Let x be a Nx1 vector that contains pseudorandom samples drawn from standard normal distribution. This represents N samples taken from a standard normal distribution at time ‘t’.
The correlation of the sequence x is given by E[xx H]
This means, we need to compute the matrix xx H M (M is a very large number) times, sum up all the matrices, and divide the resultant matrix by M. We can see that as M tends to infinity, we get a diagonal matrix as output. If the variance of the noise distribution is 1, then we get an identity matrix.
Z=10; N=1000000 Y=zeros(Z,Z); for i=0:N-1 x=randn(Z,1); X=x*x'; Y=Y+X; end Y./N