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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.

This letter investigates the impact of co-channel interference (CCI) on the performance of a decode-and-forward (DF) relaying network with a reconfigurable intelligent surface (RIS)-assisted source. We consider one source, multiple DF relays, and one destination with CCI at both the relays and destination. We derive closed-form accurate approximations for the system outage probability assuming Rayleigh fading channels. In addition, we study the system performance at the high signal-to-noise ratio (SNR) regime, where closed-form expressions are derived for the asymptotic outage probability, diversity order, and the coding gain. The results show that the number of reflecting elements N at the source has a small effect on the coding gain of the system and not on the diversity order. Furthermore, findings illustrate that the number of relays K is affecting the diversity order and is more impactful on the performance than N. Finally, results show that utilizing RIS at the source node mitigates the interference effect at the relay nodes.

This work studies and optimizes the performance of reconfigurable intelligent surface (RIS)-aided networks in Nakagami-m fading environment. First, accurate closed-form approximations for the channel distributions are derived. Then, closed-form formulas for the system outage probability, average symbol error probability (ASEP), and the channel capacity are obtained. Furthermore, we provide three different optimization approaches for finding the optimum number of reflecting elements to achieve a target outage probability. At the high signal-to-noise ratio (SNR) regime, a closed-form expression for the asymptotic outage probability is obtained to give more insights into the system performance. Results show that the considered system can achieve a diversity order of (a+1)/2, where a is a function of the Nakagami-m fading parameter m and the number of reflecting elements N. Moreover, findings show that m is more influential on the diversity order than N. Finally, the achieved expressions are applicable to non-integer values of m and any number of meta-surface elements N.