This chapter discusses small-scale fading and multipath propagation effects in mobile radio channels. It explains that multipath waves traveling along paths of different lengths interfere at the receiver, causing rapid fluctuations in signal strength over short distances. The key points are: 1) Small-scale fading is caused by multipath interference and depends on factors like surrounding objects, signal bandwidth, and mobile speed. 2) Multipath propagation can be modeled using the time-varying impulse response of the channel. 3) Important parameters used to characterize fading include coherence bandwidth, Doppler spread, coherence time, delay spread, and Ricean/Rayleigh distributions.

1. Wireless Communications
Principles and Practice
2nd Edition
T.S. Rappaport
Chapter 5: Mobile Radio Propagation:
Small-Scale Fading and Multipath

2. Introduction
 Reflection, Diffraction and Scattering of waves
 Most cellular systems operate in urban area,
where no direct line-of-site path between Rx
and Tx
 Presence of high rise buildings causes severe
diffraction loss
 Due to multiple reflections, em waves travel
along different paths of varying lengths

3.  Propagation models focused on predicting
average received signal strength at a given
distance from transmitter
 Models predicting mean signal strength for an
arbitrary T-R separation distance are large
scale models
 Models that characterize rapid fluctuations of
received signal strength over very short
distances or short time intervals are small
scale models

4. Co-channel and Adjacent Channel
Interference, Propagation

5. Small-scale and large-scale fading
Figure 4.1 Small-scale and large-scale fading.

6. Small-Scale Fading and
Multipath
 Rapid fluctuations of the amplitude,
phase or multipath delays of a radio
signal over a short period of time or
travel distance is known as small-scale
fading
 Large- scale path loss effects may be
ignored

7.  Fading is caused by interference
between two or more versions of the
transmitted signal which arrive at the
receiver at slightly different times
 Multipath waves combine at the
receiver antenna to give a resultant
signal which can widely vary in
amplitude and phase

8.  This depends on the distribution of the
intensity and relative propagation time
of the waves and the bandwidth of the
transmitted signal
 Multipath in the radio channel creates
small-scale fading effects

9. Three most important fading
effects
 Rapid changes in signal strength over a
small travel distance or time interval
 Random frequency modulation due to
varying Doppler shifts on different
multipath signals
 Time dispersion (echoes) caused by
multipath propagation delays

10.  In Built-up urban areas, fading occurs
because there is no single line-of- sight
path MS and BTS antennas
 Mobile antennas are well below the
height of surrounding structures
 Even if LOS exists, there are reflections
from ground and surrounding structures

11.  Multipath signals add vectorially at
receiver antenna and cause the signal
received by the mobile to distort or fade
 Even when the mobile is stationary,
fading may occur because of moving
objects in radio channel

12.  Due to constructive and destructive effects of
multipath waves, receiver moving at high
speed can pass through several fades in a
small period of time
 More serious case is that of a deep fade in
received signal
 Due to relative motion between mobile and
base station ,Doppler shift in frequency takes
place

13. Factors influencing Small-Scale
fading
 Multipath propagation: Presence of
reflecting objects and scatterers in the
channel creates constantly changing
environment
 Random phase and amplitudes of
different multipath signals induce small-
scale fading and or distortion

14.  Speed of the mobile: Relative motion
results in random frequency modulation
due to different Doppler shifts on each
multipath component
 Speed of surrounding objects: If
objects in radio channel are in motion, a
time varying Doppler shift is induced

15.  If surrounding objects move at a
greater rate than the mobile, this effect
dominates the small-scale fading
 Motion of surrounding objects may be
ignored otherwise and only speed of
the mobile needs to be considered
 Coherence time defines staticness of
the channel

16.  Transmission bandwidth of the signal: If
the transmitted radio signal bandwidth is
greater than bandwidth of multipath channel
,received signal will be distorted but small-
scale fading will be insignificant
 In the other case, signal will not be distorted
in time but signal will change rapidly
 Coherence bandwidth is a measure of max.
freq. difference for which signals are strongly
correlated in amplitude

17. Doppler Shift Geomerty

18.  Difference in path lengths traveled by
the wave from source S to mobile at
points X and Y is ∆l=d cosθ =v∆t cos θ
 Phase change in received signal due to
difference in path lengths is
 ∆Φ=(2π∆l)/λ = (2π v∆t cos θ) /λ
 Doppler shift is given by
 fd =(1/ 2π)*(∆Ф/∆t)= (v cos θ) /λ

19. Example 5.1
 Solved the problem with all the
students participating in the process

20. 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 the mobile radio channel
 Impulse response is a wideband channel
characterization and contains all information
necessary to simulate or analyze any type of
radio transmission through the channel

21.  Mobile radio channel may be modeled
as a linear filter with time varying
impulse response
 Time variation is due to receiver motion
in space
 Filtering nature is caused by summation
of amplitudes and delays of multiple
arriving waves at any instant of time

22.  Consider the case where time variation
is due strictly to receiver motion in
space
 Receiver moves along the ground at
some constant velocity v
 For a fixed position d, channel between
T and R can be modeled as a linear
time invariant system

23. Channel issues

24.  Due to different multipath waves which
have propagation delays which vary
over different spatial locations of the
receiver, impulse response of the
channel should be a function of the
position of the receiver
 Channel impulse response can be
expressed as h (d, t).

25.  x (t) is transmitted signal
 y(d,t) received signal at position d can
be expressed as a convolution of x(t)
with h(d,t)
 y(d,t)=x(t)©h(d,t)=∫x(τ)h(d, t- τ)d τ
 For a causal system h(d,t)=0 for t<0
 d=vt ,the position of receiver

26.  y(vt,t) =∫x(τ)h( vt,t-τ)d τ
 Since v is constant, y(vt,t) is just function of
t.
 Mobile radio channel can be modeled as a
linear time varying channel ,where the
channel changes with time and distance
 Since v may be assumed constant over a
short time interval ,we may let x(t) represent
transmitted bandpass waveform

27.  Impulse response h (t,τ)completely
characterizes the channel and is a
function of both t and τ
 Variable t represents time variations
due to motion , variable τ represents
channel multipath delay for a fixed
value of t

28.  If multipath channel is assumed to be
bandlimited channel, h(t,τ) may be
represented by a complex baseband impulse
response hb(t,τ)
 Received signal in Multipath channel consists
of a series of attenuated ,time delayed ,phase
shifted replicas of the transmitted signal, the
baseband impulse response of a multipath
channel can be expressed by

29.  hb(t,τ)=Σai(t,τ)exp[j(2πfcτ,i(t)+φi(t,τ))]§
(τ-τi(t))
 Ai and Ti are real amplitudes and
excess delays respectively of the ith
multipath component at time t
 Phase term represents the phase shift
due to free space propagation of ith
multipath component

30. Complex Baseband model for
RF systems

31. Time-varying impulse response

32. Measured impulse responses

33. Relationship between
bandwidth and received power
 In actual wireless communication
systems, the impulse response of a
multipath channel is measured in the
field using channel sounding techniques
 Illustrate how the small scale fading
behaves quite differently for two signals
with different bandwidths in identical
multipath channel

34.  Received local ensemble average
power of wideband and narrowband
signals are equivalent
 Pulse is wideband signal and CW signal
is a narrowband signal
 Received power is computed for both
the cases

35. Small Scale Multipath
measurements
 Three techniques
 Direct pulse measurements, spread
spectrum sliding correlator
measurement and swept frequency
measurements

36. Channel Sounder: Pulse type

37.  Allows engineers to determine rapidly the
power delay profile of any channel
 The system transmits a repetitive pulse of
width Tbb and uses a receiver with a wide
bandpass filter.
 BW=2/ Tbb Hz
 Signal is amplified ,detected with an envelope
detector and displayed and stored on high
speed oscilloscope

38.  This gives immediate measurement of
the square of the channel impulse
response convolved with the probing
pulse
 If oscilloscope is set on average mode,
this system can provide a local average
power delay profile

39. Channel Sounder: PN Type

40. Spread Spectrum Sliding
Correlator Channel Sounding
 A carrier is spread over a large
bandwidth by mixing it with a binary
pseudo-noise sequence having a chip
duration Tc and chip rate Rc equal to
1/Tc
 The power spectrum envelope is given
by [sin π(f-fc)Tc] / π(f-fc)Tc] 2

41.  Null-to-null RF bandwidth is BW=2Rc
 Spread spectrum signal is received,
filtered and despread using a PN
sequence generator identical to that
used at the transmitter
 Two PN sequences are identical but chip
clock rate is higher at Tx than that at
Rx

42.  Mixing the chip sequences in this fashion
implements a sliding correlator
 When faster chip clock catches up with PN
code of slower chip clock, two will be virtually
identically aligned , giving maximal
correlation
 When the two sequences are not maximally
correlated ,mixing the incoming signal with
unsynchronized receiver chip sequence will
spread the signal into the bandwidth at least
as large as receiver’s PN sequence.

43.  Narrowband filter following correlator can
reject almost all of the incoming power
 Processing gain= 2Rc/Rbb= 2Tbb/Tc
 Tbb is period of baseband signal
 When incoming signal is correlated with
received sequence, the signal is despread
,envelope detected and displayed on an
oscilloscope

44.  Different multipath signals have
different time delays, they will
maximally correlate with receiver PN
sequence at different times
 After envelope detection, channel
impulse response convolved with the
pulse shape of a single chip is displayed
on the oscilloscope

45.  Time resolution ∆τ of multipath
components using spread spectrum
system with sliding correlator is
2Tc=2/Rc
 The system can resolve two multipath
components as long as they are equal
to or greater than two chip durations
apart(2Tc seconds)

46.  The sliding correlation process gives
equivalent time measurements that are
updated every time the two sequences
are maximally correlated
 Time between maximal correlations ∆T
is given by Tc =γ l /Rc
 Tc = chip period (seconds)
 Rc=chip rate (Hz)

47.  γ =slide factor and l=sequence length
in chips
 Slide factor is defined as ratio between
transmitter chip clock rate and
difference between transmitter and
receiver chip clock rates
 γ =α/(α-β) alpha is Tx chip clock rate
and beta is Rx chip clock rate

48.  Since incoming spread spectrum signal
is mixed with a receiver PN sequence
that is slower than transmitted
sequence, the signal is essentially
down-converted to a low-frequency
narrowband signal.
 Processing gain is realized using a
narrowband filter.

49.  The equivalent time measurements
refer to the relative times of multipath
components as they are displayed on
the oscilloscope
 Observed time scale on oscilloscope is
related to actual propagation time scale
by Actual propagation time=observed
time/γ

50. Channel Sounder: Swept Freq.
type

51.  Vector network analyzer controls a
synthesized frequency sweeper
 Sweeper scans a particular frequency
band centered on the carrier by
stepping through discrete frequencies
 Number and spacings of frequency
steps impact the time resolution of
impulse measurements

52.  For each frequency step, the S
parameter test set transmits a known
signal at port 1 and monitors the
received signal level at port 2.
 These signal levels allow the analyzer to
determine the complex response which
is frequency domain representation of
channel impulse response

53. Time Dispersion Parameters
 Parameters which grossly quantify
multipath channel
 Excess delay, rms delay spread and
excess delay spread are determined
from a power delay profile(Graph of
received signal power V/s excess delay)

54.  Time dispersive properties of wideband
multipath channel are most commonly
quantified by their excess delay( τ bar)
and rms delay spread στ.
 Mean access delay is Σ[P(τk) τk ]/ P(τk)
 Rms delay spread is sqrt(tau square
bar-tau bar square)

55.  These delays are measured relative to
first detectable signal arriving at
receiver at τ0 =0
 Typical values are of the order of
microseconds in outdoor mobile and
nanoseconds in indoor radio channels

56. Measured power delay profiles

57. Indoor Power Delay Profile

58.  Maximum excess delay (X dB) of the power
delay profile is defined to be the time delay
during which multipath energy falls to X dB
below the maximum.
 In practice, values of rms delay spread, mean
excess delay and excess delay spread depend
on the choice of noise threshold

59. Typical RMS delay spreads

60. Coherence Bandwidth
 It is a statistical measure of the range of
frequencies over which channel can be
considered flat.
 Flat channel passes all spectral components
with approximately equal gain and linear
phase
 It is the range of frequencies over which two
frequency components have a strong
potential for amplitude correlation

61.  Two sinusoids with frequency
separation greater than Bc are affected
quite differently by the channel.
 If coherence bandwidth is defined as
the bandwidth over which the
frequency correlation function is above
0.9, Bc =1/(50στ) approximately

62. Doppler Spread and
Coherence Time
 These parameters describe time varying
describe the time varying nature of channel in
small-scale region
 Doppler spread BD is a measure of spectral
broadening caused by time rate of change of
mobile radio channel
 Defined as range of frequencies over which
received Doppler spectrum is non-zero

63.  Doppler spectrum is fc-fd to fc+fd
 fd is function relative velocity of mobile
and angle theta between direction of
mobile and arrival of scattered waves
 If baseband signal bandwidth is much
greater than BD the effects of Doppler
spread are negligible. This is slow
fading channel

64. Coherence Time
 Inversely proportional to Doppler
Spread
 Tc=1/Bd
 Coherence time is statistical measure of
the time duration over which channel
impulse response is essentially
invariant

65.  Coherence time is the time duration over
which two received signals have a strong
potential for amplitude correlation.
 Tc=0.423/fm where fm =maximum Doppler
shift =v/λ
 Two signals arriving with a time separation
greater than Tc are affected differently by the
channel.

66. Two independent fading issues

67. Flat-fading (non-freq.
Selective)

68. Frequency selective fading

69. Two independent fading issues

70. Rayleigh and Ricean
Distributions
 Rayleigh distribution is commonly used
to describe statistical time varying
nature of the received envelope of a flat
fading signal or the envelope of an
individual multipath component
 Mean value of Rayleigh distribution is
given by 1.2533 σ

71. Ricean Fading Distribution
 When there is a dominant stationary
signal component present, such as LOS
propagation path, the small-scale fading
envelope distribution is Ricean.
 In such a situation, random multipath
components arriving at different angles
are superimposed on a stationary
dominant signal.

72.  At the output of the envelope detector, this
has effect of adding a dc component to the
random multipath
 The effect of a dominant signal arriving with
many weaker multipath signals give rise to
the Ricean distribution.
 As dominant signal becomes weaker, the
composite signal envelope is Rayleigh
type.The Ricean distribution degenerates into
a Rayleigh distribution when the dominant
component fades away.

75. Rayleigh fading

76. Small-scale envelope
distributions

77. Ricean and Rayleigh fading
distributions

78. Small-scale fading mechanism

79. Doppler spectrum

80. Spectrum of Envelope of
doppler faded signal

81. Simulating Doppler/Small-scale
fading

82. Simulating Doppler fading

83. Simulating Doppler fading

84. Simulating multipath with
Doppler-induced Rayleigh fading

85. Simulating 2-ray multipath

86. SIRCIM – Simulation of all indoor
propagation Characteristics

87. SMRCIM – Simulation of all outdoor
propagation Characteristics

88. SIRCIM and SMRCIM
 Available from Wireless Valley
Communications, Inc.
 Source code in C is available
 www. Wirelessvalley.com

89. Angular Spread model

90. Spatial distribution of
Multipath

91. Angular Spread key to fading

92. Spatial orientation of
multipath impacts the depths
of fading

93. Angular Distribution of power

94. Angular Spread predicts correlation
distances

95. Angular Spread predicts correlation
distances