On the connectivity of large multi-channel cognitive radio networks

Cognitive Radio Networks (CRNs) have become promising network components to improve spectrum utilization efficiency, where secondary (unlicensed) users exploit spectrum opportunistically without interfering with the coexisting primary users. A challenging yet open question is how to ensure that information can be disseminated to the entire CRN, which is a prerequisite to applications of wireless networks. In this paper, we address the connectivity of large multi-channel CRNs. Particularly, we study full connectivity and percolation of secondary networks. The former is the existence of a communication path between any two nodes and the latter is the existence of a large component of secondary users. We find that the sufficient and necessary condition to achieve full connectivity is λ = Θ(log n/πr² P_s), where λ is the density, n is the number and r is the transmission range of secondary users respectively, and P_s is the probability that any two secondary users can communicate with each other without interfering with primary users. We further show that the required density for percolation is a constant, and identify an upper bound on λ, above which the network is percolated and a lower bound on λ below which the network is not percolated. Our results provide a theoretical understanding of connectivity in large multi-channel cognitive radio networks.