Analysis of 3D Deafness Effects in Highly Directional mmWave Communications

In this paper, we address a problem of 3D directional deafness, which may arise for millimeter-wave (mmWave) devices, e.g., in the contention-based access period of the IEEE 802.11ad/ay protocols. To evaluate the probability of 3D deafness, we develop an analytical framework based on stochastic geometry methods. In particular, we study a minimal feasible set of devices equipped with highly directional antennas with an arbitrary antenna pattern and provide an analytical expression for the distance-dependent 3D directional deafness probability. To abstract away from particular antenna patterns, we propose an analytically tractable model of an antenna pattern that is given by a piece-wise linear function of the beamwidth. Using this tractable equation, we derive a corresponding closed-form lower bound for the deafness probability that serves as an approximation for an arbitrary antenna with the same half-power beamwidth. Finally, we study the effects of antenna settings on the deafness probability and derive a scaling law for its lower values.