On the Connectivity of Circularly Distributed Nodes in Ad Hoc Wireless Networks

This paper examines the probability of connectivity of ad hoc wireless networks in which nodes are uniformly distributed on the circumference of a circle. We derive the exact probability that the network is composed of at most C clusters. The probability of connectivity is obtained by considering the case of C equal to unity. We also consider the distribution of nodes over a circular disk. The probability of connectivity for this case is found by fitting a log-logistic function using Minimum Mean Square Error (MMSE) criterion.