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Complexity
Volume2021,ArticleID5585892,10pages
/2021/5585892
ResearchArticle
ImprovedTomlinson–HarashimaPrecodingforUltraReliable
CommunicationinIntelligentTransportationSystems
ShibiaoHe,1XinyiYang,2andYongLiao2
1SchoolofElectronicInformation,ChongqingInstituteofEngineering,Chongqing400056,China
2SchoolofMicroelectronicsandCommunicationEngineering,ChongqingUniversity,Chongqing400044,China
CorrespondenceshouldbeaddressedtoShibiaoHe;******@
Received23February2021;Revised8March2021;Accepted24March2021;Published5April2021
AcademicEditor:RenkeHan
Copyright©2021ShibiaoHeetal.(isisanopenaccessarticledistributedundertheCreativeCommonsAttributionLicense,
whichpermitsunrestricteduse,distribution,andreproductioninanymedium,providedtheoriginalworkisproperlycited.
Cyber-physicalsystems(CPSs)
oftheapplicationoftheCPSsinallkindsofenvironments,especiallythecellularvehicle-to-everything(C-V2X)whichneedshigh
qualityend-to-endcommunication,
informationtransmissioncausedbythefadingeffectandthefasttime-varyingcharacteristicsofthechannelforC-V2X
communication,animprovedTomlinson–Harashimaprecoding(THP)algorithmformultipleinputmultipleoutput(MIMO)
(CSI)andcorrelationareexploitedtocompensateinstantaneousCSI,whichcould
reflectcurrentreal-,theiterativewaterfillingpowerallocationalgorithmandthemultiuser
schedulingalgorithmbasedonthegreedyalgorithmarejointlyoptimizedandappliedtotheTHP,whichcouldimprovethe
-speedmobility
scenariosandimprovebiterrorratio(BER)performanceaswellasspectrumutilization.
,anditisdifficulttomeetthecon-
straintsofalargenumberofcomputingrequirementsand
Inrecentyears,theconstructionofglobalsmartcityislowlatency.(erefore,mobileedgecomputing(MEC)
accelerated,whichmakescyber-physicalsystems(CPSs)canbeintroducedintotheC-V2X.(eC-V2Xbasedon
developrapidly[1].Large-scalenetworkedCPSsareMECistomovepartofthecomputingpowerofthecore
deployedtoaddressglobalneedsinareassuchasenergynetworktotheedgeoftheC-,theMEC
[2,3],transportation[4,5],powersystem[6,7],andauto-serverisequippedwithroadsideunit(RSU).(evehicle
control[8,9].Asanintelligentsystemintegratingcom-uploadsthecalculationtasktotheRSUthroughtheV2I
puting,communication,andcontrol,anyproblemsmaycommunication,andtheMECservercorrespondingto
affectthenormaloperationoftheCPSs.(us,
ofCPSswhichincludessystemreliabilityandrobustnesscompletesthecalculation,thecalculationresultis
[11].And
totheinputofthesystemtimelyandeffectively,especiallycomputingrequirementsanddelayconstraintscanbe
forcellularvehicle-to-everything(C-V2X)communica-effectivelysolvedthroughthecombinationofMECand
tionscenarios.(evehicleintheC-V2XadoptsshortC-,thehigh-speedmobilityofthe
distancewirelesscommunicationtechnologytocom-vehiclemakessignalpropagationattenuatefast,andthe
municatebetweenvehicle-to-vehicle(V2V)andvehicle-
to-infrastructure(V2I)[10].Ultrareliablelowlatencychangingreflectiveobjectsontheroadwillalsodeteri-
communication(URLLC)isrequiredforC--oratethechannelandaffectthereceivedsignalstrength
ever,
2Complexity
problems,multipleinputmultipleoutput(MIMO)thespace-timecorrelationcharacteristicsofthe
technologyhasbeenappliedintheC-V2X[12,13].channel,whichcanreflectthecurrentchannel
MIMOcansuppresschannelfading,withtwomodesofcharacteristicsaccurately.
spatialmultiplexingandspatialdiversity[14,15].(espatial(2)BasedontheproposeddynamicCSImodel,inorder
diversitycanprovidereliablecommunication,andMIMOtoobtainthediversitygainoftheMIMOsystem,an
canobtaindiversitygainbyusingprecodingatthetrans--
,thealgorithm
,appliestheiterativewaterfillingpowerallocation
-
Tomlinson–Harashimaprecoding(THP)isatypicalnon-rithmtotheTHPalgorithmforjointoptimization
linearprecodingalgorithm,,theuserschedulingalgorithmaimsto
betweencomplexityandperformance[16].maximizespectrumutilizationandselectstheop-
Whenthevehicleismovingathigh-speed,thechanneltimalusersetaccordingtothechannelinformation
stateinformation(CSI),accordingto
symboltransmissionperiod.(erefore,traditionalchanneltheuserschedulingresult,thechannelmatrixbased
estimationisnotaccurate.(efasttime-varyingcharac-onthedynamicCSImodelisselectedandrecon-
teristicsofthechannelcausethefeedbackCSIcannotac-
curatelydescribethereal-timechannel[17,18].appliedtotheTHPalgorithm,whichcaneffectively
Moreover,ifthetransmitteradoptstheunreasonableeliminatemultiuserinterference.(eiterativewater
transmissionpowerallocationalgorithm,itwillnotbeablefillingalgorithmallocatespowertoeachuser
toobtaincommunicationqualityofservice(QoS)assuranceaccordingtothechannelcharacteristicsofeachuser
andbetterspectrumutilizationwhenthechannelhasafastinthesystem,realizingtheredistributionoftotal
time-varyingcharacteristic[19].(erefore,thejointpowerpower,whichcaneffectivelyimprovethetrans-
allocationalgorithmsintheprecodingdesigncaneffectivelymissionefficiencyandmaximizingthespectrum
improvethetransmissionreliabilityandspectrumutiliza-utilizationofthesystem.
tionofthesystem[20].
Precodingdesigninhigh-speedmobilescenehasbe-(
.[21]
asimpleprecodinganddetectionschemethatimplementsbasedontheiterativewaterfillingalgorithminhigh-speed
precodingbydividingmodulateddatasymbolsinthefre-mobilityscenarios,whichcontainsadynamicCSImodel
quencydomainintogroupsandinsertingmultipleredun-anduserschedulingalgorithmbasedongreedyanditerative
dantcarriersonbothsidesofeachdatagroup.(-
,theconclusionis
performanceinhigh-speedscenes,butitdoesnotanalyzediscussedinSection5.
-
mimouneandMassicotte[22]
methodbasedonKerdockcode.(emethodisbasedon
codebookwithlowcomplexity,butitsoverallperformanceisAssumingthatinamultiuserMIMO-IoVsystem,thein-
-
,itisassumedthatinfrastructureandNvehicles
Basedontheresearchandanalysis,animprovedTHPtransmitdata,andeachvehicleisequippedwithanantenna
algorithminhigh-speedmobilityscenariosisproposed.(eNR1.(eNvehiclesdataarerepresentedbyanN-di-
T
algorithmcombinesthestatisticalinformationwiththemensionalvectora[a1,a2,...,aN]andaretakenfrom
2
space-timecorrelationcharacteristicsoftheMIMOchannelanM-QAMconstellationwithenergyσa2(M−1)/3.
(
time,theiterativewaterfillingpowerallocationalgorithmconsistsofafeedbackmatrixB,Nnonlinearoperators
√
andthemultiuserschedulingalgorithmbasedonthegreedymodM(x),andafeedforwardmatrixFwithdimensions
algorithmarejointlydesignedwithTHP,whichcaneffec-NT×N.(etransmittingsignalentersthehigh-speed
spectrumutilization.(emaincontributionsofthispapersystemphysicstoachieve,Bisstrictlylowertriangularto
areasfollows:allowdataprecodingrecursivelywhilethemodulooperator
actsindependentlyovertherealandimaginarypartsofits
(1)Inordertosuppressthechannelfadingcausedbyinputaccordingtothefollowingrule:
high-speedvehiclemovement,wecombineMIMO√
andIoVtoconstructaMIMO-V2Icommunication√x−M
mod√(x)x−2M·√,(1)
,sincethechannelinthehigh-M2M
speedmobileenvironmentofvehicleshasfasttime-
varyingcharacteristics,weadoptthedynamicCSIwhere⌊c⌋indicatesthesmallestintegerlargerthanorequal
√
,modM(x)performsaperiodicmappingof
Complexity3
n1g1User1
Modulo
AGCanda1
′decision
Feedforwardr1r1
~Channel
amod(∙)amatrix
+HngN
–FN
Modulo
and
AGCaN
Feedbackrr′decision
matrixNN
B–IUserN
Figure1:MultiuserTHPsystemmodel.
√√
therealquantityxontotheinterval(−M,M].,thereceivedvectorcanbe
way,theprecodingsymbolsanareconstrained√into√thewrittenas
squareregionℵx(R)+jx(I)|x(R),x(I)∈(−M,M]
′(a+)−1+.(6)
andthetransmitpoweriscorrespondinglyreducedwithrGHFnGHFBvGn
respecttolinearprefiltering.
Accordingto(1),weseethattheprecodingsymbolsan
canbeiterativelycomputedasfollows:
n−1FillingAlgorithm
anan−[B−I]n,ℓal+dn,n1,2,...,N,(2)
√high-speedmobilityscenarios,thechannelresponsehofthe
wheredn2Mqnandqnisacomplex-valuedquantitywirelesschannelhasthecharacteristicsoftime-domain
whoserealandimaginarypartsaresuitableintegersthatselectivefadingandfasttime-varyingunderthecombined
(2)indicatesthatinfluenceofmultipatheffectandDopplereffect[23].(e
themodulooperatorinFigure1isequivalenttoaddingachannelismodeledaccordingtothegeometricmodel.
T
vectord[d1,d2,...,dN],thechannelimpulseresponse
thefeedbackmatrixBissettostrictlylowertriangular,we(CIR)expressionofthedownlinkoftheMIMOsystemcan
havedefinedthemodifieddatavectorva+-beobtainedas[23]
ingly,theprecodingcanberewrittenasLOSSB
hpq(t)hpq(t)+hpq(t),(7)
av−(B−I)a⟹aB−1v.(3)
LOSSB
wherehpqandhpqdenotetheline-of-sight(LOS)and
(eprecodingsymbolsanarefedtotheforwardmatrixsingle-bounced(SB)componentofthep-thtransmitan-
F.(eresultingNT-dimensionalvectorxFaisfinallytennatotheq-threceiveantenna,respectively.
transmittedoverthechannelusingtheNTantennasofthe
−jftLOS−c
infrastructure.(echannelismathematicallydescribedbyaLOS−j2πfcτpq(t)2πmaxcosϕTpR
hpq(t)Cee,
N×,[H]n,irepre-
sentsthechannelgainfromthei-thtransmitantennatotheN
n
SB1−j
ψn−2πfcτpq,n(t)j2πfmaxtcos(ϕR(t)−cR)
n-threceiveantenna.(ediscrete-timesignalatthen-thhpq(t)Clim√ee,
N⟶∞N
mobilevehiclecanbewrittenasn1
(8)
rnhnFa+nn,(4)
whereC(Kpq/Kpq+1),KistheRicefactor,τdenotes
wherehnindicatesthen-throwofHwhilennisadditive
2
whiteGaussiannoisewithzero-,andthelinkdelaysondifferentpaths
Stackingthereceivedsignalsofallusersintoasinglevectoraredifferent,whichwillresultinmultipatheffects.
TLOSn
−j2πfmaxtcos(ϕT−cR)jft((t)−c)
r[r1,r2,...,rN]andsubmittingin(3),itcanbeepande2πmaxcosϕRRdenotethe
expressedas
rHFa+n,(5)channel,whichisdeterminedbythemovingspeedofthe
(AoA)ofthe
T
wheren[n1,n2,...,nN]isaGaussianvectorwithzero-beamsondifferentpaths,aDopplerspreadeffectwillbe
2
,resultingintime-domainselectivefading.(e
feedbackoperationareperformedatthetransmitter,itiscoherencetimeisinverselyproportionaltotheDoppler
,eachsamplespread.(elargertheDopplershift,theshortertheco-
rnispassedtotheautomaticgaincontrol(AGC)
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