  The point process of concurrent users is critical for the analysis of
cellular networks, in particular for the uplink and for full-duplex
communication. We analyze the properties of two popular models. For the first
one, we provide an accurate characterization of the pair correlation functions
from the user and the base station point of view, which are applied to
approximate the user process by Poisson and Ginibre point processes. For the
second model, which includes the first model asymptotically, we study the cell
vacancy probability, the mean area of vacant and occupied cells, the user-base
station distance, and the pair correlation function in lightly and heavily
loaded regimes.
