## 2 Scenario of Interference Source Moving along the Satellite Trajectory
### Derivation of Relative Angle Difference \(\psi\) with Sidelobe Gain  
For the \(J/S\) ratio in Equation (1), \(L_{s}\) can be obtained using the LEO satellite's TLE data. The TLE data consist of two lines of trajectory information, including epoch times, eccentricities, and inclination angles. Based on these data, location information, such as latitude, longitude, and altitude, is obtained to predict the trajectory. \(d_{s}\) is calculated by applying the free-space Friis equation with the slant distance between the satellite and ground station. \(J\) is then calculated from the path loss \(L_{i}\) and the sidelobe gain of the ground station antenna toward the interference source, and thus the sidelobe gain is determined by the location of the interference source. To calculate the sidelobe gain toward the interference source, the relative angle difference \(\psi\) is defined. \(\psi\) is the angle between the LEO satellite and the airborne interference source when the ground station antenna is set as the origin of the coordinate system. Latitude, longitude, and altitude coordinates are generally referred to using WGS84. For example, the latitude \(\phi_{g}\), longitude \(\lambda_{g}\) and altitude \(h_{g}\) of the ground station according to WGS84 are indicated by the green square marker in Figure 2a. To calculate the relative angle difference \(\psi\), the WGS84 coordinates of the LEO satellite, ground station, and airborne interference source are converted into  
Figure 1: Conceptual figure of the LEO satellite downlink scenario under interference situations. ENU coordinates. The ENU system uses Cartesian coordinates relative to a specific Earth location as its origin. Here, the location of the ground station is the origin for the ENU system. Converting coordinates from WGS84 to ENU requires two steps: conversion from WGS84 to Earth-centered Earth-fixed (ECEF), and then conversion from ECEF to ENU. To convert to the ECEF coordinate system, the Earth's radius \(R\) is calculated at latitude \(\phi\) by Equation (2), where \(a\) (= 6378.137 km for WGS84) is the ellipsoidal equatorial radius and \(e\) is the eccentricity of the ellipsoid (\(e^{2}\) = 0.00669437999 for WGS84). The ECEF system has the center of the Earth as the origin (0, 0, 0), which allows us to calculate \(X_{ECEF}\), \(Y_{ECEF}\), and \(Z_{ECEF}\) from latitude \(\phi\), longitude \(\lambda\), and altitude \(h\) using Equations (3)-(5):  
\[R=\frac{a}{\sqrt{1-e^{2}\sin^{2}\phi}}, \tag{2}\]  
\[X_{ECEF}=(R+h)\cos\lambda\cos\phi, \tag{3}\]  
\[Y_{ECEF}=(R+h)\sin\lambda\cos\phi, \tag{4}\]  
\[Z_{ECEF}=[(R(1-e^{2})+h]\sin\phi \tag{5}\]  
Figure 2: Schematic diagram for the conversion of the coordinate systems for the ground station, LEO satellite, and interference source: (**a**) conversion from WGS84 to the ECEF; (**b**) transformation from ECEF to ENU. Now, the locations of the ground station, LEO satellite, and airborne interference source are converted from WGS84 to ECEF, and the transformation matrices (6) and (7) can be used to obtain the ENU coordinates where the ground station is the origin. \(\overset{\rightarrow}{P_{s}}\) and \(\overset{\rightarrow}{P_{l}}\) are the position vectors of the satellite and interference source, respectively. The relative angle difference \(\psi\) can be derived by calculating the dot product of the two vectors using Equation (8). \[\overset{\rightarrow}{P_{s}}= \begin{bmatrix}x_{Es}\\ y_{Ns}\\ z_{Us}\end{bmatrix} = \begin{bmatrix}-\sin\lambda_{g}&\cos\lambda_{g}&0\\ -\sin\phi_{g}\cos\lambda_{g}&-\sin\phi_{g}\sin\lambda_{g}&\cos\phi_{g}\\ \cos\phi_{g}\cos\lambda_{g}&\cos\phi_{g}\sin\lambda_{g}&\sin\phi_{g}\end{bmatrix} \begin{bmatrix}X_{s}-X_{g}\\ Y_{s}-Y_{g}\\ Z_{s}-Z_{g}\end{bmatrix} , \tag{6}\]  
\[\overset{\rightarrow}{P_{l}}= \begin{bmatrix}x_{EI}\\ y_{Ni}\\ z_{Ui}\end{bmatrix} = \begin{bmatrix}-\sin\lambda_{g}&\cos\lambda_{g}&0\\ -\sin\phi_{g}\cos\lambda_{g}&-\sin\phi_{g}\sin\lambda_{g}&\cos\phi_{g}\\ \cos\phi_{g}\cos\lambda_{g}&\cos\phi_{g}\sin\lambda_{g}&\sin\phi_{g}\end{bmatrix}