You are required to write a code that simulate a MIMO system $($assume CSI is available at $Rx$ side only$)$:

Set $m$ and $n$ number of transmit and receive antenna

$>$ Generate $N_C($e$.$g$.,100,000)$ realizations of the channel matrix $H(mn)$

$>$ Each element $h_{ij}=|h_{ij}|e^{j{}_{ij}}$

$>|h_{ij}|$ is Rayleigh $f(h)=\frac{h}{{}^2}{e}^{-(\frac{h}{2}{}^2)}$ with $2{}^2=1($unit power on each channel$)$

$>{}_{ij}$ is uniform in the interval $0,2$

For each channel realization compute SVD to derive diagonal matrix $D$

Compute capacity based on Water Filling solution

$>p_i=$max$(0,-\frac{{}^2}{{}_i})$

$>P_T={\displaystyle \underset{i=1}{\overset{k}{}}}{p}_i$

$>C={\displaystyle \underset{i=1}{\overset{k}{}}}log(1+\frac{p_i{}_i}{{}^2})$

Average the capacity over all $N_C$ channel realizations

$($a$)$ Calculates the Ergodic Rayleigh Fading channel capacity for a MIMO system.

$($b$)$ Plot the curves of the Ergodic capacity calculated in the previous step for different SNR values and different number of antennas as shown in the below figure $($assume that the number of antennas at the transmitter and receiver are equal$).$ Using MATLAB. I want the graph to be as shown in the photo

R$-$CSI fading channel $N_R=N_T$