A reverse convex programming for beamforming in cognitive multicast transmission

The cognitive beamforming problems are naturally formulated as indefinite quadratic (nonconvex) optimization programs. The typical methods for solving such optimization problems are to transform them into convex semi-definite programs (SDPs) with additional rank-one (nonconvex and discontinuous) constraints. The rank-one constraints are then dropped to obtain solvable SDP relaxed problems and randomization techniques are employed for seeking the feasible solutions to the original nonconvex optimization problems. In many practical cases, these approaches fail to deliver satisfactory solutions, i.e., their solutions are very far from the optimal ones. In contrast, in this paper the rank-one constraints are equivalently expressed as reverse convex constraints and are incorporated into the optimization problems. Then, we propose an efficient iterative algorithm for solving the nonsmooth reverse convex optimization problems. Our simulations show that our proposed approach yields nearly global optimal solutions with much less computational load as compared to the conventional one.