Multi-MTTR Asynchronous-Asymmetric Channel-Hopping Sequences for Scalable Cognitive Radio Networks

In this paper, a family of channel-hopping (CH) sequences, so-called multi-maximum time-to-rendezvous (MTTR) asynchronous-asymmetric prime sequences (MAAPSs), for cognitive radio networks (CRNs) is designed and analyzed. They have known and enlarged cardinality (for the benefit of user identification), full degree of rendezvous, and pairwise shift invariant. For the first time, the MAAPSs can be partitioned into multiple subsets of CH sequences with adjustable MTTR. This unique property supports a trade-off between cardinality and MTTR in scalable CRNs. With a channel-contention-resolution mechanism in use, the rendezvous-success (RS) rate and variance of the MAAPSs in a practical CRN are analyzed. With short MTTR and smaller RS-rate variance, the MAAPSs can support quicker, more stable and uniform rendezvous processes than their counterparts. Finally, the analytical models of two combined metrics of TTR and RS rate, so-called maximum and average time-to-RS, are formulated and validated with computer simulation.