In Cognitive Radio Networks (CRNs), the secondary users (SUs) are allowed to access the licensed channels opportunistically. A fundamental and essential operation for SUs is to establish communication through choosing a common channel at the same time slot, which is referred to as rendezvous problem. In this paper, we study strategies to achieve fast rendezvous for two secondary users. The channel availability for secondary nodes is subject to temporal and spatial variation. Moreover, in a distributed system, one user is oblivious of the other users channel status. Therefore, a fast rendezvous is not trivial. Recently, a number of rendezvous strategies have been proposed for different system settings, but rarely have they taken the temporal variation of the channels into account. In this work, we first derive a time-adaptive strategy with optimal expected time-to-rendezvous (TTR) for synchronous systems in stable environments, where channel availability is assumed to be static over time. Next, in dynamic environments, which better represent temporally dynamic channel availability in CRNs, we first derive optimal strategies for two special cases, and then prove that our strategy is still asymptotically optimal in general dynamic cases. Numerous simulations are conducted to demonstrate the performance of our strategies, and validate the theoretical analysis. The impacts of different parameters on the TTR are also investigated, such as the number of channels, the channel open possibilities, the extent of the environment being dynamic, and the existence of an intruder.
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