1. Introduction

2. Scenario of Interference Source Moving along the Satellite Trajectory

2.1. LEO Satellite Downlink Scenario and J/S Ratio Calculation

Figure 1 shows a conceptual figure of a LEO satellite downlink scenario in an interference situation where the ground station is exposed to strong EM waves incoming from an airborne source that moves along a path parallel to the LEO satellite trajectory. The LEO satellite moves along a trajectory with an altitude of h_s and transmits image data to the ground station through an X-band downlink. When the ground station is assumed to be the center of the coordinates, _s is the elevation angle between the LEO satellite and the Earth’s surface, and d_s is the slant distance from the ground station to the satellite. As the satellite transmits image data to the ground station, the airborne interference source moves parallel to the trajectory of the LEO satellite at a distance d_p from the ground station. The elevation angle between the interference source and the Earth’s surface is _i, and the slant distance to the interference source is d_i. The satellite transmits image data between t₁ and t_n to the ground station located at a specific latitude and longitude on the Earth’ surface. The ideal data communication time is about 600 seconds, during which the relative angle difference between the LEO satellite and the airborne interference source is . To analyze the link budget under these conditions, the J/S ratio can be calculated using Equation (1)

(1)

where S is the power received by the ground station, and $P_t^s$ is the transmit power from the LEO satellite. $G_t^s$ is the bore-sight gain of the data transmission antenna in the satellite. $G_r^g$ (ξ) is the gain pattern of the ground station antenna according to the steering angle ξ, and $G_r^g$ (ξ = 0°) is the bore-sight gain of the ground station antenna. Here, it is assumed that the ground station antenna is tracking precisely in the direction of the satellite, and thus the gain of the ground station toward the satellite is always $G_r^g$ (ξ = 0°). L_s is the path loss between the LEO satellite and the ground station, calculated assuming free space. J is the power received at the ground station from the airborne interference source and is calculated in a similar way to S. $P_t^i$ is the transmission power from the airborne interference source, and $G_t^i$ is the bore-sight gain of the airborne interference source antenna. $G_r^g$ (ξ = ) is the sidelobe gain of the ground station antenna to the direction where the ground station is exposed to strong EM interference waves incoming. L_i is the path loss from the airborne interference source to the ground station.

Figure 1. Conceptual figure of the LEO satellite downlink scenario under interference situations.

Figure 1. Conceptual figure of the LEO satellite downlink scenario under interference situations.

2.2. Derivation of Relative Angle Difference 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 consists 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 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 is defined. 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 _g, longitude _g, and altitude h_g of the ground station according to WGS84 are indicated by the green square marker in Figure 2(a). To calculate the relative angle difference , the WGS84 coordinates of the LEO satellite, ground station, and airborne interference source are converted into 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 by Equation (3a), where a (= 6378.137 km for WGS84) is the ellipsoidal equatorial radius and e is the eccentricity of the ellipsoid (e² = 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 , longitude , and altitude h using Equations (3b) to (3d):

(3a)

(3b)

(3c)

(3d)

Now the locations of the ground station, LEO satellite, and airborne interference source are converted from WGS84 to ECEF, and the transformation matrices (4a) and (4b) can be used to obtain the ENU coordinates where the ground station is the origin. $\underset{P_s}{\to }$ and $\underset{P_i}{\to }$ are the position vectors of the satellite and interference source, respectively. The relative angle difference can be derived by calculating the dot product of the two vectors using equation (4c).

(4a)

(4b)

(4c)

Figure 3 shows the radiation pattern of a ground station antenna with parabolic reflector and rectangular feed horn. The bore-sight gain of the antenna is 59 dBi at 8 GHz. The blue solid line indicates the radiation pattern obtained using GO and PO methods. The GO method is used to model the antenna focusing and reflection inside the reflector, and the PO method is used to calculate the scattering and refraction on the reflector surface by considering the current distribution on the surface. By combining these two methods, the ground station antenna radiation pattern can be calculated. The parabolic diameter of the ground station antenna is 11.3 m, and a feed horn antenna with rectangular aperture is employed. Since sidelobe gain exhibits large fluctuations according to angle, we apply a regression model to it in order to more easily observe the tendency of the J/S ratio. The regression model is based on the exponential Equation (5)

(5)

where a₁ (=−31.5817), a₂ (=36.7337), b₁(=0.0046), and b₂ (=−0.0682) are the coefficients that best fit to the point, shown as the red solid line. To determine the sidelobe gain, we apply the obtained from Equation (4c) to Equation (5). Detailed parameters for the downlink interference scenarios are given in Table 1.

3. Analysis of the LEO Satellite Downlinks in Interference Situations

Figures 5(a) and 5(b) show the airborne interference source paths during data communication time on March 13, 2023. d_p is the distance between the ground station and the interference source, and the minimum d_p for paths 1, 2, and 3 is 100 km, 200 km, and 300 km, respectively, with the paths parallel to LEO satellite Trajectory 1. The paths of the interference source and satellite, and the ground station location, are illustrated on a WGS84 map. To observe the movement of the interference source from the perspective of the ground station, its elevation angle _i and slant distance d_i are derived using ENU coordinates, with the ground station as the origin location. When the altitude of the interference source is fixed at 12 km, the maximum elevation angles are 6.7° (Path 1), 3.4° (Path 2), and 2.2° (Path 3). The minimum slant distances are 101.6 km (Path 1), 201.7 km (Path 2), and 301.9 km (Path 3).

Figure 6 shows the relative angle difference and J/S ratio results obtained by varying the altitude of the airborne interference when the LEO satellite moves along Trajectory 1. In order to more easily observe the trends according to path and altitude during data communication time (n = 1, N = 600), the average and J/S ratio are obtained using Equations (6a) and (6b):

(6a)

(6b)

Figures 6(a) and 6(b) show  and the J/S ratio when the altitudes of the interference source in Path 1 are 3 km, 6 km, 9 km, and 12 km. The _ave values according to these altitudes are 73.2°, 72.2°, 71.2°, and 70.2°, respectively. The J_ave/S_ave ratios for these altitudes are −22.3 dB, −22.1 dB, −21.9 dB, and −21.7 dB, respectively. Figures 6(c) and 6(d) present the and J/S ratio according to altitude when the interference source moves along Path 2. For each altitude, the _ave values are 80.8°, 80.3°, 79.8°, and 79.3° , respectively. The J_ave/S_ave ratios are –29.5 dB, –29.4 dB, –29.2 dB, and –29.1 dB, respectively. The and J/S ratio when the interference source moves along Path 3 are illustrated in Figures 6(e) and 6(f).

Figure 7(a) shows the paths of the airborne interference source and LEO Trajectory 2 on a WGS84 map for March 16, 2023. The minimum d_p for paths 1, 2, and 3 is 100 km, 200 km, and 300 km, respectively, and the paths are parallel to LEO satellite Trajectory 2. Figure 7(b) shows the elevation angle _i and slant distance d_i for when the interference source moves along path 1, 2, and 3 at an altitude of 12 km. The maximum elevation angles are 6.7° (Path 1), 3.4° (Path 2), and 2.2° (Path 3). When the interference source is located at the maximum elevation, the slant distances are 101.2 km (Path 1), 201.5 km (Path 2), and 301.2 km (Path 3).

Figures 8(a) and 8(b) show  and the J/S ratio according to the different altitudes of the airborne interference source. When the source moves along Path 1 at altitudes of 3 km, 6 km, 9 km, and 12 km, the _ave values are 59.4°, 58.4°, 57.3°, and 56.3°, respectively, and the J_ave/S_ave ratios are −18.7 dB, −18.4 dB, −18.2 dB, and −17.9 dB, respectively. Figures 8(c) and 8(d) show the results of  and J/S depending on altitude when the interference source moves along Path 2. The _avevalues at these altitudes are 67.1°, 66.6°, 66°,and 65.5°, respectively. The J_ave/S_ave ratios are –26 dB, –25.9 dB, –25.8 dB, and –29.1 dB, respectively. Figures 8(e) and 8(f) present the and J/S ratios when the interference source moves along Path 3. _ave values are 70°, 69.7°, 69.3°, and 68.9°, and J_ave/S_ave ratios are −30.3 dB, −30.2 dB, −30.1 dB, and −30.1 dB, respectively.

Figures 10(a) and 10(b) show the and J/S ratios when the airborne interference source moves along Path 1. For altitudes of 3 km, 6 km, 9 km, and 12 km of the airborne interference source, the _ave values are 40.7°, 39.6°, 38.5°, and 37.5°, respectively. The J_ave/S_ave ratios are −12.2 dB, −11.9 dB, −11.5 dB, and −11.1 dB, respectively. Figures 10(c) and 10(d) present the  and J/S ratios for Path 2. The _ave values are 48.4°, 47.8°, 47.3°, and 46.8°, and the J_ave/S_ave ratios are –20.1 dB, –19.9 dB, –19.7 dB, and –19.6 dB, respectively.

Figures 10(e) and 10(f) illustrate the and J/S ratios when the interference source moves along Path 3. The _ave values are 51.3°, 69.7°, 69.3°, and 68.9°, with the J_ave/S_ave ratios of –30.3 dB, –30.2 dB, –30.1 dB, and –30.1 dB, respectively.

In Table 2, _ave values and J_ave/S_ave ratios are summarized. As can be seen from these results, for satellite Trajectory 1, the highest _ave value (83.6°) is observed when the interference source moves on Path 3 at an altitude of 3 km. In this case, the J_ave/S_ave ratio is also the lowest at −33.6 dB. When the satellite moves along Trajectory 3 with Path 1 (an altitude of 12 km), the lowest _ave value (37.5°) and the highest J_ave/S_ave ratio (−11.1 dB) are observed. For Trajectory 1 (with Path 1), the _ave at an altitude of 12 km is about 3° lower than that at an altitude of 3 km. On the other hand, the J_ave/S_ave ratio at 12 km is 0.6 dB higher than at 3 km. As altitude h_i increases, _ave decreases and the J_ave/S_ave ratio increases slightly. These results show that the relative angle difference between LEO satellite and interference source is critical factor for J/S ratio.

4. Conclusions

We analyzed LEO satellite downlinks under interference situations when airborne interference sources move parallel to the LEO satellite trajectory by considering relative angle differences between satellites and interference sources. To make interference situations more like actual environments, the LEO trajectories were obtained from TLE data. Airborne interference sources with various altitudes moved parallel to the satellite trajectories, and the J/S ratio was calculated according to the relative angle differences between the ground station, satellite, and interference source. In order to calculate the relative angle difference , the satellite and interference source coordinates were converted from the WGS84 to the ENU coordinate system. By applying the relative angle difference , we obtained the sidelobe gain of the ground station antenna in the direction from which the interference comes from the ground station antenna. Through comprehensive link budget analysis, the J/S ratio was found to be 22.5 dB higher in Trajectory 3, where the relative angle difference was small compared to the other trajectories. These results showed that although the distances between ground station, LEO satellite, and interference source were important from the J/S ratio perspective, the relative angle difference between interference source and satellite is the even more critical factor.

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