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.

[1]  Ian F. Akyildiz,et al.  NeXt generation/dynamic spectrum access/cognitive radio wireless networks: A survey , 2006, Comput. Networks.

[2]  Ian F. Akyildiz,et al.  CRAHNs: Cognitive radio ad hoc networks , 2009, Ad Hoc Networks.

[3]  Bojan Mohar,et al.  Eigenvalues, diameter, and mean distance in graphs , 1991, Graphs Comb..

[4]  Xiaohua Jia,et al.  Power Assignment for k-Connectivity in Wireless Ad Hoc Networks , 2005, Proceedings IEEE 24th Annual Joint Conference of the IEEE Computer and Communications Societies..

[5]  Zeev Nutov.  Approximating Minimum-Power k-Connectivity , 2010, Ad Hoc Sens. Wirel. Networks.

[6]  A. Jamakovic,et al.  On the relationship between the algebraic connectivity and graph's robustness to node and link failures , 2007, 2007 Next Generation Internet Networks.

[7]  Jie Wu,et al.  On constructing k-connected k-dominating set in wireless ad hoc and sensor networks , 2006, J. Parallel Distributed Comput..

[8]  B. Mohar.  THE LAPLACIAN SPECTRUM OF GRAPHS y , 1991 .

[9]  Hüseyin Arslan,et al.  A survey of spectrum sensing algorithms for cognitive radio applications , 2009, IEEE Communications Surveys & Tutorials.

[10]  Francesca Cuomo,et al.  Gymkhana: A Connectivity-Based Routing Scheme for Cognitive Radio Ad Hoc Networks , 2010, 2010 INFOCOM IEEE Conference on Computer Communications Workshops.

[11]  Mehran Mesbahi,et al.  K-node connected power efficient topologies in wireless networks: a semidefinite programming approach , 2005, GLOBECOM '05. IEEE Global Telecommunications Conference, 2005..

[12]  Vikram Srinivasan,et al.  Dynamic spectrum access in DTV whitespaces: design rules, architecture and algorithms , 2009, MobiCom '09.

[13]  Francesca Cuomo,et al.  Analysis of k-connectivity of a cognitive radio ad-hoc network , 2009, PE-WASUN '09.