Federal learning assisted RIS joint beamforming method based on SCA and ADMM

Abstract

The invention discloses a federal learning assisted RIS joint beamforming method based on SCA and ADMM, and relates to the technical field of mobile communication. The invention provides a joint beamforming algorithm based on continuous convex approximation (SCA) and alternating direction multiplier (ADMM) by using federated learning to assist RIS for communication. The iteration of federated learning is optimized by using an SCA algorithm, so that faster convergence is realized; the ADMM algorithm is used to optimize the base station active beamforming and the RIS passive beamforming, and the energy efficiency and the sum rate of the system are improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of mobile communications, and more specifically, relates to a federated learning-assisted RIS joint beamforming algorithm based on SCA and ADMM. Background Art

[0002] In recent years, with the rapid development of digitalization, more and more high-performance digital devices have been used, and global communication traffic has also been increasing rapidly. This trend means that communication service providers are facing challenges of high throughput and ultra-large-scale access, which requires wireless communication technologies that can efficiently utilize energy and spectrum resources. Reconfigurable intelligent surfaces (RIS) enhance the potential of wireless network capacity and coverage by intelligently reconfiguring the wireless propagation environment, and are therefore considered one of the promising technologies for the 6th generation mobile networks (6G) and have received great attention. The application scenarios of RIS include assisting physical layer security, assisting non-orthogonal multiple access, assisting multiple-input multiple-output communication, etc.

[0003] In addition, in the research on RIS, many works are about beamforming design for RIS to improve system performance. Briefly speaking, beamforming technology is a technology that utilizes spatial diversity. According to the position of the receiving antenna and the direction of arrival of the received wave, it fully utilizes the signals received on each antenna to achieve a more reliable and faster receiving performance. Some, in order to deeply study the relationship between the performance gain of passive beamforming with RIS and the number N of RIS reflection units, ignore the direct link from the base station to the device and only consider the RIS reflection link. Assuming that the channel fading coefficients of the two channels from the base station to RIS and from RIS to the user follow independent and identically distributed Rayleigh fading, it can be obtained that when N is large enough, the received power of the user is proportional to the square of N. Some have studied the RIS-assisted multi-user SISO system, assuming that RIS is deployed near the user cluster, each channel coherence interval is divided into a certain reflection time slot, and an independent random passive beamforming pattern is applied in each time slot. Some have proposed a joint beamforming algorithm for RIS-assisted MIMO systems based on statistical CSI. Under the total power constraint, beamforming is achieved by alternately optimizing the RIS reflection coefficient and the covariance matrix of the transmit symbol vector, so as to maximize the ergodic rate of the system. Some have considered the RIS-assisted single-user large-scale MIMO millimeter-wave downlink communication system. By separately designing passive beamforming and active precoding and using a decoupling strategy to reduce the computational complexity, the achievable spectral efficiency is maximized. Some have used RIS in an air computing system, significantly reducing the communication error.

[0004] Beamforming can also be combined with other optimization methods. A low-complexity framework for channel estimation and passive beamforming in RIS-assisted MIMO systems has been proposed, which improves the rate by optimizing the RIS reflection coefficients and demonstrates excellent performance under imperfect channel state information and fast time-varying channel conditions. An adaptive phase shifter design has been introduced for RIS-assisted millimeter-wave MIMO systems, which improves the positioning accuracy and data rate without the need for active sensors and proves that this method is superior to the random phase design scheme even under low signal-to-noise ratio conditions. A low-complexity cooperative beamforming design has been proposed for multi-RIS-assisted communication systems, which optimizes the sum rate of users by modeling and decoupling complex channel interactions and proves that distributing the reflecting elements in multiple RISs performs better than a single RIS deployment. The joint optimization of power allocation, transmit beamforming, and RIS phase shift has been designed to maximize the secrecy rate in the Internet of Things network, enhancing secure communication in the presence of eavesdroppers through linearization methods and alternating optimization schemes. A low-complexity method for joint positioning and synchronization of millimeter-wave systems using optimized base station precoding and RIS phase configuration has been proposed, which improves the performance through beamforming strategies and robust estimation procedures. A dual-active RIS-assisted radar-communication coexistence system has been proposed, which optimizes the beamforming of the radar and the reflection coefficients of the RIS to maximize the data rate of the communication system and solves the non-convex optimization problem using the penalty dual decomposition algorithm.

[0005] Meanwhile, as a distributed learning technology, federated learning has received attention for its ability to well protect users' privacy and security. During the process of federated learning, when users communicate with the server, only gradient parameters are transmitted, while the original data remains local. Some materials have proposed a method of allocating weight coefficients according to the cosine value of the angle between the global gradient and the local gradient. The smaller the cosine value of the angle, the closer it is to the direction of the local gradient, and a larger weight coefficient can be allocated to accelerate the convergence speed. Someone has proposed an asynchronous joint stochastic gradient descent algorithm and its two variances, which has higher efficiency compared to synchronous algorithms. Some materials have proposed a federated learning method based on adaptive mutual knowledge distillation and dynamic gradient compression technology, significantly reducing the communication cost. Someone has combined federated learning with edge computing technology to update the global AI model on the edge server by aggregating local models trained on edge devices. Some materials have designed a dynamic federated learning weighted average algorithm based on maximum mean discrepancy to aggregate the updated local models with automatically learned weights. Someone has proposed an adaptive federated learning algorithm for the model parameter update rule, improving the test accuracy while reducing the communication overhead. Some materials have proposed the FedNoise algorithm, which uses different learning rates for clients and servers to solve the problem of performance degradation caused by noise interference in federated learning, significantly improving the model convergence and outperforming existing methods on various datasets.

[0006] Regarding the federated learning-assisted RIS communication system, someone has proven that integrating RIS into the FL system for assisted communication can effectively reduce communication errors. Someone has proposed a joint design of beamforming vectors and RIS phase offsets to enhance the federated learning performance in an air computing system, solving the channel condition problem through a low-complexity algorithm that maximizes the device participation under the aggregation error constraint. Some materials have proposed a federated spectrum learning framework that uses RIS and convolutional neural networks to enhance the federated learning performance, solving the challenges in RIS phase offset, user-RIS association, and wireless resource allocation, and proving the improvement in spectrum prediction accuracy and system utility. Some materials have introduced a federated learning framework for channel estimation that uses convolutional neural networks trained on local user data, reducing the communication overhead and proving better performance and lower error compared to centralized learning schemes.

[0007] With the support of RIS and beamforming, federated learning can be carried out in a more secure communication environment, reducing the security risks of data transmission. At the same time, RIS and beamforming can reduce the transmission power requirements, thereby reducing energy consumption and improving the energy efficiency of the communication system. In addition, combined with the real-time update ability of federated learning, RIS and beamforming strategies can be dynamically adjusted to adapt to the changing network environment and user requirements. Although federated learning reduces data transmission, model updates and parameter exchanges still require a certain amount of communication bandwidth, especially in large-scale networks. Summary of the Invention

[0008] The technical problem to be solved by the present invention is to provide a federated learning-assisted RIS joint beamforming algorithm based on SCA and ADMM. By introducing a gradient-based iterative stopping criterion, it can effectively judge whether to stop the iteration according to the current gradient information, achieve faster convergence and more efficient calculation, enhance the traditional SCA algorithm, and at the same time obtain the optimal solutions of the active beamforming vector of the base station and the passive beamforming vector of the RIS through alternating iteration, realizing the optimization of the system energy efficiency and sum rate.

[0009] To solve the above technical problem, the technical solution adopted by the present invention is: a federated learning-assisted RIS joint beamforming algorithm based on SCA and ADMM, which utilizes the characteristic of transmitting gradient information in federated learning communication to enhance the traditional SCA algorithm by introducing a gradient-based iterative stopping criterion; the iterative stopping criterion can effectively judge whether to stop the iteration according to the current gradient information, achieve faster convergence and more efficient calculation; the beamforming algorithm based on the ADMM method obtains the optimal solutions of the active beamforming vector of the base station and the passive beamforming vector of the RIS through alternating iteration, realizing the optimization of the system energy efficiency and sum rate;

[0010] I. Federated Learning Aggregation Algorithm Based on Channel Quality and SCA Iterative Optimization Algorithm

[0011] In the aggregation stage of federated learning, the base station needs to aggregate the gradient information received from each device according to a certain method, and an algorithm that can perform weighted averaging and then aggregation of the gradient information according to the channel quality between the device and the base station can be used; the quality of the channel can be measured by the l2 norm of the channel matrix, and the larger its value indicates the better the channel quality; after calculating the l2 norms of the channel matrices between all devices and the base station, the base station will allocate different weight parameters for gradient aggregation according to its channel quality; users with better channel quality will obtain larger weight coefficients, so that the gradient parameters of users with good channel quality in the system account for a larger proportion of the global model, accelerating the convergence speed of the global model;

[0012] The basic process of the SCA algorithm is to approximate each non-convex part of a non-convex problem as a convex function at a certain point, then solve the approximated convex problem, approximate again at the obtained next point, and so on, until it can converge to a sub-optimal solution; the loss function of federated learning is non-convex. Therefore, a convex surrogate function with quadratic approximation is introduced to update the update formula of the global model parameters, and a precision is set. When the average value of the gradients uploaded by all devices is less than this precision, the iterative process stops;

[0013] II. Base Station and RIS Joint Beamforming Algorithm Based on ADMM

[0014] To handle the complex form in the objective function of the energy efficiency optimization problem, the objective function can be decoupled by the method of Lagrangian dual reconstruction. The objectives to be optimized in the objective function are the active beamforming vector of the base station and the passive beamforming vector of the RIS; after introducing auxiliary variables, there will be four variables in the objective function, and the method of alternating optimization can be used to cyclically optimize and update them; after taking the partial derivatives of the two auxiliary variables and setting them to zero, the optimal solutions of the auxiliary variables can be obtained;

[0015] When solving the active beamforming vector of the base station, the passive beamforming vector of the RIS can be fixed first, and using the above optimal solutions of the auxiliary variables, the optimization problem can be transformed into a quadratic constraint quadratic programming problem, and the optimal solution can be obtained through the ADMM algorithm; after constructing the augmented Lagrangian function, the variables are alternately optimized. Since it is a convex function, the analytical solution can be obtained according to the first-order optimality condition; when solving the passive beamforming vector of the RIS, it is solved after fixing three variables; with the maximization of the system energy efficiency as the optimization objective, the four variables are alternately iterated until the objective function converges.

[0016] Preferably, during the process of federated learning, the user equipment will download the latest global gradient parameters from the server for local training, and then send the local gradient parameters of the trained local model to the server. The server will then aggregate the received local gradient parameters to obtain a new global model; the goal of federated learning is to minimize the global loss function, that is

[0017]

[0018] where w is the vector of gradient parameters, K is the number of training samples, (x k ,y k ) represents the k-th input vector and output vector, and f(w; x k ,y k ) is the loss function related to (x k ,y k );

[0019] According to the gradient descent method, the update formula for the global model is:

[0020]

[0021] where ζ is the learning rate, which is used to control the step size in each iteration, and t represents the current iteration round;

[0022] In the aggregation stage of federated learning, according to the channel quality between the device and the base station, the base station performs weighted averaging and then aggregation on the gradient information received from each device. Define the channel between the k-th device and the base station as H k (Φ), then the larger the value of ||H k (Φ)||2 indicates the better the channel quality; after calculating the l2 norm of the channel matrix between all devices and the base station, the base station will allocate different weight parameters according to its channel quality for gradient aggregation. This process can be expressed as:

[0023]

[0024] where λ k is the weight parameter assigned to the k-th device, and its calculation formula is:

[0025]

[0026] where K is the number of devices, w k is the gradient of the k-th device, λ k is the weight parameter assigned to the k-th device, and H k (Φ) is the channel between the k-th device and the base station;

[0027] Users with better channel quality will get larger weight coefficients, so that the gradient parameters of users with good channel quality in the system account for a larger proportion of the global model, accelerating the convergence speed of the global model.

[0028] Preferably, the RIS-assisted communication model includes a base station and K users and considers downlink data transmission. At this time, the transmission path includes the direct communication link from the user to the base station and the communication link reflected by the RIS; it is defined that the base station is configured with multiple antennas, the number of antennas is N, the user is a single antenna, and the number of reflection elements of the RIS is L. Define the reflection coefficient of the l-th reflection unit of the RIS as l = 1, 2,..., L, then the reflection coefficient diagonal matrix of the RIS is In addition, define the signal transmitted by the base station as x, and use beamforming technology to complete the transmission of data to the user. Then, the received signal of the k-th device can be expressed as:

[0029] y k =(HBD,k +H BR ΦH RD,k )x + n k (5)

[0030] Among them, H BD,k , H BR , H RD,k respectively represent the channel matrices from the base station to the k-th device, from the base station to the RIS, and from the RIS to the k-th device, represents additive white Gaussian noise; in fact, H k (Φ) is H BD,k +H BR ΦH RD,k ;

[0031] In actual communication, in order to make the energy of signal transmission more concentrated, beamforming design is first performed on the signal at the base station; assuming that the original signal component transmitted by the system to the device is s j , then the base station can design the transmitted signal x according to the following rules:

[0032]

[0033] where θ j is the beamforming vector of the base station; therefore, the signal received by the k-th device can be rewritten as:

[0034]

[0035] The above formula can be further decomposed into three terms: desired signal, interference signal, and noise:

[0036]

[0037] where the first term is the received signal expected by the k-th device, the second term is the interference signal from other devices to the k-th device, and the third term is additive noise; then the signal-to-interference-plus-noise ratio of the k-th device can be expressed as:

[0038]

[0039] According to the Shannon formula, the achievable communication rate of all users can be expressed as:

[0040]

[0041] In order to maximize the service quality between users and the transmitter as much as possible, it is necessary to maximize the achievable communication rate of users under the condition of meeting the transmit power budget, forming the following optimization problem:

[0042]

[0043] To analyze the energy efficiency of the system, it is necessary to analyze the power consumption of the system. The total power consumption of the system consists of the transmission power of the base station and the power consumed by each component, and its expression is:

[0044] P total =ξ||θ|| 2 +P B +K·P D +N·P R , (12)

[0045] where ξ is the reciprocal of the transmission power amplifier efficiency, and PB, PD, and PR are the power consumptions of the base station, a device, and a RIS reflection element respectively; then the energy efficiency of the system can be defined as:

[0046]

[0047] The energy efficiency optimization problem of the system can be expressed as:

[0048]

[0049] where the first constraint condition limits the maximum transmission power of the base station to P max , and the second constraint condition constrains the RIS reflection coefficient with the constant modulus condition.

[0050] Preferably, the basic process of the SCA algorithm is to approximate each non-convex part of the non-convex problem as a convex function at a certain point, and then solve the approximated convex problem, approximate again at the obtained next point, and so on, and finally converge to a sub-optimal solution; the convex surrogate function with quadratic approximation introduced into federated learning using the SCA algorithm is:

[0051]

[0052] where is the gradient vector of the objective function at w t and H t is the Hessian matrix of the objective function at w t , then the update formula of the global model parameters can be written as:

[0053]

[0054] After each round of iteration, calculate the average value of the gradients uploaded by all devices:

[0055]

[0056] The stopping criterion for iteration is related to the average gradient. Set the precision ε, and when , the iteration stops.

[0057] Preferably, to handle the complex form in the objective function of the energy efficiency optimization problem, the objective function can be decoupled by the method of Lagrangian dual reconstruction; introducing an auxiliary variable α = [α1, α1,..., α K T , the original problem is equivalently transformed to obtain the following form:

[0058]

[0059] Then introduce an auxiliary variable β = [β1, β2,..., β K T , and using a quadratic transformation, the above problem is converted into the following form:

[0060]

[0061] where the objective function is:

[0062]

[0063] where, α k and β k are auxiliary variables introduced for convenient solution, θ is the active beamforming vector at the base station side, Φ is the passive beamforming vector at the RIS side, is the variance of additive white Gaussian noise, η EE is the energy efficiency, P total is the total power consumption of the system, P max is the maximum transmit power of the base station, L is the number of RIS reflection elements, is the matrix element of the RIS reflection element;

[0064] The alternating optimization method can be used to cyclically optimize and update the four variables; taking the partial derivatives of the auxiliary variables α and β in f1(θ, Φ, α, β) and setting them equal to zero, the optimal solutions α opt and β opt of the auxiliary variables α and β can be obtained, that is:

[0065] At this time, the components of the auxiliary variables α and β can be obtained as:

[0066]

[0067]

[0068] where

[0069] Preferably, when the auxiliary variables α, β and the passive beamforming vector Φ at the RIS side are fixed, the optimal solution θ​​opt ; To simplify the objective function, the following definitions can be made:

[0070]

[0071]

[0072]

[0073] Then the objective function can be rewritten as:

[0074] f1(θ) = -θ H Aθ + 2Re[V H θ]. (27)

[0075] The optimization problem can be rewritten as:

[0076]

[0077] where The above optimization problem is a quadratic constraint quadratic programming problem, and the optimal solution can be obtained through the ADMM algorithm;

[0078] Define the feasible region of the constraint function as Its indicator function is:

[0079]

[0080] where the auxiliary variable Q = θ, so the optimization problem is equivalent to:

[0081]

[0082] Construct the augmented Lagrangian function:

[0083] where ρ > 0 is the penalty factor and ω is the Lagrangian dual variable; alternately optimize the variables Q, θ, ω:

[0084]

[0085]

[0086] ω t+1 = ω t -ρ(Q t+1 -θ t+1 ) (34)

[0087] Since the above Lagrangian function is a convex function, the optimization of θ can obtain an analytical solution according to the first-order optimality condition. Taking the partial derivative of the Lagrangian function with respect to Q can obtain:

[0088]

[0089] Setting the partial derivative equal to 0 gives:

[0090] Q t+1 =(2A + ρI K ) -1 (2V + ω t + ρθ t )(36)

[0091] Next, optimize the variable θ. By taking the partial derivative of the Lagrangian function with respect to θ, we get:

[0092]

[0093] Setting the partial derivative equal to zero gives:

[0094] θ t+1 = Q t+1 - ρ -1 ω t , (38)

[0095] ω t+1 = 2AQ t+1 - 2V (39).

[0096] Preferably, when the auxiliary variables α, β, and the active beamforming vector θ at the base station side are fixed, solve the passive beamforming vector at the RIS side; at this time, the optimization problem can be rewritten as:

[0097]

[0098] Similar to the optimization process of the active beamforming vector θ at the base station side, the optimization problem can be rewritten as:

[0099]

[0100] where the matrices B and u are respectively:

[0101]

[0102]

[0103] At this time, the objective function is a convex function, but the constraint condition is non - convex. Relaxing it to the convex constraint condition can transform the optimization problem into a quadratic - constrained quadratic programming problem, and a sub - optimal solution can be obtained through the ADMM algorithm;

[0104] Define the feasible region of the constraint condition as Then its indicator function is:

[0105]

[0106] where the auxiliary variable \(q = \varPhi\), the optimization problem can be transformed into:

[0107]

[0108] Construct the augmented Lagrangian function:

[0109]

[0110] where \(\delta>0\) is the penalty factor and \(\mu\) is the Lagrangian dual variable. The variables \(q\), \(\varPhi\), and \(\mu\) can be alternately optimized:

[0111]

[0112]

[0113] \(\mu\) t+1 =\(\mu\) t -\(\delta(q\) t+1 -\(\varPhi\) t+1 ), (49)

[0114] The Lagrangian function is a convex function, and the analytical solution of \(\varPhi\) can be obtained according to the first-order optimality condition; taking the partial derivative of the Lagrangian function with respect to \(q\) gives:

[0115]

[0116] Let the partial derivative be equal to zero, and we can get:

[0117] \(q\) t+1 =(2B + \(\delta\)I N ) -1 (2u+\(\mu\) t +\(\delta\varPhi\) t ), (51)

[0118] Next, optimize the variable \(\varPhi\). Taking the partial derivative of the Lagrangian function with respect to \(\varPhi\) gives:

[0119]

[0120] Let the partial derivative be equal to zero and consider the constraint condition, and the RIS passive beamforming vector \(\varPhi\) can be obtained as:

[0121]

[0122] Finally, optimize the Lagrangian dual variable \(\mu\), and its expression can be obtained as:

[0123] \(\mu\) t+1 =2Βq t+1 -2u (54).

[0124] The beneficial effects of adopting the above technical solutions are as follows:

[0125] 1. By leveraging the characteristics of transmitting gradient information in federated learning communication, we enhanced the traditional SCA algorithm by introducing a gradient-based iterative stopping criterion. This criterion can effectively determine whether to stop the iteration based on the current gradient information, achieving faster convergence and more efficient computation.

[0126] 2. The present invention proposes a beamforming algorithm based on the ADMM method, which obtains the optimal solutions of the active beamforming vector of the base station and the passive beamforming vector of the RIS through alternating iterations, achieving the optimization of the system energy efficiency and sum rate. BRIEF DESCRIPTION OF THE DRAWINGS

[0127] Figure 1 is the downlink block diagram of the communication system;

[0128] Figure 2 is the schematic diagram of the federated learning model training process;

[0129] Figure 3 is the optimization iteration flowchart of each variable;

[0130] Figure 4 is the influence of the RIS reflection element on the system sum rate;

[0131] Figure 5 is the influence of the base station transmit power on the system sum rate;

[0132] Figure 6 is the influence of the base station transmit power on the system energy efficiency;

[0133] Figure 7 is the influence of the federated learning iteration number on the system sum rate;

[0134] Figure 8 is the influence of the federated learning iteration number on the energy efficiency. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0135] Next, the technical solutions in the embodiments of the present application will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all of the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present application without creative efforts shall fall within the protection scope of the present application.

[0136] Figure 1 is the downlink block diagram of the communication system, Figure 2 is the schematic diagram of the federated learning model training process, Figure 3It is the optimized iteration flowchart of each variable. The researchers conducted simulation experiments on the effectiveness of the algorithm proposed in the present invention, demonstrating significant improvements in terms of energy efficiency and system sum-rate performance. The specific content is as follows:

[0137] A. Setting of simulation parameters

[0138] To more accurately reflect the signal transmission characteristics in the real environment, the channel used in the simulation is the Rice channel, which is consistent with the two paths from the base station to the device and from the base station reflected by the RIS array to the device in the communication model. At the same time, the Rice channel has the characteristic of resisting multipath fading and is also relatively simple compared to models such as the Rayleigh channel. The signal-to-noise ratio of the simulation is set to 20 dB, the power consumption of both the RIS and the device is 10 dBm, the learning rate of federated learning is 0.05, the total number of users is 40, and the number of base station antennas is 4. The coordinates of the base station are (0, -50 m, 3 m), the coordinates of the RIS are (20 m, 10 m, 5 m), and the central coordinates of the device are (40 m, 0, 0). The number of RIS array reflection elements, the number of federated learning iterations, and the transmit power of the base station are the independent variables of the simulation. In the federated learning model, we used a convolutional neural network, which includes two 5×5 convolutional layers, and 2×2 max-pooling is used in each convolutional layer. Then there is a normalization layer, a fully connected layer, a ReLu activation layer, and a Softmax output layer. We used the cross-entropy function as the loss function and used the system sum-rate and energy efficiency as the evaluation metrics of the model performance. Some of the parameters used in the simulation and their values are shown in Table 1 below.

[0139] Table 1 Simulation parameter settings

[0140] Simulation parameters Numerical value Base station coordinates (0, -50m, 3m) RIS coordinates (20m, 10m, 5m) Device center coordinates (40m,0,0) RIS power consumption 10 dBm Device power consumption 10 dBm Learning rate 0.05 Number of users 40 Number of base station antennas 4

[0141] B. Simulation of RIS reflection elements

[0142] First, we compared the system sum-rate under different numbers of RIS reflection elements. In this part of the simulation, the transmit power of the base station is fixed at 1 w, and the number of federated learning iterations is set to 50. We used the P-BF algorithm for comparison. Since we are comparing the influence of RIS reflection elements, no simulation without RIS was conducted. As expected, from Figure 4It can be intuitively observed that as the number of RIS reflection elements increases, each curve rises, resulting in a higher system sum rate. After introducing federated learning, the system sum rate has a certain degree of improvement, but the effect is not significant. After using the proposed SCA-ADMM algorithm, due to the stopping criterion, the sum rate shows a significant improvement compared with the traditional SCA algorithm. Using the traditional SCA algorithm, the sum rate basically reaches the maximum value after 56 RIS reflection elements. While using the SCA-ADMM algorithm and the P-BF algorithm, when the number of RIS reflection elements reaches 64, the sum rate is still on the rise, indicating that they have not fully converged.

[0143] C. Simulation of Transmit Power

[0144] Secondly, we compared the system sum rate and energy efficiency under different base station transmission power levels. In this part of the simulation, the number of RIS reflection elements was fixed at 64, and the number of iterations of federated learning was set to 50. We used the RCG algorithm for comparison. As Figure 5 shown, under the same conditions, whether using the RIS array to reflect signals and whether using federated learning or not, the proposed SCA-ADMM algorithm is more effective than the traditional SCA algorithm and the RCG algorithm in improving the system sum rate. When using both federated learning and the RIS array, even when the base station transmission power increases to 1w, the system sum rate is still on the rise and has not converged. In contrast, when neither the RIS nor federated learning is used, the growth rate is very slow and has basically converged when the transmission power is 1w. It can also be observed that the impact of the RIS array on the system sum rate is greater than that of federated learning.

[0145] In Figure 6 we compared the system energy efficiency of several beamforming algorithms. The proposed SCA-ADMM algorithm is superior to SCA and other algorithms, but has similar performance to the RCG algorithm. In the absence of federated learning, the energy efficiency curve is similar to the curve using random phase shifts, but much better than the case without the RIS. It can be seen from Figure 6 that regardless of the beamforming algorithm used, when the transmit power increases, the energy efficiency first rises. When the transmit power reaches 1.2w, the energy efficiency begins to decline. This is because when the transmit power is low, the energy efficiency of the system depends on the system sum rate. When the transmit power increases, the power consumption of the system also increases, and the energy efficiency depends on the system power consumption. Therefore, when the transmit power is high, the energy efficiency will decline.

[0146] D. Simulation of the Number of Training Rounds

[0147] Finally, we compared the system sum rate and energy efficiency under different numbers of federated learning iterations. In this part of the simulation, the number of RIS reflection elements was fixed at 64, and the base station transmission power was set to 1 W. We used the P-BF algorithm for comparison. As Figure 7 shown, as the number of federated learning iterations increases, the system sum rate also improves, but when the number of iterations reaches about 40, it has basically converged. In addition, whether there is a RIS array or not, the proposed SCA-ADMM algorithm achieves a higher system sum rate than the traditional SCA algorithm, but its performance is similar to that of the P-BF algorithm. In the absence of a RIS array, the performance improvement of the SCA-ADMM algorithm is small; however, with a RIS array, it can effectively improve the system sum rate performance.

[0148] In Figure 8 , we compared the system energy efficiency using different beamforming algorithms. When there is no RIS for the beamforming algorithm, the energy efficiency does not change much regardless of the number of iteration rounds. All other algorithms can converge within 30 iteration rounds. The proposed SCA-ADMM algorithm is superior to the SCA, P-BF, and random phase shift beamforming algorithms because it can converge faster and achieve a higher energy efficiency under the same number of iteration rounds. Although the SCA algorithm converges faster and has a better energy efficiency performance when the number of iteration rounds is low, after both algorithms converge, its performance is similar to that of the random phase shift algorithm.

[0149] In summary, we utilized federated learning to assist RIS communication. The proposed SCA-ADMM beamforming algorithm can improve the system energy efficiency and sum rate. This algorithm can optimize the federated learning iteration process, as well as the active beamforming of the base station and the passive beamforming of the RIS. The simulation results prove that the proposed algorithm is superior to the classical SCA, random phase shift, and other beamforming algorithms in terms of sum rate and energy efficiency.

[0150] The above is only a preferred specific embodiment of the present invention, but the protection scope of the present invention is not limited thereto. Any person skilled in the art within the technical scope disclosed by the present invention, according to the technical solution and inventive concept of the present invention, makes equivalent substitutions or changes, and all should be covered by the protection scope of the present invention.

Claims

1. A federated learning-assisted RIS joint beamforming method based on SCA and ADMM, characterized in that: Taking advantage of the characteristics of gradient information transmission in federated learning communication, the traditional SCA method is enhanced by introducing a gradient-based iteration stopping criterion; the iteration stopping criterion can effectively determine whether to stop the iteration according to the current gradient information, achieving faster convergence and more efficient calculation; the beamforming method based on the ADMM method obtains the optimal solution of the active beamforming vector of the base station and the passive beamforming vector of the RIS through alternating iterations, achieving the optimization of system energy efficiency and rate; S1, federated learning aggregation method based on channel quality and SCA iterative optimization method; In the aggregation phase of federated learning, the base station needs to aggregate the gradient information received from each device according to a certain method, using a method that can re-aggregate the gradient information by weighted average according to the channel quality between the device and the base station; the quality of the channel is measured by the l2 norm of the channel matrix, and the larger the value, the better the channel quality; after calculating the l2 norm of the channel matrix between all devices and the base station, the base station will assign different weight parameters to aggregate the gradient according to its channel quality; users with better channel quality will receive a larger weight coefficient, so that the gradient parameters of users with good channel quality in the system occupy a larger proportion of the global model, accelerating the convergence of the global model; The basic process of the SCA method is to approximate each non-convex part of the non-convex problem as a convex function at a certain point, then solve the approximated convex problem, approximate it again at the next point, and so on, and finally converge to a suboptimal solution; the loss function of federated learning is non-convex, and a quadratic approximation convex proxy function is introduced to update the update formula of the global model parameters, and set a precision. When the average value of the gradients uploaded by all devices is less than this precision, the iteration process stops; S2, joint beamforming method of base station and RIS based on ADMM; In order to deal with the complex form of the objective function in the energy efficiency optimization problem, the objective function is decoupled by the Lagrangian dual reconstruction method. The targets to be optimized in the objective function are the active beamforming vector of the base station and the passive beamforming vector of the RIS. After the auxiliary variables are introduced, the objective function will have four variables, and the alternating optimization method is used to perform cyclic optimization updates on them. After taking partial derivatives of the two auxiliary variables and setting them to zero, the optimal solution of the auxiliary variables is obtained. When solving the active beamforming vector of the base station, the passive beamforming vector of the RIS is first fixed, and the above-mentioned optimal solution of the auxiliary variables is used to transform the optimization problem into a quadratic constrained quadratic programming problem, and the optimal solution is obtained by the ADMM method; after constructing the augmented Lagrangian function, the variables are alternately optimized. Since it is a convex function, an analytical solution is obtained according to the first-order optimal condition; when solving the passive beamforming vector of the RIS, the three variables are fixed before solving; Taking maximizing the system energy efficiency as the optimization goal, the four variables are iterated alternately until the objective function converges.

2. According to claim 1, the federated learning-assisted RIS joint beamforming method based on SCA and ADMM is characterized in that: In the process of federated learning, the user device will download the latest global gradient parameters from the server for local training, and then send the local gradient parameters of the trained local model to the server. The server then aggregates the received local gradient parameters to obtain a new global model. The goal of federated learning is to minimize the global loss function, that is, Among them, w is the vector of gradient parameters, K is the number of training samples, (x k ,y k ) represents the kth input vector and output vector, f(w; x k ,y k ) is the same as (x k ,y k ) related loss function; According to the gradient descent method, the update formula of the global model is: Among them, ζ is the learning rate, which is used to control the step size in each iteration, and t represents the number of rounds of the current iteration; In the aggregation phase of federated learning, according to the channel quality between the device and the base station, the base station re-aggregates the gradient information received from each device by weighted average, and defines the channel between the kth device and the base station as H k (Φ), then ||H k The larger the value of (Φ)||2, the better the channel quality. After calculating the l2 norm of the channel matrix between all devices and the base station, the base station will assign different weight parameters to aggregate the gradient according to its channel quality, which is expressed as: where λ k The weight parameter assigned to the kth device is calculated as follows: Where K is the number of devices, w k is the gradient of the kth device, λ k is the weight parameter assigned to the kth device, H k (Φ) is the channel between the kth device and the base station; Users with better channel quality will get larger weight coefficients, so that the gradient parameters of users with good channel quality in the system occupy a larger proportion of the global model, accelerating the convergence of the global model.

3. The federated learning-assisted RIS joint beamforming method based on SCA and ADMM according to claim 2 is characterized in that: The RIS-assisted communication model includes a base station and K users and considers downlink data transmission. At this time, the transmission path includes the direct communication link from the user to the base station and the communication link reflected by the RIS. The base station is defined as having multiple antennas, with the number of antennas being N, the user as a single antenna, the number of reflection elements of the RIS being L, and the reflection coefficient of the lth reflection unit of the RIS being defined as Then the reflection coefficient diagonal matrix of RIS is In addition, the signal transmitted by the base station is defined as x, and beamforming technology is used to complete the transmission of data to the user. Then, the received signal of the kth device is expressed as: y k =(H BD,k +H BR ΦH RD,k )x+n k (5) Among them, H BD,k , H BR , H RD,k They represent the channel matrices from the base station to the kth device, the base station to the RIS, and the RIS to the kth device, respectively. k ~CN(0,σ k 2 ) represents additive Gaussian white noise; H k (Φ) is H BD,k +H BR ΦH RD,k ; In actual communication, in order to make the energy of signal transmission more concentrated, the signal will be beamformed at the base station first; the original signal component transmitted by the system to the device is s j , then the base station designs the transmitted signal x according to the following rules: where θ j is the beamforming vector of the base station; therefore, the signal received by the kth device is rewritten as: The above formula is further decomposed into three terms: desired signal, interference signal and noise: The first item is the expected received signal of the kth device, the second item is the interference signal of other devices to the kth device, and the third item is the additive noise; then the signal-to-interference-to-noise ratio of the kth device is expressed as: According to Shannon's formula, the achievable communication rate of all users is expressed as: In order to improve the service quality between users and transmitters, it is necessary to maximize the user's achievable communication rate while meeting the transmission power budget, forming the following optimization problem: In order to analyze the energy efficiency of the system, it is necessary to analyze the power consumption of the system. The total power consumption of the system consists of the transmission power of the base station and the power consumed by each component, and its expression is: P total =ξ||θ|| 2 +P B +K·P D +N·P R , (12) Where ξ is the inverse of the transmit power amplifier efficiency, PB, PD, and PR are the power consumption of the base station, a device, and a RIS reflector element respectively; then the energy efficiency of the system is defined as: The energy efficiency optimization problem of the system is expressed as: The first constraint limits the maximum transmit power of the base station to P max , the second constraint condition constrains the RIS reflection coefficient using a constant modulus condition.

4. The federated learning-assisted RIS joint beamforming method based on SCA and ADMM according to claim 3 is characterized in that: The basic process of the SCA method is to approximate each non-convex part of the non-convex problem as a convex function at a certain point, then solve the approximated convex problem, approximate it again at the next point obtained, and so on, and finally converge to a suboptimal solution; the convex proxy function introduced by the SCA method for federated learning is: in is the objective function in w t The gradient vector at t is the objective function in w t The Hessian matrix at , then the update formula of the global model parameters is written as: After each iteration, the average value of the gradients uploaded by all devices is calculated: The stopping criterion of the iteration is related to the average gradient. The accuracy is set to ε. When , the iteration stops.

5. The federated learning-assisted RIS joint beamforming method based on SCA and ADMM according to claim 4 is characterized in that: In order to deal with the complex form of the objective function in the energy efficiency optimization problem, the objective function is decoupled by the Lagrangian dual reconstruction method; the auxiliary variable α=[α1,α1,...,α K ] T , the original problem is equivalent to the following form: Then introduce auxiliary variables β=[β1,β2,...,β K ] T , using the secondary transformation, the above problem is converted into the following form: The objective function is: Among them, α k and β k Auxiliary variables are introduced to facilitate the solution. θ is the active beamforming vector at the base station, and Φ is the passive beamforming vector at the RIS. is the variance of additive white Gaussian noise, η EE is the energy efficiency, P total is the total power consumption of the system, P max is the maximum transmission power of the base station, L is the number of RIS reflection elements, is the matrix element of the RIS reflection element; Use the alternating optimization method to perform cyclic optimization and update of the four variables; calculate the partial derivatives of the auxiliary variables α and β in f1(θ, Φ, α, β) and set them equal to zero to obtain the optimal solution α of the auxiliary variables α and β opt and β opt ,Right now: At this time, the components of auxiliary variables α and β are: in 6. The federated learning-assisted RIS joint beamforming method based on SCA and ADMM according to claim 5 is characterized in that: When the auxiliary variables α, β and the passive beamforming vector Φ at the RIS are fixed, the optimal solution θ of the active beamforming vector θ at the base station is solved opt ; Define as follows: Then the objective function is rewritten as: f1(θ)=-θ H Aθ+2Re[V H [i]. (27) The optimization problem is rewritten as: stθ H Dθ≤P max . in The optimization problem is a quadratic constrained quadratic programming problem, and the optimal solution is obtained by the ADMM method; The feasible domain of the constraint function is defined as Its indicator function is: Where the auxiliary variable Q = θ, so the optimization problem is equivalent to: stQ=θ Construct the augmented Lagrangian function: Where ρ>0 is the penalty factor and ω is the Lagrangian dual variable; Alternately optimize the variables Q, θ, and ω: oh t+1 =ω t -p(Q t+1 -θ t+1 ) (34) Since the above Lagrangian function is a convex function, the optimization of θ is solved analytically according to the first-order optimal condition. By taking the partial derivative of the Lagrangian function with respect to Q, we get: Setting the partial derivative equal to 0 yields: Q t+1 =(2A+ρI K ) -1 (2V+ω t +ρθ t ) (36) Then optimize the variable θ and obtain the partial derivative of θ through the Lagrangian function: Setting the partial derivative equal to zero gives: i t+1 =Q t+1 -r -1 oh t , (38) ω t+1 =2AQ t+1 -2V (39).

7. The federated learning-assisted RIS joint beamforming method based on SCA and ADMM according to claim 6 is characterized in that: When the auxiliary variables α, β and the active beamforming vector θ at the base station are fixed, the passive beamforming vector at the RIS is solved; the optimization problem is rewritten as: Similar to the optimization process of the active beamforming vector θ at the base station, the optimization problem is rewritten as: The matrices B and u are: At this time, the objective function is convex, but the constraints are not convex, so relax it to The convex constraint condition can transform the optimization problem into a quadratic constrained quadratic programming problem, and the suboptimal solution can be obtained by the ADMM method. The feasible domain of the constraints is defined as Then its indicator function is: Where the auxiliary variable q = Φ, the optimization problem is transformed into: stq=Φ Construct a Lagrangian augmented function: Where δ>0 is the penalty factor, μ is the Lagrangian dual variable, and the variables q, Φ, and μ are optimized alternately: m t+1 =μ t -δ(q t+1 -F t+1 ), (49) The Lagrangian function is a convex function. According to the first-order optimal condition, the analytical solution of Φ is obtained. By taking the partial derivative of the Lagrangian function with respect to q, we get: Setting the partial derivative equal to zero gives: q t+1 =(2B+δI N ) -1 (2u+μ t +δΦ t ) (51) Then optimize the variable Φ and obtain the partial derivative of Φ through the Lagrangian function: Let the partial derivative equal to zero and consider the constraints, and the RIS passive beamforming vector Φ is obtained as: Finally, the Lagrangian dual variable μ is optimized and its expression is obtained as follows: m t+1 =2Bq t+1 -2u (54).

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