An algorithmic solution for computing circle intersection areas and its applications to wireless communications

Abstract

The computation of the intersection area of a large number of circles with known centers and radii is a challenging geometric problem. Nevertheless, its resolution finds several applications in the analysis and modeling of wireless networks. Prior literature discusses up to three circles and even in this case there are many possible geometric configurations, each leading to a different involved close-form expression for the intersection area. In this paper, we derive two novel geometric results, that allow the check of the existence 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. Based on these results, we construct an iterative algorithm based on a trellis structure that efficiently computes the intersection areas of an arbitrary number of circles. As an example of practical application of our results, we derive the probability that a fixed number of mobiles can be reliably allocated to a set of base stations in code division multiple access-based cellular networks.