1. Introduction
Recently, the low earth orbit (LEO) satellite constellation has received much attention for its low transmission delay, small path loss, large bandwidth, and global seamless coverage ability [
1,
2]. However, the available spectrum for the emerging LEO satellite constellation is scarce. The declared frequency bands for the typical mega-constellation satellites, such as Starlink, OneWeb, and Telesat, are mainly located in Ku-band, Ka-band, and Q/V-band [
3]. Moreover, the same frequency bands available for LEO satellites will also be used by the existing geostationary earth orbit (GEO) satellite systems and terrestrial mobile systems. Thus, severe intra-system and inter-system co-channel interference will occur when the LEO satellite constellations are deployed, and interference mitigation techniques are essential to guarantee the performance of these systems. The existing interference suppression schemes can be divided into several types, including spatial isolation (SI), cognitive radio (CR), adaptive power control (APC), beam hopping (BH), beam pointing optimization (BPC), etc.
SI refers to setting the exclusion zone for the interfering system. Then, the interfering system operating outside the exclusion zone can avoid harmful interference [
4]. The fixed exclusive angle is designed for the GEO satellite earth station to reduce the in-line interference from the LEO system [
5,
6]. However, the fixed exclusion zone is not suitable for the non-geostationary earth orbit (NGEO) satellite with high mobility. Thus, a dynamic protection area is defined to mitigate the harmful interference between GEO–NGEO [
7] or NGEO–NGEO satellite systems [
8]. However, the disadvantage of SI is that the protection area for the interfered satellite is the non-communication zone for the interfering satellite.
CR is also an effective technique to mitigate co-sharing spectrum interference [
9]. It can sense the available frequency band in the spectrum for use, which can improve spectrum efficiency and reduce the mutual interference between systems [
10,
11,
12]. Zhang et al. have proposed a spectrum strategy to distinguish the GEO signal from the interfering NGEO and noise [
13], and the GEO satellite can use the appropriate power to protect its normal communication. In [
14], a spectrum-sensing and power allocation-aided spectrum-sharing method is proposed to ensure the LEO system can work simultaneously with GEO systems in the interference region. However, CR cannot guarantee the long-term performance of the secondary systems.
APC has received great attention as a solution to reduce interference between satellite systems. In [
15], an adaptive power control technique is proposed to mitigate the in-line interference for the GEO–NGEO coexistence scenario. In [
16], a dynamic beam power adjustment strategy is proposed to avoid the in-line interference between the GEO–LEO satellite systems. APC can adapt the transmit power of the interfering system to satisfy the desired quality of service while protecting the interfered system. However, the co-channel interference is severe and dynamic for the LEO mega-constellation, and the power balance among many satellites is difficult.
BH can realize full frequency reuse over a certain beam hopping pattern and suppress the co-channel interference. In [
17], a beam hopping strategy is proposed to match uneven traffic demands and avoid interference to GEO ground stations. Moreover, the multi-satellite interference avoidance problem for NGEO satellite communication systems is solved by designing BH patterns with spatial isolation characteristics [
18]. Thus, a suitable BH pattern is designed for dynamically allocating resources and resisting interference. However, the complexity of BH pattern design will rapidly increase as the number of LEO satellites increases.
BPO can be used to adjust the antenna beam pointing direction to mitigate interference. In [
8], the harmful interference can be mitigated by turning off the beam or adjusting the satellite beam pointing. In [
19], the in-line interference between the LEO and GEO system can be mitigated by tilting the normal direction of the phased array antennas of LEO satellites. In [
20], the progressive pitch method and the coverage-expanding method are proposed to reduce interference, but the interference can be only partially solved for the high latitudes [
21]. Moreover, the adjustment of the satellite antenna beam pointing of the LEO mega-constellation means a huge computational overhead, which is difficult to achieve with the limited computing resources on the satellite. If the calculation of the optimal beam pointing is completed by the ground control centers with stronger computing capabilities, the time-varying antenna adjusting information should be sent back to the satellites frequently, which leads to an additional delay and signaling overhead.
However, the co-channel interference for the dense LEO satellite systems will be more complicated due to the overlapped coverage and time-varying interfering links. The above interference mitigation techniques cannot be directly applied to the dense LEO satellite systems. Thus, a distributed beam pointing optimization method based on interference situational awareness is proposed in this paper. Firstly, the interference situational database composed of the angle of departure (AoD) and the angle of arrival (AoA) of the time-varying interfering links can be collected at each UT. Then, the optimal beam pointing at each UT can be obtained by PSO optimization. The main contributions of this paper are summarized as follows:
With the time-varying interfering satellite set and minimum elevation constraint, the AoD and AoA of communication and interfering links can be calculated. Then, the AoD and AoA of interfering links are stored to construct the interference situational aware database, which is used for further beam pointing optimization;
With the interference situational aware database, the optimal beam pointing can be modeled as a non-convex optimization problem, and a distributed method based on particle swarm optimization (PSO) is proposed to maximize the signal-to-interference plus noise ratio (SINR) of each UT;
The performance of the proposed interference situational aware beam pointing optimization technology is verified by the simulation results.
The rest of this paper is organized as follows: in
Section 2, the system model and problem formulation are described. In
Section 3, the scheme of interference situational aware beam pointing optimization is analyzed. In
Section 4, simulation results and complexity analysis are presented. In
Section 5, conclusions are drawn. Matrices and vectors are denoted by bold letters.
denotes the vector that goes from A to B.
is the magnitude of
a.
is the estimation of
a. The major variables adopted in the paper are listed in
Table 1.
4. Results
In this section, we consider the dense LEO satellite communication scenario consisting of 6372 satellites in the Ka-band and multiple UTs. The orbital parameters of the LEO constellation are listed in
Table 2 [
37]. The positions of multiple users are randomly generated in a selected ground area, and the number of users is 16. Moreover, the detailed simulation parameters are shown in
Table 3. Note that the peak gain and 3 dB beamwidth of the satellite antenna in
Table 3 are applied for a single beam. The simulation environment is built on a PC with an Intel Core i7-10700F, 16 GB of RAM, and a Windows 10 (64 bit) system. In this paper, the data of satellite position are exported from Satellite Tool Kit (STK) 11.2.0, which provides a physics-based modeling environment for analyzing platforms and payloads in a realistic mission context [
38]. Due to the movement of the satellites, the overlapping area appears first and then disappears. Thus, the entire time of users covered by the overlapping coverage area is limited, and the maximum duration time is 21 s. During the entire simulation time, the maximum number of interfering satellites is
, and the minimum time slot is 1 s [
19].
We take the exhaustive search (ES) as the reference to verify the effectiveness of beam pointing optimization based on PSO. The ES traverses all directions with
and finds the maximum SINR. The PSO algorithm is implemented on each UT and runs independently. To compare the performance of difference schemes clearly, we select a user located at (39.56° N, 116.20° E) to show the simulations in
Figure 8,
Figure 9 and
Figure 10. For clarity, the scheme without a beam pointing optimization for interference avoidance is defined as BPO-WIA, while the schemes with a beam pointing optimization using ES and PSO are denoted as BPO-ES and BPO-PSO, respectively.
In
Figure 8, the SINR using BPO-WIA initially decreases and then increases. This is because the motion of the satellites causes the overlapping area to first increase and then decrease. Thus, the interference also increases first and then decreases. The most severe interference occurs when the user is covered by the center of the maximum beam overlapping area, so the SINR is low and even close to 0 dB at time index
and
. The lowest and average SINR is
dB (time index
) and
dB, respectively. The SINR with BPO-ES has the optimal SINR performance. However, the computation complexity of BPO-ES is highest, i.e.,
, where
is 0.1°. The time consumption for BPO-ES at each time slot is
s, as shown in
Table 4.
In
Figure 8, the optimized SINR of different particles and maximum iterations are shown. Moreover, the corresponding convergence curve at the moment of the strongest interference (time index
) is depicted in
Figure 9. In
Figure 8 and
Figure 9, when the number of particles is set as
, the obtained SINR using
or
outperforms that using
. In addition, when the maximum iterations are set to
, the optimized SINR using
or
is better than that using
. It can be concluded that the optimal value can be found with proper iterative times or particles. Furthermore, the time consumption is related to the number of particles and iterations. As shown in
Table 4, the computation complexity of BPO-PSO is
. To balance optimization performance and time consumption, we choose
and
in this paper. Its runtime for the one-shot optimization is approximately
s. According to
Figure 8, BPO-PSO
and BPO-ES can achieve almost the same performance and are better than BPO-WIA during the simulation time. The SINR achieved by BP-ES and BP-PSO at the strongest interference moment is
dB (time index
), and the average SINR is
dB. Thus, BPO-PSO is more suitable for the high dynamic LEO satellite scenario than BPO-ES due to its lower time consumption.
The SINR with different numbers of beams is shown in
Figure 10. The original SINR with BPO-WIA using
is lower than
due to the influence of co-channel interference. This is because the total beam coverage area and interfering links are increased due to the increase in the number of beams, which leads to a higher interference level. Moreover, at the time index
, the improvement of SINR obtained by BPO-PSO with
and
is
dB and
dB, respectively. At time index
, the improvement of SINR obtained by BPO-PSO with
and
is
dB and
dB, respectively. Thus, the BPO-PSO proposed in this paper can improve SINR with more gains for stronger interference scenarios, and it can also be applied to scenarios with various numbers of beams.
Furthermore, the simulation results of the multi-user scenario are provided in
Figure 11,
Figure 12 and
Figure 13. The receiving antenna pointing of each user can be optimized separately and achieve the maximum SINR. Based on the above optimized SINR, the complementary cumulative distribution function (CCDF) of the SINR is depicted in
Figure 11. The minimum SINR of BPO-WIA is
dB, while the minimum SINR of BPO-ES and BPO-PSO is
dB and
dB. Compared to BPO-WIA, the probability of BPO-PSO can achieve
% and
% improvement at SINR
dB and 10 dB; thus, the SINR is effectively improved for stronger interference. The multi-user average SINR of BPO-WIA, BPO-ES, and BPO-PSO is depicted in
Figure 12. The maximum, minimum, and mean SINR of multi-user with BPO-WIA are
dB,
dB, and
dB. With BPO-ES, the maximum, minimum, and mean SINR of multi-user are
dB,
dB, and
dB. With BPO-PSO, the maximum, minimum, and mean SINR of multi-user are
dB,
dB, and
dB. The average SINR of BPO-PSO is enhanced by
% compared to BPO-WIA. Moreover, compared to BPO-ES, the relative error of mean SINR of multi-user obtained by BPO-PSO is
%. Furthermore, the equivalent power flux density (EPFD) proposed in ITU Radio Regulations is used to evaluate the interference mitigation performance [
40]; the higher EPFD means a higher interference. The cumulative distribution function (CDF) curves of EPFD are given in
Figure 13. It can be seen that the CDF curve of EPFD of BPO-PSO basically overlaps with that of BPO-ES. Furthermore, the EPFD performance of BPO-ES and BPO-PSO is better than that of BPO-WIA. For example, the probability of BPO-PSO is improved by
% compared to BPO-WIA for EPFD = 103 dBW/m
2.