Z. Ghassemlooy

Mobile Communications

Part IV- Propagation CharacteristicsMulti-path Propagation - Fading

Part IV- Propagation CharacteristicsMulti-path Propagation - Fading

Professor Z Ghassemlooy

School of Computing, Engineering and Information Sciences, University of Northumbria

U.K.http://soe.unn.ac.uk/ocr

Professor Z Ghassemlooy

School of Computing, Engineering and Information Sciences, University of Northumbria

U.K.http://soe.unn.ac.uk/ocr

Z. Ghassemlooy

Contents

Fading Doppler Shift Dispersion Summary

Z. Ghassemlooy

Fading

Is due to multipath propagation.With respect to a stationary base station, multipath propagation creates a stochastic standing wave pattern, through which the mobile station moves.

Caused by shadowing:when the propagation environment is changing significantly, but this fading is typically much slower than the multipath fading.

Modem design is affected mainly by the faster multipath fading, which can be normally assumed to be locally wide-sense stationary (WSS).

Z. Ghassemlooy

Multipath Propagation - Fading

AntennaAntennaab y = a + b

a & b are in phase a & b are out of phase by

Complete fading when 2d/ = n, d is the path difference

Diffractedwave Reflected

wave

No direct patha b

AntennaAntennab y = 0a

Z. Ghassemlooy

Multipath Propagation - contd.

• For a stationary mobile unit with no direct path, the received signal can be expressed as a sum of delayed components or in terms of phasor notation:

N

iicir fatS

1

)2(cos)(

N

iicir fatS

1

)2(cos)(A single pulse

Pulse train

Where: ai is the amplitude of the scattered signal, p(t) is the transmitted signal (pulse) shape, i is the time taken by the pulse to reach the receiver, N is the number of different paths fc is the carrier frequency

N

iiir tPatS

1

Z. Ghassemlooy

Fading - Types

• Slow (Long) Term

0 5 10 15 20 25 Distance ()

Sig

nal s

tren

gth

rela

tive

to 1

uV (

db)

0

10

20

30

Slow fading

Fast fading

Exact representation of fading characteristics is not possible, because of infinite number of situation.

Exact representation of fading characteristics is not possible, because of infinite number of situation.

•Fast (Short) Term (Also known as Rayleigh fading)

Z. Ghassemlooy

Fading - Slow (Long) Term

Slower variation in mean signal strength (distance 1-

2 km) Produced by movement over much longer distances Caused by:

- Terrain configuration (hill, flat area etc.):

Results in local mean (long term fading) attenuation

and fluctuation.

- The built environment (rural and urban areas etc.),

between base station and the mobile unit:

Results in local mean attenuation

Slower variation in mean signal strength (distance 1-

2 km) Produced by movement over much longer distances Caused by:

- Terrain configuration (hill, flat area etc.):

Results in local mean (long term fading) attenuation

and fluctuation.

- The built environment (rural and urban areas etc.),

between base station and the mobile unit:

Results in local mean attenuation

Z. Ghassemlooy

Fading - Slow (Long) Term

C. D. Charalambous et al

Transmitter

n,1

Receiver

k,1

ord

n,3n,2

k,2

k,3

k,4 one subpath

LOS

path k

path n

Sr(t)

N

iiir tPatS

10

path attenuation factorfor the ith path

Number of path

Z. Ghassemlooy

Fading- Fast (Short) Term

Describes the constant amplitude fluctuations in the received

signal as the mobile moves. Caused by

- multipath reflection of transmitted signal by local scatters

(houses, building etc.)

- random fluctuations in the received power Observed over distances = /2

Signal variation up to 30 dB. Is a frequency selective phenomenon. Can be described using

- Rayleigh statistics, (no line of sight).

- Rician statistics, (line of sight).

Z. Ghassemlooy

Fading- Fast (Short) Term - contd.

N

iicir fatS

1

)2(cos)(

A received signal amplitude is given as the sum of delayed components. In terms of phasor notation it is given as:

Or

N

iiic

N

iiicr atfatftS

11

)sin()2sin()(cos)2cos()(

N

iiic

N

iiicr atfatftS

11

)sin()2sin()(cos)2cos()(

In-phase Quadrature

Z. Ghassemlooy

Fading- Fast (Short) Term - contd.

The phase i can be assumed to be uniformly distributed in the range (0, 2), provided the locations of buildings etc. are completely random.

For a large N, the amplitude of the received signal is:

)2sin()2cos()( tfYtfXtS ccr

where

N

iii

N

iii aYaX

11

)sin(),(cos

X and Y are independent, identically distributed Gaussian random variables.

Z. Ghassemlooy

Fading- Fast (Short) Term - contd.

Rayleigh

Exponential

A or power P

Probabilitydensityfunction

The envelope of the received signal is:

5022 .)( YXA Which will be Rayleigh distributed:Assuming all components received have approximately the same power and that all are resulting from scattering.

2

2

2 2exp

rr

rp

Where 0< r < , is variance of A (the total received power in the multipath signal).

Z. Ghassemlooy

Ricean Fading

If there is one direct component in addition to scattered

components, the envelope received multipath is Ricean,

where the impulse response has a non zero mean.

Ricean distribution = Rayleigh signal + direct line of sight

signal. The distribution is:

2 is the power of the line of sight signal and I0 is a Bessel function of the first kind

202

22

2 2exp

rs

Isrr

rp

Fading- Fast (Short) Term - contd.

The probability that the realization of the random variable has a value smaller than x is defined by the cumulative distribution function:

Applying it to the Rayleigh distribution

For small r

Z. Ghassemlooy

duupdfr )()(cdf

)2/(exp1)(cdf 22 rr

22 2/~)(cdf rr

Z. Ghassemlooy

Fast Fading – Cases 1: Stationary Mobile

5

4

2

1

3

6

4

5

2

1

3

6

v

v

Stationary

tFie

ld s

tren

gth

Z. Ghassemlooy

Fast Fading – Cases 1

The number of fading depends on:– Traffic flow– Distance between the mobile and moving cars

The received signal at the MU is:

N

iiir tPatS

10

ii

Z. Ghassemlooy

N

iiN 1

1 i is additional relative delay (positive or negative)where

and

oc jtfjr etxtS 2)(

N

i

fjio

iceaatx1

2envelope

Thus

Fast Fading – Cases 1

18

1(t1) 2(t2)

tjjtxtS cc expexp

N

iicic tjtaatx

1

exp

Fast Fading – Cases 2

2 = d2/c1 = d1/c

Z. Ghassemlooy

Fast Fading – Cases 3: Non-stationary Mobile

The received signal at the mobile is:

)cos2()( xfjor

oceats

Amplitude

x = Vt

Wave number =2/

Transmitting frequency

VtF

ield

str

engt

h

Signal level No scattered signals

Z. Ghassemlooy

Fast Fading – Cases 3: Doppler Frequency

tV

fj

or

c

eats)cos(2

)(

A moving object causes the frequency of a received wave to changeSubstituting for and x, the expression for the received signal is

The Doppler frequency

coscos mD fV

f

coscos mD fV

f

The received signal frequency

cosmcr fff cosmcr fff

Z. Ghassemlooy

Fast Fading – Cases 3: Doppler Frequency

• When = 0o (mobile moving away from the transmitter)

mcr fff mcr fff

• When = 90o (I.e. mobile circling around)

cr ff cr ff

• When = 180o (mobile moving towards the transmitter)

mcr fff mcr fff

Z. Ghassemlooy

Fast Fading – Cases 4: Moving MU + Stationary Scatterer

x(t)

Vo

ltage Standing Wave Pattern

V

so(t)so(t)

t = 0 t = round trip time

MU

Z. Ghassemlooy

cos2)( Vttfjor

oceats

cococ fVttfjo

Vttfjor eaeats 222)(

and for q = 0

Incident signal Reflected signal

coc ftfjcor e

fVtajts 2

2

2sin2)(

cfnVtFading with zero amplitude occurs when

Fast Fading – Cases 4

Received signal at the MU:

Z. Ghassemlooy

Fast Fading – Cases 5: Moving MU and Scatterers

The resultant received signal is the sum of all the scattered waves from different angles qi depending upon the momentary attitude of the various scatterers.

N

i

Vttfjior

iioceaats1

cos2)(

Z. Ghassemlooy

Channel Fading Effects

Transmitting a short pulse over a

(i) frequency-selective (time-spread) fading channel:

(ii) time-selective (Doppler-spread) fading channel:

t tTp Tp + dt

Transmitted Received

t tTp Tp

Transmitted Received

Z. Ghassemlooy

Effects of Doppler shifts

Bandwidth of the signal could increase or decrease leading to poor and/or missed reception.

The effect in time is coherence time variation and signal

distortion– Coherence time: Time duration over which channel impulse response is

invariant, and in which two signals have strong potential for amplitude correlation

– Coherence time is expressed by:

– where fD-max is the maximum Doppler shift, which occurs when = 0 degrees

To avoid distortion due to motion in the channel, the symbol rate must be greater than the inverse of coherence time.

216

9

D-max

cf

T

Z. Ghassemlooy

Coherence Distance

Coherence distance is the minimum distance between points in space for which the signals are mostly uncorrelated.

This distance is usually grater than 0.5 wavelengths, depending on antenna beamwidth and angle of arrival distribution.

At the BTS, it is common practice to use spacing of about 10 and 20 wavelengths for low-medium and high antenna heights, respectively (120o sector antennas).

Z. Ghassemlooy

Coherence Bandwidth (Bc)

Effect of frequency selective fading on the received signal spectrum

Signal bandwidth Bs

Freq.

Power

Describes frequency selective phenomenon of fast fading

CoherenceBandwidth Bc

Range of frequency over which channel is “flat”

It is the bandwidth over which two frequencies have a strong potential for amplitude correlation

Z. Ghassemlooy

Estimation of Coherence Bandwidth

Coherence bandwidth is estimated using the value of delay

spread of the channel, st

For correlation > 0.9

For correlation > 0.5

Typical values of delay

spreads for various types

of terrain:

tcB

2.0

tcB

02.0

Delay spread figures

at 900 MHz

Delay in

microseconds

Urban 1.3

Urban, worst-case 10 - 25

Suburban, typical 0.2 - 0.31

Suburban, extreme 1.96 - 2.11

Indoor, maximum 0.27

Delay Spread at 1900 MHz

Buildings, average 0.07 - 0.094

Buildings, worst -

case

1.47

Z. Ghassemlooy

Channel Classification

Based on Time-Spreading

Flat Fading1. BS < BC Tm < Ts

2. Rayleigh, Ricean distrib.3. Spectral chara. of transmitted

signal preserved

Frequency Selective1. BS > BC Tm > Ts

2. Intersymbol Interference3. Spectral chara. of transmitted

signal not preserved4. Multipath components resolved

Signal

Channel

freq.BS

BC freq.BC

BS

Channel

Signal

C. D. Charalambous et al

Z. Ghassemlooy

Fading in Digital Mobile Communications

• If Bs>> Bc, then a notch appears in the spectrum. Thus resulting in inter-symbol interference (ISI).

- To overcome this, an adaptive equaliser (AE) with inverse response may be used at the receiver. Training sequences are transmitted to update AE.

• If Bs>> Bc, then a notch appears in the spectrum. Thus resulting in inter-symbol interference (ISI).

- To overcome this, an adaptive equaliser (AE) with inverse response may be used at the receiver. Training sequences are transmitted to update AE.

• If Bs<< Bc, then flat fading occurs, resulting in a burst of error.- Error correction coding is used to overcome this problem.

Z. Ghassemlooy

Multipath Delay Spread

First-arrival delay (τA)

Mean excess delay dPAe )()(

Z. Ghassemlooy

Multipath Delay Spread

The standard deviation of the distribution of multipath signal amplitudes is called delay spread. For directive antenna is characterized by the rms delay spread of the entire delay profile, which is defined as:

whereavg = Σj Pj j , j is the delay of the j th delay component of the profilePj = (power in the j th delay component) / (total power in all components

• Delay spread varies with the terrain with typical values for rural, urban and suburban areas:

j

avgjjrms P 222 )(

rurals2.0 urbans0.3 suburbans5.0

Z. Ghassemlooy

Multipath Delay Spread - Dispersion

The delay spread limits the maximum data rate:– No new impulses should arrive at the receiver before the last

replica of the pervious impulse has perished.

– Otherwise symbol spreads (dispersion) into its adjacent slot, thus

resulting in Inter Symbol Interference (ISI)

The signal arrived at the receiver directly and phase shifted– Distorted signal depending on the phases of the different parts

Transmittedsymbols

Received symbols

Z. Ghassemlooy

Mitigation Techniques for the Multipath Fading Channel

Space diversity – – Signals at the same frequency using two or three antennas located

several wavelengths a part. – Antennas are connected to two or three radio receivers.– The receiver will the strongest signal is elected– Disadvantage: Uses two or more antennas, therefore the

need for a large site. Frequency diversity –

– Signals at different frequencies received by the same antenna very rarely fade simultaneously. Thus the use of several carrier frequencies or the use of a wideband signal to combat fading.

– A single aerial connected to a number receiver, each tuned to a different frequency, whose outputs are connected in parallel. The receiver with the strongest instantaneous signal will provide the output.

– Disadvantage: Uses two or more frequencies to transmit the same signal.

Z. Ghassemlooy

Mitigation Techniques for the Multipath Fading Channel

Time diversity – Spread out the effects of errors through interleaving and coding

Multipath diversity – Consider the tapped delay line model of a channel

shown previously– If multipaths can be put together coherently at the

receiver, diversity improvement results– This is what the RAKE receiver does (see next

viewgraph)

Z. Ghassemlooy

RAKE Multipath Signal Processing

R.E. Ziemer 2002

Z. Ghassemlooy

System Design and Performance Prediction

Base station placement dependent on– Propagation environment– Anticipated geographic distribution of users– Economic considerations (minimize number of base stations)– Political and public opinion considerations– Traffic types (3G)

Performance figure of merit– Spectrum efficiency for voice: ηv voice circuits/MHz/base station

– Spectrum efficiency for information: ηi bps/MHz/base station

– Dropped call rate – fraction of calls ended prematurely

Z. Ghassemlooy

Summary

• If there is a relative motion between transmitter and receiver (mobile) the result is Doppler shift

• If maximum Doppler shift is less than the data rate, there is “slow” fading channel.

• If maximum Doppler shift is larger than the data rate, there is “fast” fading channel.

• The random fluctuations in the received power are due to fading.

Z. Ghassemlooy

Questions and Answers

Tell me what you think about this lecture– fary@ieee.org

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