Free Space Optical communication channel model

How to develop a channel (like awgn) in matlab for free space gamma-gamma model. Or does matlab have any such inbuild channel?

[Ahmed Rayhan]

hi did you find any asnwer to this?

[Edwin]

Using Gamma Gamma channel model formula It should be possible to create a function handle

Answer 1

[Umeshraja]

Hi @Ekata Niraula,

As per MATLAB R2024b documentation, there are no built-in function to model Gamma-Gamma(GG) channel. The GG Distribution is used in modelling atmospheric turbulence in free-space optical communication channels.

This distribution can be simulated as the product of two independent gamma-distributed random variables: one representing large-scale atmospheric effects and the other representing small-scale atmospheric effects.

You can use the gamrnd function to model the channel, as demonstrated in the code below

alpha = 4;
beta = 2;
num_samples = 10000;
   
x = linspace(0, 5, 1000); 

% Generate samples
gamma1 = gamrnd(alpha, 1/alpha, [1, num_samples]);
gamma2 = gamrnd(beta, 1/beta, [1, num_samples]);

% Generate samples using the fact that Gamma-Gamma is a product of two Gamma RVs
samples = gamma1 .* gamma2;

% Calculate PDF (Refer to the attached research article)
pdf = 2*(alpha*beta)^((alpha+beta)/2) / (gamma(alpha)*gamma(beta)) .* ...
  x.^(((alpha+beta)/2)-1) .* ...
  besselk(alpha-beta, 2*sqrt(alpha*beta*x));

% PDF plot
subplot(2,1,1);
plot(x, pdf);
title('Probability Density Function');
xlabel('Intensity');
ylabel('PDF');
grid on;

% Histogram of samples
subplot(2,1,2);
histogram(samples, 50, 'Normalization', 'pdf');
hold on;
plot(x, pdf, 'r', 'LineWidth', 2);
title('Histogram of Samples vs PDF');
xlabel('Intensity');
ylabel('Frequency');
grid on;

For a deeper understanding of the mathematical derivations and statistical properties, you might want to refer to the following resource:

Al-Habash, Andrews, and Phillips, "Mathematical model for the irradiance probability density function of a laser beam propagating through turbulent media" (2001)

Additionally, you can refer the following MATLAB documentation on generating gamma random numbers

https://www.mathworks.com/help/stats/gamrnd.html

Hope it helps!