How to generate 2D complex white Gaussian sequence with a zero mean and identity covariance?

I'm trying to create a 2D complex white Gaussian with a mean of zero and a covariance of (N/2)I where N is the size of the matrix.

I've been trying it with the following code:

w = randn(N) + i*randn(N);

but if I do cov(w) or mean(w) it doesn't fit that criteria. I feel like my process is a gross oversimplification of making a 2D complex Gaussian.

Answer 1

[Shaik]

N = 100;  % Size of the matrix
w_real = randn(N) * sqrt(N/2);  % Real part with mean 0 and variance N/2
w_imag = randn(N) * sqrt(N/2);  % Imaginary part with mean 0 and variance N/2
w = w_real + 1i * w_imag;  % Combine real and imaginary parts

% Verify mean and covariance properties
mean_w = mean(w(:))  % Mean of w

mean_w = -0.0326 - 0.0201i

cov_w = cov([real(w(:)), imag(w(:))])  % Covariance of w (real and imaginary parts)

cov_w = 2×2

51.1531 -0.5130 -0.5130 50.2423

Hey, can you check this modified code.