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

摘要

A novel iterative algorithm for the efficient computation of the intersection areas of an arbitrary number of circles is presented. The algorithm, on the basis of 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 in a wireless network with cooperative access points as a function of the transmission power and access point density is presented. Copyright (c) 2012 John Wiley & Sons, Ltd.