Understanding of wireless communication system from MATLAB point of view I am dealing with a communication model described as  

$$\overrightarrow{y(n)}=\pmb{H(n)}\overrightarrow{x(n)}+\overrightarrow{w(n)}$$

where $\pmb{H(n)}$ is the $M\times M$ fading coefficient matrix at time $n$. What is difference between time instant  $n$ and length $M$?
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.