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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) withzero-forcing transmit beamforming (ZF-BF), US and continuous VP (CVP) (US-CVP)and data-dependent US (DD-US) are investigated. The replica method, developedin statistical physics, is used to analyze the energy penalties for the twoUS-VP schemes in the large-system limit, where the number of users, the numberof selected users, and the number of transmit antennas tend to infinity withtheir ratios kept constant. Four observations are obtained in the large-systemlimit: First, the assumptions of replica symmetry (RS) and 1-step replicasymmetry breaking (1RSB) for DD-US can provide acceptable approximations forlow and moderate system loads, respectively. Secondly, DD-US outperforms CVPwith 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 thatof US-CVP for low system loads. Finally, a greedy algorithm of DD-US proposedin authors' previous work can achieve nearly optimal performance forlow-to-moderate system loads.

Large-System Analysis of Joint User Selection and Vector Precoding with Zero-Forcing Transmit Beamforming for MIMO Broadcast Channels