Integral Approximations for Coverage Probability

TL;DR

This paper develops and evaluates four integral approximation methods for calculating the downlink coverage probability in stochastic geometry models, providing guidance on their applicability in different interference and noise conditions.

Contribution

It introduces four novel approximation techniques for a key integral in coverage probability analysis and identifies conditions for their validity.

Findings

Laplace approximation is recommended for intermediate cases.

Numerical results confirm the accuracy of the proposed approximations.

Conditions for the validity of each approximation are clearly identified.

Abstract

This letter gives approximations to an integral appearing in the formula for downlink coverage probability of a typical user in Poisson point process (PPP) based stochastic geometry frameworks of the form $\int_0^\infty \exp\{ - (Ax + B x^{\alpha/2}) \} \ud x$. Four different approximations are studied. For systems that are interference-limited or noise-limited, conditions are identified when the approximations are valid. For intermediate cases, we recommend the use of Laplace approximation. Numerical results validate the accuracy of the approximations.