Connectivity Analysis of Cognitive Radio Ad-hoc Networks with Shadow Fading

In this paper, we analyze the connectivity of cognitive radio ad-hoc networks in a log-normal shadow fading environment. Considering secondary user and primary user's locations and primary user's active state are randomly distributed according to a homogeneous Poisson process and taking into account the spectrum sensing efficiency of secondary user, we derive mathematical models to investigate the connectivity of cognitive radio ad-hoc networks in three aspects and compare with the connectivity of ad-hoc networks. First, from the viewpoint of a secondary user, we study the communication probability of that secondary user. Second, we examine the possibility that two secondary users can establish a direct communication link between them. Finally, we extend to the case of finding the probability that two arbitrary secondary users can communicate via multi-hop path. We verify the correctness of our analytical approach by comparing with simulations. The numerical results show that in cognitive radio ad-hoc networks, high fading variance helps to remarkably improve connectivity behavior in the same condition of secondary user's density and primary user's average active rate. Furthermore, the impact of shadowing on wireless connection probability dominates that of primary user's average active rate. Finally, the spectrum sensing efficiency of secondary user significantly impacts the connectivity features. The analysis in this paper provides an efficient way for system designers to characterize and optimize the connectivity of cognitive radio ad-hoc networks in practical wireless environment.