Performance of ED-Based Non-Coherent Massive SIMO Systems in Correlated Rayleigh Fading

In recent studies, a simple non-coherent communications' scheme based on energy detection is proposed for massive single-input multiple-output systems, where transmit symbols are decoded by averaging the received signal energy across all antennas. In this paper, we investigate the effect of correlated Rayleigh fading on the performance of the aforementioned systems. Specifically, we derive the analytical expressions of the symbol error rate, achievable rate, and outage probability. Furthermore, the asymptotic behaviors of these expressions in regimes of large numbers of receive antennas, high channel correlation, and high signal-to-noise ratio are investigated. The analytical results demonstrate the adverse impact of channel correlation on the error probability, which can be attributed to the fact that channel correlation reduces the degrees of freedom. Our analysis also shows that channel correlation poses little influence on the achievable rate. Besides, an upper bound of the achievable rate is given when the number of receive antennas goes to infinity. Finally, the numerical results are presented to verify our analysis.