## 4 Simulation Experiments
### Performance Comparison for High and Low UAV Speed Scenarios  
The purpose of this group of experiments is to compare the DoA estimation and beamforming performance of the proposed and baseline methods. Here, two scenarios are studied to consider the high and moderate mobilities of the UAV, for which the UAV's speed is set to 160 km/h and 60 km/h, respectively. Horizontally, the trajectory of the target UAV is a curve with a radius of 80 m. We set the initial distance between the UAV and the BS as 100 m. For both beamforming schemes, we adopt two widely studied beamformers, a nonrobust method and a robust method, namely, the linearly constrained minimum variance (LCMV) beamformer and the DL beamformer, respectively. Because the typical transmission frequency of FSI messages is 4-5 Hz, the pilot signal interval is set to 200 ms for the proposed algorithm. The prediction process has low complexity and thus can be executed at a high frequency. However, given the limited change in the position of the UAV within a short time duration, the prediction process is executed every 1 ms in our experiments. The improved MUSIC algorithm considered for comparison uses reference signals to perform DoA estimation; considering that the reference signals usually have a higher transmission frequency than the telemetry messages, the DoA estimation interval for the traditional beamforming scheme is set to 50 ms. The errors of both DoA estimation methods and of the beamforming output are examined every 10 ms. Each time the averaged absolute error output of 20 times DoA estimation results are obtained. The widely adopted GPS multivariate Gaussian positioning error model is applied for the proposed method. Both the vertical and horizontal errors have means of zero. Based on a review of popular commercial products [36; 37; 38], the standard variances of the vertical and horizontal errors are selected to be \(\sqrt{3}\) m and \(\sqrt{2}\) m, respectively. We compare the computational complexity of both DoA estimation algorithms using simulation experiments in Matlab. The general setting is as follows: considering the realistic execution frequency of both algorithms, the proposed algorithm is performed once and the prediction is executed once per 1 ms; the improved MUSIC algorithm is performed four times. The algorithm execution time is obtained by averaging 100 independent executions. The average time duration in executing the conventional MUSIC algorithm is 0.0540 s, while the proposed method is 0.0029 s. The MUSIC algorithm is approximately 19 times higher in computation time than the proposed method. Therefore, the proposed method is of significantly lower computational complexity. The DoA estimation errors for the high-speed and low-speed scenarios are shown in Figure 5a,b, respectively. From these figures, it can be seen that the proposed method has obtained better DoA estimation performance. In Figure 5a, we have marked the pilot signal intervals for the proposed algorithm during the period of 400-600 ms and for the improved MUSIC algorithm during the period of 450-500 ms. For the conventional method, it can be seen that during 450-500 ms, the UAV's mobility causes the DoA estimation errors to increase. These errors are larger in Figure 5a than in Figure 5b due to the higher speed of the UAV. The proposed prediction method, on the other hand, continues tracking the variations in the DoA value, causing the errors to remain low during the DoA estimation interval. Besides during the intervals, the proposed algorithm is also more accurate on DoA estimations via pilot signals, e.g., at 600 ms. This is because it explores LoS signals directly, thus avoiding the destructive influence of the angular spread effect. It should be noted that if no LoS paths exist, the proposed method can be less accurate.