Tight Lower Bounds for Channel Hopping Schemes in Cognitive Radio Networks

In this paper, we consider the two-user multichannel rendezvous problem in a cognitive radio network (CRN) and derive tight lower bounds for maximum time-to-rendezvous (MTTR) and maximum conditional time-to-rendezvous (MCTTR) of various channel hopping (CH) schemes under a channel loading constraint. In the symmetric and synchronous setting, we propose a novel Cycle-Adjustable Channel Hopping (CACH) scheme to achieve the MTTR lower bound (when the channel loading is bounded above by 1/u with u being a prime power). Thus, the MTTR lower bound is tight and the CACH scheme is optimal in minimizing MTTR among all the symmetric and synchronous CH schemes under the same channel loading constraint. In the asymmetric setting, we show that the classical wait-for-mommy strategy can be used to achieve the MCTTR lower bound, and thus it is optimal. In the symmetric and asynchronous setting, we also show a hierarchical construction of an asynchronous CH sequence by using two smaller asynchronous CH sequences. To further understand the effect of channel loading to the other performance metrics in a CRN, we perform various computer simulations for various CH schemes. Our simulation results show that the average time-to-rendezvous of CACH is independent of the total number of channels, and it is also robust to the disturbance of primary users.