This document provides an overview of wireless fading channels. It discusses various phenomena that cause signal attenuation over wireless channels including path loss, shadowing, and multipath fading. It describes Rayleigh fading that occurs when there are many reflected signals and no line-of-sight path. Time dispersion and delay spread are discussed as well as their effects on flat and frequency selective fading. Doppler spread due to mobility is also summarized, including its impact on coherence time and fast/slow fading conditions.

1. An Introductionto
Wireless Fading
Channels
Dr. Manwinder Singh

2. Contents
P
P
S
h y s ic a l P h e n o m e n o n
a t h lo s s m o d e l
h a d o w F a d in g
L a r g e a n d s m a ll s c a le f a d in g
M u lt ip a t h F a d in g
R a y le ig h F a d in g
T im e d is p e r s io n
D e la y s p r e a d
F la t a n d f r e q u e n c y s e le c t iv e f a d in g
T im e v a r ia n c e
D o p p le r f a d in g
S lo w a n d f a s t f a d in g
S u m m a r y o f F a d in g
R e f e r e n c e s

3. The Wireless Channel
•
•
•
Path Loss
Shadowing
Multipath Fading
Amplitude
Distance x
• Doppler Fading

4. Physical Phenomena

5. Physical Phenomena
Reflection - caused by smooth surface with very
large dimensions compared to wavelength
Diffraction- Obstruction caused by a dense body
with large dim. > wavelength. EM waves get bend
around objects. Reason for shadowing and RF
energy being present without LOS
Scattering- Large
wavelength
rough surface with dim. ~

6. Path Loss Model
If there are no objects which are between transmitter
receiver so that no reflection, refraction or
absorption/diffraction happens.
Atmosphere is a uniform and non absorbing medium.
Earth is treated as being infinitely far away from the
propagating signal (having a negligible reflection
coefficient ).
Under these conditions, RF power attenuates a s per
inverse square law. For an isotropic antenna, this
attenuation of Tx power is:
and

7. Wireless Propagation
Path loss inversely proportional to 1/dn,
2 to 4 for mobile channels: Large scale
attenuation in signal strength
n =
Shadowing - Terrain dependent, medium
scale variation in signal strength, comes
because of big obstacles like buildings, hills
Multipath Fading - Small scale or short term
variation on the order of λ/2

8. Path Loss Model
Different, often complicated,
for different environments.
models are used
A simple model for path loss, L, is
Path loss exponent
in free space and
in typical environments

9. Free Space Path Loss
log (distance)
Rx
signal
power(dBm)

10. Shadow Fading
As mentioned earlier, when the received signal is
shadowed by observations such as hills and buildings,
it results in variation of local mean received power,
Where
&
is received signal power due to path loss
implications:
Nonuniform coverage
Increases the required transmit power

11. With Shadow Fading
Shadow Fading
Path loss
log (distance)
Rx
signal
power(dBm)

12. Large, medium and small scale fading
Large Scale Fading: Average signal power attenuation/path
loss due to motion over large areas.
Medium scale fading: Local variation in the average signal
power around mean average power due to shadowing by
local obstructions
Small scale fading: large variation in the signal power due
to small changes in the distance between transmitter and
receiver (Also called Rayleigh fading when no LOS
available). It is called Rayleigh fading due to the fact that
various multipaths at the receiver with random amplitude
& delay add up together to render rayleigh PDF for total
signal.

13. Cause of Multipath Fading
Fading : Fluctuation in the received signal power
due to
Variations in the received singal amplitude
(Different objects present on radio signal path
produce attenuation of it’s power as they can
scatter or absorb part of the signal power, thus
producing
Variations
Variations
a variation of the amplitude
in the signal phase
in the received signal angle of arrival
(different paths travelling different distances
may have different phases & angle of arrival)

14. Causes of Multipath fading Cont..
Reflections and diffraction from object create many
different EM waves which are received in mobile
antenna. These waves usually come from many
different directions and delay varies.
In the receiver, the waves are added either
constructively or destructively and create a Rx signal
which may very rapidly in phase and amplitude
depending on the local objects and how mobile
moves

15. Practical examples of small scale
multipath fading
Common examples of multipath fading are
temporary failure of communication due to a
severe drop in the channel signal to noise ratio
(You may have also experienced this. And you
moved a steps away & noted that reception is
better
. It is due to small scale fading effects. )
FM radio transmission experiencing intermittent
loss of broadcast when away from station.

16. Multipath Fading- Most difficult
Fades of 40 dB or more below local average level
are frequent, with successive nulls occurring
every half wavelength or so
Referred to as Rayleigh Fading

17. Rayleigh Fading Mechanism
Rayleigh fading manifests in two mechanism
Time spreading due to multipath (time dispersion)
Time variant behaviour of the channel due to the
motion and subsequent changes in propagation
paths
Rayleigh PDF:

18. Rayleigh Fading
The Rayleigh pdf is

19. With Rayleigh Fading

20. Rayleigh Fading waveform envelope

21. Time Dispersion phenomenon
h(t)
time
Freq transform
Different frequencies
suffer different
attenuation
Freq

22. Delay Spread –Time Domain
interpretation

23. Delay Spread
h(t)
h(t)
time
time Excess delay spread
Excess delay spread
Multiple impulses of varying power correspond to various
multipaths. This time dispersion is also referred to as multipath
delay spread.
Delay between first significant path & last significant paths
loosely termed as channel excess delay spread.
Two totally different channels can have same excess delay
spread.
A better measure of delay spread is rms delay spread
L is the number of paths & is the amplitude of the path i arriving at time
is
is the second moment

24. Delay Spread- Freq. Domain Interpretation

25. Time spreading : Coherence Bandwidth
W
Freq
f0
W
Freq
Channel
frequency
response
Channel
frequency
response

26. More on
f0
flat fading
•
W
Freq
Condition f0 > W does not guarantee flat fading. As shown
above, frequency nulls (frequency selective fading) may be
there occasionally even though f0 > W.
Similarly, frequency selective fading channel may also show
flat fading sometimes.
Channel
frequency

27. Bit Rate Limitations by Delay Spread

28. Coherence Bandwidth and delay
spread
There is no exact relationship between Coherence bandwidth
and delay spread. For at least 0.9 correlation for channel’s
complex frequency transfer function, Coherence bandwidth f0 is
approximated by following relation:
Where is r.m.s. delay spread
For dense scatterer model which is useful for urban
surroundings, coherence bandwidth is defined as assuming at
least 0.5 correlation:
Another popular approximation assuming at least 0.5
correlation:

29. Effects of Flat & frequency selective
fading
Flat fading
Reduces SNR forcing various mitigation
techniques to handle that. Not such a bad
Frequency selecting fading
ISI distortion (need equalizer in receiver)
Pulse mutilation
Irreducible BER
thing.

30. Summary of Time dispersion
Small scale fading
( based on multipath delay spread)
Flat Fading
BW of signal < BW of
channel
Or
Delay Spread <
Symbol period
Frequency selective
Fading
BW of signal > BW of
channel
Or
Delay Spread >
Symbol period

31. Time variant behavior of the
h(t)
channel
Impulse
response
time
Excess delay spread
h(t)
Impulse
response time
Excess delay spread
Relative movement between transmitter and receiver or objects between those
causes variation in channel’s characteristics over time. This happens due to
propagation path change over time. Relative movement also creates frequency
spreading due to Doppler effect

32. Time Variance
Variance
important
in channel conditions over time
a
is an
factor when designing mobile
communication system.
If fast variations happen, it can lead to severe pulse
distortion and loss
irreducible BER.
of SNR subsequently causing

33. Basic Dopp
t)
ler effect
c is the light velocity and vm is the car
speed
Propagation time is a function of time due
to mobile car.

34. Doppler spread in Multipath
vm cos (θ1)
θ1
vm
θ2
vm cos (θ2)
|Y(f)|
|X(f)| After passing through
multipath channel f + f
c d
fc + fd1 fc + fd2 freq
fc freq
Due to multipaths, a single sinusoid by base station is perceived as
summation of 3 sinusioids fc+fd1, fc+fd2 and fc+fd , where fd is maximum
doppler frequency = fc*(vm/d). Due to different arrivals of angle due to
multipaths, perceived velocity is different for multipaths.

35. Doppler Spectrum
Imagine now multiple paths
with different angles of arrival
causing
various
amagamalation of
frequencies between
fc +fd & fc-fd.
A popular model assumes that
distribution of angle of arrival is
distributed uniformly between 0 &
2π which leads to following
spectrum
This is called classical Doppler spectrum & shows how a single sinusoid ends up
having a broad spectrum due to multipath & relative motion between Tx
and Rx.

36. Time variant Channel: Coherence Time
Maximum doppler frequency is an important measure of time
variance of channel characteristics. It depends on relative speed of
any movement between Tx & Rx and the carrier frequency
Coherence time: Approximate time duration
channel’s response remains invariant
over which the
Where is Maximum Doppler Frequency

37. Frequency Dual
Fourier
Transform
T0
Function denotes space time correlation for the
channel response to a sinusoid . So this indicates the
amount of correlation between two sinusoids sent at
different times t1 & t2 .

38. Waveform
Signal
of Rayleigh Fading

39. Time Variance : Fast Fading
Fast Fading :
Where Ts : Transmitted Symbol time
Or
Where W: Transmitted bandwidth
Above relationship means that channel changes drastically
times while a symbol is propagating;
many
Only highly mobile systems (~500 Km/Hr) will have fd ~1 kHz so
systems having signalling rate of that order will be fast fading.
Impact of fast fading:
Severe distortion of baseband pulse leading to detection
problems
Loss in SNR
Synchronization problems (e.g. Failure of PLL)

40. Time
Slow Fading :
where
Or
where
variance: Slow Fading
Ts : Transmitted Symbol time
W: Transmitted bandwidth
Above relationship means that channel does not change
drastically during symbol duration
Most of the modern communication systems are slow fading
channels
Impact of fast fading:
Loss in SNR

41. Summary of Overall Fading

42. Summary of Multipath Fading
characterization

43. References
B Skalar. “Rayleigh fading channels in mobile digital
communication systems, Part I: characterization”. IEEE
communication magazine. July 1997, pp 90-100.