What is the best way to generate samples from a multivariate complex normal distribution with an arbitrary covariance matrix?

Is there a simple way to generate samples from X ~ CN(0,R), where X is Mx1 and R can be chosen arbitrarily?

[wenhao chen]

I am trying to figure out this problem too!

Answer 1

[Bruno Luong]

% Generate test complex covariance matrix R sdp (m x m)
m = 3;
A = randn(m)+1i*randn(m);
R = A'*A

% Generate x, n-samples of complex normal random vector
% (in R^m) that have R as covariance matrix
n = 10000;
L = chol(R)
x = L'*(randn(m,n)+1i*randn(m,n))/sqrt(2);

[Pratish Dwivedi]

This is defined for 0 mean right ?

[Bruno Luong]

Yes. See original question

Answer 2

[the cyclist]

Do you have the Statistics Toolbox? If so, you can generate a 2-d vector using mvnrnd(), and take the first component as the real part, and second component as the imaginary part.

[Disclaimer: I just read about the complex normal distribution on Wikipedia, and I think what I said is accurate, but you might want to check.]

[wenhao chen]

The answer is good for the condition when M = 1,but for M > 1,we need to find other way!

[Pratish Dwivedi]

I don't get what you meant by taking the first component as real and second as complex.