2x2 channel model
DESCRIPTION
this is document for multipath fading channelTRANSCRIPT
Abdul-Aziz .M Al-Yami Abdul-Aziz .M Al-Yami Khurram MasoodKhurram Masood
Channel Model and Simulation
Using Matlab
Channel ModelChannel 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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Sampling and Doppler BandwidthSampling 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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ParametersParameters
• 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 weightsGeneration of Tap weights
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Tap Input Process DataTap 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 FilterDoppler 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 ModelJake’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 FilterDoppler Filter
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-100 -80 -60 -40 -20 0 20 40 60 80 1000
1
2
3
4
5
6
PSD of Jakes filter with fD = 100 Hz
Frequency [Hz]
PS
D
Doppler spreadDoppler spread
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0 200 400 600 800 1000 1200 1400 1600 18000
0.5
1
Frequency (Hz)
Inpu
t P
SD
0 200 400 600 800 1000 1200 1400 1600 18000
0.5
1
1.5
Frequency (Hz)
Out
put
PS
D
Linear InterpolationLinear 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 carrierProcessing of QPSK signal and carrier
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Channel Input / OutputChannel Input / Output
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0 50 100 150 200 250 300 350 400 450 500-2
-1
0
1
2
Sample Index
Dire
ct I
nput
0 50 100 150 200 250 300 350 400 450 500-4
-2
0
2
4
Sample Index
Dire
ct O
utpu
t
Envelope of outputEnvelope of output
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0 500 1000 1500 2000 2500 3000 35000
0.5
1
1.5
2
2.5
3
Sample Index
Env
elop
e M
agni
tude