1
Fredrik Tufvesson
Department of Electrical and Information Technology
Lund University, Sweden
Channel Modelling – ETI 085
Lecture no:
2012-01-16 Fredrik Tufvesson - ETIN10 1
1
Introduction
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Contents
• Course information
• Why channel modelling?
• Review of concepts
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COURSE INFORMATION
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Course web-site
• All course information is available at:
http://www.eit.lth.se/course/ETIN10
(or www.eit.lth.se, -Education, -Courses, -Channel mod.)
• Most important:
– Continuously updated schedule
– Lecture handouts (available before each lecture)
– Any additional material
2
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Textbook
Andreas F. Molisch
Wireless Communications, 2nd ed
ISBN: 047084888X
Wiley/IEEE press
The second edition is available since
Dec 2010, which will be used 2012
• Available, e.g., through:
– Lexis, www.lexis.se
– Amazon U.K., www.amazon.co.uk
– Wiley, eu.wiley.com
• Authored by Andreas F. Molisch, former professor of Radio Systems at Lund University/LTH.
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Schedule
• Three recurring components
– Lectures: Fredrik Tufvesson
Mondays (13-15, 2311) and Fridays(10-12, E:2311)
– Exercise classes: Meifang Zhu
Thursdays (8-10), E:2349
• Two special components
– Assignments:
Three assignments, where reports are handed in
– Oral exam:
– March 5-9, in groups of 6 students, time to be decided
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Lectures
• Overview of the content in the textbook
• Additional material
• Application examples
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Exercise classes
• Selection of suitable exercises on the course web-site in
advance
• During exercise classes, some of the exercises will be
analysed in detail
• By working through the exercises beforehand, you can give
valuable input on which exercises to focus on during
classes
3
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Assignments
• There are three compulsory assingments.
• Performed in groups of two students.
• You will receive measured channel data in MATLAB-format,
– analysis
– parameter extraction
– conclusions
• Short reports are handed in within 7 days.
• THIS IS A COMPULSORY PART OF THE COURSE!
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Oral exam
• How?
– appr 3 hours
– Both theoretical questions and calculations
– “A group discussion”, but with individual questions
– Prepare as for a written exam
– No assignments, no oral exam
• When?
March 5-9, depending on the group.
• Where?
Room E:2349 (?)
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Why channel modelling?
• The performance of a radio system
is ultimately determined by the radio
channel
• The channel models basis for
– system design
– algorithm design
– antenna design etc.
• Trend towards more interaction
system-channel
– MIMO, multiple antenna systems
– UWB, ultra wideband
– Localization services
Without reliable
channel models, it
is hard to design
radio systems that
work well in real environments.
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A rough breakdown into areas
Fundamental problems
in wireless communications
Propagation
and antennas
Deterministic Probabilistic
Channel models
Narrow-band
channels
Wide-band
channels
Antennas
Digital transmission
over wireless channels
Modulation
Speech and
channel coding
Equalization
Diversity
Mobile communications
systems
Multiple access
Cellular telephony
Wireless data networks
Speech coding
4
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Noise
NNoise reference level
THE RADIO CHANNEL
... in the link budget
Transmitter Receiver
”POWER” [dB]
Transmit
power
TXP
Feeder
loss
TXfL ,
Antenna
gain
TXaG ,
Propagation
loss
pL
Antenna
gain
RXaG ,
Feeder
loss
RXfL ,
C
Received
power
Ga
in
Lo
ss
Required
C/N at
receiver
input
CRITERION
TO MEET:
This is a simple
version of the
link budget.
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THE RADIO CHANNEL
It is more than just a loss
• Some examples:
– behavior in time/space?
– behavior in frequency?
– directional properties?
– bandwidth dependency?
– behavior in delay?
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A narrowband system described in
complex notation (noise free)
exp 2 cj f expt j t exp 2 cj f
Transmitter Receiver Channel
Attenuation Phase
x t y t
expA t t j t t
expx t A t j tIn:
exp exp 2 exp exp 2c cy t A t j t j f t t j t j f t Out:
It is the behavior of the channel attenuation and phase we
are going to model.
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THE RADIO CHANNEL
Some properties
• Path loss
– Roughly, received power decays exponentially with distance
• Large-scale fading
– Large objects, compared to a wavelength, in the signal path
obstruct the signal
• Small-scale fading
– Objects reflecting the signal causes multipath propagation
from transmitter to receiver
exponentn PropagatioDistance power dTransmitte power Received
5
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THE RADIO CHANNEL
Path loss
Received power [log scale]
Distance, d [log scale]
TX RX
2/1 d
4/1 d
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THE RADIO CHANNEL
Path loss
”POWER” [dB]
dBTXG |
dBTXP |
dBRXG |
10
| 2
10
420log , free space
20log , ground plane
dB
TX RX
d
L dd
h h
dBRXP |
|dBL
Two theoretical expressions for
the deterministic propagation loss as
functions of distance:
There are other models, which we
will discuss later.
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Large-scale fading
Basic principle
d
Received power
Position
A B C C
A
B
C
D
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Large-scale fading
Log-normal distribution
Measurements confirm that in many situations, the large-scale
fading of the received signal strength has a normal distribution
in the dB domain.
”POWER” [dB]
dBTXP |
dBRXP |
|dBL
2
| 0|
| 2
||
1exp
22
dB dB
dB
F dBF dB
L Lpdf L
Note dB
scale
dB Deterministic mean
value of path loss, L0|dB
|dBpdf L
Standard deviation | 4 10 dBF dB
6
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Small-scale fading
Two waves
Wave 1 + Wave 2
Wave 2
Wave 1
At least in this case, we can see that the interference pattern
changes on the wavelength scale.
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THE RADIO CHANNEL
Small-scale fading (cont.)
RX TX
With a large number of
reflection points the
interference pattern
becomes extremly
complicated.
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Small-scale fading
Many incoming waves
1 1,r 2 2,r
3 3,r 4 4,r
,r
1 1 2 2 3 3 4 4exp exp exp exp expr j r j r j r j r j
1r1
2r 2
3r
3
4r4
r
Many incoming waves with
independent amplitudes
and phases
Add them up as phasors
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THE RADIO CHANNEL
Small-scale fading (cont.)
Illustration of interference pattern from above
Transmitter
Reflector
Movement
Position
A B
A B
Received power [log scale]
7
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Small-scale fading
Rayleigh fading
No dominant component
(no line-of-sight)
2D Gaussian
(zero mean)
Tap distribution
2
2 2exp
2
r rpdf r
Amplitude distribution
Rayleigh
0 1 2 3 0
0.2
0.4
0.6
0.8
r a
No line-of-sight
component
TX RX X
Im a Re a
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Small-scale fading
Doppler shifts
c
rv
0f f
Frequency of received signal:
0 cosrvf
c
where the Doppler shift is
Receiving antenna moves with
speed vr at an angle θ relative
to the propagation direction
of the incoming wave, which
has frequency f0. The maximal Doppler shift is
max 0
vf
c
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Small-scale fading
Doppler spectrum
Isotropic uncorrelated
scattering
RX
Uniform incoming
power distribution
(isotropic)
Uncorrelated
amplitudes
and phases
Time correlaion
*
0 max2t E a t a t t J t
0 0.5 1 1.5 2 -0.5
0
0.5
1
max t
RX movement
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Small-scale fading
Rice fading
A dominant component
(line of sight)
2D Gaussian
(non-zero mean)
Tap distribution
A
Line-of-sight (LOS)
component with
amplitude A.
2 2
02 2 2
2
2
exp2
Power in LOS component
Power in random components 2
r r A rApdf r I
Ak
Amplitude distribution
Rice
r
0 1 2 3 0
0.5
1
1.5
2
2.5
k = 30
k = 10
k = 0
TX RX
Im a Re a
8
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DELAY (TIME) DISPERSION
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Delay (time) dispersion
A simple case
Transmitted impulse Received signal
(channel impulse response)
h
1 1 2 2 3 3h a a a
1
1a
2
2a
33a
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Delay (time) dispersion
One reflection/path, many paths
2 3 4 0
“Impulse
response”
Each bin consists
of incoming waves
that are too close in
time to resolve. What do we
mean by “too
close in time”? Delay in excess
of direct path
Since each bin consists of
contributions from several
waves, each bin will fade
if we introduce movement.
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Delay (time) dispersion
Bandwidth and time-resolution
Band-limiting
to B Hz
Radio systems are band-limited, which makes our infinitely short
impulses become waveforms with a certain width in time.
1
B
The time-width of the pulses is inversely
proportional to the bandwidth.
9
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Narrow- versus wide-band
Channel impulse response
The same radio propagation environment is experienced
differently, depending on the system bandwidth.
“High” BW “Medium” BW “Low” BW
h h h
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2B
A wide-band system
(bandwidth B2) will however
experience both frequency
selectivity and delay
dispersion.
1B
A narrow-band system
(bandwidth B1) will not
experience any significant
frequency selectivity or
delay dispersion.
Narrow- versus wide-band
Channel frequency response
|dB
H f
f
Note that narrow- or wide-band depends on the
relation between the channel and the system
bandwidth. It is not an absolute measure.
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It’s much more complicated than
what we have discussed!
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The WSSUS model
Assumptions
A very common wide-band channel model is the WSSUS-model.
Recalling that the channel is composed of a number of different
contributions (incoming waves), the following is assumed:
The channel is Wide-Sense Stationary (WSS), meaning
that the time correlation of the channel is invariant over time.
(Contributions with different Doppler frequency are
uncorrelated.)
The channel is built up by Uncorrelated Scatterers (US),
meaning that the frequency correlation of the channels is
invariant over frequency. (Contributions with different delays
are uncorrelated.)
10
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The WSSUS model
The tapped delay-line
Recall that a narrow-band (complex) channel was modeled as
expt j t
where the fading characteristic depended on the time-varying
attenuation and phase.
The generalization we need to describe wide-band channels is
the delay characteristics (more than one “tap” in the channel):
1
, expN
i i i
i
h t t j t
Each of the N taps of the channel may have their own fading
characteristic (power, Doppler spectrum, etc.). They are
however required to be independent.
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Condensed parameters
Power-delay profile
One interesting channel property is the power-delay profile (PDP),
which is the expected value of the received power at a certain delay:
2
E ,tP h t
Et denotes
expectation
over time.
2
1
2 2
1 1
E exp
E 2
N
t i i i
i
N N
t i i i i
i i
P t j t
t
For our tapped-delay line we get:
Average power of tap i.
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Condensed parameters
Power-delay profile (cont.)
We can “reduce” the PDP into more compact descriptions of the channel:
mP P d
m
m
P dT
P
2
m
m
P dS T
P
2
1
2N
m i
i
P
2
1
2N
i i
im
m
TP
2 2
1
2N
i i
im
m
S TP
Total power (time integrated):
Average mean delay:
Average rms delay spread:
For our tapped-delay line
channel:
2 2
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Condensed parameters
Frequency correlation
A property closely related to the power-delay profile (PDP) is the frequency
correlation of the channel. It is in fact the Fourier transform of the PDP:
exp 2f f P j f d
2
1
2
1
2 exp 2
2 exp 2
N
f i i
i
N
i i
i
f j f d
j f
For our tapped delay-line channel we get:
11
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Condensed parameters
Coherence bandwidth
Given the frequency correlation of a channel, we can define the
coherence bandwidth BC:
f f
f
0f
0
2
f
CB
What does the coherence
bandwidth tell us?
It shows us over how large
bandwidth we can assume
that the channel is fairly
constant.
Radio systems using a
bandwidth much smaller
than BC will not notice
the frequency selectivity
of the channel.
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Condensed parameters
The time correlation
A property closely related to the Doppler spectrun is the time correlation
of the channel. It is in fact the inverse Fourier transform of the Doppler
spectrum:
exp 2t Bt P j t d
2
2 21
,max
2
2 21
,max
2
0 ,max
1
2exp 2
2exp 2
2 2
Ni
t
ii
Ni
ii
N
i i
i
t j t d
j t d
J t
For our tapped-delay line channel we get
Sum of time
correlations for
each tap.
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Condensed parameters
Coherence time
Given the time correlation of a channel, we can define the
coherence time TC:
t t
t
0t
0
2
t
CT
What does the coherence
time tell us?
It shows us over how long
time we can assume
that the channel is fairly
constant.
E.g. radio systems transmitting
data in frames much shorter
than TC will not experience any
fading within a single frame.
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