  In this paper, we consider the multi-user detection problem in a
multiple-input multiple-output (MIMO) system, where the number of receive
antennas at the base station (BS) grows infinitely large. We propose a new
performance metric, called antenna efficiency, to characterize how fast the
vector error probability (VEP) decreases as the number of receive antennas
increases in the large system limit. We analyze the optimal maximum-likelihood
(ML) detector and the simple zero-forcing (ZF) detector and prove that their
antenna efficiency admits a simple closed form, which quantifies the impacts of
the user-to-antenna ratio, the signal-to-noise ratio (SNR), and the
constellation set on the VEP. Numerical results show that our analysis can well
describe the empirical detection error performance in a realistic massive MIMO
system.
