Hello, everyone,

My problem is a quadratically constrained quadratic program (QCQP) and can be find as follows:

min V’ * P * V

s.t. **sum( V’ * A_i * V ) >=0, i=1,…,m** (1)

sum( V’ * B_j * V ) <=0, j = 1,…n

Trace( V * V’ ) >0

where P,A_i,B_j are positive semidefinite. V is a N * 1 vector.

My question is that I can use **SDP method** to solve this problem and get Q=V * V’, and then decompose Q to get x in order to get the mmse receiving beamformer Ummse. However, the problem is that Q are often **full rank** according to my simulation results via with the aid of cvx tools. This will conflict with **Rank(Q)=1**.

If there is no (1), I can solve this QCQP via cvx instead of SDP method . However, since the first constraint is a convex >=0, perhaps the problem above is nonconvex one. How to relax it or deal with it in that case?

I will be appreciated if anyone can transform it to a convex problem which can be solved via the aid of cvx tools.

Look forward to your reply!

Jules

Edit by MLS: Corrected typo in thread title from “concave” to “convex”.