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. In [1], the authors 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 in [1] 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: i) increases with the density
and the transmit power of base stations, and ii) decreases with
the density of mobile terminals and the transmission bandwidth.