Active reconfigurable intelligent surface enabled satellite-ground RSMA network resource allocation device and algorithm

Abstract

The invention belongs to the technical field of wireless communication, and particularly relates to an active reconfigurable intelligent surface enabled satellite-ground RSMA network resource allocation device and algorithm. The algorithm comprises the following steps: establishing a satellite-ground RSMA system model containing nonlinear energy collection; jointly optimizing satellite active beam forming, an ARIS reflection coefficient matrix and a user power distribution ratio, and constructing a system spectrum efficiency maximization optimization problem; the method comprises the following steps: aiming at satellite beam forming and power distribution ratio optimization sub-problems, fixing an ARIS reflection coefficient matrix, and solving through a convex optimization technology to obtain an optimal solution; and aiming at an ARIS reflection coefficient optimization sub-problem, satellite beam forming and a power distribution ratio are fixed, and a feasible solution is obtained through iterative solution by a positive semi-definite relaxation and penalty function method. A simulation result shows that the algorithm is obviously superior to a traditional multiple access technology and a passive RIS auxiliary scheme in the aspect of spectrum efficiency, and the effectiveness and superiority of the algorithm are verified.

Description

Technical Field

[0001] This invention belongs to the field of wireless communication technology, specifically relating to an active reconfigurable smart surface-enabled satellite-to-ground RSMA network resource allocation device and algorithm. Background Technology

[0002] Rate-Splitting Multiple Access (RSMA), as one of the key candidate technologies for sixth-generation (6G) mobile communication, effectively manages multi-user interference by splitting user messages into public and private streams and combining them with continuous interference cancellation technology. This significantly improves the system's robustness and spectral efficiency under imperfect channel conditions. On the other hand, satellite communication, with its advantages of wide coverage, high reliability, and flexible networking, is becoming a crucial pillar for achieving seamless global coverage. Combining RSMA with satellite networks can effectively address the high-speed transmission needs in scenarios such as terrestrial network coverage blind spots and emergency communications.

[0003] A reconfigurable intelligent surface (RIS) is a planar structure composed of a large number of programmable passive reflective elements. It can dynamically adjust the phase of incident electromagnetic waves through software, thereby intelligently reconfiguring the wireless propagation environment. However, traditional passive RIS can only adjust the signal phase, resulting in a "multiplicative fading effect," which leads to severe end-to-end channel attenuation and limits its performance in scenarios with strong direct links. An active reconfigurable intelligent surface (ARIS), by integrating a low-noise amplifier into the reflective elements, can simultaneously adjust the amplitude and phase of the reflected signal, effectively compensating for cascaded channel fading and transforming multiplicative fading into additive fading, thus significantly improving system capacity.

[0004] Furthermore, with the surge in IoT device connection density, the dual challenges of spectrum scarcity and energy constraints are becoming increasingly severe. Wireless information and energy co-transmission technology, by collaboratively decoding information and harvesting energy in a shared wireless channel, offers a new approach to jointly optimizing spectrum and energy efficiency. However, most existing studies employ simplified linear energy harvesting models, failing to reflect the nonlinear saturation characteristics of actual RF-DC conversion circuits, leading to a mismatch between resource allocation strategies and actual hardware responses.

[0005] Therefore, deeply integrating ARIS, RSMA, and nonlinear energy harvesting models with satellite communications, and jointly optimizing satellite beamforming, ARIS reflection coefficient, and user power allocation ratio, is of great significance for building an efficient, reliable, and energy-saving next-generation space-ground converged network. Currently, research on collaborative optimization in this field is still insufficient. Summary of the Invention

[0006] The purpose of this invention is to propose a joint resource allocation algorithm and device to maximize the system spectral efficiency in an actively reconfigurable smart surface-enabled satellite-to-ground RSMA network.

[0007] In a first aspect, the present invention provides a method for resource allocation in a satellite-to-ground RSMA network with active reconfigurable smart surface empowerment, comprising:

[0008] S1: Establish a system model that includes a multi-antenna satellite, ARIS, and multiple ground users employing a power-sharing architecture. The system model considers Ricean fading, shadowing fading effects, and nonlinear energy harvesting characteristics on the user side.

[0009] S2: With the goal of maximizing the system spectral efficiency, construct a joint optimization problem involving the satellite active beamforming vector, the ARIS active reflection coefficient matrix, and the user power allocation ratio.

[0010] S3: For the aforementioned non-convex optimization problem, an alternating optimization framework is proposed, decomposing it into two solvable subproblems: 1) Optimizing the satellite beamforming and user power allocation ratio while fixing the ARIS phase shift; 2) Optimizing the ARIS reflection coefficient matrix while fixing the satellite beamforming and power allocation ratio. The subproblems are solved using convex optimization techniques and the semi-definite relaxation (SDR) algorithm, and an approximate optimal solution to the original problem is obtained through iterative updates.

[0011] Preferably, step S1 specifically includes:

[0012] The system includes a satellite (SAT) equipped with N antennas, an active reconfigurable smart surface (ARIS) equipped with M reflector units, and F single-antenna ground users.

[0013] Preferably, step S2 specifically includes:

[0014] System spectral efficiency is defined as the sum of the reachable rates of the common streams and the reachable rates of all private streams, expressed as: The optimization problem to maximize spectral efficiency is then modeled as follows:

[0015] (1a)

[0016] (1b)

[0017] (1c)

[0018] (1d)

[0019] (1e)

[0020] (1f)

[0021] (1g)

[0022] in and These represent the maximum transmit power available at the satellite and the forward power at the actively reconfigurable smart surface, respectively. Furthermore, Represents the phase shift matrix The m-th element, where .parameter Corresponding to the predetermined minimum rate of public messages, and Indicates the first The minimum acceptable power for each user. Constraints (1b) and (1c) impose power limits on the satellite and the reconfigurable smart surface, respectively, and set an upper limit on the maximum reflected power. Constraint (1e) ensures the minimum acceptable power for each user. The minimum total rate for each user, while the constraint (1g) ensures an effective power allocation ratio.

[0023] Preferably, step S3 specifically includes:

[0024] Due to variables , and Due to the coupling nature of the problem, problem (1) is non-convex and cannot be solved directly. The original problem is decomposed into two sub-problems using an alternating optimization framework for iterative solution. First, the ARIS reflection coefficient is fixed, transforming the problem into a convex optimization problem concerning satellite beamforming and user power allocation ratio. Then, the satellite beamforming and power allocation ratio are fixed, transforming the ARIS optimization problem into a semidefinite programming problem, and a semidefinite relaxation algorithm based on a penalty function is used to handle the rank-one constraint. The two sub-problems are solved alternately until convergence, yielding the optimal resource allocation scheme. Numerical simulations verify the performance of the algorithm, effectively reducing computational complexity.

[0025] An active, reconfigurable, intelligent surface-enabled satellite-to-ground RSMA network resource allocation device and method, comprising:

[0026] The model building module is used to construct the satellite-to-ground communication system, which includes satellite, ARIS, multi-user, and nonlinear energy harvesting models, and to define relevant channel and signal models.

[0027] The equation construction module is used to construct a joint optimization problem based on the system model, with the goal of maximizing the system spectral efficiency. The problem includes the satellite beamforming matrix, the ARIS reflection coefficient matrix, and the user power allocation ratio as optimization variables, and is constrained by the maximum transmit power of the satellite and ARIS, the minimum reachable rate of the user, and the minimum energy harvesting requirement.

[0028] The iterative processing module is used to solve the optimization problem using an alternating optimization framework, decomposing the original problem into two sub-problems: the first sub-problem is to fix the ARIS reflection coefficient and optimize the satellite beamforming and user power allocation ratio; the second sub-problem is to fix the satellite beamforming and power allocation ratio and optimize the ARIS reflection coefficient; the sub-problems are iteratively solved using a combination of convex optimization and semidefinite relaxation with a penalty function until the algorithm converges.

[0029] The modeling module includes:

[0030] The first modeling unit establishes the system topology and hardware architecture, including a satellite equipped with N antennas, an ARIS equipped with M reflector units, and F single-antenna ground users. Each user adopts a power distribution architecture to simultaneously perform information decoding and energy harvesting.

[0031] The second modeling unit establishes the channel model, in which the satellite-user and satellite-ARIS links adopt the shadow-Rice fading model, and the ARIS-user link adopts the Rice fading model.

[0032] The third modeling unit establishes a signal and energy harvesting model. The satellite uses an RSMA architecture to transmit signals containing both public and private flows. After power allocation, the received signals are decoded and energy is harvested based on a nonlinear model.

[0033] The equation-building module defines the system spectral efficiency as the sum of the reachability of the common flow and the reachability of all private flows:

[0034] (2)

[0035] in , and Representing users respectively The achievable rates for public and private flows are related to the signal-to-interference-plus-noise ratio (SINR).

[0036] The joint optimization problem is expressed as follows:

[0037] (3a)

[0038] (3b)

[0039] (3c)

[0040] (3d)

[0041] (3e)

[0042] (3f)

[0043] (3g)

[0044] Because the problem is non-convex and the variables are coupled, an alternating optimization algorithm is used to solve it. First, given the ARIS configuration, ... and Perform a lower bound approximation, transforming the original objective function into a function of... and The concave function. Simultaneously, the nonlinear energy harvesting constraint is equivalently transformed into a linear constraint on the received power. The subproblem ultimately transforms into a convex optimization problem, in the following form:

[0045] (4a)

[0046] (4b)

[0047] (4c)

[0048] (4d)

[0049] Given a fixed phase shift matrix The objective function of problem (4) becomes convex. Therefore, the optimal beamforming vector can be efficiently solved using the CVX toolbox. and power distribution ratio .

[0050] Then the phase shift vector is expressed as And introduce auxiliary variables The original question is transformed into a question about The optimization problem exists, but with rank-one constraints. By neglecting this constraint through semidefinite relaxation and a series of mathematical transformations, the semidefinite programming problem is obtained:

[0051] (5a)

[0052] (5b)

[0053] (5c)

[0054] (5d)

[0055] (5e)

[0056] The resulting problem (5) is a semidefinite programming problem that can be solved using CVX. To handle the non-rank problem of the solution after relaxation, a penalty term is added to the objective function. Furthermore, convex approximation is performed using the first-order eigenvalue inequality, and the solution is forced to converge to the rank-one matrix by iteratively solving the penalty optimization problem.

[0057] Finally, these two subproblems are solved alternately under the control of the iterative processing module, that is, subproblem one is solved first for updating. and Then solve subproblem two and update. Then based on the new Solve subproblem one again, and repeat this process until the objective function value of the system spectral efficiency converges to a steady state. At this point, output the jointly optimized satellite beamforming, ARIS reflection coefficient, and user power allocation scheme.

[0058] As can be seen from the above technical solution, by using an alternating optimization algorithm to solve the system optimization problem, the original problem is decomposed into two sub-problems: satellite beamforming and user power allocation ratio optimization, and ARIS reflection coefficient optimization. The satellite beamforming optimization problem is transformed into a convex optimization problem for solution using convex optimization techniques and a semi-definite relaxation method. Simultaneously, a semi-definite relaxation method based on a penalty function is used to effectively optimize the ARIS reflection coefficient, and an iterative update strategy ensures that the rank-one constraint is satisfied, ultimately maximizing the system's spectral efficiency. Attached Figure Description

[0059] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art are briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0060] Figure 1 This is a schematic diagram of a satellite-to-ground rate segmented multiple access network resource allocation device and method with active reconfigurable smart surface empowerment provided in an embodiment of the present invention;

[0061] Figure 2 This is a model diagram of the system implementing the present invention;

[0062] Figure 3 This is a graph showing the convergence performance of the algorithm provided in this embodiment of the invention;

[0063] Figure 4This is a graph showing the relationship between system spectral efficiency and the number of satellite antennas provided in an embodiment of the present invention;

[0064] Figure 5 This is a graph showing the relationship between system spectral efficiency and satellite transmission power provided in an embodiment of the present invention;

[0065] Figure 6 This is a graph showing the relationship between the system spectral efficiency and the number of ARIS reflection units provided in an embodiment of the present invention. Detailed Implementation

[0066] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0067] S1: Establish a model of a satellite-to-ground RSMA system with active reconfigurable intelligent surface empowerment;

[0068] S2: Propose a resource allocation algorithm for maximizing spectral efficiency. Under the constraints of maximum transmit power of satellite and ARIS, amplitude and phase constraints of ARIS reflection coefficient, minimum reachable rate of users, and nonlinear energy harvesting requirements, jointly optimize satellite active beamforming, ARIS reflection coefficient matrix and user power allocation ratio to construct the optimization problem of maximizing system spectral efficiency.

[0069] S3: The objective problem is solved by combining an alternating optimization algorithm with a semidefinite relaxation and a penalty function, decomposing it into two convex optimization subproblems with deterministic solutions. Finally, an efficient resource allocation algorithm based on alternating iteration is proposed.

[0070] Specifically, step S1 includes:

[0071] The method described in this embodiment is applicable to, for example... Figure 2 The system model shown includes the following system parameters: equipped with Satellite with root transmitting antenna, Actively reconfigurable smart surface (ARIS) with reflective units, and Each ground user has a single antenna, and each user employs a power-sharing (PS) architecture for simultaneous information decoding and energy harvesting. The ARIS's location coordinates are (0m, 0m, 10m), and users are randomly distributed within a circular area with a radius of 1m centered at (1.5m, 2m, 1.5m). The satellite's maximum transmit power... ARIS maximum power consumption The path loss at a reference distance of 1m is... Rice factor The non-line-of-sight (NLOS) component of the channel follows a Rayleigh distribution. User-received noise power. ARIS effective noise power Noise power of information decoding circuit The energy harvesting circuit parameters are set to , , .

[0072] Further, step S2 includes: The system contains information sent from the base station to the user, and ARIS enhances signal quality and overcomes multiplicative fading effects through active reflection. The signal transmitted from the satellite is... ,in and These represent the beamforming vectors for the public and private flows, respectively. and For the corresponding data symbols.

[0073] Therefore, users The received signal is

[0074] (6)

[0075] in , and These represent the distance from the satellite to the user. From ARIS to users The channel vector, This represents the channel matrix from the satellite to ARIS. Here is the reflection coefficient matrix of ARIS. This represents the effective noise at RIS, while Indicates the first Additive white Gaussian noise at each user location.

[0076] user The signal-to-interference-plus-noise ratio (SIR) for the common flow is:

[0077] (7)

[0078] The signal interference of private streams is

[0079] (8)

[0080] The corresponding reachable rates are respectively and The system spectral efficiency is the sum of the rates of the common flow and all private flows:

[0081] (9)

[0082] Considering nonlinear energy harvesting models, users The energy collected is:

[0083] (10)

[0084] in , .

[0085] The problem of maximizing the system's spectral efficiency is then:

[0086] (11a)

[0087] (11b)

[0088] (11c)

[0089] (11d)

[0090] (11e)

[0091] (11f)

[0092] (11g)

[0093] in and These represent the maximum transmit power available at the satellite and the forward power at the actively reconfigurable smart surface, respectively. Furthermore, Represents the phase shift matrix The m-th element, where .parameter Corresponding to the predetermined minimum rate of public messages, and Indicates the first The minimum acceptable power for each user. Constraints (11b) and (11c) impose power limits on the satellite and the reconfigurable smart surface, respectively, and set an upper limit on the maximum reflected power. Constraint (11e) ensures the minimum acceptable power for each user. The minimum total rate for each user, while constraints (11g) ensure an effective power allocation ratio.

[0094] Since the objective problem is not only non-convex but also has coupled optimization variables, we decompose the problem into two sub-problems. First, we fix the phase shift matrix of ARIS. Optimize satellite beamforming vectors and user power allocation ratio Secondly, it is known and Time-optimized ARIS phase shift matrix .

[0095] Furthermore, step S3 includes: first, introducing Theorem 1 to explore... and The lower bound is approximately equal to .

[0096] Theorem 1: For any feasible variable and The following inequalities hold.

[0097] (12)

[0098] in Indicates a fixed point.

[0099] Based on Theorem 1, we obtain The lower bound is

[0100] (12)

[0101] in .

[0102] Similarly, The lower bound is described as follows:

[0103] (13)

[0104] in , .

[0105] To further facilitate handling of (11), constraint (11f) is equivalent to

[0106] (14)

[0107] We then transform (14) into the following constraint

[0108] (15)

[0109] in .

[0110] Through the above transformation, and given The following optimization problem can be obtained.

[0111] (16a)

[0112] (16b)

[0113] (16c)

[0114] (16d)

[0115] in The specific definition is given by formula (17).

[0116]

[0117]

[0118] (17)

[0119]

[0120]

[0121] Given a fixed phase shift matrix The objective function of problem (16) becomes convex. Therefore, the optimal beamforming vector can be efficiently solved using the CVX toolbox. and user power allocation ratio .

[0122] Next, fix and The focus is on optimizing the phase shift matrix by solving problem (11). The converted formula is shown below.

[0123] (18a)

[0124] (18b)

[0125] (18c)

[0126] (18d)

[0127] (18e)

[0128] First, let's define the phase shift vector as... And indicate variable substitution For a given and Question (11) is further restated regarding ϵ.

[0129] Due to the quadratic inequality and equality constraints, problem (18) remains nonconvex. To address this, we employ SDR to transform (18) into a convex formula. Specifically, we define an auxiliary matrix... , In addition, we have also formulated It must satisfy and By relaxing the rank-one nonconvex constraint, problem (18) is re-expressed as

[0130] (19a)

[0131] (19b)

[0132] (19c)

[0133] (19d)

[0134] (19e)

[0135] in As given by formula (20), and It is a matrix extended with additional zero rows and zero columns. The resulting problem (19) is an SDP problem that can be solved using CVX.

[0136]

[0137] (20)

[0138]

[0139] Solving (19) using SDR, the relaxed solution Θ does not necessarily satisfy the rank-one constraint. Therefore, we propose a penalty-based strategy to approximate the near-optimal RIS phase configuration. Since... Constrained to be a positive semi-definite matrix, it inherently satisfies ,in express The largest eigenvalue. Equation The necessary and sufficient condition for it to be established is To strengthen this property, we introduce a penalty term. Let's rephrase the problem (19)

[0140] Then formula (19) can be expressed as:

[0141] (21a)

[0142] (21b)

[0143] in This represents the penalty factor, which must be large enough to be enforced. However, due to It is a convex function, and we have reformulated the problem (21) by iterative approximation. Therefore, the following theorem is needed to simplify this approximation.

[0144] Theorem 2: For any two positive semi-definite matrices and The subsequent inequalities hold.

[0145] (twenty two)

[0146] in This corresponds to the largest eigenvalue. The unit eigenvector.

[0147] In Theorem 2, given the first Feasibility of the next iteration , It can be approximated as

[0148] (twenty three)

[0149] In the In the next iteration, the convex subproblem is reformulated as

[0150] (24a)

[0151] (24b)

[0152] The convexity of Equation (24) allows for efficient solutions via the CVX Toolbox

[41] .

[0153] As can be seen from the above technical solution, the present invention provides a satellite-to-ground RSMA network resource allocation method based on active reconfigurable smart surface empowerment. By jointly optimizing satellite active beamforming, ARIS reflection coefficient matrix and user power allocation ratio, a calculation method for achieving the maximum spectral efficiency of the system is derived.

[0154] The system configuration parameters for this implementation are shown in the table below:

[0155] The method described in this embodiment is applicable to, for example... Figure 2 The system model shown includes the following system parameters: equipped with Satellite with root transmitting antenna, Actively reconfigurable smart surface (ARIS) with reflective units, and Each ground user has a single antenna, and each user employs a power-sharing (PS) architecture for simultaneous information decoding and energy harvesting. The ARIS's location coordinates are (0m, 0m, 10m), and users are randomly distributed within a circular area with a radius of 1m centered at (1.5m, 2m, 1.5m). The satellite's maximum transmit power... ARIS maximum power consumption The path loss at a reference distance of 1m is... Rice factor The non-line-of-sight (NLOS) component of the channel follows a Rayleigh distribution. User-received noise power. ARIS effective noise power Noise power of information decoding circuit The energy harvesting circuit parameters are set to , , .

[0156]

[0157] Figure 3 The convergence of the system's spectral efficiency with the number of iterations is shown. The proposed algorithm converges after approximately 7 iterations for different numbers of ARIS elements M, verifying the algorithm's effectiveness and stability. The larger the number of transmit antennas N, the higher the system's spectral efficiency, because more antennas provide greater spatial freedom to optimize the beam direction.

[0158] Figure 4 The relationship between system spectral efficiency and base station transmit power is presented. This relationship increases with the satellite's maximum transmit power. With the increase of power, the system spectral efficiency improves accordingly. The ARIS-assisted scheme achieves significant performance improvements compared to the non-RIS scheme because ARIS introduces an additional controllable link, which can effectively compensate for channel fading. The proposed ARIS-RSMA scheme outperforms other benchmark schemes at all power levels.

[0159] Figure 5 The relationship between system spectral efficiency and the number of ARIS reflector elements M is shown. As M increases, the performance of all RIS-assisted schemes improves. More reflector elements provide greater beamforming gain and spatial degrees of freedom. The proposed scheme performs optimally for all values ​​of M, and its performance advantage over the random phase-shift scheme becomes more pronounced as M increases.

[0160] Figure 6The relationship between system spectral efficiency and the number of satellite antennas N is shown. Increasing the number of antennas provides more spatial dimensions for optimizing beamforming, thereby significantly improving system performance. The ARIS-RSMA scheme consistently outperforms other comparative schemes, demonstrating the synergistic advantages of ARIS active amplification and RSMA interference management.

[0161] In this embodiment, the model building specifically includes:

[0162] The model building module is used to build a satellite-to-ground RSMA system model based on an active reconfigurable smart surface: it includes a satellite equipped with N antennas, an active reconfigurable smart surface equipped with M reflector units, and F single-antenna ground users. All users adopt a power-sharing architecture to simultaneously perform information decoding and energy harvesting.

[0163] The equation construction module constructs an optimization problem for maximizing the system's spectral efficiency by jointly optimizing satellite beamforming, ARIS reflection coefficient, and user power allocation ratio.

[0164] (25a)

[0165] (25b)

[0166] (25c)

[0167] (25d)

[0168] (25e)

[0169] (25f)

[0170] (25g)

[0171] in and These represent the maximum transmit power available at the satellite and the forward power at the actively reconfigurable smart surface, respectively. Furthermore, Represents the phase shift matrix The m-th element, where .parameter Corresponding to the predetermined minimum rate of public messages, and Indicates the first The minimum acceptable power for each user. Constraints (25b) and (25c) impose power limits on the satellite and the reconfigurable smart surface, respectively, and set an upper limit on the maximum reflected power. Constraint (25e) ensures the minimum acceptable power for each user. The minimum total rate for each user, while the constraint (25g) ensures an effective power allocation ratio.

[0172] In this example, the iterative solution module specifically includes:

[0173] The iterative processing module decomposes the constructed non-convex joint optimization problem into two sub-problems using an alternating optimization algorithm, optimizing satellite beamforming and power allocation ratio, and the ARIS reflection coefficient matrix, respectively. By introducing auxiliary variables and semi-definite relaxation techniques, the non-convex sub-problems are transformed into solvable convex optimization problems. Existing convex optimization tools are then used to efficiently solve the sub-problems, ultimately obtaining the optimal resource allocation scheme that maximizes the system's spectral efficiency. Numerical simulations verify the effectiveness and convergence of the proposed algorithm. The results show that the algorithm significantly reduces computational complexity while maintaining performance, revealing the significant technical advantages and application potential of active reconfigurable smart surfaces in improving the spectral efficiency of satellite-to-ground RSMA networks.

Claims

1. A resource allocation algorithm for a satellite-to-ground RSMA network with active reconfigurable intelligent surface empowerment, characterized in that: include S1: Establish a system model that includes multi-antenna satellites, ARIS, and multiple ground users using a power-sharing architecture; S2: To maximize the system spectral efficiency, a joint optimization problem is constructed involving the satellite active beamforming vector, the ARIS active reflection coefficient matrix, and the user power allocation ratio. S3: For the aforementioned non-convex optimization problem, an alternating optimization framework is proposed, which decomposes it into two solvable subproblems: 1) Optimize the satellite beamforming and user power allocation ratio while fixing the ARIS phase shift; 2) Optimize the ARIS reflection coefficient matrix while fixing the satellite beamforming and power allocation ratio. The subproblems are solved using convex optimization techniques and the semidefinite relaxation (SDR) algorithm, and the approximate optimal solution of the original problem is obtained through iterative updates.

2. The satellite-to-ground RSMA network resource allocation algorithm with active reconfigurable intelligent surface empowerment as described in claim 1, characterized in that, Step S1 specifically includes: The system includes a satellite (SAT) equipped with N antennas, an active reconfigurable smart surface (ARIS) equipped with M reflector elements, and F single-antenna ground users.

3. The satellite-to-ground RSMA network resource allocation algorithm with active reconfigurable intelligent surface empowerment as described in claim 1, characterized in that, Step S2 specifically includes: System spectral efficiency is defined as the sum of the reachable rates of the common streams and the reachable rates of all private streams, expressed as: The optimization problem of maximizing spectral efficiency is then modeled as follows: (1a) (1b) (1c) (1d) (1e) (1f) (1g) in and These represent the maximum transmit power available at the satellite and the forward power at the actively reconfigurable smart surface, respectively; furthermore... Represents the phase shift matrix The m-th element, where ;parameter Corresponding to the predetermined minimum rate of public messages, and Indicates the first The minimum acceptable power for each user; constraints (1b) and (1c) impose power limits on the satellite and the reconfigurable smart surface, respectively, and set an upper limit on the maximum reflected power; constraint (1e) ensures that the first user has the minimum acceptable power; The minimum total rate for each user, while the constraint (1g) ensures an effective power allocation ratio.

4. The satellite-to-ground RSMA network resource allocation algorithm with active reconfigurable intelligent surface empowerment according to claim 1, characterized in that, Step S3 specifically includes: Due to variables , and Due to the coupling properties of the problem, problem (1) is non-convex and cannot be solved directly. The original problem is decomposed into two sub-problems by an alternating optimization framework and solved iteratively: First, the ARIS reflection coefficient is fixed, and the problem is transformed into a convex optimization problem about satellite beamforming and user power allocation ratio. Then, the satellite beamforming and power allocation ratio are fixed, and the ARIS optimization problem is transformed into a semidefinite programming problem. A semidefinite relaxation algorithm based on a penalty function is used to handle the rank-one constraint. The two sub-problems are solved alternately until convergence, and the optimal resource allocation scheme is obtained. First, let's introduce Theorem 1 to explore... and The lower bound is approximately; Theorem 1: For any feasible variable and The following inequalities hold. (2) in Indicates a fixed point; Based on Theorem 1, we obtain The lower bound is (3) in ; Similarly, The lower bound is described as follows: (4) in , ; To further facilitate the handling of (1), constraint (1f) is equivalent to (5) We then convert (5) into the following constraints. (6) in ; Through the above transformation, and given The following optimization problem can be obtained. (7a) (7b) (7c) (7d) in The specific definition is given by formula (8). (8) Given a fixed phase shift matrix The objective function of problem (7) becomes convex; therefore, the optimal beamforming vector can be efficiently solved using the CVX toolbox. and user power allocation ratio ; Next, fix and The focus is on optimizing the phase shift matrix by solving problem (1). The converted formula is shown below. (9a) (9b) (9c) (9d) (9e) First, let's define the phase shift vector as... And indicate variable substitution For a given and Question (1) requires further restatement of ϵ; Due to the quadratic inequality and equality constraints, problem (9) remains non-convex; to address this, we employ SDR to transform (9) into a convex formula; specifically, we define an auxiliary matrix. , In addition, we have also formulated It must satisfy and By relaxing the rank-one nonconvex constraint, problem (9) is reformulated as follows: (10a) (10b) (10c) (10d) (10e) in As given by formula (11), and It is a matrix extended with additional zero rows and zero columns; the resulting problem (10) is an SDP problem that can be solved using CVX; (11) The relaxation solution is obtained by solving (10) using SDR. It may not necessarily satisfy the rank-one constraint, therefore we propose a penalty-based strategy to approximate the optimal RIS phase configuration; since Constrained to be a positive semi-definite matrix, it inherently satisfies ,in express The largest eigenvalue; equation The necessary and sufficient condition for it to be established is To strengthen this property, we introduce a penalty term. Let's rephrase the problem (10) Then formula (10) can be expressed as: (12a) (12b) in This represents the penalty factor, which must be large enough to be enforced. However, due to It is a convex function, and we have reformulated the problem (12) by iterative approximation; therefore, the following theorem is needed to simplify this approximation; Theorem 2: For any two positive semi-definite matrices and The subsequent inequalities hold. (13) in This corresponds to the largest eigenvalue. eigenvectors of units; In Theorem 2, given the first Feasibility of the next iteration , It can be approximated as (14) In the In the next iteration, the convex subproblem is reformulated as (15a) (15b) The convexity of Equation (15) allows for efficient solutions via the CVX Toolbox [41].

5. A satellite-to-ground RSMA network resource allocation device with active reconfigurable intelligent surface empowerment, characterized in that, include: The model building module is used to construct the satellite-to-ground communication system, which includes satellite, ARIS, multi-user, and nonlinear energy harvesting models, and to define relevant channel and signal models. The equation construction module is used to construct a joint optimization problem based on the system model, with the goal of maximizing the system spectral efficiency. The problem includes the satellite beamforming matrix, the ARIS reflection coefficient matrix, and the user power allocation ratio as optimization variables, and is constrained by the maximum transmit power of the satellite and ARIS, the minimum reachable rate of the user, and the minimum energy harvesting requirement. The iterative processing module is used to solve the optimization problem using an alternating optimization framework, decomposing the original problem into two sub-problems: the first sub-problem is to fix the ARIS reflection coefficient and optimize the satellite beamforming and user power allocation ratio; the second sub-problem is to fix the satellite beamforming and power allocation ratio and optimize the ARIS reflection coefficient. The subproblem is solved iteratively by combining convex optimization with semidefinite relaxation and a penalty function until the algorithm converges. The modeling module includes: The first modeling unit establishes the system topology and hardware architecture, including a satellite equipped with N antennas, an ARIS equipped with M reflector units, and F single-antenna ground users. Each user adopts a power distribution architecture to simultaneously perform information decoding and energy harvesting. The second modeling unit establishes the channel model, in which the satellite-user and satellite-ARIS links adopt the shadow-Rice fading model, and the ARIS-user link adopts the Rice fading model. The third modeling unit establishes a signal and energy harvesting model. The satellite uses an RSMA architecture to transmit signals containing both public and private flows. After power allocation, the received signals are decoded and energy is harvested based on a nonlinear model.

6. The actively reconfigurable intelligent surface-empowered satellite-to-ground RSMA network resource allocation device according to claim 5, characterized in that, include: The equation-building module defines the system spectral efficiency as the sum of the reachability of the common flow and the reachability of all private flows: (16) in , and Representing users respectively The achievable rates for public and private flows are related to the signal-to-interference-plus-noise ratio (SINR). The joint optimization problem is expressed as follows: (17a) (17b) (17c) (17d) (17e) (17f) (17g) Because the problem is non-convex and the variables are coupled, an alternating optimization algorithm is used to solve it. First, given the ARIS configuration, ... and Perform a lower bound approximation, transforming the original objective function into a function of... and The concave function, and the nonlinear energy harvesting constraint is equivalently transformed into a linear constraint on the received power; the subproblem is ultimately transformed into a convex optimization problem, in the following form: (18a) (18b) (18c) (18d) Given a fixed phase shift matrix The objective function of problem (4) becomes convex; therefore, the optimal beamforming vector can be effectively solved using the CVX toolbox. and power distribution ratio ; Then the phase shift vector is expressed as And introduce auxiliary variables ; The original question is transformed into a question about The optimization problem is a problem with rank-one constraints. By neglecting the constraint through semidefinite relaxation and a series of mathematical transformations, the semidefinite programming problem is obtained: (19a) (19b) (19c) (19d) (19e) The resulting problem (5) is a semidefinite programming problem that can be solved using CVX; to handle the non-rank problem of the relaxed solution, a penalty term is added to the objective function. Furthermore, convex approximation is performed using the first-order eigenvalue inequality, and the solution is forced to converge to the rank-one matrix by iteratively solving the penalty optimization problem.

7. The actively reconfigurable intelligent surface-empowered satellite-to-ground RSMA network resource allocation device according to claim 5, characterized in that, include: Finally, these two subproblems are solved alternately under the control of the iterative processing module, that is, subproblem one is solved first for updating. and Then solve subproblem two and update. Then based on the new Solve subproblem one again, and repeat this process until the objective function value of the system spectral efficiency converges to a steady state. At this point, output the jointly optimized satellite beamforming, ARIS reflection coefficient, and user power allocation scheme.

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