Impact of primary users on the connectivity of a cognitive radio network

We analyze the impact of primary users on the secondary network connectivity in a cognitive radio network. The analysis is based on the second smallest Laplacian eigenvalue, i.e., the algebraic connectivity, re-elaborated in a cognitive scenario. The contribution of this paper is twofold: first we derive the form of the average Laplacian matrix of the network, averaged over the random activity of the primary users, and compute the second smallest Laplacian eigenvalue of this matrix. We derive in this way the compact cognitive algebraic connectivity and we show that, in the scenarios we are interested in, it represents a valid estimation of the expected value of the cognitive algebraic connectivity. The second contribution is the evaluation of the impact of different topological parameters on the compact cognitive algebraic connectivity.