A Stochastic Geometry Framework for RIS-Assisted Cellular Networks

This thesis investigates the impact of deploying reconfigurable intelligent surfaces (RIS), which can engineer spatial diversity in complex cellular networks, at a system level. We develop a framework to characterize the performance of RIS-assisted cellular networks, focusing on downlink coverage probability and ergodic rate, where we consider that multiple RISs can serve one UE simultaneously. 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 Matérn cluster process (MCP), where each RIS cluster is a finite PPP with support of 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 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. Furthermore, the proposed framework enables techno-economic analysis of RIS-assisted networks. We introduce a relative cost model considering the total cost of ownership (TCO) of deploying both BSs and RISs, along with a return on investment (ROI) model that is proportional to spectral efficiency. This approach gives operators quantitative insights to develop investment strategies regarding whether to invest in RISs based on current BS and RIS densities. To assess performance and conduct techno-economic analysis, the analytical expressions involving multiple integrals are computationally complex. We address this challenge by developing a novel numerical solver based on the Genz-Malik rule and parallel computing, allowing efficient evaluation within acceptable time consumption and improving the practical applicability of the proposed framework. Based on this solver, numerical evaluations of the analytical expressions and Monte-Carlosimulations jointly validate the proposed analytical approach and provide valuable insights into the design of future RIS-assisted cellular networks.