An UTD Model for the Analysis of Complex Indoor Radio Environments in Microwave WLAN Systems

AnAccurateUTDModelfortheAnalysisofComplexIndoorRadioEnvironmentsin

MicrowaveWLANSystems

PaoloBernardi,LifeFellow,IEEE,RenatoCicchetti,SeniorMember,IEEE,andOrlandinoTesta

Abstract—Anaccurateuniformtheoryofdiffraction(UTD)modelfortheanalysisofcomplexindoorradioenvironments,inwhichmicrowaveWLANsystemsoperate,ispresented.ThemodelemploysaheuristicUTDcoefficientsuitabletotakeintoaccounttheeffectsofbuildingfloors,walls,windows,andthepresenceofmetallicandpenetrablefurniture.Anumericaltoolbasedonanenhancedtridimensionalbeam-tracingalgorithm,whichincludesdiffractionphenomena,hasbeendevelopedtocomputethefielddistributionwithahighdegreeofaccuracy.Afterthevalidationofthemodel,obtainedbymeansofsomecomparisonswithmeasurementsavailableinliterature,anaccurateelectromag-neticcharacterizationoftypicalindoorenvironmentshasbeenperformed.Thenumericalresultsshowthattheelectromagneticfielddistributionandthechannelperformancesaresignificantlyinfluencedbythediffractionprocessesarisingfromthepresenceoffurniture.

IndexTerms—Indoorradiopropagation,wirelessLANsystems,penetrableobjects,electromagneticscattering,heuristicdiffrac-tioncoefficient,beamtracing.

I.INTRODUCTION

T

HEPERFORMANCESofmodernwirelesscommunica-tionsystemsstronglydependontheelectromagneticchar-acteristicsoftheenvironmentinwhichtheyoperate.Thisas-pectisparticularlyimportantforcellularphones,wirelesslocalareanetworks(WLANs)andpersonalcommunicationsystemsoperatingincomplexenvironments(buildings,factories,hospi-tals,railwaystations,airports,etc.).Intheseenvironmentsthefieldpropagationisdominatedbymanyscatteringprocessesduetoobstacles(walls,openings,furniture,etc.),therefore,manywavesarriveatthemobilereceiverfromdifferentdirectionsandwithdifferenttimedelays[1]–[6].Inaddition,thepresenceofhumanbeings,electronicapparatusandsensibleequipmentsre-quiresthatWLANsystemsguaranteeelectromagneticcompat-ibility(EMC)requirements.TosatisfybothsystemandEMCrequirementsitisnecessarythepreliminaryevaluation,directlyduringthedesignphase,ofthefieldcoverage,theperformancesoftheradiochannel,andthepotentialEMC/electromagneticin-terference(EMI)problems[7],[8].Tothisend,toovercomeex-

ManuscriptreceivedNovember20,2001;revisedJuly14,2003.ThisworkwassupportedbytheItalianMinistryforUniversityandScientificandTechno-logicalResearch(MURST)underContractENEA2001/10100/D23“Protectionofhumanbeingsandenvironmentagainstelectromagneticemissions.”

TheauthorsarewiththeUniversityofRome“LaSapienza,”De-partmentofElectronicEngineering,18-00184Rome,Italy(e-mail:bernardi@mail.die.uniroma1.it;cicchetti@mail.die.uniroma1.it).DigitalObjectIdentifier10.1109/TAP.2004.830260

pensivemeasurementcampaigns,anumericalpredictiontooltoinvestigatetheelectromagneticpropagationcharacteristicscanbeusefullyemployed.

Inthelastfewyears,predictionmodels,suitabletoanalyzeindoorradioenvironments,bothemptyandwithmetallicfurni-ture,havebeenpresented[5],and[9]–[18].Anempiricalmodelhasbeenproposedin[9]toevaluatethepowerdelayprofilewithinemptyindoorenvironments.Ageometricaloptics(GO)modelhasbeenusedin[10]–[12]topredictthefielddistributioninemptyindoorenvironments,whilein[13]–[15]themetallicuniformtheoryofdiffraction(UTD)coefficient[19]hasbeenemployedtomodelthescatteringarisingfrommetallicfurni-ture.Finally,in[5],and[16]–[18]thefieldscatteredbysimplepenetrablewedges,modelingindoorpartitions,havingalocalinteriorwedgeanglelessthanhasbeentakenintoaccountbymeansoftheheuristicdiffractioncoefficientsproposedin[20],[21].Asdiscussedin[22],suchcoefficientscanbeemployedonlyforalimitedclassofpenetrablestructuresandforparticularincidencesituations.Therefore,penetrablefurnitureandjunc-tionsbetweenpartitionscannotbeadequatelymodeled.Sincethefieldpropagationinindoorenvironmentscanbeconsider-ablyinfluencedbythepresenceoftheseconstituents[6],[23],itisnecessarytoemploysuitableelectromagneticfieldpredictionmodelsforarealisticevaluationoftheradiochannelcharacter-isticsandtheidentificationofzoneswherethefieldstrengthex-ceedsspecificthresholds.Acomprehensivereviewofthestateofartconcerningthepropagationpredictionmodelsforwirelesscommunicationsystemshasbeenrecentlypublishedin[6].Inthispaper,ahigh-frequencymodeltoanalyzecomplexin-doorenvironments,inwhichWLANsystemsoperate,ispre-sented.Themodel,basedonanenhancedbeam-tracingalgo-rithm,employsanewheuristicdiffractioncoefficienttoeval-uatethefieldinteractionwithpenetrableobjects.Suchcoeffi-cient,derivedusingthemethodologyproposedin[22],ispar-ticularlyusefultomodeltypicalindoorscenariosandprovidesanaccuratedescriptionofthescatteredfield[24],[25],yieldingphysicalinsightintothemechanismsresponsibleforthemulti-pathphenomenon.

Theformatofthispaperisasfollows.Themodelsadoptedforthehigh-frequencyfieldpredictionandfortheevaluationoftheradiochannelparametersaredescribedinSectionsIIandIII,respectively.InSectionIV,afterapreliminaryanalysistovali-datetheproposedmodelandtoestablishitsaccuracy,numericalresultsconcerningthefieldcoverageandchannelperformancesofsometypicalindoorenvironmentsarepresented.

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II.HIGH-FREQUENCYFIELDPREDICTIONMODEL

Themodeladoptedtopredictthehigh-frequencyfieldisbasedontheUTD.Theelectromagneticfieldisrepresentedintermsofdiffractedandray-opticalfields.Thevariouselementsoftheenvironmentaremodeledasjunctionsofthinflatmulti-stratelossy/losslessstructures[17].Thegeometricoptics(GO)fieldiscomputedbymeansofreflectionandtransmissiondyadics[26],whilethediffractedfieldisevaluatedbymeansofasuitableUTDheuristicdyadicdiffractioncoefficientderivedusingthemethodologyproposedin[22].Theadopteddiffractioncoefficientaccuratelymodelsthefieldinteractionwithedgesandjunctionsbetweenthinflatplatesofdifferentmaterials,sothatallthesignificantfieldprocesseswhichtakeplaceintheenvironmentarerigorouslymodeled.Sinceinindoorenvironmentsthefieldcontributionsarisingfromdoublediffractionaresmall[13],[16],onlyasinglediffractionprocessisconsidered.Accordingtothehigh-frequencyapproximation,theradiosourceismodeledusingitsvector-effectiveheighttodescribethegainpatternandthepolarizationproperties[27].Forcompletenessandforreader’sconvenience,thefieldpre-dictionproceduredescribedaboveisoutlinedinAppendixA.A.HeuristicDiffractionCoefficientforJunctionsFormedbyThinDielectricPlates

Theheuristicdiffractioncoefficient,derivedhereaccordingtothemethodologyproposedin[22],issuitabletoanalyzethefieldpropagationinindoorenvironmentsandtosolveawideva-rietyofelectromagneticscatteringproblemssuchasthosecon-cerningradartargetdetection,andradiationpatternsofantennasmountedonaircraft,shipsandbuildings.Sincethediffractioncoefficientforthevariousjunctionssuitabletomodelrealisticenvironmentscanbederivedinthesameway,onlythederiva-tionofthatconcerninga-junctionformedbythreethindielec-tricplates(seeFig.1)ispresentedbelow.

Assumingthattheincidentelectricfield

consistsofasphericalwavepropagatinginthe

direction,thehigh-fre-quencyelectricfield

scatteredfromthejunctionisgivenby(1)

whereisthespreadingfactor[28],

isthedyadicdiffractioncoefficient,andistheopticalpath

lengthfromthediffractionpoint

totheobservationpoint.Intheglobalreferencesystemformedbytheunit-vectors

,and(seeFig.1),theunit-vectorsdefiningthepropaga-tiondirectionfortheincidentandthediffractedraysareexpressedby

(2)(3)

where,andaretheusualsphericalangles.

WithreferencetotheincidencesituationshowninFig.1(b),thesphericalangleswhichidentifythecharacteristicopticraysontheKeller’scone,acrosswhichtheGOfieldisdiscontinuous,are

(4)

Fig.1.FielddiffractedfromaT-junctionformedbythreethinflatdielectricplateshavingdifferentelectricalcharacteristics.(a)Three-dimensionalviewand(b)crossview.Theray-basedreferencesystemsadoptedtodefinetheincidentandthescatteredfieldsareshown.

(5)(6)(7)

Consequently,theheuristicdyadicdiffractioncoefficient,de-rivedaccordingtothemethodologypresentedin[22],takes

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Fig.2.(a)BeamsshootingfromaTxantenna.Eachbeamisformedbythreerays.(b)Beamsplittingadoptedwhenabeamimpingesonathinplateedge.Theincidentbeamissubdividedintofourbeams.(c)DiffractedbeamsshootingfromthesegmentABbelongingtoathinplateedgeexcitedbyanincidentbeam.Thediffractedraytubeissubdividedinbeamshavingtriangularcrosssection.

thefollowingformshownin(8)atthebottomofthepage,

(with),andarethejumpwhere

indicator,thetransitiondyadicfunctions,andthe-fieldraytransferdyadrelatedtothethcharacteristicopticray,respec-tively[22].

In(8),thejumpindicatorsassumethefollowingvalues:

andbeingthewith

scalarcoefficientsforthesoftandhardpolarization,respec-tively[22].Theunit-vectorsdefiningthedyadsin(10)aregivenby

(11)(12)(13)(14)

where

(9)

andthetransitiondyadicfunctionstaketheform

(10)(15)

(8)

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withbeingtheunit-vectorofthethcharacteristicopticray.

Finally,the-fieldraytransferdyads

appearingin(8)arecomputedas

(16)(17)(18)

(19)

(20)

with

(21)

and

(22)

Intheaboveexpressions,andarethereflectionandtransmissioncoefficientsforathinflatdielectricplate,respectively[26].Theunit-vectorsappearingin(16)–(20)

definetheusualparallel

andorthogonalfieldpolariza-tion.

B.TheBroadcastBeam-TracingAlgorithm

Thebeam-tracingmethod,employingthebroadcasttech-nique[1],[5],[12],[13],and[24]isusedforthecomputationoftheelectromagneticfieldandthecharacteristicsoftheradiochannel.Anenhancedversionofthistechniquehasbeendevelopedinthispaperinordertoimprovethenumericalaccuracyandtheefficiency.

Twopartsformthenumericalalgorithm.Thefirst,deter-minestherayopticalpaths,thesecondtheelectromagneticfielddistribution.Thehigh-frequencyfieldpropagationisdescribedbymeansofelectromagneticraybeams.Inthecomputationalmodel,eachbeamisformedbythreeraysbelongingtotheedgesofaraytubehavingatriangularcrosssection.Thefieldradiatedfromtheantennaismodeledbymeansofbeamsshootingfromtheantennalocationtowardallspacedirections,independentlyoftheobservationpoint[Fig.2(a)].Togeneratebeamshavingaboutthesametriangularcrosssectionarea[Fig.2(a)],themethodproposedin[12]hasbeenadopted.Duringthepropagation,thebeamcanimpinge,totallyorpartially,onasurfacedescribingtheenvironment[Fig.2(b)],itcancapturetheobservationpoint,or,finally,itmaynotinterceptanyoftheenvironmentelements.Inthefirstcase,usingSnell’slaw,thetransmittedandthereflectedbeamsareevaluated.Ifthebeampartiallyimpingesonthesurface,itissplittedinnewbeamsinawaythattheytotallyintercept,ornot,thesurfaceunderconsideration[Fig.2(b)].Then,therayopticalpathsofthediffractedfieldaredetermined.Tothisend,asubdivisionofthediffractedraytube,identifiedbythetwoKeller’sconeswhosetips,AandB,aretheextremesofthesegmentexcitedbytheincidentraybeam[Fig.2(c)],isperformed.Ifthebeamdoesnotinterceptanyenvironment

Fig.3.Channelpowerdelayprofile.DistancebetweenTxandRx:(a)3.03mand(b)22.42m.Thesolidlinecorrespondstothecomputedresults,whiletheshort-dotlinestothemeasurementsreportedin[11].Frequency950MHz.

elements,itdoesnotproduceanysecondarybeams,and,con-sequently,itcomesoutfromthefieldcomputationprocedure.Thesamehappenswhenthebeamhasacrosssectionlessthanadefinitearea,oritcarriesafieldamplitudelessthanaspecificthreshold,or,finally,itexceedsamaximumnumberofpermissiblebounces.Foreachobservationpointlightedbythebeam,theexactraypathiscomputedbymeansoftheimagemethodusingonlythesurfacesthathaveinteractedwiththebeam.Doingso,themultiplecounterrortypicaloftechniquesbasedonthereceptionsphere[1],[29],[30]iscompletelyeliminated.Inaddition,theproposedcomputationproceduredoesnotsufferfromthefieldapproximationerrorthatoccursinthosetechniquesusingthereceptionsphere[1],[5]orinthoseemployingthecomputationofthebeammedian-ray[12].Inthesecondpartofthebeam-tracingalgorithmtheGOanddiffractedfieldsareevaluatedusingthereflection,transmission,anddiffractiondyadicsatthepointswheretheincidentfieldimpinges.Inthenumericalprocedure,onlytheedgediffractionprocessesexcitedbytheGOfieldhavebeentakenintoaccount.ToobtainahighnumericalaccuracythecomputationshavebeenperformedtakingintoaccounttheGOfieldcontributionsthathaveexperienceduptofivereflections/transmissions.The

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Fig.4.Firstfloorofabuildingformedbytwoidenticalstoreys.Eachfloorconsistsoftworoomsandacorridor.TheTxpointindicatesthelocationofthehalf-wavedipolereflectorantennaworkingat2.44GHzandradiating10mW.Thefurniturewithintheroomsareevidencedinbold.Woodencabinetsarelabeled1,metalliccabinetislabeled2.

diffractedfieldarisingfromanyscatteringobjectisconsideredexcitedeitherbythelineofsightGOfield,orbytheGOcontri-butionsthathaveexperienceduptothreereflections/transmis-sions.Finally,thediffractedfieldcontributionistakenintoac-countwhetheritreachestheobservationpointdirectlyorafterthreereflection/transmissionprocesses.

Toestimatethenumericalefficiencyoftheabovementionedalgorithm,anexpressionusefultoevaluateitscomputationalburdenisgiveninAppendixB.

III.RADIOCHANNELMODEL

Anaccuratedescriptionoftheindoorradiochannelisimpor-tantbecausemultipathpropagationandtimedispersionsignif-icantlyinfluencetheperformancesofWLANcommunicationsystems.Inthesesystems,theimpulseresponseiscomposedofsinglepulsesthathavetemporalspreadofthesameorderofthetimedelaybetweenadjacentechoes.ThissuggeststoemploytheTurin’smodelbasedonfinite-durationpulses[2],[3],[17],and[25],tomodelthechannelbehavior.Therefore,assumingthattheeffectofthetimedispersionforeachechocanbemod-eledasaGaussianpulse,thepowerdelayprofile[1],[2]oftheradiochannelcanbewrittenasfollows

(23)

where

(24)

isthenumberofraypathsthatcontributetothesignal.and

In(23)–(24),theparameters,andaremagnitude,phase,

TABLEI

MATERIALCHARACTERISTICS

andtimedelayofthethcontribution,respectively,andisthetimevarianceoftheGaussianpulse.Using(23),thermsmulti-whichestab-pathdelayspreadofthepowerdelayprofile

lishesthemaximumusablebitrateinadigitalcommunicationsystem[1],[2],iscomputedas

(25)

where

istheexcessmeandelay,definedas

(26)

Toderivetheparametersappearingin(23)theelectromagneticfieldduetothetransmittingantennaatthereceiverpointisfirstcomputed,thentheopen-circuitvoltageatthereceivingan-tenna,linkedtotheimpulseresponse,isevaluatedusingthean-tennavectoreffectiveheight[27].

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Fig.5.Electricfieldmagnitudeat1mabovethefloorofthefirststorey.Emptyroomscase.Frequency2.44GHz.

Fig.6.Electricfieldmagnitudeat1mabovethefloorofthefirststorey.Furnishedroomscase.Frequency2.44GHz.

IV.NUMERICALRESULTS

Tovalidatetheproposedmodelsomenumericalcomparisonswithresultspublishedinliteraturehavebeenpreliminarlyper-formed.Afirstvalidation,concerningthefieldpredictioninanemptycorridor,wasreportedin[25].Inthispaper,afurtherval-idationconcerningthepowerdelayprofileofacommunicationsystemworkinginamorecomplexenvironmenthasbeenper-formed.Theconsideredcasereferstotheindoorcommunicationsystemanalyzedin[11].Suchsystemconsistsoftwoomnidi-rectionaldisconeantennasoperatingat950MHzandlocatedat1.51mabovethefloor.Theroomwheretheantennasarelo-catedhasdimensions14.2431.123.3m.Theroomfloorandwallsaremadeofconcreteblockswithoutreinforcingsteel,whiletheconvexwoodenroofishiddenbyastippledceilingmadeofdrywallsheeting.Theroomwasemptyexceptforchairsandkitchenappliancesthatwerecollectedalongthewalls.Theimpulseresponsemeasurementsystemhasatemporalresolu-tionof25ns.Asin[11],sincetheinformationaboutdoors,win-dows,chairsandkitchenapplianceswereomitted,theindoorenvironmenthasbeenmodeledasanemptyparallelepipedalroomwith16cmthickwalls.Theparametersofthematerialsformingtheroomwalls,ceiling,andfloor,determinedtuningthenumericalresultswiththemeasurementsgivenin[11],are

mS/mforthefloor,theceilingandthelong

mS/mfortheshortwalls.Thecom-walls,and

putedresults,showninFig.3(a),areingoodagreementwiththeexperimentalmeasurements.Usingthesameparameters,afurthercomparison[Fig.3(b)]concerningthepowerdelaypro-filemeasuredinadifferentpointwithintheroomhasbeenper-formed.Asitcanbenoticed,theagreementisstillgood.

Afterthenumericalvalidation,theelectromagneticfielddis-tributionandtheradiochannelcharacteristicshavebeencarriedoutformorecomplexindoorenvironments.Forbrevity’ssakeonlyarepresentativeexampleisreported.

InFig.4,thefirstfloorofabuildingformedbytwoidenticalstoreys,wherea2.44GHzWLANsystemoperates,isshown.Theroomsareprovidedwithwoodentablesanddoors,woodenandmetalliccabinets,andglasswindows.ThecharacteristicsofthematerialsusedinthenumericalcomputationsaregiveninTableI.Theradiatingsystem,locatedattheTxpoint,consistsof

dipolereflectorantennaradiating10averticallypolarized

mW.Thefieldcomputationzoneisthehorizontalplaneat1mabovethefloor.Thepowerreceivedfromaverticallyoriented

dipoleantenna(Rx)hasbeenevaluatedalongthe-ori-entedlinescrossingthecenterofthetableslocatedatthefirstfloor.Theparameterofthecommunicationsystemhasbeenassumedof1ns.Suchavalueistypicalofagoodmeasurementsystemsuitabletodeterminethechannelimpulseresponse.ThemagnitudeoftheelectricfielddistributionatthefirstfloorofthebuildingisshowninFigs.5(emptyrooms)and6(furnishedrooms).Inthesefiguresthefastandslowmultipathfadingduetothescatteringprocessescausedbythefurnitureiswellevident.Inaddition,inthecorridorandinthesecondroomsignificantfieldlevelsduetothetransmissionthroughthepar-titionscanbenoticed.Theselevelshavemeanvaluesofabout

dBlessthanthoseintheroomcontainingtheRFsource.

Thespatialfielddistributiononthesecondstoreyissimilartothatobservedonthefirstfloor,whilethelevelsarelowerof

dBduetothesubstantialattenuationcausedbyabout

thetransmissionthroughtheceilingofthefirstfloor(seeFig.7).

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Fig.7.Electricfieldmagnitudeonaverticalsectionatx=5mwithfurnishedrooms.Frequency2.44GHz.

Fig.9.Cumulativedistributionfunctionofthereceivedsignalmagnitude.Antennascharacteristics:Tx(3.05m,4.52m,2.60m),half-wavedipolereflectorantenna;(Room1)Rx(5.24m,6.24m,1.00m),(Room2)Rx(5.24m,11.25m,1.00m),half-wavedipoleantenna.Frequency2.44GHz.

Fig.8.NormalizedpowerreceivedfromtheRxlocatedatthefirstfloor,versusdistancex.Antennascharacteristics:Tx(3.05m,4.52m,2.60m),half-wavedipolereflectorantenna;(a)Rx(x,6.24m,1.00m),(b)Rx(x,11.25m,1.00m),half-wavedipoleantenna.Frequency2.44GHz.Dotverticallinesindicatethelocationoftheinternalroomwallandthetableedges.

InFig.8(a)and(b),thepowerreceivedfromtheRxantennamovedalongthe-orientedlinelocatedatthecenteroftheta-blesinthetworoomsisshown.Asitcanbeobserved,thedif-fractedfieldhasasignificanteffectparticularlyevidentinthe

nonline-of-sight(NLOS)zoneandneartheedgesoftheobjectswherethediffractedfieldbecomesdominant.ThemeanlevelofthepowerreceivedbytheRxinthesecondroomisabout

dBlowerthanthatreceivedbytheRxintheroomcontainingtheradiosource,inagreementwiththefieldlevelsshowninFig.5(b).

Usingthepowerreceivedalongan-orientedsegmentof

,centeredatthecenterofthetables,andchoosing,length

,anestima-assuggestedin[31],asamplingrateofabout

tionofthelocalfastfadingstatisticshasbeenperformed.Todothat,theprocedureproposedin[32]hasbeenadopted.Fig.9,showsthecumulativedistributionfunctionofthereceivedsignalmagnitudecomputedinthetworooms.Asitcanbeobservedthecomputedcurvesareinexcellentagreementwiththoseob-tainedusingtheRiciandistribution.Inparticular,weobservethatintheroom1,containingtheradiosource,thestatisticsis

,describedbymeansofaRiciandistributionhaving

whileintheroom2(NLOSregion)theRiciandistributionex-hibitsa-factorofabout1.59,whichis,asobservedin[2],[33],and[34],veryclosetotheRayleighdistributionfunction.ThermsdelayspreadevaluatedalongthesamelineofFig.8(a)isshowninFig.10(a)[emptyrooms]and(b)

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Fig.10.RMSdelayspreadversusdistance.Turin’smodelbasedonGaussianpulseshaving󰀛=1ns:(a)emptyrooms,(b)and(c)furnishedrooms.AntennacharacteristicsasinFig.8.Dotverticallinesindicatethelocationoftheinternalroomwallandthetableedges.

[furnishedrooms],whilethermsdelayspreaddepictedinFig.10(c)isthatcomputedinthesecondroomalongthesamelineofFig.8(b).Comparingthesecurves,itisevident,almosteverywhere,thereductionofthermsspreadduetothefieldinteractionwithpenetrablefurniture.Inparticular,Fig.10(b)showsthatintheline-of-sight(LOS)regionthefieldscatteredfromthefurnitureisresponsibleforanimprovementofthechannelperformances,whileadifferentbehaviorisobservedintheNLOSregionsasitisconfirmedinFig.10(c).Infact,sinceintheseregionstheGOanddiffractedfieldlevelscanresultcomparable,thediffractiveeffectsimprovethechannelcharacteristicsonlyinspecificzones.Itisinterestingtonotethat,incontrasttotheresultsbasedontheGaussianpulsemodel[Fig.10(a)],thosebasedonthedeltaTurin’smodel[1],[2]predictasignificantincrementofthermsdelayspreadbothintheLOSandintheNLOSregions(seeFig.11).

Finally,inFig.12thechannelpowerdelayprofilecomputedwiththeRxplacedclosetothecenterofthetableinthefirstandinthesecondroomisshown.Comparingthesefigures,itisofinteresttonotethatincontrastwiththeLOScase[Fig.12(a)],intheNLOScase[Fig.12(b)]theleadingechoisnotthefirstthatappearsinthepowerdelayprofile.Thismeansthattheelectro-magneticraypathalongwhichthepathlossisminimumisnot

Fig.11.RMSdelayspreadversusdistance.Turin’smodelbasedondeltapulses.AntennacharacteristicsasinFig.8.Dotverticallinesindicatethelocationoftheinternalroomwallandthetableedges.

theshortest.Consequently,thermsspreadisgreaterthanthatcomputedintheroomcontainingtheradiosource.

Inconclusion,fromtheanalysisofthenumericalresultsitappearsthatthepresenceofpenetrablefurnitureintheLOSre-

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Fig.12.Normalizedchannelpowerdelayprofile.Turin’smodelbasedonGaussianpulseshaving󰀛=1ns.Antennascharacteristics:Tx(3.05m,4.52m,2.60m)half-wavedipolereflectorantenna;(a)Rx(5.24m,6.24m,1.00m),(b)Rx(5.24m,11.25m,1.00m),half-wavedipoleantennas.Frequency2.44GHz.Thecomputedrmsspreadisalsoindicated.

gion,givingrisetogreaterfielddiffusion,isresponsibleforareductionofthelevelsofthereceivedsignalechoes.Thiseffectimprovesthechannelperformancesofawirelesscommunica-tionsystemasconfirmedfrommeasurementsreportedinliter-ature[3].

V.CONCLUSION

AUTDmodelfortheanalysisofcomplexindoorradioen-vironments,inwhichmicrowaveWLANsystemsoperate,hasbeenpresented.ThediffractionphenomenahavebeentakenintoaccountbymeansofasuitableUTDheuristicdiffractioncoef-ficientforpenetrableobjects.Themodelemploysanenhancedthree-dimensionalbeam-tracingalgorithmtocomputethefielddistributionandthechannelcharacteristicswithanadequatede-greeofaccuracy.Usingtheproposedmodel,theperformancesofmicrowavewirelesscommunicationsystemsoperatinginre-alisticindoorenvironmentshavebeenanalyzed.Aninvestiga-tionofthepropagationprocessesshowsthattheelectromagneticfielddistributionandthecharacteristicsoftheradiochannelaresignificantlyinfluencedbythediffractionphenomenadueto

Fig.13.Structureformedbyathinflatpenetrableplatelocatednearapartiallyreflectingplane.PandPindicatethesourceandtheobservationpoint,respectively.TheopticalraysexcitedbytheincidentelectricfieldEareindicated.

thepresenceofthefurniture.Inparticular,ithasbeenobservedthat,almosteverywhereintheLOSregion,thefieldscatteredfrompenetrablefurnitureisresponsibleforareductionofthermsdelayspread,whilethisparticulareffectisnotgenerallyobservableintheNLOSregion.Duetoitsnumericalaccuracyandlimitedcomputationalrequirements,theproposedmodelcanbesuccessfullyemployedtoestimatethechannelperfor-mances,thefielddistribution,andpotentialEMCproblemsdi-rectlyduringthedesignphaseofanindoorwirelesscommuni-cationsystem.

APPENDIXA

Inordertooutlinethehigh-frequencyfieldpredictionproce-dureadoptedinthepaper,inFig.13arepresentativestructureformedbyathinflatpenetrableplatelocatednearapartiallyre-flectingplane,excitedbyanincidentelectricfield,isshown.Tosimplifythegraphicalrepresentation,onlytheraysthathaveexperienceduptotwointeractionsaretakenintoaccount.WithreferencetothefieldprocessesshowninFig.13,theelectricfieldattheobservationpointisgivenbythesumofthefol-lowingcontributions.a)DirectRayField:

(A1)

b)ReflectedRayField:

(A2)

c)TransmittedandReflectedRayField:

(A3)

d)DiffractedRayField:

(A4)

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e)DiffractedandReflectedRayField:

(A5)

In(A1)–(A5),isthewavenumberandistheoptical

pathlengthbetweenthepointsand.

APPENDIXB

Thecomputationalburdenoftheimplementedbeamtracingmethod,basedonalinearcostalgorithmtosearchthenearestsurfacethatishitfromtheray,isderivedconsideringtheray-surfaceintersectionprocessasthebasiccostelement.Asin[35],theworstcasesituationisconsideredtodeterminethecompu-tationalcost.Underthisassumptionalltheraybeamsshotbytheantennaareconsideredtodeterminetheparametereventhoughtalotofthemcouldnotparticipate,asdiscussedinSec-tionII,tothefieldattheobservationpoint.Thecomputa-tionalcost,basedonthegeometricalcharacteristicsofthebeampropagation,canbeevaluatedusingthefollowingequa-tion

(B1)

withandbeingtheGOandUTDprocedurecom-putationalburden,respectively.In(B1),isgivenby

(B2)

where

isthetotalnumberofthecomputedGObeamsand

isthenumberofthesurfacesdescribingthefurnitureandtheenvironment.Thefactor3intheright-handsideof(B2)referstothechosenbeamimplementationthat,asexplainedinSectionII,isbasedonthreeelectromagneticrays.

Intheworstcase,

canbeevaluatedconsideringthenumberoftheelectromagneticbeamsshooting

fromthesource,andthenumber

ofthereflec-tion/transmissionprocessesallowedtocomputetheGOfield.Theresultingexpressionis

(B3)

Thetermappearingin(B3)canbeestimatedcon-sideringthesolidangleofthebeamsthathaveexperienced

successivebounces.Itsespressionis

(B4)

whereistherayaveragepathlengthbetweentwoconsec-utivebounces,andistheaveragesurfaceofthebeamcross-section.

Combining(B2),(B3),and(B4),theterm,appearingin

(B1)isgivenby

(B5)

Theterm

in(B1)canbeestimatedasfollows

(B6)

whereisthenumberoftheedgesegmentsexcitedby

theimpingingGOfield,and

isthetotalnumberofthecomputedscatteredbeamsforeachedgesegment.In(B6),

canbeevaluatedas

(B7)

where

istheaveragelengthoftheedgesdescribingtheobjectboundaries,

representsthenumberoftheallowedtransmission/reflectionprocessesfirstthattheGOfield

interactswithanedge,

istheaveragesideofthebeamcross-section.Thisparametercanberoughlyevaluatedas

(B8)

Theterm

in(B6)hasthefollowingexpression

(B9)

whereisthesubdivisionsnumberofthediffractedraytube,identifiedbythetwoKeller’sconeswhosetipscoin-cidewiththeextremesofthesegmentexcitedbytheincidentray

beam[seeFig.2(c)],and

representsthenumberoftheconsideredtransmission/reflectionprocessesinthecompu-tationofthediffractedfield.Theterm

appearingin(B9)canbeestimatedconsideringtheangledefiningthedif-fractedbeamsthathaveexperienced

successivebounces.Itsespressionisgivenby

(B10)

Finally,theterm

in(B1)canbeeasilyobtainedusing(B6)–(B10).Doingso,itresults

(B11)

From(B5)and(B11),itisevidentthatthebeam-tracingtech-niqueisadvantageouswithrespecttotheimagemethod[35]whenthenumberofthesurfacesdescribingtheenvironmentandofthefieldobservationpointsislarge.Inaddition,thepro-posedenhancedbeam-tracingtechniqueismoreefficientwithrespecttotheconventionalbroadcastmethod[1],because,asdiscussedinSectionII,notemployingareceptionsphere,itcanusealargerbeamcross-sectiontoobtainthesamefieldspatialresolution.

BERNARDIetal.:ACCURATEUTDMODELFORANALYSISOFINDOORRADIOENVIRONMENTS1519

ACKNOWLEDGMENT

TheauthorsgratefullyacknowledgeM.Fascettiforhishelpinthegraphicalpresentationoftheresults.

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PaoloBernardi(M’66–SM’73–F’93–LF’01)wasborninCivitavecchia,Italy,in1936.HereceivedtheelectricalengineeringandLiberaDocenzadegreesfromtheUniversityofRome“LaSapienza,”Rome,Italy,in1960and1968,respectively.

Since1961,hehasbeenwiththeDepartmentofElectronics,UniversityofRome“LaSapienza,”wherehebecameaFullProfessorin1976andwasDirectoroftheDepartmentofElectronicsfrom1982to1988.HewasVice-ChairmanoftheEuropeanCommunityCOSTProject244onBiomedical

EffectsofElectromagneticRadiationfrom1993to1997,ProjectCoordinatoroftheEuropeanCommunityProjectCEPHOS,devotedtoEMdosimetryandcompliancewithstandardsofmobilecellularphones,from1998to2000,andfrom2001to2004,hehasbeentheScientificCoordinatoroftheItaliannationalprojectdevotedtotheprotectionofpeopleandenvironmentfromtheEMemissions.Hehasauthoredover190scientificpapersandnumerousinvitedpresentationsatinternationalworkshopsandconferences.Currently,heisanEditorialBoardmemberforMicrowaveandOpticalTechnologyLetters.HewastheGuestEditoroftheAltaFrequenzaSpecialIssueonNonionizingElectromagneticRadiation(March1980)andtheWirelessNetworksSpecialIssueonExposureHazardsandHealthProtectioninPersonalCommunicationServices(Dec.1997).HisresearchhasdealtwiththepropagationofEMwavesinferrites,microwavecomponents,biologicaleffectsofEMwaves,andEMcompatibility.

Dr.BernardiisaMemberoftheBioelectromagneticsSociety(BEMS),Eu-ropeanBioelectromagneticsAssociation(EBEA),and“SocioFedele”oftheItalianElectricalandElectronicSociety(AEI).HewasChairmanoftheIEEEMiddleandSouthItalySectionfrom1979to1980andtheInternationalSci-entificRadioUnion(URSI)CommissionKonElectromagneticsinBiologyandMedicinefrom1993to1996.HewasarecipientoftheIEEECentennialMedalin1984andwaselectedFellowoftheIEEEfor“contributionstomi-crowaveinteractionswithbiologicalsystems,”in1993.HewasanAssociateEditorfortheURSIRadioScienceBulletinandanEditorialBoardMemberforIEEETRANSACTIONSONMICROWAVETHEORYANDTECHNIQUES.

1520IEEETRANSACTIONSONANTENNASANDPROPAGATION,VOL.52,NO.6,JUNE2004

RenatoCicchetti(S’83–M’83–SM’01)wasborninRieti,Italy,inMay1957.HereceivedtheLaureade-greeinelectronicsengineering(summacumlaude)fromtheUniversityofRome“LaSapienza,”Rome,Italy,in1983.

From1983to1986,hewasanAntennaDesigneratSeleniaSpazioS.p.A.(nowAleniaAerospazioS.p.A.),Rome,Italy,wherehewasinvolvedinstudiesontheoreticalandpracticalaspectsofan-tennasforspaceapplicationandscatteringproblems.From1986to1994,hewasaResearcher,andfrom

1994to1998,hewasanAssistantProfessorattheDepartmentofElectronicsEngineering,UniversityofRome“LaSapienza,”whereheiscurrentlyanAssociateProfessor.In1998,hewasVisitingProfessorattheMotorolaFloridaCorporateElectromagneticsResearchLaboratory,FortLauderdale,FL,whereOrlandinoTestawasborninAugust1972,inMinturno,Italy.Hereceivedtheelectronicengi-neeringdegree(cumlaude)andthePh.D.degreefromtheUniversityofRome“LaSapienza”,Rome,Italy,in1997and2003,respectively.

Since2001,heisahighschoolTeacherattheI.T.I.S.“G.Armellini”InstituteofRome,whereheisinvolvedinteachingelectronicsandtelecommu-nications.HeisalsocurrentlycollaboratingwiththeDepartmentofElectronicEngineering,UniversityofRome“LaSapienza.”Atpresent,heisstudying

high-frequencymodelsfortheanalysisofcomplexindoorradioenvironmentswithparticularattentiontoEMC/EMIproblems.Hismainresearchinterestsarepropagationandradiationofelectromagneticfields,electromagneticcom-patibility,microwaveandmillimeter-waveintegratedcircuits,andantennas.

hewasinvolvedwithantennasforcellularandwirelesscommunications.Presently,heiscoordinatoroftheactivity“EMC/EMIcharacterizationofanairportenvironmentinpresenceofcomplexelectromagneticsources”oftheItaliannationalproject2001to2004MIUR/CNR-ENEA,devotedtotheprotectionofpeopleandenvironmentfromEMemissions.HealsoservesasaReviewerofseveralscientificjournals.Hiscurrentresearchinterestsincludeelectromagneticfieldtheory,asymptotictechniques,electromagneticcompatibility,wirelesscommunications,microwaveandmillimeter-waveintegratedcircuits,andantennas.HeislistedinMarquisWho’sWhointheWorldandWho’sWhoinScienceandEngineering.

Dr.CicchettiisaMemberoftheItalianElectricalandElectronicSociety(AEI).