Page 1
Muhammad Ali Jinnah University, Islamabad Campus, Pakistan
© Dr. Noor M Khan
EE, MAJU Multi-Path Fading
Channel
1 EE5713 Advanced Digital Communications
Week 6-7; Spring - 2013
Fading Channel
Base
Station
Mobile
Station
Lecturer: Assoc. Prof. Dr. Noor M Khan
Department of Electronic Engineering,
Muhammad Ali Jinnah University,
Islamabad Campus, Islamabad, PAKISTAN
Ph: +92 (51) 111-878787, Ext. 129 (Office), 186 (ARWiC Lab)
Fax: +92 (51) 2822743
email: [email protected] , [email protected]
Page 2
Muhammad Ali Jinnah University, Islamabad Campus, Pakistan
© Dr. Noor M Khan
EE, MAJU Multi-Path Fading
Channel
2 EE5713 Advanced Digital Communications
Week 6-7; Spring - 2013
Mobile Channel Parameters
• Time delay spread |
• Coherence Bandwidth | -> ISI
• Doppler Spread |
• Coherence Time | -> Unstable channel
• Flat fading
• Frequency selective fading
• Fast fading
• Slow fading
Page 3
Muhammad Ali Jinnah University, Islamabad Campus, Pakistan
© Dr. Noor M Khan
EE, MAJU Multi-Path Fading
Channel
3 EE5713 Advanced Digital Communications
Week 6-7; Spring - 2013
Multi-path Propagation
• Multi-path smears or spreads out the signal
– delay spread
• Causes inter-symbol interference
– limits the maximum symbol rate
Transmitted
Symbol Received
Symbol
Base
Statio
n
Mobile
Statio
n
t
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Muhammad Ali Jinnah University, Islamabad Campus, Pakistan
© Dr. Noor M Khan
EE, MAJU Multi-Path Fading
Channel
4 EE5713 Advanced Digital Communications
Week 6-7; Spring - 2013
Delay Spread
Transmitted
Symbol Received
Symbol
Base
Station
Mobile
Station
t
Time
Space
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Muhammad Ali Jinnah University, Islamabad Campus, Pakistan
© Dr. Noor M Khan
EE, MAJU Multi-Path Fading
Channel
5 EE5713 Advanced Digital Communications
Week 6-7; Spring - 2013
Intersymbol Interference
Transmitted
Symbol of
Interest
Received
Symbol of
Interest
t
Received
Symbols Transmitted
Symbols
t
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Muhammad Ali Jinnah University, Islamabad Campus, Pakistan
© Dr. Noor M Khan
EE, MAJU Multi-Path Fading
Channel
6 EE5713 Advanced Digital Communications
Week 6-7; Spring - 2013
Average Delay Spread
• Average delay spread
k
k
k
kk
k
k
k
kk
P
P
a
a
)(τ
)τ(ττ
2
2
τ
τ
Multi-path
Profile
(Discrete)
t
)(τkP
0τ0 1τ 2τ kτ
)(τ1P
)(τ0P
)(τ2P
)(τkP
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Muhammad Ali Jinnah University, Islamabad Campus, Pakistan
© Dr. Noor M Khan
EE, MAJU Multi-Path Fading
Channel
7 EE5713 Advanced Digital Communications
Week 6-7; Spring - 2013
RMS Delay Spread
(Discrete)
• RMS delay spread
22
τ ττσ
k
k
k
kk
k
k
k
kk
P
P
a
a
)(τ
)τ(ττ
τ
2
2
22
2
Page 8
Muhammad Ali Jinnah University, Islamabad Campus, Pakistan
© Dr. Noor M Khan
EE, MAJU Multi-Path Fading
Channel
8 EE5713 Advanced Digital Communications
Week 6-7; Spring - 2013
Average Delay Spread
(Continuous Delay Profile)
• Average delay spread
• Representative delay functions
0
0
)(
)(
τdttP
dttPt
elsewherezeroandttP
etP
d
t
202
)(uniform
1)(exp
τ
Page 9
Muhammad Ali Jinnah University, Islamabad Campus, Pakistan
© Dr. Noor M Khan
EE, MAJU Multi-Path Fading
Channel
9 EE5713 Advanced Digital Communications
Week 6-7; Spring - 2013
Measurements
Type of
EnvironmentDelay Spread d
(s)
Open area <0.2
Suburban area 0.5
Urban area 3
Page 10
Muhammad Ali Jinnah University, Islamabad Campus, Pakistan
© Dr. Noor M Khan
EE, MAJU Multi-Path Fading
Channel
10 EE5713 Advanced Digital Communications
Week 6-7; Spring - 2013
Coherence Bandwidth
• Coherence bandwidth Bc is a range of frequencies
over which the channel can be considered flat
– passes all spectral components with approximately equal
gain and liner phase
• Bandwidth where the correlation function RT() for
signal envelopes is high
• Therefore two sinusoidal signals with frequencies
that are farther apart than the coherence bandwidth
will fade independently.
Page 11
Muhammad Ali Jinnah University, Islamabad Campus, Pakistan
© Dr. Noor M Khan
EE, MAJU Multi-Path Fading
Channel
11 EE5713 Advanced Digital Communications
Week 6-7; Spring - 2013
Coherence Bandwidth
• If RT() > 0.9
• If RT() > 0.5
• An exact relationship between coherence
bandwidth & delay spread does not exist
50
1CB
5
1CB
Page 12
Muhammad Ali Jinnah University, Islamabad Campus, Pakistan
© Dr. Noor M Khan
EE, MAJU Multi-Path Fading
Channel
12 EE5713 Advanced Digital Communications
Week 6-7; Spring - 2013
Doppler Shift
• fc broadening from fc to (fc + fm )
BS1 v
c
vff
cm
v
Page 13
Muhammad Ali Jinnah University, Islamabad Campus, Pakistan
© Dr. Noor M Khan
EE, MAJU Multi-Path Fading
Channel
13 EE5713 Advanced Digital Communications
Week 6-7; Spring - 2013
Doppler Spread & Coherence
Time
• Describes the time varying nature of the channel
in a local area
• Doppler Spread BD, is a measure of the spectral
broadening caused by the time rate of change
• fc broadening from (fc - fm) to (fc + fm )
• If the base-band signal bandwidth is much greater
than BD, the effects of Doppler spread are
negligible at the receiver
Page 14
Muhammad Ali Jinnah University, Islamabad Campus, Pakistan
© Dr. Noor M Khan
EE, MAJU Multi-Path Fading
Channel
14 EE5713 Advanced Digital Communications
Week 6-7; Spring - 2013
Coherence Time
• Coherence Time is the time domain dual of Doppler spread
• Doppler spread and coherence time are inversely proportional
• TC = 1/fm
• Statistical measure of the time duration over which the channel impulse response is invariant
Page 15
Muhammad Ali Jinnah University, Islamabad Campus, Pakistan
© Dr. Noor M Khan
EE, MAJU Multi-Path Fading
Channel
15 EE5713 Advanced Digital Communications
Week 6-7; Spring - 2013
Coherence Time
• If the coherence time is defined as the time over
which the correlation function is above 0.5, then
• Rule of thumb for modern digital communication
defines TC as the geometric mean of the above two
expressions for TC
m
Cf
T16
9
216
9
m
Cf
T
Page 16
Muhammad Ali Jinnah University, Islamabad Campus, Pakistan
© Dr. Noor M Khan
EE, MAJU Multi-Path Fading
Channel
16 EE5713 Advanced Digital Communications
Week 6-7; Spring - 2013
Types of Small-Scale Fading
Page 17
Muhammad Ali Jinnah University, Islamabad Campus, Pakistan
© Dr. Noor M Khan
EE, MAJU Multi-Path Fading
Channel
17 EE5713 Advanced Digital Communications
Week 6-7; Spring - 2013
Flat Fading 1
• If the mobile radio channel has a constant gain and
linear phase over a bandwidth greater than the
bandwidth of the transmitted signal - the received
signal will undergo flat fading
• Please, observe that the fading is flat (or frequency
selective) depending on the signal bandwidth
relative to the channel coherence bandwidth.
Page 18
Muhammad Ali Jinnah University, Islamabad Campus, Pakistan
© Dr. Noor M Khan
EE, MAJU Multi-Path Fading
Channel
18 EE5713 Advanced Digital Communications
Week 6-7; Spring - 2013
Flat Fading 2
• BS << BC & TS >>
Page 19
Muhammad Ali Jinnah University, Islamabad Campus, Pakistan
© Dr. Noor M Khan
EE, MAJU Multi-Path Fading
Channel
19 EE5713 Advanced Digital Communications
Week 6-7; Spring - 2013
Frequency Selective Fading 1
• If the mobile radio channel as a constant gain and
linear phase over a coherence bandwidth, smaller
than the bandwidth of the transmitted signal - the
received signal will undergo frequency selective
fading
• Again, the signal bandwidth is wider then the
channel coherence bandwidth, causing one or
more areas of attenuation of the signal within the
signal bandwidth
Page 20
Muhammad Ali Jinnah University, Islamabad Campus, Pakistan
© Dr. Noor M Khan
EE, MAJU Multi-Path Fading
Channel
20 EE5713 Advanced Digital Communications
Week 6-7; Spring - 2013
Frequency Selective Fading 2
• BS > BC & TS <
Page 21
Muhammad Ali Jinnah University, Islamabad Campus, Pakistan
© Dr. Noor M Khan
EE, MAJU Multi-Path Fading
Channel
21 EE5713 Advanced Digital Communications
Week 6-7; Spring - 2013
Fast Fading
• The channel impulse response changes rapidly within the symbol duration - coherence time < symbol period
• TS > Tc and BS < BD
• Channel specifies as a fast or slow fading channel does not specify whether the channel is flat fading or frequency selective fading
Page 22
Muhammad Ali Jinnah University, Islamabad Campus, Pakistan
© Dr. Noor M Khan
EE, MAJU Multi-Path Fading
Channel
22 EE5713 Advanced Digital Communications
Week 6-7; Spring - 2013
Slow Fading
• The channel impulse response changes at a rate much slower than the transmitted base-band signal.
• Doppler spread is much less than the bandwidth of the base-band signal
• TS << Tc and BS >> BD
• Velocity of the MS and the base-band signaling determines whether a signal undergoes fast or slow fading
Page 23
Muhammad Ali Jinnah University, Islamabad Campus, Pakistan
© Dr. Noor M Khan
EE, MAJU Multi-Path Fading
Channel
23 EE5713 Advanced Digital Communications
Week 6-7; Spring - 2013
Fading in Short
Large Doppler Spread
Time-Selective Fading
Large Delay Spread
Frequency-Selective Fading
Large Angle Spread
Space-Selective Fading
Page 24
Muhammad Ali Jinnah University, Islamabad Campus, Pakistan
© Dr. Noor M Khan
EE, MAJU Multi-Path Fading
Channel
24 EE5713 Advanced Digital Communications
Week 6-7; Spring - 2013
Fading in Short
Delay Spread Coherence Bandwidth
Frequency separation at which two
frequency components of Tx signal undergo
independent attenuations
Doppler Spread Coherence Time
Time separation at which two time
components of Tx signal undergo
independent attenuations
Page 25
Muhammad Ali Jinnah University, Islamabad Campus, Pakistan
© Dr. Noor M Khan
EE, MAJU Multi-Path Fading
Channel
25 EE5713 Advanced Digital Communications
Week 6-7; Spring - 2013
Fading (Continued)
Time
Bc
Tc
Bandwidth
Flat in Time and
Selective in Frequency
Flat in Time and
Frequency
Flat in Frequency and
Selective in Time
Selective in both
Time and Frequency
Page 26
Muhammad Ali Jinnah University, Islamabad Campus, Pakistan
© Dr. Noor M Khan
EE, MAJU Multi-Path Fading
Channel
26 EE5713 Advanced Digital Communications
Week 6-7; Spring - 2013
Fading (Continued)
Fast and Slow Fading
If the channel response changes within a symbol
interval, then the channel is regarded FAST FADING
Otherwise
the channel is regarded as SLOW FADING
Page 27
Muhammad Ali Jinnah University, Islamabad Campus, Pakistan
© Dr. Noor M Khan
EE, MAJU Multi-Path Fading
Channel
27 EE5713 Advanced Digital Communications
Week 6-7; Spring - 2013
Fast Fading
When?
The channel impulse response changes rapidly within
the symbol period of the transmitted signal.
What?
The Doppler Spread causes frequency dispersion
which leads to signal distortion.
Page 28
Muhammad Ali Jinnah University, Islamabad Campus, Pakistan
© Dr. Noor M Khan
EE, MAJU Multi-Path Fading
Channel
28 EE5713 Advanced Digital Communications
Week 6-7; Spring - 2013
Doppler Spread
The Doppler effect (in addition to the fading effect)
renders the received pulse to be time-varying
The State Transitions are determined from the
dynamics of the fading channel (Fading Correlation
Function or The Doppler Spectrum)
Page 29
Muhammad Ali Jinnah University, Islamabad Campus, Pakistan
© Dr. Noor M Khan
EE, MAJU Multi-Path Fading
Channel
29 EE5713 Advanced Digital Communications
Week 6-7; Spring - 2013
Doppler Spread (Continued)
f: carrier frequency
c: speed of light
v: mobile speed
θ: Angle of motion with
incoming multipath
Scattering Point
Incoming
multipath
BS
MS
Line of
Sight
y
x
v
θ
Page 30
Muhammad Ali Jinnah University, Islamabad Campus, Pakistan
© Dr. Noor M Khan
EE, MAJU Multi-Path Fading
Channel
30 EE5713 Advanced Digital Communications
Week 6-7; Spring - 2013
Doppler Spread (Continued)
cosd
f vf
c
f: carrier frequency
c: speed of light
v: mobile speed
θ: Angle of motion with
incoming multipath
Page 31
Muhammad Ali Jinnah University, Islamabad Campus, Pakistan
© Dr. Noor M Khan
EE, MAJU Multi-Path Fading
Channel
31 EE5713 Advanced Digital Communications
Week 6-7; Spring - 2013
Doppler Spread (Continued)
For the land mobile fading spectrum,
The Auto-Correlation Function Doppler Fading Spectrum
Page 32
Muhammad Ali Jinnah University, Islamabad Campus, Pakistan
© Dr. Noor M Khan
EE, MAJU Multi-Path Fading
Channel
32 EE5713 Advanced Digital Communications
Week 6-7; Spring - 2013
Doppler Spread (Continued)
h is the channel impulse response
h has a complex normal distribution with zero mean
|h| is Raleigh distributed
Phase φ is uniformly distributed between 0 and 2π
is Chi-square distributed
Page 33
Muhammad Ali Jinnah University, Islamabad Campus, Pakistan
© Dr. Noor M Khan
EE, MAJU Multi-Path Fading
Channel
33 EE5713 Advanced Digital Communications
Week 6-7; Spring - 2013
Rayleigh Fading 1
• The received envelope (amplitude) of a flat
fading signal is described as a Rayleigh
distribution
– Square root sum r, of two quadrature Gaussian
noise signals xI and yQ has a Rayleigh
distribution (Papoulis65)
22
QI yxr )0(;2
exp)(2
2
2
r
rrrp
Page 34
Muhammad Ali Jinnah University, Islamabad Campus, Pakistan
© Dr. Noor M Khan
EE, MAJU Multi-Path Fading
Channel
34 EE5713 Advanced Digital Communications
Week 6-7; Spring - 2013
Rayleigh Fading 2
Page 35
Muhammad Ali Jinnah University, Islamabad Campus, Pakistan
© Dr. Noor M Khan
EE, MAJU Multi-Path Fading
Channel
35 EE5713 Advanced Digital Communications
Week 6-7; Spring - 2013
Rayleigh Fading PDF
Page 36
Muhammad Ali Jinnah University, Islamabad Campus, Pakistan
© Dr. Noor M Khan
EE, MAJU Multi-Path Fading
Channel
36 EE5713 Advanced Digital Communications
Week 6-7; Spring - 2013
Rayleigh Fading 3
• - rms value of the received voltage signal before
envelope detection
• 2 - time average power before envelope detection
• The probability that the received signal envelope
does not exceed R is given by:
)0(2
exp)(2
2
2
r
rrrp
2
2
02
exp1)()Pr()(
RdrrpRrRP
R
Page 37
Muhammad Ali Jinnah University, Islamabad Campus, Pakistan
© Dr. Noor M Khan
EE, MAJU Multi-Path Fading
Channel
37 EE5713 Advanced Digital Communications
Week 6-7; Spring - 2013
Rayleigh Fading 4
• The median value of r is found by solving
• Mean and median differ by only 0.55dB
77.1
)(2
1
0
median
r
r
drrpmedian
Page 38
Muhammad Ali Jinnah University, Islamabad Campus, Pakistan
© Dr. Noor M Khan
EE, MAJU Multi-Path Fading
Channel
38 EE5713 Advanced Digital Communications
Week 6-7; Spring - 2013
Ricean Fading 1
• When there is a dominant stationary signal
component
• At the output of an envelope detector -
adding a DC component ot the random
multi-path
)0,0(;)(20
2
)(2
22
rAforAr
Ier
rp
Ar
e
Page 39
Muhammad Ali Jinnah University, Islamabad Campus, Pakistan
© Dr. Noor M Khan
EE, MAJU Multi-Path Fading
Channel
39 EE5713 Advanced Digital Communications
Week 6-7; Spring - 2013
Ricean Fading 2
• A - peak amplitude of the dominant signal
• I0 () - modified Bessel function of the first
kind and zero order
• Described in terms of a Ricean factor, K
)(2
log10)(2
2
dBA
dBK