Percolation theory based connectivity and latency analysis of cognitive radio ad hoc networks

Authors:
Pu Wang;Ian F. Akyildiz;Abdullah M. Al-Dhelaan
Affiliations:
Broadband Wireless Networking Laboratory, School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332;Broadband Wireless Networking Laboratory, School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332 and College of Computer & Information Sciences, Kin ...;College of Computer & Information Sciences, King Saud University, Riyadh, Saudi Arabia
Venue:
Wireless Networks
Year:
2011

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Abstract

This paper investigates the dynamic connectivity and transmission latency of cognitive radio ad-hoc networks (secondary networks) coexisting with licensed networks (primary networks) that experience time-varying on-off links. It is shown that there exists a critical density 驴 s * such that if the density of secondary networks is larger than 驴 s * , the secondary network percolates at all time t 0, i.e., there exists always an infinite connected component in the secondary network under the time-varying spectrum availability. Furthermore, the upper and lower bounds of 驴 s * are derived and it is shown that they do not depend on the random locations of primary and secondary users, but only on the network parameters, such as active/inactive probability of primary users, transmission range, and the user density. Moreover, due to the dynamic behavior of the unoccupied spectrum, the secondary network can be disconnected at all times. It is proven that it is still possible for a SU to transfer its message to any destination with a certain delay with probability one. This delay is shown to be asymptotically linear in the Euclidean distance between the transmitter and receiver.