The asymptotic connectivity of random cognitive radio networks

In this paper, we investigate the connectivity of random cognitive radio networks with different routing schemes. Two coexisting ad hoc networks are considered with m primary users (PUs) and n secondary users (SUs) randomly distributed in a unit area. The relation between n and m is assumed to be n = m^β. We show that with the HDP-VDP routing scheme, which is widely employed in the analysis of throughput scaling laws of ad hoc networks, the connectivity of a single SU can be guaranteed when β > 1, and the connectivity of a single secondary path can be guaranteed when β > 2. While circumventing routing can improve the connectivity of cognitive radio ad hoc network (CRAHN), we verify that the connectivity of a single SU as well as a single secondary path can be guaranteed when β > 1. Thus to achieve the connectivity of secondary networks, the density of SUs should be larger (asymptotically) than that of the PUs. A smart routing scheme can also improve the connectivity of CRAHN. Our results serve as a guide to deployment and routing design for cognitive radio networks.