I have bulit a MIMO system, Now I want to verify the effects of imperfect CIS on MIMO BER? As the depicted in the picture, I need help to construct this model in MATLAB.
This is just one of the many ways to model imperfect CSI, so make sure that you understand the underlying assumptions of the model that you have selected.
Your screenshot only reveals a part of the modeling assumptions that were made in the paper, so I cannot give any precise answer.
If you want to generate two complex Gaussian variables h1 and h2 with unit variance and correlation rho, then you can do that like:
a = (randn(1,1)+1i*randn(1,1))/sqrt(2);
b = (randn(1,1)+1i*randn(1,1))/sqrt(2);
c = (randn(1,1)+1i*randn(1,1))/sqrt(2);
h1 = sqrt(rho)*a + sqrt(1-rho)*b;
h2 = sqrt(rho)*a + sqrt(1-rho)*c;
These variables are made up by one part a that is equal and one part b or c that is independent.
You could consider either bounded CSI error model or statistical CSI error model. With bounded CSI error, you assume a specific maximum value for the CSI error. With statistical error model, we assume that the probability of a specific event under imperfect CSI does not exceed a specific threshold value.