Large-system analysis of joint user selection and vector precoding with zero-forcing transmit beamforming for MIMO broadcast channels

Multiple-input multiple-output (MIMO) broadcast channels (BCs) (MIMO-BCs) with perfect channel state information (CSI) at the transmitter are considered. As joint user selection (US) and vector precoding (VP) (US-VP) with zero-forcing transmit beamforming (ZF-BF), US and continuous VP (CVP) (US-CVP) and data-dependent US (DD-US) are investigated. The replica method, developed in statistical physics, is used to analyze the energy penalties for the two US-VP schemes in the large-system limit, where the number of users, the number of selected users, and the number of transmit antennas tend to infinity with their ratios kept constant. Four observations are obtained in the large-system limit: First, the assumptions of replica symmetry (RS) and 1-step replica symmetry breaking (1RSB) for DD-US can provide acceptable approximations for low and moderate system loads, respectively. Secondly, DD-US outperforms CVP with random US in terms of the energy penalty for low-to-moderate system loads. Thirdly, the asymptotic energy penalty of DD-US is indistinguishable from that of US-CVP for low system loads. Finally, a greedy algorithm of DD-US proposed in authors´ previous work can achieve nearly optimal performance for low-to-moderate system loads.