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WirelessandMobile

Networking

Dr.FaramarzHendessi

Is a anUniv.o Tec .Spring2009

BasicPrinciples

FadingDistributionand

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TypesofSmallscaleFading

Small-scale Fading(Based on Multipath Tme Delay Spread)

Flat Fading

1. BW Signal < BW of Channel

2. Delay Spread < Symbol Period

Frequency Selective Fading

1. BW Signal > Bw of Channel

2. Delay Spread > Symbol Period

Small-scale Fading(Based on Doppler Spread)

Fast Fading

1. High Doppler Spread

2. Coherence Time < Symbol Period

3. Channel variations faster than baseband

signal variations

Slow Fading

1. Low Doppler Spread

2. Coherence Time > Symbol Period3. Channel variations smaller than baseband

signal variations

Fading Distributions Describeshowthereceivedsignalamplitudechangeswithtime.

Rememberthatthereceivedsignaliscombinationofmultiple

signalsarrivingfromdifferentdirections,phasesandamplitudes.

,

envelope ofthereceivedsignal(i.e.r(t)).

Itisastatistical characterizationofthemultipathfading.

Twodistributions RayleighFading

RiceanFading

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RayleighDistributions Describesthereceivedsignalenvelopedistributionforchannels,

whereallthecomponentsarenonLOS:

i.e.thereisnolineofsight(LOS)component.

RiceanDistributions Describesthereceivedsignalenvelopedistributionforchannelswhere

oneofthemultipathcomponentsisLOScomponent.

i.e.thereisoneLOScomponent.

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RayleighFading

RayleighFading

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RayleighFadingDistribution

TheRayleigh

distribution

iscommonly

used

to

describethestatisticaltimevaryingnatureofthereceivedenvelopeofaflatfadingsignal,or

component.

TheenvelopeofthesumoftwoquadratureGaussiannoisesignalsobeysaRayleighdistribution.

p r

r rr

r

( )exp( )

=

1,theRicean pdf isapproximatelyGaussianaboutthemean.

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Ricetimeseries

NakagamiModel NakagamiModel

mmr

mrm ex2 212

r:envelopeamplitude

=:timeaveragedpowerofreceivedsignal

m:theinverseofnormalizedvarianceofr2

mm

rp

=)(

)(

et ay e g w enm=

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Smallscalefadingmechanism

Assume

signals

arrive

fromallanglesinthehorizontalplane0

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CarrierDopplerspectrum

SpectrumEmpiricalinvestigationsshow

resultsthatdeviatefromthismodelPowerModelPowergoestoinfinityatfc+/fm

BasebandSpectrumDopplerFadedSignal

Causebasebandspectrumhasamaximum

frequencyof2fm

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SimulatingDoppler/Smallscalefading

SimulatingDopplerfading Procedureinpage222

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LevelCrossingRate(LCR)

Threshold (R)

LCR is defined as the expected rate at which the Rayleigh fading

envelope, normalized to the local rms signal level, crosses a specified

threshold level R in a positive going direction. It is given by:

2

=

secondpercrossings

rms)tonormalizedvalueenvelope(specfied

where

:

/

R

rms

mR

N

rR=

AverageFadeDuration

Defined as the average period of time for which the received signal is

below a specified level R.

For Rayleigh distributed fading signal, it is given by:

( )RR

Re

eN

RrN

=

=

==

,1

11]Pr[1

2

2

rmsm

Example5.7,5.8,5.9

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FadingModel:GilbertElliotModel

Fade Period

Signal

Amplitude

Time t

Threshold

Good(Non-fade)

Bad(Fade)

GilbertElliotModel

GoodNon-fade

BadFade

1/AFD

1/ANFD

The channel is modeled as a Two-State Markov Chain.

Each state duration is memory-less and exponentially distributed.

The rate going from Good to Bad state is: 1/AFD (AFD: Avg Fade Duratio

The rate going from Bad to Good state is: 1/ANFD (ANFD: Avg Non-Fade

Duration)

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Simulating2raymultipath

a1 anda2 areindependentRayleighfading 1 and2 areuniformlydistributedover

,

SimulatingmultipathwithDopplerinducedRayleighfading

EE542/452Spring2008

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SalehandValenzuelaIndoorModel Measuredsamefloorindoorcharacteristics

Foundthat,withafixedreceiver,indoorchannelisveryslowlytimevarying

RMSdelayspread:mean25ns,max50ns

Maximaldelayspread100ns200ns

WithnoLOS,pathlossvariedover60dBrangeandobeyedlogdistancepowerlaw,3>n >4

Modelassumesastructureandmodelscorrelatedmultipathcomponents.

Multipathmodel Multipathcomponentsarriveinclusters,followPoisson

distribution.Clustersrelatetobuildin structures.

Withincluster,individualcomponentsalsofollowPoissondistribution. ClustercomponentsrelatetoreflectingobjectsneartheTXorRX.

AmplitudesofcomponentsareindependentRayleighvariables,decayexponentiallywithclusterdelayandwithintraclusterdelay

SIRCIMandSMRCIM

indoor/outdoorModels ThesemodelsweredevelopedbyRappaportandseidelSIRCIMisa

computerprogram,thatgeneratessmallscaleindoorchannel

responsemeasurements.

Themostsalientfeatureofthemodelisthatitproducesmultipathchannel

conditionsthatareveryrealisticsincetheyarebasedonrealworld

measurementsandmaythusbeusedformeaningfulsystemdesignin

factoriesandofficebuildings

Theseprogramsareveryusefulandpoplarandareusedinover100

institutions.

Modelcanmeasureindividualmultipathfadingandsmallscale

receiverspacing.

Multipathdelayinsidethebuildingwasfoundtobe40nsto800ns.

Meanmultipathdelayrangedfrom30300ns.

ArrivingmultipathcomponenthasaGaussiandistribution.

Averagenumberofmultipathcomponentsrangefrom9to36

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SIRCIMandSMRCIM

indoor/outdoorModels

SIRCIMModel Basedonmeasurementsat1300MHzin5

Modelpowerdelayprofileasapiecewise

function