Title: SINR Outage Evaluation in Cellular Networks: Saddle Point Approximation (SPA) Using Normal Inverse Gaussian (NIG) Distribution,
Abstract: Signal-to-noise-plus-interference ratio (SINR) outage probability is among
one of the key performance metrics of a wireless cellular network. In this
paper, we propose a semi-analytical method based on saddle point approximation
(SPA) technique to calculate the SINR outage of a wireless system whose SINR
can be modeled in the form $\frac{\sum_{i=1}^M X_i}{\sum_{i=1}^N Y_i +1}$ where
$X_i$ denotes the useful signal power, $Y_i$ denotes the power of the
interference signal, and $\sum_{i=1}^M X_i$, $\sum_{i=1}^N Y_i$ are independent
random variables. Both $M$ and $N$ can also be random variables. The proposed
approach is based on the saddle point approximation to cumulative distribution
function (CDF) as given by \tit{Wood-Booth-Butler formula}. The approach is
applicable whenever the cumulant generating function (CGF) of the received
signal and interference exists, and it allows us to tackle distributions with
large skewness and kurtosis with higher accuracy. In this regard, we exploit a
four parameter \tit{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 (CoMP) from the
base stations (BSs) that are modeled by homogeneous Poisson point process. We
characterize the outage of the typical user in scenarios such as (a)~when the
number and locations of interferers are random, and (b)~when the fading
channels and number of interferers are random. Numerical results are presented
to illustrate the accuracy of the proposed set of approximations.