1. Abdul-Aziz .M Al-YamiKhurramMasood Channel Model and Simulation Using Matlab

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

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)

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]

5. Generation of Tap weights

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

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.

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

9. Doppler Filter

10. Doppler spread

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.

12. Processing of QPSK signal and carrier

13. Channel Input / Output

14. Envelope of output