Unmanned Aerial Vehicles (UAVs) are steadily being considered for scenarios demanding high bandwidth, low latency communications for video and sensor data transfer as well as real-Time control. UAVs may also be used as mobile aerial Base Station (BS) for maintaining the communication in emergency scenarios. The millimeter wave (mmWave) bands, including the sub-THz frequencies above 100 GHz, are an attractive technology for high data rate UAV connectivity due to the wide bandwidths available at these frequencies. This paper studies antenna and codebook design for UAV communication at both 28 and 140 GHz with realistic antenna simulations and flight patterns. The analysis shows that multi-Array configurations with proper codebook design are necessary for uniform spherical coverage and become particularly important in long range applications. The paper thus proposes a four array design with patch antennas. Simulations indicate that the design can achieve in excess of 1 Gbps data rates at a range of 1 km, with reasonable power levels and moderate rain fades. A simulation with a real public safety mission flight shows that beam tracking can be maintained even under high drone movements and rotations.