WIRELESS CHANNELS
Large scale path loss – Path loss models: Free
Space and Two-Ray models -Link Budget design –
Small scale fading- Parameters of mobile
multipath channels – Time dispersion parameters-
Coherence bandwidth – Doppler spread &
Coherence time, Fading due to Multipath time
delay spread – flat fading – frequency selective
fading – Fading due to Doppler spread – fast
fading – slow fading.
Dr.S.Mary Praveena,ASP/ECE 2
10/1/2021

4
Problems Unique to Wireless (not wired) systems:
• Paths can vary from simple line-of-sight to
ones that are severely obstructed by buildings,
mountains, and foliage.
• Radio channels are extremely random and
difficult to analyze.
• Interference from other service providers
• out-of-band non-linear Tx emissions
Dr.S.Mary Praveena,ASP/ECE
10/1/2021

5
Interference from other users (same
network)
– CCI due to frequency reuse
– ACI due to Tx/Rx design limitations & large
# users sharing finite BW
Shadowing
– Obstructions to line-of-sight paths cause
areas of weak received signal strength
10/1/2021

6
Fading
– When no clear line-of-sight path exists, signals
are received that are reflections off obstructions
and diffractions around obstructions
– Multipath signals can be received that interfere
with each other
– Fixed Wireless Channel → random &
unpredictable
must be characterized in a statistical fashion
field measurements often needed to characterize radio
channel performance
10/1/2021

7
** The Mobile Radio Channel (MRC) has
unique problems that limit performance **
– A mobile Rx in motion influences rates of
fading the faster a mobile moves, the more
quickly characteristics change
10/1/2021

•Electromagnetic wave propagation
•reflection
•diffraction
•scattering
•Urban areas
•No direct line-of-sight
•high-rise buildings causes severe diffraction loss
•multipath fading due to different paths of varying lengths
•Large-scale propagation models predict the mean signal strength for an
arbitrary T-R separation distance.
•Small-scale (fading) models characterize the rapid fluctuations of the
received signal strength over very short travel distance or short time
duration.
Introduction to Radio Wave Propagation
10/1/2021

Radio Propagation Models
• As the mobile moves over small distances, the
instantaneous received signal will fluctuate rapidly
giving rise to small-scale fading
• The reason is that the signal is the sum of many
contributors coming from different directions and
since the phases of these signals are random, the sum
behave like a noise (Rayleigh fading).
• In small scale fading, the received signal power may
change as much as 3 or 4 orders of magnitude (30dB or
40dB), when the receiver is only moved a fraction of
the wavelength.
10/1/2021

Radio Propagation Models
• As the mobile moves away from the transmitter
over larger distances, the local average received
signal will gradually decrease. This is called large-
scale path loss.
• l Typically the local average received power is computed by
averaging signal measurements over a measurement track of
5 to 40 (For PCS, this means 1m-10m track)
• The models that predict the mean signal strength
for an arbitrary-receiver transmitter (T-R)
separation distance are called large-scale
propagation models
• l Useful for estimating the coverage area of transmitters
10/1/2021

Path Loss Models
• Free Space Propagation Model
• Two Ray Model
10/1/2021

Free-Space Propagation Model
• Used to predict the received signal strength when
transmitter and receiver have clear, unobstructed LOS
path between them.
• The received power decays as a function of T-R
separation distance raised to some power.
• Path Loss: Signal attenuation as a positive quantity
measured in dB and defined as the difference (in dB)
between the effective transmitter power and received
power.
10/1/2021

13
transmitted
signal
received
signal
Ts
tmax
LOS
LOS
Reflection
Diffraction
Scattering
10/1/2021

Free Space Propagation Model
• The free space propagation model is used to predict
received signal strength when the transmitter and receiver
have a clear line-of-sight path between them.
– satellite communication
– microwave line-of-sight radio link
• Friis free space equation
: transmitted power : T-R separation distance
: received power : system loss
: transmitter antenna gain : wave length in meters
: receiver antenna gain
L
d
G
G
P
d
P r
t
t
r 2
2
2
)
4
(
)
(


=
t
P
)
(d
Pr
t
G
r
G
d
L

10/1/2021

• The gain of the antenna
: effective aperture is related to the physical size of the
antenna
• The wave length is related to the carrier frequency by
: carrier frequency in Hertz
: carrier frequency in radians
: speed of light (meters/s)
• The losses are usually due to transmission line
attenuation, filter losses, and antenna losses in the
communication system. A value of L=1 indicates no loss in the
system hardware.
2
4

 e
A
G =
e
A

c
c
f
c



2
=
=
f
c

c
)
1
( 
L
10/1/2021

• Isotropic radiator is an ideal antenna which radiates power with
unit gain.
• Effective isotropic radiated power (EIRP) is defined as
and represents the maximum radiated power available from
transmitter in the direction of maximum antenna gain as
compared to an isotropic radiator.
• Path loss for the free space model with antenna gains
• When antenna gains are excluded
• The Friis free space model is only a valid predictor for for
values of d which is in the far-field (Fraunhofer region) of the
transmission antenna.
t
tG
P
EIRP =








−
=
= 2
2
2
)
4
(
log
10
log
10
)
(
d
G
G
P
P
dB
PL r
t
r
t










−
=
= 2
2
2
)
4
(
log
10
log
10
)
(
d
P
P
dB
PL
r
t


r
P
10/1/2021

• The far-field region of a transmitting antenna is defined as the
region beyond the far-field distance
where D is the largest physical linear dimension of the antenna.
• To be in the far-filed region the following equations must be
satisfied
and
• Furthermore the following equation does not hold for d=0.
• Use close-in distance and a known received power at
that point
or

2
2D
d f =
D
d f  

f
d
L
d
G
G
P
d
P r
t
t
r 2
2
2
)
4
(
)
(


=
0
d )
( 0
d
Pr
2
0
0 )
(
)
( 





=
d
d
d
P
d
P r
r
f
d
d
d 
 0






+






=
d
d
d
P
d
P r
r
0
0
log
20
W
001
.
0
)
(
log
10
dBm
)
( f
d
d
d 
 0
10/1/2021

• Expressing the received power in dBm and dBW
l Pr(d) (dBm) = 10 log [Pr(d0)/0.001W] + 20log(d0/d)
where d >= d0 >= df and Pr(d0) is in units of watts.
l Pr(d) (dBW) = 10 log [Pr(d0)/1W] + 20log(d0/d)
where d >= d0 >= df and Pr(d0) is in units of watts.
• Reference distance d0 for practical systems:
l For frequencies in the range 1-2 GHz
• 1 m in indoor environments
• 100m-1km in outdoor environments
10/1/2021

Example Problems
A transmitter produces 50W of power.
A) Express the transmit power in dBm
B) Express the transmit power in dBW
C) If d0 is 100m and the received power at that
distance is 0.0035mW, then find the received power
level at a distance of 10km.
L Assume that the transmit and receive antennas have
unity gains.
10/1/2021

Solution
A)
Pt(W) is 50W.
Pt(dBm) = 10log[Pt(mW)/1mW)]
Pt(dBm) = 10log(50x1000)
Pt(dBm) = 47 dBm
B)
Pt(dBW) = 10log[Pt(W)/1W)]
Pt(dBW) = 10log(50)
Pt(dBW) = 17 dBW
10/1/2021

Solution
c) Pr(d) = Pr(d0)(d0/d)2
Substitute the values into the equation:
lPr(10km) = Pr(100m)(100m/10km)2
Pr(10km) = 0.0035mW(10-4)
Pr(10km) = 3.5x10-10W
Pr(10km) [dBm] = 10log(3.5x10-10W/1mW)
= 10log(3.5x10-7)
= -64.5dBm
10/1/2021

The Three Basic Propagation Mechanisms
• Basic propagation mechanisms
– reflection
– diffraction
– scattering
• Reflection occurs when a propagating electromagnetic
wave impinges upon an object which has very large
dimensions when compared to the wavelength, e.g.,
buildings, walls.
• Diffraction occurs when the radio path between the
transmitter and receiver is obstructed by a surface that
has sharp edges.
• Scattering occurs when the medium through which the
wave travels consists of objects with dimensions that are
small compared to the wavelength.
10/1/2021

23
Ground Reflection (2-Ray) Model
– Good for systems that use tall towers (over 50 m
tall)
– Good for line-of-sight microcell systems in urban
environments
10/1/2021

24
• ETOT is the electric field that results from a
combination of a direct line-of-sight path and a
ground reflected path
is the amplitude of the electric field at distance d
ωc = 2πfc where fc is the carrier frequency of the signal
Notice at different distances d the wave is at a different
phase because of the form similar to
10/1/2021

25
• For the direct path let d = d’ ; for the reflected path
d = d” then
for large T−R separation : θi goes to 0 (angle of
incidence to the ground of the reflected wave) and
Γ = −1
• Phase difference can occur depending on the phase
difference between direct and reflected E fields
• The phase difference is θ∆ due to Path difference ,
∆ = d”− d’, between
10/1/2021

26
Using method of images (fig below) , the path difference can be expressed as:-
• From two triangles with sides d and (ht + hr) or (ht – hr)
10/1/2021

• Using taylor series the expression can be simplified as:-
• Now as P.D is known , Phase difference and time delay
can be evaluated as:-
• If d is large than path difference become negligible and
amplitude ELOS & Eg are virtually identical and differ only in
phase,.i.e
&
10/1/2021

If than ETOT can be expressed as:-
10/1/2021

Referring to the Phasor diagram below:-
10/1/2021

or
As E-field is function of “sin” it decays in oscillatory fashion with
local maxima being 6dB greater than free space and local minima
reaching to-∞ dB.
10/1/2021

31
note that the magnitude is with respect to a
reference of E0=1 at d0=100 meters, so near 100
meters the signal can be stronger than E0=1
– the second ray adds in energy that would have
been lost otherwise
for large distances it can be shown that
10/1/2021

32
10/1/2021

33
Radio Signal Propagation
10/1/2021

34
• The smoothed line is the average signal
strength. The actual is the more jagged line.
• Actual received signal strength can vary by
more than 20 dB over a few centimeters.
• The average signal strength decays with
distance from the transmitter, and depends on
terrain and obstructions.
10/1/2021

Two main channel design issues
Communication engineers are generally concerned
with two main radio channel issues:
Link Budged Design
• Link budget design determines fundamental quantities such as transmit
power requirements, coverage areas, and battery life
• It is determined by the amount of received power that may be expected
at a particular distance or location from a transmitter
Time dispersion
• It arises because of multi-path propagation where replicas of the
transmitted signal reach the receiver with different propagation delays
due to the propagation mechanisms that are described earlier.
• Time dispersion nature of the channel determines the maximum data
rate that may be transmitted without using equalization.
10/1/2021

Link Budget Design Using Path Loss Models
Radio propagation models can be derived
• By use of empirical methods: collect measurement,
fit curves.
• By use of analytical methods
• Model the propagation mechanisms mathematically and
derive equations for path loss
Long distance path loss model
• Empirical and analytical models show that
received signal power decreases logarithmically
with distance for both indoor and outdoor
channels
10/1/2021

Long distance path loss model
• The average large-scale
path loss for an arbitrary T-
R separation is expressed as
a function of distance by
using a path loss exponent
n:
• The value of n depends on
the propagation
environment: for free space
it is 2; when obstructions are
present it has a larger value.
PL(d) denotes the average large -scale path loss
at a distance d (denoted in dB)
PL(dB)= PL(d0 ) + 10n log( ) (eqn-A)
PL(d)  (
d
)n
0
d0
d
d
10/1/2021

Path Loss Exponent for Different
Environments
Environment Path Loss Exponent, n
Free space 2
Urban area cellular radio 2.7 to 3.5
Shadowed urban cellular radio 3 to 5
In building line-of-sight 1.6 to 1.8
Obstructed in building 4 to 6
Obstructed in factories 2 to 3
10/1/2021

Selection of free space reference distance
• In large coverage cellular systems
1km reference distances are commonly used
• In microcellular systems
Much smaller distances are used: such as 100m
or 1m.
• The reference distance should always be in
the far-field of the antenna so that near-field
effects do not alter the reference path loss.
10/1/2021

Log-normal Shadowing
• (Equation A) does not consider the fact the
surrounding environment may be vastly
different at two locations having the same
T-R separation
• This leads to measurements that are different
than the predicted values obtained using the
above equation.
• Measurements show that for any value d, the
path loss PL(d) in dBm at a particular location
is random and distributed normally.
10/1/2021

PL(d ) denotes the average large-scale path loss (in dB) at a distance d.
X is a zero-mean Gaussian (normal) distributed random variable (in dB)
with standard deviation  (also in dB).
PL(d0 ) is usually computed assuming free space propagation model between
transmitter and d0 (or by measurement).
Equation B takes into account the shadowing affects due to
cluttering on the propagation path. It is used as the propagation model for
log-normal shadowing environments.
Log-normal Shadowing- Path Loss
PL(d)[dB] = PL(d0 ) +10nlog(
d
) + X
Then adding this random factor:
PL(d)[dB] = PL(d) + X
d
0
Equation B
10/1/2021

Log-normal Shadowing- Received Power
• The received power in log-normal shadowing
environment is given by the following formula
(derivable from Equation B)
l The antenna gains are included in PL(d).
Pr (d)[dBm] = Pt [dBm]− PL(d0 )[dB]+10nlog(
d
) + X [dB]




Pr (d)[dBm] = Pt [dBm]− PL(d)[dB]
0
d
10/1/2021

Log-normal Shadowing, n and

• The log-normal shadowing model indicates
the received power at a distance d is normally
distributed with a distance dependent mean
and with a standard deviation of 
• In practice the values of n and  are
computed from measured data using linear
regression so that the difference between the
measured data and estimated path losses are
minimized in a mean square error sense.
10/1/2021

Example of determining n and

• Assume Pr(d0) = 0dBm and
d0 is 100m
• Assume the receiver power
Pr is measured at distances
100m, 500m, 1000m, and
3000m,
• The table gives the measured
values of received power
Distance from
Transmitter
Received Power
100m 0dBm
500m -5dBm
1000m -11dBm
3000m -16dBm
10/1/2021

45
Log-Normal Shadowing
PL (d) = PL (do ) + 10 n log (d / do ) + Xσ
– describes how the path loss at any specific location may vary
from the average value
• has a the large-scale path loss component we have already seen
plus a random amount Xσ.
10/1/2021

46
• Xσ : zero mean Gaussian random variable, a “bell
curve”
• σ is the standard deviation that provides the second
parameter for the distribution takes into account
received signal strength variations due to
shadowing
10/1/2021

Small Scale Fading
• Describes rapid fluctuations of the amplitude,
phase of multipath delays of a radio signal
over short period of time or travel distance
• Caused by interference between two or more
versions of the transmitted signal which arrive
at the receiver at slightly different times.
• These waves are called multipath waves and
combine at the receiver antenna to give a
resultant signal which can vary widely in
amplitude and phase.
10/1/2021

Small Scale Multipath Propagation
Effects of multipath
• Rapid changes in the signal strength
• Random frequency modulation due to varying Doppler shifts
on different multiples signals
• Time dispersion (echoes) caused by multipath propagation
delays
Multipath occurs because of
• Reflections
• Scattering
10/1/2021

Multipath
• At a receiver point Radio waves generated from the
same transmitted signal may come from different directions
l with different propagation delays
l with (possibly) different amplitudes (random)
l with (possibly) different phases (random)
l with different angles of arrival (random).
• These multipath components combine vectorially at the
receiver antenna and cause the total signal
• to fade
• to distort
10/1/2021

Multipath Components
Component 1
Component
2
Component
N
Radio Signals Arriving from different directions to
receiver
Receiver may be stationary or mobile.
10/1/2021

Factors Influencing Small Scale Fading
Multipath propagation
• Presence of reflecting objects and scatterers cause
multiple versions of the signal to arrive at the receiver
• With different amplitudes and time delays
• Causes the total signal at receiver to fade or distort
Speed of mobile
• Cause Doppler shift at each multipath
component
• Causes random frequency modulation
Speed of surrounding objects
• Causes time-varying Doppler shift on the
multipath components
10/1/2021

Factors Influencing Small Scale Fading
Transmission bandwidth of the channel
• The transmitted radio signal bandwidth and
bandwidth of the multipath channel affect the
received signal properties:
• If amplitude fluctuates or not
• If the signal is distorted or not
10/1/2021

Doppler Effect
“When a transmitter or receiver is moving, the
frequency of the received signal changes, i.e. İt is
different than the frequency of transmission. This is
called Doppler Effect.”
• The change in frequency is called Doppler Shift.
• It depends on
• The relative velocity of the receiver with respect to
transmitter
• The frequency (or wavelength) of transmission
• The direction of traveling with respect to the direction of
the arriving signal.
10/1/2021

Doppler Shift – Transmitter is moving
The frequency of the signal
that is received in front of
the transmitter will be bigger
The frequency of the
signal that is received
behind the transmitter will
be smaller
10/1/2021

Doppler Shift –Receiver is moving
v
A mobile receiver is traveling from point X to point
Y
X  Y
l
d
S

=
v
cos
2 t 
1
f =
d
10/1/2021

Doppler Shift
• The Doppler shift is positive
If the mobile is moving toward the direction of arrival
of the wave.
• The Doppler shift is negative
If the mobile is moving away from the direction of
arrival of the wave.
10/1/2021

Impulse Response Model of a Multipath
Channel
• The wireless channel characteristics can be
expressed by impulse response function
• The channel is time varying channel when the
receiver is moving.
• Lets assume first that time variation due strictly to
the receiver motion (t = d/v)
• Since at any distance d = vt, the received power
will ve combination of different incoming signals,
the channel charactesitics or the impulse
response funcion depends on the distance d
between trandmitter and receiver
10/1/2021

Channel
d = vt
v
d
• A receiver is moving along the ground at some constant velocity v.
• The multipath components that are received at the receiver will have
different propagation delays depending on d: distance between transmitter
and receiver.
• Hence the channel impulse response depends on d.
Lets x(t) represents the transmitter signal
y(d,t) represents the received signal at position d.
h(d,t) represents the channel impulse response which is dependent on d
(hence time-varying d=vt).
10/1/2021

Multipath Channel Model
Multipat
h
Channel
Multipat
h
Channel
Mobile
1
Mobile
2
Base
Statio
n
1st MC
2nd MC
3rd MC
(Multipath
Component)
4th MC
1st MC
2nd MC
10/1/2021

Channel
• The channel is linear time-varying channel, where the channel
characteristics changes with distance (hence time, t = d/v)

y(d , t) = x(t)  h(d , t) =  x(t )h(d , t −t )dt
−
• For a causal system, h(d,t) = 0 for t  0; hence
t
y(d , t) =  x(t )h(d , t −t )dt
−
Wireless Multipath Channel
h(d,t)
x(t) y(t)
10/1/2021

Impulse Response Model
t
y(vt, t) =  x(t )h(vt, t −t )dt
−
t
y(t) =  x(t )h(vt, t −t )dt = x(t)  h(vt, t) = x(t)  h(d , t)
−
• We assume v is constant over short time.
x(t): transmitted waveform
y(t): received waveform
h(t,t): impulse response of the channel. Depends on d (and therefore t=d/v)
and also to the multiple delay for the channel for a fixed value of t.
t is the multipath delay of the channel for a fixed value of t.

y(t) =  x(t )h(t,t )dt = x(t)  h(t,t )
−
assume v is constant over time
d = vt
10/1/2021

h(t,t ) = Re 
j t
b
c
h (t,t )e
 
y(t) = x(t)  h(t,t )
y(t) = Re r(t)e jct
r(t) = c(t)
1
h (t,t )
2
b
1
h (t,t )
2
b
x(t)
x(t) = Re
c(t)e jct

y(t)
c(t) r(t)
Bandpass Channel Impulse Response
Model
Baseband Equivalent Channel Impulse Response Model
10/1/2021

2
x(t) = Re
c(t)e 
y(t) = Re
r(t)e j2fct

c = 2fc
j 2fct
r(t) = c(t)  hb (t,t )
1
• c(t) is the complex envelope representation of the transmitted
signal r(t) is the complex envelope representation of the
received signal
• hb(t,t) is the complex baseband impulse response
10/1/2021

• For small-scale fading, the power delay profile of the channel is found by
taking the spatial average of over a local area (small-scale area).
• If p(t) has a time duration much smaller than the impulse response of the
multipath channel, the received power delay profile in a local area is given
by:
Power Delay Profile
2
h (t;t )
b
2
P(t )  k hb (t;t )
• Gain k relates the transmitter power in the probing pulse p(t) to the
total received power in a multipath delay profile.
The bar represents the average over the local area of
2
h (t;t )
b
10/1/2021

Small-Scale Multipath Measurements
Several Methods
• Direct RF Pulse System
• Spread Spectrum Sliding Correlator Channel
Sounding
• Frequency Domain Channel Sounding
These techniques are also called channel
sounding techniques
10/1/2021

Direct RF Pulse Sys
Txtem
Pulse Generator
BPF Detector
Digital
Oscilloscope
RF Link
fc
Rx
10/1/2021

Parameters of Mobile Multipath Channels
• Time Dispersion Parameters
l Grossly quantifies the multipath channel
l Determined from Power Delay Profile
l Parameters include
§ Mean Access Delay
§ RMS Delay Spread
§ Excess Delay Spread (X dB)
• Coherence Bandwidth
• Doppler Spread and Coherence Time
10/1/2021

Measuring PDPs
l Power Delay Profiles
l Are measured by channel sounding techniques
l Plots of relative received power as a function of
excess delay
l They are found by averaging intantenous power
delay measurements over a local area
§ Local area: no greater than 6m outdoor
§ Local area: no greater than 2m indoor
§ Samples taken at /4 meters approximately
§ For 450MHz – 6 GHz frequency range.
10/1/2021

Timer Dispersion Parameters
Determined from a power delay profile.
Mean excess delay(
t ):
 = t 2
− (
t )2
P(tk )
k

k

k

k
=
=
2
k
k
2
k
k k P(t )(t
a
a t )
2 2
t 2
t
Rms delay spread (t)
P(tk )
k
a t  P(t k )(t k )

k
 k k
=
t = 2
k
k
a
2
k
10/1/2021

Timer Dispersion Parameters
• Maximum Excess Delay (X dB):
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.
10/1/2021

RMS Delay Spread
10/1/2021

Noise Threshold
l The values of time dispersion parameters also
depend on the noise threshold (the level of
power below which the signal is considered as
noise).
l If noise threshold is set too low, then the noise
will be processed as multipath and thus
causing the parameters to be higher.
10/1/2021

Coherence Bandwidth (BC)
• Range of frequencies over which the channel can be
considered flat (i.e. channel passes all spectral
components with equal gain and linear phase).
§ It is a definition that depends on RMS Delay Spread.
• Two sinusoids with frequency separation greater than
Bc are affected quite differently by the channel.
f1
Receiver
f2
Multipath
Channel
Frequency Separation: |f1-f2|
10/1/2021

Coherence Bandwidth
Frequency correlation between two sinusoids: 0 <= Cr1, r2 <= 1.
50
1
BC =
• If we define Coherence Bandwidth (BC) as the range of frequencies over
which the frequency correlation is above 0.9, then
• If we define Coherence Bandwidth as the range of frequencies over
which the frequency correlation is above 0.5, then
5
1
BC =
is rms delay spread.
This is called 50% coherence bandwidth.
10/1/2021

Coherence Bandwidth
Example:
• For a multipath channel,  is given as 1.37s.
• The 50% coherence bandwidth is given as: 1/5 = 146kHz.
• This means that, for a good transmission from a transmitter to a
receiver, the range of transmission frequency (channel bandwidth)
should not exceed 146kHz, so that all frequencies in this band
experience the same channel characteristics.
• Equalizers are needed in order to use transmission frequencies that
are separated larger than this value.
• This coherence bandwidth is enough for an AMPS channel (30kHz
band needed for a channel), but is not enough for a GSM channel
(200kHz needed per channel).
10/1/2021

Coherence Time
• Delay spread and Coherence bandwidth
describe the time dispersive nature of the
channel in a local area.
• They don’t offer information about the time varying nature of
the channel caused by relative motion of transmitter and
receiver.
• Doppler Spread and Coherence time are
parameters which describe the time varying
nature of the channel in a small-scale region.
10/1/2021

Doppler Spread
• Measure of spectral broadening caused by
motion
• We know how to compute Doppler shift: fd
• Doppler spread, BD, is defined as the
maximum Doppler shift: fm = v/
• If the baseband signal bandwidth is much
greater than BD then effect of Doppler spread
is negligible at the receiver.
10/1/2021

• 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 .
Coherence Time
fm
C
T  1
Coherence time (TC) is defined
as:
TS
TC
t=t2 - t1
t1 t2
f1
f2
10/1/2021

Coherence Time
• Coherence time is also defined as:
m
16f 2
TC 
f
m
0.423
=
9
• Coherence time definition implies that two signals arriving with a
time separation greater than TC are affected differently by the
channel.
10/1/2021

Types of Small-scale Fading
Small-scale Fading
(Based on Multipath Tİme Delay Spread)
Flat Fading
1. BW Signal < BW of Channel
2. Delay Spread < Symbol
Period
Frequency Selective
Fading
1. BW Signal > Bw of Channel
2. Delay Spread > Symbol
Period
Small-scale Fading
(Based on Doppler Spread)
Fast
Fading
1. High Doppler Spread
2. Coherence Time < Symbol Period
3. Channel variations faster than
baseband signal variations
Slow
Fading
1. Low Doppler Spread
2. Coherence Time > Symbol Period
3. Channel variations smaller than
baseband signal variations
10/1/2021

Flat Fading
• Occurs when the amplitude of the received
signal changes with time
• For example according to Rayleigh Distribution
• Occurs when symbol period of the
transmitted signal is much larger than the
Delay Spread of the channel
• Bandwidth of the applied signal is narrow.
• May cause deep fades.
• Increase the transmit power to combat this situation.
10/1/2021

s(t)
Flat Fading
h(t,t) r(t)
0 TS 0 t 0 TS+t
t  TS
Occurs when:
BS << BC
and TS >> t
BC: Coherence bandwidth
BS: Signal bandwidth
TS: Symbol period
t: Delay Spread
10/1/2021

Frequency Selective Fading
• Occurs when channel multipath delay spread
is greater than the symbol period.
• Symbols face time dispersion
• Channel induces Intersymbol Interference (ISI)
• Bandwidth of the signal s(t) is wider than the
channel impulse response.
10/1/2021

Frequency Selective Fading
h(t,t)
s(t) r(t)
0 TS 0 t 0 TS TS+t
t  TS
Causes distortion of the received baseband signal
Causes Inter-Symbol Interference (ISI)
Occurs when:
BS > BC
and TS < t
As a rule of thumb: TS <  t
10/1/2021

Fast Fading
• Due to Doppler Spread
• 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 transmitter signal
Occurs when:
BS < BD
and TS > TC
BS: Bandwidth of the
signal BD: Doppler Spread
TS: Symbol Period
TC: Coherence Bandwidth
10/1/2021

Slow Fading
• Due to Doppler Spread
• Rate of change of the channel characteristics is
much smaller than the Rate of change of the
transmitted signal
Occurs when:
BS >> BD
and TS << TC
BS: Bandwidth of the
signal BD: Doppler Spread
TS: Symbol Period
TC: Coherence Bandwidth
10/1/2021

Different Types of Fading
TS
TC
TS
Transmitted Symbol Period
With Respect To SYMBOL PERIOD
Symbol Period of
Transmitting
Signal
 t
Flat Slow
Fading
Flat Fast
Fading
Frequency
Selective Slow
Fading
Frequency
Selective Fast
Fading
10/1/2021

Different Types of Fading
Transmitted Baseband Signal Bandwidth
With Respect To BASEBAND SIGNAL BANDWIDTH
BS
BD
Flat Fast
Fading
Frequency
Selective Slow
Fading
Frequency
Selective Fast
Fading
BS
Transmitted
Baseband
Signal
Bandwidth
Flat Slow
Fading
BC
10/1/2021

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 we mean the baseband signal,
namely the envelope of the received signal (i.e. r(t)).
• Its is a statistical characterization of the
multipath fading.
• Two distributions
• Rayleigh Fading
• Ricean Fading
10/1/2021

Rayleigh and Ricean
Distributions
l Describes the received signal envelope
distribution for channels, where all the
components are non-LOS:
l i.e. there is no line-of–sight (LOS) component.
l Describes the received signal envelope
distribution for channels where one of the
multipath components is LOS component.
l i.e. there is one LOS component.
10/1/2021

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