Optimum beamforming for MIMO multicasting

This paper investigates the transmit (Tx) beamforming design to maximize the throughput of a multiple-input multiple-output multicast channel, where common information is sent from the base station to K users simultaneously. This so-called max-min fair beamforming problem is known to be NP-hard. When the base station is equipped with two Tx antennas, we prove that the original complex-valued beamforming problem can be transformed into a real-valued problem and the globally optimal solution can be found by exhausting at most C1 K + C2 K + C3 K hypothesis tests. Moreover, a prune and search algorithm (PASA) is proposed for searching the optimal beamformer with computational complexityO(K3) in the worst case. When the base station has more than two Tx antennas, we develop an efficient algorithm named iterative two-dimensional optimization which converts the original beamforming problem into a series of two-antenna subproblems by iterations and hence, the beamformer is improved using PASA iteratively. Simulations results are presented to demonstrate the superior performance of the proposed algorithms.