MIMO Communications for Inhome PLC Networks Measurements and Results up to 100 MHz中英文对照.docx
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MIMO Communications for Inhome PLC Networks Measurements and Results up to 100 MHz中英文对照.docx
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MIMOCommunicationsforInhomePLCNetworksMeasurementsandResultsupto100MHz中英文对照
MIMOCommunicationsforInhomePLCNetworks:
MeasurementsandResultsupto100MHz
RehanHashmat
(1),PascalPagani
(1),AhmedZeddam
(1),ThierryChonavel
(2)
(1)OrangeLabs,2av.PierreMarzin,22300Lannion,France
e-mail:
rehan.hashmat,pascal.pagani,ahmed.zeddam@orange-
(2)TelecomBretagne,CS83818,TechnopôleBrestIroise,29238BrestCedex,France
e-mail:
thierry.chonavel@telecom-bretagne.eu
Abstract—PowerLineCommunications(PLC)is
usedforinformationexchangeoverthelines
installedfordeliveringtheelectricalpower.
InhomePLCisatechnologywhichdelivers
telecomservicestoeverycornerofahousehold
throughalreadyexistingelectricalwiring.In
recentyears,PLChasemergedasapotential
candidatefordomestichighbitrateservices.The
currentinhomePLCtechnology,basedonSingle-
InputSingle-Output(SISO)configuration,under
achievesthecapacityofferedbythephysicalPLC
channel.TheinhomePLCchanneloffersmultiple
signalfeedportsas,usually,itcomprisesofthree
wires:
Phase,NeutralandProtectiveEarth.The
measurementsandresultspresentedinthispaper
demonstratethatupto90%enhancementin
inhomePLCchannelcapacityispossiblebyusing
multiple-inputmultiple-output(MIMO)technique.
IndexTerms—Channeltransferfunction,MIMO,Channel
capacity,Powerlinecommunications
I.INTRODUCTION
HEPLCtechnologydeliversinformationonelectrical
powerlines.Generallytheelectricalpowerdelivery
networksarecomposedofthreelevelsdependingonvoltage:
transmission,distributionandutilization.Transmissionand
distributionareaccomplishedbythreephasenetworkswitha
voltagelevelof11kVorabove.Attheutilizationstagethe
industryusesthree-phase,380volts;whileforhouseholds
single-phase,230voltsisacommonpractice.Three-phase
networksaremadeupofthreeconductors,oneforeachphase.
Theremaybeafourthconductorforneutral.Theseconductors
aresufficientlyisolatedfromeachother,eitherbyairorby
protectiveinsulation.Therefore,suchnetworksinherently
offerspacediversity.InthePLCliterature,variousSpace-
TimeCoding(STC)techniqueshavebeendiscussed,generally
for3-phaseindustrialnetworks,in[5][6][7][8][9][10].
Inmostdevelopedcountries,theinhomesinglephase
electricalwiringconsistsofthreecopperwires:
liveorphase
(P),neutral(N)andprotectiveearth(PE).Theexistinginhome
PLCsystems,however,utilizeonlyPandNforsignal
transportation.Asaresult,theinhomePLCtechnology
remainedconfinedtoSISOconfiguration.Nevertheless,
recentlyMIMOforsinglephase,inhomePLChasbeen
reportedin[1][4].TheinclusionofPEoffersmultiplesignal
transmit/receiveports:
P-N,P-PEandN-PE.AMIMO
scenariothuscreatedcanbeexploitedfortheenhancementof
PLCchannelcapacity.
WeperformedMIMOtransferfunctionmeasurementson
variousinhomePLCchannels.Westartedwithan
experimentalPLCnetworkdisconnectedfromtheACmains
andthenreplicatedthemeasurementsonareal-lifeinhome
PLCnetwork.
Inthispaper,sectionIIdescribesthetheoreticalbackgroundof
MIMOtechnique,sectionIIIshowsthemeasurements,
calculationsandresultsforexperimentalPLCnetwork,section
IVpresentsthemeasurementsandresultsforreal-lifeinhome
PLCnetworkandsectionVisforconclusions.
II.MIMOSYSTEMMODEL
MIMOcommunicationisawellestablishedtechniqueinradio
transmissionsystemsandcanbeequallyapplicabletoPLCby
replacingtransmitandreceiveantennaswithsignalfeedand
receiveports,andtheradiochannelwithelectricalwiring.
ConsideraMIMOtransmissionchannelwithMtransmitandN
receiveantennas,asshowninfigure1.Thechannelcanbe
describedbyaNxMchannelmatrixH.Theentryhn,mof
matrixHrepresentsthechannelcoefficientfromthemth
transmitantennaelementtothenthreceiveantennaelement.
Thesignalynreceivedatthenthreceiveantennacanbegiven
as
yn=n
M
nmm_hxw
=
+
m1
(1)
wherexmisthesignalsentbythemthtransmitantennaandwn
isthenoisereceivedatthenthreceiver.Thechannelinputoutput
relationshipcanbedescribedas
y=Hx+w
(2)
ThedescribedMIMOsystemispowerconstrainedatthe
transmitter,thatis,thetotaltransmittedpowerisnotmorethan
Pwatts.ThecapacityCofMIMOchannelisdefinedasthe
maximumdataratethatcanbetransmittedoverthechannel
withaprobabilityoferrorarbitrarilyclosetozero[12].
[logdet()]2
H
MHH
M
CI
ρ
=+(3)
where_denotesthesignal-to-noiseratio(SNR)ateachreceive
antennaandHindicatesaHermitiantranspose.ForM=N,the
equation(3)simplifiesto
_
=
=+
r
i
iM
C
1
2log(1λ)
ρ
(4)
whereristherankofHHHandi
λistheitheigenvalueofHHH
obtainedbyeigenvaluedecomposition(EVD).
HHAADH=(5)
HereAisthematrixcomposedoftheeigenvectorsofHHH,
andDisthematrixwhosediagonalentriesaretheeigenvalues.
ForM_N,singularvaluedecomposition(SVD)isusedinstead
ofEVD.TheSVDisgivenbythefollowingequation:
H=U∆V(5)
whereUandVareunitarymatrices,and_isthematrixwhose
diagonalentriesarethesingularvaluesofH.Singularvalues,
denotedbyδ,arerelatedtoeigenvalueasshownbyEq(6).
δ=λ(6)
ThematrixDisusefulincalculatingtheparameterRamong
channelcoefficientshn,m,whichgivesanideaofthecorrelation
amongthechannelcoefficients.
_=
()
max,()
diagD
diagD
R(7)
Rvariesfrom0.5(lowcorrelation)to1(highcorrelation)as
thediagonalentriesofDmovefrom0.5to1.0.
III.EXPERIMENTALPLCNETWORK
A.PLCChannelTransferFunctionMeasurement
ThefirstsetofPLCMIMO-channelmeasurementswas
performedonanexperimentalPLCnetworkatOrangeLabs
whoseschematicdiagramisshowninfigure2.
A,B,CandDrepresentelectricsockets.Sixdistinct
combinationsoffoursocketsprovidesixnetworkbranches:
AB,
A-C,A-D,B-C,B-DandC-D.Eachbranchcanbetreated
asaPLCMIMOchannel.Itshouldbenotedthatthenetwork
undertestisneitherconnectedtoACmainsof230voltsnor
earthed.Suchanisolatednetworkisusefultounderstandthe
behaviorofthephysicalwiresandeffectofbranchinginthe
absenceofexternalfactorssuchasimpulsivenoise,effectof
appliancepluggingandde-plugging,effectofload
mismatchingetc.
ThePLCchannelconsistsofP,NandPEwires.Itprovides
threepossibleports,P-N,P-PEandN-PE,fordifferential
signalstransmissionandreception.
Figure3showstheschematicdiagramofasplitterforMIMO
measurementsthatwehavedesignedandrealizedatOrange
Labs.ItisapassivedevicewhichsimplypairsupP,NandPE
intoP-N,P-PEandN-PEports.Thesplitterprovidesan
interfacebetweenthePLCnetworkandtheVectorNetwork
Analyzer(VNA).
DuetoKirchhoff'scircuitlaw,simultaneousrealizationof
threedifferentialfeedportsisnotphysicallypossible.
However,a2x2MIMOsystem,withtwodifferentialfeedand
receiveportsisrealizable.Forthispurpose,weperformed
three2x2MIMOmeasurementsoneachofthesixnetwork
branches(figure4a).ChannelTransferFunctions(CTF)h11,
h12,h21andh22aremeasured(bymeasuringS21)at1601
discretefrequenciesfrom2MHzupto100MHzbyaVNA.It
shouldbenotedthath11andh22areco-channels,andh12andh21
arecross-channels.
TheseCTFmeasurementsarethenarrangedinto2(rows)x2
(columns)x1601(layers)3-dimensionalchannelmatrices,as
showninfigure4b,forfurtheranalysis.
Figure6showstypicalco-channelandcrosschannel
transferfunctionsforthePLCchannelA-B.Wehaveobserved
thattransferfunctionsarestrongerforco-channelsas
comparedtocrosschannels.
B.PLCMIMO-ChannelCapacityCalculation
InthegeneralcaseofaMIMOsystemcomprisingofM
emitterportsandNreceiverports,thechannelmatrixH(f)can
bewrittenas:
wherehnm(f)representsthecomplexchanneltransfer
coefficientfromthemthemittertothenthreceiver,ata
frequencyf.Transmissionchannelsrepresentedbyhn,mwith
m=narecalledco-channels,andthoserepresentedbyhn,mwith
m_narecalledcross-channels.MIMOcapacityofradio
channelsisawellestablishedfact[2].Employing
beamformingstrategyforpowerallocation,theMIMO
capacityCMIMOforamulti-portchanneliscalculatedbyusing
theequation:
CMIMO=
()__
==
∆+
N
niRnt
Tnin
nt
x
x
Nfn
Pff
f
11
2)
()
()
log(1
λ
bits/sec(9)
wherei
λ()nfdenotestheeigenvaluesofHH
H
atagiven
measurementfrequency,Hstandsforchannelmatrixand
superscriptHrepresentsaHermitiantransposeofH.
Similarly,
TxP()nfisthetransmittedpower,
RxN()nfisthe
noiseatthereceiver,tnisthenumberoftransmitports,Nis
thenumberofpointsonthefrequencyaxisand∆fisthe
frequencystepsize.The
TxP()nfmask,asshowninfigure6,
recommendedbytheregulationauthoritieshasbeenselected,
accordingtowhich,a
TxPof-50dBm/Hzistransmittedfrom
0to30MHzand-80dBm/Hzonwardsupto100MHz.
Fornoise,wehaveconsideredacoloredGaussiannoisemodel
insteadofaflatnoise,seefigure7.ThePowerSpectral
Density(PSD)of
RxN()nfisamodeldescribedinICT
OMEGAproject[3].Thismodelwasextractedfrom
measurementsonpracticalPLCnetworks.Itcloselyresembles
thenoisemodelmentionedin[11].
RxN()nfisrepresented
byequation10.
RxN()nf=15.5
210
1−+
f
mW/Hz(10)
ForthecalculationofSISOcapacityCSISO,weselectedthe
channeltransferfunctionmeasuredforP-Nport.Thatis,the
mea
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