  In this paper, we investigate the performance of a reconfigurable intelligent
surface (RIS) assisted large-scale network by characterizing the coverage
probability and the average achievable rate using stochastic geometry.
Considering the spatial correlation between transmitters (TXs) and RISs, their
locations are jointly modelled by a Gauss-Poisson process (GPP). Two
association strategies, i.e., nearest association and fixed association, are
both discussed. For the RIS-aided transmission, the signal power distribution
with a direct link is approximated by a gamma random variable using a moment
matching method, and the Laplace transform of the aggregate interference power
is derived in closed form. Based on these expressions, we analyze the channel
hardening effect in the RIS-assisted transmission, the coverage probability,
and the average achievable rate of the typical user. We derive the coverage
probability expressions for the fixed association strategy and the nearest
association strategy in an interference-limited scenario in closed form.
Numerical results are provided to validate the analysis and illustrate the
effectiveness of RIS-assisted transmission with passive beamforming in
improving the system performance. Furthermore, it is also unveiled that the
system performance is independent of the density of TXs with the nearest
association strategy in the interference-limited scenario.
