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.

翻译：毫米波的传播特性为空间和频谱共享创造了多种可能，包括认知频谱共享（CSS）。然而，在毫米波频段，由于传输的定向特性，基于全向传感的CSS效率低下，这限制了次级网络接入频谱的能力。这启发我们提出一种基于随机几何的分析方法，研究定向认知传感在毫米波网络中的影响。我们探讨了一个场景：多个次级收发对与一个主收发对共存，构成认知网络。次级发射机的位置采用齐次泊松点过程（PPP）建模，对应的次级接收机分布于其周围。为限制次级发射机对主接收机的干扰，每个次级发射机设置定向传输阈值。我们推导了次级用户的中介接入概率以及任一时刻活跃次级发射机的比例。为评估认知可行性，推导了主链路与次级链路的覆盖概率。通过数值结果提供了多种设计见解，例如，在确保两条链路覆盖的前提下研究干扰阈值的最优值及其对多种参数的依赖性。我们发现定向性作为关键因素能提升两条链路的性能。此外，允许位置感知的次级定向性有助于所有次级链路实现相似的覆盖。