Beam hopping method based on dynamic beam position division

Abstract

The invention discloses a wave beam hopping method based on dynamic wave position division, which relates to the technical field of satellite communication, and comprises the following specific steps: carrying out dynamic wave position division on a communication ground area according to the geographic position of a user terminal in the communication ground area corresponding to a target satellite; constructing a channel model between the target satellite and the user terminal in the beam hopping period and a beam hopping scheme design optimization problem model of the target satellite in the beam hopping period; and on the basis of the number of beam position cells determined by dynamic beam position division, in combination with a beam spatial isolation condition, solving a target satellite beam hopping scheme design optimization problem model, and determining a target satellite beam hopping scheme design. According to the invention, the in-satellite interference between adjacent beams on the same frequency is reduced, the problem that unbalanced communication service requirements are difficult to meet in a low-flow scene is solved, and the utilization rate of satellite resources is improved.

Description

Technical Field

[0001] The present invention relates to the technical field of satellite communication, and particularly relates to a hopping beam method based on dynamic wave position division. Background Art

[0002] Satellite communication, as an important part of the integrated sky-earth network, has the advantages of wide coverage and low construction cost. In recent years, the non-geostationary orbit (NGSO) constellation has developed rapidly. However, the uneven geographical distribution of users and the high mobility of NGSO satellites will lead to the non-uniformity of service demands in space and time. Therefore, how to effectively utilize limited satellite resources to meet unbalanced service demands is the main challenge faced by the NGSO satellite system. To solve this problem, the hopping beam technology has been proposed, which generates a large number of beams and flexibly allocates them to match unbalanced demands, thereby improving the communication efficiency of the system.

[0003] The wave position division of traditional multi-beam satellites lacks the consideration of flexible wave position division according to the user location through the beam width. Therefore, when the users under the satellite are sparse and the service load is low, inevitable resource waste will be caused. Therefore, it is necessary to design a hopping beam scheme that dynamically divides wave positions considering the user location under the satellite to effectively utilize satellite resources. Summary of the Invention

[0004] To solve the above technical problems, the present invention provides a hopping beam method based on dynamic wave position division.

[0005] To achieve the above object, the present invention adopts the following technical solutions:

[0006] A hopping beam method based on dynamic wave position division determines the hopping beam scheme of a target satellite according to the following steps in a hopping beam cycle including N slot time slots:

[0007] Step A: Dynamically divide the communication ground area corresponding to the target satellite according to the geographical locations of user terminals in the communication ground area corresponding to the target satellite.

[0008] Step B: Construct a channel model between the target satellite and user terminals in each wave position cell in the hopping beam cycle, and a design optimization problem model for the hopping beam scheme of the target satellite in the hopping beam cycle.

[0009] Step C: Based on the number of wave position cells determined by the dynamic wave position division, combined with the beam space isolation condition, solve the design optimization problem model of the target satellite hopping beam scheme to determine the design of the target satellite hopping beam scheme.

[0010] Further, the specific steps of Step A include: Based on the preset geographical location set of user terminals in the communication ground area corresponding to the target satellite as Aiming at minimizing the number of wave position cells, the following wave position division model is constructed to achieve dynamic beam division:

[0011]

[0012] Among them, represents the geographical location of the user terminal, c j represents the position of the candidate center point, p is the number of candidate center points, r max is the maximum beam width supported by the target satellite;

[0013] Furthermore, the step B includes the following steps:

[0014] Step B1, based on the antennas equipped on the target satellite, the target satellite generates L beams to illuminate n wave position cells in its communication ground area, and each beam serves k user terminals in one wave position cell. Then, when the nth wave position cell is illuminated by the target satellite and the kth user terminal in the nth wave position cell is served by the lth beam, the corresponding channel coefficient is:

[0015]

[0016] Among them, h k,l is the channel coefficient between the kth user terminal and the lth beam, G t (θ k,l ) is the transmitting antenna gain of the lth beam to the kth user terminal, θ k,l is the off-axis angle between the kth user terminal and the main lobe direction of the lth beam, is the receiving antenna gain of the kth user terminal, d k,l is the distance between the kth user terminal and the lth beam, and λ is the wavelength;

[0017] Step B2, based on the preset total bandwidth of the target satellite, and there is in-satellite co-frequency interference among the L beams generated by the target satellite under the hopping beam cycle, a channel model between the target satellite and the user terminals in its communication ground area is constructed. Then, when the nth wave position cell is illuminated by the target satellite and the kth user terminal in the nth wave position cell is served by the lth beam, the corresponding channel model is:

[0018]

[0019] Among them, is the channel model, P l is the transmitting power of the lth beam, h k,l is the channel coefficient between the kth user terminal and the lth beam, k B is the Boltzmann constant, T rxis the receiver noise temperature, B is the preset total bandwidth of the target satellite, and i is other beams generated by the target satellite except the l-th beam;

[0020] Step B3, define the lighting indication variable of the target satellite for the n-th wave position cell in its communication ground area at the t-th time slot of the hopping beam period Indicates that the target satellite lights up the n-th wave position cell in its communication ground area at the t-th time slot, Indicates that the target satellite does not light up the n-th wave position cell in its communication ground area at the t-th time slot, and determines whether each wave position cell in the communication ground area corresponding to the target satellite at the t-th time slot of the hopping beam period is lit according to the lighting indication variable. If so, calculate the transmission rate and available throughput of the lit wave position cell at the t-th time slot according to the following formula, otherwise the transmission rate of the unlit wave position cell is 0:

[0021]

[0022] Among them, is the transmission rate of the n-th wave position cell at the t-th time slot, B is the total bandwidth of the target satellite, is the channel model;

[0023]

[0024] Among them, is the available throughput of the n-th wave position cell at the t-th time slot, is the transmission rate of the n-th wave position cell at the t-th time slot, T slot is the t-th time slot;

[0025] Step B4, obtain the service demand of each wave position cell in the communication ground area corresponding to the target satellite under the hopping beam period, and combine the available throughput of each wave position cell to define the service satisfaction degree corresponding to each wave position cell as And aiming at maximizing the service satisfaction degree of each wave position cell, construct the optimization problem model of the hopping beam scheme design of the target satellite under the hopping beam period as follows:

[0026]

[0027] Among them, X is the hopping beam scheme of the target satellite under the hopping beam period, is the service satisfaction degree corresponding to each wave position cell, D n is the service demand of each wave position cell under the hopping beam period, Indicates that the target satellite generates L beams to light up each wave position cell, Indicates the available throughput of each wave position cell under the hopping beam period,

[0028] Indicates whether the nth wave position cell in the tth time slot is lit, P tot Is the preset power threshold for the target satellite, Indicates that the sum of the powers of the beams generated by the target satellite is less than the preset power threshold of the target satellite.

[0029] Further, the step C includes the following steps:

[0030] Step C1, based on the preset total number of beams generated by the target satellite, combined with the number of wave position cells determined by the dynamic wave position division, determine the number of beams enabled by the target satellite simultaneously according to the following principle:

[0031]

[0032] Among them, M i Is the number of beams enabled by the target satellite simultaneously, L is the preset total number of beams generated by the target satellite, N c Is the number of wave position cells in the communication ground area corresponding to the target satellite;

[0033] Step C2, define the adjacent matrix of the wave position cells in the tth time slot of the hopping beam cycle And the element vector a in the adjacent matrix ij Is as follows:

[0034]

[0035] Among them, a ij Is the element vector in the adjacent matrix, and a ij = 1 indicates that the wave position cell i and the wave position cell j are adjacent, a ij = 0 indicates that the wave position cell i and the wave position cell j are the same wave position cell or not adjacent, dist(i,j) represents the central distance between the wave position cell i and the wave position cell j, r max Is the preset maximum beam width supported by the target satellite;

[0036] Step C3, define the hopping beam matrix in the tth time slot of the hopping beam cycle as And Among them Indicates that the nth wave position cell is lit by the target satellite, Indicates that the nth wave position cell is not lit by the target satellite, and determine the effective hopping beam scheme that meets the satellite spatial isolation condition according to the following principle:

[0037]

[0038] Among them, N c Is the number of wave position cells in the communication ground area corresponding to the target satellite, is the transpose matrix of the hopping beam matrix, and A is the adjacent matrix of the wave position cell, is the hopping beam matrix;

[0039] Step C4, define the service vector corresponding to each effective hopping beam scheme in the t-th time slot of the hopping beam period as and all service vectors form a service matrix where N c is the number of wave position cells in the communication ground area corresponding to the target satellite, and N v is the number of effective hopping beam schemes. Then, when the target satellite selects the m-th effective hopping beam scheme v m to serve the j-th wave position cell, the corresponding service vector is:

[0040]

[0041] where v mj is the j-th element of the m-th effective hopping beam scheme v m , c mj is the j-th element of the service vector c m corresponding to the m-th effective hopping beam scheme, and r j is the transmission rate of the j-th wave position cell in the t-th time slot, and T slot is the t-th time slot;

[0042] Step C5, define φ m as the number of times the target satellite selects the m-th effective hopping beam scheme within the hopping beam period. Combining the service vectors corresponding to each effective hopping beam scheme, update the target satellite hopping beam scheme design optimization problem model as follows:

[0043]

[0044] where represents the service satisfaction corresponding to each wave position cell, and D n is the service demand of each wave position cell under the hopping beam period, represents that the number of times of selecting the effective hopping beam scheme satisfies one hopping beam period, represents the available throughput of each wave position cell, m = 1..., N v represents that the target satellite selects a beam scheme from the effective hopping beam schemes to illuminate its communication ground area;

[0045] Step C6, define the auxiliary variable and the auxiliary variable satisfies Further update the optimization problem model of the target satellite's hopping beam scheme design, and use the MOSEK solver to solve the optimization problem model of the satellite hopping beam scheme design in combination with the branch and bound method to determine the hopping beam scheme design.

[0046] Beneficial effects brought by adopting the above technical solutions:

[0047] (1) The present invention adopts dynamic beam position division, reduces the number of wave position cells for on-satellite services, reduces the complexity of the hopping beam scheme design, solves the problem of difficult to meet the unbalanced communication service requirements in low-traffic scenarios, and improves the utilization rate of satellite resources;

[0048] (2) Based on the beam space isolation condition, the present invention determines the hopping beam scheme that meets the satellite space isolation condition, reducing the in-satellite interference between adjacent beams at the same frequency. Description of the Drawings

[0049] Figure 1 is the flowchart of the present invention;

[0050] Figure 2 is the schematic diagram of the service scenario of the present invention;

[0051] Figure 3 is the comparison chart of the wave position division results between the method of the present invention and the comparative method;

[0052] Figure 4 is the comparison chart of the system satisfaction between the method of the present invention and the comparative scheme under the same total traffic volume;

[0053] Figure 5 is the comparison chart of the overall system satisfaction between the method of the present invention and the comparative scheme. Detailed Embodiments

[0054] The technical solutions of the present invention will be described in detail below with reference to the drawings.

[0055] Refer to Figure 1 and Figure 2 , a hopping beam method based on dynamic wave position division, to determine the hopping beam scheme of the target satellite in a hopping beam cycle including N slot time slots as follows:

[0056] Step A: Dynamically divide the communication ground area corresponding to the target satellite according to the geographical locations of the user terminals in the communication ground area corresponding to the target satellite;

[0057] Step B: Construct the channel model between the target satellite and the user terminals in each wave position cell in the hopping beam cycle, and the optimization problem model of the hopping beam scheme design of the target satellite in the hopping beam cycle;

[0058] Step C: Based on the number of wave position cells determined by dynamic wave position division and combined with the beam space isolation condition, solve the model of the optimization problem for the design of the hopping beam scheme of the target satellite to determine the design of the hopping beam scheme of the target satellite.

[0059] Further, the specific steps of step A include: Based on the set of geographical locations of user terminals in the communication ground area corresponding to the preset target satellite Taking the minimization of the number of wave position cells as the goal, construct the following wave position division model to achieve dynamic beam division:

[0060]

[0061] where represents the geographical location of the user terminal, c j represents the position of the candidate center point, p is the number of candidate center points, and r max is the maximum beam width supported by the target satellite;

[0062] Further, step B includes the following steps:

[0063] Step B1: Based on the antennas equipped on the target satellite, the target satellite generates L beams to illuminate n wave position cells in its communication ground area, and each beam serves k user terminals in one wave position cell. Then, when the nth wave position cell is illuminated by the target satellite and the kth user terminal in the nth wave position cell is served by the lth beam, the corresponding channel coefficient is:

[0064]

[0065] where h k,l is the channel coefficient between the kth user terminal and the lth beam, G t (θ k,l ) is the transmit antenna gain of the lth beam to the kth user terminal, θ k,l is the off-axis angle between the kth user terminal and the main lobe direction of the lth beam, is the receive antenna gain of the kth user terminal, d k,l is the distance between the kth user terminal and the lth beam, and λ is the wavelength;

[0066] Step B2: Based on the preset total bandwidth of the target satellite and there is in-satellite co-frequency interference among the L beams generated by the target satellite under the hopping beam period, construct the channel model between the target satellite and the user terminals in its communication ground area. Then, when the nth wave position cell is illuminated by the target satellite and the kth user terminal in the nth wave position cell is served by the lth beam, the corresponding channel model is:

[0067]

[0068] Among them, is the channel model, P l is the transmission power of the l-th beam, h k,l is the channel coefficient between the k-th user terminal and the l-th beam, k B is the Boltzmann constant, T rx is the receiver noise temperature, B is the preset total bandwidth of the target satellite, and i is the other beams generated by the target satellite except the l-th beam;

[0069] Step B3, define the lighting indication variable of the target satellite for the n-th wave position cell in its communication ground area at the t-th time slot of the hopping beam period indicates that the target satellite lights up the n-th wave position cell in its communication ground area at the t-th time slot, indicates that the target satellite does not light up the n-th wave position cell in its communication ground area at the t-th time slot, and determines whether each wave position cell in the communication ground area corresponding to the target satellite at the t-th time slot of the hopping beam period is lit according to the lighting indication variable. If so, calculate the transmission rate and available throughput of the lit wave position cell at the t-th time slot according to the following formula, otherwise the transmission rate of the unlit wave position cell is 0:

[0070]

[0071] Among them, is the transmission rate of the n-th wave position cell at the t-th time slot, B is the total bandwidth of the target satellite, is the channel model;

[0072]

[0073] Among them, is the available throughput of the n-th wave position cell at the t-th time slot, is the transmission rate of the n-th wave position cell at the t-th time slot, T slot is the t-th time slot;

[0074] Step B4, obtain the service demand of each wave position cell in the communication ground area corresponding to the target satellite under the hopping beam period, combine the available throughput of each wave position cell, and define the service satisfaction corresponding to each wave position cell as and, with the goal of maximizing the service satisfaction of each wave position cell, construct the following optimization problem model for the hopping beam scheme design of the target satellite under the hopping beam period:

[0075]

[0076] Among them, X is the hopping beam scheme of the target satellite under the hopping beam period, is the service satisfaction corresponding to each beam position cell, D n is the service demand of each beam position cell under the hopping beam period, indicates that the target satellite generates L beams to illuminate each beam position cell, is the available throughput of each beam position cell under the hopping beam period, indicates whether the nth beam position cell is illuminated at the tth time slot, P tot is the preset power threshold of the target satellite, indicates that the sum of the powers of the beams generated by the target satellite is less than the preset power threshold of the target satellite.

[0077] Further, step C includes the following steps:

[0078] Step C1, based on the preset total number of beams generated by the target satellite, combined with the number of beam position cells determined by dynamic beam position division, determine the number of beams simultaneously enabled by the target satellite according to the following principle:

[0079]

[0080] where M i is the number of beams simultaneously enabled by the target satellite, L is the preset total number of beams generated by the target satellite, N c is the number of beam position cells in the communication ground area corresponding to the target satellite;

[0081] Step C2, define the adjacent matrix of the beam position cells at the tth time slot of the hopping beam period and the element vector a in the adjacent matrix ij is as follows:

[0082]

[0083] where a ij is the element vector in the adjacent matrix, and a ij =1 indicates that beam position cell i and beam position cell j are adjacent, a ij =0 indicates that beam position cell i and beam position cell j are the same beam position cell or not adjacent, dist(i,j) represents the central distance between beam position cell i and beam position cell j, r max is the preset maximum beam width supported by the target satellite;

[0084] Step C3, define the hopping beam matrix at the tth time slot of the hopping beam period as and where indicates that the nth beam position cell is illuminated by the target satellite, indicates that the nth beam position cell is not illuminated by the target satellite, and determine an effective hopping beam scheme that satisfies the satellite spatial isolation condition according to the following principle:

[0085]

[0086] Among them, N c is the number of wave position cells in the communication ground area corresponding to the target satellite, is the transpose matrix of the hopping beam matrix, A is the adjacent matrix of the wave position cells, is the hopping beam matrix;

[0087] Step C4, define the service vector corresponding to each effective hopping beam scheme in the t-th time slot of the hopping beam period as And all service vectors form a service matrix Among them, N c is the number of wave position cells in the communication ground area corresponding to the target satellite, N v is the number of effective hopping beam schemes, then when the target satellite selects the m-th effective hopping beam scheme v m to serve the j-th wave position cell, the corresponding service vector is:

[0088]

[0089] Among them, v mj is the j-th element of the m-th effective hopping beam scheme v m , c mj is the j-th element of the service vector c m corresponding to the m-th effective hopping beam scheme, r j is the transmission rate of the j-th wave position cell in the t-th time slot, T slot is the t-th time slot;

[0090] Step C5, define φ m as the selection times of the m-th effective hopping beam scheme of the target satellite within the hopping beam period. Combining the service vectors corresponding to each effective hopping beam scheme, update the design optimization problem model of the target satellite's hopping beam scheme as follows:

[0091]

[0092] Among them, represents the service satisfaction corresponding to each wave position cell, D n is the service demand of each wave position cell under the hopping beam period, represents that the selection times of the effective hopping beam scheme satisfy one hopping beam period, represents the available throughput of each wave position cell, m = 1..., N v represents that the target satellite selects a beam scheme from the effective hopping beam schemes to illuminate its communication ground area;

[0093] Step C6, define an auxiliary variable and the auxiliary variable satisfies Further update the optimization problem model for the design of the target satellite hopping beam scheme. Use the MOSEK solver and combine the branch and bound method to solve the optimization problem model for the satellite hopping beam scheme design, and determine the hopping beam scheme design.

[0094] The technical effects of the present invention will be further described in detail below in conjunction with simulation experiments.

[0095] Figure 3 It is a comparison chart of the results of the dynamic wave position division and the fixed wave position division of the present invention in the same scenario. It can be observed from the figure that, compared with the fixed wave position division, the present invention performs dynamic wave position division according to the geographical locations of user terminals in the communication ground area corresponding to the target satellite, significantly reducing the number of wave position cells.

[0096] Figure 4 It is a comparison chart of the system satisfaction degrees of the method of the present invention and the comparative scheme under the same total traffic volume. It can be observed from the figure that during the four groups of Monte Carlo simulations, the total traffic volume of each group is the same, and the traffic volume of each user terminal is random. However, the system satisfaction degree of the method of the present invention is higher than that of the comparative scheme, indicating that the present invention uses dynamic beam position division to enable the satellite communication system to better serve unbalanced communication service demands and improve the utilization rate of satellite resources.

[0097] Figure 5 It is a comparison chart of the overall system satisfaction degrees of the method of the present invention and the comparative scheme. It can be observed from the figure that as the total demand traffic volume increases, the overall system satisfaction degree gradually decreases. However, when the total demand traffic volume is low, the present invention can still better meet unbalanced communication service demands.

[0098] The above are only the preferred embodiments of the present invention, and do not impose any limitations on the present invention. Any simple modifications, changes, and equivalent structural changes made to the above embodiments according to the technical essence of the present invention still fall within the protection scope of the technical solution of the present invention.

Claims

1. A hopping beam method based on dynamically dividing wave positions, characterized in that, Determine the hopping beam scheme of the target satellite in a hopping beam period containing N slot time slots according to the following steps: Step A: Dynamically divide the communication ground area corresponding to the target satellite according to the geographical locations of user terminals in the communication ground area corresponding to the target satellite. Step B: Construct a channel model between the target satellite and user terminals in each beam position cell under the hopping beam period, and an optimization problem model for designing the hopping beam scheme of the target satellite under the hopping beam period. Step C: Based on the number of beam position cells determined by the dynamic beam position division, and combined with the beam space isolation condition, solve the optimization problem model for designing the hopping beam scheme of the target satellite to determine the design of the hopping beam scheme of the target satellite.

2. The hopping beamforming method based on dynamically dividing beam positions according to claim 1, wherein, The specific steps of step A include: Based on the geographical location set of user terminals in the communication ground area corresponding to the preset target satellite, Taking the minimization of the number of wave position cells as the goal, construct the following wave position division model to achieve dynamic beam division: Among them, represents the geographical location of the user terminal, c j represents the position of the candidate center point, p is the number of candidate center points, r max is the maximum beam width supported by the target satellite.

3. The hopping beamforming method based on dynamically dividing beam positions according to claim 1, characterized in that Step B includes the following steps: Step B1: Based on the antenna equipped on the target satellite, the target satellite generates L beams to illuminate n beam position cells in its communication ground area, and each beam serves k user terminals in one beam position cell. Then, when the nth beam position cell is illuminated by the target satellite and the kth user terminal in the nth beam position cell is served by the lth beam, the corresponding channel coefficient is: where h k,l is the channel coefficient between the k-th user terminal and the l-th beam, G t (θ k,l ) is the transmit antenna gain from the l-th beam to the k-th user terminal, θ k,l is the off-axis angle between the k-th user terminal and the main lobe direction of the l-th beam, is the receive antenna gain of the k-th user terminal, d k,l is the distance between the k-th user terminal and the l-th beam, and λ is the wavelength; Step B2: Based on the preset total bandwidth of the target satellite, and there is in-satellite co-frequency interference among the L beams generated by the target satellite under the hopping beam period, construct a channel model between the target satellite and user terminals in its communication ground area. Then, when the nth beam position cell is illuminated by the target satellite and the kth user terminal in the nth beam position cell is served by the lth beam, the corresponding channel model is: Among them, is the channel model, P l is the transmission power of the l-th beam, h k,l is the channel coefficient between the k-th user terminal and the l-th beam, k B is the Boltzmann constant, T rx is the receiver noise temperature, B is the preset total bandwidth of the target satellite, and i is other beams generated by the target satellite except the l-th beam; Step B3: Define the lighting indication variable of the target satellite for the nth beam position cell in its communication ground area in the tth time slot of the hopping beam cycle Indicates that the target satellite lights up the nth beam position cell in its communication ground area in the tth time slot, Indicates that the target satellite does not light up the nth beam position cell in its communication ground area in the tth time slot, and determines whether each beam position cell in the communication ground area corresponding to the target satellite in the tth time slot of the hopping beam cycle is lit according to the lighting indication variable. If so, calculate the transmission rate and available throughput of the lit beam position cell in the tth time slot according to the following formula, otherwise the transmission rate of the unlit beam position cell is 0: Among them, is the transmission rate of the nth wave position cell in the tth time slot, B is the total bandwidth of the target satellite, is the channel model; Among them, is the available throughput of the nth wave position cell in the tth time slot, is the transmission rate of the nth wave position cell in the tth time slot, and T slot is the tth time slot; Step B4: Obtain the service demand of each wave position cell in the communication ground area corresponding to the target satellite under the hopping beam period. Combining the available throughput of each wave position cell, define the service satisfaction corresponding to each wave position cell as And aiming at maximizing the service satisfaction of each wave position cell, construct the optimization problem model for the design of the hopping beam scheme of the target satellite under the hopping beam period as follows: Among them, X is the beam hopping scheme of the target satellite under the beam hopping period, is the service satisfaction corresponding to each wave position cell, D n is the service demand of each wave position cell under the beam hopping period, indicates that the target satellite generates L beams to illuminate each wave position cell, represents the available throughput of each wave position cell under the beam hopping period, indicates whether the nth wave position cell is illuminated at the tth time slot, P tot is the preset power threshold of the target satellite, indicates that the sum of the powers of the beams generated by the target satellite is less than the preset power threshold of the target satellite.

4. The hopping beamforming method based on dynamically partitioning beam positions according to claim 1, wherein Step C includes the following steps: Step C1: Based on the preset total number of beams generated by the target satellite, and combined with the number of beam position cells determined by the dynamic beam position division, determine the number of beams simultaneously enabled by the target satellite according to the following principle: Among them, M i is the number of beams simultaneously enabled for the target satellite, L is the preset total number of beams generated by the target satellite, and N c is the number of wave position cells in the communication ground area corresponding to the target satellite; Step C2, define the adjacent matrix of the wave position cell in the t-th time slot of the beam hopping period And the element vector a in the adjacent matrix ij is as follows: Among them, a ij is an element vector in the adjacent matrix, and a ij = 1 indicates that wave position cell i and wave position cell j are adjacent, and a ij = 0 indicates that wave position cell i and wave position cell j are the same wave position cell or not adjacent, dist(i, j) represents the central distance between wave position cell i and wave position cell j, and r max is the preset maximum beam width supported by the target satellite; Step C3, define the hopping beam matrix in the t-th time slot of the hopping beam period as and where indicates that the n-th beam position cell is illuminated by the target satellite, indicates that the n-th beam position cell is not illuminated by the target satellite, and determine the effective hopping beam scheme that meets the satellite spatial isolation condition according to the following principle: Among them, N c is the number of wave position cells in the corresponding communication ground area of the target satellite, is the transpose matrix of the hopping beam matrix, A is the adjacent matrix of the wave position cells, is the hopping beam matrix; Step C4, define the service vector corresponding to each effective hopping beamforming scheme in the t-th time slot of the hopping beamforming period as and all service vectors form a service matrix where N c is the number of wave position cells in the communication ground area corresponding to the target satellite, and N v is the number of effective hopping beamforming schemes. When the target satellite selects the m-th effective hopping beamforming scheme v m to serve the j-th wave position cell, the corresponding service vector is: Among them, v mj is the j-th element of the m-th effective hopping beamforming scheme v m , c mj is the j-th element of the service vector c m corresponding to the m-th effective hopping beamforming scheme, r j is the transmission rate of the j-th beam position cell in the t-th time slot, T slot is the t-th time slot; Step C5, define φ m is the number of selections of the m-th effective hopping beam scheme of the target satellite within the hopping beam period. Combining the service vectors corresponding to each effective hopping beam scheme, the design optimization problem model of the target satellite hopping beam scheme is updated as follows: Among them, represents the service satisfaction corresponding to each beam position cell, D n is the service demand of each beam position cell under the hopping beam period, indicates that the selection times of the effective hopping beam scheme satisfy one hopping beam period, represents the available throughput of each beam position cell, indicates that the target satellite selects a beam scheme from the effective hopping beam schemes to illuminate its communication ground area; Step C6, define auxiliary variables and the auxiliary variables satisfy Further update the model of the satellite hopping beam scheme design optimization problem, use the MOSEK solver, and combine the branch and bound method to solve the model of the satellite hopping beam scheme design optimization problem to determine the hopping beam scheme design.

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