Approximation of antenna directivity gain for directional deafness analysis in three-dimensional space

The paper deals with the problem of “directional deafness” that arises when a device cannot detect an occupied radio channel due to the highly directional communication link between other devices interacting at that time. The “deafness” situation can arise between operating in the millimeter band devices, for example, during carrier-sense multiple access stage, in particular, in accordance with the IEEE 802.11ad/ay protocols. An analytical expression has been obtained for the “directional deafness” probability for several variants of the devices location in three-dimensional (3D) space and for the proposed linear approximation of the antenna directivity gain. The proposed formula for the lower bound of the deafness probability for three realistic antenna patterns and four variants of phased antenna arrays is investigated.