Towards an optimal beamforming algorithm for physical layer multicasting

The increasing popularity of applications involving group communications in wireless networks has led to the need for efficient multicasting solutions. The ability of smart antennas to beamform and hence improve the signal quality at the clients has made them especially attractive for multicasting applications. Unfortunately, the problem of multicast beamforming design is a non-convex optimization problem for which only suboptimal solutions has been proposed in the literature. In this work, we uncover a hidden convexity of the problem under certain channel conditions which happens frequently for practical systems with Rayleigh fading channel model. We propose a solution based on this observation which consists of two steps: (1) we solve the dual problem and check for a uniqueness condition; if satisfied, we show that the duality gap is zero and the solution of the primal problem is obtained based on the solution of the dual problem; (2) if the uniqueness condition is not satisfied, we use a gradient descent based approach. Our evaluations reveal that the proposed algorithm significantly improves the multicast performance over state-of-the-art solutions. Simulation results show that in most scenarios of interest the algorithm converges within a required limit in the first step with high probability. We also obtain the performance bounds for the primal problem based on the dual formulation.