Channel Model and Simulation
Using Matlab
Abdul-Aziz .M Al-Yami
Khurram Masood
Channel Model
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Discrete Multipath fading channel (2 paths)
Doppler filter
– Jake’s model
– fd = 100 Hz
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Delay between paths = 8 samples = 0.5 *Ts
Power of paths = [1 0.5]
Signal Bandwidth (Lowpass equivalent) Bs = 10 kHz
Symbol time, Ts = 1/Bs = 0.1 msec
Data Rate = 10k sym/sec
Sampling rate = 160k samples/sec
Samples/symbol = 16
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Sampling and Doppler Bandwidth
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An important aspect of the Tapped Delay Line (TDL) model is the sampling rate for
simulations.
In simulation we use sampled values which should be sampled at 8 to 32 times the
bandwidth
The doppler bandwidth, or the doppler spread, Bd, is the bandwidth of the doppler
spectrum Sd(λ), and is an indicator of how fast the channel characteristics are changing
(fading) as a function of time. If Bd is of the order of the signal bandwidth Bs (≈ 1/Ts),
the channel characteristics are changing (fading) at a rate comparable to the symbol
rate, and the channel is said to be fast fading. Otherwise the channel is said to be slow
fading. Thus
– Bd << Bs ≈ 1/Ts (Slow fading channel)
– Bd >> Bs ≈ 1/Ts (Fast fading channel)
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Parameters
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Signal bandwidth = Bs = 10kHz
Ts = 0.1 msec
Maximum doppler frequency = fd = 100 Hz
Sampling frequency = fs = 16*Bs = 160k samples/sec
Simulation length = 5 / (fd) = 50 msec = 8k samples
Interpolation factor = 100
Delay between taps = 8 samples = 0.5 Ts
Carrier
– c(t) = exp[j2π(1000)t]
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Generation of Tap weights
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Tap Input Process Data
• Two independent Gaussian random variables x1 and x2 are
generated
– X1,X2 ~ N(0,1)
• For a given Doppler Frequency fd and system symbol rate
1/Ts.
• The term fdTs is known as the fade rate.
• Each I and Q components should have this fade rate.
• The envelope should be Rayleigh distributed and the phase
should be uniformly distributed
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Doppler Filter
• The models for doppler power spectral densities for mobile
applications assume:
– there are many multipath components
– each multipath has different delays
– all components have the same doppler spectrum.
• Each multipath component (ray)
– made up of a large number of simultaneously arriving unresolvable
multipath components
– angle of arrival with a uniform angular distribution at the receive
antenna.
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Jake’s Model
• Jakes derived the first comprehensive mobile radio channel
model for both doppler effects and amplitude fading effects
• The classical Jake’s doppler spectrum has the form
• where
– fd is the maximum doppler shift
• The Jakes filter is implemented via FIR filter in time domain
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Doppler Filter
PSD of Jakes filter with fD = 100 Hz
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5
PSD
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3
2
1
0
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-100
-80
-60
-40
-20
0
20
Frequency [Hz]
40
60
80
100
9
Doppler spread
Input PSD
1
0.5
0
0
200
400
600
800
1000
Frequency (Hz)
1200
1400
1600
1800
0
200
400
600
800
1000
Frequency (Hz)
1200
1400
1600
1800
Output PSD
1.5
1
0.5
0
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Linear Interpolation
• In generating the tap gain processes it should be noted that the
bandwidth of the tap gain processes for slowly time-varying channels
will be very small compared to the bandwidth of the signals that flow
through them.
• In this case, the tap gain filter should be designed and executed at a
slower sampling rate.
• Interpolation can be used at the output of the filter to produce denser
samples at a rate consistent with the sampling rate of the signal coming
into the tap.
• Designing the filter at the higher rate will lead to computational
inefficiencies as well as stability problems.
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Processing of QPSK signal and carrier
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Channel Input / Output
Direct Input
2
1
0
-1
-2
0
50
100
150
200
250
300
Sample Index
350
400
450
500
0
50
100
150
200
250
300
Sample Index
350
400
450
500
Direct Output
4
2
0
-2
-4
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Envelope of output
3
Envelope Magnitude
2.5
2
1.5
1
0.5
0
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0
500
1000
1500
2000
Sample Index
2500
3000
3500
14