A Multi-Domain Resource Allocation Method Based on Beam-Skip Interference Avoidance for Low-Earth Orbit Satellites

Abstract

This invention relates to the field of satellite communications and addresses the problem of low resource utilization caused by existing hopping beam technology, which only considers the resource allocation of a single satellite and intra-satellite co-channel interference. The method analyzes intra-satellite and inter-satellite interference between two LEO satellites, sets cell weight priorities, and adaptively allocates power based on these priorities to obtain a cell power allocation matrix. Using the average traffic satisfaction of the cell as the optimization objective, the method first considers intra-satellite interference by designing the hopping beam pattern for a single LEO satellite, obtaining the time allocation matrix for each satellite throughout the hopping beam period. Secondly, considering inter-satellite interference, the method rearranges the obtained time allocation matrix using a heuristic algorithm to obtain the final required time slot scheduling matrix. This achieves the avoidance of intra-satellite and inter-satellite interference, significantly improving system throughput while ensuring fairness in user service.

Description

Technical Field

[0001] This invention relates to the field of satellite communications, and more specifically to a resource allocation method to avoid interference from low-Earth orbit satellites. Background Technology

[0002] Low Earth Orbit (LEO) satellites, with their low orbital altitude, wide coverage, and short communication latency, are poised to become a crucial component of integrated space-air-ground networks in recent years, thanks to the large-scale deployment of LEO constellations. However, the coverage areas of LEO satellites are unevenly distributed due to terrain and environmental factors, leading to uneven distribution of service demand. Continuing with the traditional method of evenly allocating resources would inevitably reduce resource utilization and system service quality. Furthermore, with the increasing number of LEO satellites in space, inter-satellite interference becomes significant. Beam hopping technology utilizes spatial and temporal isolation to avoid co-channel interference, while simultaneously providing more resources to areas with higher service demand, thereby improving resource utilization and ensuring fairness in cell service.

[0003] Current research on beam-hopping technology mostly focuses on high-orbit satellites, while the few studies on low-orbit satellites mainly focus on avoiding intra-satellite interference, lacking research on jointly optimizing multi-domain resources based on avoiding inter-satellite interference. Several studies on beam-hopping technology for low-orbit satellites exist: in 2020, LKZhao studied the resource optimization problem of a single low-orbit satellite, introducing a deep reinforcement learning network to improve system throughput; in 2019, WANGY X et al. adjusted beam size based on uneven service distribution to manage beam resources, allowing more users to access the system by covering more beam locations; in 2018, TANGJY et al. proposed a joint optimization algorithm for time, frequency, and power domain resources of low-orbit satellite systems based on beam-hopping, but this did not guarantee fairness in user service. Regarding interference avoidance, in 2021, WANGY et al. used the concept of clustering in low-orbit satellite systems based on beam-hopping, defining a minimum beam spacing to avoid inter-satellite co-frequency interference; and in 2019, KIBRIAM G et al. combined precoding and beam-hopping technology, using precoding to equalize inter-beam interference.

[0004] In summary, current research on beam hopping technology for low-Earth orbit (LEO) satellites is still very limited. Further research is needed in areas such as system model building, optimization problem setting, and performance evaluation. Moreover, existing beam hopping resource allocation algorithms have high computational complexity, and the limited computing power of LEO satellites prevents them from being directly applied to LEO satellites. Summary of the Invention

[0005] This invention aims to address the problems of low resource utilization and poor fairness in user services caused by existing beam-hopping technology, which only considers the resource allocation of a single satellite and intra-satellite co-frequency interference. Therefore, it provides a multi-domain resource allocation method based on beam-hopping to avoid interference from low-Earth orbit satellites.

[0006] The technical solution adopted in this invention is as follows:

[0007] A multi-domain resource optimization method based on beam skipping to avoid interference from low-Earth orbit satellites includes the following steps:

[0008] Step 1: Establish a low-Earth orbit (LEO) satellite system model, which includes two LEO satellites: LEO_1 and LEO_2. Both LEO satellites are equipped with controllable multi-hop beam antennas for downlink service transmission. Each LEO satellite covers M cells, where M is a positive integer; and each LEO satellite can generate a maximum of K beams, where K is a positive integer; and K << M. The total transmit power P of each LEO satellite is... total According to different power allocation schemes, the two low-orbit satellites serve each cell. Both satellites adopt a frequency reuse mode with full frequency reuse, that is, the available frequency band for the two satellites to light up their beams at the same time is the full bandwidth.

[0009] Step 2: Based on the low-Earth orbit satellite system model established in Step 1, analyze the communication link of the low-Earth orbit satellite system, specifically as follows:

[0010] The ground gateway assigns weights and priorities to each cell based on the cell's traffic demand and sends the data to the low-orbit satellite system through the gateway station. The low-orbit satellite system avoids interference from intra-satellite and inter-satellite co-frequency beams through beam scheduling and jointly optimizes multi-domain resources such as time slots, beam power resources, and signal-to-interference-plus-noise ratio (SINR).

[0011] Step 3: Perform adaptive power allocation for each cell based on the weight priority of each cell as described in Step 2. Obtain the optimal power allocation matrix by setting the number of iterations for the low-Earth orbit satellite system.

[0012] Step 4: Define the traffic satisfaction of the cell, wherein the traffic satisfaction is based on the traffic C provided by the low-Earth orbit satellite system. m With the required flow rate D m It is expressed as a ratio, that is: C m / D m The traffic satisfaction rate is used to measure the service quality of the low-Earth orbit satellite system.

[0013] Step 5: Decompose the traffic satisfaction of the cell described in Step 4 into the problem of designing the hopping beam pattern of a single satellite and the problem of rationally designing the time slot scheduling matrix to avoid inter-satellite interference.

[0014] Step Six: The solution method for the single-satellite hopping beam pattern design problem is as follows:

[0015] Among all beam selection schemes, select the effective hopping beam pattern BHTP that satisfies the space isolation condition, and obtain the number of times all effective hopping beam patterns BHTP are selected in the entire hopping beam period; then, based on the optimal power allocation matrix obtained in step three, obtain the solution to the hopping beam pattern design problem of a single satellite.

[0016] Step 7: The specific solution method for the problem of rationally designing the time slot scheduling matrix to avoid inter-satellite interference is as follows:

[0017] Define an interference penalty matrix and use existing heuristic algorithms to solve the time slot scheduling matrix of two low-Earth orbit satellites to avoid intra-satellite and inter-satellite interference; thus, obtain the solution to the problem of reasonably designing the time slot scheduling matrix to avoid inter-satellite interference.

[0018] Complete a multi-domain resource optimization based on beam skipping to avoid interference from low-Earth orbit satellites.

[0019] This invention has the following outstanding substantive features and significant progress:

[0020] This invention proposes a multi-domain resource allocation method based on beam hopping to avoid interference from low-Earth orbit (LEO) satellites. It analyzes intra-satellite and inter-satellite interference between two LEO satellites, sets cell weight priorities, and adaptively allocates power based on these priorities to obtain a cell power allocation matrix. Using the average traffic satisfaction of the cells as the optimization objective, the method first designs a beam hopping pattern for a single LEO satellite to address intra-satellite interference, obtaining a time allocation matrix for each satellite throughout the entire beam hopping period. Secondly, for inter-satellite interference, the obtained time allocation matrix is ​​rearranged using a heuristic algorithm to obtain the final required time slot scheduling matrix, thereby avoiding intra-satellite and inter-satellite interference and significantly improving system throughput while ensuring fairness in user services. Attached Figure Description

[0021] Figure 1 This is a schematic diagram of a system model for avoiding interference from low-Earth orbit satellites based on hopping beams.

[0022] Figure 1 The numbers within a cell covered by a medium-narrow beam are the cell numbers;

[0023] Figure 2 This is a schematic diagram of two BH scheme modes for two satellites in the same time slot;

[0024] Figure 3 This is a schematic diagram illustrating the convergence of the priority-based adaptive power allocation (JP-APAI) algorithm;

[0025] Figure 4This is a diagram comparing the service scenarios of four power allocation methods: priority-based adaptive power allocation (JP-APAI), average power allocation, on-demand power allocation, and priority-based power allocation.

[0026] Figure 5 This is a diagram comparing the average flow satisfaction of four power allocation algorithms.

[0027] Figure 6 yes Figure 5 A diagram showing the comparison of system throughput for four power allocation algorithms. Detailed Implementation

[0028] Detailed Implementation Method 1: Referring to the accompanying drawings in the instruction manual... Figure 1-6 The present invention provides a more detailed description of a multi-domain resource allocation method based on beam skipping to avoid interference from low-orbit satellites.

[0029] 1. Communication model

[0030] In the forward link of a hopping beam satellite communication system, assuming that the user receiver has already canceled out the Doppler shift, rain attenuation, shadow attenuation, etc. caused by the high-speed motion of the low-Earth orbit satellite, the channel coefficient between the k-th user and the j-th beam can be expressed as:

[0031]

[0032] Among them, G t (·) represents the transmit antenna gain, θ k,j G represents the angle between the line connecting the satellite and the user and the main axis of the beam. r (·) indicates the receiving antenna gain. Normally, the receiving antenna radiates omnidirectionally, i.e. That is, the maximum gain of the antenna at the receiving end, d k,j λ represents the distance between user k and beam j, and λ represents the wavelength of the carrier signal.

[0033] The radiation pattern of the multi-beam antenna is 3GPPTR 38.811, and its expression is:

[0034]

[0035] Where λ represents the wavelength, and a represents the radius of the antenna aperture. J1(·) is a class of first-order Bessel functions. θ is the off-axis angle. G m This indicates the maximum gain for satellite launch.

[0036] The expression for the signal-to-interference-plus-noise ratio (SINR) received by user k in time slot t is:

[0037]

[0038] Where B is the bandwidth, k is the Boltzmann constant, T represents the equivalent noise temperature, and P k P j S(k) and S(j) represent the transmit power of beam k and beam j, respectively, and S(k) and S(j) represent the satellites to which beam k and beam j belong, respectively.

[0039] Available throughput r of the cell m,t It can be represented as:

[0040]

[0041] II. Power Distribution

[0042] The cell weight priority is determined based on the traffic demand of the ground cell, using I. m This represents the cell weight priority, I = [I1, I2, ..., I...]. M ], M represents the number of satellite-covered cells, and the weight priority of the m-th cell can be expressed as:

[0043]

[0044] Where, d m This represents the traffic demand of the m-th cell.

[0045] Based on priority, multiple iterations are performed. Due to the limited onboard computing power of low-Earth orbit satellites, the number of iterations needs to be reasonably set to obtain the optimal power allocation matrix. The power of beam k during the iteration process can be expressed as:

[0046]

[0047] Where P total δ represents the total power of the satellite launch. k The ratio of the supplied capacity to the requested capacity, expressed as the average normalized weighted average, can be represented as:

[0048]

[0049] Among them, l k,m =1 indicates that cell m in time slot t is served by beam k, l k,m Otherwise, Q = 0. m C represents the required flow rate of the cell. m This represents the traffic provided by the system to the cell. During the iteration process, C is updated multiple times according to formula (6) and the capacity calculation formula. m This yields the optimal power allocation matrix. The capacity calculation formula can be expressed as:

[0050]

[0051] Where, N slot C represents the total number of time slots.m,t The flow provided by the system to cell m in time slot t can be expressed as:

[0052] C m,t =r m,t ×T slot (9)

[0053] Among them, T slot Indicates the time slot length.

[0054] Cell m in a hopping beam pattern period T H The required system capacity can be expressed as:

[0055] Q m =d m ·T H (10)

[0056] III. Optimizing Problem Modeling

[0057] For a binary system consisting of two low-Earth orbit satellites, the average traffic satisfaction of the system is defined with the goal of improving the average traffic satisfaction of the cell. It can be represented as

[0058]

[0059] in, M represents the traffic satisfaction level of cell m. i This represents the number of cells covered by the satellite. Based on the above, the optimization objective function for the two-satellite system is constructed as follows:

[0060]

[0061] In this matrix, X1 and X2 are both 0-1 matrices representing the hopping beam pattern BHTP of two hopping beam satellites. C1 limits each satellite to a maximum of K beams, C2 limits the capacity provided by the system within a BHTP, C3 indicates that the values ​​in the matrix can only be 0 or 1, and C4 indicates that the sum of the beam powers should not exceed the total transmit power P of the satellites. total S i This represents the set of beams belonging to satellite i.

[0062] Problem (12) is a non-convex NP-hard problem with high computational complexity. Therefore, in the process of solving it, it is decomposed into two subproblems that are easier to solve: the design of the hopping beam pattern of a single satellite and the avoidance of inter-satellite interference. This yields a suboptimal solution to the non-convex NP-hard problem, reduces the complexity of the algorithm, and ensures the accuracy and logic of the algorithm.

[0063] IV. Single Satellite Beam Jumping Pattern Design

[0064] Theoretically speaking, there are a total of beam allocation schemes. However, not all beam assignment schemes satisfy the spatial isolation principle of beam hopping. Therefore, we need to select a beam assignment scheme that meets the spatial isolation condition from all the schemes. First, we need to define an adjacency matrix. The element a ij ∈{0,1} indicates whether cell i and cell j are adjacent, and its value is determined by the following formula:

[0065]

[0066] Where, d ij Let R represent the distance between cell i and cell j, and let R represent the point beam radius, i.e., the cell radius. We take 4R as the critical value for analysis because previous studies have demonstrated that if the distance between users is greater than four beam radii, the co-channel interference between them can be ignored.

[0067] In addition, a binary vector is defined. This represents a hopping beam pattern, where elements in w that are 1 indicate that the cell is illuminated by the beam, and the number of 1s equals the number of illuminated beams K of the satellite. Similarly, a BHTP with spatial isolation conditions should satisfy the constraint that illuminated cells are not adjacent, i.e., satisfy:

[0068] w T Aw = 0 (14)

[0069] The optimization problem of single-satellite hopping beam pattern design can be expressed as:

[0070]

[0071] Among them, c i,m,n N represents the traffic provided by satellite i to cell m in the nth BHTP effective mode. i,v The number of valid patterns satisfying spatial isolation is represented by NTotal, and the number of times a valid pattern appears in the entire beam-hopping cycle is represented by NTotal. Constraints C1 and C4 are: the total number of valid BH patterns equals the number of time slots in one BH cycle; C2 is the traffic provided by satellite i to cell m in one beam-hopping cycle; C3 is that the number of BH patterns appears is a natural number; and C4 introduces an auxiliary variable to reduce the difficulty of the solution without affecting the fact that the solution is optimal.

[0072] V. Allocate time slots reasonably to avoid inter-satellite interference

[0073] Avoiding inter-satellite interference also utilizes the concept of spatial isolation, defining an interference penalty factor for two low-Earth orbit satellites operating in the same time slot for any two effective modes. Its expression is:

[0074]

[0075] Where, d pq This represents the distance between cell p and cell q. To represent two beam skipping pattern design schemes for two satellites, This represents the minimum distance between any two cells under both modes.

[0076] The interference penalty matrices for satellites a and b can be expressed as:

[0077]

[0078] Where, N a,v N b,v Let represent the number of effective modes for satellite a and satellite b, respectively. The optimization problem of solving the time slot scheduling matrix can be expressed as:

[0079]

[0080] Where Tr(·) represents the sum of the diagonal elements of the matrix, τ1 and τ2 represent the time slot scheduling matrices of the two low-orbit satellites, and C1 represents the number of times the x-th effective mode of the i-th satellite occurs within the entire beam hopping period. C2 indicates that a time slot has one and only one valid BH mode, and C3 restricts the values ​​of the time slot scheduling matrix elements.

[0081] Considering the high computational complexity of the algorithm and the fact that the matrix operation is a non-convex problem, a heuristic algorithm is used to calculate the time slot scheduling matrices τ1 and τ2 for the two low-orbit satellites during the solution process.

[0082] VI. Multi-domain resource allocation algorithm based on beam skipping to avoid interference from low-Earth orbit satellites

[0083] As shown in Table 1, the JP-APAI algorithm obtains the optimal power allocation matrix through reasonable iteration based on the defined cell weight priority. The original problem is decomposed into two sub-problems: single-satellite hopping beam pattern design and reasonable time slot allocation to avoid inter-satellite interference. For single-satellite hopping beam pattern design, an adjacency matrix is ​​defined, and the number of selections of all effective BHTPs within the entire hopping beam period is obtained. The D-BHTP algorithm is shown in Table 2. For reasonable time slot allocation to avoid inter-satellite interference, an interference penalty matrix is ​​defined, and the time slot scheduling matrix for two low-Earth orbit satellites is solved based on a heuristic algorithm. The H-TSSM algorithm is shown in Table 3.

[0084] Table 1: Priority-based Adaptive Power (JP-APAI) Algorithm

[0085]

[0086] Table 2: Single Satellite Beam Hopping Pattern Design (D-BHTP)

[0087]

[0088] Table 3: Heuristic Allocation of Time Slots to Avoid Inter-Satellite Interference (H-TSSM)

[0089]

[0090] VII. Simulation Experiment

[0091] The invention will now be described in detail with reference to simulation experiments. The simulation parameters are shown in Table 4.

[0092] Table 4 Simulation Parameters

[0093]

[0094] Figure 1 This is a schematic diagram of the system model of the present invention;

[0095] Figure 2 This is a schematic diagram of two BH scheme modes for two satellites in the same time slot;

[0096] Figure 2 As can be seen, the smaller the shortest distance between the two BH schemes, the larger the interference factor, and the lower the probability that the two BH modes of the two satellites will appear in the same time slot.

[0097] Figure 3 This is a schematic diagram illustrating the convergence of the priority-based adaptive power allocation (JP-APAI) algorithm;

[0098] Figure 3 As can be seen from the results, the algorithm has good convergence. It can converge to the optimal value in the fourth iteration, making it suitable for on-board computing on low-Earth orbit satellites.

[0099] Figure 4 This is a comparison chart of the service status of four power allocation methods: priority-based adaptive power allocation (JP-APAI), average power allocation, on-demand power allocation, and priority-based power allocation.

[0100] Figure 4 The data shows the supply-demand ratio of each cell throughout the entire beam hopping cycle. For unserved cells under each power allocation algorithm, this is because there are very few or no effective modes that meet the spatial isolation conditions for that cell, so there are unserved cases.

[0101] Figure 5 This is a diagram comparing the average system flow satisfaction of four power allocation algorithms;

[0102] The average supply-demand ratio of all cells is defined as an indicator to measure the average traffic satisfaction of cells. The larger the value, the higher the average traffic satisfaction of the cells. As can be seen from the figure, the JP-APAI algorithm has a higher average value than the average power allocation, on-demand power allocation, and priority power allocation, which means that the average traffic satisfaction of this algorithm is better than the other three algorithm systems.

[0103] Figure 6 yes Figure 5 A diagram comparing the system throughput of four power allocation algorithms in China;

[0104] from Figure 6 As can be seen, using system throughput as a performance indicator, the JP-APAI algorithm shows a significant increase compared to the other three power allocation algorithms. Figure 5 and Figure 6 It can be seen that the JP-APAI algorithm improves the system throughput while ensuring the average system flow satisfaction.

[0105] The above description is merely illustrative of the technical solution of the present invention and is not intended to limit it. The present invention should not be limited to the content disclosed in the embodiments and accompanying drawings. Any modifications made within the spirit and principles of the present invention are within the protection scope of the present invention.

Claims

1. A multi-domain resource optimization method based on beam skipping to avoid interference from low-Earth orbit satellites, characterized by: It includes the following steps: Step 1: Establish a low-Earth orbit (LEO) satellite system model, which includes two LEO satellites: LEO_1 and LEO_2. Both LEO_1 and LEO_2 are equipped with controllable multi-hop beam antennas for downlink service transmission. Each LEO satellite covers M cells, where M is a positive integer; and each LEO satellite can generate a maximum of K beams, where K is a positive integer; and K << M. The total transmit power P of each LEO satellite is... total According to different power allocation schemes, the two low-orbit satellites serve each cell. Both satellites adopt the frequency reuse method of full-frequency reuse, that is, at the same time, the available frequency band for the two low-orbit satellites to light up the beams is the full bandwidth. Step 2: Based on the low-Earth orbit satellite system model established in Step 1, analyze the communication link of the low-Earth orbit satellite system, specifically as follows: The ground gateway assigns weights and priorities to each cell based on the cell's traffic demand and sends the data to the low-orbit satellite system through the gateway station. The low-orbit satellite system avoids interference from intra-satellite and inter-satellite co-frequency beams through beam scheduling and jointly optimizes multi-domain resources such as time slots, beam power resources, and signal-to-interference-plus-noise ratio (SINR). Step 3: Perform adaptive power allocation for each cell based on the weight priority of each cell as described in Step 2. Obtain the optimal power allocation matrix by setting the number of iterations for the low-Earth orbit satellite system. Step 4: Define the traffic satisfaction of the cell, wherein the traffic satisfaction is based on the traffic C provided by the low-Earth orbit satellite system. m With the required flow rate D m It is expressed as a ratio, that is: C m / D m The traffic satisfaction rate is used to measure the service quality of the low-Earth orbit satellite system. Step 5: Decompose the traffic satisfaction of the cell described in Step 4 into the problem of designing the hopping beam pattern of a single satellite and the problem of rationally designing the time slot scheduling matrix to avoid inter-satellite interference. Step Six: The solution method for the single-satellite hopping beam pattern design problem is as follows: Among all beam selection schemes, select the effective hopping beam pattern BHTP that satisfies the space isolation condition, and obtain the number of times all effective hopping beam patterns BHTP are selected in the entire hopping beam period; then, based on the optimal power allocation matrix obtained in step three, obtain the solution to the hopping beam pattern design problem of a single satellite. Step 7: The specific solution method for the problem of rationally designing the time slot scheduling matrix to avoid inter-satellite interference is as follows: Define an interference penalty matrix and use existing heuristic algorithms to solve the time slot scheduling matrix of two low-Earth orbit satellites to avoid intra-satellite and inter-satellite interference; thus, obtain a solution to the problem of rationally designing the time slot scheduling matrix to avoid inter-satellite interference. Complete a multi-domain resource optimization based on beam skipping to avoid interference from low-Earth orbit satellites.

2. The multi-domain resource optimization method based on beam skipping to avoid low-Earth orbit satellite interference as described in claim 1, characterized in that... In step two, the expression for the signal-to-interference-plus-noise ratio (SINR) received by user k in time slot t is: Where: B is the bandwidth; k is the Boltzmann constant; T represents the equivalent noise temperature; P k P j S(k) and S(j) represent the transmit power of beam k and beam j, respectively, and S(k) and S(j) represent the satellites to which beam k and beam j belong, respectively.

3. The multi-domain resource optimization method based on beam skipping to avoid low-Earth orbit satellite interference as described in claim 1, characterized in that... In step three, the optimal power allocation matrix is ​​expressed as: Where: P total δ represents the total power of the satellite launch. k This represents the ratio of provided capacity to requested capacity after average normalized weighting.

4. The multi-domain resource optimization method based on beam skipping to avoid low-Earth orbit satellite interference according to claim 1, characterized in that... In step four, the defined traffic satisfaction level for the cell is... Its expression is: in: Q represents the traffic satisfaction of cell m. m M represents the traffic demand of the community. i This represents the number of cells covered by the satellite, where i is a positive integer.

5. The multi-domain resource optimization method based on beam skipping to avoid low-Earth orbit satellite interference according to claim 1, characterized in that... In step six, the problem of designing the hopping beam pattern for a single satellite is solved using the formula: Solved; Where: c i,m,n N represents the bandwidth provided by satellite i to cell m in the nth type of BHTP effective beam pattern. i,v The number of valid patterns that satisfy spatial isolation is represented by NTotal, which represents the number of times a valid pattern appears in the entire hop beam cycle. The constraint C1 represents the total number of valid beam patterns that appear, which is equal to the number of time slots contained in one beam pattern cycle. C2 represents the traffic provided by satellite i to cell m in one hop beam cycle. C3 represents the number of times the beam pattern BHTP appears is a natural number. C4 introduces an auxiliary variable.

6. The multi-domain resource optimization method for avoiding low-Earth orbit satellite interference based on beam skipping as described in claim 1, characterized in that... In step seven, the interference penalty matrix is ​​defined as follows: Where, N a,v N b,v These represent the number of valid modes for LEO_1 and LEO_2 low-Earth orbit satellites, respectively.

7. The multi-domain resource optimization method for avoiding low-Earth orbit satellite interference based on beam skipping as described in claim 6, characterized in that... In step seven, the solution to the problem of avoiding inter-satellite interference by rationally designing the time slot scheduling matrix is ​​obtained through the formula: Solved; Where Tr(·) represents the sum of the diagonal elements of the matrix, and τ1 and τ2 represent the time slot scheduling matrices of the two low-Earth orbit satellites, respectively. The time slot scheduling matrices τ1 and τ2 are obtained using existing heuristic algorithms; C1 represents the number of times the x-th effective mode of the i-th satellite occurs during the entire beam hopping period. C2 indicates that a time slot has one and only one valid beam pattern BHTP mode; C3 is used to restrict the values ​​of the elements in the time slot scheduling matrix.

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