## 3 Analysis of the Received Jamming Power in the UAV Jamming Link Due to the Attitude Change
As shown in Figure 6b-d, the larger the height difference between the two antennas, the greater the variation in the PLF, because the jammer location is closer to the null direction of the omnidirectional antenna. Figure 5: Contour and shadow map of the variation in the UAV antenna gain to the UAV roll (\(\hat{n}_{R}=\hat{x}\), \(\theta_{R}=20^{\circ}\)); where the UAV height \(h\) is at (**a**) 0 m, (**b**) 250 m, (**c**) 500 m, and (**d**) 1000 m, and the jammer is on plane ground. When the UAV has a constant height and the jammer is over a simulated terrain, the variation in the PLF due to the UAV roll according to the \((x,\,y)\) position of the jammer is shown as a contour and a shadow map, as shown in Figure 7. The UAV roll rotation has a roll axis \(\hat{\mathbf{n}}_{R}\) of \(\hat{\mathbf{x}}\) and a roll angle \(\theta_{R}\) of \(20^{\circ}\). The simulated terrain has a distribution from 0 m to about 700 m and is displayed on the map as thin lines at 50 m height intervals. As shown in Figure 7a, when the UAV is at a height of 0 m, it can have a higher PLF when the jammer is located on a high terrain. As shown in Figure 7d, when the UAV is located at a height of 1000 m, it may have a high PLF when the jammer is located on a low terrain rather than a high terrain. Our analysis revealed that the greater the height difference between the UAV and the jammer, the higher the PLF can be for the terrain close to the vertical plane containing the axis of rotation. The method was applied to a small hovering UAV jamming application by a ground jammer. The method was applied to a plane ground and over a simulated terrain. It is normally expected that there is a PLF of \(10\log\left(\cos(\theta_{R})^{2}\right)\). However, when the UAV is at a high altitude and the jammer antenna is near the vertical plane containing the rotation axis, the PLF tends to be larger than expected. Figure 6: Contour and shadow map of the variation in the PLF to the UAV roll (\(\hat{\mathbf{n}}_{R}=\hat{\mathbf{x}},\,\theta_{R}=20^{\circ}\)) where the UAV height \(h\) is at (**a**) 0 m, (**b**) 250 m, (**c**) 500 m, and (**d**) 1000 m, and the jammer is on plane ground. In practice, the roll axis \(\hat{\mu}_{R}\) and the roll angle \(\theta_{R}\) may be unknown values. When a hovering UAV remains horizontal, the roll axis of the UAV \(\hat{\mathbf{n}}_{R}\) is defined in the horizontal plane and can be modeled as follows:  
\[\hat{\mathbf{n}}_{R}=\cos\phi_{R}\hat{\mathbf{x}}+\sin\phi_{R}\hat{\mathbf{y}}, \tag{17}\]  
where \(\phi_{R}\) is the azimuthal angle of \(\hat{\mathbf{n}}_{R}\). The roll angle \(\theta_{R}\) is a time-varying quantity. If the roll angle \(\theta_{R}\) has a uniform distribution probability from \(-\theta_{R,\,\max}\) to \(+\theta_{R,\,\max}\), the expected value of the PLF in the UAV jamming link can be expressed as the following equation:  
\[PL_{expected}(EL,\theta_{R,\max})=\frac{1}{2\pi}\frac{1}{2\theta_{R,\max}} \int_{0}^{2\pi}\int_{-\theta_{R,\max}}^{+\theta_{R,\max}}PL(EL,\,\theta_{R}, \,\hat{\mathbf{n}}_{R})\,d\theta_{R}\,d\phi_{R}, \tag{18}\]  
where \(EL\) is the elevation angle from the jammer to the UAV in reference to the global coordinate system. \(EL\) can be calculated as:  
Figure 2:0  
Figure 2:1 Contour and shadow map of the variation in the PLF due to the UAV roll (\(\hat{\mathbf{n}}_{R}=\hat{\mathbf{x}}\), \(\theta_{R}=20^{\circ}\)) where the UAV height \(h\) is at (**a**) 0 m, (**b**) 250 m, (**c**) 500 m, (**d**) 1000 m, and the jammer height is over a simulated terrain. where \(h\) is the height difference between the jammer and the UAV, and \(d\) is the distance between the jammer and the UAV. The expected values of PLF according to \(EL\) and \(\theta_{R,\max}\) are shown in Figure 2:2 The larger the maximum roll angle \(\theta_{R,\max}\) and the larger the elevation angle \(EL\), the greater the expected polarization loss \(PLF_{expected}\).