1. Introduction
Low-Earth orbit (LEO) satellites have been widely used to perform various Earth observation missions, such as resource monitoring, weather surveillance, and military reconnaissance, while circling the Earth along a trajectory below 2,000 km in altitude [
1,
2]. To perform these missions effectively, the satellites often employ synthetic aperture radars to capture high-resolution images of the Earth’s surface, and the image data is then transmitted at high speed to ground stations using X-band downlinks. The data communication time between LEO satellites and ground stations is limited to a maximum of 10 minutes, though this varies slightly depending on the satellite trajectory. In order to predict whether or not image data can be received within such a short period of time, link budget analysis that considers various environmental factors is essential. Link budget analysis considering natural earth environment, such as atmospheric impact [
3,
4,
5] and Doppler shift [
6,
7,
8], has been previously conducted. In addition, studies on link budget in interference environments where ground station antennas are exposed to intentional electromagnetic (EM) interference sources, have also been investigated [
9,
10,
11]. Although some research has been conducted in various interference situations, there is a lack of studies analyzing real LEO satellite trajectories and airborne interference sources. Additionally, more in-depth research is required to accurately derive link budgets by considering the sidelobe gain of the ground station antenna based on the relative angle difference between the LEO satellite and the airborne interference source.
In this paper, we analyze LEO satellite downlinks under interference situations when airborne interference sources move parallel to the satellite trajectory by considering the relative angle differences between the satellites and the interference sources. To make interference situations more like actual environments, we use two-line element set (TLE) data of LEO satellite trajectory information including geodetic coordinates provided by the Joint Space Operations Center at Vandenberg Air Force Base. Airborne interference sources with various altitudes (3 km, 6 km, 9 km, and 12 km) move parallel to the trajectories of the LEO satellites, and the jamming to signal (
J/
S) ratio is calculated based on the relative angle differences between the ground station, satellite, and interference source. In order to express the positions of these three elements, the World Geodetic System 1984 (WGS84) coordinates are converted to the ground station-centered east-north-up (ENU) system [
12,
13]. Based on the ENU coordinates, the relative angle difference between the satellite and the interference source is calculated, and the sidelobe gain of the ground station antenna to the direction where interference electromagnetic (EM) waves are incoming. The radiation pattern of the ground station antenna is obtained using geometrical optics (GO) and physical optics (PO) [
14], and the sidelobe gain is then obtained and applied to the
J/
S ratio calculation. We investigate the link budget under interference situations in which airborne interference sources move at a minimum distance of 100 km (Path 1), 200 km (Path 2), and 300 km (Path 3) from the ground station. For each path, the elevation angle and slant distance between interference source and ground station are calculated during data communication time according to altitudes of the airborne interference source. In all scenarios, the data communication time between the LEO satellite and the ground station is assumed to be approximately 600 seconds. We examine the
J/
S ratio results according to satellite trajectories with maximum elevation angles of 86.8° (Trajectory 1), 62.7° (Trajectory 2), and 37.3° (Trajectory 3). The trends in relative angle difference and
J/
S ratio according to the paths and altitudes of the interference source are observed, and the results confirm that the
J/S ratio increases as the relative angle difference decreases. These results show that although the distances between ground station, LEO satellite, and interference source are important from a
J/
S ratio perspective, the relative angle difference between interference source and satellite is an even more critical factor.
3. Analysis of the LEO Satellite Downlinks in Interference Situations
Figure 4(a) shows the satellite trajectories obtained from the TLE data. The blue, red, and green solid lines with circle markers represent the trajectories of the LEO satellite for March 13 (Trajectory 1), March 16 (Trajectory 2), and March 21 (Trajectory 3), 2023, respectively. The ground station is located at latitude 36.33° and longitude 127.26°. The time at which communication between this ground station and the LEO satellite begins is defined as
t_{1}, and when communication ends is defined as
t_{n}. In general, the data communication time is less than 600 seconds, so
t_{1} and
t_{n} are respectively defined as 0 and 600 seconds in this scenario.
Figure 4(b) shows the slant distance
d_{s} and elevation angle
q_{s} between the ground station and the LEO satellite for each trajectory. The maximum elevation angles of Trajectory 1, Trajectory 2, and Trajectory 3 are 86.8°, 62.7°, and 37.3°, respectively, and the slant distances from the ground station to the satellite at the maximum elevation angle of each trajectory are 550.9 km, 618.6 km, and 908.1 km, respectively.
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):
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.
Figure 9(a) is for the case of Trajectory 3 (March 21, 2023). The maximum elevation angles for Paths 1, 2, and 3 are 6.7°, 3.4°, and 2.2°, respectively, and the slant distances are 101.6 km, 201.7 km, and 301.9 km, 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.