wireless propagation lec 7-8
Post on 10-Apr-2018
235 Views
Preview:
TRANSCRIPT
-
8/8/2019 Wireless Propagation Lec 7-8
1/20
Wireless Communications
Lecture 7-8Propagation Modelling
Multipath Fading
-
8/8/2019 Wireless Propagation Lec 7-8
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
-
8/8/2019 Wireless Propagation Lec 7-8
3/20
Backgrounds
-
8/8/2019 Wireless Propagation Lec 7-8
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.
-
8/8/2019 Wireless Propagation Lec 7-8
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.
-
8/8/2019 Wireless Propagation Lec 7-8
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
-
8/8/2019 Wireless Propagation Lec 7-8
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
-
8/8/2019 Wireless Propagation Lec 7-8
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.
-
8/8/2019 Wireless Propagation Lec 7-8
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)
-
8/8/2019 Wireless Propagation Lec 7-8
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.
-
8/8/2019 Wireless Propagation Lec 7-8
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
-
8/8/2019 Wireless Propagation Lec 7-8
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 .
-
8/8/2019 Wireless Propagation Lec 7-8
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.
-
8/8/2019 Wireless Propagation Lec 7-8
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
-
8/8/2019 Wireless Propagation Lec 7-8
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.
-
8/8/2019 Wireless Propagation Lec 7-8
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
-
8/8/2019 Wireless Propagation Lec 7-8
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
-
8/8/2019 Wireless Propagation Lec 7-8
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.
-
8/8/2019 Wireless Propagation Lec 7-8
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
-
8/8/2019 Wireless Propagation Lec 7-8
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 ?
top related