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

Reconfigurable Intelligent Surfaces (RIS) technology are a promising physical-layer candidate for sixth-generation (6G) cellular networks. This paper provides a system-level performance assessment of RIS-assisted multi-input multi-output (MIMO) cellular networks in terms of downlink coverage probability and ergodic rate. To capture the inherent randomness in the spatial deployments of both Base Stations (BSs) and RISs, we propose a new stochastic geometry model for such systems based on the Matern Cluster Process (MCP). This model consists in randomly distributed RISs around BSs, whose placement is according to a Poisson Point Process (PPP). The RISs provide the multipath diversity and the multiple antenna receiver provide the antenna diversity. The system is assumed to use 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. We show that the coverage probability and the ergodic rate can be evaluated when considering RISs operate as batched powerless beamformers. The resulting analytical expressions provide a generic methodology to evaluate the impact of key RIS-related parameters, such as the size of RIS and the density of nodes, on system level performance. 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 radio cellular networks.