Effective beamforming and efficient scheduling for multi-user MIMO broadcast channels

In this paper, we focus on multi-user MIMO broadcast channels with few users feeding back their channel estimates, i.e. K linear in the number M of transmitting antennas. Under this condition, the chance of finding a subset of users almost orthogonal vanishes when M gets large. For this reason, we show that the zero forcing (ZF) beamformer, commonly accepted for practical implementations, can be easily outperformed by other schemes based on QR decomposition, approaching the channel capacity. Our beamformer construction is less complex than ZF greedy algorithms and more robust than semi-orthogonal construction. At high SNR, we show that even the sub-optimal Tomlinson-Harashima encoding technique outperforms the ZF beamforming, halving the gap with respect to dirty paper coding.