In this letter, we consider a network assisted by multiple reconfigurable intelligent surfaces (RISs). Assuming that the RIS with the highest instantaneous end-to-end signal-to-noise ratio (SNR) is selected to aid the communication, the outage probability (OP) and average sum-rate are investigated. Specifically, an exact analysis for the OP is developed. In addition, relying on the extreme value theory, a closed-form expression for the asymptotic sum-rate is derived, based on which the capacity scaling law is established. Our results are corroborated through simulations and insightful discussions are provided. In particular, our analysis shows that the number of RISs as well as the number of reflecting elements play a crucial role in the capacity scaling law of multiple RIS-aided networks. Also, comparisons with relay-aided systems are carried out to demonstrate that the proposed system setup outperforms relaying schemes both in terms of the OP and average sum-rate.

中文翻译：

---

多个RIS辅助网络的中断概率和容量缩放定律

在这封信中，我们考虑了由多个可重新配置的智能表面（RIS）辅助的网络。假设选择了具有最高瞬时端到端信噪比（SNR）的RIS来辅助通信，则会研究中断概率（OP）和平均求和率。具体而言，为OP开发了精确的分析。另外，根据极值理论，推导了渐近求和率的闭式表达式，在此基础上建立了容量缩放定律。模拟结果证实了我们的结果，并提供了深入的讨论。特别是，我们的分析表明，RIS的数量以及反射元素的数量在多个RIS辅助网络的容量缩放定律中起着至关重要的作用。还，