Question

Matlab
Implement Fading Channel Simulation: Jakes Model with using Matlab

Answer 1

The rayleigh fading model is implemented as a function in matlab with following parameters :

M = number of multipaths in the fading channel

N = number of samples to generate

f_d = maximum doppler spread in Hz

T_s = sampling period

Function to simulate Rayleigh Fading

function [h] = rayleighFading (M, N, f_d,T_s)

% function to generate rayleigh Fading samples based on Jake's model

% M = number of multipaths in the channel

% N = number of samples to generate

% f_d = maximum doppler frequency

% T_s = sampling period

We will use the Jake's Rayleigh Fading model and check the statistical properties of the random process generated by model against the statistical properties of Rayleigh distribution.

Jake's Channel model is a sum of sinusoids model. It gives pdf of scaling as a function of angle of an arrival for each path.

Mathematically, we have

Cn² = f () d

where, f () = 1 / 2

d = 2/N

then, we get

Cn² = [(1 / 2) (2/N)]

Cn = 1 / N

An equation for r (t) will be given as :

r (t) = r_I (t) + j r_Q (t)

We know that, r_I = (1 / N) cos (2 F_d cos _m t + a_m)

And                r_Q = (1 / N) sin (2 F_d cos _m t + b_m)

Where, a_m & b_m = random phases uniformly distributed over (0, 2)

_m = angle of arrival

In Jakes' model, the cross-correlation was lower than Clarke's model.

Simulating Jake's Channel Model