## 4 Results and Analysis
The underlying reason for this is that the antenna vibration induces a larger phase rotation of the wave with a shorter wavelength, leading to a rapidly time-varying channel and a lower temporal ACF. This result aligns with the theoretical analysis in (23), which indicates that a higher carrier frequency or a shorter wavelength results in a larger Doppler frequency caused by the antenna vibration, leading to a rapid decorrelation of the channel over time. Figure 8: The temporal ACFs of the proposed A2A channel model with different vibration amplitudes, vibration frequencies, and carrier frequencies. Figure 7: The spatial CCFs of the proposed A2A channel model with different UAV heights and scattering-lobe widths (\(f_{c}=2.4\) GHz). Figure 9 illustrates the impact of UAV vibration angles on the temporal ACFs of the proposed model. The analysis reveals that the strongest temporal correlation occurs when the UAVs vibrate perpendicular to the line connecting the Tx and Rx. As the vibration azimuth angle decreases, the temporal ACF gradually reduces. Moreover, the temporal ACF further reduces by decreasing the vibration elevation angle. Note that in the case of rotary-wing UAVs, vibration is mainly caused by the imbalance in the rotor blades, leading to predominantly horizontal vibrations. This can cause a significant decrease in the temporal ACF and result in rapid temporal variations in the channel. Figure 10 compares the proposed model with the model in [19] regarding the temporal ACF at different speeds of the transmit UAV. The A2A channel model in [19] employs a geometric method with a scattering region defined as an ellipsoid truncated by the ground plane, with the Tx and Rx positioned as the focal points. To ensure a fair comparison, both models were assessed under the same experimental conditions, including the carrier frequency, Tx-Rx distance, UAV heights, movement directions, and speeds. The results demonstrate that the temporal ACFs of both models diminish as the UAV speed increases. Furthermore, the model in [19] fails to consider the impacts of UAV vibration and significant ground reflections, resulting in higher temporal correlations than those observed in the proposed model. Figure 10: Comparison of the proposed A2A channel model and the model in [19] in terms of temporal ACF for different speeds of the transmit UAV (\(f_{c}=20\) GHz, \(f_{t}=f_{r}=24\) GHz, \(a_{ttm}=a_{rm}=0.005\) m, \(D=50\) m, \(h_{t}=h_{r}=25\) m). Figure 9: The temporal ACFs of the proposed A2A channel model with different vibration angles of the UAV (\(f_{c}=20\) GHz, \(f_{t}=f_{r}=24\) GHz). Figure 11 shows the Doppler PSDs of the proposed A2A channel model with different degrees of UAV vibrations. With the amplification of the vibration amplitude, the Doppler PSD demonstrates a more extensive dispersion across the Doppler frequency axis, indicating an abundance of Doppler frequency components. Similarly, as the vibration frequency increases, the Doppler PSD spreads more extensively. This finding aligns with the theoretical results in (23), indicating that UAV vibrations bring in extra Doppler frequencies, which are influenced by both the vibration amplitudes and frequencies. Figure 12 illustrates the effects of the vibration angles on the Doppler PSD of the model. It is shown that when the UAVs vibrate perpendicular to the line connecting the Tx and Rx, the influence on the Doppler PSD is negligible. The impact of UAV vibration becomes more pronounced as the vibration azimuth angle decreases. A smaller vibration azimuth angle leads to a broader dispersion of the Doppler PSD across the Doppler frequency axis. It is worth noting that when the UAVs vibrate along the LoS path, the Doppler PSD exhibits the widest range of frequency components. This observation indicates a rich variety of Doppler frequencies present in the channel. Figure 13 shows the coherence times of the proposed model with different degrees of UAV vibrations and carrier frequencies. It can be observed that the coherence times are in the order of microseconds.