Performance Analysis of RIS-assisted MIMO-OFDM Cellular Networks Based on Matern Cluster Processes

The Reconfigurable Intelligent Surface (RIS) technology is a promising physical-layer candidate for sixth-generation (6G) cellular networks. In this work, we provide a system-level performance assessment of RIS-assisted multi-input multi-output (MIMO) cellular networks in the downlink in terms of both the coverage probability and the ergodic rate. To accurately capture the random layouts of the spatial deployments of both Base Stations (BSs) and RISs, we propose a new stochastic geometry model for the RIS-assisted radio cellular system based on the Matern Cluster Process (MCP). This MCP model consists in adding randomly distributed RISs around BSs, whose placement is modeled as a Poisson Point Process (PPP). Two types of diversity are available in this model, namely, the multipath diversity provided by the multiple RISs and the antenna diversity provided by the multiple antenna receiver. The system employs the orthogonal frequency division multiplexing (OFDM) technique to modulate the former and employ the maximal ratio combining (MRC) technique at the receiver to exploit the latter. The coverage probability is then evaluated when considering RISs operating as batched powerless beamformers. Based on the analysis of the coverage probability, we further derive expressions for the ergodic rate. These analytical expressions provide a new methodology to evaluate the impact of randomly located RISs around the BSs, given the RIS-related parameters, such as the density, size, and cluster radius. Numerical evaluations of the analytical expressions and Monte-Carlo simulations jointly validate the proposed analytical approach and provide valuable insights into deploying RIS-assisted radio cellular networks.