Saddle Point Approximation for Outage Probability Using Cumulant Generating Functions

TL;DR

This paper introduces a saddle point approximation method based on cumulant generating functions to efficiently evaluate outage probability in wireless networks, avoiding complex numerical integrations.

Contribution

It presents a novel, generic SPA approach applicable to various fading distributions, validated through numerical results on Nakagami, Hoyt, and Rician channels.

Findings

SPA provides accurate outage probability estimates

Method works across multiple fading distributions

Numerical validation confirms effectiveness

Abstract

This letter proposes the use of saddle point approximation (SPA) to evaluate the outage probability of wireless cellular networks. Unlike traditional numerical integration-based approaches, the SPA approach relies on cumulant generating functions (CGFs) and eliminates the need for explicit numerical integration. The approach is generic and can be applied to a wide variety of distributions, given that their CGFs exist. We illustrate the usefulness of SPA on channel fading distributions such as Nakagami-$m$, Nakagami-$q$ (Hoyt), and Rician distributions. Numerical results validate the accuracy of the proposed SPA approach.