Joint beam hopping and precoding scheduling method for RSMA multicast satellite systems

Abstract

The present application discloses a joint beam hopping and precoding scheduling method for an RSMA multicast satellite system, which relates to the field of satellite communication technologies. The method includes constructing a multicast multi-beam satellite communication system model based on satellite communication system simulation parameters; the model includes a plurality of antenna feeds and clusters; through time slot allocation and beam hopping patterns, determining the total provided capacity of different clusters within each time slot; based on the total provided capacity of different clusters, determining the optimization problem of the model; the optimization variables of the optimization problem are precoding vectors, common rate allocation, and CBH strategy vectors, and solving the optimal solutions of the precoding vectors and common rate allocation based on the weighted minimum mean square error method. Solving the optimal solution of the CBH strategy vector based on the integer programming method. Combining the optimal precoding vectors, common rate allocation, and CBH strategy vectors to determine the optimized multicast multi-beam satellite communication system model. The present application reduces the interference between beams within a cluster and improves the reliability of communication.

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, including:

[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, solve the CBH policy vector to obtain the optimal CBH policy vector;

[0012] Based on the optimal precoding vector, optimal common rate allocation, and optimal CBH policy vector, determine the optimized multicast multi-beam satellite communication system model;

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

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

[0015] This application provides a joint beam hopping and precoding scheduling method for an RSMA multicast satellite system. First, collect and organize the simulation parameters related to the satellite communication system. Subsequently, based on these parameters, a model of a multicast multi-beam satellite communication system is constructed. This model is equipped with multiple antenna feeds and corresponding cluster structures. The antenna feeds are responsible for generating beams within the specified clusters to serve ground users, ensuring that each user can obtain exclusive beam services. Using time slot allocation and beam hopping mode, accurately measure the capacity demand and supply of different clusters within each time slot. Based on this real-time data, define the optimization problem of the system model, and its core optimization variables include precoding vectors, common rate allocation, and CBH policy vectors. To solve this optimization problem, the weighted minimum mean square error method is used to determine the optimal precoding vector and common rate allocation, and the integer programming method is used to solve the optimal CBH policy vector. Integrate these optimal solutions to construct an optimized multicast multi-beam satellite communication system model. According to this optimized model, the 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 use of beam hopping technology successfully reduces the interference between beams. By comprehensively applying these technologies, the user requirements can be more accurately met, thereby improving the overall reliability and efficiency of the communication system. Description of the Drawings

[0016] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the following will briefly introduce the drawings required in the embodiments. Obviously, the drawings in the following description are only some embodiments of this application. For those of ordinary skill in the art, without creative efforts, other drawings can be obtained based on these drawings.

[0017] Figure 1 It is a schematic flowchart of a joint beam hopping and precoding scheduling method for an RSMA multicast satellite system in an embodiment of this application;

[0018] Figure 2Schematic diagram of a multi-cast multi-beam satellite communication system model provided by an embodiment of the present application;

[0019] Figure 3 A hopping beam pattern based on clustering provided by an embodiment of the present application. Detailed implementation manners

[0020] Next, the technical solutions in the embodiments of the present application will be clearly and completely described with reference to the accompanying drawings in the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present application without creative efforts shall fall within the protection scope of the present application.

[0021] To make the above objects, features, and advantages of the present application more obvious and understandable, the present application will be further described in detail below with reference to the accompanying drawings and specific implementation manners.

[0022] Embodiment 1

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

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

[0025] Step 102: Based on the satellite communication system simulation parameters, construct a multi-cast multi-beam satellite communication system model; the multi-cast 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 ground user is served by one beam;

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

[0027] Step 104: Based on the total provided capacity of different clusters in each time slot, determine the optimization problem of the multi-cast multi-beam satellite communication system model; the optimization variables of the optimization problem are precoding vectors, common rate allocation, and CBH policy vectors;

[0028] Step 105: Based on the weighted minimum mean square error method, solve the precoding vector and common rate allocation to obtain the optimal precoding vector and optimal common rate allocation;

[0029] Step 106: Based on the integer programming method, solve the CBH policy vector to obtain the optimal CBH policy vector;

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

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

[0032] Among them, in some embodiments, when performing step 101, specifically, it can be as follows:

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

[0034] Specifically, as shown in Table 1 below:

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

[0036]

[0037]

[0038] Among them, in some embodiments, when performing step 102, specifically, it can be as follows:

[0039] Construct a multi - cast multi - beam satellite communication system model based on the satellite communication system simulation parameters; the multi - cast multi - beam satellite communication system model includes a number of antenna feeds and a number of clusters; the antenna feeds are used to generate beams in the set clusters; the beams are used to provide services for ground users; each ground user is served by one beam.

[0040] Specifically, as Figure 2 shown, this embodiment considers a multi - group multi - cast multi - beam satellite communication system for a downlink. The satellite is a geostationary orbit satellite (GEO), equipped with N t antenna feeds, generating M beams in N c clusters to serve K ground users. Among them, it is assumed that one feed generates one beam (N t = M). Define as the set of all clusters, as the set of all beams in the j - th cluster, Denote the set of all beams in the \(j\)-th cluster. Since the multi-beam satellite system is actually overloaded with users, in this embodiment, it is assumed that \(\rho(\rho\gt1)\) users are served by each beam simultaneously. \(K = \rho N\). t Denote the total number of users in the beam coverage area. Denote the set of users in the \(i\)-th beam in the \(j\)-th cluster. Each user is served by only one beam, so in this embodiment, there is And \(\mu(jk)=m\) indicates the mapping of the \(k\)-th user in the \(j\)-th cluster to the \(m\)-th beam.

[0041] Among them, when performing step 103, specifically, it can be as follows:

[0042] In the multi-cast multi-beam satellite communication system model, through time slot allocation and hopping beam pattern, determine the total available capacity of different clusters in each time slot, specifically including:

[0043] Determine the satellite channel model, transmit signal model and user received signal expression in the multi-cast multi-beam satellite communication system model;

[0044] Based on the channel vector solved in the satellite channel model, the transmit signal solved in the transmit signal model and the user received signal solved in the user received signal expression, determine the total available capacity of different clusters in each time slot.

[0045] Specifically, as Figure 3 shown, within a hopping beam duration period \(T\) H , this period is composed of several time slots in an orderly manner. One cluster hop covers multiple such time slots, and within a CBH (Coherent Beamforming Hopping) window, a specific cluster hop pattern will appear.

[0046] In this embodiment, it is defined that \(T\) H \(=N\) slot \(\times T\) slot , where \(N\) slot represents the number of time slots of one \(T\) H , denoted by to represent the set of \(N\) slot , and \(T\) slot is the definition of the duration of the time slot. Denote the required capacity of \(N\) c clusters, where \(D\) j represents the required capacity of all beams in the \(j\)-th cluster. Denote the cluster vector of size \(N\) c \(\times1\), where represents the required capacity of the \(j\)-th cluster in one \(T\) H . Denote N c as the provided capacity of the clusters, where R j denotes the provided capacity of all the beams in the j-th cluster. Denote as a cluster vector of size N c ×1, where denotes the capacity provided by the j-th cluster within one time slot.

[0047] Among them, determine the satellite channel model, transmit signal model, and user received signal expression in the multicast multi-beam satellite communication system model, specifically as follows:

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

[0049]

[0050] As Figure 2 shown, this embodiment proposes a rate matching scheme based on RSMA in the multicast multi-beam satellite system. At time slot n, the multicast message of the N j -th beam in the j-th cluster is These messages are respectively split into a common message part and a private message part, for example All the common parts are integrated together and encoded into a public message, that is shared by all the beams in the j-th cluster at time slot n. All the private parts are respectively encoded into the private stream messages of each beam, that is Therefore, the vector of the satellite information stream can be expressed as where The precoding matrix of the j-th cluster is expressed as where denotes the common precoding of the i-th beam in the j-th cluster, denotes the private precoding.

[0051] At time slot n at the satellite side, the transmitted signal is expressed as:

[0052]

[0053] At time slot n, the signal received by the k-th user in the j-th cluster is expressed as:

[0054]

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

[0056] where, 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 from the user received signal expression, the total available capacity of different clusters in each time slot is determined, specifically including:

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

[0058] In each time slot of a T H the signal-to-interference-plus-noise ratio (SINR) for the k-th user in the j-th cluster to decode is expressed as:

[0059]

[0060] The achievable rate corresponding to the common message is expressed as:

[0061]

[0062] To ensure that all users in the j-th cluster can decode the available rate of the common message is defined as:

[0063]

[0064] where, C ji represents the common rate of the i-th beam in the j-th cluster. After is decoded and removed through SIC, each user decodes its own private message by treating the private messages of other users as noise. In each time slot of a T H the SINR and private message rate for the k-th user in the j-th cluster to decode m n,jμ(jk) are expressed as:

[0065]

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

[0067]

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

[0069]

[0070] Among them, when performing step 104, specifically, it can be as follows:

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

[0072]

[0073]

[0074] Among them, the optimization variables are the precoding vector Common rate allocation And the CBH policy vector Variable u n Is a binary variable of size N c ×1, u n,j ∈{0,1} represents the j-th element of u n When taking 1, it means that the j-th cluster is lit in time slot n, and vice versa. Constraint (11b) ensures the data traffic demand; Constraint (11c) is to ensure that Can be decoded by each user in the j-th cluster; In constraint (11e) represents the maximum transmit power of a cluster; N w In constraint (11f) represents the number of clusters lit in each time slot; In constraint (11g), A represents the adjacent matrix between clusters. If A ij =1, it means that cluster i is adjacent to cluster j, and vice versa. Constraint (11h) represents the capacity provided by the cluster within a T H Here, ⊙ represents element-wise multiplication.

[0075] Among them, when performing step 105, specifically, it can be as follows:

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

[0077] Substitute the optimal minimum mean square error, and based on the equalizer, derive the expression of the weighted mean square error;

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

[0079] Rewrite the optimization problem P1 as an optimization problem P2 that includes auxiliary variables, weights, and a set of equalizers;

[0080] Utilize the decoupling property of the weighted mean square error in the equalizer and weights to establish the equivalence between optimization problem P1 and optimization problem P2;

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

[0082] Adopt an alternating optimization algorithm to solve the weighted mean square error problem to the optimal precoding vector and optimal common rate allocation.

[0083] Specifically, adopt the WMMSE method to solve the precoding vector and common rate allocation

[0084] Since problem P0 is a mixed integer non-convex programming problem (MINCP) and is difficult to solve directly. Therefore, this embodiment considers an alternating optimization (AO) method to iteratively solve the precoding vector, common rate allocation, and CBH policy vector respectively. This embodiment first fixes the CBH policy vector to solve the precoding vector and common rate allocation

[0085] Problem P0 can be rewritten as sub-problem P1:

[0086] Taking the k-th user in the j-th cluster at the n-th time slot as an example, by using the equalizer the common stream is estimated as the private stream is estimated as after the common stream is successfully decoded and removed from y n,jk The common and private mean square errors (MSEs) are defined as and Therefore, this embodiment can obtain:

[0087]

[0088] where, and

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

[0090]

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

[0092]

[0093]

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

[0095]

[0096]

[0097] where, 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 common rate of the k-th user in the j-th cluster; ξ jk represents the weighted minimum mean square error of the private rate of the k-th user in the j-th cluster. By solving and the optimal equalizer and By substituting the optimal MMSE equalizer into WMSEs, this embodiment can obtain:

[0098]

[0099]

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

[0101]

[0102]

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

[0104]

[0105]

[0106]

[0107]

[0108]

[0109] where θ and denote auxiliary variables, denotes the set of weights, denotes the set of equalizers. By observing that the WMSEs are decoupled in their equalizers and weights, the equivalence between problem P2 and problem P1 is established. Therefore, the optimal v and g are obtained by minimizing each WMSE, as shown in (22) and (23), resulting in the MMSE solution.

[0110] The WMSE problem in problem P2 can be solved by the AO algorithm, which exploits block convexity. At a given iteration of the algorithm, v and g are first updated with the optimal MMSE solutions of (22) and (23). Next, the set of precoding matrices W for all auxiliary variables in problem P2 is updated by solving where is obtained by fixing v and g in problem P2. This is a convex problem and can be efficiently solved by the CVX toolbox.

[0111] where, when performing step 106, specifically it can be as follows:

[0112] An integer programming method is adopted to solve the CBH policy vector

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

[0114]

[0115] s.t. C1, C5, C6, C7. (25b).

[0116] Problem P3 is a binary optimization problem with a huge search space, which includes CBH modes, where This embodiment adopts a graph-theory-based method to reduce the search space. This embodiment defines a binary matrix to store all possible CBH modes. If where m l represents each column of M, this embodiment can use to represent all valid clusters, N ss represents the number of all feasible CBH patterns, z k represents each column of Z. In this way, the constraints C5 and C6 in problem P3 are solved. Therefore, the CBH pattern design problem can be further rewritten as:

[0117]

[0118]

[0119]

[0120] wherein, represents the valid clusters and the corresponding illuminated cluster time periods. represents at time slot T slot the capacity provided by the precoded clusters to be served. According to the valid cluster matrix Z, in this embodiment, is defined as a matrix, where the vector of the k-th column is s k = z k ⊙R′, representing the capacity provided under the influence of each CBH pattern. By introducing a slack variable λ to simplify this problem, along with introducing a new constraint, in this embodiment, λ j is defined as a non-negative integer variable to represent the active time slot duration of each valid cluster set. Therefore can be rewritten as The optimization problem is transformed into:

[0121]

[0122]

[0123]

[0124]

[0125] wherein, the number of CBH patterns is given by the number of non-zero optimization variables η i and the corresponding illumination period is given by the value of η i . Problem P5 is an integer programming problem and can be solved by the integer programming solver of CVX.

[0126] To sum up, the present application has the following technical effects:

[0127] This application provides a scheme for jointly beam hopping and precoding in a multicast multi-beam satellite communication system based on rate-splitting multiple access (RSMA), considering the downlink transmission from a multi-beam satellite to ground users. In this embodiment, an optimization problem of maximizing the minimum ground user rate matching is formulated. The optimization variables include the common precoding vector, the private precoding vector, the common rate allocation, and the cluster beam hopping (CBH) strategy vector. 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, and iteratively solves them through the weighted minimum mean square error (WMMSE) method and the integer programming method respectively. This scheme can make full use of on-board resources to achieve rate matching and can effectively reduce the interference between beams within a cluster.

[0128] The technical features of the above embodiments can be combined arbitrarily. For the sake of concise description, 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, it should be considered as the scope recorded in this specification.

[0129] Specific examples are used in this article to elaborate on the principle and implementation manner of this application. The description of the above embodiments is only used to help understand the method and its core idea of this application; at the same time, for those of ordinary skill in the art, according to the idea of this application, there will be changes in the specific implementation manner and application scope. In summary, the content of this specification should not be construed as a limitation to 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; The optimization problem of the multicast multi-beam satellite communication system model is specifically: 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.

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: Among them, n jk 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: 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.

9. The method for joint beam hopping and precoding scheduling based on RSMA multicast satellite system according to claim 8, characterized in that: The optimization problem P2 is specifically: Among them, θ and represents auxiliary variables, represents a set of weights, and v jk represents the weight of the k-th user in the j-th 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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