Reconfigurable intelligent surface (RIS) is a promising solution to build a programmable wireless environment with reconfigurable passive elements, which can achieve high spectral and energy efficiency. In this paper, we investigate the ergodic capacity of RIS-assisted multi-user multiple-input single-output (MISO) wireless systems in both uplink and downlink scenarios. Unlike most of prior works, where instantaneous channel state information (CSI) is assumed, we consider the realistic scenario with only statistical CSI. For both scenarios, we first present an analytical expressions for the ergodic sum capacity of the system. Based on which, the joint power control (or transmit beamforming) and phase shift design problem maximizing the ergodic sum capacity is formulated. Capitalizing on the alternating direction method of multipliers (ADMM), fractional programming (FP) and alternating optimization (AO) methods, efficient suboptimal solutions are obtained for the non-convex design problems. Simulation results are presented to validate the accuracy of the analytical ergodic sum capacity expressions and evaluate the impact of key system parameters such as CSI, Rician $K$ factor, number of RIS elements, and RIS location on the ergodic capacity performance. The findings suggest that the proposed statistical CSI design achieves decent performance compared with the instantaneous CSI based design. Moreover, a signal hot spot can be created when placing the RIS close to the users.

中文翻译：

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利用统计 CSI 的 RIS 辅助多用户 MISO 通信

可重构智能表面 (RIS) 是一种很有前景的解决方案，可构建具有可重构无源元件的可编程无线环境，可实现高光谱和能量效率。在本文中，我们研究了 RIS 辅助多用户多输入单输出 (MISO) 无线系统在上行链路和下行链路场景中的遍历容量。与假设瞬时信道状态信息 (CSI) 的大多数先前工作不同，我们考虑仅具有统计 CSI 的现实场景。对于这两种情况，我们首先给出系统遍历总容量的解析表达式。在此基础上，提出了使遍历和容量最大化的联合功率控制（或发射波束成形）和相移设计问题。利用乘法器的交替方向法（ADMM），分数规划（FP）和交替优化（AO）方法，为非凸设计问题获得了有效的次优解。仿真结果用于验证分析遍历和容量表达式的准确性，并评估关键系统参数（如 CSI、Rician）的影响 $K$ RIS 元素的数量和 RIS 位置对遍历容量性能的影响。研究结果表明，与基于瞬时 CSI 的设计相比，所提出的统计 CSI 设计实现了不错的性能。此外，当将 RIS 放置在靠近用户的位置时，可以创建信号热点。