Small-Scale Fading and Multipath measurements consists of PPT of UPTU Unit-1 Part 2

1. Unit-I (P-II)
Small-Scale Fading and Multipath
measurements
1Vrince Vimal,Asst.Prof, Deptt Of EC, MIT,
MIET Group, Meerut.

2. I. Fading
• Fading: rapid fluctuations of received signal strength
over short time intervals and/or travel distances
• Caused by interference from multiple copies of Tx
signal arriving @ Rx at slightly different times
• Three most important effects:
1. Rapid changes in signal strengths over small travel
distances or short time periods.
2. Changes in the frequency of signals.
3. Multiple signals arriving a different times. When added
together at the antenna, signals are spread out in time.
This can cause a smearing of the signal and interference
between bits that are received.
2
Vrince Vimal,Asst.Prof, Deptt Of EC, MIT,
MIET Group, Meerut.

3. • Fading signals occur due to reflections from
ground & surrounding buildings (clutter) as
well as scattered signals from trees, people,
towers, etc.
– often an LOS path is not available so the first
multipath signal arrival is probably the desired
signal (the one which traveled the shortest
distance)
– allows service even when Rx is severely
obstructed by surrounding clutter
3
Vrince Vimal,Asst.Prof, Deptt Of EC, MIT,
MIET Group, Meerut.

4. • Even stationary Tx/Rx wireless links can
experience fading due to the motion of
objects (cars, people, trees, etc.) in
surrounding environment off of which come
the reflections
• Multipath signals have randomly distributed
amplitudes, phases, & direction of arrival
– vector summation of (A ∠θ) @ Rx of multipath
leads to constructive/destructive interference as
mobile Rx moves in space with respect to time
4
Vrince Vimal,Asst.Prof, Deptt Of EC, MIT,
MIET Group, Meerut.

5. • received signal strength can vary by Small-scale fading
over distances of a few meter (about 7 cm at 1 GHz)!
1. This is a variation between, say, 1 mW and 10-6 mW.
2. If a user stops at a deeply faded point, the signal quality
can be quite bad.
3. However, even if a user stops, others around may still
be moving and can change the fading characteristics.
4. And if we have another antenna, say only 7 to 10 cm
separated from the other antenna, that signal could be
good.
5
Vrince Vimal,Asst.Prof, Deptt Of EC, MIT,
MIET Group, Meerut.

6. Vrince Vimal,Asst.Prof, Deptt Of
EC, MIT, MIET Group, Meerut.
6
• fading occurs around received signal strength predicted from
large-scale path loss models

7. Physical Factors Influencing Fading in Mobile Radio
Channel (MRC)
1) Multipath Propagation
• # and strength of multipath signals
• time delay of signal arrival
– large path length differences → large differences in
delay between signals
• urban area w/ many buildings distributed over
large spatial scale
– large # of strong multipath signals with only a few
having a large time delay
• suburb with nearby office park or shopping mall
– moderate # of strong multipath signals with small to
moderate delay times
• rural → few multipath signals (LOS + ground
reflection)
7
Vrince Vimal,Asst.Prof, Deptt Of
EC, MIT, MIET Group, Meerut.

8. Vrince Vimal,Asst.Prof, Deptt Of EC, MIT,
MIET Group, Meerut.
8
2) Speed of Mobile
– relative motion between base station & mobile
causes random frequency modulation due to
Doppler shift (fd)
– Different multipath components may have
different frequency shifts.
3) Speed of Surrounding Objects
– also influence Doppler shifts on multipath
signals
– dominates small-scale fading if speed of objects
> mobile speed
• otherwise ignored

9. 4) Tx signal bandwidth (Bs)
 The mobile radio channel (MRC) is modeled as
filter w/ specific bandwidth (BW)
 The relationship between the signal BW & the
MRC BW will affect fading rates and distortion,
and so will determine:
 a) if small-scale fading is significant
 b) if time distortion of signal leads to inter-symbol
interference (ISI)
 An MRC can cause distortion/ISI or small-scale
fading, or both.
 But typically one or the other.
9
Vrince Vimal,Asst.Prof, Deptt Of EC, MIT,
MIET Group, Meerut.

10. Doppler Shift
• motion causes frequency modulation due to Doppler
shift (fd)
• v : velocity (m/s)
• λ : wavelength (m)
• θ : angle between
mobile direction
and arrival direction of RF energy
» + shift → mobile moving toward S
» − shift → mobile moving away from S
10
Vrince Vimal,Asst.Prof, Deptt Of EC, MIT,
MIET Group, Meerut.

11. • Two Doppler shifts to consider above
1. The Doppler shift of the signal when it is received
at the car.
2. The Doppler shift of the signal when it bounces
off the car and is received somewhere else.
• Multipath signals will have different fd’s for
constant v because of random arrival
directions!!
11
Vrince Vimal,Asst.Prof, Deptt Of EC, MIT,
MIET Group, Meerut.

12. • Note: What matters with Doppler shift is not
the absolute frequency, but the shift in
frequency relative to the bandwidth of a
channel.
– For example: A shift of 166 Hz may be significant
for a channel with a 1 kHz bandwidth.
– In general, low bit rate (low bandwidth) channels
are affected by Doppler shift.
12
Vrince Vimal,Asst.Prof, Deptt Of EC, MIT,
MIET Group, Meerut.

13. . MRC Impulse Response Model
• Impulse response is wideband characterization containing all
the information required to analyze the radio X’mission through
channel.
• We can Model the MRC as a linear filter with a time varying
characteristics due to position of Rx.
• Vector summation of random amplitudes & phases of
multipath signals results in a "filter“
• That is to say, the MRC takes an original signal and in the
process of sending the signal produces a modified signal at the
receiver.
13
Vrince Vimal,Asst.Prof, Deptt Of EC, MIT,
MIET Group, Meerut.

14. Vrince Vimal,Asst.Prof, Deptt Of EC, MIT,
MIET Group, Meerut.
14
• Time variation due to mobile motion results in time delay of
multipath signals varies with location of Rx
 Can be thought as a "location varying" filter.
 As mobile moves with time, the location changes with time;
hence, time-varying characteristics.
• The MRC has a fundamental bandwidth limitation → model
as a band pass filter

15. Vrince Vimal,Asst.Prof, Deptt Of EC, MIT,
MIET Group, Meerut.
15
Assume Rx moving along X –axis with constant velocity v.
For fixed d channel can be modeled as linear time invariant system
But for different d signal received at Rx will vary due to multipath
and Doppler shift.
That is the channel response is dependent on d so impulse response
Should be expressed as h(d,t).

16. Vrince Vimal,Asst.Prof, Deptt Of EC, MIT,
MIET Group, Meerut.
16
Let x(t)-transmitted signal than received signal y(d,t) at d
Ca be expressed as convolution of x(t) & h (d,t)
For causal system h (d,t)=0, for t<0 eq reduces to
If v is constant
d=vt than

17. Vrince Vimal,Asst.Prof, Deptt Of EC, MIT,
MIET Group, Meerut.
17
As v is constant so y(vt,t) is function of t, so
If v is assumed to be constant for short distance,
= x’mitted bandpass waveform
=received bandpass waveform
= impulse response of multipath radio channel

18. Vrince Vimal,Asst.Prof, Deptt Of EC, MIT,
MIET Group, Meerut.
18

19. Vrince Vimal,Asst.Prof, Deptt Of
EC, MIT, MIET Group, Meerut.
19
• How is the impulse response of an MRC determined?
– “channel sounding” → like radar
– transmit short time duration pulse (not exactly an impulse,
but with wide BW) and record multipath echoes @ Rx

20. • short duration Tx pulse ≈ unit impulse
• define excess delay bin as
• amplitude and delay time of multipath returns change as mobile
moves
• Fig. 5.4, pg. 184 → MRC is time variant
1i i
 

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Vrince Vimal,Asst.Prof, Deptt Of EC, MIT,
MIET Group, Meerut.

21. Vrince Vimal,Asst.Prof, Deptt Of EC, MIT,
MIET Group, Meerut.
21
• model multipath returns as a sum of unit impulses
– ai ∠ θ i = amplitude & phase of each multipath signal
– N = # 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.

22. • The useful frequency span of the model :
• The received power delay profile in a local area:
• Assume the channel impulse response is time
invariant, or WSS
2
( ) ( ; )b
P k h t 
2 / 
22
Vrince Vimal,Asst.Prof, Deptt Of EC, MIT,
MIET Group, Meerut.

23. Relationship between Bandwidth and Received Power
• A pulsed, transmitted RF signal of the form
23
Vrince Vimal,Asst.Prof, Deptt Of EC, MIT,
MIET Group, Meerut.

24. Vrince Vimal,Asst.Prof, Deptt Of EC, MIT,
MIET Group, Meerut.
24
• For wideband signal

25. • The average small-scale received power
– The average small scale received power is simply the
sum of the average powers received in each multipath
component
– The Rx power of a wideband signal such as p(t) does
not fluctuate significantly when a receiver is moved
about a local area.
25
Vrince Vimal,Asst.Prof, Deptt Of EC, MIT,
MIET Group, Meerut.

26. Vrince Vimal,Asst.Prof, Deptt Of EC, MIT,
MIET Group, Meerut.
26
• CW signal (narrowband signal ) is transmitted in to
the same channel

27. • Average power for a CW signal is equivalent to the average
received power for a wideband signal in a small-scale region.
• The received local ensemble average power of wideband and
narrowband signals are equivalent.
• Tx signal BW > Channel BW Rx power varies very small
• Tx signal BW < Channel BW large signal fluctuations
(fading) occur
– The duration of baseband signal > excess delay of channel
– due to the phase shifts of the many unsolved multipath components
27
Vrince Vimal,Asst.Prof, Deptt Of EC, MIT,
MIET Group, Meerut.

28. 28
Vrince Vimal,Asst.Prof, Deptt Of
EC, MIT, MIET Group, Meerut.

29. • The Fourier Transform of hb ( t,τ) gives the spectral
characteristics of the channel → frequency response
• MRC filter passband → “Channel BW” or Coherence
BW = Bc
– range of frequencies over which signals will be transmitted
without significant changes in signal strength
– channel acts as a filter depending on frequency
– signals with narrow frequency bands are not distorted by the
channel
29
Vrince Vimal,Asst.Prof, Deptt Of EC, MIT,
MIET Group, Meerut.

30. 30
Vrince Vimal,Asst.Prof, Deptt Of EC, MIT,
MIET Group, Meerut.

31. 31
Vrince Vimal,Asst.Prof, Deptt Of EC, MIT,
MIET Group, Meerut.

32. 32
Vrince Vimal,Asst.Prof, Deptt Of EC, MIT,
MIET Group, Meerut.

33. 33
Vrince Vimal,Asst.Prof, Deptt Of
EC, MIT, MIET Group, Meerut.

34. Vrince Vimal,Asst.Prof, Deptt Of EC, MIT,
MIET Group, Meerut.
34

35. Vrince Vimal,Asst.Prof, Deptt Of EC, MIT,
MIET Group, Meerut.
35

36. Small scale Multipath measurement
• Direct RF pulse(uses wideband pulse bistatic
radar)
• Spread Spectrum sliding correlator channel
sounding
Vrince Vimal,Asst.Prof, Deptt Of EC, MIT,
MIET Group, Meerut.
36

37. Channel Sounder: Pulse type
37
Vrince Vimal,Asst.Prof, Deptt Of EC, MIT,
MIET Group, Meerut.

38. Disadvantages
• Interference
• If first pulse is faded severe fading occurs
• Phase of multipath is not received
Vrince Vimal,Asst.Prof, Deptt Of
EC, MIT, MIET Group, Meerut.
38

39. Channel Sounder: PN Type
39
Vrince Vimal,Asst.Prof, Deptt Of EC, MIT,
MIET Group, Meerut.

40. Vrince Vimal,Asst.Prof, Deptt Of EC, MIT,
MIET Group, Meerut.
40
•Pseudo –noise is added to carrier signal
•The power sprctrum envelope of X’mitted SS is given by-
•With BW=2Rc
•at receiver again PN sequence is added to incoming SS signal
but with slower clock rate .
•This is called as SLIDING CORRELATION.

41. Vrince Vimal,Asst.Prof, Deptt Of EC, MIT,
MIET Group, Meerut.
41
•Processing gain is given by:-
•The time resolution of MPC with SS using SC is given by

42. Channel Sounder: Swept Freq. type
42
Vrince Vimal,Asst.Prof, Deptt Of EC, MIT,
MIET Group, Meerut.

43. IV. Multipath Channel Parameters
• Derived from multipath power delay
 P (τk) : relative power amplitudes of multipath signals
(absolute measurements are not needed)
 Relative to the first detectable signal arriving at the
Rx at τ0
– use ensemble average of many profiles in a small
localized area →typically 2 − 6 m spacing of
measurements→ to obtain average small-scale
response
43
Vrince Vimal,Asst.Prof, Deptt Of EC, MIT,
MIET Group, Meerut.

44. 44
Vrince Vimal,Asst.Prof, Deptt Of EC, MIT,
MIET Group, Meerut.

45. • Time Dispersion Parameters
– “excess delay” : all values computed relative to the time of first signal
arrival τo
– mean excess delay →
– RMS delay spread →
– Central moment
where Avg( τ2) is the same computation as above as used for except
that
• A simple way to explain this is “the range of time within which most of the
delayed signals arrive”. Do not rerlyon absolute power
45
Vrince Vimal,Asst.Prof, Deptt Of EC, MIT,
MIET Group, Meerut.

46. – outdoor channel ~ on the order of microseconds
– indoor channel ~ on the order of nanoseconds
46
Vrince Vimal,Asst.Prof, Deptt Of EC, MIT,
MIET Group, Meerut.

47. • maximum excess delay ( τX): the largest time where the
multipath power levels are still within X dB of the maximum
power level
– worst case delay value
– depends very much on the choice of the noise threshold
47
Vrince Vimal,Asst.Prof, Deptt Of
EC, MIT, MIET Group, Meerut.

48. • τ and στ provide a measure of propagation
delay of interfering signals
– Then give an indication of how time smearing
might occur for the signal.
– A small στ is desired.
– The noise threshold is used to differentiate
between received multipath components and
thermal noise
48
Vrince Vimal,Asst.Prof, Deptt Of EC, MIT,
MIET Group, Meerut.

49. • Coherence BW (Bc) and Delay Spread ( )
– The Fourier Transform of multipath delay shows
frequency (spectral) characteristics of the MRC
– Bc : statistical measure of frequency range where MRC
response is flat
• MRC response is flat = passes all frequencies with ≈
equal gain & linear phase
• amplitudes of different frequency components are
correlated
• if two sinusoids have frequency separation greater
than Bc, they are affected quite differently by the
channel


49
Vrince Vimal,Asst.Prof, Deptt Of EC, MIT,
MIET Group, Meerut.

50. – amplitude correlation → multipath signals have
close to the same amplitude → if they are then
out-of-phase they have significant destructive
interference with each other (deep fades)
– so a flat fading channel is both “good” and “bad”
• Good: The MRC is like a bandpass filter and
passes signals without major attenuation from
the channel.
• Bad: Deep fading can occur.
50
Vrince Vimal,Asst.Prof, Deptt Of EC, MIT,
MIET Group, Meerut.

51. –so the coherence bandwidth is “the range
of frequencies over which two frequency
components have a strong potential for
amplitude correlation.” (quote from
textbook)
51
Vrince Vimal,Asst.Prof, Deptt Of
EC, MIT, MIET Group, Meerut.

52. • estimates
– 0.9 correlation → Bc ≈ 1 / 50 (signals are 90% correlated
with each other)
– 0.5 correlation → Bc ≈ 1 / 5 Which has a larger
bandwidth and why?
• specific channels require detailed analysis for a
particular transmitted signal – these are just rough
estimates




52
Vrince Vimal,Asst.Prof, Deptt Of EC, MIT,
MIET Group, Meerut.

53. • 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.
– Note: The definition of flat or frequency
selective fading is defined with respect to the
bandwidth of the signal that is being
transmitted.
53
Vrince Vimal,Asst.Prof, Deptt Of EC, MIT,
MIET Group, Meerut.

54. • Bc and στ are related quantities that
characterize time-varying nature of the MRC
for multipath interference from frequency &
time domain perspectives
54
Vrince Vimal,Asst.Prof, Deptt Of EC, MIT,
MIET Group, Meerut.

55. • these parameters do NOT characterize the time-varying
nature of the MRC due to the mobility of the mobile
and/or surrounding objects
– that is to say, Bc and characterize the statics, (how multipath
signals are formed from scattering/reflections and travel
different distances)
– Bc and στ do not characterize the mobility of the Tx or Rx.


55
Vrince Vimal,Asst.Prof, Deptt Of
EC, MIT, MIET Group, Meerut.

56. • Doppler Spread (BD) & Coherence Time (Tc)
– BD : measure of spectral broadening of the Tx signal
caused by motion → i.e., Doppler shift
• BD = max Doppler shift = fmax = vmax / λ
• In what direction does movement occur to create this worst
case?
• if Tx signal bandwidth (Bs) is large such that Bs >> BD then
effects of Doppler spread are NOT important so Doppler
spread is only important for low bps (data rate) applications
(e.g. paging)
56
Vrince Vimal,Asst.Prof, Deptt Of EC, MIT,
MIET Group, Meerut.

57. • Tc : statistical measure of the time interval
over which MRC impulse response remains
invariant → amplitude & phase of multipath
signals ≈ constant
– Coherence Time (Tc) = passes all received signals
with virtually the same characteristics because
the channel has not changed
– time duration over which two received signals
have a strong potential for amplitude correlation
57
Vrince Vimal,Asst.Prof, Deptt Of EC, MIT,
MIET Group, Meerut.

58. – Two signals arriving with a time separation
greater than Tc are affected differently by the
channel, since the channel has changed within
the time interval
– For digital communications coherence time and
Doppler spread are related by
2
9 0.423
16
c
m m
T
f f
 
58
Vrince Vimal,Asst.Prof, Deptt Of EC, MIT,
MIET Group, Meerut.