Percolation in multi-channel secondary cognitive radio networks under the SINR model

In this paper, we use concepts and results from percolation theory to investigate and characterize the effects of primaries on the connectivity of a secondary cognitive radio network under the SINR model. The SINR requirements of the secondaries along with the interference tolerance of the primaries determine which secondary nodes can communicate and which ones are rendered invisible from each other. Such invisibility is even more pronounced when there are plenty of channels to choose from- a phenomenon which we define as channel abundance. With no node-to-node coordination and a naive channel rendezvous protocol, it becomes difficult for the nodes to select a common channel. Invisibility caused by interference and channel abundance is modeled using Poisson thinning. We study their combined effects on the formation of a communication link between two nodes and also on the overall connectivity of the secondary network. Representing multiple channels as parallel edges in a graph, we use the projection of multiple graphs on R2 and show how the network percolates in continuum R2 by coupling it with a typical discrete lattice percolation. We define and characterize the connectivity of the secondary network in terms of the available number of channels, deployment density, number of transceivers per node and interference cancellation coefficient, both in the presence and absence of primaries. When primaries are absent, we derive the number of channels for which the sub and super-criticality of the secondary network are achieved. When primaries are present, we identify the channel abundance region, the optimal point, and the channel deprivation region. Further, we show how cooperation between primary and secondary networks can increase the connectivity of both.