Successive convex approximation for system performance optimization in a multiuser network with multiple mimo relays

We consider the problem of jointly optimizing amplify-and-forward (AF) multiple-input multiple-output (MIMO) relays and single-antenna receivers for multipoint-to-multipoint (MP2MP) communications using weighted summean-square-error (MSE) as a system performance measure. This optimization problem is nonconvex and the optimal solution cannot be obtained in polynomial time. By applying first-order approximation for the quadratic term, we show that this problem can be approximately reformulated as a semidefinite programming (SDP) problem, which is then solved successively in an iterative way. The performance of the proposed scheme is compared with the lower bound (LB) of the global optimal solution that is obtained with increased complexity using the MSE-profile approach, and the bisection and semidefinite relaxation (SDR) techniques. Numerical results show that the performance of the proposed successive convex approximation (SCA) approach is very close to the LB of the global optimal solution and is much better than the zero-forcing MIMO relays.