Non-Asymptotic Outage Probability of Large-Scale MU-MIMO Systems with Linear Receivers

Abstract

This paper considers the uplink of a single-cell large-scale multiuser multiple-input multiple-output (MU-MIMO) system. The transmitted data is detected by linear receivers at the base station (BS), that is, maximum ratio combining (MRC), zero-forcing (ZF) and minimum mean square error (MMSE). New non-asymptotic outage expressions that are valid for any number of BS antennas are derived. It is shown that the MMSE scheme always achieves the best outage performance, and the ZF scheme outperforms the MRC scheme in the high signal-to-noise-ratio (SNR) regime, while the opposite holds in the low SNR regime. We also demonstrate that when the number of BS antennas is very large and the number of users is fixed, the asymptotic outage probability tends to zero, providing that the channel state information (CSI) is perfect. However, if both the number of BS antennas and the number of users grow large, it would be a different matter. Extensive numerical results are presented to verify the theoretical analysis.