A Tractable Closed-Form Expression of the Coverage Probability in Poisson Cellular Networks

The coverage probability of cellular networks is usually defined as the probability that the signal-to-interference+noise-ratio (SINR) is greater than a reliability threshold. Based on this definition, the coverage probability cannot, in general, be formulated in a tractable closed-form expression. Di Renzo et al. have introduced a new definition of coverage that explicitly accounts for the cell association phase and that is proved to be analytically tractable for system-level optimization. In this letter, we conduct a thorough comparison between the two definitions of coverage. We show that the definition introduced by Di Renzo et al. provides one with a tractable and closed-form approximation of the SINR-coverage, which is proved to be an upper-bound in relevant operating regimes. We prove that the coverage probability monotonically: 1) increases with the density and the transmit power of base stations and 2) decreases with the density of mobile terminals and the transmission bandwidth.