Connectivity-Driven Routing for Cognitive Radio Ad-Hoc Networks

We design a routing scheme based on an extension of the algebraic connectivity concept for cognitive radio ad hoc networks. We observe that a cognitive radio network topology and its connectivity are highly influenced by the behavior of the primary users. In some cases, even if the physical proximity of secondary nodes would give rise to a connected topology, the primary user behavior could impact the secondary network connectivity. In graph theory the second smallest Laplacian eigenvalue, i.e., the algebraic connectivity, has numerous relationships with the graph characteristics, including connectivity, diameter, mean distance of vertexes. We then propose to elaborate the algebraic connectivity in a cognitive scenario where we derive the form of the average Laplacian matrix of the network, averaged over the random activity of the primary users, and compute the algebraic connectivity. On the basis of this mathematical model we build up an utility function which is shown to be effective for capturing some key characteristics of networks paths and can be used to compare them for routing purposes. We then design a routing scheme which, by modeling a path with a graph and its Laplacian, captures the connectivity characteristics of the path itself and suitably selects the best route in a uncertain and high variable connectivity scenarios.