MMSE Receiver Capacity

clear all;close all;clc;

syms M K p d(x) l m v0 v1 v2 k f1 f2 f3

L = 1;

cellRadius = 1000;

cellHole = 100;

sshadow = 8; % dB

gamma = 3.8;

M = 100;

K = 10;

p = 10;

start = 2;

d = randn(1,K); %GenerateRandomBetav4(L,K,cellRadius,cellHole,sshadow,gamma);

f1 = 1./( M.*p.*d.*(1 - ((K-1)./M) + ((K-1)./M).*m ) + 1 );
v0 = (1/(K-1))*sum(f1(start:K));

f2 = (p.*d)./(( M.*p.*d.*(1 - ((K-1)./M) + ((K-1)./M).*m ) + 1 ).^2);
v1 = k*( 1 + sum(f2(start:K)) );

f3 = (p.*d.*m + 1)./(( M.*p.*d.*(1 - ((K-1)./M) + ((K-1)./M).*m ) + 1 ).^2);
v2 = sum(f3(start:K));

eqns = [m == v0, v1 == v2];
vars = [m k];
%[solv, solu] = solve(eqns, vars);
[solv, solu] = vpasolve(eqns, vars, [-Inf Inf]);
solutions = [solv solu];

m = eval(solutions(1,1));

k = eval(solutions(1,2));

v0_eval = eval(v0);

v1_eval = eval(v1);

v2_eval = eval(v2);


alpha = ((M - K + 1 + (K-1)*m)^2) / (M - K + 1 + (K-1)*k);

theta = ((M - K + 1 + (K-1)*k) / (M - K + 1 + (K-1)*m))*p*d(1);

R = log2(1 + (alpha-1)*theta);