SINR Outage Evaluation: Saddle Point Approximation Using Normal Inverse Gaussian Distribution

Abstract

Signal-to-noise-plus-interference ratio (SINR) outage probability is among one of the key performance metrics of a wireless network. In this paper, we propose a semi-analytical method based on the saddle point approximation (SPA) technique to calculate the SINR outage of a wireless system whose SINR can be modeled in the form $\left({\sum _{i=1}^{M} X_{i}}/ \left(1+\sum _{i=1}^{N} Y_{i}\right) \right)$ where $X_{i}$ denotes the useful signal power and $Y_{i}$ denotes the power of the interference signal. Both $M$ and $N$ can also be random variables. The proposed approach is based on the saddle point approximation to cumulative distribution function as given by Wood-Booth-Butler formula . The approach is applicable whenever the cumulant generating function of the received signal and interference exists, and it allows us to tackle distributions with large skewness and kurtosis with higher accuracy. In this paper, we exploit a four parameter normal-inverse Gaussian (NIG) distribution as a base distribution. Given that the skewness and kurtosis satisfy a specific condition, NIG-based SPA works reliably. When this condition is violated, we recommend SPA based on normal or symmetric NIG distribution, both special cases of NIG distribution, at the expense of reduced accuracy. For the purpose of demonstration, we apply SPA for the SINR outage evaluation of a typical user experiencing a downlink coordinated multi-point transmission from the base stations that are modeled by homogeneous Poisson point process. Numerical results are presented to illustrate the accuracy of the proposed set of approximations.