I am regenerating the results of a paper published in IEEE transactions in Array signal processing where they used CVX to solve a convex optimization problem. They are minimizing the following function

among them,R^-1Is the known matrix of the input,T is hermitian toeplitz matrix, X is complex matrix.

I tried many ways to formulate this problem using CVX. none of them scceeded.

e.g.

cvx_begin sdp

variable delta_k(sensor_num,1) ;

variable T(sensor_num,sensor_num) hermitian toeplitz ;

variable X(sensor_num,sensor_num) complex ;

minimize (trace(R_tlide_inv*T)+trace(R_tlide_inv*diag(delta_k))+trace(X))

subject to

[X , R_tlide_half ; R_tlide_half , T+diag(delta_k)] == hermitian_semidefinite(2*sensor_num);

T == hermitian_semidefinite(sensor_num);

diag(delta_k)== semidefinite(sensor_num);

cvx_end

But I obtain following error

Error using minimize (line 36)

Disciplined convex programming error:

Cannot minimize a(n) complex affine expression.

Error in CVX_fun(line 26)

minimize (trace(R_tlide_inv*T)+trace(R_tlide_inv*diag(delta_k))+trace(X)) .

I dont know how to solve this. Can some one help?

Sincere thanks