Average Vector-Symbol Error Rate Closed-Form Expression for ML Group Detection Receivers in Large MU-MIMO Channels with Transmit Correlation

In this paper, we derive a closed-form expression for the evaluation of the average vector-symbol error rate (VER) of group detection followed by maximum-likelihood (GD-ML) receivers in large multi-user multiple-input multiple-output (MU-MIMO) systems with transmit side correlated Rayleigh channels. We assume M antennas at the base station (BS), N closely-located, single-antenna user equipment (UEs) with load factor λ = NM, and Ngg 1; consequently, we evaluate the performance of GD-ML receivers as the load factor grows to unity. The derived expression requires a negligible correlation at the receive side of the communication channel. Hence, from a practical point-of-view, when considering scenarios with a large number of UEs, the derived analytical expression is generally more applicable for systems with a distributed massive number of BS antennas. Numerical results are provided to validate our derived expression. We observe that the GD-ML with N_u group size achieves a diversity order proportional to M-N+N_u. Moreover, we show that for small group sizes, the analytical and simulation results remain close, and at moderate to high signal-to-noise ratio (SNR), the derived expression very closely matches the simulations, whereas this match becomes perfect as the users' side correlation increases. We also demonstrate that GD-ML outperforms the zero-forcing (ZF) and minimum mean-squared error (MMSE) receivers, in terms of VER; where for high λ, GD-ML exploits the maximum spatial multiplexing gain. Moreover, in terms of floating-point operations (FLOPs), we show that GD-ML receivers have almost the same complexity as ZF and MMSE where the ML detection stage adds a negligible complexity compared to the channel matrix inversion operation.