  In cognitive radio networks (CRNs), the connectivity of secondary users (SUs)
is difficult to be guaranteed due to the existence of primary users (PUs). Most
prior studies only consider cognitive radio networks equipped with
omni-directional antennas causing high interference at SUs. We name such CRNs
with omni-directional antennas as Omn-CRNs. Compared with an omni-directional
antenna, a directional antenna can concentrate the transmitting/receiving
capability at a certain direction, consequently resulting in less interference.
In this paper, we investigate the connectivity of SUs in CRNs with directional
antennas (named as Dir-CRNs). In particular, we derive closed-form expressions
of the connectivity of SUs of both Dir-CRNs and Omn-CRNs, thus enabling
tractability. We show that the connectivity of SUs is mainly affected by two
constraints: the spectrum availability of SUs and the topological connectivity
of SUs. Extensive simulations validate the accuracy of our proposed models.
Meanwhile, we also show that Dir-CRNs can have higher connectivity than
Omn-CRNs mainly due to the lower interference, the higher spectrum availability
and the higher topological connectivity brought by directional antennas.
