Satellite slant beam interferences avoidance method and system based on cost flow and dynamic graph coloring

Abstract

The application discloses a satellite slant beam inter-beam interference avoidance method and system based on cost flow and dynamic graph coloring, and accurately models the interference range of slant beams in a multi-satellite satellite hop-beam system, considers the influence of the slant beams when modeling the anti-beam inter-beam interference hop-beam pattern design problem, divides the dynamic graph coloring problem into two sub-problems of satellite-wave position matching and hop-beam time slot allocation which are coupled with each other, pre-solves the satellite-wave position matching problem by using a minimum cost maximum flow algorithm, obtains a satellite-wave position matching initial solution which maximizes the sum of satellite elevation angles of all wave positions in the system under the constraint of the maximum number of simultaneously opened beams of the satellite, and on the basis, combines a tabu search algorithm and a graph coloring algorithm to jointly optimize the two sub-problems, so as to further improve the inter-beam interference avoidance performance of the same hop-beam time slot opened beam. The application can obtain a multi-satellite hop-beam scheme with minimum inter-beam interference, and the algorithm has low complexity and is convenient for actual system implementation.

Description

Technical Field

[0001] This invention belongs to the field of satellite communication, specifically relating to a method and system for avoiding inter-beam interference in satellite oblique beams based on cost flow and dynamic graph coloring. Background Technology

[0002] Large-scale low-Earth orbit (LEO) satellite communication systems are a key technology for achieving ubiquitous connectivity and seamless global coverage. To fully utilize the limited and precious space, time, frequency, and power resources on board and achieve effective coverage of all ground areas, satellites often employ beam hopping, generating beams in different time slots to serve different ground cells. However, with the rapid increase in the number of satellites, satellite beam density also increases rapidly. How to efficiently avoid inter-beam interference has become a key factor limiting the performance of large-scale satellite communication systems.

[0003] Traditional methods for allocating anti-jamming resources in satellite hopping beam systems typically employ relatively simple interference assessment metrics, such as geographical distance between beam positions, beam angles, and the number of beams activated in the same hopping beam time slot. However, these metrics are insufficient to effectively describe the interference characteristics of oblique beams, easily leading to missed interference detection and decreased interference avoidance performance. When the satellite beam elevation angle is small, the interference region becomes irregular in shape, and the interference area increases dramatically. Accurate modeling of the interference range for such beams requires knowing the coordinates of both the satellite and ground beam positions. Currently, there is a lack of methods for designing anti-jamming hopping beam patterns in scenarios involving accurate modeling of oblique beam interference. Summary of the Invention

[0004] Purpose of the invention: The purpose of this invention is to provide a method and system for avoiding inter-beam interference in satellite oblique beams based on cost flow and dynamic graph coloring, so as to obtain a hopping beam pattern with better inter-beam interference avoidance performance.

[0005] Technical Solution: To achieve the above-mentioned objectives, the first aspect of this invention provides a method for avoiding inter-beam interference in satellite oblique beams based on cost flow and dynamic graph coloring, comprising the following steps:

[0006] Considering the characteristics of the interference region of oblique satellite beams, a three-dimensional tensor with dimensions of satellite, target wave position, and interfered wave position is established to characterize the interference of satellite beams on wave positions other than the target wave position;

[0007] The design problem of anti-inter-beam interference hopping beam pattern for multi-satellite hopping beam systems is modeled as a dynamic graph coloring problem. The optimization variable satellite-position matching determines the topology of the system interference graph, thereby determining the optimization variable hopping beam time slot allocation. The edges in the interference graph are determined based on the optimization variable satellite-position matching and the three-dimensional tensor. The dynamic graph coloring problem is divided into two mutually coupled sub-problems: satellite-position matching and hopping beam time slot allocation.

[0008] The minimum cost maximum flow algorithm is used to pre-solve the satellite-wave position matching subproblem, and the initial solution of satellite-wave position matching is obtained to maximize the sum of the elevation angles of all wave position serving satellites in the system under the constraint of the maximum number of beams that can be opened simultaneously by the satellite.

[0009] Based on the initial solution of satellite-wave position matching, the tabu search algorithm and graph coloring algorithm are combined to jointly optimize the two sub-problems of satellite-wave position matching and hopping beam slot allocation, so as to further reduce the interference between open beams in the same hopping beam slot.

[0010] Furthermore, the three-dimensional tensor is established. Its elements Indicates when the target wave position by satellite During service, wave position Whether it will be subject to strong interference; if so, record it as 1, indicating the current wave position. Cannot be with wave position If a signal is received in the same hop beam time slot, it is served; otherwise, it is recorded as 0, indicating that the signal can be served in the same hop beam time slot. Let i be the ground location within the interfered wave position i, where Indicates ground location The corresponding wave position For satellite beams in The received power at that location, This is the preset interference threshold.

[0011] Furthermore, the optimized variables satellite-position matching and hopping beam slot allocation are respectively denoted as... , ,in Representing wave positions The serving satellites and the servicing hop beam time slots, The ground spectral density is denoted as ; the interference diagram of the system is denoted as . ,in The set of points is equal to the set of wave positions. For each wave position node, the set of edges is defined. It needs to send to all satellites to wave position Beam interference wave position node Edges, i.e., nodes With all elements at corresponding positions that satisfy the three-dimensional tensor nodes Connect the edges.

[0012] Furthermore, the solution for the initial solution of the satellite-wave position matching includes:

[0013] Describe the cost flow network as Establish source point Hehuidian Then the set of nodes The set of edges is the union of the source point, sink point, satellite set, and ground wave position set. There are three types of directed edges in the graph. The first type of edge starts from the source vertex. Points to all satellite nodes, and the capacity of each edge is the same as that of the satellite nodes. Maximum number of beams that can be opened Positive correlation function The first type of edge has a cost of 0 and is used to limit the number of wavelengths served by each satellite to no more than its service capacity; the second type of edge points from all satellite nodes to all wavelength nodes, has a capacity of 1, and its cost is the cost of the corresponding satellite. to wave position Beam elevation angle The opposite of the value is used to minimize the total cost of all beams by solving the minimum-cost maximum flow problem, thereby maximizing the sum of the elevation angles of all serving beams in the system; the third type of edge points from all beam position nodes to the sink. The cost is 0, and the capacity is [wavelength value]. Number of times it needs to be covered within a single beam hopping cycle This is used to ensure that the coverage requirements of each wavelength are met;

[0014] The minimum cost maximum flow algorithm is used to find the maximum flow on the network that minimizes the total cost, thereby obtaining the maximum satellite-beam matching scheme with the highest elevation angle for all service beams in the system.

[0015] Furthermore, the joint optimization algorithm starts from a pre-set sufficiently low interference threshold. Initially, the interference threshold is used to determine the values ​​of elements in the three-dimensional tensor; each time, the current interference threshold is... Add an increment The joint optimization algorithm determines the appropriate use of the interference threshold. If it is possible to achieve conflict-free coloring, then the current threshold is the optimal threshold, the obtained conflict-free coloring scheme is the optimal anti-interference beam hopping pattern, and the algorithm terminates; otherwise, continue adding more colors. Perform a search; among which The number of hop beam periods is included in the hop beam period.

[0016] Furthermore, when performing threshold feasibility judgment, the joint optimization algorithm uses a tabu search algorithm as the outer framework and a nested graph coloring algorithm as the inner framework, performing several rounds of iteration until convergence. In each round of iteration, neighboring solutions are first generated, and these neighboring solutions are among the current optimal satellite-wave position matching schemes. The service satellite is generated by randomly changing one wavelength, and is generated independently and randomly. Next, a quality test is performed on each neighboring solution, and an interference graph is generated based on the neighboring solutions, which is then used for application. The graph is colored using various colors to obtain the optimal coloring scheme. Finally, among all neighboring solutions, the one with the smallest conflict number and not in the taboo list is selected, and the optimal coloring scheme is updated. The tabu list records the optimal solution obtained in the previous several iterations to prevent cyclic search.

[0017] Furthermore, each iteration of the joint optimization algorithm specifically includes:

[0018] Generate neighboring solutions ;in , For a random wave position, For its randomly switching satellites, Wave position in the current optimal solution Selected satellite;

[0019] For each neighboring solution, generate an interference map. ;

[0020] The minimum conflict number is solved using a graph coloring algorithm on the interference graph corresponding to each neighboring solution. ;

[0021] Update the current optimal solution ;

[0022] Update the taboo list in for The optimal solution before the first iteration. The taboo table length.

[0023] Secondly, the present invention provides a satellite oblique beam interference avoidance system based on cost flow and dynamic graph coloring, used to implement the satellite oblique beam interference avoidance method based on cost flow and dynamic graph coloring described in the first aspect, comprising:

[0024] The interference modeling module is used to consider the characteristics of the interference area of ​​oblique satellite beams and establish three-dimensional tensors with dimensions of satellite, target wave position and interfered wave position to characterize the interference of satellite beams on wave positions other than the target wave position.

[0025] The optimization problem modeling module is used to model the anti-inter-beam interference hopping beam pattern design problem of multi-satellite hopping beam system as a dynamic graph coloring problem. The optimization variable satellite-wave position matching determines the topology of the system interference graph, thereby determining the optimization variable hopping beam time slot allocation. The edges in the interference graph are determined according to the three-dimensional tensor. The dynamic graph coloring problem is divided into two mutually coupled sub-problems: satellite-wave position matching and hopping beam time slot allocation.

[0026] The minimum cost maximum flow algorithm module is used to pre-solve the satellite-wave position matching subproblem using the minimum cost maximum flow algorithm, and obtain the initial solution of satellite-wave position matching that maximizes the sum of the elevation angles of all wave position serving satellites in the system under the constraint of the maximum number of beams that can be opened simultaneously by the satellite.

[0027] The joint optimization algorithm module is used to jointly optimize the two sub-problems of satellite-wave position matching and hopping beam slot allocation based on the initial solution of satellite-wave position matching, combining the tabu search algorithm and the graph coloring algorithm, so as to further reduce the interference between open beams in the same hopping beam slot.

[0028] Thirdly, the present invention provides a computer system including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the computer program is executed by the processor, it implements the steps of the satellite oblique beam interference avoidance method based on cost flow and dynamic graph coloring as described in the first aspect.

[0029] Fourthly, the present invention provides a computer program product, including a computer program that, when executed by a processor, implements the steps of the satellite oblique beam interference avoidance method based on cost flow and dynamic graph coloring as described in the first aspect.

[0030] Beneficial Effects: This invention provides a satellite oblique beam interference avoidance method based on cost flow and dynamic graph coloring. By accurately modeling the interference range of small-elevation oblique beams in a multi-satellite hopping beam system, the problem of anti-interference hopping beam pattern design is transformed into a dynamic graph coloring problem. Then, the minimum cost maximum flow algorithm, tabu search algorithm, and graph coloring algorithm are used in combination to solve the problem, achieving inter-beam interference avoidance. Experiments show that this method significantly improves the inter-beam interference avoidance performance of the obtained hopping beam pattern compared to traditional methods that do not consider the characteristics of oblique beam interference. Furthermore, compared to anti-interference beam resource allocation methods based on mathematical optimization and artificial intelligence, it has a significant advantage in low complexity and is more suitable for use in satellite systems with real-time requirements. Attached Figure Description

[0031] To more clearly illustrate the technical solutions in this invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of this invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0032] Figure 1 The flowchart shows a satellite oblique beam interference avoidance method based on cost flow and dynamic graph coloring provided by the present invention.

[0033] Figure 2 This is a schematic diagram of the satellite oblique beam interference judgment method provided by the present invention.

[0034] Figure 3 This is an example diagram of a construction case of the cost flow graph in the minimum cost maximum flow algorithm designed in this invention.

[0035] Figure 4 This is a comparison chart of the lowest signal-to-noise ratio within the service area in the simulation experiment results.

[0036] Figure 5 This is a comparison chart of community service satisfaction rates in the simulation experiment results. Detailed Implementation

[0037] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. The following description of at least one exemplary embodiment is merely illustrative and is in no way intended to limit the invention or its application or use. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without inventive effort are within the scope of protection of this invention.

[0038] This invention discloses a satellite oblique beam interference avoidance method based on cost flow and dynamic graph coloring, applicable to scenarios where satellites use hopping beams to serve multiple fixed ground positions, such as... Figure 1 As shown, the main steps include:

[0039] Step S1: Considering the characteristics of the interference region of the oblique-sun satellite beam (the area of ​​the region increases sharply and becomes irregular as the elevation angle decreases), establish a three-dimensional tensor with dimensions of satellite, target wave position, and interfered wave position to characterize the interference of the satellite beam on other wave positions besides the target wave position;

[0040] Step S2: The design problem of anti-inter-beam interference hopping beam pattern for a multi-satellite hopping beam system is modeled as a dynamic graph coloring problem. The optimization variable satellite-position matching determines the topology of the system interference graph, thereby determining the optimization variable hopping beam time slot allocation. The edges in the interference graph are determined based on the optimization variable satellite-position matching and the three-dimensional tensor. The dynamic graph coloring problem is divided into two mutually coupled sub-problems: satellite-position matching and hopping beam time slot allocation.

[0041] Step S3: Use the minimum cost maximum flow algorithm to pre-solve the satellite-wave position matching subproblem to obtain the initial solution of satellite-wave position matching that maximizes the sum of elevation angles of all wave position serving satellites in the system under the constraint of the maximum number of beams that can be opened simultaneously by the satellite.

[0042] Step S4: Based on the initial solution of satellite-wave position matching, combine the tabu search algorithm and the graph coloring algorithm to jointly optimize the two sub-problems of satellite-wave position matching and hopping beam slot allocation, so as to further reduce the interference between open beams in the same hopping beam slot.

[0043] The following describes the detailed process of an embodiment of the present invention using a specific satellite beam-hopping system. In step S1, the number of satellites in the system is denoted as... The number of ground wavelets is The collection of satellites is The set of ground wave potentials is ,satellite The maximum number of beams that can be opened simultaneously is The satellite system uses a hopping beam pattern to serve ground wavebands. The hopping beam period includes the number of hopping beam time slots. The hopping beam time slot set is All open beams occupy the full system bandwidth, and each beam position is served by the satellite beam in only one time slot within a hop beam cycle. A three-dimensional tensor is established. Its three dimensions are satellite, target wave position, and interfered wave position, and elements. Indicates when the target wave position by satellite During service, wave position Whether it will be subject to strong interference; if so, record it as 1, indicating the current wave position. Cannot be with wave position If a signal is received in the same hop beam time slot, it is served; otherwise, it is recorded as 0, indicating that the signal can be served in the same hop beam time slot. Figure 2 As shown, Let i be the ground location within the interfered wave position i, where Indicates ground location The corresponding wave position For satellite beams in The received power at the location, where For satellite beam transmission power, This is the channel gain coefficient. This is the preset interference threshold.

[0044] In step S2, the design problem of anti-inter-beam interference hopping beam pattern for a multi-satellite hopping beam system is modeled as a dynamic graph coloring problem. Its optimization variables include satellite-wave position matching and hopping beam time slot allocation. Specifically, the system's satellite-wave position matching and hopping beam time slot allocation are denoted as follows: , ,in Representing wave positions The serving satellites and the servicing hop beam time slots. System interference map and satellite-wavelength matching scheme. Related, recorded as ,in The set of points is equal to the set of wave positions, and remains constant. For the edge set, when the satellite-wave position matching scheme is At that time, for each wave position node It needs to send to all satellites to wave position Beam interference wave position nodes (i.e., all nodes that satisfy) nodes Connect edges. After constructing the interference graph, use it by finding edges on the graph. The solution to the graph coloring problem yields the beam hopping time slot allocation results. Then through combination and A complete anti-interference hopping beam pattern is obtained.

[0045] In step S3, the minimum cost maximum flow algorithm is used to obtain the satellite-wave position matching scheme. The initial solution, and its cost flow network construction method are as follows:

[0046] Describe the cost flow network as Establish source point Hehuidian Then the set of nodes edge set There are three types of directed edges in the array, with capacity... and unit expenses Construct them according to the following formulas respectively:

[0047]

[0048] The first type of edge is formed by the source point. Pointing to all satellite nodes, each edge has a capacity of [value] times the number of satellite nodes. Maximum number of beams that can be opened Positive correlation function In this embodiment, it can be taken as The first type of edge has a cost of 0 and is used to limit the number of wavelengths served by each satellite to no more than its service capacity; the second type of edge points from all satellite nodes to all wavelength nodes, has a capacity of 1, and its cost is the cost of the corresponding satellite. to wave position Beam elevation angle The opposite of the value is used to minimize the total cost of all beams by solving the minimum-cost maximum flow problem, thereby maximizing the sum of the elevation angles of all serving beams in the system; the third type of edge points from all beam position nodes to the sink. The cost is 0, and the capacity is [wavelength value]. Number of times it needs to be covered within a single beam hopping cycle This is used to ensure that the coverage requirement of each wavelength is met. In this embodiment, the capacity is 1, such as... Figure 3 As shown. It should be noted that the method of the present invention is not limited to this specific situation and can be extended to other applications such as multi-connection. The case where the value is any positive integer.

[0049] After constructing the cost flow network, any minimum-cost maximum flow algorithm can be used, such as the cost-enhanced Edmonds-Karp algorithm, to find the maximum flow on the network that minimizes the total cost, thereby obtaining the elevation angles of all serving beams in the system. The largest satellite-beam matching scheme. This scheme can meet the constraint of the limited number of satellite beams that can be opened. At the same time, since the interference area of ​​the satellite beam decreases sharply with the increase of elevation angle, the initial solution obtained by this method already has good interference avoidance performance in the beam domain.

[0050] In step S4, based on the initial satellite-wave position matching scheme obtained in step S3, tabu search and graph coloring algorithms are further used to jointly optimize the two sub-problems of satellite-wave position matching and hopping beam slot allocation, so as to obtain a hopping beam pattern with better anti-interference performance.

[0051] The joint optimization algorithm starts from a pre-set sufficiently low interference threshold. Starting with (e.g., -125dB), the current interference threshold is adjusted each time. Increase by a tiny increment (e.g., 1dB), the use of this interference threshold is determined through a joint optimization algorithm. If it is possible to achieve conflict-free coloring, then the current threshold is the optimal threshold, the obtained conflict-free coloring scheme is the optimal anti-interference beam hopping pattern, and the algorithm terminates; otherwise, continue adding more colors. A search is performed. When determining threshold feasibility, a tabu search algorithm is used as the outer framework, with a nested graph coloring algorithm as the inner framework, undergoing several iterations until convergence. In each iteration, neighbor generation is performed first. Let... For the current optimal satellite-wave potential matching scheme, each time in The service satellite that randomly changes one wavelength, i.e., the neighboring solution is based on... Generate, where For a random wave position, For its randomly switching satellites, Wave position in the current optimal solution The selected satellite.

[0052] This method generates random numbers independently. There are several neighboring solutions. Next, a quality test is performed on each neighboring solution. Based on the neighboring solutions... Generate its interference map Then use it. To solve the graph coloring problem using any number of colors, any graph coloring algorithm that minimizes the number of conflicting edges (connecting two nodes of the same color) can be used to obtain the optimal coloring scheme. Finally, among all neighboring solutions, the one with the smallest conflict number and not in the taboo list is selected, and the solution is updated. The tabu list records the optimal solutions obtained in the previous several iterations to prevent cyclic searching. The above process can be formally described as follows:

[0053] (1) Generate neighboring solutions .

[0054] (2) Generate interference map .

[0055] (3) Solve for the minimum number of conflicts on the interference graph corresponding to each neighboring solution using the graph coloring algorithm. .

[0056] (4) Update the current optimal solution .

[0057] (5) Update the taboo list in for The optimal solution before the first iteration. The taboo table length.

[0058] like Within the first iteration, a conflict-free coloring scheme was obtained, i.e. If the condition is met, return the optimal solution and terminate the algorithm; otherwise, increment the interference threshold. And continue the search, as shown in Table 1.

[0059] Table 1. Flowchart of the joint optimization algorithm for tabu search and graph coloring

[0060]

[0061] The effectiveness and advantages of the embodiments of the present invention will be verified through specific experiments below.

[0062] This simulation uses constellation orbital parameters as shown in Table 2, totaling 12,300 satellites.

[0063] Table 2 Constellation Orbit Parameters

[0064]

[0065] This simulation selects a circular ground region on Earth within the range of 3°W-3°E longitude and 3°S-3°N latitude, dividing it into 928 circular ground cells with a radius of 12km. Based on orbital parameters and ephemeris data, all satellites above this ground region within the range of 5°W-5°E longitude and 5°S-5°N latitude are sampled, with a total of 25 satellites selected to serve this region. Some of these satellites are located diagonally above the cells, requiring oblique beam transmission for service. Assume a maximum of 16 beams can be simultaneously activated by a single satellite, a satellite transmit power of 50W, a ground receiver noise temperature of 400K, and a system bandwidth of 30MHz.

[0066] Figure 4 and Figure 5 This is a performance comparison chart of the conventional pattern-coloring beam-hopping method (ignoring oblique beam interference) and the dynamic pattern-coloring beam-hopping method (considering oblique beam interference) proposed in this invention. It can be seen that, under different beam-hopping periods... Under these conditions, the proposed hopping beam has significant advantages over traditional methods in both the lowest signal-to-noise ratio (SNR) within the service area and the cell service satisfaction rate, improving the former by 4dB to 8dB and the latter by 7% to 24%. Cell service satisfaction is defined as an SNR of 16dB at all locations within the cell.

[0067] This invention also discloses a satellite oblique beam interference avoidance system based on cost flow and dynamic graph coloring, used to implement the aforementioned satellite oblique beam interference avoidance method based on cost flow and dynamic graph coloring. The system includes: an interference modeling module, used to consider the characteristics of the oblique satellite beam interference region and establish a three-dimensional tensor with dimensions of satellite, target beam position, and interfered beam position to characterize the interference of the satellite beam to other beam positions besides the target beam position; and an optimization problem modeling module, used to model the anti-inter-beam interference hopping beam pattern design problem of a multi-satellite hopping beam system as a dynamic graph coloring problem, wherein the optimization variable satellite-beam position matching determines the topology of the system interference graph, thereby determining the optimization variable hopping beam slot. The edges in the interference graph are determined based on the three-dimensional tensor. The dynamic graph coloring problem is divided into two coupled subproblems: satellite-wave position matching and hop beam time slot allocation. A minimum cost maximum flow algorithm module is used to pre-solve the satellite-wave position matching subproblem using the minimum cost maximum flow algorithm to obtain an initial solution for satellite-wave position matching that maximizes the sum of elevation angles of all beam-serving satellites in the system under the constraint of the maximum number of beams that can be opened simultaneously. A joint optimization algorithm module is used to jointly optimize the two subproblems of satellite-wave position matching and hop beam time slot allocation based on the initial solution of satellite-wave position matching, combining the tabu search algorithm and the graph coloring algorithm, so as to further reduce the interference between beams opened in the same hop beam time slot.

[0068] This invention also discloses a computer system, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the computer program is executed by the processor, it implements the steps of the aforementioned method for avoiding inter-beam interference between satellite oblique beams based on cost flow and dynamic graph coloring.

[0069] This invention also discloses a computer program product, including a computer program that, when executed by a processor, implements the steps of the aforementioned method for avoiding inter-beam interference in satellite oblique beams based on cost flow and dynamic graph coloring.

[0070] The above description is only one embodiment of the present invention. It should be noted that, for those skilled in the art, without departing from the principle of the present invention, any method of modeling the interference of obliquely fired satellite beams using the proposed three-dimensional tensor form of satellite-target beam position-interfered beam position for any form of satellite hopping beam system, using the cost flow algorithm to solve the satellite-beam position matching scheme, and using tabu search and graph coloring to jointly optimize satellite-beam position matching and hopping beam time slot allocation should be considered within the scope of protection of the present invention.

Claims

1. A method for avoiding inter-beam interference in satellite oblique beams based on cost flow and dynamic graph coloring, characterized in that, Includes the following steps: Considering the characteristics of the interference region of oblique satellite beams, a three-dimensional tensor with dimensions of satellite, target wave position, and interfered wave position is established to characterize the interference of satellite beams on wave positions other than the target wave position; The design problem of anti-inter-beam interference hopping beam pattern for multi-satellite hopping beam systems is modeled as a dynamic graph coloring problem. The optimization variable satellite-position matching determines the topology of the system interference graph, thereby determining the optimization variable hopping beam time slot allocation. The edges in the interference graph are determined based on the optimization variable satellite-position matching and the three-dimensional tensor. The dynamic graph coloring problem is divided into two mutually coupled sub-problems: satellite-position matching and hopping beam time slot allocation. The minimum cost maximum flow algorithm is used to pre-solve the satellite-wave position matching subproblem, and the initial solution of satellite-wave position matching is obtained to maximize the sum of the elevation angles of all wave position serving satellites in the system under the constraint of the maximum number of beams that can be opened simultaneously by the satellite. Based on the initial solution of satellite-wave position matching, the tabu search algorithm and graph coloring algorithm are combined to jointly optimize the two sub-problems of satellite-wave position matching and hopping beam slot allocation, so as to further reduce the interference between open beams in the same hopping beam slot.

2. The satellite oblique beam interference avoidance method based on cost flow and dynamic graph coloring according to claim 1, characterized in that, Establish the three-dimensional tensor Its elements Indicates when the target wave position by satellite During service, wave position Whether it will be subject to strong interference; if so, record it as 1, indicating the current wave position. Cannot be with wave position If a signal is received in the same hop beam time slot, it is served; otherwise, it is recorded as 0, indicating that the signal can be served in the same hop beam time slot. Let i be the ground location within the interfered wave position i, where Indicates ground location The corresponding wave position For satellite beams in The received power at that location, This is the preset interference threshold.

3. The satellite oblique beam interference avoidance method based on cost flow and dynamic graph coloring according to claim 1, characterized in that, The optimized variables, satellite-position matching and hopping beam slot allocation, are respectively denoted as... , ,in Representing wave positions The serving satellites and the servicing hop beam time slots, The ground spectral density is denoted as ; the interference diagram of the system is denoted as . ,in The set of points is equal to the set of wave positions. For each wave position node, the set of edges is defined. It needs to send to all satellites to wave position Beam interference wave position node Edges, i.e., nodes With all elements at corresponding positions that satisfy the three-dimensional tensor nodes Connect the edges.

4. The satellite oblique beam interference avoidance method based on cost flow and dynamic graph coloring according to claim 1, characterized in that, The solution to the initial solution of the satellite-position matching includes: Describe the cost flow network as Establish source point Hehuidian Then the set of nodes The set of edges is the union of the source point, sink point, satellite set, and ground wave position set. There are three types of directed edges in the graph. The first type of edge starts from the source vertex. Points to all satellite nodes, and the capacity of each edge is the same as that of the satellite nodes. Maximum number of beams that can be opened Positive correlation function The first type of edge has a cost of 0 and is used to limit the number of wavelengths served by each satellite to no more than its service capacity; the second type of edge points from all satellite nodes to all wavelength nodes, has a capacity of 1, and its cost is the cost of the corresponding satellite. to wave position Beam elevation angle The opposite of the value is used to minimize the total cost of all beams by solving the minimum-cost maximum flow problem, thereby maximizing the sum of the elevation angles of all serving beams in the system; the third type of edge points from all beam position nodes to the sink. The cost is 0, and the capacity is [wavelength value]. Number of times it needs to be covered within a single beam hopping cycle This is used to ensure that the coverage requirements of each wavelength are met; The minimum cost maximum flow algorithm is used to find the maximum flow on the network that minimizes the total cost, thereby obtaining the maximum satellite-beam matching scheme with the highest elevation angle for all service beams in the system.

5. The satellite oblique beam interference avoidance method based on cost flow and dynamic graph coloring according to claim 1, characterized in that, The joint optimization algorithm starts from a pre-set sufficiently low interference threshold. Initially, the interference threshold is used to determine the values ​​of elements in the three-dimensional tensor; each time, the current interference threshold is... Add an increment The joint optimization algorithm determines the appropriate use of the interference threshold. If it is possible to achieve conflict-free coloring, then the current threshold is the optimal threshold, the obtained conflict-free coloring scheme is the optimal anti-interference beam hopping pattern, and the algorithm terminates; otherwise, continue adding more colors. Perform a search; among which The number of hop beam periods is included in the hop beam period.

6. The satellite oblique beam interference avoidance method based on cost flow and dynamic graph coloring according to claim 5, characterized in that, When performing threshold feasibility assessment, the joint optimization algorithm uses a tabu search algorithm as the outer framework and a nested graph coloring algorithm as the inner framework, performing several iterations until convergence. In each iteration, neighboring solutions are first generated, and these neighboring solutions are among the current optimal satellite-wave position matching schemes. The service satellite is generated by randomly changing one wavelength, and is generated independently and randomly. Next, a quality test is performed on each neighboring solution, and an interference graph is generated based on the neighboring solutions, which is then used for application. The graph is colored using various colors to obtain the optimal coloring scheme. Finally, among all neighboring solutions, the one with the smallest conflict number and not in the taboo list is selected, and the optimal coloring scheme is updated. The tabu list records the optimal solution obtained in the previous several iterations to prevent cyclic search.

7. The satellite oblique beam interference avoidance method based on cost flow and dynamic graph coloring according to claim 6, characterized in that, The joint optimization algorithm undergoes several iterations until convergence. Each iteration process specifically includes: Generate neighboring solutions ;in , For a random wave position, For its randomly switching satellites, Wave position in the current optimal solution Selected satellite; For each neighboring solution, generate an interference map. ; The minimum conflict number is solved using a graph coloring algorithm on the interference graph corresponding to each neighboring solution. ; Update the current optimal solution ; Update the taboo list in for The optimal solution before the first iteration. The taboo table length.

8. A satellite oblique beam interference avoidance system based on cost flow and dynamic graph coloring, characterized in that, A method for avoiding inter-beam interference in satellite oblique beams based on cost flow and dynamic graph coloring as described in any one of claims 1-7 includes: The interference modeling module is used to consider the characteristics of the interference area of ​​oblique satellite beams and establish three-dimensional tensors with dimensions of satellite, target wave position and interfered wave position to characterize the interference of satellite beams on wave positions other than the target wave position. The optimization problem modeling module is used to model the anti-inter-beam interference hopping beam pattern design problem of multi-satellite hopping beam system as a dynamic graph coloring problem. The optimization variable satellite-wave position matching determines the topology of the system interference graph, thereby determining the optimization variable hopping beam time slot allocation. The edges in the interference graph are determined according to the three-dimensional tensor. The dynamic graph coloring problem is divided into two mutually coupled sub-problems: satellite-wave position matching and hopping beam time slot allocation. The minimum cost maximum flow algorithm module is used to pre-solve the satellite-wave position matching subproblem using the minimum cost maximum flow algorithm, and obtain the initial solution of satellite-wave position matching that maximizes the sum of the elevation angles of all wave position serving satellites in the system under the constraint of the maximum number of beams that can be opened simultaneously by the satellite. The joint optimization algorithm module is used to jointly optimize the two sub-problems of satellite-wave position matching and hopping beam slot allocation based on the initial solution of satellite-wave position matching, combining the tabu search algorithm and the graph coloring algorithm, so as to further reduce the interference between open beams in the same hopping beam slot.

9. A computer system comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the computer program is executed by the processor, it implements the steps of a satellite oblique beam interference avoidance method based on cost flow and dynamic graph coloring according to any one of claims 1-7.

10. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by the processor, it implements the steps of a satellite oblique beam interference avoidance method based on cost flow and dynamic graph coloring according to any one of claims 1-7.

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