2024年智能超表面技术白皮书：信道建模与仿真（英文版）-智能超表面技术联盟（RISTA）

ReconfigurableIntelligentSurface

TechnologyWhitePaper:

ChannelModellingandSimulation

RISTECHAlliance

Nov.2024

ReconfigurableIntelligentSurfaceTechnologyWhitePaper:AChannelModellingPerspective

I

Contributorsarelistedasfollows.

Companies

Contributors

BeijingUniversityofPostsand

Telecommunications

ZhangJianhua

(jhzhang@)

ZhangYuxiang

(zhangyx@)

GongHuiwen

(birdsplan@)

ZhangJiwei

(rediaose@)

ZhangShiyu

(zhangsy@)

ChinaMobile

YuanYifei

(yuanyifei@)

SuXin

(suxin@)

ZTECorporation

DouJianwu

(dou.jianwu@)

ZhaoYajun

(zhao.yajun1@)

JianMengnan

(jian.mengnan@)

SoutheastUniversity

LiXiao

(li_xiao@)

SangJian

(sangjian@)

TangWankai

(tangwk@)

JinShi

(jinshi@)

BeijingJiaotongUniversity

HeRuisi

(ruisi.he@)

AiBo

(boai@

)

YuanYuan

(22110033@

)

ChinaTelecom

ChengZhenqiao

(chengzq@)

LiNanxi

(linanxi@)

ChinaUnicom

LiuQiuyan

(liuqy95@)

ZhaoMingyang

(zhaomy65@)

ReconfigurableIntelligentSurfaceTechnologyWhitePaper:AChannelModellingPerspective

II

Preface

Benefitingfromtherecentbreakthroughinmeta-surfacetechnologyandvastresearchofmulti-inputmulti-output(MIMO)technology,reconfigurableintelligentsurface(RIS)hasbecomeapotentialenablingtechnologyof6Gmobilenetworkstobestudiedin3GPPstartingfromJune2025.Oneimportantaspectoftechnologystudyin3GPPistheperformanceevaluationwherechannelmodelsandsimulationmethodologiesarethefundamentalblockstobeagreedupon.Differentfromactivenodessuchaslowpowernodes,orfromsensingobjects,RISdevicesarequasi-passive,e.g.,withoutpoweramplifiersoractivefilters,butwithregularshapesandsmoothsurfaces.AllthesemeanthatthechannelmodelingandsimulationmethodologyusedfortraditionalmobilenetworksorforintegratedsensingandcommunicationscannotbedirectlyusedbyRIS.

ThewhitepaperisdevotedtothechannelmodelingandsimulationmethodologyforRISstudy,withthepurposeofsettingabaselinefortheperformanceevaluationofRISin3GPP6Gstudynextyear.

ReconfigurableIntelligentSurfaceTechnologyWhitePaper:AChannelModellingPerspective

III

Contents

1.DeploymentScenarios 1

2.RISTypes&Assumption 5

3.ChannelModellingMethodology 7

3.1.GeneralFramework 7

3.2.RISPhysicalModel 11

3.2.1.RISphysicalmodelbasedonequivalentradiationpattern 12

3.2.2.ElectromagneticRCSmodel 13

3.2.3.Cosineradiationpatternmodel 25

3.3.ModelsforRISChannel 26

3.3.1.Pathlossmodel 28

3.3.2.Fastfadingmodel 29

3.3.3.Modelcomplexityreductionmethods 33

3.3.4.Optionalfeatures 36

4.EvaluationParametersforRISChannel 37

4.1.Largescaleparametersupdate 37

4.2.DelaySpread(DS) 38

4.3.RicianKFactor 39

5.System-LevelSimulationAssumptionforCalibration 40

5.1.SimulationAssumption 40

5.1.1.Networklayoutmodel 40

5.1.2.Propagationmodel 45

5.1.3.Antennaandbeamformingpatternmodelling 46

5.1.4.Othersimulationparameters 49

5.2.SimulationMethodology 50

6.Conclusions 52

7.Reference 53

ReconfigurableIntelligentSurfaceTechnologyWhitePaper:AChannelModellingPerspective

1

1.DeploymentScenarios

ReconfigurableIntelligentSurface(RIS)isoneofthemostpromisingtechniquesduetoitspotentialcapabilityofestablishingalowcostandlowpowerconsumptioncommunicationenvironment.Basedonconfigurablemeta-materials,RISiscapableofadjustingtheimpingingwirelesssignal’sphaseor/andamplitude,andthencontrolitspropagationdirection,whichmakesthedynamicallyfluctuatingwirelesspropagationenvironmentprogrammable.

Tillnow,aseriousofRISprototypeshavebeenlaunchedbydifferentcollegesandcompanies,meantime,anabundantoftestsandverificationsforRISprototypeshavebeendoneandpromisingcoverage/capacitygaincanbeobservedundervariousofscenarios.AlltheseprogressesrevealthepotentialcapabilityofRISforfuturewirelessnetworks.

TopromotethecommercialimplementationofRISinpracticalnetwork,oneofthemostimportantissuesistoidentifythehighvaluedeploymentscenariosforRIS.Fromoperator’sperspective,themostpromisingusageofRISistoenhancethecoverageandcapacity,sincetheyarethekeyfactorsthatanoperatorconsiderswhencommercializingcellularcommunicationnetworksduetoitsdirectimpactonservicequalityaswellasCAPEXandOPEX.Thus,thedeploymentscenariosforRIShavebeenstudiedbasedonalistofcharacteristics.Thefollowingscenariosaredefinedforthepurposeofpotentialevaluation.

Table1-1SummaryofpotentialRISdeploymentscenarios

Scenarios

Diagramofthescenario

Descriptionofthescenario

Enhanced

featureinthe

scenario

Outdoorblind

areacoverage

enhancement

(OCE)

NLOS

Reflectionpath

Staticorsemi-

staticand

dynamicplane

Outdoorcoverage

2

ReconfigurableIntelligentSurfaceTechnologyWhitePaper:AChannelModellingPerspective

Outdoorwide

anglecoverage

enhancement

(OACE)

LOS

Activearray

element

Dynamicplane

Radiationangle

Energy

conservation

Indoorcoverage

enhancement

(InCE)

NLOS

Reflectionpath

Staticorsemi-

staticand

dynamicplane

Indoorcoverage

O2I/I2O

[1]

coverage

enhancement(O2I/I2OCE)

O2I:

NLOS

Transmission

path

Staticorsemi-

staticand

dynamicplane

Transmittance

Interference

shield

I2O:

Lowattitude

coverage

enhancement

(LACE)

CollaborationofNLOSandLOSReflectionpathDynamicplane

SensingPositioning

Outdoor

throughput

enhancement

(OTE)

SU-MIMO:

MU-MIMO:

Collaborationof

NLOSandLOS

Reflectionpath

Staticorsemi-

staticand

dynamicplane

MIMO

Spacedivision

multiple

ReconfigurableIntelligentSurfaceTechnologyWhitePaper:AChannelModellingPerspective

3

Proposal1:RIScouldbeconsideredasastartingpointforprioritizeddeploymentinthefollowingscenarios:

lOutdoorstaticorsemi-staticcoverageenhancementinFR2

lIndoorstaticorsemi-staticcoverageenhancementinFR2

lO2I/I2Ostaticorsemi-staticcoverageenhancementinFR2

lOutdoordynamiccoverageenhancementinFR2

lIndoordynamiccoverageenhancementinFR2

lO2I/I2OdynamiccoverageenhancementinFR2

lLowattitudedynamiccoverageenhancementinFR2

lOutdoorthroughputenhancementinFR2,etc.

ThefollowingtableofEvaluationparametersforRISdeploymentscenariosisconsidered.(M)indicatesavaluemandatoryforevaluation,(O)indicatesoptionalforevaluation.

Table1-2EvaluationparametersforRISdeploymentscenarios

Parameters

Value

Themainaffectedscenarios

Transmittersandreceivers’properties

UE/BS

Locations

UE/BSlocationsareselectedinthecorrespondingcommunication

scenario

All

BS

configuration

BSconfigurationdecidesthesupportedRIStype

OACE

UE

performance

Receivingdirection

ALL

RIS

properties

RISsLocations

Horizontalposition,height,distancefromBS

ALL

Pitchangle

Variouspitchanglefordifferentapplications

LACE

Area(m2)

0.5,1,2

ALL

Martial

Nonopaqueandopaque

O2I/I2OCE

Angle

resolution

5°(M)，30°(O)

LACE,OTE

4

ReconfigurableIntelligentSurfaceTechnologyWhitePaper:AChannelModellingPerspective

Signal

properties

Center

frequency

26GHz(M),10GHz(O),sub6GHz(O)

ALL

Bandwidth

Fullband(M),Fixnarrowband(O)

ALL

Waveform

Continueswave(M),Pulsewave(O)

ALL

UEvelocity

3km/h(M),45km/h(O)

ALL

Proposal2:EvaluationparametersforRISdeploymentscenarioscanbecategorizedintothree

sections:characteristicsoftransmittersandreceivers,propertiesoftheRIS,andsignalattributes.Theparametervaluesshouldbechosenandanalyzedregardingtheprimaryscenariosthatareimpacted.

ReconfigurableIntelligentSurfaceTechnologyWhitePaper:AChannelModellingPerspective

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2.RISTypes&Assumption

Asapotential6Gtechnology,RIScanbeusedinwirelesscommunication,informationmodulation,energytransferring,sensing,positioningaswellasimaging.VarioustypesofRISweredevelopedandstudiedinacademiaandindustryincludingrefectionRIS,transmissionRIS,STAR(SimultaneousTransitionandReflectionRIS),absorberRISetc.,whichweremadebasedondifferentelectriccomponentssuchasPIN,varactor,liquidcrystal,CMOSswitchandnon-volatilecomponent.Meanwhile,besidestraditionalpassiveRISwithoutpoweramplifier,theactiveRIS,sensingRISandnon-reciprocalRISareproposedinacademiaaswell.

RefIectionRIS

TransmissionRIS

AbsorberRIS

STARRIS

Figure2-1DemonstrationofRIStypes

ForthestandardizationofRISchannelmodeling,itisnecessarytodownselectthecombinationofdifferentkindsofRISattributestofocusonthemostimportantaspectsintheinitialstageof6Gstandardizationtofacilitatetheprioritizedrequirements.

Inthefollowing,theassumptionsandtheprioritizedattributesofRISareidentifiedbasedontherequirementsofinitialRISdeploymentandtheconsensusinRISTA(RISTechnicalAlliance).

PrioritizetheattributesofRISasshowninTable2-1inRISchannelmodelinginitialstage.

Table2-1PrioritizedCombinationofRISattributes

No

Attributes

Candidates

1stPriority

2ndPriority

1

Type

Reflected,Transmitted,STAR,Absorber

Reflected

Transmitted

2

Mode

Passive,Active,Hybrid,Sensing

Passive

3

Utility

Relay,NewtypeAntenna

Relay

4

PanelShape

Plane,non-plane

Plane

6

ReconfigurableIntelligentSurfaceTechnologyWhitePaper:AChannelModellingPerspective

5

InformationModulation

Non-information-modulationInformation-modulation

Non-

information-modulation

6

Modulation

physical

component

Phase,Amplitude,Both

Phase

7

ModulationGranularity

1-bit,2-bit,…,Continuous

ALL

8

Polarization

Single,Dual

ALL

Assumptions:

LorenzreciprocityofwirelesschannelbasedonthelinearassumptionofRISphysicalmodel.Frequency:from0.5GHzupto100GHz,followthesamerangeasin3GPP.

Bandwidth:nomorethan10%ofthecarrierfrequency.FarfieldassumptionbetweenRISelementandreceiver.

MaxbouncingnumberinRIScascadingscenariofromBStoUE:2

ThereflectedortransmittedEMwavebyRISwillnotbeimpingedtothesameRISanymore.

ReconfigurableIntelligentSurfaceTechnologyWhitePaper:AChannelModellingPerspective

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3.ChannelModellingMethodology

3.1.GeneralFramework

Figure3-1ComparisonBetweenTraditionalCommunicationModelsandRIS-AssistedCommunicationChannelModels

[2]

ThechannelmodelingframeworkforRIS-assistedcommunicationlinksdiffersfromthetraditionalcommunicationmodelingframework.Asshownin

Figure3-1,

traditionalcommunicationchannelsonlyconsiderthechannelbetweenthetransmitter(BS)andreceiver(UE).Incontrast,RIS-assistedcommunicationchannelmodelingrequiresconsiderationofthreeinterconnectedcomponents:theBS-RISchannel,theRIS-UEchannel,andthephysicalmodeloftheRISitself.

Therefore,comparedtotraditionalcommunicationchannels,thecoreofRISchannelmodelingliesinaccuratelycapturingchannelcharacteristicsinthepropagationenvironmentthroughhigh-precisionyetlow-complexitymodelingmethods,whileenablingchannelsimulationacrossawiderangeoffrequencies,bandwidths,andvariousapplicationscenarios.Toachievethis,RISchannelmodelingmustmeetthefollowingrequirements:

-First,high-precisionlinkmodelingrequiresindependentmodelingoftheBS-RISandRIS-UElinks,whileconsideringtheinterrelationshipbetweenmultiplelinkstoaccuratelyreflectpathlossandscatteringcharacteristicsinthechannel.

-Second,high-precisionphaseshiftmodelingoftheRISneedstoaccountforitsscatteringpattern,idealphaseshifts,andangledependencies,whilealsoincorporatingthenon-idealquantizationeffectspresentinrealenvironments.

ReconfigurableIntelligentSurfaceTechnologyWhitePaper:AChannelModellingPerspective

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-Moreover,themodelshouldbecapableofsimulatingcomplexscenarios,includingUMi,UMa,InH,andIIoT,allowingflexibleadjustmentsforthelocationsofbasestations,userterminals,andtheRIS.

Toachieveaccuratesimulationatthelinklevel,theRISchannelmodelmusthandlemultipathfading,reflectingchannelfadingcharacteristicsincomplexenvironments.Additionally,physicalsimplificationsandoptimizationsofsystemsimulationsarenecessarytoimprovemodelingefficiency.

Forthepurposesofthepresentdocument,theframeworkofRISchannelmodellingisaddressedwiththeconsiderationsinthefollowingproposals.

Proposal4:theassumptionfortheframeworkofRISchannelmodelingandenhancementof

3GPPTR38.901

[1]:

1)Themethodologyin3GPPTR38.901isasthestartpointofRISchannelmodelling.

Figure3-2RISchannelmodelimplementbasedonthestartpointof3GPPTR38.901

[2].

2)Theper-hopbasicchannelmodelbetweenBS-UE,BS-RIS,RIS-RISorRIS-UEareconstructedbasedontheenhanced3GPPTR38.901channelmodel,wheretheisotropicantennaisassumedforbasicchannelmodel.

3)AphysicalRISpanelwiththepre-definedphase-shiftcodebookforRISelementscanberepresentedbyvirtualRISbasestationsinducedbyimpingingEMwaveswithdifferentdelay,incidentorpolarization.

4)Whatareexpectedtobeenhancedin3GPPTR38.901include:

-HeightdependentPL/LOSprobabilitymodel;

ReconfigurableIntelligentSurfaceTechnologyWhitePaper:AChannelModellingPerspective

9

-Absolutetimeofarrivalmodel.

5)ThefinalchannelmodelbetweenBSandUEarecomprehensiveofdirectpathandcascadedpath:

-Directpath:BS-UEchannel.

-Cascadedpath:BS-RIS-UEchannel.

RIS1RIS2

BS

UE

Figure3-3RISdeploymentscenarioforathree-hopcaselogical.Path4:BS→RIS1→RIS2→UE

ForthescenarioofRISdeploymentwiththree-hopthroughtwoRISpanels,asshownin

Figure

3-3,

therearefournodesincludingBS,RIS1,RIS2andUE.ForthelogicalpathwayfromBStoUE,therearefivecandidatelogicalpaths:

-logicalpath1:BS→UE

-logicalpath2:BS→RIS1→UE

-logicalpath3:BS→RIS2→UE

-logicalpath4:BS→RIS1→RIS2→UE

-logicalpath5:BS→RIS2→RIS1→UE

Notallthelogicalpathwayscontributesignificantlytothefinalchannelresponse,whichimpliesthatsomelogicalpathscanbeomittedbasedontheprincipleoftrade-offbetweencomplexityandaccuracy.

ReconfigurableIntelligentSurfaceTechnologyWhitePaper:AChannelModellingPerspective

10

Thefourthpathof“BS→RIS1→RIS2→UE”isselectedtodemonstratetheprocedureof

constructingthecascadedchannelfromBStoRISsandtoUE.Itcanbeobservedin

Figure3-3

thattherearethreehopsforlogicalpath4fromBStoUEbythereflectionofRIS1andRIS2,respectively.

-Hop1inlogicalpath4:BS-RIS1

-Hop2inlogicalpath4:RIS1-RIS2

-Hop3inlogicalpath4:RIS2-UE

Foreachhop,thetraditionalchannelmodellingmethodologyin3GPPTR38.901canalsoberecognizedbetweentwonodeswithsingleLOSand/ormulti-NLOSrays.

ForeachRIS,theimpingingEMwavewithspecificdelay,polarizationandincidentwillinduceavirtualRISbasestationwithcorrespondingTRPandpolarizedantennapatternifthecodebooksofRISpanelintwopolarizeddirectionsareconfigured.

0

FortheTRPandpolarizedantennapatternofavirtualRISbasestationinducedbyimpingingEMwave,thedetailscanbefoundinRISphysicalmodelsection.

Tx

V

...

1

2

3

BS-UEVV:

BS-UEVH:

\\

/

\\

V11V12V12

RIS2

H1,0,τ1,0

V1

RIS1

H2,1,τ2,1

V11

H3,2,τ3,2

V11VV11h

Rx

V11V

/ //

/V12V

V12VV12h

V2

\V11h

V12h

\

Figure3-4DirectionaltreegraphforthecascadedRISchannelmodel(logicalpath4)

Asshownin

Figure3-4,

eachrownumberedbyinteger0~3representaphysicalentityfromBS,RIS1,RIS2andUE,respectively.Thelinesbetweentworowsrepresenttherayscorrespondingtotwo

physicalnodesbasedon3GPPchannelmodel,withtheattributesofdelay,channelcoefficients,and

ReconfigurableIntelligentSurfaceTechnologyWhitePaper:AChannelModellingPerspective

11

AOA/AOD/ZOA/ZOD.EachlinebeforeRISrow(row1androw2)willinduceavirtualRISbasestationassociatedtoaRISpolarizationdirectionnumberby1and2,respectively.

AcombinedpathfromBStoUEinthedirectionaltreegraphiscomposedofsub-pathsbetweenadjacentrows,subsequently.

ThechannelresponseforacombinedpathbetweenBSandUEisillustratedasthefollowing:

-Channelcoefficients:themultiplicationofthecoefficientsofallsub-paths

-Absolutiondelay:thesumoftheabsolutedelayofallsub-paths

-AOA/ZOA:theAOAandZOAofthefirstsub-path

-AOD/ZOD:theAODandZODofthelastsub-path

Proposal5:DirectionaltreegraphscanbeusedforconstructingthecascadedRISchannelmodelwithmulti-logicalpathways.

3.2.RISPhysicalModel

ThephysicalmodelofaRISisfundamentallybasedondefiningtheradiationpatternofRISarrayelements,alsoknownasRadarCrossSection(RCS).Currently,themainmethodsformodelingRISincludethefollowing:

1)Physicalmodelbasedonequivalentradiationpattern

[2]:

ThismodelrepresentstheRISresponsetosignalsthroughanequivalentradiationpattern.ItfirstderivesthefielddistributionofRISelementsusingphysicaloptics,thenappliestheequivalenceprincipletocalculatethesecondaryradiationoftheelements.TheradiationpatternofeachRISelementisdefinedandcomputed,ultimatelyformingtheoverallradiationpatternoftheRIS.

2)RCSModelBasedonElectromagneticTheory

[3]:

ThismethoduseselectromagnetictheorytoestablishaccurateRCSmodelsunderdifferentpolarizationconditions.ThismodelingapproachaccuratelydescribesthereflectioncharacteristicsofRISelementsincomplexelectromagneticenvironments,providingatheoreticalfoundationforevaluatingtheperformanceofRIS.

3)SimplifiedCosineRadiationPatternModel

[4]:

Thismodelusesasimplifiedantennaradiationpatternassumptionandadoptsthecos!θmodeltodescribethedirectionalcharacteristicsofRISelements.Whilethismethodiscomputationallysimpleandsuitableforscenarioswithlowersystemrequirements,itsaccuracymaybeinferiortothatoftheRCSmodelbasedonelectromagnetictheory.

ReconfigurableIntelligentSurfaceTechnologyWhitePaper:AChannelModellingPerspective

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3.2.1.RISphysicalmodelbasedonequivalentradiationpattern

Figure3-5TheillustrationofRISequivalentradiationpattern

[2]

UndertheilluminationofaTE-polarizedincidentsignal(Ei,Hi)atanangleof(θin,φin),the

electricandmagneticfieldsonthereflectionsideofthedual-polarizationcoherentRISelementcanbeexpressedas:

.(3-1)

where!risthewavevectorofthereflectedelectromagneticfield.Theelectricandmagneticfieldsonthetransmissionsideofthedual-polarizationcoherentRISelementcanbeexpressedas:

(3-2)

Accordingtotheelectromagneticequivalenceprinciple,thesignalleavingthereflectionsideoftheRISelementcanberegardedasradiatedbythefollowingequivalentelectricandmagneticcurrents:

(3-3)

Selectingareferencepoint!inthe(θ!ut,φ!ut)direction,theequivalentelectricandmagnetic

currents'radiationfieldEsatthispoint!iscalculated.BycomparingEswiththeincidentelectricfieldEi,wegettheequivalentradiationpatternofRISelement:

ReconfigurableIntelligentSurfaceTechnologyWhitePaper:AChannelModellingPerspective

13

whereλisthesignalwavelength,risthedistancefrom!totheRISelement,Eisthe

parallelpolarizationcomponentofEs,andEiisthescalarformofEi.TheoverallradiationpatternoftheRISpanelisthesuperpositionoftheeffectsoftheRISelements:

(3-5)

Proposal6:ThemodulationeffectofRISonsignalscanbecharacterizedusinganequivalentradiationpattern.TheradiationpatternofindividualRISelementscanbederivedandcalculatedusingphysicaloptics,whiletheoverallradiationpatternoftheRISpanelisobtainedbycombiningtheradiationpatternsofitselements.

3.2.2.ElectromagneticRCSmodel

.LocalcoordinatesofRISelement

TherectangularRISelementisassumedinRISchannelmodelling.

ForaRISelement,thelocalcoordinatesisconstructedasshownin

Figure3-6,

wheretheoriginislocatedatthecentreoftheRISelement,thex-axisisparalleltothelengthdirection,they-axisis

paralleltothewidthdirectionandthez-axisisperpendiculartotheplaneoftheRISelement.n

Z

y

ly

VPOI2

O

VPOI1

lx

x

RISeIement

14

Figure3-6ThelocalRISelementcoordinates

ThetwoindependentpolarizationvectorofRISelementarerepresentedbyvpol1andvpol2in

thelocalcoordinatesofRISelement,respectively,asshownin

Figure3-6,

and

pol1,pol2.

v=1v=1

pol1pol2,

vr.v=0

.BasicphysicalmodelofRIS(Reflection)

Undertheassumptionofphysicaloptics,PEC,far-fieldandrectangularpatchofRISelement,thebistaticRCSforeachofindependentpolarizationcomponentsinRISelementcanbederivedas

inEq.(3-6a)and(3-6b),respectively

[3].

(&2HS2)'

whereσpol1andσpol2areRCSofRISelementcorrespondingtotheindependentpolarizationofvpol1andvpol2,respectively;risthedistancefromthecentreofRISelementtothetargetfieldpoint;Hsisthemagneticfieldstrengthatthetargetfieldpoint;Hiisthemagneticfieldstrengthattheincidentpoint;nisthenormalizednormalvectorofRISelement;ks=k.ks0=ksxx0+ksyy0+ksz乙0isthe

scatteringwavevector,ksoisthenormalizedvectorinscatteringdirection;sthewave

numberandλisthewavelengthincarrierfrequency;x0,y0,乙0aretheunitvectorsalongthex,y,andzaxesofthelocalCartesiancoordinatesinRISelement,respectively;ki=k.ki0=kixx0+kiyy0+kiz乙0

ReconfigurableIntelligentSurfaceTechnologyWhitePaper:AChannelModellingPerspective

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istheincidentwavevector,ki!isthenormalizedvectorinincidentdirection;lxand"yarethelengthandwidthoftheRISelement,respectively.

Whenksx-kix=!，

(3-7a)

Whenksy-kiy=!，

(3-7b)

Hio-pol1andHio-pol2arethenormalizedvectorcomponentscorrespondingtoRISpolarizationvectors,vpol1andvpol2,respectively.

Asshownin

Figure3-7,

basedonPECassumption,theinducedelectriccurrentcorresponding

tovpol1andvpol2,aremainlyinducedbythemagneticfieldinHio-pol1andHio-pol2,respectively,whichoffersaflexiblecontrolforthephase-shiftineachpolarizationofRISelement.

Figure3-7DecompositionoftheincidentmagneticfieldvectoraccordingtotheRISpolarizedcomponents

ReconfigurableIntelligentSurfaceTechnologyWhitePaper:AChannelModellingPerspective

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(3-8)

LetpLsbethepathlossfromthecentreoftheRISelementtothetargetfieldpoint;!iisthepowerimpingingintotheRISelement;Assumingasimpleinsertionlossmodel,theamplitudeofthereflectionsignalintargetfieldpointcanberepresentedbyAs一pol1andAs一pol2,respectively.

.exp(jφi1).exp(jφpol1).exp(jφs1).Ilosspol1

一pol11'*λ2/(4τ),(si1pol1s1pol(3-9)

=Fs.w.'(Eio一pol1.Ai2)(..exp(jφ).exp(jφ).exp(jφ).,

where,

一pol1=(3-11)

—pol2=(3-12)

whereAi=Ai一pol1+Ai一pol2，Ai=，φi"andφi2arethephaseofincidentEMwaveofthefirstandthesecondpolarizationcomponentinRISelement,respectively;φpol1andφpol2arethephaseshiftofthefirstandthesecondpolarizationcomponentinRISelement,respectively;φs1andφs2arethe

opticaldistancephaseinthedirectionofscatteringcorrespondingtothefirstandthesecond

17

polarizationcomponent,respectively;Ilosspol!andIlosspol2aretheinsertionlossinthefirstandsecondpolarization,respectively.

ThedirectionofAicanbedeterminedbytheoneofEi;.Ai一pol1andAi一pol2canbedeterminedbasedonthedecompositionofAiasfollows:

1)Asshownin

Figure3-6,

thedirectionofHicanbedeterminedbykio×Ei;

2)AccordingtoParallelogramrule,Hicanbedecomposedintothetwocomponent:Hio-pol1andHio-pol2,and,

Hi=w1.Hi0—pol1+w2.Hi0—pol2.(3-13)wherew!andW2aretheweightsofthetwocomponentsofHio-pol1andHio-pol2,respectively,whichcanbecalculatedbysolvingtheoverdeterminedEq(3-13);

3)Definetwonon-orthogonalcomponentsforincidentelectricfield

E=-H

io—pol1io—pol2

,

E=H

io—pol2io—pol1

,

Ai-pol1=w1.Ei0-pol1.Ai

i-pol22i0-pol2i

A=w.E.A

.

,

(3-14)(3-15)(3-16)(3-17)

TocalculatethetotalscatteredfieldoftheRISpanel,wecanfirstcalculatethescatteredfieldcomponentsofeachelementbasedonEq(3-9)andEq(3-10)afterconfiguringthecodebook,andthensumthemup.

ForthelinearpolarizationimpingingEMwavefromanydirection,thepolarizationantenna

patternforRISelementcanbedeterminedbythefollowing:

(3-18)

whereFp"l"∈C3×",Fp"l2∈C3×1arethenormalizedpolarizationantennapatterncorrespondingtothefirstandthesecondpolarizationcomponentsinRISelement,respectively,and,

18

ReconfigurableIntelligentSurfaceTechnologyWhitePaper:AChannelModellingPerspective

(3-19)

(3