  By exploiting the degree of freedom on the altitude, unmanned aerial vehicle
(UAV) communication can provide ubiquitous communication for future wireless
networks. In the case of concurrent transmission of multiple UAVs, the
directional beamforming formed by multiple antennas is an effective way to
reduce co-channel interference. However, factors such as airflow disturbance or
estimation error for UAV communications can cause the occurrence of beam
misalignment. In this paper, we investigate the system performance of a
multi-tier UAV communication network with the consideration of unstable beam
alignment. In particular, we propose a tractable random model to capture the
impacts of beam misalignment in the 3D space. Based on this, by utilizing
stochastic geometry, an analytical framework for obtaining the outage
probability in the downlink of a multi-tier UAV communication network for the
closest distance association scheme and the maximum average power association
scheme is established. The accuracy of the analysis is verified by Monte-Carlo
simulations. The results indicate that in the presence of random beam
misalignment, the optimal number of UAV antennas needs to be adjusted to be
relatively larger when the density of UAVs increases or the altitude of UAVs
becomes higher.
