Asymptotic SEP Analysis for Correlated Large MIMO Channels with ZF-DF Detection

In this paper, we consider correlated multiple-antenna communication systems having $M$ transmitter antennas and $N$ receiver antennas ($M \leq N$) with a zero-forcing (ZF) decision-feedback (DF) detector. We assume that the full knowledge of channel state information is available at the receiver and only the first- and the second-order channel statistics are known at the transmitter.By scaling up the antenna array size of both terminals without bound for such multiple-antenna systems, we propose a novel method based on the Szeg$\ddot{\text{o}}$'s theorem and the well-known limit $\lim_{x\to \infty} (1+1/x)^x=e$ to analyze the asymptotic behaviour on the error performance of an equal-diagonal QRS precoded large MIMO system when employing an abstract Toeplitz correlation model. This new approach bears a simple expression with a fast convergence rate and thus, is efficient and effective for error performance evaluation. Then, the impact of channel correlation on the error performance is studied for different correlation coefficients. In addition, an explanation of this approach in terms of the entropy power of the channel is also provided. Finally, computer simulations are carried out to verify our analysis in comparison with a uniform power allocation strategy.