Beam forming and phase shift optimization method based on RIS auxiliary satellite communication system

Abstract

According to the beam forming and phase shift optimization method based on the RIS auxiliary satellite communication system provided by the invention, the maximization of the multi-user weighted resultant rate WSR of the system is realized by jointly designing the beam forming matrix of the low earth orbit satellite LEO and the phase shift matrix of the RIS. Specifically, an alternating optimization algorithm and a scalar replacement strategy are combined, a WSR optimization problem is decoupled into a plurality of sub-problems through Lagrange dual transformation, a beam forming matrix and a phase shift matrix are optimized respectively, the calculation complexity is effectively reduced, and the method is more efficient and applicable to a large-scale system. Compared with a traditional method, the method shows better performance in a communication system with large-scale users or a large number of antennas, meanwhile, the method has remarkable advantages in calculation efficiency, and an efficient solution is provided for future large-scale wireless communication.

Description

Technical Field

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

[0002] With the development of low-orbit satellite (LEO) communication networks and the widespread application of reconfigurable smart surfaces (RIS) in the field of wireless communications, future multi-user communication systems need to meet the needs of efficient resource allocation for large-scale terminals while ensuring high transmission rates. However, due to the complexity of channels, dynamic changes in user locations, and frequent occlusion problems in satellite communications, traditional communication path selection and resource scheduling methods face severe challenges. Existing beamforming technology is difficult to effectively deal with the interference problem between multiple users, and the complexity of large-scale optimization calculations limits the application of algorithms in real-time communications.

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

[0004] Traditional communication system optimization algorithms mostly use highly complex matrix operations, such as iterative algorithms, which place extremely high demands on 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 low latency and high rate requirements of communication systems. Summary of the invention

[0005] This paper proposes a multi-user communication resource scheduling method based on joint optimization of LEO satellite and RIS, aiming to solve the problem of communication rate improvement and resource allocation optimization in multi-user scenarios. This method maximizes the system weighted sum rate (WSR) by alternately optimizing the beamforming matrix of the LEO satellite and the phase shift matrix of the RIS, and reduces the computational complexity while satisfying the power constraints and channel conditions.

[0006] To achieve the above objectives, the present invention adopts the following technical solution, including the following steps: S1, scene description; S2, model establishment; 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. 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 combined rate of all users.

[0007] Furthermore, 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 IRS; 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.

[0008] Furthermore, 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 :

[0009] 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:

[0010] ; ; 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.

[0011] Furthermore, step S3 includes proposing a low-complexity algorithm to solve the problems 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.

[0012] Further, step S31 specifically includes: By introducing auxiliary variables , the original optimization problem Refactoring into subproblems :

[0013]

[0014]

[0015] in , ; Sub-problem of S31 when When fixed, for any , through the order Can get Auxiliary variables The optimal solution is , .

[0016] Furthermore, in the fixed RIS phase shift matrix and auxiliary variables In the case of Refactoring into subproblems of S32 :

[0017]

[0018] 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 :

[0019]

[0020]

[0021] in ; By setting , find the optimal :

[0022] Sure After that, there , by setting , to obtain the given The optimal W of

[0023] 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 .

[0024] Furthermore, in the fixed RIS phase shift matrix and auxiliary variables In the case of , the optimization problem P2.1 is reconstructed into a subproblem of S33 :

[0025] ; 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:

[0026] Introducing auxiliary variables , the function To refactor:

[0027] 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 : , st

[0028]

[0029] in, , ; Where:

[0030]

[0031]

[0032] and Respectively expressed as:

[0033]

[0034] Using matrix transformation, we can get the RIS reflection matrix elements: The quadratic function of :

[0035] 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:

[0036] Among them, the optimal solution of RIS phase shift is obtained ; express No. elements, represented by .

[0037] Furthermore, the above three sub-problems P2.1, P2.2 and P2.3 are iteratively solved using an alternating optimization method, wherein 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, the algorithm converges and outputs the current optimal solution; otherwise, continue to alternately optimize W, Θ and ; (f) Iterative update, set k = k + 1, enter the next round of iteration, 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.

[0038] Through the above technical scheme, the present invention provides a new solution for resource allocation, path selection and communication performance improvement in the context of cooperative communication between LEO satellites and RIS. The method is suitable for future 5G / 6G networks, the Internet of Things and other large-scale wireless communication scenarios, providing technical support for the development of future networks.

[0039] Therefore, the present invention proposes a joint optimization algorithm based on Lagrange dual transformation and scalar replacement strategy, which can realize the dynamic optimization of LEO satellite beamforming and RIS phase shift matrix while reducing the computational complexity. Through multiple rounds of alternating iterations, this method can ensure that the weighted sum rate (WSR) of the system is optimal and provide high-quality communication services for multiple users.

[0040] The present invention proposes a beamforming and phase shift optimization method based on RIS-assisted satellite communication system. The method not only optimizes the computational complexity of LEO and RIS systems in communication, but also maximizes the weighted sum rate (WSR) of the system.

[0041] Specifically, unlike the traditional satellite communication system, the present invention proposes a low-complexity beamforming and phase shift optimization method for the collaborative optimization system of LEO satellite 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 reducing the computational overhead and improving the system performance.

[0042] 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, the system adjusts the beamforming and phase shift configuration to maximize the system sum rate.

[0043] 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, the heavy calculation process in the traditional algorithm is avoided, and excellent performance is shown in large-scale multi-user systems in particular. This method can quickly converge to the global optimal solution, thereby maximizing the performance of the multi-user system. By optimizing the beamforming matrix of the LEO satellite and the phase shift matrix of the RIS, the communication efficiency of the system is further improved. This innovative solution is not only suitable for diverse application scenarios such as LEO communications, the Internet of Things (IoT) and 5G / 6G networks, but also provides an efficient and low-cost solution for large-scale wireless communications, with significant technical advantages. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 It is a flowchart of the present invention; Figure 2 It is a comparison diagram of the combined rates of different calculation methods in the embodiments of the present invention. DETAILED DESCRIPTION

[0045] To make the purpose, technical solution and advantages of the embodiments of the present invention clearer, the technical solution in the embodiments of the present invention will be described clearly and completely below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of them.

[0046] like Figure 1 As shown, the beamforming and phase shift optimization method based on the RIS-assisted satellite communication system of the present invention is The following steps are included: S1. Scenario description; S2. Model establishment; S3. Model solution.

[0047] In step S1, the scenario description refers to deploying a reconfigurable intelligent surface (RIS) in the LEO satellite communication system to work with the LEO satellite to complete the transmission of user signals. That is, each user can transmit data through these two data transmission paths: Direct link: LEO satellite communicates directly with the user terminal. Reflection link: LEO satellite reflects the signal through RIS to achieve indirect communication with the user terminal.

[0048] The model building in step S2 refers to modeling 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 to maximize the system weighted sum rate (WSR) while satisfying power and phase constraints.

[0049] Step S3: Model solving refers to using an alternating optimization algorithm and a scalar replacement strategy to solve the optimal solution of the beamforming matrix and the phase shift matrix with lower computational complexity. Specifically: Optimization of the beamforming matrix: Under the condition of a fixed phase shift matrix Θ, optimize the beamforming matrix W to improve the transmission rate of the direct link. Optimization of the phase shift matrix: Under the condition of a fixed beam matrix W, adjust the phase shift matrix elements of the RIS one by one to enhance the channel gain of the reflection link. By alternately solving the beamforming and phase shift configurations using an alternating optimization algorithm and a scalar replacement strategy, the system can quickly converge to the optimal solution, maximize the system communication rate while satisfying power resource and delay constraints, and reduce computational complexity.

[0050] The following are specific instructions: The invention proposes a beamforming and phase shift optimization method based on a RIS-assisted satellite communication system, which comprises a scene description module, a model building module and a model solving module.

[0051] Scenario description module, which is used to describe the scenario of RIS-assisted satellite communication system, deploy RIS in LEO communication system, cooperate with LEO satellite to complete the transmission of user signals, and reasonably configure beamforming and phase to maximize the combined rate of all user terminals on the ground. Data in LEO can be transmitted to user terminals in two ways: direct link: LEO satellite sends data directly to the terminal user. Reflection link: LEO satellite reflects the signal to the user terminal through RIS.

[0052] 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, so the transmitted signal at LEO can be expressed as , since the signal needs to support multipath transmission, including LEO-RIS-USER link and LEO-USER link, the channel of each user can be divided into two parts: LEO-USER link and LEO-RIS-USER link. Therefore, the channel from LEO to the i-th user can be expressed as , where , , Represents the equivalent baseband channels from LEO to user i, LEO to RIS, and 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: .in 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: in , represents the signal to interference and noise ratio (SINR) of the i-th user.

[0053] Furthermore, 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 as follows: Weighted Total Rate of Users in RIS-Assisted Satellite Communication System :

[0054] 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 .

[0055] The optimal Modeling, that is, the following optimization problem:

[0056] ; ; In the above formula ,in, is the maximum transmit power of LEO. represents the phase shift matrix at RIS, which is a diagonal matrix. ,in is the phase of the mth reflector element on the RIS, where we assume that the phase Can be controlled continuously, namely: .

[0057] Step S3 includes: A low-complexity algorithm is proposed to solve the W-based and The method is divided into three stages: First, 31) Auxiliary variable solution problem: In order to effectively solve the non-convex problem in the joint optimization of LEO satellite and RIS, auxiliary variables are introduced. , used to decouple complex coupling relationships and simplify the optimization process, 32) fixed phase shift matrix In the case of , optimize W to improve the channel gain of the LEO-USER link; 33) 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.

[0058] Since the joint beamforming and phase optimization problem is a very difficult problem. Since the objective function is non-convex, optimizing variables and W are deeply coupled and difficult to handle. The Lagrangian dual transformation is applied to decouple the original optimization problem.

[0059] To deal with the WSR maximization problem The complex "logarithms and ratios" problem involved in is decoupled by introducing the Lagrangian dual transformation.

[0060] S31, by introducing auxiliary variables , the original optimization problem is equivalent to:

[0061]

[0062]

[0063] in , The function is:

[0064] in .

[0065] S31 sub-problem when When fixed, for any ,pass Auxiliary variables can be obtained The optimal solution is , .Will Substitute into the objective function After that, it can be found that the objective function is only related to the variable and Related, auxiliary variables The impact of has been eliminated. Therefore, at this stage, the problem is further simplified to only target and optimization problem, which will be solved in the subsequent stages.

[0066] S32 sub-problem ,when When fixed, the corresponding WSR maximization problem It can be rewritten as the following optimization problem:

[0067]

[0068] in .

[0069] because In is a high-dimensional non-convex function, subproblem is the sum of multiple FP problems, which is difficult to solve directly. To solve this problem, the quadratic transformation method is used to introduce an auxiliary variable ,but Re-expressed as:

[0070]

[0071]

[0072] in .

[0073] By setting , the optimal ξ for a given W is:

[0074] Then, confirm , the problem of optimizing the variable W is reformulated as:

[0075]

[0076] By setting , the optimal W is:

[0077] in is the optimal dual variable corresponding to the constraint condition.

[0078] During the optimization process, the variables and The solution is solved by alternating optimization. First, fix W and directly calculate the optimal ; then fix , update the optimal The whole process requires multiple iterations until the objective function convergence.

[0079] For larger N, the optimization process has higher computational complexity, especially when searching for the optimal This may significantly increase the computational burden when obtaining the optimal W. 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.

[0080] Lemma 1: Let ,in .function ,exist There are:

[0081] Lemma 1 provides an equivalent transformation rule for the objective function. Its core function is to replace the complex nonlinear objective function with an easy-to-handle form, thereby reducing the computational complexity and avoiding the high-cost operations of matrix operations. At the same time, Lemma 1 lays the theoretical foundation for the objective function transformation of the following Lemma 2, ensuring that the subsequent optimization is mathematically reasonable. Generally, in problems involving FP, if the problem is solved by introducing auxiliary variables, the update process of the auxiliary variables is optimized by generating a proxy function. Combined with the Majorization-Minimization (MM) method, by introducing intermediate parameters, the complex nonlinear terms are transformed into a resolvable form, thereby greatly simplifying the solution. On this basis, a new method based on Lemma 1 is introduced. As an equivalent transformation of auxiliary variables. Therefore, by constructing a close relationship with the equivalent transformation through the surrogate function, a new transformation can be derived.

[0082] Lemma 2: Let , , the following questions:

[0083] Can be equivalently converted into:

[0084] Lemma 2 further reconstructs the objective function based on Lemma 1 and uses intermediate variables to linearize or decompose it into a quadratic form, thereby reducing the computational complexity and improving the flexibility of the optimization algorithm.

[0085] Therefore, based on Lemma 2, Substitute the optimal value of ) can be converted to:

[0086] It is worth noting here that It can be set to the optimal value for each w update.

[0087] By using the above formula, we can get The first-order derivative of , and setting it equal to 0, we can get The optimal value of is:

[0088] It can be seen that the denominator is a scalar, so the complex operations caused by matrix inversion are avoided and will not lead to higher computational complexity.

[0089] S33 sub-question 3. Use scalar transformation to obtain the optimal phase shift ,make , then the channel can be converted into:

[0090] definition ; Where 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. can be written as:

[0091] Observation formula , Only with Therefore, we only need to transform this item and then optimize it to get the optimal solution. , using the second transformation we can get:

[0092] in, . Then Taking the first-order partial derivative we get:

[0093] Among them, let it be equal to 0, we have:

[0094] therefore, .Will Bring in Get , we only need to optimize Among them, It can be rewritten as:

[0095]

[0096] Among them, The expansion can be expressed as:

[0097]

[0098] in, and They are expressed as:

[0099]

[0100] Will Bring in You can get:

[0101]

[0102] in, .therefore, It can be rewritten as:

[0103] in:

[0104]

[0105]

[0106] Therefore, optimizing The problem can be formulated as: , st

[0107] In order to effectively solve the optimization problem, a low-complexity phase shift optimization method is proposed to avoid the computational complexity problem that may occur in traditional methods.

[0108] from The objective function in It can be observed that it is about An element in A quadratic function of . It can be expressed as:

[0109] in, , , , Respectively represent matrices No. diagonal elements, vector No. elements, matrix No. OK The elements of the column and OK The elements of the column. C represents Therefore, we can get the RIS reflection that we want to optimize. elements of a scalar quadratic function, and then Taking the derivative we get:

[0110] Then set it equal to 0 and get:

[0111] Since the reflection coefficient of RIS needs to satisfy the constraint condition, an auxiliary vector is introduced. , put it into the above formula, we have:

[0112] Among them, the optimal solution of RIS phase shift is .

[0113] It can be observed that The calculation involves only scalar operations rather than complex matrix operations. This calculation method effectively simplifies the optimization process and significantly reduces the computational complexity compared to traditional matrix operation methods. express No. elements. May be expressed as: .

[0114] The above three sub-problems 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 LEO satellite to user. H2 represents the composite channel from LEO satellite to user through RIS. Initialize the beamforming matrix W and phase shift matrix Θ, and set the total transmit power constraint .

[0115] (b) Lagrange dual transformation and auxiliary variable solution: In order to decouple the complexity of the problem, auxiliary variables are introduced. , which is used to simplify the solution process. These variables are directly related to the user's channel gain and system rate. The original non-convex optimization problem is decomposed into two sub-problems using Lagrange dual transformation. Fix the beamforming matrix W and the phase shift matrix Θ, and calculate the optimal auxiliary variables for each user ,Right now:

[0116] in, is the signal to interference plus noise ratio (SINR) of the ith user. By introducing auxiliary variables, the problem is simplified to solving the optimal values ​​of these variables to maximize the user's communication rate.

[0117] (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). 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:

[0118] (d) Optimization of the phase shift matrix Θ, with fixed 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.

[0119] (e) Convergence condition judgment: if the objective function value after this iteration changes less than the preset threshold, the algorithm converges and outputs the current optimal solution. Otherwise, continue to optimize W, Θ and .

[0120] (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.

[0121] (g) Return the optimal beamforming matrix W, the optimal phase shift matrix Θ and auxiliary variables , and output the maximized weighted total rate.

[0122] like Figure 2 As shown in the figure, the optimization algorithm of the present invention shows 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 through beamforming and phase optimization to achieve the highest achievable total rate and converges quickly in the initial iteration. The results show that direct link and phase optimization are crucial to system performance, and the use of RIS significantly improves communication quality and system capacity. The algorithm has shown excellent performance in improving system communication efficiency and fast convergence, verifying its practical application value in the design of efficient communication systems.

[0123] In another embodiment of the present invention, a computer program product including instructions is provided. When the computer program product is run on a computer, the computer is enabled to execute the LEO satellite and RIS collaborative optimization method in the above embodiments.

[0124] It can be understood that the system, device and storage medium provided in the embodiments of the present invention correspond to the method provided in the present invention, and the explanation of the relevant contents and beneficial effects can refer to the relevant parts of the above methods.

[0125] In the embodiments of the present invention, the entire system can be implemented by software, hardware, firmware or a combination thereof. When implemented by software, it can be in the form of a computer program product. The program product includes a plurality of computer instructions, and when these instructions are loaded and executed on a computer, all or part of the steps and functions in the above technical solution can be executed.

[0126] The computer may be a general-purpose computer, a special-purpose computer, a computer network or other programmable device, all of which can support the optimization calculation of the beamforming matrix and the phase shift matrix. The computer instructions may be stored in a computer-readable storage medium, or transmitted from one storage medium to another storage medium via a computer network. For example, the computer instructions may be transmitted from a website, a computer, a server or a data center to another website, server or computer, and the transmission method may be wired transmission (such as optical fiber, DSL) or wireless transmission (such as infrared, Wi-Fi, microwave, etc.).

[0127] Readable storage media include any storage media accessible by a computer, such as integrated servers, data centers, or magnetic media (such as floppy disks, hard disks, tapes), optical media (such as DVDs), and semiconductor media (such as solid-state drives SSDs).

[0128] It should be noted that in this specification, terms such as "first" and "second" are only used to distinguish different elements or operations, and do not represent the actual order relationship. In addition, the term "include" or "comprise" refers to non-exclusive inclusion, meaning that a process, method, device or system may also include other elements or inherent components that are not explicitly listed.

[0129] The various embodiments of the present invention are described in the same or similar manner, and the same or similar parts between the various embodiments can be described with reference to each other. The focus of each embodiment is to explain the differences between other embodiments. For the part of system implementation, since it is similar to the method implementation part, the description is relatively brief, and the specific implementation can refer to the description of the method part.

[0130] Finally, it should be emphasized that the above embodiments are only used to illustrate the technical solutions of the present invention and do not constitute a limitation of the present invention. Those skilled in the art can modify or replace the above technical solutions without departing from the core idea of ​​the present invention, and these modifications and replacements should also be regarded as within the scope of protection 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. 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 combined rate of all users.

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 IRS; 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 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.

5. The beamforming and phase shift optimization method based on the RIS-assisted satellite communication system according to claim 4 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 , .

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 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 , find 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 .

7. The beamforming and phase shift optimization method based on the RIS-assisted satellite communication system according to claim 6 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 Elements of the column, represents the matrix Q OK 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 .

8. The beamforming and phase shift optimization method based on the RIS-assisted satellite communication system according to claim 7, 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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