Performance Analysis of RIS-Assisted Full-Duplex Communication Over Correlated Nakagami-<inline-formula><tex-math notation="LaTeX">$m$</tex-math></inline-formula> Fading Channel

In this article, we investigate the performance of a reconfigurable intelligent surface (RIS) assisted full-duplex (FD) communication network, where each user is facilitated by a specific RIS in the network. The correlated Nakagami-<inline-formula><tex-math notation="LaTeX">$m$</tex-math></inline-formula> fading channel is first considered in a RIS system, which is a general channel model that can capture the spatial correlation effect inherent in the RIS-assisted communication system. Using the two-dimensional Laplace transform and its inverse, the closed form expressions of the mean and variance of the signal power distribution are obtained. Then, the outage probability and average achievable rates of the uplink and downlink users are derived in closed form. Furthermore, the impact of the residual self-interference (SI) on FD communication performance is discussed. It is demonstrated that FD communication outperforms HD communication when the residual SI is below a threshold, and the threshold is derived in closed form. Simulation results are presented to confirm the accuracy of the theoretical analysis and show the negative impact of channel correlation on the system performance. Moreover, it is illustrated that the outage probability and the average achievable rate of the uplink user will converge to a constant when the residual SI is linearly dependent on the transmit power.