Joint beam hopping and precoding scheduling method based on RSMA multicast satellite system

Abstract

The invention discloses a joint beam hopping and precoding scheduling method based on an RSMA multicast satellite system, and relates to the technical field of satellite communication, and the method comprises the steps: building a multicast multi-beam satellite communication system model based on simulation parameters of a satellite communication system; the model comprises a plurality of antenna feed sources and clusters; determining the total provided capacity of different clusters in each time slot through time slot allocation and a beam hopping mode; determining the optimization problem of the model according to the total provided capacity of different clusters; the optimization variables of the optimization problem are the optimal solutions of the precoding vector, the common rate allocation and the CBH strategy vector, which are solved based on a weighted minimum mean square error method. And solving the optimal solution of the CBH strategy vector based on an integer programming method. And determining an optimized multicast multi-beam satellite communication system model by integrating the optimal precoding vector, the common rate allocation and the CBH strategy vector. According to the invention, the interference between beams in the cluster is reduced, and the communication reliability is improved.

Description

Technical Field

[0001] The present application relates to the field of satellite communication technology, and in particular to a joint beam hopping and precoding scheduling method based on RSMA multicast satellite system. Background Art

[0002] Beam-hopping (BH) satellite technology, as a key innovation in the future mobile Internet field, has the potential to achieve precise matching of supply capacity and demand capacity by flexibly scheduling beam sets in different time slots. However, when facing hot spots with high traffic demand, the system needs to activate multiple adjacent beams at the same time. While this operation fully utilizes satellite resources, it also causes significant interference between adjacent beams. Given the preciousness and limited nature of satellite-borne resources, how to effectively manage and mitigate these interferences has become a technical challenge that needs to be solved urgently. Summary of the invention

[0003] The purpose of this application is to provide a joint beam hopping and precoding scheduling method based on RSMA multicast satellite system, adopt a multi-group multicast transmission mode based on RSMA, and apply it to a satellite system in cluster hopping mode, which can solve the significant interference problem between adjacent beams.

[0004] To achieve the above objectives, this application provides the following solutions:

[0005] In a first aspect, the present application provides a joint beam hopping and precoding scheduling method based on an RSMA multicast satellite system, comprising:

[0006] Obtain satellite communication system simulation parameters;

[0007] Based on the satellite communication system simulation parameters, a multicast multi-beam satellite communication system model is constructed; the multicast multi-beam satellite communication system model includes a plurality of antenna feeds and a plurality of clusters; the antenna feeds are used to generate beams in a set cluster; the beams are used to provide services for ground users; each of the ground users is served by one beam;

[0008] In the multicast multi-beam satellite communication system model, the total provided capacity of different clusters in each time slot is determined through time slot allocation and beam hopping pattern;

[0009] Determine an optimization problem of the multicast multi-beam satellite communication system model based on the total provided capacity of different clusters in each time slot; the optimization variables of the optimization problem are precoding vector, common rate allocation and CBH strategy vector;

[0010] Based on the weighted minimum mean square error method, the precoding vector and the public rate allocation are solved to obtain the optimal precoding vector and the optimal public rate allocation;

[0011] Based on the integer programming method, the CBH strategy vector is solved to obtain the optimal CBH strategy vector;

[0012] Based on the optimal precoding vector, the optimal public rate allocation and the optimal CBH strategy vector, the optimized multicast multi-beam satellite communication system model is determined;

[0013] According to the optimized multicast multi-beam satellite communication system model, multicast requests are scheduled.

[0014] According to the specific embodiments provided in this application, this application discloses the following technical effects:

[0015] The present application provides a joint beam hopping and precoding scheduling method based on RSMA multicast satellite system. First, the simulation parameters related to the satellite communication system are collected and sorted. Subsequently, based on these parameters, a model of a multicast multi-beam satellite communication system is constructed. This model is provided with multiple antenna feeds and corresponding cluster structures. The antenna feeds are responsible for generating beams in a specified cluster to serve ground users and ensure that each user can obtain exclusive beam services. The time slot allocation and beam hopping mode are used to accurately measure the capacity demand and supply of different clusters in each time slot. Based on these real-time data, the optimization problem of the system model is defined, and its core optimization variables include precoding vectors, public rate allocation, and CBH strategy vectors. To solve this optimization problem, the weighted minimum mean square error method is used to determine the optimal precoding vector and public rate allocation, and the integer programming method is used to solve the optimal CBH strategy vector. By integrating these optimal solutions, an optimized multicast multi-beam satellite communication system model can be constructed. According to this optimization model, multicast requests can be scheduled more efficiently and accurately. The RSMA technology introduced in this application effectively improves the flexibility of signal allocation; the application of precoding technology significantly improves the signal transmission quality; and the application of beam hopping technology successfully reduces the mutual interference between beams. The comprehensive use of these technologies can more accurately meet user needs, thereby improving the overall reliability and efficiency of the communication system. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0017] Figure 1 A flowchart of a joint beam hopping and precoding scheduling method based on an RSMA multicast satellite system in an embodiment of the present application;

[0018] Figure 2A schematic diagram of a multicast multi-beam satellite communication system model based on RSMA provided in one embodiment of the present application;

[0019] Figure 3 A clustering-based beam hopping pattern is provided in one embodiment of the present application. DETAILED DESCRIPTION

[0020] The following will be combined with the drawings in the embodiments of the present application to clearly and completely describe the technical solutions in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, not all of the embodiments. Based on the embodiments in the present application, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of this application.

[0021] In order to make the above-mentioned objects, features and advantages of the present application more obvious and easy to understand, the present application is further described in detail below in conjunction with the accompanying drawings and specific implementation methods.

[0022] Embodiment 1

[0023] like Figure 1 As shown, this embodiment provides a joint beam hopping and precoding scheduling method based on RSMA multicast satellite system, including:

[0024] Step 101: Acquire satellite communication system simulation parameters;

[0025] Step 102: constructing a multicast multi-beam satellite communication system model based on the satellite communication system simulation parameters; the multicast multi-beam satellite communication system model includes a plurality of antenna feeds and a plurality of clusters; the antenna feeds are used to generate beams in a set cluster; the beams are used to provide services for ground users; each of the ground users is served by one beam;

[0026] Step 103: in the multicast multi-beam satellite communication system model, determining the total provided capacity of different clusters in each time slot through time slot allocation and beam hopping mode;

[0027] Step 104: determining an optimization problem of the multicast multi-beam satellite communication system model based on the total provided capacity of different clusters in each time slot; the optimization variables of the optimization problem are precoding vector, common rate allocation and CBH strategy vector;

[0028] Step 105: Solve the precoding vector and the public rate allocation based on the weighted minimum mean square error method to obtain the optimal precoding vector and the optimal public rate allocation;

[0029] Step 106: Solve the CBH strategy vector based on the integer programming method to obtain the optimal CBH strategy vector;

[0030] Step 107: Determine an optimized multicast multi-beam satellite communication system model based on the optimal precoding vector, the optimal public rate allocation and the optimal CBH strategy vector;

[0031] Step 108: Schedule the multicast request according to the optimized multicast multi-beam satellite communication system model.

[0032] In some embodiments, when executing step 101, the specific steps may be as follows:

[0033] The obtained simulation parameters of the satellite communication system include satellite altitude, beam radius, maximum transmitting antenna gain, user receiving antenna gain, system bandwidth, carrier frequency, noise temperature, 3dB angle, rain attenuation parameter, noise variance value of the kth user in the jth cluster, number of beams, number of clusters, number of users served by each beam, number of time slots in a cluster hopping cycle, number of clusters served in each time slot, time slot duration, period of cluster hopping mode, required capacity, tolerance and transmit power of each cluster.

[0034] Specifically, it is shown in the following Table 1:

[0035] Table 1 Main simulation parameters of satellite communication system

[0036]

[0037]

[0038] In some embodiments, when executing step 102, the specific steps may be as follows:

[0039] Based on the simulation parameters of the satellite communication system, a multicast multi-beam satellite communication system model is constructed; the multicast multi-beam satellite communication system model includes a plurality of antenna feeds and a plurality of clusters; the antenna feeds are used to generate beams in a set cluster; the beams are used to provide services for ground users; each of the ground users is served by a beam.

[0040] Specifically, Figure 2 As shown, this embodiment considers a multi-beam satellite communication system with multiple groups of downlink multicast. The satellite is a geostationary orbit satellite (GEO) equipped with N t Antenna feeds, in N c M beams are generated in each cluster to serve K ground users. Assume that one feed generates one beam (N t =M). Definition As the set of all clusters, As the set of all beams of the jth cluster, represents the set of all beams of the jth cluster. Because the multi-beam satellite system is actually overloaded with users, this embodiment assumes that there are ρ (ρ>1) users served by each beam at the same time. K=ρN t Indicates the total number of users in the beam coverage area. represents the user set of the i-th beam in the j-th cluster. Each user is served by only one beam, so this embodiment has and μ(jk)=m represents the mapping of the kth user in the jth cluster to the mth beam.

[0041] When executing step 103, the specific steps may be as follows:

[0042] In the multicast multi-beam satellite communication system model, the total provided capacity of different clusters in each time slot is determined through time slot allocation and beam hopping mode, including:

[0043] Determine the satellite channel model, transmission signal model and user receiving signal expression in the multicast multi-beam satellite communication system model;

[0044] Based on the channel vector solved in the satellite channel model, the transmitted signal solved in the transmitted signal model and the user received signal solved by the user received signal expression, the total provided capacity of different clusters in each time slot is determined.

[0045] Specifically, Figure 3 As shown, in a beam hopping period T H In a CBH (Coherent Beamforming Hopping) window, a specific cluster hop pattern is presented.

[0046] In this embodiment, T is defined H =N slot ×T slot , where N slot Represents a T H The number of time slots, N slot The collection of T slot Defined for the duration of the time slot. N c The required capacity of clusters, where D j represents the required capacity of all beams in the jth cluster. Indicates size N c ×1 cluster vector, where Indicated in a T H The required capacity of the j-th cluster. N c The capacity provided by clusters, where R j represents the provided capacity of all beams in the jth cluster. Indicates size N c ×1 cluster vector, where It represents the capacity provided by the jth cluster in a time slot.

[0047] Among them, the satellite channel model, transmission signal model and user receiving signal expression in the multicast multi-beam satellite communication system model are determined as follows:

[0048] Since the orbit of the GEO satellite communication system considered in this embodiment is relatively stable, the channel model is H is static. The downlink channel matrix is ​​expressed as Vector h jk represents the channel vector between the satellite and the kth user in the jth cluster on the ground, represents element-wise multiplication, b jk The vector represents the receiving antenna gain, free space loss and antenna gain of the multi-beam satellite of the kth user in the jth cluster; q jk represents the rain attenuation effect and signal phase of the kth user in the jth cluster, that is, the formula is:

[0049]

[0050] like Figure 2 As shown, this embodiment proposes a rate matching scheme based on RSMA in a multicast multi-beam satellite system. j The multicast message of beams is These messages are split into public and private parts, respectively, e.g. All the public parts are combined and encoded into a public message, namely At time slot n, it is shared by all beams in the jth cluster. All private parts are encoded into private stream messages of each beam, namely Therefore, the vector of satellite information flow can be expressed as in The precoding matrix of the jth cluster is expressed as in represents the common precoding of the i-th beam in the j-th cluster, Indicates private precoding.

[0051] When the satellite is in time slot n, the signal sent is expressed as:

[0052]

[0053] At time slot n, the signal received by the kth user in the jth cluster is expressed as:

[0054]

[0055] in, represents the additive Gaussian white noise of the kth user in the jth cluster. In particular, this embodiment assumes that the two clusters lit in the same time slot are far enough apart that the distance between them can be ignored.

[0056] The total provided capacity of different clusters in each time slot is determined based on the channel vector solved in the satellite channel model, the transmission signal solved in the transmission signal model, and the user received signal solved by the user received signal expression, specifically including:

[0057] The user first decodes its own public message, and then decodes its own private message after performing serial interference cancellation technology; the expressions of the user's public signal-to-noise ratio and public rate and private signal-to-noise ratio and private rate are given;

[0058] In a T H In each time slot of The signal to interference and noise ratio (SINR) is expressed as:

[0059]

[0060] The corresponding achievable rate of public messages is expressed as:

[0061]

[0062] To ensure that all users in the jth cluster can decode The availability rate of public messages is defined as:

[0063]

[0064] Among them, C ji represents the common rate of the i-th beam in the j-th cluster. After being decoded and removed by SIC, each user decodes his own private message by treating other users’ private messages as noise. H In each time slot of n,jμ(jk) The SINR and private message rate are expressed as:

[0065]

[0066] To ensure that the multicast message is decoded by the i-th beam in the j-th cluster, the i-th beam in the j-th cluster shares the private rate It is determined by the user with the smallest rate in the beam and is defined as:

[0067]

[0068] Therefore, the total capacity provided by the jth cluster can be expressed as:

[0069]

[0070] When executing step 104, the specific steps may be as follows:

[0071] The optimization scheme of the multicast multi-beam satellite communication system model is to abstract the optimization problem into a mixed integer non-convex programming problem, namely:

[0072]

[0073]

[0074] Among them, the optimized variables are the precoding vector Public Rate Allocation and CBH strategy vector Variable u n is a size of N c ×1 binary variable, u n,j ∈{0,1} represents u n The jth element of , when 1, indicates that the jth cluster is lit in time slot n, and vice versa. Constraint (11b) guarantees the data flow requirement; constraint (11c) guarantees can be decoded by every user in the jth cluster; Constraint (11e) represents the maximum transmission power of a cluster; N in constraint (11f) w represents the number of clusters lit in each time slot; in constraint (11g), A represents the adjacency matrix between clusters. If A ij = 1, it means cluster i is adjacent to cluster j, and vice versa. Constraint (11h) means that in a T H The capacity provided by the inner cluster. Here ⊙ represents element-wise multiplication.

[0075] When executing step 105, the specific steps may be as follows:

[0076] Based on the optimization problem P0, the weighted mean square error is used to solve the weight and equalizer to obtain the optimal minimum mean square error;

[0077] Substituting the optimal minimum mean square error, the expression of weighted mean square error is derived based on the equalizer;

[0078] Solve the minimum mean square error weight to obtain the final weighted mean square error expression;

[0079] Rewrite the optimization problem P1 into an optimization problem P2 that includes auxiliary variables, weights, and equalizer sets;

[0080] By using the decoupling property of weighted mean square error in equalizer and weight, the equivalence between optimization problem P1 and optimization problem P2 is established.

[0081] Minimize each weighted mean square error separately to obtain the optimal weight and equalizer;

[0082] An alternating optimization algorithm is used to solve the weighted mean square error problem to obtain the optimal precoding vector and the optimal public rate allocation.

[0083] Specifically, the WMMSE method is used to solve the precoding vector and Public Rate Allocation

[0084] Since problem P0 is a mixed integer non-convex programming problem (MINCP), it is difficult to solve directly. Therefore, this embodiment considers the method of alternating optimization (AO) to iteratively solve the precoding vector and the public rate allocation, and the CBH strategy vector. This embodiment first fixes the CBH strategy vector To solve the precoding vector and Public Rate Allocation

[0085] Problem P0 can be rewritten as subproblem P1:

[0086] Taking the kth user in the jth cluster at the nth time slot as an example, by using the equalizer The common flow is estimated to be The private stream is successfully decoded in the public stream and read from y n,jk After removal, it is estimated to be The public and private mean squared errors (MSEs) are defined as and Therefore, this embodiment can obtain:

[0087]

[0088] in, and

[0089] The optimal MSE equalizer can be obtained by solving and The minimum mean square error (MMSEs) can be given by the following formula:

[0090]

[0091] By substituting (14) (15) into (12) and (13), we can obtain the optimal MMSE equalizer:

[0092]

[0093]

[0094] The relationship between MMSEs and SINR is: and Therefore, the corresponding rate relation can be written as and The weighted mean square error is given by:

[0095]

[0096]

[0097] in, and v jk represents the weight of the k-th user in the j-th cluster with respect to MSEs, represents the weighted minimum mean square error of the public rate of the kth user in the jth cluster; ξ jk represents the weighted minimum mean square error of the private rate of the kth user in the jth cluster. By solving and Get the optimal equalizer and By substituting the optimal MMSE equalizer into WMSEs, this embodiment can obtain:

[0098]

[0099]

[0100] By solving and Get the optimal MMSE weight and By substituting these values ​​into (20) and (21), this embodiment can obtain:

[0101]

[0102]

[0103] By substituting constraint C7 in problem P1 into constraint C1 and replacing T slot Set to 1s, based on the relationship between rate and WMMSE in (22) and (23), the optimization problem P1 can be rewritten as:

[0104]

[0105]

[0106]

[0107]

[0108]

[0109] Among them, θ and represents auxiliary variables, represents a set of weights, Denotes the set of equalizers. The equivalence of Problem P2 and Problem P1 is established by observing that the WMSEs are decoupled in their equalizers and weights. Therefore, the optimal v and g are obtained by minimizing each WMSE, as shown in (22) and (23), respectively, resulting in the solution of MMSE.

[0110] The WMSE problem in problem P2 can be solved by the AO algorithm, which exploits block convexity. In a given iteration of the algorithm, v and g are first updated by the optimal MMSE solution of (22) and (23). Next, the set of precoding matrices W for all auxiliary variables in problem P2 is solved by To update, By fixing v and g in problem P2 and , we get . This is a convex problem that can be solved efficiently using the CVX toolbox.

[0111] When executing step 106, the specific steps may be as follows:

[0112] Integer programming is used to solve the CBH strategy vector

[0113] After optimizing the precoding vector and common rate allocation, the CBH mode design problem can be rewritten as:

[0114]

[0115] stC1,C5,C6,C7.(25b).

[0116] Problem P3 is a binary optimization problem with a huge search space, including CBH modes, among which This embodiment uses a graph-based method to reduce the search space. This embodiment defines a binary matrix to store all possible CBH modes. Where m l Representing each column of M, this embodiment can be used To represent all valid clusters, N ss represents the number of all feasible CBH modes, z k represents each column of Z. This solves the constraints C5 and C6 in problem P3, so the CBH pattern design problem can be further rewritten as:

[0117]

[0118]

[0119]

[0120] in, Indicates the valid clusters and the corresponding light-up cluster time periods. Indicates that in time slot T slot The capacity provided by the served cluster after precoding. According to the effective cluster matrix Z, this embodiment defines Matrix, where the vector of the kth column is s k =z k ⊙R′, represents the capacity provided by each CBH mode. By introducing a slack variable λ, the problem is simplified. With the introduction of a new constraint, In this embodiment, λ is defined j As a non-negative integer variable representing the duration of active time slots of each valid cluster set. can be rewritten as The optimization problem is transformed into:

[0121]

[0122]

[0123]

[0124]

[0125] The number of CBH modes is determined by the non-zero optimization variable η. i The corresponding photoperiod is given by η i The value of is given. Problem P5 is an integer programming problem and can be solved by the integer programming solver of CVX.

[0126] In summary, this application has the following technical effects:

[0127] The present application provides a scheme for combined beam hopping and precoding of a multicast multi-beam satellite communication system based on rate-splitting multiple access (RSMA), taking into account the downlink transmission from multi-beam satellite to ground users. This embodiment formulates an optimization problem of maximizing and minimizing ground user rate matching, and the optimization variables include public precoding vectors, private precoding vectors, public rate allocation and cluster hopping (CBH) strategy vectors, and the constraints include power constraints, rate allocation constraints and beam hopping (BH) mode constraints. This embodiment decomposes the original mixed integer non-convex programming problem (MINCP) into two sub-problems, which are iteratively solved by weighted minimum mean square error (WMMSE) method and integer programming method respectively. This scheme can make full use of satellite resources to achieve rate matching, and can effectively reduce interference between beams within a cluster.

[0128] The technical features of the above embodiments may be combined arbitrarily. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0129] This article uses specific examples to illustrate the principles and implementation methods of this application. The description of the above embodiments is only used to help understand the method and core ideas of this application. At the same time, for those skilled in the art, according to the ideas of this application, there will be changes in the specific implementation methods and application scope. In summary, the content of this specification should not be understood as limiting this application.

Claims

1. A joint beam hopping and precoding scheduling method based on RSMA multicast satellite system, characterized in that: include: Obtain satellite communication system simulation parameters; Based on the satellite communication system simulation parameters, a multicast multi-beam satellite communication system model is constructed; the multicast multi-beam satellite communication system model includes a plurality of antenna feeds and a plurality of clusters; the antenna feeds are used to generate beams in a set cluster; the beams are used to provide services for ground users; each of the ground users is served by one beam; In the multicast multi-beam satellite communication system model, the total provided capacity of different clusters in each time slot is determined through time slot allocation and beam hopping pattern; Determine an optimization problem of the multicast multi-beam satellite communication system model based on the total provided capacity of different clusters in each time slot; the optimization variables of the optimization problem are precoding vector, common rate allocation and CBH strategy vector; Based on the weighted minimum mean square error method, the precoding vector and the public rate allocation are solved to obtain the optimal precoding vector and the optimal public rate allocation; Based on the integer programming method, the CBH strategy vector is solved to obtain the optimal CBH strategy vector; Based on the optimal precoding vector, the optimal public rate allocation and the optimal CBH strategy vector, the optimized multicast multi-beam satellite communication system model is determined; According to the optimized multicast multi-beam satellite communication system model, multicast requests are scheduled.

2. The method for joint beam hopping and precoding scheduling based on RSMA multicast satellite system according to claim 1, characterized in that: The satellite communication system simulation parameters include satellite altitude, beam radius, maximum transmitting antenna gain, user receiving antenna gain, system bandwidth, carrier frequency, noise temperature, 3dB angle, rain attenuation parameter, noise variance value of the kth user in the jth cluster, number of beams, number of clusters, number of users served by each beam, number of time slots in a cluster hopping cycle, number of clusters served in each time slot, time slot duration, period of cluster hopping mode, required capacity, tolerance and transmission power of each cluster.

3. The method for joint beam hopping and precoding scheduling based on RSMA multicast satellite system according to claim 1, characterized in that: In the multicast multi-beam satellite communication system model, the total provided capacity of different clusters in each time slot is determined through time slot allocation and beam hopping mode, including: Determine the satellite channel model, transmission signal model and user receiving signal expression in the multicast multi-beam satellite communication system model; Based on the channel vector solved in the satellite channel model, the transmitted signal solved in the transmitted signal model and the user received signal solved by the user received signal expression, the total provided capacity of different clusters in each time slot is determined.

4. The method for joint beam hopping and precoding scheduling based on RSMA multicast satellite system according to claim 3, characterized in that: The satellite channel model is specifically: Among them, the vector h jk represents the channel vector between the satellite and the kth user in the jth cluster on the ground, represents element-wise multiplication, b jk The vector represents the receiving antenna gain, free space loss and antenna gain of the multi-beam satellite of the kth user in the jth cluster; q jk represents the rain attenuation effect and signal phase of the kth user in the jth cluster.

5. The method for joint beam hopping and precoding scheduling based on RSMA multicast satellite system according to claim 3, characterized in that: The transmission signal model is specifically: in, Indicates public news. Indicates private precoding, represents the common precoding of the jth cluster, m n,ji Indicates that the private part is encoded into private stream messages of each beam, N j represents the beam of the jth cluster.

6. The method for joint beam hopping and precoding scheduling based on RSMA multicast satellite system according to claim 3, characterized in that: The expression of the user receiving signal is as follows: Where njk represents the additive Gaussian white noise of the kth user in the jth cluster, represents the common precoding of the jth cluster, Indicates public news. represents private precoding, m n,ji Indicates that at time slot n, the Nth j The multicast message of beams, H is the transposed matrix.

7. The method for joint beam hopping and precoding scheduling based on RSMA multicast satellite system according to claim 3, characterized in that: The total provided capacity is specifically expressed as follows: in, represents the private rate shared by the i-th beam in the j-th cluster, C ji represents the common rate of the i-th beam in the j-th cluster, R j represents the provided capacity of all beams in the jth cluster.

8. The method for joint beam hopping and precoding scheduling based on RSMA multicast satellite system according to claim 1, characterized in that: The optimization problem of the multicast multi-beam satellite communication system model is specifically: stC1: represents the required capacity of the th cluster in a C2: C3: C4: C5: C6: C7: in, represents the precoding vector, Indicates public rate allocation, represents the CBH strategy vector; variable u n is of size N c ×1 binary variable, u n,j ∈{0,1} represents u n The jth element of , when 1, indicates that the jth cluster is lit in time slot n; represents the achievable rate of public messages, represents the available rate of public messages, C ji represents the public rate of the i-th beam in the j-th cluster, k represents the k-th user; the constraint C4 represents the maximum transmit power of a cluster, represents the common precoding of the jth cluster, Indicates private precoding; constrains N of C5 w Indicates the number of clusters lit in each time slot; in constraint C6, A represents the adjacent matrix between clusters; Indicated in a T H The capacity provided by the inner cluster, Indicated in a T H The capacity provided by the jth cluster of ; ⊙ represents element-wise multiplication; Indicates size N c ×1 cluster vector, Indicated in a T H The required capacity of the j-th cluster.

9. The method for joint beam hopping and precoding scheduling based on RSMA multicast satellite system according to claim 8, characterized in that: Based on the weighted minimum mean square error method, the precoding vector and the public rate allocation are solved to obtain the optimal precoding vector and the optimal public rate allocation, which specifically includes: Based on the optimization problem P0, the weighted mean square error is used to solve the weight and equalizer to obtain the optimal minimum mean square error; Substituting the optimal minimum mean square error, the expression of weighted mean square error is derived based on the equalizer; Solve the minimum mean square error weight to obtain the final weighted mean square error expression; Rewrite the optimization problem P1 into an optimization problem P2 that includes auxiliary variables, weights, and equalizer sets; By using the decoupling property of weighted mean square error in equalizer and weight, the equivalence between optimization problem P1 and optimization problem P2 is established. Minimize each weighted mean square error separately to obtain the optimal weight and equalizer; An alternating optimization algorithm is used to solve the weighted mean square error problem to obtain the optimal precoding vector and the optimal public rate allocation.

10. The method for joint beam hopping and precoding scheduling based on RSMA multicast satellite system according to claim 9, characterized in that: The optimization problem P2 is specifically: P2: s.t. Among them, θ and represents auxiliary variables, represents a set of weights, and vjk represents the weight of the kth user in the jth cluster with respect to MSEs, represents a collection of equalizers, represents the weighted minimum mean square error of the public rate of the kth user in the jth cluster; ξ jk represents the weighted minimum mean square error of the private rate of the kth user in the jth cluster.

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