Rate Coverage of a Cellular Network with Users Distributed as Poisson Cluster Process

The analytical modeling of cellular networks using stochastic geometry has gone through a major transition with the emergence of Poisson cluster process (PCP)-based random spatial models. The main motivation of using the PCP-based network models is the resemblance with the spatial patterns of the users and small cells in third generation partnership project (3GPP)-compliant industry-level network simulations. Despite the richness in spatial modeling, the analytical framework of the PCP-based models has so far been limited to the characterization of the downlink coverage probability, or the distribution of the signal-to-interference-plus-noise-ratio (SINR) experienced by a user. While the SINR-coverage is indeed a useful first-order performance indicator of the network, the analysis of more sophisticated metrics like the distribution of the downlink data rate, known as the rate coverage, still remains an open problem. This is because of the intractability of the distribution of the cell load or the number of users associated to a base station (BS). In this paper, we make the first attempt towards the derivation of the probability mass function (PMF) of the cell load for the PCP-based network model wherein the users are distributed as a PCP and the BS locations are either independent of or coupled to the user locations. The PMF of the cell load is further leveraged to derive the accurate expressions of the downlink rate coverage.