现代无线通信系统电波传播_第六章.

PropagationinthePresenceofBuildingsonFlatTerrainContents6.1Modelingpropagationoverrowsofbuildings6.1aComponentsofthepathgain6.1bModelingPG2bydiffractionoftherooftopfields6.2ApproachestocomputingthereductionPG1oftherooftopfields6.2aPhysicalopticsapproachtocompotingfieldredution6.2bSolutionsforuniformrowspacingandbuildingheight6.3Planewaveincidenceformacrocellpredictions6.3aSoutionintermsofBorsma'sfuntions6.3bUsingthesettledfieldtofindthepathloss6.4Cylindricalwavetincidenceformicrocellpredictions6.4aSolutionintermsofBorsmasfuntions6.4bPathlossforlowbasestationantennas6.4cPathlossformobile-to-mobilepropagation6.4dPropagationobliquetorowsofbuildings6.5Numericalevaluationoffieldsforvariablebuildingheightandrowspacing6.5aWindowingtoterminatetheintegration6.5bDiscretizationoftheintegration6.5cHeightdependenceofthesettledfield6.5dInfluenceofroofshape6.6SummaryInthischapterweintegratethepropagation,reflection,anddiffractionconceptsofthepreviouschaptersinordertounderstandanpredictthepathlosscharacteristicsthathavebeenobservedoverlargeportionsofmetropolitanregions.BeijingChengdu6.1Modelingpropagationoverrowsofbuildings•Transmissionlossthrougharowofhouseswillbe8to14dB.•Theradiosignalexperiencesaverylargereducetioninstrengthcomparedtofree-spacepropagation.•Propagationpathsinwhichthewavesgooverthebuildingsandarediffracteddowntothesubscribermayinvolvelessexcesspathloss.6.1aComponentsofthepathgainThinkingintoaccounttheforegoingdiscussion,thepathgainistheproductofthreefactors:(1)thefree-spacepathgainPG0(2)thereductionPG1inthefieldsarrivingatthebuildingnearthemobileduetodiffractionpastthepreviousrowsofbuildings(3)thereductionPG2inthefieldsastheydiffractdowntogroundlevelWhenexpressedindecibels,thepathgainisThefree-spacepathgainforisotropicantennasis6.1bModelingPG2bydiffractionoftherooftopfields•Fourpossiblepath•Weaddthepowersoftheindividualrays•Wetakethefieldsoverbothbuildingtobethoseofhorizontallypropagatingplanewavesofunitamplitude•PG2forisotropicantennasisgivenby6.1bModelingPG2bydiffractionoftherooftopfields•Thedistanceρiin(6-3)aregivenby•theanglesθiare•ForsimplicityweusetheFelsencoefficient(5-48)foranabsorbingscreen,whosemagnitudesquaredforfourrayscanbeapproximatedby•Theerrorintroducedbytheapproximationindicatedin(6-6)islessthan14%evenforanglesapproaching45°.ρ1=ρ4,6.1bModelingPG2bydiffractionoftherooftopfields•|θ1|issubstantiallythanπ/2,thelastternissmallerthanthefirsttermandwillbeneglected.•therelativesizesofthesecondandthirdternsaregivenbythereflectionandtransmissioncoeffients.•approximatetheangles|θi|fori=1,2,3bysin|θi|andsubstitutingforsin|θi|from(6-5),6.1bModelingPG2bydiffractionoftherooftopfields•Fornarrowstreetsand/ortallerbuildings,bothofwhichcausetheangle|θ1|tobelarge•Formorereflectivebuildings,thefirstandsecondtermsaremorenearlyequal•Thereareotherpathsbywhichtherooftopfieldsreachgroundlevel,Allthesepathsareexpectertogivesmallercontributionstothetotalsignalthanpath1•Assumethattheirtotalcontributionisaboutthesameasthatofpath1,so6.1bModelingPG2bydiffractionoftherooftopfields6.1bModelingPG2bydiffractionoftherooftopfields6.2ApproachestocomputingthereductionPG1oftherooftopfields•Suposethatthereductionofthefieldatthetopofthebuildingsisexpressedasafactormultiplyingthefree-spacefieldintheabsenceofbuilding•replacetherowsofbuildingsbydiffractingscreensForverticalpolarizationandforpropagationthatisessentiallyhorizontal,thereductionintherooftopfieldscanbefoundfromthesolutionofatwo-dimensionallinesourceproblem,thenthedistance6.2aPhysicalopticsapproachtocompotingfieldredution•xn+1-xn=d•becausethepropagationisessentiallyhorizontal,theprimarycontributiontotheintegralin(6-12)comesfromvaluesofynneartoyn+1•ρcanberepalcedbyd,andintheexponentbyFresnelapproximation6.2bSolutionsforuniformrowspacingandbuildingheight•Since,cascadingtheintegrals(6-12)pastNscreensgives•wecanobtainsolutionsto(6-15)atthetopoftheN+1sceen.6.2bSolutionsforuniformrowspacingandbuildingheight/12/k•Inmacrocellularapplications,fieldsatrooftopwillsettletoavaluerelativetofree-spacethedependsonlyonangleα.•Assumingthatanincidentplanewaveofunitamplitudepropagatesdownwardatanangleαtothehorizontal,thefieldintheplanex1=dis•Forsmallanglesα,cosα≈1,thefiledforyN+1isgivenby6.3Planewaveincidenceformacrocellpredictions•changethevariablesofintegrationfromyntovnusingthetransformations•introducingthedimensionlessparametergp,defineby•substituting(6-18)and(6-19)in(6-17),6.3Planewaveincidenceformacrocellpredictions•thefinalintheevaluation(6-2)expandthefirstexponentialoftheintegrandinTaylorseries•substituting(6-21)into(6-20),givesthefieldattherooftopsas•IN,qisoneofBorsma'sfunctionsIN,q(β)forβ=1.6.3aSoutionintermsofBorsma'sfuntions•Borsmahasshownthatthefunctionsdefinedby(6-23)canbeevaluatedusingthefollowingrecursionrelationforq≧2,•Forβ=1thestartingfunctionsintherecursionrelationare6.3aSoutionintermsofBorsma'sfuntions•In(6-26)and(6-27)thetern(1/2)ndenotesPochhammer'ssymbol,defineby•Asimpleclosed-formresultisobtainwhentheincidentplanewaveispropagationparalleltothelineoftherooftop,α=0,•T