Propagation Chapter III ALUMNO

8/12/2019 Propagation Chapter III ALUMNO

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PROPAGATION

ChapterIIIIng.EdgarOchoaFigueroa,MgT


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FadingandMultipathCharacterization Fadingisroughlygroupedintotwocategories:large-scaleandsmall-scalefading.

Large-scalefadingissometimescalledslowfadingorshadowing,althoughthetermslowfadinghasamoreprecisedefinitioninthecontextofsmall-scalefading.

Large-scalefadingisoftencharacterizedbyalog-normalprobabilitydensity function(pdf)and isattributedtoshadowing,andtheresultingdiffractionand/ormultipath.

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FadingandMultipathCharacterization Changesinlarge-scalefadingareassociatedwithsignificantchangesinthetransmitter/receivergeometry,suchaswhenchanginglocationwhiledriving.

Small-scalefadingisassociatedwithverysmallchangesinthetransmitter/receivergeometry,ontheorderofawavelength.

Small-scale fadingmaybeeither fastorslowand isduetochangesinmultipathgeometryand/orDopplershiftfromchangesinvelocityorthechannel.



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GROUND-BOUNCEMULTIPATH Mostterrestrialcommunicationsystemsdonotoperateinafree-spaceenvironment,butrathermustaccountfortheeffectoftheearthssurfaceonthepropagationpath.

Therearetwokeyeffects:groundreflectionandpathblockageand/ordiffractionwhenpartofthepathisbeyondlineofsight.

Whenthepropagationpathisneartheearthssurfaceandparalleltoit,severefadingcanoccurifthegroundissufficientlyreflective.



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GROUND-BOUNCEMULTIPATH Considerapoint-to-pointcommunicationslinkoperatingincloseproximitytotheearthssurface,forthisanalysis,aflat,smooth,andreflectivegroundsurfaceisassumed.



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GROUND-BOUNCEMULTIPATH Thustherewillbespeculargroundreflectionfromaflatearth.

Specularreflectionoccursifandonlyiftheangleofincidenceequals theangleofdepartureat the reflectionpoint1=2.

Theslantrangeis And



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GROUND-BOUNCEMULTIPATH Expressionsforthereflectionanglesareasfollows:

From

these

expressions

and

the

fact

that

the

two

angles

areequal,itisclearthat

thefollowingequationcanbewritten:



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GROUND-BOUNCEMULTIPATHSolvingthisequationford1yields

Replacingd1byd-d

2inthisequationandsolvingford

2,

providesthefollowingequationsford2.

Thusthespecularreflectionpointbetweenthetwoantennascanbedeterminedbyknowingtheheightsoftheantennas.



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GROUND-BOUNCEMULTIPATH The following equations follow from the speculargeometry:

Andalsofromthegeometry,theslantrangeisfoundtobe



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GROUND-BOUNCEMULTIPATH Thereceivedsignalcanbefoundbytakingthevectorsumofthedirectandreflectedwaveatthereceiveantenna.

Themagnitudeandphaseofthereflectedsignalaredeterminedbythepath-lengthdifference(primarilyphasesincethedistancesarenearlyequal)andthereflectioncoefficientoftheground.

Thereflectioncoefficient,oftendenotedby,isacomplexparameterthatmodifiesboththemagnitudeandphaseofthereflectedwave.



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GROUND-BOUNCEMULTIPATH Thus for the ground-bounce case the reflectioncoefficient iswell-approximatedby= -1as longas thesurfaceissmoothandconductiveandtheangleofincidenceissmall.

Thereflectioncoefficientofthegrounddependsuponfourfactors:Angle

of

incidence

(assumed

to

be

very

small)

Groundmaterialproperties(flat,smooth,andconductive)FrequencyPolarization (if the grazing angle is small enough, thepolarizationdoesnotaffectthereflection)



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GROUND-BOUNCEMULTIPATH Sincethegrazingangleisassumedtobesmall,thereflectionundergoesa180degreephaseshiftatthepointofreflectionregardlessofpolarization.Thesmallgrazinganglealsomeansthat||~1.

Forgeometrieswhereds>>htandds>>hr(isverysmall),thefollowingapproximationcanbemade:



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GROUND-BOUNCEMULTIPATH Thusthepathloss(free-spaceloss)isapproximatelythesameforthedirectandreflectedpaths.

In thiscase, if thewavesareexactly inphase, therewillbea6dBincreaseinthereceivedsignal(twicetheamplitudeimpliesfourtimethepower).

Ifthewavesareexactly180degreesoutofphase,thesignalwillcancelcompletelyandnosignalwillbereceived.

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GROUND-BOUNCEMULTIPATH TheEfieldatthereceivercanbeexpressedas

EistheelectricfieldatthereceiverEdistheelectricfieldduetothedirectwaveatthereceiveristhephasedifferencebetweenthedirectandreflectedwavefrontsduetothepath-lengthdifference.

For

the

small

grazing

angle

case,

=

-1

and

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GROUND-BOUNCEMULTIPATH ThemagnitudeoftheEfieldcanbeexpressedas

TheexpressionforthemagnitudeofEcanbeexpandedasfollows:

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GROUND-BOUNCEMULTIPATH

TheexpressionforthemagnitudeofEcanbeexpandedasfollows:

Whereisthephasedifferenceduetopath-lengthdifferenceandEdistheEfieldduetothedirectreturnonly.

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GROUND-BOUNCEMULTIPATH Thephasedifferencebetweenthedirectandthereflectedwave(duetopath-lengthdifference)is

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GROUND-BOUNCEMULTIPATHin thebinomialexpansion, it isclear that ifd>>hrandd>>ht,then

Thususingonlythefirsttwotermsofthebinomialexpansionwillbeagoodapproximation.Makingthedesignatedsubstitutions

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GROUND-BOUNCEMULTIPATH whichsimplifiesto

whichindicatesthatthereceivedpowerisproportionaltothemagnitudesquaredoftheEfield:

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GROUND-BOUNCEMULTIPATH Therefore,thereceivedsignalpowerwillbe

whereisthecharacteriticimpedanceoffreespace,but,fromthefree-spacelossequation,themagnitudesquaredofthedirectpathEfieldatthereceiver,Ed,isgivenby

so

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GROUND-BOUNCEMULTIPATH whichresultsinthefollowing(approximate)expressionforthepathlossonanear-earthpropagationpathoveraflat,smoothconductingsurface:

Theexactground-bounceexpressionisseldomusedsincethegeometryisrarelypreciseenoughtolocatethepeaksandnullsaccurately.

Therecommendedapproachistocompute thefree-spaceloss andtheapproximateground-bounce pathloss andusewhichever givesgreaterloss .

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GROUND-BOUNCEMULTIPATH Thecrossoverpointisdefinedasthedistanceatwhichthe1/d4approximationandfree-spacelossareequal.

The crossover point is found by equating theapproximateground-bouncepathlossandthefreespacelossandsolvingford.

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GROUND-BOUNCEMULTIPATH Example: Consider the following point-to-pointcommunicationslink: hT=hR=10md=4kmf=2GHz

Whatisthepredictedpathlossforthislink?



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SurfaceRoughness Whendeterminingifgroundreflectionislikelytobesignificant,ameansofquantifyingthesmoothness(flatness)ofthereflectingsurfaceisrequired.

TheRayleighcriterionprovidesametricofsurfaceroughness. TheRayleighroughnessisderivedbasedontheterrainvariation(h)thatwillprovidea90-degreephaseshiftatthereceiverbetweenareflectionataterrainpeakversusareflectionfromaterrainvalleyatthesamedistance.



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SurfaceRoughness

TheRayleighroughnessisderivedbasedontheterrainvariation(h)thatwillprovidea90-degreephaseshiftatthereceiverbetweenareflectionataterrainpeakversusareflectionfromaterrainvalleyatthesamedistance.

TheRayleighcriterionisgivenby



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SurfaceRoughness TheRayleighcriterioncanthenbeexpressedas

Whentheextentoftheterrainfeatures,h,islessthanHR,thesurfacecanbetreatedasbeingsmooth.

Whenareflectivesurfaceisrough,meaningthattheextentoftheterrainfeatures,h,ismuchlargerthanHR,thenthereflectionsfromthesurfacewillbediffuseandarecharacterizedasscatteringratherthanreflection.



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FresnelZones

ThevectorTRisthelineofsightbetweenthetransmitterandthereceiverandthelinkdistanceisd1+d2.

IfthereisadiffractionpointatP,thesignalTPRwillcombinewithTRatR.

TPRtraversesaslightlygreaterdistancethanTRandthereforewillhaveadifferentphase.Thedirectandreflected/diffractedpathlengthscanbeexpressedas



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FresnelZones

Sothepath-lengthdifferenceis

Ifh


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FresnelZones Makingtheappropriatesubstitutionsintheequationfor,yields

Thecorrespondingphasedifferenceis



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FresnelZones TheFresnelKirchhoffdiffractionparameterisoftenusedtoshortenthenotationinFresnelzoneanalysesandisdefinedas

Ifthedif fract ionpo in t isbelowthel ineo fs ight (LOS),thenhisnegat iveandvwi l l alsobenegative.

WhenthediffractionpointislocatedontheLOS,handvarebothequaltozero.Iftheblockageisthehorizon,thenthehandvequalzerocasecorrespondstothemaximumLOSdistance.



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FresnelZones Thecaseswhere=n/2,wherenisaninteger,canbefoundbysetting=n,whichyieldsthefollowingequation:

Thedestructivereflection/diffractionpointscanthenbeidentifiedbydefiningaterm,hn,suchthat



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FresnelZonesReflectors/diffractionathn foroddvaluesofnwillcausedestructiveinterference.

Since thedifference inpath lengths ison theorderof,thereflected/diffractedsignalmaybeasstrongasthedirectsignalandcausecancellation.

Theequationforhndefinesasequenceofellipsoidswiththetransmitandreceiveantennasasthefoci.



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FresnelZones DiffractorsorreflectorsattheoddnumberedFresnelzoneboundarieswillcausedestructiveinterference.TheFigureshowsadiagramoftheFresnelzonesdefinedbyapoint-to-pointlink.



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FresnelZones Notethatthisdiagramistwo-dimensional,whereastheactualFresnelzonesarethreedimensionalellipsoids.

Forlargehorsmalld1andd2,theantennapatternmayattenuatetheundesiredsignal.

Foromnidirection(vertical)antennas,theremaybeattenuationoftheundesiredsignalinelevation,butnotinazimuth.



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FresnelZones Fromtheprecedinganalysis,itisclearthatanyreflectors/diffractorswithinthefieldofviewshouldnotbenearanoddFresenelzoneboundarytoavoidsignalloss.

It isalso important that the firstFresnelzonebeclearofobstructionsbecausethiscanseriouslydegradetheavailablesignalenergy.

If thefirstFresnelzone isnotclear,then free-space lossdoesnotapplyandanadjustmenttermmustbeincluded.



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FresnelZones Having60%offirstFresnelzoneclearissufficient. Atthe0.6hpoint,theFresnelKirchhoffdiffractionparameterisv=-0.8andtheresultingdiffractionlosswillbe0dB



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FresnelZones Example:Considerapoint-to-pointcommunicationsystem,withd=1kmandf=28GHz.Ifthereisabuildingpresent,300mfromoneendofthe link,howfarmustitbe(inelevationorheight)fromtheLOStonotimpedetransmission?



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DiffractionandHuygensPrinciple Diffractionisthephysicalphenomenonwherebyanelectromagneticwavecanpropagateoveroraroundobjectsthatobscurethelineofsight.

Diffractionhastheeffectoffillinginshadows,sothatsomeamountofelectromagneticenergywillbepresentintheshadowedregion.

Huygens

Principle

states

that

each

point

on

a

wavefront

actsasthesourceofasecondarywaveletandallofthesewaveletscombinetoproduceanewwavefront inthedirectionofpropagation.



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DiffractionandHuygensPrinciple



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QuantifyingDiffractionLoss TheeffectofaplanewaveincidentonaperpendicularconductivebarriercanbedividedintothreeshadowregionsasshowninFigure.

RegionIcontainsdirect,reflected,anddiffractedrays,regionIIcontainsdirectanddiffractedraysonly,andregionIIIcontainsdiffractedraysonly.

This

explains

why

aknife

edge

that

isbelow

the

line

of

sightmaystillaffectthereceivedwave.



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QuantifyingDiffractionLoss



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QuantifyingDiffractionLoss Theanalysisinthissectionisbasedonaconductivebarrier.

Theseresultsareoftenappliedtoscenarioswherethebarriersarenotconductive;however,theymaynotbeasprecise,dependinguponthereflectionpropertiesofthebarrier.

The

knife-edge

diffracting

point

may

be

above,

below,

or

directlyonthelineofsightbetweenthetransmitterandreceiver.



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QuantifyingDiffractionLoss Theelectricfieldduetothediffractedpathisgivenbythediffractionintegral,

whereE0istheelectricfieldatthereceiverbasedonfree-spacelossonlyandvistheFresnelKirchhoffdiffractionparameterdefinedearlier.

Evaluationofthediffractionintegralisusuallydonenumerically or graphically. Lee provides anapproximationtothediffractionintegral.



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QuantifyingDiffractionLossExample:Consideracommunication linkcomprisedoftwo150MHzhand-heldradiosseparatedby1kmasshowninFigure. The barrier between the two radios runsperpendiculartothelineofsightandis5mbelowthelineofsight.

Assume

that

the

barrier

isathin,

solid

fence

that

is

200mfromoneendofthelink.Howmuchadditionalpathloss(beyondfree-spaceloss)canbeexpectedduetothediffractionfromthefence?



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QuantifyingDiffractionLoss Thediffractionfromaroundedhilltoporsurfaceisdeterminedbycomputingtheknife-edgediffractionfortheequivalentheight, h,and thencomputing theexcessdiffractionloss,Lex,duetotheroundedsurface.



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QuantifyingDiffractionLoss Thefirststep istodeterminetheradius,r,ofthecylinderthatcircumscribestheactualdiffractionpointsontheobstacle.

Thentheextentofthediffractionsurface,DS,canbefound.Theexpressionfortheexcessdiffractionlossis



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QuantifyingDiffractionLossExample:Considerapoint-to-multipointcommunicationslinkoperatingat5GHzoveradistanceof1kmshowninFigure.Thereisapairofnarrowhilltopsinbetweenthetransmitter and receiver, located 300 m from the

transmitter,find

the

total

diffraction

loss

if

the

hilltops

are

10

mapartand3mabovethelineofsight.



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ThuscOCisanisosoliclestrianglewiththeequalsidesbeing

of

length

r.

Solving

for

ryields



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wheremust,

ofcourse,

beexpressed

inradians,

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DelaySpread Thedirectpath(ifoneexists)istheshortestpathbetweenthetransmitterandreceiver. Anymultipathswillhavetraveledgreaterdistancesandwillthereforebedelayedintimerelativetothedirectsignal.

Thusthereflectedsignal(s)willnotalignwiththedirectsignal,

and

the

cumulative

signal

will

be

smeared

in

time.



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DelaySpread



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DelaySpread Itisdesirabletohavethemaximumdelayspreadtobesmallrelativetothesymbolintervalofadigitalcommunicationsignal.

An analogous requirement is that the coherencebandwidthbegreaterthanthesignalbandwidth.

Coherencebandwidthisdefinedasthebandwidthoverwhich

the

channel

can

beconsidered

flat

with

linear

phase.



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DelaySpread Flatfrequencyresponsewithlinearphaseimpliesnosignaldistortion. Thecoherencebandwidthisoftenapproximatedas

dependingupontheflatnessrequiredandthechannelsspectralshape.

Thermsdelayspreadisdenotedbyt



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DelaySpread Ifthesignalbandwidthislessthanthecoherencebandwidth,B


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DelaySpread Theremedyforflatfadingistodeterminetheallowableoutage timeand thenuse theRayleighpdf todeterminetherequiredfademargintomeettherequirement.

Forselectivefading,somemodulationsarerelativelytolerantoffrequencydropouts,whereasinothercasesanequalizermaybeused.

Anotherapproachissimplyconsiderthesymboltime,thentohaveadelayspreadthat issignificantly lessthanT,t


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DelaySpreadExample:Givenadigitalcommunicationsystemwithasymbolrateof50,000symbolspersecond,whatisanacceptableamountofrmsdelayspread?



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DelaySpreadExample:GiventhecommunicationsystemandtheenvironmentshowninFigure,ifallofthebuildingsaregoodreflectorsandboththetransmitterandreceiverareusingwide-angleantennas,what isthemaximumexpecteddelay

spread

value?

Base

on

that

value,

what

is

the

highest

symbolratethatyouwouldrecommend?Assumethatthere isnoequalizerpresentand thatbothendsof the linkareatthesameheight.



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DelaySpread



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DelaySpread



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DopplerSpread RelativemotionbetweenthetransmitterandreceiverimpartsaDopplershiftonthesignal,wheretheentiresignalspectrumisshiftedinfrequency.

Whenmultipathiscombinedwithrelativemotion,theelectromagneticwavemayexperiencebothpositiveandnegativeDopplershift,smearingorspreadingthesignalinfrequency.

ThiseffectiscalledDopplerspread



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DopplerSpreadandvRelisthemaximumrelativevelocity.

Thecoherencetimeissometimestakentobe

IfthesignalbandwidthismuchlargerthantwicethemaximumDopplershift,thechanneliscalledaslowfadingchannelandtheeffectsofDopplerspreadarenegligible.Asimilarrequirementis

thesymboltimeislessthanthecoherencetimeofthechannel.



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IndoorPropagationModeling Indoorpropagationofelectromagneticwavesiscentralto theoperationofwirelessLANs,cordlessphones,andany other indoor systems that rely on RFcommunications.

Modeling indoorpropagation iscomplicatedby the largevariabilityinbuildinglayoutandconstructionmaterials.

Inaddition, theenvironmentcanchange radicallyby thesimplemovementofpeople,closingofdoors,andsoon.



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IndoorPropagationModeling While an understanding of indoor propagation isessential,anotherimportantelementofindoorwirelessoperationthatshouldbeconsideredisinterference.

Unlikeoutdoorenvironments,wheretheoperatingdistancesaregreater,inanindoorenvironment,itispossible,andinfactcommon,tohaveaninterferingsystemoperatingwithinafewfeetorlessofagivensystem.

AclassicexampleisthedesktopcomputerwithawirelessLANcardthatalsoemploysawirelesskeyboardand/ormouse.



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IndoorPropagationModeling ThewirelesskeyboardandmousearelikelytousetheBluetoothstandard,whichusesfrequencyhoppinginthe2.4-GHzISMband.

IfthewirelessLANcardisan802.11borg[directsequence spread spectrum (DSSS) or orthogonalfrequencydivisionmultiplexing(OFDM)]system,thenitwillbeoperatinginthesamefrequencybandandthepotentialforinterferenceexists.



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TheITUIndoorPathLossModel TheITUmodelforsite-generalindoorpropagationpathlosspredictionis

Where

NisthedistancepowerlosscoefficientfisthefrequencyinMHzdisthedistanceinmeters(d>1m)Lf(n)isthefloorpenetrationlossfactornisthenumberoffloorsbetweenthetransmitterandthereceiver



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Valuesforthefloorpenetrationlossfactor.



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IndoorPropagationModeling TheITUmodelcanbeshowntobeequivalenttotheequationforfreespacelosswiththedistancepowerbeingN=20(whennottraversingfloors).

ThustheITUmodelisessentiallyamodifiedpowerlawmodel. Thiscanbeseenasfollows:Theexpressionforfree-spacelossexpressedindBisgivenby



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IndoorPropagationModeling whenN=20.Thefirsttermontheright-handsidecanbeexpressedas

Usingthefactthat theexpressionforthepathlosssimplifiesto



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IndoorPropagationModeling ApowerlosscoefficientvalueofN=20correspondstofree-spaceloss,andthiswillusuallyapplyinopenareas.

CorridorsmaychannelRFenergy,resultinginapowerlosscoefficientofN=18.(slightlylessthanfree-spaceloss).

Inthecaseofpropagationaroundcornersorthroughwalls,N=40isused.

Forlongpaths,thereflectedpath(s)mayinterfere,resultinginN=40beingusedhereaswell.



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IndoorPropagationModelingExample:Considerapplicationofa5.2-GHzwirelessLANinanofficebuilding. If the longest link is100m,what is themaximumpathloss?Howmuchadditionalpathlosswillexistbetweenfloors?Istheinterfloorlosssufficienttopermitfrequencyre-use?



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IndoorPropagationModeling

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Propagation Chapter III ALUMNO

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