Analysis of RIS-Aided Communications Over Nakagami-$m$ Fading Channels

Reconfigurable intelligent surface (RIS) has been attracted lots of attention due to the fact that it can reconfigure propagation environment with low cost for resource-constrained systems. In this article, RIS is considered to support wireless communication system by taking both reflection path and direct path into consideration and investigate the system performance under general Nakagami-
$m$
fading. A novel analytical closed-form expression is first derived for outage probability. To get more insights, we provide simplified approximations for the high SNR regime and obtain the diversity order and coding gain in closed form. We demonstrate that
$\sum _{l = 1}^{N + 1} {m_{l}^*}$
diversity order which can be obtained by RIS-assisted system, where
$N$
is the number of reflect elements in the RIS and
${m_{l}^*}$
refers to the channel fading parameters. Furthermore, we investigate the performance of ergodic achievable rate and provide tight bounds for it in closed form. Based on these results, high SNR slope is discussed. Notably, our analytical results are suitable for any integer fading parameters and arbitrary topologies, transmit power. Numerical results validate the accuracy of our analytical results and show the great performance improvement provided by the RIS-assisted system.