Symmetric Channel Hopping for Blind Rendezvous in Cognitive Radio Networks Based on Union of Disjoint Difference Sets

Abstract

In order to exchange control information without relying on any fixed control channel, neighboring cognitive users (CUs) in a multichannel cognitive radio network (CRN) can tune their transceivers to hop among a common set of spectrum channels and communicate when they rendezvous at a common channel in the blind fashion. Based on the combinatorial concept of the union of disjoint difference sets ( UDDS ), the present paper proposes two novel symmetric channel hopping (CH) schemes, namely UDDS-SCH and UDDS-ACH , for CUs with or without a synchronized time clock, respectively, to achieve blind rendezvous. By deriving their performance metrics, we then point out that both UDDS-SCH and -ACH can be optimized by adopting a special UDDS, which can be partitioned into mutually disjoint minimal difference sets ( MDSs ) as many as possible. This stimulates us to further develop exhaustive and heuristic solutions for searching the optimal and suboptimal numbers of mutually disjoint MDSs at high and low computational complexities, respectively. Based on these searching results, we finally show that both UDDS-SCH and -ACH can achieve better performance metrics than most existing symmetric CH schemes and remedy one major shortcoming of the best known ones, i.e., incapability to rendezvous at an arbitrary number of spectrum channels. Numerical simulation demonstrates that, when primary users may appear at part of or all rendezvous channels, the proposed CH schemes will outperform the existing ones in terms of the average transmission throughput and time of the CRN.