Stochastic Geometry Analysis for RIS-Assisted Large-Scale Cellular Networks

In this paper, we analyze the coverage probability of a reconfigurable intelligent surface (RIS) aided cellular network with the theory of stochastic geometry. A Poisson cluster process (PCP) is applied to model the positions of transmitters (TXs) and RISs, capturing their spatial correlations. Considering the general Nakagami-m fading channel model, we derive the approximate distributions of the composite channel gains with RIS-assisted transmission, representing the desired signal channel and the interference channel, respectively. The coverage probability of the typical user is then obtained. The derived coverage probability is in a closed form, which can be evaluated efficiently. Simulation results are presented to show that the presented analysis is effective, demonstrate the significant performance gains brought by the passive beamforming of a RIS with a large number of elements, and show the impact of TX density on the performance of the proposed system.