I persume it is log_det(Omega_o) leads to this problem, where Omega_o is a matrix optimization variable

Anyone knows how to solve this problem, thank you bery much.

Code:

cvx_begin

variable R_Int_o(RRH_Num * RRH_Ant,RRH_Num * RRH_Ant) complex

variable R_User_o(RRH_Num * RRH_Ant,RRH_Num * RRH_Ant,UE_Num) complex

% variable R_Radar_o(RRH_Num * RRH_Ant, RRH_Num * RRH_Ant * RRH_Num * RRH_Ant) complex

variable alpha_o

variable Omega_o(RRH_Num

*RRH_Ant,RRH_Num*RRH_Ant) complex

expression obj_sub1

obj = 0;

for grid = 1 : Tot_Grid

obj_sub1 = obj_sub1 + real( pow_abs(a_Steer(:,grid)’ * Theta_temp * Cas_IR_G * R_Int_o * Cas_IR_G’ * Theta_temp’ * a_Steer(:,grid) - alpha_o * Des_Beam(grid),2) );

end

minimize 1 / Tot_Grid * obj_sub1

subject to

```
(R_Int_o - sum(R_User_o,3) - Omega_o) == hermitian_semidefinite(RRH_Num * RRH_Ant)
R_Int_o == hermitian_semidefinite(RRH_Num * RRH_Ant)
for r = 1 : RRH_Num
real( trace(R_Int_o( (r-1)*RRH_Ant+1 : r*RRH_Ant , (r-1)*RRH_Ant+1 : r*RRH_Ant) ) ) == PR_mW
end
for ue = 1 : UE_Num
(1 + Tau^-1) * real( Int_Cha(ue,:) * R_User_o(:,:,ue) * Int_Cha(ue,:)' ) - real( Int_Cha(ue,:) * R_Int_o * Int_Cha(ue,:)' ) - n_sigma >= 0;
R_User_o(:,:,ue) == hermitian_semidefinite(RRH_Num * RRH_Ant);
end
for r = 1 : RRH_Num
real(log_det(Sigma(:,:,r))) - RRH_Ant ...
+ real(trace( Sigma(:,:,r) \ R_Int_o( (r-1)*RRH_Ant+1:r*RRH_Ant,(r-1)*RRH_Ant+1:r*RRH_Ant ) ))...
-real(log_det(E(:,:,r)' * Omega_o * E(:,:,r)))- C_l_ <= 10^-10;
end
Omega_o == hermitian_semidefinite(RRH_Num * RRH_Ant)
cvx_end
```