Hello, please if anyone could help me with this.
N=3;
h1=(1/sqrt(2))(randn(N,1)+1irandn(N,1));
sigma_ch = 0.05;
cvx_begin
variable w(N,1) complex
minimize(square_pos(norm(sqrtm(z_theta)*w,‘fro’)))
subject to
abs(h1’*w) /(norm(w,“fro”)*sigma_ch/sqrt(2))<=1;
cvx_end
I’m getting this error
“Disciplined convex programming error:
Cannot perform the operation: {convex} ./ {convex}”
I think is because of the ratio constraint. Is there a way to solve this with cvx?
I will assume that constraint, and therefore the optimization problem, are non-convex, unless you show otherwise.
z_theta is defined as follows:
theta_l = [-60,0,60];
a_theta_l = exp(1j2pi0.5(0:N-1)‘sin(theta_l));%steer vector
z_theta = Neye(N)-(a_theta_lctranspose(a_theta_l));
z_theta is is Hermitian semidefinite.
My objective function is trace(z_thetaw*w’) which i write as square_pos(norm(sqrtm(z_theta)*w,‘fro’))
This objective function is convex and the problem can be solved without any constraint. But when I add the constraint, I get the error.
This
abs(h1’*w) /(norm(w,“fro”)*sigma_ch/sqrt(2))<=1;
is not a convex constraint. How do you conclude it is convex?
@Deylos,
@Erling is correct. You need to carefully read the link in my previous post. If your background in convex analysis and optimization is not strong, perhaps read at least the first 5 chapters and solve some of the exercises in Convex Optimization – Boyd and Vandenberghe