An Algorithmic Solution for Computing Circle Intersection Areas and its Applications to Wireless Communications

TL;DR

This paper introduces an efficient iterative algorithm based on a trellis-structure for computing intersection areas of multiple circles, with applications in wireless network performance analysis, including outage probability studies.

Contribution

The paper presents a novel geometric algorithm that simplifies intersection area calculations for multiple circles, enhancing wireless network analysis tools.

Findings

Efficient computation of circle intersection areas using the proposed algorithm.

Application to analyze uplink outage probability in wireless networks.

Demonstrated usefulness in sensor and cellular network performance evaluation.

Abstract

A novel iterative algorithm for the efficient computation of the intersection areas of an arbitrary number of circles is presented. The algorithm, based on a trellis-structure, hinges on two geometric results which allow the existence-check and the computation of the area of the intersection regions generated by more than three circles by simple algebraic manipulations of the intersection areas of a smaller number of circles. The presented algorithm is a powerful tool for the performance analysis of wireless networks, and finds many applications, ranging from sensor to cellular networks. As an example of practical application, an insightful study of the uplink outage probability of in a wireless network with cooperative access points as a function of the transmission power and access point density is presented.