Coverage analyses on directional transmissions ultra-dense networks with imperfect beam alignment

Blockage and imperfect beam alignment are two principal difficulties in high-frequency bands directional transmissions. In this paper, the coverage performance of downlink directional transmissions in ultra-dense networks is analyzed, with the consideration of beam alignment error and link blockage through stochastic geometry. Numerical experiments demonstrate that narrower beam leads to higher coverage probability with perfect beam alignment, but it is not the case with imperfect beam alignment. Therefore, the optimal beamwidth that maximize the coverage probability is characterized and a closed-form approximation of the optimal beamwidth is derived under imperfect beam alignment, accordingly. Furthermore, the optimal beamwidth is a monotonically increasing function of the standard deviation of the beam alignment error, and a monotonically decreasing function of the beamwidth of correspondent communication end, indicating that the beamwidth of the communication pairs ought to be jointly designed.