I want to maximize this capacity function:
maximize(log_det(I + inv(sigma^2.I)HFH’)) subject to the constrains:
(1) trace(F) <= Pt should be a positive value
(2) trace(GFG’) <= Ith should be a positive value
such that:
(’): is the complex conjugate of a matrix
F : 12x12 is a variable complex hermitian positive definite matrix
I : is a 6x6 identity matrix
H : 6x12 is a constant matrix
G : 3x12 is a constant matrix
Pt: is a scalar constant
Ith: is a scalar constant
sigma: is a scalar constant
H & G were just randn complex matrices
the code is
Nr = 6;
Nt = 10;
Np = 3;
H = randn(Nr,Nt)+randn(Nr,Nt);
G = randn(Np,Nt)+randn(Np,Nt);
I = eye(Nr,Nr);
Pt = 10;
Ith = 1;
sigma = 5;
cvx_begin sdp
variable F(Nt,Nt) complex hermitian semidefinite
% variable F(Nt,Nt) symmetric semidefinite
minimize(-det_rootn(I+(5^-2.I)HFH’))
% minimize(-log_det(I+(5^-2.I)HFH’))
subject to
trace(GFG’) >=0;
trace(F) >=0;
trace(F) <= Pt;
trace(GFG’) <= Ith;
cvx_end
result:
Status: Unbounded
Optimal value (cvx_optval): -Inf