Abstract-In millimeter-wave communication, large antenna arrays are required to achieve high power gain by steering towards each other with narrow beams, which poses the problem to efficiently search the best beam direction in the angle domain at both Tx and Rx sides. As the exhaustive search is time consuming, hierarchical search has been widely accepted to reduce the complexity, and its performance is highly dependent on the codebook design. In this paper, we propose two basic criteria for the hierarchical codebook design, and devise an efficient hierarchical codebook by jointly exploiting sub-array and deactivation (turning-off) antenna processing techniques, where closed-form expressions are provided to generate the codebook. Performance evaluations are conducted under different system and channel models. Results show superiority of the proposed codebook over the existing alternatives.Index Terms-Millimeter wave communication, mmWave, beamforming, codebook design, hierarchial search.

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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. Index TermsUAV, millimeter wave, mmWave, UAV cellular, blockage, user discovery. I. INTRODUCTIONUnmanned aerial vehicles (UAVs) have received increasing attention in the past decade [1],[2], thanks to potential applications in reconnaissance, fire-fighting, aerial photo, remote sensing, disaster rescue and others. For the above scenarios where a fixed infrastructure network is Zhenyu Xiao is with the department of EIE, BKL-NCATM and BL-GAT of Beihang University.Pengfei Xia is with Tongji University.Xiang-Gen Xia is with University of Delaware.A typical UAV cellular network is shown in Fig. 1, where the base station (BS) is mounted on a flying UAV in the air, and mobile stations (MS) are distributed on the ground or in the low-altitude air. The UAV BS may be connected with the terrestrial networks via a satellite link or an air-to-ground wireless link. Typically, the traffic between MS and UAV BS includes circumstance information, control commands, and sensing data from various sensors, e.g. camera sensors [1], [2]. In many cases where the large video monitoring traffic data from many camera sensors need to be collected and sent back to a control station for fast response, high data rate communication links between the MS and UAV BS are desirable. For this reason, we study in the paper millimeter wave communications for UAV cellular, as abundant frequency spectrum resource exists in the millimeter-wave (mmWave) frequency band [3], [4].The main difference between a mmWave UAV cellular network and a regular mmWave cellular network with fixed BS is that the UAV BS may move around. Hence, the challenges of a regular mmWave cellular apply to the mmWave UAV cellular as well, including range and directional communications, rapid channel variation, multi-user access, blockage and others [4].Some of the existing challenges are intensified due to UAV movement. For example, more efficient beamforming training and tracking are needed to account for UAV movement, and

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