## 1 Introduction  
With the rapid development of UAVs, these devices are revolutionizing a large quantity of civil application fields, including industrial construction, products inspection, safety monitoring, agriculture, rescue and search, bird-eye viewing and so on [1, 2]. Some common functions of UAVs in these applications are photographing and video recording from the air, and transfering high-resolution photos or videos requires a robust and fast communication link between the UAV and the ground server. It is thus useful to incorporate UAVs into the cellular system such as aUEs, due to the large geological coverage and stable communication it provides. In wireless communications between UAVs and cellular networks, the channels are usually dominated by line-of-sight (LoS) components accounting for 90% of the total power [3; 4]. The LoS channel characteristics enhance the receiving power during communications, but also cause strong inter-cell interference [5; 6; 7; 8]. Beamforming has been given considerable attention due to its ability to suppress such interference [9; 10; 11] and direct power to the desired direction (in this case, the receiver), as well as its potentially significant role in current and future communication systems such as 5G networks [12; 13]. However, pilot-assisted channel state information (CSI) estimation, which is the basis of most current beamforming schemes, faces severe challenges from pilot contamination effects [14; 15]. In the UAV-ground link, with less blockage the inter-cell uplink pilot interference is often so strong that it could intensify interference among pilot signals [7; 15]. Thus, traditional beamforming faces decreased performance to support aerial users in current and future cellular networks. On the other hand, beamforming based on signals' DoA estimations, as an alternative to the CSI based solution, is shown to achieve better performance in recent years [16; 17]. DoA estimation algorithms can extract the channel information from nonorthogonal signals, and therefore avoid the destructive effects of pilot contamination. Designs of combined DoA estimation and beamforming schemes for cellular system are proposed in [16; 18], showing performance approaching that of the corresponding CSI based scheme with perfect CSI knowledge. Therefore, applying such method has now become a hot research topic and has the potential to supplant the conventional beamforming scheme in future cellular networks. Despite the high potential, the research on applying DoA based beamforming in cellular system and especially on UAVs are merely at the early stage. One major challenge it faces is that the target's mobility affects the accuracy of current estimation methods. Traditionally, the beamforming weight vector is updated only when the DoA is updated by processing a pilot signal. During the intervals between the pilot signals, the high mobility of a UAV results in a difference between its true and estimated DoA values. This problem is illustrated in the upper half of Figure 1. In the figure, a timeline is shown on the left side, and the beams formed at the corresponding time points are displayed by red curves on the right. Suppose that two consecutive pilot-assisted DoA estimations are executed at \(t_{p1}\) and \(t_{p2}\). However, during \(t_{p1}\) and \(t_{p2}\), e.g., at \(t_{1}\) and \(t_{2}\), the UAV's movement causes the DoA to vary. Such angle variance is further illustrated in Figure 2. The figure shows the UAV's positions \(pr_{p1}\) and \(pr_{1}\) at \(t_{p1}\) and \(t_{1}\), respectively, with the corresponding signal arrival angles \(\eta_{p1}\) and \(\eta_{1}\). At \(t_{p1}\), the BS obtains an estimated DoA \(\gamma_{p1}\) (an estimated position \(pe_{p1}\) is also obtained in some algorithms). It can be observed that the estimation error is increased from (\(\eta_{p1}-\gamma_{p1}\)) at \(t_{p1}\) to (\(\eta_{1}-\gamma_{p1}\)) at \(t_{1}\). The same situation applies to \(t_{2}\), which is not implied in the figure.