I am trying to simulate the following convex problem:

Basically, trying to minimize the power of two users in UL transmission which are assigned to the same subcarrier of a BS. Therefore, interference is also included for the calculation of the rate.

However, only the interference of the weak user h_w < h_s is included, assuming the strong user can apply a Successive interference cancellation (SIC) technique.

I have formulated the following code, but I must have done something wrong because I get the following error message: Cannot perform the operation: {real affine} ./ {real affine}
Can I get some feedback please, so I can figure out what I am doing wrong?Preformatted text

K= 2;
R_min = 10^-2;
Power_total = 10;
h = complex(randn(2,1),randn(2,1))/sqrt(2); %CSI
cvx_begin
variable p(2) nonnegative
minimize sum(p)
subject to
expression Interference(1,2);
for i=1:K
Interference(i) = 0;
for j=1:K
if (i ~= j) && (abs(h(i)) > abs(h(j)))
Interference(i) = Interference(i) + p(j)*norm(h(j))^2;
end
end
end
% Minimum rate
log(1+p(1)*norm(h(1))^2/(1+Interference(1))) >= R_min
log(1+p(2)*norm(h(2))^2/(1+Interference(2))) >= R_min
% MAC contraints
log(1+p(1)*norm(h(1))^2/(1+Interference(1))) <= log(1+p(1)*norm(h(1))^2)
log(1+p(2)*norm(h(2))^2/(1+Interference(2))) <= log(1+p(2)*norm(h(2))^2)
log(1+p(1)*norm(h(1))^2/(1+Interference(1)))+log(1+p(2)*norm(h(2))^2/(1+Interference(2))) <= log(1+p(1)*norm(h(1))^2 + p(2)*norm(h(2))^2)
sum(p) <= Power_total
p >= 0
cvx_end

The error is occurring in the constraint log(1+p(1)*norm(h(1))^2/(1+Interference(1))) >= R_min
because Interference(1) is (equal to) p(1)
This constraint is convex because the LHS is conccave in p(1).

The constraint log(1+p(2)*norm(h(2))^2/(1+Interference(2))) >= R_min
is o.k. as is because Interference(2) = 0.

However, the MAC constraints violate the DCP rules, and will be rejected by CVX. Why isn't CVX accepting my model? READ THIS FIRST! . The 2nd of these MAC constraint trivially holds, and so can be eliminated.

However, the first MAC constraint is non-convex; if the constraint is formulated as LHS - RHS <= 0, then LHS -RHS has 2nd derivative with respect to p(1) being either positive or negative for various values of p(1) >= 0; therefore it is non-convex I haven’t checked the convexity of the 3rd of the MAC constraints.

Those constraints are not convex. The right-hand sides are indefinite, i.e., neither convex nor concave. The numerators inside the log are “going the wrong way”.