Stochastic Geometry Modeling of Coverage and Rate of Cellular Networks Using the Gil-Pelaez Inversion Theorem

In this letter, we introduce new mathematical frameworks to the computation of coverage probability and average rate of cellular networks, by relying on a stochastic geometry abstraction modeling approach. With the aid of the Gil-Pelaez inversion formula, we prove that coverage and rate can be compactly formulated as a twofold integral for arbitrary per-link power gains. In the interference-limited regime, single-integral expressions are obtained. As a case study, Gamma-distributed per-link power gains are investigated further, and approximated closed-form expressions for coverage and rate in the interference-limited regime are obtained, which shed light on the impact of channel parameters and physical-layer transmission schemes.