Optimal receive array beamforming for non-collaborative MIMO space division multiple access

In this paper, multi-user multiple input multiple output (MIMO) beamforming techniques with reduced overhead compared to hitherto known works are examined. In previous works, the subscriber station (SS) feeds back the entire channel matrix to the base station (BS) and the BS designs its zero-forcing transmit beamformer and each user´s receive beamformer, and feeds forward each user its respective receive beamformer. In this paper, each SS designs its receive beamformer using only its own channel and independent of the other user´s channels and feeds back only a vector this framework is called non-collaborative. Assuming zero-forcing beamforming (ZFBF) with a single stream to each SS, we derive the optimal receive beamformer using the average SNR metric and determine the feedback vector based on this optimal receive beamformer. We show that the average receive SNR per user degrades linearly with increasing number of users assuming isotropically distributed MIMO channels and that the dominant right singular vector of the channel matrix is the optimal SS receive beamformer. This optimality holds even when the MIMO channels are correlated. Furthermore, we propose a receive beamformer design in the presence of external interference which can be caused due to aggressive time-frequency reuse in neighboring cells.