How to generate Rayleigh/Weibull distributed complex random variable?

I would like to generate ground clutter with a Rayleigh/Weibull distribution. I need to generate a complex discrete signal and maintain a specific power level for this signal.

Answer 1

[Kautuk Raj]

To generate a complex random variable with a Rayleigh or Weibull distribution, you can use the raylrnd or wblrnd functions in MATLAB, respectively. Here is an example code snippet that generates a complex random variable with a specified power level:

% Parameters
N = 1000; % number of samples
P = 1; % desired power level
sigma = sqrt(P/2); % standard deviation of the real and imaginary parts

% Generate real and imaginary parts with Rayleigh distribution
x = raylrnd(sigma, N, 1);
y = raylrnd(sigma, N, 1);

% Combine real and imaginary parts into complex signal
s = x + 1j*y;

% Normalize the signal to have the desired power level
s = s / sqrt(mean(abs(s).^2)) * sqrt(P);

To generate a complex random variable with a Weibull distribution, you can replace the raylrnd function with the wblrnd function in the code above. You'll need to adjust the shape and scale parameters of the Weibull distribution to achieve the desired standard deviation and shape of the distribution.

Note that this code snippet generates a discrete-time signal, but you can apply the same principle to generate a continuous-time signal by using a smaller time step and interpolating the signal if necessary.