Observations on sum user rate for cellular downlink

In this paper, we consider cellular downlink communication from a set of fixed stations to a set of users with uncertain locations modeled by a spatial distribution. Each user is associated with a transmitter through association zones that maximize the signal-to-interference-plus-noise ratio (SINR) to that user. We define an expected spatial capacity metric that captures the expected rate summed over all of these zones. Network performance is measured using an expectation of the spatial capacity, subject to the assumed user density function. We examine the sensitivity of this performance metric to the number of stations and the number of orthogonal (frequency or time) channels, and present some counter-intuitive properties of this metric through illustrative examples, simulation, and optimization.