Alternating maximization algorithm for the broadcast beamforming

Semidefinite relaxation (SDR) is a powerful approach to solve nonconvex optimization problems involving rank condition. However its performance becomes unacceptable for certain cases. In this paper, a nonconvex equivalent formulation without the rank condition is presented for the broadcast beamforming problem. This new formulation is exploited to obtain an alternating optimization method which is shown to converge to the local optimum rank one solution. Proposed method opens up new possibilities in different applications. Simulations show that the new method is very effective and can attain global optimum especially when the number of users is low.