  Satellite networks are emerging as vital solutions for global connectivity
beyond 5G. As companies such as SpaceX, OneWeb, and Amazon are poised to launch
a large number of satellites in low Earth orbit, the heightened inter-satellite
interference caused by mega-constellations has become a significant concern. To
address this challenge, recent works have introduced the concept of satellite
cluster networks where multiple satellites in a cluster collaborate to enhance
the network performance. In order to investigate the performance of these
networks, we propose mathematical analyses by modeling the locations of
satellites and users using Poisson point processes, building on the success of
stochastic geometry-based analyses for satellite networks. In particular, we
suggest the lower and upper bounds of the coverage probability as functions of
the system parameters, including satellite density, satellite altitude,
satellite cluster area, path loss exponent, and Nakagami parameter $m$. We
validate the analytical expressions by comparing them with simulation results.
Our analyses can be used to design reliable satellite cluster networks by
effectively estimating the impact of system parameters on the coverage
performance.
