Transmit beamforming for MIMO multicast channels

Consider a MIMO multicast channel where a multi-antenna base station (BS) sends common messages to K multi-antenna users. Assuming that the channel state information (CSI) of the K users are known at the BS, we study the optimal downlink rank-one beamforming which maximizes the postprocessing SNRs of the bottleneck users. We first study the special case where the BS has two transmit antennas. Denoting γ ϵ R^K as a vector consisting of the SNRs of the K users, we derive the closed-form expression of the feasible set of γ as a two-dimension ellipsoid embedded in a K-dimension space. Based on this observation, we develop a prune and search algorithm (PASA) which guarantees to find a global optimal Tx beamforming vector and meanwhile is computationally faster than the existing suboptimal algorithms. For the general case where the BS has an arbitrary number of Tx antennas, we leverage the two-antenna result and propose an iterative 2-dimensional optimization (I2DO) method, which at each iterative step transforms the original problem into the two-antenna one and improves the solution using PASA. The simulation results show that the proposed methods outperform the existing ones in both performance and complexity.