  In cognitive radio networks (CRNs), establishing a communication link between
a pair of secondary users (SUs) requires them to rendezvous on a common channel
which is not occupied by primary users (PUs). Under time-varying PU traffic,
asynchronous sequence-based channel hopping (CH) with the maximal rendezvous
diversity is a representative technique to guarantee an upper bounded
time-torendezvous (TTR) for delay-sensitive services in CRNs, without requiring
global clock synchronization. Maximum TTR (MTTR) and maximum conditional TTR
(MCTTR) are two commonly considered metrics for evaluating such CH sequences,
and minimizing these two metrics is the primary goal in the sequence design of
various paper reported in the literature. In this paper, to investigate the
fundamental limits of these two metrics, we first derive lower bounds on the
MCTTR and MTTR, and then propose an asymmetric design which has the minimum
MCTTR and an improvement on MTTR than other previously known algorithms.
Moreover, when the number of licensed channels is odd, our proposed design
achieves the minimum MTTR. We also present the TTR performance of the proposed
design via simulation.
