Understanding of wireless communication system from MATLAB point of view
Below is a sample MATLAB/pseudocode to generate a 4x4 MIMO system, for 1000 Monte Carlo trials:

M=4; MC=1000; 
H= randn(M,M,MC); 
x=randn(M,1,MC); 
w=randn(M,1,MC); 
Y=zeros(M,1,MC); 
for j = 1:MC
   Y(:,:,j)= H(:,:,j)*x(:,:,j) + w(:,:,j); 
end


This would generate y according to the equation in the question. You can view the MC values as different time instances. Meaning different channel, transmit vector and noise matrix for each instance.