Multiple RISs-Aided Networks: Performance Analysis and Optimization

This paper analyzes the performance of multiple reconfigurable intelligent surfaces (RISs)-aided networks. The paper also provides some optimization results on the number of reflecting elements on RISs and the optimal placement of RISs. We first derive accurate closed-form approximations for RIS channels' distributions assuming independent non-identically distributed (i.ni.d.) Nakagami-\emph{m} fading environment. Then, the approximate expressions for outage probability (OP) and average symbol error probability are derived in closed-form. Furthermore, to get more insights into the system performance, we derive the asymptotic OP at the high signal-to-noise ratio regime and provide closed-form expressions for the system diversity order and coding gain. Finally, the accuracy of our theoretical analysis is validated through Monte-Carlo simulations. The obtained results show that the considered RIS scenario can provide a diversity order of $\frac{a}{2}K$, where $a$ is a function of the Nakagami fading parameter $m$ and the number of meta-surface elements $N$, and $K$ is the number of RISs.