1. Mobile Communications
Part IV- Propagation Characteristics
Multi-path Propagation - Fading
Professor Z Ghassemlooy
School of Computing, Engineering and
Information Sciences, University of Northumbria
U.K.
Z. Ghassemlooy

2. Contents
Fading
Doppler Shift
Dispersion
Summary
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3. Fading Is due to multipath propagation. Caused by shadowing:
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).
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4. Multipath Propagation - Fading
Diffracted
wave
Reflected
No direct path a b
Antenna a b
y = a + b
Antenna b
y = 0 a
a & b are in phase
a & b are out of phase by 
Complete fading when
2d/ = n, d is the path difference
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5. 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:
Pulse train
A single pulse
Where: ai is the amplitude of the scattered signal,
p(t) is the transmitted signal (pulse) shape,
ti is the time taken by the pulse to reach the receiver,
N is the number of different paths
fc is the carrier frequency
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6. Fading - Types Slow (Long) Term
Fast (Short) Term (Also known as Rayleigh fading)
Signal strength relative to 1uV (db) 10 20 30
Fast fading
Slow fading 5 10 15 20 25
Distance ()
Exact representation of fading characteristics is not possible,
because of infinite number of situation.
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7. 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
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8. Fading - Slow (Long) Term
Transmitter
tn,1
Receiver
tk,1
t or d
tn,3
tn,2
tk,2
tk,3
tk,4
one subpath
LOS
path k
path n
Sr(t)
Number of path
path attenuation factor
for the ith path
C. D. Charalambous et al
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9. 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).
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10. Fading- Fast (Short) Term - contd.
A received signal amplitude is given as the sum of delayed
components. In terms of phasor notation it is given as: Or
In-phase
Quadrature
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11. 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:
where
X and Y are independent, identically distributed Gaussian random
variables.
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12. Fading- Fast (Short) Term - contd.
The envelope of the received signal is:
Which will be Rayleigh distributed:
Assuming all components received
have approximately the same power
and that all are resulting from scattering.
Rayleigh
Exponential
A or power P
Probability
density
function
Where 0< r < , s2 is
variance of A (the total received
power in the multipath signal).
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13. 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
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14. 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
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15. Fast Fading – Cases 1: Stationary Mobile5 4 2 1 3 6 t4 t5 t2 t1 t3 t6 v
Stationary t
Field strength
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16. 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:
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17. Fast Fading – Cases 1 where
is additional relative delay (positive or negative)
and
Thus
envelope
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18. Fast Fading – Cases 2
t1(t1)
t2(t2)
T1 = d1/c
T2 = d2/c

19. Fast Fading – Cases 3: Non-stationary Mobile
Field strength
Signal level
No scattered signals  V
The received signal at the mobile is:
Wave number =2/
x = Vt
Transmitting frequency
Amplitude
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20. Fast Fading – Cases 3: Doppler Frequency
A moving object causes the frequency of a received wave to change
Substituting for  and x, the expression for the received signal is
The Doppler frequency
The received signal frequency
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21. Fast Fading – Cases 3: Doppler Frequency
When  = 0o (mobile moving away from the transmitter)
When  = 90o (I.e. mobile circling around)
When  = 180o (mobile moving towards the transmitter)
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22. Fast Fading – Cases 4: Moving MU + Stationary Scatterer
x(t)
Voltage
Standing Wave Pattern V
so(t)
t = 0
t = round trip time MU
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23. Fast Fading – Cases 4 Received signal at the MU: and for q = 0
Incident signal
Reflected signal
Fading with zero amplitude occurs when
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24. 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.
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25. Channel Fading Effects
Transmitting a short pulse over a
(i) frequency-selective (time-spread) fading channel:
(ii) time-selective (Doppler-spread) fading channel: t Tp
Tp + dt
Transmitted
Received t Tp
Transmitted
Received
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26. 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 q = 0 degrees
To avoid distortion due to motion in the channel, the symbol rate must be greater than the inverse of coherence time. 2 16 9
D-max c f T p =
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27. 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).
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28. Coherence Bandwidth (Bc)
Range of frequency over which channel is “flat”
It is the bandwidth over which two frequencies have a strong potential for amplitude correlation
Signal bandwidth Bs
Freq.
Power
Describes frequency selective
phenomenon of fast fading
Coherence
Bandwidth Bc
Effect of frequency selective fading on the received signal spectrum
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29. 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: t c B  02 . t c B  2 .
Delay spread figures
at 900 MHz
Delay in
microseconds
Urban
1.3
Urban, worst-case
Suburban, typical
Suburban, extreme
Indoor, maximum
0.27
Delay Spread at 1900 MHz
Buildings, average
Buildings, worst -
case
1.47
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30. Channel Classification
Based on Time-Spreading
Flat Fading
BS < BC  Tm < Ts
Rayleigh, Ricean distrib.
Spectral chara. of transmitted
signal preserved
Frequency Selective
BS > BC  Tm > Ts
Intersymbol Interference
signal not preserved
Multipath components resolved
Signal
Channel
freq. BS BC
C. D. Charalambous et al
Z. Ghassemlooy

31. 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 flat fading occurs, resulting in a
burst of error.
- Error correction coding is used to overcome this
problem.
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32. Multipath Delay Spread
First-arrival delay (τA)
Mean excess delay
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33. 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:
where
avg = Σj Pj  j ,
 j is the delay of the j th delay component of the profile
Pj = (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: ( )
rural s m 2 .
urban 3
suburban 5
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34. 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
Transmitted
symbols
Received
symbols
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35. 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.
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36. 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)
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37. RAKE Multipath Signal Processing
R.E. Ziemer 2002
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38. 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
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39. Summary The random fluctuations in the received power are due to
fading.
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.
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40. Questions and Answers Tell me what you think about this lecture
Next lecture: Modulation Techniques
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