  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 user's 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.
