Uplink User Process in Poisson Cellular Network

Stochastic geometry provides a convenient approach to analyze the cellular networks. Adoption of Poisson point process, for example, has been proven to be an efficient tool to obtain the pessimistic bounds of the capacity and outage probability in the downlink channel. However, due to the correlated distribution of the interfering users, analysis of uplink communication has never been an easy task. Although some of the current literature has attempted to resolve this problem by assuming suitable interferer distributions, an accurate yet tractable description of the uplink user process has always been sought after. In this letter, we provide an exact description of the uplink user process by characterizing the counting measure in an arbitrary bounded Borel set. For computational tractability, we obtain an approximation of the exact result and verify its accuracy through Monte Carlo simulation.