K-connectivity of cognitive radio networks

The fc-connectivity of cognitive radio networks is discussed in this paper. By combining asymptotic k-connectivity and percolation, we define that the cognitive radio networks are k-connected if there exists an infinite k-connected component in the secondary network. Utilizing continuum percolation theory, we prove that the secondary network is k-disconnected if secondary users´ density λ_s <; log l + (k -1-θ) log, log l/πr², where l → ∞ is the side length of a square-shaped network, r is the transmission range of the secondary network, and θ = Ω(1). And the network is k-connected when λ_s ≥ log l + (k - 1 - + ξ) log, log l/πr², where ξ = Ω(1). Finally, we provide the necessary condition and sufficient condition of k-connectivity on primary user density λ_p.