Connectivity in one-dimensional ad-hoc cognitive radio networks

This paper studies the connectivity of one-dimensional cognitive radio networks. Cognitive radio networks are such heterogeneous networks that are composed of a primary network and a secondary network, and we consider the connectivity of the secondary network which is defined as the probability of communication between an arbitrary pair of nodes in the network. In this paper, we consider a two-dimensional Poisson distributed primary network together with a one-dimensional secondary network with the nodes distributed according to a Poisson point distribution and uniform distribution, and analyze the connectivity probability respectively. Using methodologies from random graph and stochastic geometry, we derive the probability expression of the secondary network connectivity under P.P.P. and an approximation under uniform distribution. Through simulation, we show the accuracy of our formulas, which will provide basis for realizations of such cognitive radio networks.