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In this paper, we consider the multichannel rendezvous problem in cognitiveradio networks (CRNs) where the probability that two users hopping on the samechannel have a successful rendezvous is a function of channel states. Thechannel states are modeled by stochastic processes with joint distributionsknown to users. However, the exact state of a channel at any time is notobservable. We first consider two channel models: (i) the fast time-varyingchannel model (where the channel states are assumed to be independent andidentically distributed in each time slot), and (ii) the slow time-varyingchannel model (where the channel states remain unchanged over time). Among theclasses of the blind rendezvous policies that randomly hop on channelsaccording to certain channel selection probabilities, we show the optimalchannel selection policy that minimizes the expected time-to-rendezvous (ETTR)is the single selection policy that hops on the ``best'' channel all the timein the fast time-varying channel model. However, for the slow time-varyingchannel model, it is much more difficult to find the optimal channel selectionpolicy. By using the majorization ordering, we derive a lower bound and anupper bound for the ETTR under the assumption that the channel states areexchangeable random variables. Bases on these bounds, we then prove variousapproximation solutions. We then extend our results to general channel modelswhere the joint distribution of the channel states is only assumed to bestationary in time.

ETTR Bounds and Approximation Solutions of Blind Rendezvous Policies in Cognitive Radio Networks with Random Channel States