I want to solve this problem

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Sitthipong on 1 Jul 2022
Commented: Torsten on 6 Jul 2022
The constraints are not convex so cvx is inapplicable. (I tried CVX previously.)
I am thinking of using matlab optimization toolbox. I tried the following codes but they failed.
Nt = 4 ;
M = 64 ;
Gamma_R = 10^(3/10);
Gamma_T = 10^(3/10);
gamma_r = 0 ;
gamma_t = 0 ;
noise_variance_dBm = -70;
noise_variance = 10^(-70/10)*1E-3 ;
h_r =(randn(M,1)+1i*randn(M,1))/sqrt(2);
h_t =(randn(M,1)+1i*randn(M,1))/sqrt(2);
h_d =(randn(Nt,1)+1i*randn(Nt,1))/sqrt(2);
Phi_r =(diag(diag(rand(M,M)+1i*rand(M,M))))/sqrt(2);
Phi_t =(diag(diag(rand(M,M)+1i*rand(M,M))))/sqrt(2);
for n = 1:length(Nt)
N = Nt(n);
G = (randn(M,N)+1i*randn(M,N))/sqrt(2);
theta_r = zeros(M,M) ;
theta_t = zeros(M,M) ;
zeta = zeros(M,M) ;
a_r = [h_r'*Phi_r*G+h_d' , h_r'*Phi_r*G+h_d']*[eye(Nt), zeros(Nt,Nt);zeros(Nt,Nt),zeros(Nt,Nt)]; %.*[2*Nt,2*Nt] ;
a_t = [h_r'*Phi_r*G+h_d' , h_r'*Phi_r*G+h_d']*[zeros(Nt,Nt), zeros(Nt,Nt);zeros(Nt,Nt),eye(Nt)]; %.*[2*Nt,2*Nt] ;
b_r = [h_t'*Phi_t*G , h_t'*Phi_t*G ]*[eye(Nt), zeros(Nt,Nt);zeros(Nt,Nt),zeros(Nt,Nt)] ;
b_t = [h_t'*Phi_t*G , h_t'*Phi_t*G ]*[zeros(Nt,Nt), zeros(Nt,Nt);zeros(Nt,Nt),eye(Nt)] ;
Asc = a_r;
bsc = sqrt(Gamma_R)*sqrt(abs(a_t).^2 + noise_variance^2);
dsc = 0;
gamma = 0 ;
conecons(2) = secondordercone(Asc,bsc,dsc,gamma);
Error using assert
Number of columns in the first argument must equal the number of elements in the third argument.

Error in secondordercone (line 13)
assert(numel(d) == size(A, 2), message('optim:coneprog:SizeMismatchColsOfSocAandD'));
Does anyone have ideas how Matlab toolboxes can be used to solve the problem or how the problem can be solved with matlab based libraries?
Torsten on 6 Jul 2022
Include your code - we cannot run a graphics snapshot.

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Answers (1)

Alan Weiss
Alan Weiss on 1 Jul 2022
You can use secondordercone by making a new variable m, a linear objective m, and another second-order cone constraint:
Minimize m such that .
You have to be careful when using complex numbers. Optimization toolbox solvers generally don't work well with complex numbers. Please check that you are satisfying the assumptions of the toolbox.
Good luck,
Alan Weiss
MATLAB mathematical toolbox documentation


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