wireless propagation lec 7-8

8/8/2019 Wireless Propagation Lec 7-8

1/20

Wireless Communications

Lecture 7-8Propagation Modelling

Multipath Fading


2/20

BackgroundsLarge Scale Propagation

Path loss, Shadowing etcPredicts mean received signal strength at large Tx-

Rx distances (hundreds of thousands of meters)Importance

Proper site planningSmall-scale Propagation

Fading

Characterize the rapid fluctuation over the shortdistances or timeImportance

Proper receiver design to handle fluctuations


3/20

Backgrounds


4/20

M ultipath fadingM ultiple reflected waves arrive at the receiver

Different waves have different phases.These waves my cancel or amplify each other.This results in a fluctuating (fading) amplitude of the

total received signal.


5/20

Small-scale fadingWireless communication typically happens at very

high carrier frequency. (eg. f c = 900MH z or 1.8 GH zfor cellular)M ultipath fading due toconstructiveand destructive

interference of the transmitted waves.Channel varies when mobile moves a distance of theorder of the carrier wavelength. This is about 0.3 mfor 900M hz cellular.For vehicular speeds, this translates to channel

variation of the order of 100H z.Primary driver behind wireless communicationsystem design.


6/20

Factors influencing Small-scale fading

M ultipath propagationsignal arrives at Rx through different paths

Speed of mobileinduces Doppler shiftSpeed of surrounding objects

The transmission B/W of the signal


7/20

Doppler ShiftDoppler shift is given by the apparent change in

frequencyf d =(1/2 ) ( / t)

Where is the change in received signal due tomultipath As =2 l/ where l=v t cos so

=2 / (v t cos ) therefore

f d =(v/ ) cos


8/20

Doppler ShiftConsider a transmitter which radiates a sinusoidal

carrier frequency of 1850MH z. for a vehicle moving60mph, compute the received carrier frequency if the mobile is moving

a) Directly towards the transmitter b) Directly away from the transmitter c) In a direction which is perpendicular to the direction

of the arrival of the transmitted signal.


9/20

Impulse response of a multipath channel

Small-scale fading can be directly related to the impulseresponse of a mobile radio channel. The mobile radiochannel may be modeled as a linear filter with a timevarying impulse response, where the time variation isdue to receiver motion in space.x(t) y(d,t)

Suppose a receiver moves along a constant velocity v.Let h(d,t) be the impulse response andx(t) represent the transmitted signal thenY(d,t) is the received signal.

So y(d,t) = x(t) * h(d,t)

h(d,t)


10/20

Impulse responseThe received signal y(t) can be expressed as a

convolution of the transmitted signal x(t) with thechannel impulse response h(t, ).Where h(t, ) is the channel impulse response which

completely characterizes the channel and is afunction of both t and .t is the time variation due to motion and is the

multipath delay for a fixed value of t.


11/20

Impulse responseSince the received signal in a multipath channel consist of a series

of attenuated, phase shifted replicas of the transmitted signal,the base band impulse response of a multipath channel can beexpressed as

h b (t, ) = a i (t, ) Exp[ j(2 fc i(t) + i(t, ))] ( - i(t))

Where ai(t, ) = amplitude of the ith multipath componenti(t)= is the ith excess delay and

2 fc i(t) + i(t, ) represents the total phase shift experienced by

the ith multipath component.and( - i(t) is the unit impulse function which measures the specificmultipath bins that have components at time t and excess delay


12/20

E xcess delay binsIt is useful to discretize the multipath delay axis into equal time

delay segments called excess delay binsAny no of multipath signals received within the ith bin are

represented by a single resolvable multipath component havingdelay iE ach bin time delay width is i+1 iwhere 0=0 = width of time delay bin, for i=0 0=0, 1= and i=i

E xcess delay is the relative delay of the ith multipath componentas compared to the first arriving componentThe maximum excess delay of the channel is given by N .


13/20

Power delay profileFor small-scale channel modeling, the power delay

profile of the channel is found by taking the spatialaverage of the hb(t, )2 over the local area. Bymaking several local area measurements in differentlocations, it is possible to build an ensemble of power delay profiles, each representing a possible smallscale multipath channel state.

P( )= limt hb(t, )2dt.


14/20

Power delay profilePower delay profile in practice

Requires channel measurement and data analysisDifferent delay profile is generated for different

application at different environments e.g. Urban,indoor, rural etc for 900MH z, 1800, 2400MH z

Power delay profile of multipath channel is calculatedusing techniques likedirect pulse measurement ,spread spectrum sliding correlator measurement andswept frequency measurement techniques


15/20

Time-dispersion parametersIn order to compare different multipath channels and to

develop some general design guidelines for wirelesssystems, some of the parameters are used toquantify the multipath channels.

These parameters include:M ean excess-delayRms delay spread and

E xcess delay spread. All these parameters are calculated from the power

delay profile of the multipath channel.


16/20

Time-dispersion parametersDetermined from power delay profileTreat the power delay profile as a probability mass function and

calculate the mean, second moment and standard deviation for this.

Mean excess delay This is the first moment of the power delay profile (The first

moment, if it exists, is the expectation of X , i.e. the mean of theprobability distribution of X ) and is defined as the

=E[ ]= Pk k

= [ak

2 / ak

2]kSubstituting for a k2 as P( ) we get

= k [P ( k) / k P ( k)] k


17/20

Time dispersion parametersR MS Delay Spread It is the square root of the second central moment of the

power delay profile andsecond moment can be represented as

2=E[ 2 ]= P k k2= [a k2 / a k2] k2

Now the second central moment is the variance, thesquare root of which is the standard deviation, . Wecall it Rms delay spread.

t = 2- ( ) 2


18/20

Time dispersion parametersMaximum Excess Delay This is defined to be the time delay during which

multipath energy falls to X dB below the maximum.M athematically expressed asM ax excess delay (X dB) =x 0Where 0 is the first arriving signal andx is the

maximum delay at which the multipath component iswithin X dB of the strongest arriving multipath signal.


19/20

Coherence bandwidthDerived from the rms delay spreadStatistical measure of the range of frequencies over which the

channel can be considered as flat,.Flat channel means channel which passes all spectral

components with appr equal gain and linear phase.M aximum allowable difference in frequency while amplitudesare still strongly correlated.Two sinusoids with frequency difference greater than Bc, are

affected quiet differently by the channel.Bc= 1/50 if B

cis defined as coherence B/W over which

frequency correlation function is above 0.9 andBc = 1/5 if Bc if the frequency correlation function is relaxed to

0.5 and


20/20

Time dispersion parametersE xampleCalculate the mean excessdelay, rms delay spread and themaximum excess delay for themultipath profile given in thefigure.E stimate the 50% coherencebandwidth of the channel.Would this channel be suitablefor AM PS or GSM without the

use of an equalizer ?

wireless propagation lec 7-8

Documents