotesthepseudofrequencyofthesinusoid,tpisthearrivaltimeoftheimpulses,'krepresentsthephaseofthekthsinusoid,kisthedampingfactor,and(t)denotesasquarepulsewithadurationoft.TheamplitudevalueAofsquarepulse(t)is TheamplitudeofeachdampedsinusoidAkisselectedtobesN(0;Gk2n)whereGkdenotestheincrementoftheimpulseoverthebackgroundnoisewithavarianceof2n.ValuesofGkcanchangebetween2030dB. Throughoutthesimulations,impulsivenoisetypesinPLCchannelsareanalyzedintotwocategories3.3.1PeriodicImpulsiveNoise

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wheretp(n)representsthearrivaltimeofnthaperiodicimpulse.Thetotaldurationofape-riodicimpulsesaresetto100sandtheiramplitudevariationareadjustedtobedistributedasGaussianliketheperiodicimpulses. Realandimaginarypartsofasimulatedimpulsewithatimedurationof50saredepictedinFig.3.4andFig.3.5,respectively.Finally,byusingthesimulationenvironmentarealisticnoisedataforPLCchannelsisgeneratedandplottedinFig.3.6.Lengthofthegeneratednoiseisestimatedas80mswhichisfourACcycles. Figure3.4Realizationofrealpartofanimpulsenoise39

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Figure3.6SimulatedPLCnoise40

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However,unlikethewirelesscommunicationmediums,sincethetopologyofanindoorPLNisstableandimmovable,analyticalcalculationofthefrequencyresponseofanypoint-to-pointchannelispossiblebyanalyzingthemultipathcomponentsofanyspecicindoorPLN.Itisworthmentioningthat,multipathcomponentsaremostlyaectedbythephysicaltopologyofthenetwork,lengthofthecables,characteristicimpedancesofthecablesandloadspluggedintotheterminationpointsofthePLN.Inordertocomeupwitharealisticsolution,prioriknowledgeaboutthePLNisneeded. Inthissection,rst,multipathcharacteristicsofPLCchannelsisgiven.Next,attenu-ationmodel,whichisasignicantfactorwhilecalculatingthetransferfunctionofaPLCchannel,isderived.Measurementresultsarecomparedwiththesimulationresults.4.1MultipathPhenomenoninPower-LineChannel

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ExampleofasimpleindoorPLNisdepictedinFig.4.1.Thepossiblesignalpropagationsegmentsareshownandnumbered.Ascanbeseenfromthegure,everylineconnectedtothepowergridcausestwomoredirectionalpathswhichareoppositedirections.So,thenumberofpossiblesegmentsofaPLNistwicethetotalnumberoflines.InFig.4.1,thenetworkconsistsof8nodes,7lines,and14possibledirectionalsegments.Forinstance,ifthetransmitterislocatedattheterminationpointnamedasT2andthereceiverislocatedatT5,variouspropagationpathscanbedenedbyusingnumbereddirectionalsegmentssuchas4!13!9(whichisassumedasthelineofsight(LOS)path)4!13!14!13!94!3!4!13!94!11!12!13!94!1!2!13!7!8!9...42

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Characteristicimpedanceofacableisdependenttothecable'scircuitcoecientsandoperatingfrequency,however,ithasnothingtodowiththelengthofthecable.Z0canbecalculatedasZ0=s G+jwC(4.1) whereZ0representsthecharacteristicimpedanceofthelinethesignalpropagates,wistheangularfrequency,andR,L,G,andCrepresenttheper-unit-lengthresistance,induc-tance,conductance,andcapacitancevalues,respectively.Asitisshownin[33,34],forthe43

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C(4.2) Consequently,forthecablesthatarecommonlyusedinpowerlines,characteristicsimpedanceZ0andtheimpedancevaluesoftheloadsconnectedtotheterminationnodesZLareas-sumedasrealvaluedandindependentfromtheoperatingfrequency[33]. Sincereectionandtransmissioncoecientsarerelatedtotheimpedancevalues,theyarebecomingfrequency-independenttoo. (f)=andT(f)=Tfor30kHzf30MHz(4.4) whereandTdenotethereectioncoecientandtransmissioncoecient,respectively.Thesetwocoecientsataparticularimpedancediscontinuityaregivenbythefollowingequations(seeAppendixA)[35]: =ZLZ0 whereZListheimpedancethatthesignalseesatthediscontinuity. Adierentwaytocalculatecharacteristicimpedanceofacableisbymeasuringtheinputimpedancesofthecablewithshortandopen-circuitterminationendings[36].Thesquare-rootoftheproductofthesetwoinputimpedancesgivesthecharacteristicimpedanceZ0=p whereZscandZocrepresentinputimpedancevaluesofthecablewithshortandopen-circuitendings,respectively.44

PAGE 56

whereKandMarethetotalreectionsandtransmissionsseenbythetransmitsignalalongatheparticularpropagationpath,respectively. However,sinceeachreceivedreplicaofthetransmittedsignaltravelsdierentlengthofpaths,denotedasdi,timedelaysoccuramongthemanditshiftsthephaseofthesignal.Thisfactordependsonthelengthofthepropagationpathandthevelocityofthepropagationwithinthepowerline.Thedelayoftheithpathcanberepresentedas;i=di wherevrepresentsthepropagatingvelocitywithinthecablewhichdependsonthespeedoflightc0andtherelativedielectricconstant"roftheinsulatingmaterialsofthecable.Notethatthespeedofthepropagationwithinthepowerlineisassumedtobe60%ofthespeedoflightinthisstudy[37].4.2.3TNetworkStructure

PAGE 57

Ifasignalleavesnodejandreectionoccursatnodeiandthensignalpropagationcontinuesbackwardtonodej,thereectionfactoratnodeiisrepresentedasij.Ifasignalleavesthenodeiandatransmissiontakesplacethroughnodej,thetransmissioncoecientfornodejisrepresentedasTji.Sothereectionandtransmissioncoecients46

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Signalpropagatingnodes Reectionfactor Lengthofpropa-gation 1 TAB TAB:CB:TCB TAB:2CB:BC:TCB ... ... ... A!B!C!N1B!D TAB:N1CB:N2BC:TCB whereZCrepresentstheloadimpedanceconnectedtothenodeC.TheNstrongestmul-tipathcomponentsarelistedinTable4.1. Consequently,whenasignalistransmittedoveraPLN,thereceivedsignalconsistsofattenuated,delayed,andphase-shiftedversionofthetransmittedsignal.Ifthetotalnumberofreceivedmulti-pathsignalsislimitedtoN,anexpressionforthefrequencyresponseof47

PAGE 59

whereA(f;di)meansthefrequencyanddistancedependentattenuationwhichwillbedis-cussedinthenextsection.4.3AttenuationAnalysis InordertohaveabetterunderstandingaboutattenuationinPLNs,severalmeasure-mentswithdierentlengthsofcablesataparticularfrequencyrangewerecarriedoutinthisstudy.Itsdependencyonbothfrequencyandlengthisinvestigated.ThecabletypewhichiswidelyavailableinthePLNsestablishedinTurkey,wasusedinthemeasurements.Thecross-sectionofthemeasuredcableisdepictedinFig.4.3.MeasurementcampaignswereperformedbyusingAgilentvectornetworkanalyzer(VNA).Themeasuredfrequencyrangewasfrom30kHzto30MHzandcableswithlengthof10m,15m,25m,40m,50m,65m,75m,90m,100m,and200mwereexamined. Figure4.3Multi-corecablewithcopperconductor48

PAGE 60

whereA(f;di)isthesignalattenuationrelatedtothelengthandfrequency.Forinstance,thecomparisonofthemeasuredattenuationofacablewith100manditsestimateobtainedfrom(4.17)isplottedinFig.4.4.Ascanbeseen,theestimatetswellwiththemeasuredresults. Figure4.4Attenuationproleof100mcable49

PAGE 61

Inthissection,asimulationenvironmentisintroduced.ThealgorithmconsidersthePLNtopologyasagroupofmatriceswheretheconnectionpoints,reectionandtransmis-sioncoecients,terminationimpedances,andlengthsareregisteredintomatrices.Everyconnectionbetweenthenodesandthephysicalcharacteristicsoftheinterconnectionsarerepresentedassetofmatrices.Everyreectionandtransmissioncoecientofthenetworkiscalculatedbycomputingtheinputimpedancesandappliedtoeachmultipathcomponenttoestimatetheirreectioncoecients.5.1MappingNetworkTopology

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wherethetotalnumberofterminationpointsisdenotedbyh,krepresentsthetotalnumberofbranchingpoints,andmisthetotalnumberofnodeswherem=h+k.EachelementoftheconnectionmatrixCM[mm]correspondstoaninterconnectionbetweentwonodes.Sinceeachterminationpointisconnectedtoasinglebranchingnodeandnoconnectionexistsbetweenterminationpointstherst[hh]elementsofCMmatrixis0.Therefore,cijis1whenthereisaninterconnectionbetweenthecorrespondingtwonodes,otherwiseitis0.TheCMmatrixexhibitssymmetrywithrespecttoitsdiagonal.cij=cji(5.2) So,itispossibletoshowtheCMmatrixas;CM[(h+k)x(h+k)]=0B@0[hxh]CT[hxk]CTT[kxh]CB[kxk]1CA(5.3)51

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LengthsofeachinterconnectionbetweenthenodesareenteredintoanmmmatrixLMwhichisgeneratedbyreplacingtheonesinCMmatrixwiththecorrespondinglengths.Eachlengthoftheinterconnectionsisdescribedwithlij.ThelengthmatrixLMcanbedescribedasLM[(h+k)x(h+k)]=0B@0[hxh]LT[hxk]LTT[kxh]LB[kxk]1CA(5.5) whereLTcorrespondstothelengthmatrixofthecablesbetweenterminationpointsandbranchingsandLBmatrixdescribesthelengthsofthecablesamongthebranchingpoints.5.2PathSelection

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ItispossibletondinnitelynumberofdierentmultipathcomponentsevenforasmallPLN.However,onlyLnumberofmultipathcomponentsmakerelevantcontributionstotheoveralltransferfunctionofthePLCchannel.TheseLmutipathcomponentsareregardedassignicantpaths.Theselectioncriteriaofsignicantpathsisbasedonsettingapowerthresholdvalue.Thecomparisonismadewiththerstreceivedmultipathcomponentwhichisthemostpowerfuloneamongalltheotherreplicas.Thethresholdvalueissetto30dB; 10log10jh0j2 whereh0andhicorrespondstotherstandtheithpaths,respectively,andjj2representsthepowermagnitude.5.3ReectionCoecients Howeveratabranchingnode,ZLisbasedontreatingeachbranchextendingfromthenodeasparallelconnection.Ifahomogeneousnetworkisassumed,theimpedanceseenbytheincidentsignalarrivingatabranchingnodeisgivenbythefollowingexpression:ZL=Z0

PAGE 65

Consequently,thematrixR,whoseelementsexpressesthereectioncoecientforeachnode,isdenedas: andthetransmissioncoecientmatrixTTisformedas:T=t1:::thb1:::bkT1:::ThTh+1:::Tm(5.10) Itisworthmentioningthatcharacteristicimpedanceandloadimpedancesaremostlyfre-quencydependentvalues.However,sincenostatisticalinformationregardingtheimpedancesisavailable,theyareassumedtobeconstantsteady-stateimpedancevaluesforallfrequen-cies.Inordertocalculatethereectionfactorforeachmulti-pathcomponent,theprop-agationpathnodesequenceisusedtodeterminetheappropriatetransmission/reectioncoecients.TheprocesscontinueswithcalculationofchanneltransferfunctionH(f)givenby(4.16).ByapplyingtheinversefastFouriertransform(IFFT)operationonchannelfrequencyresponse,channelimpulseresponseisobtainedasfollows whereidenotesthedelayoftheitharrivingpath.54

PAGE 66

The5strongestpathsaredenedinTable5.1.Duetothereectionsoccurredattheopenterminationpoint,multipathcomponentsarereceivedperiodically.Receivedcompo-nentscanalsobeidentiedfromtheimpulseresponse,aswell.TheresultingfrequencyresponseofthechannelisshowninFig.5.2(a).Deepnotchesareobservedaround4:5MHz,13:5MHz,and22:5MHz.55

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(b)PhasedetailsFigure5.2FrequencyresponseandphasedetailsofthechannelbetweennodeAandD5.4.1EectofPhysicalTopologyonPLCChannels

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Paths Reectionfactor Lengthofpropagation(m) 1 0:6667 30 2 0:4444 50 3 70 4 0:0494 90 5 110 FromFig.5.3(a),sincedelaysbetweenmultipathcomponentsarerelatedtothelengthofthebranch,delaysbetweentherstcomingpathandtheothersdonotchangewiththedistancebetweentransmitterandreceiverchanges.However,duetotheattenuation,distortionincreasesandtheshapeofthechannelimpulseresponselosesitsoriginalshape. TransferfunctionsaredepictedinFig.5.3(b).Ascanbeseen,thenotchesdonotvarywitheitherfrequencyorlinelength.Thereasonforthatisthedelaysofthemultipathcomponentsarenotrelatedtothedistancebetweentransmitterandreceiver.ThemainfactorthatcanchangethedelaysisthelengthofthebranchBC.Additionally,attenuationtendstoincreaseasthedistanceandfrequencyincrease.57

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(b)Frequencyresponse

PAGE 70

(b)Frequencyresponse AscanbeseenfromFig.5.4(a),withtheincrementinthelengthofbranchBC,delayandattenuationvaluesforeachreceivedmultipathcomponentincrease,whilethedelay59

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Sincethepositionofthenotchesinfrequencydomaindependonthelengthofthebranch,ageneralizedexpressioncanbegiven;fN=45 whereLrepresentsthelengthofthebranchBCinmeterandtheresultisinMHz.5.4.1.3LoadImpedance

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Inordertoseetheeectofloadimpedance,theT-networktopology,whichhasbeenusedfortheprevioussimulations,wasused.Distancebetweentransmitterandreceiverwaskeptconstantat50mandlengthofthebranchingwas10m.Loadimpedancevaluesweredenedas5,10,25,and50.TransferfunctionsareshowninFig.5.5. SincereectioncoecientCBincreasesastheloadimpedanceincreasestowardZ0,reectedmultipathcomponentsattenuateless.Thus,strongermultipathcomponentswillbereceived.Thisleadstoanincrementinthedepthofthenotchesintransferfunctions. 61

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InordertoseetheeectofloadimpedanceshigherthanZ0,theT-networktopologywasused.Distancebetweentransmitterandreceiverwaskeptconstantat50mandlengthofthebranchingwas10m.Loadimpedancevaluesweredenedas200,500,1k,and50k.TransferfunctionsareshowninFig.5.6. SincereectioncoecientCBincreasesastheloadimpedancetendstogethighervaluesthanZ0,reectedmultipathcomponentsattenuateless.Thus,strongermul-tipathcomponentswillbereceived.Thisleadstoanincrementinthedepthofthenotchesintransferfunctions.AscanbeseenfromFig.5.6,notchesbecomemoreprominentwithhighervaluesofloadimpedance.5.4.1.4NumberofBranchings Fig.5.8(a)showsthechannelimpulseresponsesforallcases.Itisseenthat,increasingthenumberofbranches,whichareconnectedatthesamenode,increasestheattenua-62

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(b)Frequencyresponse

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TheRMSdelayspreaddescribesthecapabilityofthecommunicationchannelofsupport-inghighdataratecommunicationsbyimplyingtheprobabilityofperformancedegradationbecauseoftheISIeect.Itiscalculatedastakingthesquarerootofthesecondcentralmomentofthepowerdelayproleandisdenedtobe

PAGE 76

Themaximumexcessdelay(XdB)ofthepowerdelayproleisdenedastherelativetimedelayfromtherstarrivedmultipathtothelastmultipathcomponentthatfallstoXdBbelowthemaximumone.If0representstherstarrivingmultipathcomponentandXisthedelayofthelastmultipathcomponentwhichisstillwithinXdBofthestrongestarrivingmultipathsignal,thenmaximumexcessdelaycanbecalculatedas whereXdBrepresentsthemaximumexcessdelaywithathresholdvalueofXdB.Pleasenotethat,itisnotnecessarytoreceivethestrongestamplitudevalueat0.Withrespecttothesedenitions,thethresholdvalueforbothRMSdelayspreadandmaximumexcessdelayissetto20dB. Inordertounderstandtheeectofthenetworktopologyonthechannelcharacterizationparameters,dierentPLNtopologiesaregenerated.ThegenericformofthePLNtopologyisillustratedinFig.5.9.Inthissection,impactofloadingatterminationnodesandnumberofbranchingnodesbetweentransmitterandreceiverisanalyzed.Impedancevaluesofterminationpointswerevariedascharacteristicimpedance,250,2500,andopencircuit.Thenetworkisconsideredwithtwo,fourandsixbranchesinthelinkbetweensendingandreceivingends.Foreachnetworktopology,dierentpowerdelayproleswithdierentterminationloadsareanalyzed.65

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BranchLoads Char.Imp. 0:0741 0.2 250 0:1457 0.4333 2500 0:1847 0.4667 Opencircuit 0:1896 0.4667

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BranchLoads Char.Imp. 0:1434 0.4333 250 0:2403 0.5 2500 0:3882 0.6333 Opencircuit 0:4189 0.6667 receiverwhichleadstoanincrementinthedelayparametervalues.Itisobservedthatthehighestvaluesamongthedelayparametervaluesareobservedfortheshortcircuitcase.5.5.2PLNwithFourBranches

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BranchLoads Char.Imp. 0:2288 0.6 250 0:4479 0.7 2500 0:6326 0.7333 Opencircuit 0:6572 0.7333 Figure5.12SimulatedpowerdelayprolesforthePLNwithfourbranchesandalltermi-natedin(I)characteristicimpedance,(II)250,(II)2500,and(IV)opencircuit5.5.3PLNwithSixBranches

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AmongtheseveraldierentphysicalcharacteristicsofPLNs,impactofthefollowingitemsonthedelayspreadparameters,namely,RMSdelayspreadandmaximumexcessdelay(20dB),willbeexaminedinthissection: Inordertoanalyzetheseparameters,morecomplicatedPLNtopologiesareformedasdepictedinFig.5.13wherenodesdenotedbyBandTarebranchingandterminationpoints,respectively.Thetotalnumberofbranchingpointsbetweentransmitterandreceiver70

PAGE 82

Asshownintheprevioussectionandanalyzedin[44,45],delayspreadparameterstakethemaximumvalueswhereterminationloadingsareterminatedinverylowimpedancesorveryhighimpedanceswhichareclosertoinnity.InordertoconsidertheworstcasescenariosforallthePLNtopologiesandsolelyfocusonthetopicslistedabove,alltheterminationpointsareassumedtobeopencircuits[54]. Inthisanalysis,matrixbasedPLCsimulationtechniqueproposedinSection5.1willbeconsidered.However,matricesaremodiedinawaythatthesimulationmoduleletsusgeneraterandomPLCnetworkswithdierentphysicalcharacteristics.Atthesametime,thesimulationenvironmentstillgivesusthecontrolofthespecicparametersofthephysicaltopologywhichthefocusison.Thetopologyofthenetworkisgeneratedbygeneratingdierentconnectionmatrices whereCTmatrixdescribestheinterconnectionsbetweentheterminationpointsandbranch-ingpoints,CBmatrixshowstheconnectionsamongthebranchingpoints.Totalnumberofterminationpointsandthetotalnumberofbranchingpointsaredescribedbyhandk,respectively.Thenumber\2"comesfromtheinterconnectionsoftransmitterandre-ceivertothePLN.Numberofbranchesextendingfromeachbranchingpointisuniformly71

PAGE 83

DierentPLCtopologieswithdierentphysicalattributesaregeneratedbymanipulat-ingthevaluesofh,k,andlengthsofinterconnectionslxy.DierenceonhandkvaluesresultsinachangeinthedimensionsofthesubmatricesdenotedasCBandCT.How-ever,itisworthsayingthat,inordertofocussolelyontheimpactofspecicphysicalcharacteristics,simulationsareperformedwithconstantnumberofbranchingpoints.Forexample,impactofdistancebetweentransmitterandreceiverisanalyzedwherethenumberofbranchingpointsiskeptconstantat4orimpactofnumberofbranchingsareanalyzedbysettingconstantnumberofkforeach20000realizations.Consequently,thereisnoneedtochangetheCBmatrixthroughoutthesimulationsforconstantbranchingpointnumber.CBmatrixcanbeshownas However,sincenumberofbranchesdistributedfromeachbranchingpointisuniformlydistributed,thiscaseisnotvalidforCTmatrix.SizeofCTmatrixwillbechangedwiththetotalnumberofbranchesh.

PAGE 84

00:::1 10:::0 ............ 10:::0 01:::0 ............ 01:::0 ............ 00:::1 ............ 00:::1 wheretherstandthesecondrowsrepresenttheinterconnectionsfromtransmittertonodeB1andfromreceivertoBk,respectively.TherestofCTmatrixisexpressingotherconnectionsbetweentheterminationnodesandbranchingpoints. AsdiscussedindetailinSection5.1,thecorrespondinglengthsofeachinterconnectionandimpedancesatterminationpointsarekeptinseparatematrices.WithanychangeinthedimensionsofCMmatrix,dimensionsoflengthandimpedancematriceswillalsochange. TheimpactofnumbernodesbetweentransmitterandreceiveronRMSdelayspreadandmaximumexcessdelaycanbeseeninFig.5.14(a).Whilederivingthisgure,distancebetweentransmitterandreceiverandlengthstatisticsofthebrancheswereconsideredtobe150mandU[10m30m],respectively,whereUreferstouniformdistribution.Upontheanalysisperformed,itisconcludedthatanincreaseinthenumberofbranchingnodesgivesrisetoanincreaseinRMSdelayspreadsvalue.Thisbehaviorcanberelatedtomoremultipathcomponentsreceivedandtothemultipathcomponentsarrivingatlargerdelaysaskincreased.73

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(b)Maximumexcessdelay

PAGE 86

(b)Maximumexcessdelay

PAGE 87

(b)Maximumexcessdelay Finally,theimpactofbranchlengthstatisticsisseeninFig.5.16(a)andFig.5.16(b)wherethenumberofbranchingpointsbetweentransmitterandreceiverwassetto4andseparationdistancebetweentransmitterandreceiverwas150m.Amongalltheanalyzedfactors,changeinbranchlengthstatisticsseemstoyieldthemostdrasticchangeindelay76

PAGE 89

Noiseisregardedasoneofthemainchallengesthathastobeaddressedfortheestablish-mentofreliablePLCbasedcommunicationsystems.Impulsivenoise,generatedbyhouseappliancesconnectedtothenetwork,beingoneofthenoisetypespresentinPLCsystems,needsspecialattention.InChapter2,inordertohaveabetterunderstandingofnoisegeneratedbyelectricaldevices,anovelandreliablemeasurementsetupwasestablished.Theeectivenessofthemeasurementsetupwasshown.Severalelectricalhomeapplianceswereanalyzedandthemostsignicantnoisesourceshavebeenidentied.Theirfeaturesbothintimeandfrequencyareextracted.Peakexcursionandmaximumpowerchangeofeachdevicehasbeenidentied.Additionally,theadditiveeectofnoiseinPLCchannelsisinvestigated. InChapter3,anoisesimulationmodelwasintroduced.Theproposedmodeltakesallthenoisesourcesunderconsiderationandgenerateseachtypeofnoise,namelycoloredback-groundnoise,narrowbandnoise,andimpulsivenoise,individually.Resultsweredepictedanddiscussed. MutlipathandattenuationcharacteristicsofPLCchannelswereinvestigatedinChapter4.Reectionandtransmissioncoecientswerederived.MultipathanalysisforaTnetworkisdone.Inordertohaveabetterunderstandingonattenuation,areliablemeasurement78

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InChapter5,amatrixbasedPLCmultipathsimulationenvironmentwasintroduced.Auniquepathselectionalgorithmwasproposed.Channeltransferfunctionsofseveralsimplenetworksareanalyzedwithrelevantdiscussions.Eectof wereinvestigated.Importantrelationsbetweentheabovementionedphysicalattributesandthechanneltransferfunctionsaredrawnbaseduponthesimulationresults.BesidestheinvestigationofsomespecicPLNs,impactofthephysicalcharacteristicsofPLCnetworkonthechanneldelayspreadparameters,namelyRMSdelayspreadandmaximumexcessdelay,arestudiedstatistically.Eectof areanalyzed.Foreachattributeexamined,statisticsregardingthechanneldelayspreadpa-rametersarepresentedbyobservingcorrespondingcumulativedistributionfunction(CDF)curves.Relationsbetweentheattributeslistedaboveandthechanneldelayparametersarerevealed. Thisthesiscanbeconsideredasabasisforfuturestudiesinthiseld.Futureworksareplannedas

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ThepurposeofthisstudyistohighlighttheimportanceandtheeectivenessofPLCfornextgenerationcommunicationsystems.80

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S.T.Mak,\Apowerlinecommunicationtechnologyforpowerdistributionnetworkcontrolandmonitoring,"PowerDelivery,IEEETransactionson,vol.1,no.1,pp.66{72,jan.1986.[2] E.Owen,\Theoriginsof60-hzasapowerfrequency,"IndustryApplicationsMagazine,IEEE,vol.3,no.6,pp.8,10,12{14,nov/dec1997.[3] Y.-J.Lin,H.Latchman,M.Lee,andS.Katar,\Apowerlinecommunicationnetworkinfrastructureforthesmarthome,"WirelessCommunications,IEEE,vol.9,no.6,pp.104{111,dec.2002.[4] A.PasdarandS.Mirzakuchaki,\Asolutiontoremotedetectingofillegalelectricityusagebasedonsmartmetering,"aug.2007,pp.163{167.[5] I.Cavdar,\Asolutiontoremotedetectionofillegalelectricityusageviapowerlinecommunications,"june2004,pp.896{900Vol.1.[6] D.Hong,J.Lee,J.Choi,A.Pasdar,andS.Mirzakuchaki,\Powerqualitymonitoringsystemusingpowerlinecommunication,"Dec.2005.[7] D.CooperandT.Jeans,\Narrowband,lowdataratecommunicationsonthelow-voltagemainsinthecenelecfrequencies.i.noiseandattenuation,"PowerDelivery,IEEETransactionson,vol.17,no.3,pp.718{723,jul2002.[8] http://www.homeplug.com,TheHomePlugPowerlineAlliance.[9] Y.-J.Lin,H.Latchman,R.Newman,andS.Katar,\Acomparativeperformancestudyofwirelessandpowerlinenetworks,"CommunicationsMagazine,IEEE,vol.41,no.4,pp.54{63,april2003.[10] M.Hazen,\Thetechnologybehindhomeplugavpowerlinecommunications,"Com-puter,vol.41,no.6,pp.90{92,june2008.[11] S.GalliandO.Logvinov,\Recentdevelopmentsinthestandardizationofpowerlinecommunicationswithintheieee,"CommunicationsMagazine,IEEE,vol.46,no.7,pp.64{71,july2008.81

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H.B.Celebi,S.Guzelgoz,T.Guzel,H.Arslan,andM.K.Mihcak,\Noise,atten-uationandmultipathanalysisofplcnetworks,"in2010EuropeanSignalProcessingConference,Aug2010,submitted.[14] S.Guzelgoz,H.B.Celebi,T.Guzel,H.Arslan,andM.K.Mihcak,\Timefrequencyanalysisofnoisegeneratedbyelectricalloadsinplc,"inIEEEInternationalConferenceonTElecommunications,ICT,April2010,accepted.[15] S.Guzelgoz,H.B.Celebi,andH.Arslan,\Articulatingfactorsdeningrmsdelayspreadinlvplcchannels,"IEEETransactionsonPowerDelivery,submitted.[16] ||,\Statisticalcharacterizationofthepathsinmultipathplcchannels,"IEEETrans-actionsonPowerDelivery,submitted.[17] M.Zimmermann,\Ananalysisofthebroadbandnoisescenarioinpowerlinenetworks,"Int.Symp.Power-LineCommun.Appl.,ISPLC,2000.[18] Balakirsky,\Potentiallimitsonpower-linecommunicationoverimpulsivenoisechan-nels,"ISPLC,2003.[19] V.Degardin,M.Lienard,P.Degauque,A.Zeddam,andF.Gauthier,\Impulsivenoiseonindoorpowerlines:characterizationandmitigationofitseectonplcsystems,"inElectromagneticCompatibility,2003.EMC'03.2003IEEEInternationalSymposiumon,vol.1,May2003,pp.166{169Vol.1.[20] D.Umehara,S.Hirata,S.Denno,andY.Morihiro,\Modelingofimpulsenoiseforindoorbroadbandpowerlinecommunications,"Proc.ISITA2006,pp.195{200.[21] H.Meng,Y.Guan,andS.Chen,\Modelingandanalysisofnoiseeectsonbroadbandpower-linecommunications,"PowerDelivery,IEEETransactionson,vol.20,no.2,pp.630{637,April2005.[22] G.Avril,M.Tlich,F.Moulin,A.Zeddam,andF.Nouvel,\Time/frequencyanalysisofimpulsivenoiseonpowerlinechannels,"HomeNetworking,pp.143{150.[23] [Online].Available:http://www2.ssm.gov.tr/katalog2007/data/397/uruning/19.htm[24] J.Cortes,F.Canete,L.Diez,andJ.Entrambasaguas,\Characterizationofthecyclicshort-termvariationofinddorpower-linechannelresponse,"in2005InternationalSym-posiumonPowerLineCommunicationsandItsApplications.[25] F.Corripio,J.Arrabal,L.delRio,andJ.Munoz,\Analysisofthecyclicshort-termvariationofindoorpowerlinechannels,"SelectedAreasinCommunications,IEEEJournalon,vol.24,no.7,pp.1327{1338,July2006.[26] M.Gotz,M.Rapp,andK.Dostert,\Powerlinechannelcharacteristicsandtheireectoncommunicationsystemdesign,"CommunicationsMagazine,IEEE,vol.42,no.4,pp.78{86,apr2004.[27] H.Meng,Y.Guan,andS.Chen,\Modelingandanalysisofnoiseeectsonbroadbandpower-linecommunications,"ISPLC,2002.82

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N.AndreadouandF.-N.Pavlidou,\Modelingthenoiseontheofdmpower-linecom-municationssystem,"PowerDelivery,IEEETransactionson,vol.25,no.1,pp.150{157,jan.2010.[29] R.Hormis,I.Berenguer,andX.Wang,\Asimplebasebandtransmissionschemeforpowerlinechannels,"SelectedAreasinCommunications,IEEEJournalon,vol.24,no.7,pp.1351{1363,july2006.[30] W.Bo,Q.Yinghao,H.Peiwei,andC.Wenhao,\Indoorpowerlinechannelsimulationandcapacityanalysis,"dec.2007,pp.154{157.[31] M.ZimmermannandK.Dostert,\Analysisandmodelingofimpulsivenoiseinbroad-bandpowerlinecommunications,"ElectromagneticCompatibility,IEEETransactionson,vol.44,no.1,pp.249{258,feb2002.[32] V.Degardin,M.Lienard,A.Zeddam,F.Gauthier,andP.Degauquel,\Classicationandcharacterizationofimpulsivenoiseonindoorpowerlineusedfordatacommuni-cations,"ConsumerElectronics,IEEETransactionson,vol.48,no.4,pp.913{918,nov2002.[33] M.ZimmermannandK.Dostert,\Amultipathmodelforthepowerlinechannel,"Communications,IEEETransactionson,vol.50,no.4,pp.553{559,Apr2002.[34] ||,\Amulti-pathsignalpropagationmodelforthepowerlinechannelinthehighfrequencyrange,"Int.Symp.Power-LineCommun.Appl.,ISPLC,1999.[35] T.S.Rappaport,MicrowaveEngineering.Toronto:JohnWiley&Sons,1998.[36] R.A.Chipman,Schaum'sOutlineofTheoryandProblemsofTransmissionLines.NewYork:McGrow-Hill,1968.[37] T.MaenouandM.Katayama,\Studyonsignalattenuationcharacteristicsinpowerlinecommunications,"0-02006,pp.217{221.[38] H.Phillips,\Modelingofpowerlinecommunicationchannels,"inProceedingsofInter-nationalSymposiumonPowerLineCommunicationsandItsApplications,1999.[39] C.HensenandW.Schulz,\Timedependenceofthechannelcharacteristicsoflowvoltagepower-linesanditseectsonhardwareimplementation,"inAEUInt'l.J.ElectronicsandCommun.,vol.54,no.1,Feb2000,pp.23{32.[40] D.AnastasiadouandT.Antonakopoulos,\Multipathcharacterizationofindoorpower-linenetworks,"PowerDelivery,IEEETransactionson,vol.20,no.1,pp.90{99,Jan.2005.[41] T.BanwellandS.Galli,\Anovelapproachtothemodelingoftheindoorpowerlinechannelparti:circuitanalysisandcompanionmodel,"PowerDelivery,IEEETransactionson,vol.20,no.2,pp.655{663,April2005.[42] ||,\Anovelapproachtothemodelingoftheindoorpowerlinechannelpart2:Transferfunctionsanditsproperties,"PowerDelivery,IEEETransactionson,vol.20,no.3,pp.1869{1878,July2005.83

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T.Rappaport,Wirelesscommunications:principlesandpractice.PrenticeHallPTRUpperSaddleRiver,NJ,USA,2001.[44] J.Anatory,N.Theethayi,R.Thottappillil,andN.Mvungi,\Abroadbandpower-linecommunicationsystemdesignschemefortypicaltanzanianlow-voltagenetwork,"PowerDelivery,IEEETransactionson,vol.24,no.3,pp.1218{1224,july2009.[45] J.Anatory,N.Theethayi,andR.Thottappillil,\Channelcharacterizationforindoorpower-linenetworks,"PowerDelivery,IEEETransactionson,vol.24,no.4,pp.1883{1888,oct.2009.[46] ||,\Performanceofundergroundcablesthatuseofdmsystemsforbroadbandpower-linecommunications,"PowerDelivery,IEEETransactionson,vol.24,no.4,pp.1889{1897,oct.2009.[47] J.Anatory,N.Theethayi,R.Thottappillil,M.Kissaka,andN.Mvungi,\Theinuenceofloadimpedance,linelength,andbranchesonundergroundcablepower-linecom-munications(plc)systems,"PowerDelivery,IEEETransactionson,vol.23,no.1,pp.180{187,jan.2008.[48] ||,\Broadbandpower-linecommunications:Thechannelcapacityanalysis,"PowerDelivery,IEEETransactionson,vol.23,no.1,pp.164{170,jan.2008.[49] J.Anatory,M.M.Kissaka,andN.H.Mvungi,\Channelmodelforbroadbandpower-linecommunication,"PowerDelivery,IEEETransactionson,vol.22,no.1,pp.135{141,jan.2007.[50] J.Anatory,N.Theethayi,R.Thottappillil,M.Kissaka,andN.Mvungi,\Theeectsofloadimpedance,linelength,andbranchesinthebplc;transmission-lineanalysisforindoorvoltagechannel,"PowerDelivery,IEEETransactionson,vol.22,no.4,pp.2150{2155,oct.2007.[51] C.Konate,M.Machmoum,andJ.Diouris,\Multipathmodelforpowerlinecommu-nicationchannelinthefrequencyrangeof1mhz-30mhz,"sept.2007,pp.984{989.[52] H.Meng,S.Chen,Y.Guan,C.Law,P.So,E.Gunawan,andT.Lie,\Modelingoftransfercharacteristicsforthebroadbandpowerlinecommunicationchannel,"PowerDelivery,IEEETransactionson,vol.19,no.3,pp.1057{1064,july2004.[53] Y.T.Ma,K.H.Liu,andY.N.Guo,\Articialneuralnetworkmodelingapproachtopower-linecommunicationmulti-pathchannel,"june2008,pp.229{232.[54] I.Papaleonidopoulos,C.Capsalis,C.Karagiannopoulos,andN.Theodorou,\Statis-ticalanalysisandsimulationofindoorsingle-phaselowvoltagepower-linecommuni-cationchannelsonthebasisofmultipathpropagation,"ConsumerElectronics,IEEETransactionson,vol.49,no.1,feb.2003.84

PAGE 97

Reectioncoecientintransmissionlinesisanalyzedinaterminatedlosslesstransmis-sionlineasdepictedinFig.A.1. Thetotalvoltageonlinecanbewrittenasthesumoftheincidentandreectedwaves whereV+0istheamplitudeofincidentwaveandejshowsthephasedierence.Thetotalvoltageandcurrentattheloadarerelatedbytheloadimpedance,soatz=0 Sincethereectioncoecientistheratiobetweentheincidentandreectedwaves,reectioncoecientcanbewrittenas86

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=V0 whererepresentsthereectioncoecient.Ifwesolve(A.4)forV0 Sothetermreectioncoecientcanbewrittenas =ZLZ0 Transmissioncoecientdescribestheamplitudeofthetransmittedwaverelativetotheincidentwave.Inordertoderivethetransmissioncoecient,consideratransmissionlineconnectedtoanotherlineofdierentcharacteristicimpedance.Iftheloadlineisinnitelylongandterminatedwithitsowncharacteristicimpedance,itcanbeassumedthatnoreectionswillreceivefromitsend.AtransmissionlinefeedinganotheroneisdepictedinFig.A.2. 87

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Vrefl=V+0where=Z1Z0 Sothevoltageforz<0andforz>0,intheabsenceofreections,canbewrittenas Thetotalvoltageatz=0shouldbeequal.Byequating(A.10)and(A.11)atz=0 bysolving(A.12)transmissioncoecientcanbecalculatedas Itisobviousthatreectioncoecientcangetavaluebetween[1;1],wherereectioncoecientof1representstheterminationendedbyshortcircuitand1representsatermi-nationendedwithopencircuit.Consequently,itmaybesurprisingbutTmaybegreater88

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Inordertoshowtheaccuracyofthisstatement,powervaluesoftheincidentwaveandreectedandtransmittedwavesarecompared.Accordingtotheconservationofenergy,thetotalpowerofthesignalsaftertheimpedancediscontinuitypointshouldremainsamewiththepoweroftheincidentsignal. IfthetransmissionlinedepictedinFig.A.2istakenintoconsideration,voltageandcurrentvaluesonthelineforz<0are Thetime-averagepowerowalongthelineforz<0is 2ReVz<0(z)Iz<0(z)(A.18)=1 2ReV+0ejz(1+e2jz)V+0 Pleasenotethat,characteristicimpedancevaluesaremostlyrealnumbersasexplainedinSec.4.2.1.Themiddletwotermsinthebracketsareofthetermformxx=2jIm(x)andsotheyarepurelyimaginary.Thissimpliestheresultto89

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{z }Pincjj2V+02 {z }Prefl(A.22) Thetime-averagepowerowalongthelineforz>0,whichisequaltothepoweroftransmittedwave,is 2ReVz>0(z)Iz>0(z)(A.23) where then 2ReTV+0ejzTV+0 Accordingtotheconservationofenergy equalityshouldbemaintained.Poweroftheincidentwaveis90

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andthetotalpowerofreectedandtransmittedwavescanbewrittenas so whichprovesthat,itispossibletondvaluesoftransmissioncoecientthataregreaterthanunity.91