1. Abdul-Aziz .M Al-Yami Khurram Masood
Channel Model and Simulation
Using Matlab  
Abdul-Aziz .M Al-Yami Khurram Masood

2. Channel Model Discrete Multipath fading channel (2 paths)
Doppler filter
Jake’s model
fd = 100 Hz
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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3. Sampling and Doppler Bandwidth
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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4. Parameters 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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5. Generation of Tap weights
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6. 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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7. 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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8. 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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9. Doppler Filter
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10. Doppler spread
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11. 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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12. Processing of QPSK signal and carrier
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13. Channel Input / Output
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14. Envelope of output
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