Beamforming and Phase Shift Optimization Method for RIS-Assisted Satellite Communication Systems

Abstract

The present invention provides a beamforming and phase shift optimization method for RIS-assisted satellite communication systems, which maximizes the multi-user weighted sum rate (WSR) of the system by jointly designing the beamforming matrix of low-earth orbit (LEO) satellites and the phase shift matrix of RIS. Specifically, the present invention combines the alternating optimization algorithm with the scalar replacement strategy, decouples the WSR optimization problem into multiple sub-problems through Lagrangian dual transformation, and optimizes the beamforming matrix and the phase shift matrix respectively, effectively reducing the computational complexity and making the method more efficient and applicable in large-scale systems. Compared with traditional methods, this method exhibits better performance in communication systems with a large number of users or a large number of antennas, and at the same time has a significant advantage in computational efficiency, providing an efficient solution for future large-scale wireless communication.

Description

Technical Field

[0001] The present invention relates to the technical fields of wireless communication and satellite communication, and particularly relates to a multi-user communication resource scheduling method based on the joint optimization of LEO satellites and RIS (Reconfigurable Intelligent Surface). Background Art

[0002] With the development of low Earth orbit (LEO) satellite communication networks and the wide application of reconfigurable intelligent surfaces (RIS) in the field of wireless communication, future multi-user communication systems need to ensure high transmission rates while meeting the efficient resource allocation requirements of a large number of terminals. However, due to the channel complexity in satellite communication, the dynamic changes in user locations, and frequent occlusion problems, traditional communication path selection and resource scheduling methods face severe challenges. Existing beamforming techniques are difficult to effectively handle interference problems between multiple users, and the complexity of large-scale optimization calculations limits the application of algorithms in real-time communication.

[0003] LEO satellite communication networks have shown broad application prospects in the fields of Internet of Things (IoT), 5G / 6G networks, remote monitoring, etc. due to their wide coverage and low latency advantages. However, in large-scale user systems, how to achieve optimal resource allocation by dynamically adjusting communication paths (direct links or reflected links via RIS) remains an urgent problem to be solved. The introduction of RIS brings a new optimization dimension to satellite communication. By controlling the phase shift matrix to improve the channel gain, the communication quality can be enhanced with low energy consumption. However, there is a complex coupling relationship between the optimization of RIS and LEO satellite beamforming, and how to effectively decouple and achieve joint optimization is the focus of current research.

[0004] Traditional communication system optimization algorithms mostly use high-complexity matrix operations, such as iterative algorithms, which pose extremely high requirements for computing power. In large-scale systems where LEO satellites and RIS work together, these methods are often difficult to apply in real time and cannot meet the requirements of low latency and high rate of communication systems. Summary of the Invention

[0005] The present invention proposes a multi-user communication resource scheduling method based on the joint optimization of LEO satellites and RIS, aiming to solve the problems of improving communication rate and optimizing resource allocation in multi-user scenarios. This method realizes the maximization of the system weighted sum rate (WSR) by alternately optimizing the beamforming matrix of LEO satellites and the phase shift matrix of RIS, and reduces the computational complexity while meeting power constraints and channel conditions.

[0006] To achieve the above objectives, the present invention adopts the following technical solutions, including the following steps: S1, scenario description; S2, model establishment; S3, model solution;

[0007] In step S1, the scenario is described as deploying a reconfigurable intelligent surface (RIS) in a low Earth orbit (LEO) satellite communication system. The LEO satellite serves as the main signal transmitter, transmitting signals to multiple user terminals through beamforming. The RIS reflects signals to enhance signal coverage and quality. In this scenario, each user terminal can receive direct signals from the LEO satellite or signals reflected by the RIS.

[0008] In step S2, under the scenario described in S1, the system model is established by constructing a joint optimization problem. The goal is to maximize the weighted sum rate of all users by optimizing the beamforming matrix of the LEO satellite and the phase shift matrix of the RIS.

[0009] In step S3, based on the model established in S2, the model is solved using an alternating optimization algorithm and a scalar substitution strategy. By gradually optimizing the beamforming matrix of the LEO satellite and the phase shift matrix of the RIS, the optimization problem is solved to maximize the weighted sum rate of all users.

[0010] Furthermore, step S1 specifically includes

[0011] Assume is the symbol transmitted to the i-th user. In the downlink, the symbol is first precoded at the LEO by the corresponding transmit beamformer , where N represents the number of LEO satellite antennas, represents the complex domain, including real and imaginary parts. The transmitted signal at the LEO is expressed as , where represents the beamforming vector of the i-th user, and K represents the total number of users in the system. Since the signal needs to support multipath transmission, including the LEO-RIS-USER link and the LEO-USER link, the channel of each user is divided into two parts: the LEO-USER link and the LEO-RIS-USER link. The channel from the LEO to the i-th user is expressed as , represents the total channel of the i-th user, which consists of two parts: one is the signal path from the LEO satellite , and the other is the signal path through the RIS , represents the channel from the LEO to the RIS, represents the phase control matrix of the reflection unit on the RIS. The dimensions of each symbol are as and represent the sizes of complex vectors and matrices, N represents the number of LEO satellite antennas, and M represents the number of reflection units of the RIS. represents the phase shift matrix at the RIS, which is a diagonal matrix , where is the phase of the m-th reflecting element on the RIS; the signal received by the i-th user is expressed as: ; where represents the noise received by the i-th user obeys a complex Gaussian distribution with zero mean and variance ;

[0012] Then the downlink data rate of the i-th user is: , where , represents the signal-to-interference-plus-noise ratio SINR of the i-th user, where is the noise power, representing the power of the additive white Gaussian noise in the received signal.

[0013] Furthermore, the maximum system sum rate configuration scheme in step S2 is expressed as the scheme that maximizes the weighted sum rate WSR of all users in the optimal system, specifically as follows:

[0014] The weighted sum rate of users in the RIS-assisted satellite communication system :

[0015] In the above formula , where represents the weight coefficient of the i-th user; represents the downlink data rate of the i-th user, where ;

[0016] The steps to maximize the weighted sum rate of all users are as follows:

[0017]

[0018] ;

[0019] ;

[0020] In the above formula is a complex matrix used to describe the beamforming coefficients of each user; represents the phase shift matrix at the RIS, which is a diagonal matrix, , is the phase of the m-th reflecting element on the RIS, j is the imaginary unit, is the phase angle of the n-th reflecting unit; the constraint condition indicates that: the sum of the beamforming vector powers of all users cannot exceed the maximum power allowed by the system ; the constraint condition indicates that: the phase can be continuously controlled.

[0021] Furthermore, in step S3, a low-complexity algorithm is proposed to solve the optimization problems based on W and respectively; this algorithm is carried out in three stages:

[0022] S31. Auxiliary variable solving problem: An auxiliary variable is introduced to decouple the complex coupling relationship and simplify the optimization process;

[0023] S32. Optimize W to enhance the channel gain of the LEO-USER link while fixing the phase shift matrix ;

[0024] S33. Phase shift matrix solving problem: The optimization objective of the phase shift matrix is to enhance the reflection path of the RIS and thus further improve the communication performance of the system while fixing the beamforming matrix .

[0025] Furthermore, step S31 specifically includes

[0026] By introducing the auxiliary variable , the original optimization problem is reconstructed into a sub-problem :

[0027]

[0028]

[0029]

[0030] where , ; The sub-problem of S31 When is fixed, for any , by setting the optimal solution of the auxiliary variable in can be obtained as .

[0031] Furthermore, in the case of fixing the RIS phase shift matrix and the auxiliary variable , the optimization problem is reconstructed into the sub-problem of S32

[0032]

[0033]

[0034] where is the weighted parameter of the user, representing the channel gain of the user; meanwhile, an auxiliary variable is introduced to reconstruct the optimization problem into a sub-problem :

[0035]

[0036]

[0037]

[0038] where ;

[0039] By setting , the optimal for the given W is obtained:

[0040]

[0041] After determining , there is . By setting , the optimal W for the given is obtained:

[0042]

[0043] where is the optimal dual variable corresponding to the constraint condition, represents the identity matrix; the variables and are solved by an alternating optimization method. First, fix W and directly calculate the optimal using an analytical formula; then fix and update the optimal using an analytical formula. The whole process requires multiple iterations until the objective function converges to obtain the optimal value of :

[0044] ,

[0045] where, can be set as the optimal value of each w update, is expressed as the optimal value of

[0046] Furthermore, by fixing the RIS phase shift matrix and the auxiliary variable In the case of, the optimization problem P2.1 is reconstructed as a sub - problem of S33 :

[0047]

[0048] ;

[0049] where is the weighted parameter of the user; meanwhile, let represent the phase control of all reflection elements on the RIS. Then, according to the channel , define ; ; In the formula represents the direct - channel vector between the LEO satellite and the k - th user, represents the product of the RIS phase - shift matrix and the conjugate transpose of the channel vector from the RIS to the k - th user. Thus, we can obtain:

[0050]

[0051] Introduce the auxiliary variable , and reconstruct the function :

[0052]

[0053] where , by solving the partial derivative, the optimal solution of the auxiliary variable is obtained; on this basis, the optimization problem of the RIS phase - shift matrix is further reconstructed as :

[0054] ,

[0055] s.t.

[0056]

[0057] where , ;

[0058] In the formula:

[0059]

[0060]

[0061]

[0062] and are respectively expressed as:

[0063]

[0064]

[0065] Using matrix transformation, the elements of the RIS reflection matrix are obtained as a quadratic function of:

[0066]

[0067] where, represents the j-th diagonal element of matrix Q, represents the row column element of matrix Q, represents the row column element of matrix Q, represents the n-th element of matrix w, C represents a constant term independent of , and at the same time, taking the partial derivative with respect to and setting its derivative equal to zero, the analytical solution of the RIS reflection matrix is obtained; since the elements of the RIS reflection matrix must satisfy the unit modulus constraint, a normalization variable is introduced so that the optimal solution satisfies this constraint condition, and the optimal solution of the elements of the RIS reflection matrix is obtained:

[0068]

[0069] where the optimal solution of the RIS phase shift is obtained; represents the -th element of .

[0070] Furthermore, the above three sub-problems P2.1, P2.2, and P2.3 are iteratively solved using the alternating optimization method, and the specific steps are as follows:

[0071] (a) Initialization: The system first generates two main channel matrices: represents the direct channel from the LEO satellite to the user; H2 represents the composite channel from the LEO satellite reflected by the RIS to the user. Initialize the beamforming matrix W and the phase shift matrix Θ, and set the total transmit power constraint ;

[0072] (b) Lagrangian dual transformation and auxiliary variable solution: Fix the beamforming matrix W and the phase shift matrix Θ, and calculate the optimal auxiliary variable , by introducing auxiliary variables, the problem is simplified to solving the optimal values of these variables to maximize the user's communication rate;

[0073] (c) Optimization of the beamforming matrix W. With the fixed phase shift matrix Θ and auxiliary variables , optimize the beamforming matrix W to maximize the system weighted sum rate WSR, and solve this optimization problem by the Majorization-Minimization method;

[0074] (d) Optimization of the phase shift matrix Θ. After fixing W and , optimize the phase shift matrix of the RIS, and use the scalar replacement strategy to optimize one by one to ensure the maximization of the channel gain;

[0075] (e) Convergence condition judgment. If the change in the objective function value after this iteration is less than the preset threshold compared with the previous time, the algorithm converges and outputs the current optimal solution; otherwise, continue to alternately optimize W, Θ and ;

[0076] (f) Iterative update. Let k = k + 1, enter the next round of iteration, and repeat the solution steps until the convergence condition is met; if the maximum number of iterations K is reached, stop the algorithm;

[0077] (g) Return the optimal beamforming matrix W, the optimal phase shift matrix Θ and the auxiliary variables , and output the maximized weighted sum rate.

[0078] Through the above technical solutions, in the context of the collaborative communication between LEO satellites and RIS, the present invention provides a brand-new solution for resource allocation, path selection and communication performance improvement. This method is applicable to future 5G / 6G networks, the Internet of Things and other large-scale wireless communication scenarios, providing technical support for the development of future networks.

[0079] Therefore, the present invention proposes a joint optimization algorithm based on Lagrangian dual transformation and scalar replacement strategy, which realizes the dynamic optimization of LEO satellite beamforming and RIS phase shift matrix while reducing the computational complexity. Through multiple rounds of alternating iteration, this method can ensure that the weighted sum rate (WSR) of the system reaches the optimum, providing high-quality communication services for multiple users.

[0080] The present invention proposes a beamforming and phase shift optimization method for RIS-assisted satellite communication systems. This method not only realizes the optimization of the computational complexity in the communication between LEO and RIS systems, but also maximizes the weighted sum rate (WSR) of the system.

[0081] Specifically, different from traditional satellite communication systems, the present invention proposes a low-complexity beamforming and phase shift optimization method for the collaborative optimization system of LEO satellites and RIS. By reasonably designing the optimization algorithm, the joint optimization problem of the beamforming matrix and the RIS phase shift matrix is decomposed into multiple low-complexity sub-problems, thereby improving the system performance while reducing the computational overhead.

[0082] The present invention adopts a step-by-step iterative optimization method to maximize the weighted sum rate (WSR) of the system by reducing the computational complexity while ensuring the overall communication quality. During the task execution process, the system adjusts the beamforming and phase shift configurations to maximize the sum rate of the system.

[0083] The core advantage of the present invention is that by combining the alternating optimization algorithm with the scalar replacement strategy, the computational complexity is significantly reduced, avoiding the heavy operation process in traditional algorithms, especially showing excellent performance in large-scale multi-user systems. This method can quickly converge to the global optimal solution, thereby maximizing the performance of multi-user systems. By optimizing the beamforming matrix of LEO satellites and the phase shift matrix of RIS, the communication efficiency of the system is further improved. This innovative solution is not only applicable to diverse application scenarios such as LEO communication, Internet of Things (IoT), and 5G / 6G networks, but also provides an efficient and low-cost solution for large-scale wireless communication, with significant technical advantages. Brief Description of the Drawings

[0084] Figure 1 is a flowchart of the present invention;

[0085] Figure 2 is a comparison diagram of the system sum rate of different calculation methods in the embodiments of the present invention. Detailed Embodiments

[0086] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are some, but not all, of the embodiments of the present invention.

[0087] As Figure 1 shown, the beamforming and phase shift optimization method for the RIS-assisted satellite communication system described in the present invention

[0088] includes the following steps: S1. Scenario description; S2. Model establishment; S3. Model solution.

[0089] In step S1, the scenario description refers to deploying a reconfigurable intelligent surface (RIS) in a LEO satellite communication system to cooperate with LEO satellites to complete the transmission of user signals. That is, each user can transmit data through these two data transmission paths: Direct link: The LEO satellite communicates directly with the user terminal. Reflection link: The LEO satellite reflects signals through the RIS to achieve indirect communication with the user terminal.

[0090] In step S2, the model establishment refers to formulating the optimization of the LEO beamforming matrix W and the RIS phase shift matrix Θ as a joint optimization problem. The goal of this model is to solve the optimization problem using a low computational complexity algorithm under power and phase constraint conditions to maximize the system weighted sum rate (WSR).

[0091] Step S3: Model solution refers to using the alternating optimization algorithm and scalar replacement strategy to solve the optimal solutions of the beamforming matrix and the phase shift matrix with lower computational complexity. Specifically: Optimization of the beamforming matrix: With the phase shift matrix Θ fixed, optimize the beamforming matrix W to improve the transmission rate of the direct transmission link. Optimization of the phase shift matrix: With the beam matrix W fixed, adjust each element of the RIS phase shift matrix one by one to enhance the channel gain of the reflection link. By alternately solving the beamforming and phase shift configurations through the alternating optimization algorithm and scalar replacement strategy, the system can quickly converge to the optimal solution, maximizing the system communication rate while satisfying power resource and delay constraints and reducing computational complexity.

[0092] The following is a specific description:

[0093] The present invention proposes a beamforming and phase shift optimization method for a RIS-assisted satellite communication system, including a scenario description module, a model establishment module, and a model solution module.

[0094] The scenario description module is used to describe the RIS-assisted satellite communication system scenario, deploy the RIS in the LEO communication system, cooperate with LEO satellites to complete the transmission of user signals, and reasonably configure beamforming and phase to maximize the sum rate of all ground user terminals. Data in LEO can be transmitted to user terminals in two ways. Direct link: The LEO satellite directly sends data to the end user. Reflection link: The LEO satellite reflects signals to the user terminal through the RIS.

[0095] Assume is the symbol transmitted to the i-th user. In the downlink, the symbol is first precoded at the LEO by the corresponding transmit beamformer Therefore, the transmitted signal at the LEO can be expressed as , since the signal needs to support multipath transmission, including the LEO-RIS-USER link and the LEO-USER link, the channel of each user can be divided into two parts: the LEO-USER link and the LEO-RIS-USER link. Therefore, the channel from LEO to the i-th user can be expressed as , where , , represent the equivalent baseband channels from LEO to user i, from LEO to RIS, and from RIS to user i. represents the phase shift matrix at the RIS, which is a diagonal matrix. The signal received by the i-th user can be expressed as: . Where represents the additive white Gaussian noise at the receiver of the i-th user. In summary, the downlink data rate of the i-th user is: where , represents the signal-to-interference-plus-noise ratio (SINR) of the i-th user.

[0096] Furthermore, the maximum system sum rate configuration scheme in step S2 is expressed as the scheme that maximizes the weighted sum rate (WSR) of all users in the optimal system, as follows:

[0097] The weighted sum rate of users in the RIS-assisted satellite communication system :

[0098]

[0099] In the above formula , where represents the weight coefficient of the i-th user. represents the downlink data rate of the i-th user, where .

[0100] Then the optimal modeling, that is, the following optimization problem:

[0101]

[0102] ;

[0103] ;

[0104] In the above formula , where, is the maximum transmission power of LEO. represents the phase shift matrix at the RIS, which is a diagonal matrix. , where is the phase of the m-th reflecting element on the RIS. Here, it is assumed that the phase It can be continuously controlled, i.e.:

[0105] .

[0106] Step S3 includes

[0107] A low-complexity algorithm is proposed to solve the optimization problems based on W and respectively. This method is carried out in three stages: First, 31) Auxiliary variable solving problem: To effectively solve the non-convex problem in the joint optimization of LEO satellites and RIS, an auxiliary variable is introduced to decouple the complex coupling relationship and simplify the optimization process. 32) Optimize W to improve the channel gain of the LEO-USER link while fixing the phase shift matrix ; 33) Phase shift matrix solving problem: The optimization objective of the phase shift matrix is to enhance the reflection path of RIS while fixing the beamforming matrix so as to further improve the communication performance of the system.

[0108] Since the joint beamforming and phase optimization problem is a very difficult problem. Since the objective function is non-convex and the optimization variables and W are deeply coupled and difficult to handle. The Lagrangian dual transformation is applied to decouple the original optimization problem.

[0109] To handle the complex "log-sum ratio" problem involved in the WSR maximization problem , the Lagrangian dual transformation is introduced to decouple these logarithms.

[0110] S31. By introducing the auxiliary variable , the original optimization problem is equivalent to:[[]]

[0111]

[0112]

[0113]

[0114] where , The function is:[[]]

[0115]

[0116] where .

[0117] S31 sub-problem When When fixed, for any , the auxiliary variable can obtain the optimal solution of as . . Substituting into the objective function , it can be found that the objective function is only related to the variables and . The influence of the auxiliary variable has been eliminated. Therefore, in this stage, the problem is further simplified to an optimization problem only for and , and will be solved in the subsequent stage.

[0118] Sub-problem S32 , when is fixed, the corresponding WSR maximization problem can be rewritten as the following optimization problem:

[0119]

[0120]

[0121] where .

[0122] Because in is a high-dimensional non-convex function, and the sub-problem is the sum of multiple ratio FP problems, which is difficult to solve directly. To solve this problem, the quadratic transformation method is used, and an auxiliary variable is introduced. Then is re-expressed as:

[0123]

[0124]

[0125]

[0126] where .

[0127] By setting , the optimal ξ for the given W is:

[0128]

[0129] Then, by determining , the problem of optimizing the variable W is reformulated as:

[0130]

[0131]

[0132] By setting , the optimal W is:

[0133]

[0134] where is the optimal dual variable corresponding to the constraint condition.

[0135] During the optimization process, the variables and are solved by using the alternating optimization method. First, fix W and directly calculate the optimal through the analytical formula; then fix and update the optimal through the analytical formula. The whole process requires multiple iterations until the objective function converges.

[0136] For a relatively large N, the computational complexity is relatively high during the optimization process. Especially when searching for the optimal to obtain the optimal W, this may significantly increase the computational burden. To reduce the overall computational complexity, the following lemma can be used to redesign the form of the optimization solution, thereby effectively simplifying the solution process.

[0137] Lemma 1: Let , where . The function has at :

[0138]

[0139] Lemma 1 provides an equivalent transformation rule for the objective function. Its core role is to replace the complex non-linear objective function with an easily processed form, thereby reducing the computational complexity and avoiding the high-cost operations of matrix operations. At the same time, Lemma 1 lays a theoretical foundation for the objective function transformation of Lemma 2 to follow, ensuring the mathematical rationality of subsequent optimizations. Generally, in problems involving FP, if the problem is solved by introducing auxiliary variables, the update process of its auxiliary variables is realized by generating a surrogate function to achieve optimization. Combining with the Majorization-Minimization (MM) method, by introducing intermediate parameters, the complex non-linear terms are transformed into an analytical form, thereby greatly simplifying the solution. On this basis, a new equivalent transformation based on in Lemma 1 is introduced as an auxiliary variable. Therefore, through the close relationship between the construction of the surrogate function and the equivalent transformation, a new transformation can be derived.

[0140] Lemma 2: Let , B L, the following problems:

[0141]

[0142] can be equivalently transformed into:

[0143]

[0144] Lemma 2 further reconstructs the objective function based on Lemma 1, linearizes it or decomposes it into quadratic form using intermediate variables, thereby reducing the computational complexity and enhancing the flexibility of the optimization algorithm.

[0145] Therefore, based on Lemma 2, substituting the optimal value of into ) can be transformed into:

[0146]

[0147] It is worth noting here that can be set as the optimal value for each update of w.

[0148] By obtaining the first-order derivative function of the above formula with respect to and setting it equal to 0, the optimal value of can be obtained as:

[0149] It can be seen from this that the denominator is a scalar, so the complex operations caused by matrix inversion are avoided, and high computational complexity will not be brought.

[0150] S33 sub-problem 3. Using scalar transformation to obtain the optimal phase shift , let , then the channel can be transformed into:

[0151]

[0152] Define ; . In the formula represents the direct channel vector between the LEO satellite and the k-th user. represents the product of the RIS phase shift matrix and the conjugate transpose of the channel vector from the RIS to the k-th user. Then can be written as:

[0153]

[0154] Observing the formula , only depends on It is related. Therefore, only this item needs to be transformed and then optimized to obtain the optimal solution. Introduce the auxiliary variable , and using the quadratic transformation, we can get:

[0155]

[0156] Among them, . Then, take the first-order partial derivative of to get:

[0157]

[0158] Among them, let it be equal to 0, and we have:

[0159]

[0160] Therefore, . Substitute into to get , and only need to optimize . Among them, can be written as:

[0161]

[0162]

[0163] Among them, expand to be expressed as:

[0164]

[0165]

[0166] Among them, and are respectively expressed as:

[0167]

[0168]

[0169] Substitute into to get:

[0170]

[0171]

[0172] Among them, . Therefore, can be written as:

[0173]

[0174] Among them:

[0175]

[0176]

[0177]

[0178] Therefore, the problem of optimizing can be formulated as:

[0179] ,

[0180] s.t.

[0181] To effectively solve the optimization problem, a low-complexity phase-shift optimization method is proposed to avoid the computational complexity problems that may occur in traditional methods.

[0182] From the objective function in it can be observed that it is a quadratic function of an element in . It can be expressed as:

[0183]

[0184] Among them, , , , respectively represent the -th diagonal element of the matrix , the -th element of the vector , and the elements of the -th row and -th column and the -th row and -th column of the matrix . C represents the term independent of . Therefore, the scalar quadratic function for optimizing the -th element of the RIS reflection can be obtained from the above. Then, taking the derivative of gives:

[0185]

[0186] Then, setting it equal to 0, we get:

[0187]

[0188] Since the reflection coefficient of the RIS needs to satisfy the constraint conditions, an auxiliary vector is introduced again. , substituting it into the above formula, we have:

[0189]

[0190] Among them, the optimal solution of the RIS phase shift is .

[0191] It can be observed that The calculation of only involves scalar operations, rather than complex matrix operations. This calculation method effectively simplifies the optimization process, and the computational complexity is significantly reduced compared with the traditional matrix operation method. denotes the -th element of. can be expressed as:

[0192] .

[0193] The above three sub-problems are solved iteratively by using the alternating optimization method. The specific steps are as follows:

[0194] (a) Initialization: The system first generates two main channel matrices: denotes the direct channel from the LEO satellite to the user. H2 represents the composite channel from the LEO satellite reflected by the RIS to the user. Initialize the beamforming matrix W and the phase shift matrix Θ, and set the total transmit power constraint .

[0195] (b) Lagrangian dual transformation and auxiliary variable solution: To decouple the complexity of the problem, auxiliary variables are introduced to simplify the solution process. These variables are directly related to the channel gain of the user and the system rate. The original non-convex optimization problem is decomposed into two sub-problems by using the Lagrangian dual transformation. Fix the beamforming matrix W and the phase shift matrix Θ, and calculate the optimal auxiliary variable for each user, that is:

[0196]

[0197] Among them, is the signal-to-interference-plus-noise ratio (SINR) of the i-th user. By introducing auxiliary variables, the problem is simplified to solve the optimal values of these variables to maximize the communication rate of the user.

[0198] (c) Optimization of the beamforming matrix W, while fixing the phase shift matrix Θ and the auxiliary variable In this case, the beamforming matrix W is optimized to maximize the system weighted sum rate (WSR). The optimization problem is solved by the Majorization-Minimization (MM) method, which avoids interference between multiple users and reduces complex matrix operations. The optimal beamforming vector can be obtained by the following formula:

[0199]

[0200] (d) Optimization of the phase shift matrix Θ. After fixing W and the phase shift matrix of the RIS is optimized using the scalar replacement strategy to optimize each individually to ensure the maximization of the channel gain.

[0201] (e) Convergence condition judgment. If the value of the objective function after this iteration changes less than the preset threshold compared with the previous time, the algorithm converges and outputs the current optimal solution. Otherwise, continue to alternately optimize W, Θ and .

[0202] (f) Iterative update. Let k = k + 1, enter the next iteration, and repeat the solution steps until the convergence condition is met. If the maximum number of iterations K is reached, stop the algorithm.

[0203] (g) Return the optimal beamforming matrix W, the optimal phase shift matrix Θ and the auxiliary variable , and output the weighted sum rate after maximization.

[0204] As Figure 2 shown, the optimization algorithm of the present invention exhibits significant performance advantages under different conditions. Compared with the ADMM algorithm, random phase shift, and the case without RIS support, the proposed algorithm introduces RIS and achieves the highest achievable total rate through beamforming and phase optimization, and converges rapidly in the initial iteration. The results show that the direct link and phase optimization are crucial for system performance, and the use of RIS significantly improves the communication quality and system capacity. The algorithm demonstrates excellent performance in improving system communication efficiency and rapid convergence, verifying its practical application value in the design of high-efficiency communication systems.

[0205] In another embodiment of the present invention, a computer program product containing instructions is further provided. When it runs on a computer, it enables the computer to execute the LEO satellite and RIS collaborative optimization method in the above embodiments.

[0206] It can be understood that the system, device, and storage medium provided in the embodiments of the present invention correspond to the method provided by the present invention, and the explanations and beneficial effects of the relevant content can refer to the relevant parts of the above methods.

[0207] In an embodiment of the present invention, the entire system can be implemented by software, hardware, firmware, or a combination thereof. When implemented by software, it can take the form of a computer program product. The program product includes a plurality of computer instructions that, when loaded and executed on a computer, can perform all or part of the steps and functions in the above technical solution.

[0208] The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable devices, all of which can support the optimization calculation of the beamforming matrix and the phase shift matrix. The computer instructions can be stored in a computer-readable storage medium or transmitted from one storage medium to another through a computer network. For example, the computer instructions can be transmitted from a website, a computer, a server, or a data center to another website, server, or computer, and the transmission method can be wired transmission (such as optical fiber, DSL) or wireless transmission (such as infrared, Wi-Fi, microwave, etc.).

[0209] The readable storage medium includes any storage medium accessible by a computer, such as an integrated server, a data center, or a magnetic medium (such as a floppy disk, a hard disk, a magnetic tape), an optical medium (such as a DVD), and a semiconductor medium (such as a solid-state drive SSD).

[0210] It should be noted that in this specification, terms such as "first", "second", etc. are only used to distinguish different elements or operations and do not represent an actual order relationship. In addition, the term "comprising" or "including" means non-exclusive inclusion, which means that a process, method, device, or system may also include other elements not explicitly listed or its inherent components.

[0211] The various embodiments of the present invention are described in the same or similar manner. The same or similar parts between the embodiments can be referred to and explained with each other. The focus of each embodiment is to illustrate the differences from other embodiments. For the part implemented by the system, since it is similar to the part implemented by the method, the description is relatively brief, and the specific implementation can refer to the description of the method part.

[0212] Finally, it should be emphasized that the above embodiments are only used to illustrate the technical solution of the present invention and do not constitute a limitation to the present invention. Those skilled in the art can modify or replace the above technical solution without departing from the core idea of the present invention, and these modifications and replacements should also be regarded as within the protection scope of the present invention.

Claims

1. A beamforming and phase shift optimization method based on RIS-assisted satellite communication system, characterized in that: The following steps are involved: S1, scenario description; S2, model building; S3, model solution; In step S1, the scenario is described as deploying a reconfigurable intelligent surface, i.e., RIS, in a LEO satellite communication system; the LEO satellite serves as the main signal transmission source, transmitting signals to multiple user terminals through beamforming, and RIS reflection is used to enhance signal coverage and quality. In the scenario, each user terminal can receive a direct signal from the LEO satellite or a signal reflected by the RIS; In step S2, under the scenario described in S1, the system model establishment includes constructing a joint optimization problem, the goal of which is to maximize the weighted combined rate of all users by optimizing the beamforming matrix of the LEO satellite and the phase shift matrix of the RIS; In step S3, based on the model established in S2, the model is solved by using an alternating optimization algorithm and a scalar replacement strategy, and the optimization problem is solved by gradually optimizing the beamforming matrix of the LEO satellite and the phase shift matrix of the RIS to maximize the weighted combined rate of all users. Step S3 includes proposing a low-complexity algorithm to solve the problem based on W and The optimization problem is: the algorithm is divided into three stages: S31, Auxiliary variable solution problem: Auxiliary variables are introduced , used to decouple complex coupling relationships and simplify the optimization process; S32, fixed phase shift matrix In the case of , W is optimized to improve the channel gain of the link between LEO and USER; S33, Phase shift matrix solution problem: Phase shift matrix The optimization goal is to fix the beamforming matrix In this case, the reflection path of RIS is enhanced, thereby further improving the communication performance of the system.

2. The beamforming and phase shift optimization method based on the RIS-assisted satellite communication system according to claim 1, characterized in that: Step S1 specifically includes: Assumptions is the symbol transmitted to the i-th user; in the downlink, the symbol First, at LEO, the corresponding transmit beamformer Precoding is performed, where N represents the number of LEO satellite antennas. represents the complex domain, including real and imaginary parts; the transmitted signal at LEO is expressed as ,in represents the beamforming vector of the i-th user, K represents the total number of users in the system. Since the signal needs to support multipath transmission, including LEO-RIS-USER link and LEO-USER link, the channel of each user is divided into two parts: LEO-USER link and LEO-RIS-USER link; the channel from LEO to the i-th user is expressed as , represents the total channel of the i-th user, which consists of two parts: one is the signal path from the LEO satellite , and the other is the signal path through RIS , Indicates the channel from LEO to RIS, represents the phase control matrix of the reflection unit on RIS; the dimensions of each symbol are as follows and It represents the size of complex vectors and matrices, N represents the number of LEO satellite antennas, and M represents the number of reflection units of RIS; Represents the phase shift matrix at RIS, which is a diagonal matrix ,in is the phase of the mth reflector element on the RIS; the signal received by the i-th user is expressed as: ;in represents the noise received by the i-th user Follows a complex Gaussian distribution with zero mean and variance ; Then the downlink data rate of the i-th user is: ,in , represents the SINR of the i-th user, where is the noise power, which represents the power of the additive white Gaussian noise in the received signal.

3. The beamforming and phase shift optimization method based on the RIS-assisted satellite communication system according to claim 2 is characterized in that: The maximum system combined rate configuration scheme included in step S2 is represented as a scheme for maximizing the weighted combined rate WSR of all users in the optimal system, which is specifically as follows: Weighted Total Rate of Users in RIS-Assisted Satellite Communication System : In the above formula ,in It represents the weight coefficient of the i-th user; represents the downlink data rate of the i-th user, where ; The steps to maximize the weighted combined rate of all users are as follows: ； ； In the above formula is a complex matrix describing the beamforming coefficients for each user; represents the phase shift matrix at RIS, which is a diagonal matrix, , is the phase of the mth reflector element on the RIS, j is the imaginary unit, is the phase angle of the nth reflection unit; constraint condition Indicates that the sum of the beamforming vector powers of all users cannot exceed the maximum power allowed by the system ; Constraints Indicates: Phase Can be controlled continuously.

4. The beamforming and phase shift optimization method based on the RIS-assisted satellite communication system according to claim 3 is characterized in that: Step S31 specifically includes: By introducing auxiliary variables , the original optimization problem Refactoring into subproblems : in , ; Sub-problem of S31 when When fixed, for any , through the order get Auxiliary variables The optimal solution is , .

5. The beamforming and phase shift optimization method based on the RIS-assisted satellite communication system according to claim 4 is characterized in that: In a fixed RIS phase shift matrix and auxiliary variables In the case of Refactoring into subproblems of S32 : in is the user's weighted parameter, Represents the user's channel gain; at the same time, an auxiliary variable is introduced , the optimization problem Refactoring into subproblems : in ; By setting , find the optimal : Sure After that, there , by setting , to obtain the given The optimal W of in is the optimal dual variable corresponding to the constraint condition, express The identity matrix of and The solution is solved by alternating optimization. First, W is fixed and the optimal solution is directly calculated by analytical formula. ; then fix , update the optimal The whole process requires multiple iterations until the objective function Converge, get The optimal value of: ， in, can be set to the optimal value for each w update, Expressed as The optimal value of .

6. The beamforming and phase shift optimization method based on the RIS-assisted satellite communication system according to claim 5 is characterized in that: In a fixed RIS phase shift matrix and auxiliary variables In the case of Refactoring into subproblems of S33 : ； in is the user's weighted parameter; let Indicates the phase control of all reflection units on the RIS, according to the channel ,definition ; ; In the formula represents the direct channel vector between the LEO satellite and the kth user, represents the product of the RIS phase shift matrix and the conjugate transpose of the channel vector from RIS to user k, from which we can obtain: Introducing auxiliary variables , the function To refactor: in, , by solving the partial derivatives, we can get the optimal solution of the auxiliary variables ; On this basis, the optimization problem of RIS phase shift matrix Further refactored into : , s.t. in, , ; Where: and Respectively expressed as: Using matrix transformation, we can get the RIS reflection matrix elements: The quadratic function of : in, represents the j-th diagonal element of the matrix Q, represents the matrix Q OK The elements of the column, represents the matrix Q OK The elements of the column, represents the nth element of matrix w, and C represents Irrelevant constant terms, and Find the partial derivative and set it equal to zero to obtain the analytical solution of the RIS reflection matrix; since the elements of the RIS reflection matrix must satisfy the unit modulus constraint, a normalized variable needs to be introduced , so that the optimal solution satisfies the constraint condition, and the RIS reflection matrix element is obtained The optimal solution is: Among them, the optimal solution of RIS phase shift is obtained ; express No. elements, represented by .

7. The beamforming and phase shift optimization method based on the RIS-assisted satellite communication system according to claim 6 is characterized in that: The above three sub-problems P2.1, P2.2 and P2.3 are iteratively solved using the alternating optimization method, where the specific steps are as follows: (a) Initialization: The system first generates two main channel matrices: represents the direct channel from the LEO satellite to the user; H2 represents the composite channel reflected from the LEO satellite to the user through the RIS, initializes the beamforming matrix W and the phase shift matrix Θ, and sets the total transmit power constraint ; (b) Lagrangian dual transformation and auxiliary variable solution: Fix the beamforming matrix W and the phase shift matrix Θ and calculate the optimal auxiliary variable for each user. ,By introducing auxiliary variables, the problem is simplified to solving the optimal values ​​of these variables to maximize the user’s communication rate; (c) Optimization of the beamforming matrix W, with fixed phase shift matrix Θ and auxiliary variables In the case of , the beamforming matrix W is optimized to maximize the system weighted sum rate WSR, and the optimization problem is solved by the Majorization-Minimization method; (d) Optimization of the phase shift matrix Θ, fixing W and Finally, the phase shift matrix of RIS is optimized, and the scalar replacement strategy is used to optimize one by one. , to ensure that the channel gain is maximized; (e) Convergence condition judgment: if the objective function value after this iteration changes less than the preset threshold value compared with the previous one, the algorithm converges and outputs the current optimal solution; Otherwise, continue to optimize W, Θ, and ; (f) Iterative update, set k = k + 1, enter the next round of iteration, and repeat the solution steps until the convergence condition is met; If the maximum number of iterations K is reached, stop the algorithm; (g) Return the optimal beamforming matrix W, the optimal phase shift matrix Θ and auxiliary variables , and output the maximized weighted total rate.

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