clear all;close all;clc

M = 1;

d = 2;

p = 10;

numIter = 1000000;

%% -------------------- Problem 1: First option (l != k) ----------------------
simulated = 0;
for iter = 1:1:numIter
    h= (sqrt(d))*(1/sqrt(2))*complex(randn(M,1),randn(M,1));

    w = (sqrt(1/p))*(1/sqrt(2))*complex(randn(M,1),randn(M,1));

    num = (h'*(h*h')*h);

    den = (h + w)'*(h + w);

    simulated = simulated + real(num/den);
end

simulated = simulated/numIter;