Robust Beamforming for BDMA Massive MIMO

In this paper, we design robust downlink beamforming against the imperfect channel state information (CSI) for beam division multiple access (BDMA) massive multiple-input multiple output (MIMO) systems. Different from conventional approach, the optimality of semi-definite relaxation (SDR) is strictly proved by showing the rank-one property of the optimal beamforming with the orthogonal BDMA massive channels, where globally optimal robust beamforming solutions are derived. More importantly, we make one step further by deriving the optimal beamforming directions and optimal beamforming power allocation of the SDR in closed-form, which greatly reduces the optimization complexity and makes the proposed design practical for a real word massive MIMO system. Simulation results are provided to demonstrate the efficiency of the proposed algorithm.