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Rendezvous is a prerequisite and important process for secondary users (SUs) to establish data communications in cognitive radio networks (CRNs). Recently, there has been a proliferation of different channel hopping- (CH-) based schemes that can provide rendezvous without relying on any predetermined common control channel. However, the existing CH schemes were designed with omnidirectional antennas which can degrade their rendezvous performance when applied in CRNs that are highly crowded with primary users (PUs). In such networks, the large number of PUs may lead to the inexistence of any common available channel between neighboring SUs which result in a failure of their rendezvous process. In this paper, we consider the utilization of directional antennas in CRNs for tackling the issue. Firstly, we propose two coprimality-based sector hopping (SH) schemes that can provide efficient pairwise sector rendezvous in directional antenna CRNs (DIR-CRNs). Then, we propose an efficient CH scheme that can be combined within the SH schemes for providing a simultaneous sector and channel rendezvous. The guaranteed rendezvous of our schemes are proven by deriving the theoretical upper bounds of their rendezvous delay metrics. Furthermore, extensive simulation comparisons with other related rendezvous schemes are conducted to illustrate the significant outperformance of our schemes

Combined Sector and Channel Hopping Schemes for Efficient Rendezvous in Directional Antenna Cognitive Radio Networks