Reconfigurable intelligent surfaces (RISs) consisting of multiple reflective elements are a promising technique to enhance communication quality as they can create favorable propagation conditions. In this letter, we characterize the fundamental relations between the number of reflective elements and the system sum-rate in RIS-assisted multi-user communications. It is known from previous works that the received signal-to-noise ratio (SNR) can linearly increase with the squared number of RIS reflective elements, but how many elements are sufficient to provide an acceptable system sum-rate still remains an open problem. To this end, we derive the asymptotic capacity with zero-forcing (ZF) precoding, and then analyze how many reflective elements are required so that the ratio of the system sum-rate to the capacity can exceed a predefined threshold. Numerical results verify our analysis.

中文翻译：

---

可重构智能表面辅助多用户通信：我们需要多少个反射元件？

由多个反射元件组成的可重配置智能表面（RIS）是提高通信质量的一种有前途的技术，因为它们可以创建有利的传播条件。在这封信中，我们描述了RIS辅助的多用户通信中反射元件的数量与系统求和率之间的基本关系。从以前的工作中知道，接收到的信噪比（SNR）可以随RIS反射元件的平方数线性增加，但是多少个元件足以提供可接受的系统总速率仍然是一个悬而未决的问题。为此，我们使用零强制（ZF）预编码导出渐近容量，然后分析需要多少个反射元素，以便系统求和率与容量之比可以超过预定义的阈值。