Large-System Analysis of Joint User Selection and Vector Precoding for Multiuser MIMO Downlink

Joint user selection (US) and vector precoding (US-VP) is proposed for multiuser multiple-input multiple-output (MU-MIMO) downlink. The main difference between joint US-VP and conventional US is that US depends on data symbols for joint US-VP, whereas conventional US is independent of data symbols. The replica method is used to analyze the performance of joint US-VP in the large-system limit, where the numbers of transmit antennas, users, and selected users tend to infinity while their ratios are kept constant. The analysis under the assumptions of replica symmetry (RS) and 1-step replica symmetry breaking (1RSB) implies that optimal data-independent US provides nothing but the same performance as random US in the large-system limit, whereas data-independent US is capacity-achieving as only the number of users tends to infinity. It is shown that joint US-VP can provide a substantial reduction of the energy penalty in the large-system limit. Consequently, joint US-VP outperforms separate US-VP in terms of the achievable sum rate, which consists of a combination of vector precoding (VP) and data-independent US. In particular, data-dependent US can be applied to general modulation, and implemented with a greedy algorithm. Index Terms Multiuser multiple-input multiple-output (MU-MIMO) downlink, Multiple-input multiple-output broadcast channel (MIMOBC), zero-forcing transmit beamforming, user selection, vector precoding, energy penalty, achievable rate, large-system analysis, order statistics, statistical physics, replica method, replica symmetry breaking (RSB).