Simulating Channel Model Impairments with Rayleigh Fading in MATLAB

This document explains how to simulate channel model impairments and the Rayleigh channel effect on a constellation diagram using MATLAB code.

MATLAB Source Code

The MATLAB code is divided into parts. Parts A and C are assumed to be the same as in the AWGN (Additive White Gaussian Noise) example. This section focuses on Part B, which adds the Rayleigh channel.

Part B: Adding Rayleigh Channel

% Adding Rayleigh channel
choice=input('Enter 1 to apply the channel, other no. to bypass:');
% 10 Hz;sample time=0.1e-3;
if(choice==1)
  ts=(256/4e6);
  doppler=0.1;
  tau=[0.0 0.4 0.9];
  pdb=[0 -15 -20];
  chan = rayleighchan(ts,doppler,tau,pdb);
  % TS is the sample time of the input signal, in seconds.
  % FD is the maximum Doppler shift, in Hertz.
  % 100 Hz
  map_out_chl=filter(chan,mapper_out_ori);
  figure;plot(real(map_out_chl),imag(map_out_chl),'r+');title('constellation with channel');
else
  disp('no channel applied proceed to DC offset');
end

Explanation:

• The code first prompts the user to choose whether to apply the Rayleigh channel or not.
• If the user enters 1, the Rayleigh channel is applied.
• The rayleighchan function creates a Rayleigh fading channel object. The parameters are:
  • ts: Sample time of the input signal (calculated as 256/4e6 in this example).
  • doppler: Maximum Doppler shift (set to 0.1 Hz here).
  • tau: Delay vector (set to [0.0 0.4 0.9] in this example). These represent the delays of different paths in the channel.
  • pdb: Power delay profile (set to [0 -15 -20] in this example). These represent the average power of the paths specified in tau, in dB.
• The filter function applies the Rayleigh fading to the output of the mapper (mapper_out_ori).
• Finally, the constellation diagram of the signal after passing through the channel (map_out_chl) is plotted.
• If the user enters anything other than 1, the channel is bypassed and the script proceeds (presumably to a DC offset adjustment, based on the disp message).

Input and Output Constellation Diagrams

Here are example constellation diagrams, before and after the channel effect.