Optimal beamforming for single group multicast systems based on weighted sum rate

In this paper, a novel optimization objective namely weighted sum rate is proposed for beamformer design in single group multicast systems. As an upper bound and special case of maximizing minimum rate, it can overcome previous disadvantages of computation complexity and sensitivity to channel state when the weights are chosen properly. Although the corresponding optimization problem is nonconvex, some properties of the optimal solution and closed-form solutions under some usual special cases are derived. In addition, an iterative algorithm with low computation complexity for general case is proposed. Simulation results show that the beamformer obtained by the iterative algorithm not only improves the minimum rate and average rate, but also gets better fairness and overall performance compared with previous schemes.