The reconfigurable intelligent surface (RIS) technology allows one to engineer spatial diversity in complex cellular networks. This paper provides a framework for the system-level performance assessment of RIS-assisted networks and in particular downlink coverage probability and ergodic rate. To account for the inherent randomness in the spatial deployments of base stations (BSs) and RISs, we model the placements of the RISs as point processes (PPs) conditioned on the associated BSs, which are modeled by a Poisson point process (PPP). These RIS PPs can be adapted based on the deployment strategy. We focus on modeling the RISs as a Mat\'ern cluster process (MCP), where each RIS cluster is a finite PPP with support a disc centered on the association BS. We assume that the system uses the orthogonal frequency division multiplexing (OFDM) technique to exploit the multipath diversity provided by RISs. The coverage probability and the ergodic rate can be evaluated when RISs operate as batched powerless beamformers. The resulting analytical expressions provide a general methodology to evaluate the impact of key RIS-related parameters, such as the batch size and the density of RISs, on system-level performance. To demonstrate the framework's broad applicability, we also analyze a RIS placement variant where RISs are deployed around coverage holes. Numerical evaluations of the analytical expressions and Monte-Carlo simulations jointly validate the proposed analytical approach and provide valuable insights into the design of future RIS-assisted cellular networks.

翻译：可重构智能表面（RIS）技术使得在复杂蜂窝网络中构建空间分集成为可能。本文提出了一个用于RIS辅助网络系统级性能评估的框架，特别关注下行覆盖概率和遍历速率。为刻画基站（BS）与RIS空间部署的固有随机性，我们将RIS的布设建模为以关联基站为条件的点过程（PP），其中基站由泊松点过程（PPP）建模。这些RIS点过程可根据部署策略进行调整。我们重点将RIS建模为Matérn聚类过程（MCP），其中每个RIS聚类是一个有限PPP，其支撑集为以关联基站为中心的圆盘。假设系统采用正交频分复用（OFDM）技术以利用RIS提供的多径分集。当RIS作为无源批处理波束成形器工作时，可评估其覆盖概率与遍历速率。所得解析表达式提供了一种通用方法，用于评估关键RIS相关参数（如批处理规模与RIS密度）对系统级性能的影响。为证明该框架的广泛适用性，我们还分析了一种RIS布设变体，其中RIS部署于覆盖空洞周围。对解析表达式的数值评估与蒙特卡洛仿真共同验证了所提出的分析方法，并为未来RIS辅助蜂窝网络的设计提供了重要见解。