We provide accurate approximations of the sum-rate capacity of a time-division multiple access (TDMA) down-link, when a reconfigurable intelligent surface (RIS) assists the transmission from a single-antenna base station (BS) to K single-antenna user equipments (UEs). We consider the fading effects of both the direct (i.e., BS-to-UEs) and reflection (i.e, BS-to-RIS-to-UEs) links, by developing two approximations: the former one is based on hardening of the reflection channel for large values of the number Q of meta-atoms at the RIS; the latter one relies on the distribution of the sum of Nakagami variates and does not require channel hardening. Our derivations show the dependence of the sum-rate capacity as a function of both K and Q, as well as to establish a comparison with a TDMA downlink without an RIS. Numerical results corroborate the accuracy of the proposed approximations and the validity of the mathematical analysis.

翻译：本文针对单天线基站（BS）通过智能可重构表面（RIS）向K个单天线用户设备（UE）传输的时分多址（TDMA）下行链路，提供了总速率容量的精确近似表达式。为分析直视链路（即BS→UE）和反射链路（即BS→RIS→UE）的衰落效应，我们提出了两种近似方法：第一种基于RIS元原子数量Q较大时反射链路的硬化特性；第二种依赖于Nakagami变量之和的分布，无需信道硬化条件。推导结果揭示了总速率容量与K和Q的函数依赖关系，并与无RIS的TDMA下行链路进行了性能对比。数值结果验证了所提近似方法的准确性及数学分析的有效性。