Millimeter-waves' propagation characteristics create prospects for spatial and temporal spectrum sharing in a variety of contexts, including cognitive spectrum sharing (CSS). However, CSS along with omnidirectional sensing, is not efficient at mmWave frequencies due to their directional nature of transmission, as this limits secondary networks' ability to access the spectrum. This inspired us to create an analytical approach using stochastic geometry to examine the implications of directional cognitive sensing in mmWave networks. We explore a scenario where multiple secondary transmitter-receiver pairs coexist with a primary transmitter-receiver pair, forming a cognitive network. The positions of the secondary transmitters are modelled using a homogeneous Poisson point process (PPP) with corresponding secondary receivers located around them. A threshold on directional transmission is imposed on each secondary transmitter in order to limit its interference at the primary receiver. We derive the medium-access-probability of a secondary user along with the fraction of the secondary transmitters active at a time-instant. To understand cognition's feasibility, we derive the coverage probabilities of primary and secondary links. We provide various design insights via numerical results. For example, we investigate the interference-threshold's optimal value while ensuring coverage for both links and its dependence on various parameters. We find that directionality improves both links' performance as a key factor. Further, allowing location-aware secondary directionality can help achieve similar coverage for all secondary links.

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