  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.
