Outage Probability in Arbitrarily-Shaped Finite Wireless Networks

TL;DR

This paper introduces two analytical frameworks to compute outage probability at any location within arbitrarily-shaped finite wireless networks, accounting for boundary effects and fading, applicable to various network geometries.

Contribution

The paper presents novel general frameworks for outage analysis in finite wireless networks with arbitrary shapes and locations, extending beyond prior shape-specific or fixed-location assumptions.

Findings

Outage probability varies significantly with location within the network.

Boundary effects are crucial for accurate outage analysis.

Frameworks are demonstrated for disk and polygon regions with Nakagami-m fading.

Abstract

This paper analyzes the outage performance in finite wireless networks. Unlike most prior works, which either assumed a specific network shape or considered a special location of the reference receiver, we propose two general frameworks for analytically computing the outage probability at any arbitrary location of an arbitrarily-shaped finite wireless network: (i) a moment generating function-based framework which is based on the numerical inversion of the Laplace transform of a cumulative distribution and (ii) a reference link power gain-based framework which exploits the distribution of the fading power gain between the reference transmitter and receiver. The outage probability is spatially averaged over both the fading distribution and the possible locations of the interferers. The boundary effects are accurately accounted for using the probability distribution function of the distance of a random node from the reference receiver. For the case of the node locations modeled by a Binomial point process and Nakagami-$m$ fading channel, we demonstrate the use of the proposed frameworks to evaluate the outage probability at any location inside either a disk or polygon region. The analysis illustrates the location dependent performance in finite wireless networks and highlights the importance of accurately modeling the boundary effects.