Meta Distribution-optimal Base Station Deployment for Finite-Area Mobile Networks

User mobility in cellular networks deployed in finite areas, results in the non-uniform spatial distribution of the mobile users (MUs), necessitating the effective deployment of base stations (BSs) in order to enhance the network connectivity. In this paper, we analyze the optimal non-uniform distribution of the BSs that provides ultra-reliable connectivity in the context of finite-area cellular networks, where the MUs employ the random waypoint (RWP) model. By using stochastic geometry tools, we first establish an analytical and tractable mathematical framework to investigate the uplink success probability in the context of non-uniform cellular networks. Furthermore, analytical expressions for the moments of the conditional success probability are derived, and a simple approximation of the meta-distribution (MD) is calculated, leveraging the moment-matching method with the Beta-distribution. Finally, we exploit the MD as a criterion for defining the optimal BS distribution, conditioned on the user’s mobility. Our results reveal that the developed framework
provides guidance in the design of cellular networks to efficiently
determine the optimal network spatial deployment that offer
ultra-reliable connectivity based on the mobility of MUs.