  To support high data rate urgent or ad hoc communications, we consider mmWave
UAV cellular networks and the associated challenges and solutions. To enable
fast beamforming training and tracking, we first investigate a hierarchical
structure of beamforming codebooks and design of hierarchical codebooks with
different beam widths via the sub-array techniques. We next examine the Doppler
effect as a result of UAV movement and find that the Doppler effect may not be
catastrophic when high gain directional transmission is used. We further
explore the use of millimeter wave spatial division multiple access and
demonstrate its clear advantage in improving the cellular network capacity. We
also explore different ways of dealing with signal blockage and point out that
possible adaptive UAV cruising algorithms would be necessary to counteract
signal blockage. Finally, we identify a close relationship between UAV
positioning and directional millimeter wave user discovery, where update of the
former may directly impact the latter and vice versa.
