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, wherea
s 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.
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 beamfo
rming (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.
Training-based transmission over Rayleigh block-fading multiple-input multiple-output (MIMO) channels is investigated. As a training method a combination of a pilot-assisted scheme and a biased signaling scheme is considered. The achievable rates of
successive decoding (SD) receivers based on the linear minimum mean-squared error (LMMSE) channel estimation are analyzed in the large-system limit, by using the replica method under the assumption of replica symmetry. It is shown that negligible pilot information is best in terms of the achievable rates of the SD receivers in the large-system limit. The obtained analytical formulas of the achievable rates can improve the existing lower bound on the capacity of the MIMO channel with no channel state information (CSI), derived by Hassibi and Hochwald, for all signal-to-noise ratios (SNRs). The comparison between the obtained bound and a high SNR approximation of the channel capacity, derived by Zheng and Tse, implies that the high SNR approximation is unreliable unless quite high SNR is considered. Energy efficiency in the low SNR regime is also investigated in terms of the power per information bit required for reliable communication. The required minimum power is shown to be achieved at a positive rate for the SD receiver with no CSI, whereas it is achieved in the zero-rate limit for the case of perfect CSI available at the receiver. Moreover, numerical simulations imply that the presented large-system analysis can provide a good approximation for not so large systems. The results in this paper imply that SD schemes can provide a significant performance gain in the low-to-moderate SNR regimes, compared to conventional receivers based on one-shot channel estimation.
