Small-scale fading and multipath propagation can cause rapid fluctuations in the strength of received mobile radio signals over short time periods and distances. This is caused by interference between multiple versions of the transmitted signal which take slightly different paths to the receiver. There are three main effects: rapid changes in signal strength, random frequency modulation from varying Doppler shifts, and time dispersion caused by multipath delays. The factors influencing small-scale fading include multipath propagation, the speed of the mobile receiver and surrounding objects, the signal bandwidth, and the coherence bandwidth of the channel. Fading can be characterized as flat if the signal bandwidth is narrow compared to the coherence bandwidth, or frequency selective otherwise. It can also be fast or slow fading depending on if

1. Mobile Radio Propagation:
SMALL-SCALE FADING AND MULTIPATH
KNCET 1

2. FADING
• Fading: rapid fluctuations(reduction) of received
signal strength over short time intervals and/or travel
distances
• Caused by an interference between two or more
versions of the transmitted signal being slightly out
of phase due to the different propagation time
• This is also called multipath propagation
KNCET 2

3. MULTI-PATH PROPAGATION
More version of the transmitted signal takes more than
one transmission path to reach the receiver from the
transmitter at a slightly different times.
KNCET 3

4. FADING
• At a receiver the radio waves generated by same
transmitted signal may come
- From Different direction
- With Different propagation delays
- With Different amplitudes
- With Different phase
• The multipath components combine vectorially at the
receiver and produce a fade or distortion
KNCET 4

5. EFFECTS OF FADING/MULTIPATH
Multi-Path in the radio channel creates small-scale
fading. The three most important effects of fading are:
– Rapid changes in signal strength over a small
travel distance or time interval
– Random frequency modulation due to varying
Doppler shifts on different multi-path signals
– Time dispersion (echoes) caused by multi-path
propagation delays
Even when a mobile receiver is stationary, the received
signal may fade due to a non-stationary nature of the
channel (reflecting objects can be moving)
KNCET 5

6. FACTORS INFLUENCING SMALL SCALE FADING
1. Multipath Propagation
– Presence of reflecting objects and scatterers in the channel
creates a constantly changing environment.
– Due to time delay of signal arrival
• Multiple version of transmitted signal arrive at the
receiving antenna
– Causes the signal at receiver to fade or distort
2. Speed of Mobile Receiver
– Relative motion between base station & mobile causes
random frequency modulation due to different Doppler shift
on each multipath signals.
– Doppler shift may be positive or negative depending on
movement of mobile terminal towards or away from base
station KNCET 6

7. FACTORS INFLUENCING SMALL SCALE FADING
3) Speed of Surrounding Objects
– If the speed of surrounding objects is greater than mobile, the
fading is dominated by those objects
– If the surrounding objects are slower than the mobile, then
their effect can be ignored
4) Transmission bandwidth of the signal
– Depending on the relation between the signal bandwidth and
the coherence bandwidth of the channel, the signal is either
distorted or faded
– If the signal bandwidth is greater than coherence bandwidth it
creates distortion
– If the signal bandwidth is smaller than coherence bandwidth,
amplitude of the signal will change rapidly but signal is not
distorted, creates fading 7

8. COHERENCE BANDWIDTH
• It is a measure of the maximum frequency difference
for which the signals are correlated in amplitude
• The coherence bandwidth of a wireless channel is the
range of frequencies that are allowed to pass through
the channel without distortion.
KNCET 8

9. Doppler Shift (fd)
• Change in the apparent frequency of a signal, as Tx and Rx
move towards or away from each other
• If mobile is moving towards the direction of arrival of the
signal, the Doppler shift is positive(apparent received
frequency is increased i.e. fc+fd) and vice versa
• v : velocity (m/s)
• λ : wavelength (m)
• θ : angle between mobile
direction and arrival direction
of RF energy
+ shift → mobile moving towards remote source,S
− shift → mobile moving away from remote source,S

10. DOPPLER SHIFTS
• Phase change in the received signal due to the difference in
path lengths,
• Apparent change in frequency or Doppler shift,
• If the mobile is moving toward the direction of arrival of the
wave, Doppler Shift is positive
• If the mobile is moving away from the direction of arrival of
the wave, Doppler Shift is negative.
KNCET 10

11. Impulse Response Model of a Multipath Channel
• The small scale variations of a mobile radio signal can be
directly related to the impulse response of mobile radio
channel.
• Impulse response contains information to Simulate and
Analyze the channel
• The mobile radio channel can be modeled as Linear filter with
time varying impulse response
• In case of mobile reception, the length and attenuation of
various paths will change with time i.e. Channel is time
varying
KNCET 11

12. Impulse Response Model of a Multipath Channel
• The time variation is strictly due to receiver movement (t=d/v)
• At any distance d=vt, the received signal is the combination of
different signals coming with different propagation delays
depending on the distance between transmitter and receiver.
• So the impulse response is a function of d, which is the
separation between the transmitter and receiver.
KNCET 12

13. Impulse Response Model of a Multipath Channel
• Short duration Tx pulse ≈ unit impulse
• Discretize Multipath delay axis, τ of impulse response into
equal time delay segments called excess delay bins
• Amplitude and delay time of multipath returns change as
mobile moves
• τ1-τ0 =Δ τ
• Depending on the choice of Δ τ and physical channel delay
properties there may be two or more multipath signals
KNCET 13

14. Discrete time Impulse Response Model of a
Multipath Channel
• Such situation cause multipath amplitude within an excess
delay bin to fade over local area
KNCET 14

15. Discrete time Impulse Response Model of a Multipath
Channel
• Baseband impulse response of a multipath channel
– ai ∠ θ i = amplitude & phase of each multipath signal
– N = possible number of multipath components
– ai is relatively constant over an local area
• But θ i will change significantly because of different
path lengths (direct distance plus reflected distance) at
different locations.
KNCET 15

16. Impulse Response Model of a Multipath Channel
• The useful frequency span of the model :
• Used to analyse transmitted RF signals having
bandwidth less than this.
• The received power delay profile in a local area:
• Bar represents the average over the local area
KNCET 16
2/ 

2
( ) ( ; )
b
P k h t
 


17. PARAMETERS OF MOBILE MULTIPATH CHANNELS
• Time Dispersion Parameters
• Grossly quantifies the multipath channel
• Determined from Power Delay Profile
• Parameters include
- Mean Excess Delay
- RMS Delay Spread
- Excess Delay Spread (X dB)
• Coherence Bandwidth
• Doppler Spread and Coherence
KNCET 17

18. TIME DISPERSION PARAMETERS
– “excess delay” : all values computed relative
to the time of first signal arrival τo
__
Mean excess delay (τ)→Average delay
measured with respect to the first (arrival)
moment of the power delay profile
KNCET 18

19. RMS DELAY SPREAD
– Square root of the second central moment of the power
delay profile
• It is “the range of time within which most of the delayed
signals arrive”
KNCET 19

20. Maximum excess delay ( XdB ):
• Defined as the time delay value after which the multipath
energy falls to X dB below the maximum multipath energy
(not necessarily belonging to the first arriving component).
• It is also called excess delay spread
KNCET 20

21. Parameters of mobile multipath channels
Coherence BW (Bc)
– Bc : Range of frequencies over which the channel
can be considered flat
– Response is flat = passes all frequencies with
≈ equal gain & linear phase.
• Used to characterize the channel in the frequency
domain.
– It is inversely proportional to RMS delay spread
Bc = 1 /
KNCET 21

22. DOPPLER SPREAD
• Measure of spectral broadening caused by motion
• Doppler spread, BD, is defined as the maximum
Doppler shift:
fm = v/λ
• if Tx signal bandwidth (Bs) is large such that
Bs >> BD
then effects of Doppler spread are negligible, so
Doppler spread is only important for low bps (data
rate) applications (e.g. paging), slow fading channel
KNCET 22

23. COHERENCE TIME (TC)
• Coherence time is the time duration over which the channel
impulse response is essentially invariant.
• If the symbol period of the baseband signal (reciprocal of the
baseband signal bandwidth) is greater the coherence time, than
the signal will distort, since channel will change during the
transmission of the signal.
KNCET 23

24. COHERENCE TIME (Tc)
– Used to characterize the time varying nature of the frequency
dispersiveness of the channel in the time domain
– Doppler spread and coherence time are inversely proportional to
one another
Tc = 1 / fm
– For digital communications coherence time and Doppler spread
are related by
– Coherence time implies that two signals arriving with a time
separation greater than TC are affected differently by the channel.
KNCET 24
2
9 0.423
16
c
m m
T
f f

 

25. Types of Small-Scale Fading
KNCET 25

26. Classification of Multipath Channels
KNCET 26
• Depending on the relation between signal parameters
(bandwidth and symbol period) and channel
parameters (delay spread and Doppler spread) different
signals undergo different types of fading
• Based on delay spread the types of small scale fading
are
- Flat fading
- Frequency selective fading
• Based on Doppler spread the types of small scale fading
are
- Fast fading
- Slow fading

27. FLAT FADING
A）Flat Fading → Bs << Bc or
• Occurs when the amplitude of the received signal
changes with time
• Symbol period of transmitted signal > Delay spread of
the channel
• Bandwidth of the applied signal is narrow
• The channel has a flat transfer function with
almost linear phase, thus affecting all spectral
components of the signal in the same way
• May cause deep fades.
• Increase the transmit power to combat this
situation. KNCET 27
10
s
T 



28. FLAT FADING
KNCET 28

29. Frequency Selective Fading
Frequency Selective Fading → Bs > Bc or
– A channel that is not a flat fading channel is called frequency
selective fading because different frequencies within a signal
are attenuated differently by the MRC
– Symbol period < Channel multipath Delay spread
– Symbols face time dispersion
– Channel induces Inter symbol Interference (ISI)
– Bandwidth of the signal s(t) is wider than the channel
impulse response
KNCET 29
10
s
T 



30. Frequency Selective Fading
KNCET 30

31. Fading due to Doppler Spread
A) Fast Fading → Bs < BD or Ts > Tc
• Rate of change of the channel characteristics is larger
than the Rate of change of the transmitted signal
• The channel changes during a symbol period.
• The channel changes because of receiver motion
• Coherence time of the channel is smaller than the
symbol period of the transmitted signal
• Signal distortion increases relative to the bandwidth of
the transmitted signal
– uncommon in most digital communication systems
KNCET 31

32. Slow Fading
B) Slow Fading → Ts << Tc or Bs >> BD
–Rate of change of the channel characteristics is much
smaller than the Rate of change of the transmitted
signal
–Slow amplitude fluctuations
–Velocity of the mobile and the baseband signaling
determines whether a signal undergoes fast fading or
slow fading.
KNCET 32

33. Fading Distributions
• Describes how the received signal amplitude changes with
time.
• Remember that the received signal is combination of multiple
signals arriving from different directions, phases and
amplitudes.
• With the received signal is a statistical characterization of the
multipath fading.
Two distributions
• Rayleigh Fading
• Ricean Fading
KNCET 33

34. Rayleigh and Rician Distribution
A close approximation of attenuation due to multipath fading in
wireless channels can be done by Rayleigh fading (for the case
where no line of sight component present) and Rician fading (for
the case where line of sight component present).
KNCET 34
Rayleigh Rician
No line of sight
component present
Line of sight
component present

35. Rayleigh Distribution
• Rayleigh distribution can be calculated by taking two
independent and identically distributed zero mean
gaussian random variables as real and imaginary parts
of a complex number and then taking its magnitude
• For a wireless channel, the envelope of the channel
response is modeled to have a Rayleigh distribution
• Rayleigh Fading is a reasonable model when there are
many objects in the environment that scatter the radio
signal before it reaches the receiver.
KNCET 35

36. Rayleigh Distribution
• Rayleigh probability distribution function →
– Used for flat fading signals.
– Formed from the sum of two Gaussian noise signals.
– σ : RMS value of Rx signal before detection
(demodulation)
– common model for Rx signal variation
• urban areas → heavy clutter → no LOS path
– probability that signal does not exceeds predefined
threshold level R
KNCET 36
2
2 2
( ) exp 0
2
r r
P r r
 
 
    
 
 

37. Rayleigh Probability Density function
KNCET 37

38. Rician Probability Density function
KNCET 38
– When there is a stationary (non-fading) LOS signal present,
then the envelope distribution is Ricean.
– The Ricean distribution degenerates to Rayleigh when the
dominant component fades away.
– The Pdf of Ricean function is given as

39. Rician Probability Density function
KNCET 39

40. KNCET 40
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