CVX answer in difference from article

1

Hello;
I’m new in CVX.
I wrote a code of a convex problem and I get answer.
but my objected function respect to answer is way difference from article.
this is my code:

M = 5;
UE = 2;
d = randi([1 50],1,UE);
beta = 3.8;
R_min = [1, 1.5, 2, 2.5, 3];
gamga_min=2.^R_min-1;
N0 = 0.01;
power = zeros(length(R_min),1);
h = (sqrt(1/2)*complex(randn(M,UE),randn(M,UE))).*sqrt(d.^(-beta));
[hs, hi] = sort(vecnorm(h));
h = h(:,hi);
for i=1:length(R_min)
    cvx_clear
    cvx_begin
    variable W(M,M,UE) hermitian semidefinite
    trace_W = 0;
    for ii=1:UE
        trace_W = trace_W + trace(W(:,:,ii));
    end
    minimize(trace_W)
    subject to
    for k=1:UE
        s = 0;
        for l=k:UE 
            H = h(:,l)*h(:,l)';
            for m=k+1:UE    
                s = s + trace(H*W(:,:,m));
            end
            real(trace(H*W(:,:,k)))>=gamga_min(i)*(real(s)+N0); %#ok<VUNUS>
        end
    end
    cvx_end
    power(i) = trace_W;
end
disp(power)
plot(R_min, power)

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but power output is in range of 10e4 for different R_min and in article the answer is in range of 10
this is optimization problem in artilce:
Screenshot (101)
can you please help me.

2 Likes
2

There is variation in result depending on random numbers. Running it 10 times with different random number draws, here are the low and the high resulting power values:

Low:
10.518550073421324
19.618560360573895
33.730709087357205
57.006863758977957
97.909538362361900

High:
1.0e+05 *
0.143430836355955
0.308233930137237
0.625969817029513
1.264125990435457
2.549542044221298

The high is more than 3 orders of magnitude greater than the low. So aside from any differences in the program and whether it was implemented correctly by you and/or the article authors, obviously the input data values matter in your program…

1 Like
3

Thanks for your help
there is another optimization in this article that should have same result as this one.
In comparison of these two methods this one does not give right answer all the time (with same random numbers)
and also add more constraint to problem to control “The high”, did not help.
is there anything else that can solve this issue?

1 Like
4

That description it too vague to be actionable.

1 Like
5

thank you for your help