A wireless federated learning method based on next-generation multiple access technology

Abstract

The application discloses a wireless federated learning method based on a next-generation multiple access technology, integrates centralized learning and federated learning, so that devices with weak computing power can also participate in the training of a global model, and an intelligent metasurface capable of simultaneously reflecting and refracting is deployed to dynamically change a channel environment, so that the system can meet different task requirements of heterogeneous users, supports parallel transmission of data of communication-centered CL users and calculation-centered FL users on the same time-frequency resource, avoids waste of data resources, thereby enriching data acquisition of a base station and helping to improve global model accuracy. Meanwhile, the method also fuses a user power distribution and a STAR-RIS configuration joint optimization strategy to reduce total uplink transmission power consumption of the system and prolong the life cycle of the intelligent Internet of Things network.

Description

Technical Field

[0001] This invention relates to the field of federated learning technology, and in particular to a wireless federated learning method (Semi-Federated Learning, SemiFL) based on Next-Generation Multiple Access (NGMA) technology. Background Technology

[0002] With the rapid development and integration of machine learning (ML) and wireless communication, massive distributed devices can generate large amounts of real-time information and multimodal data. In large-scale wireless IoT scenarios, scarce spectrum resources lead to communication bottlenecks, and the vast number of devices with varying computing capabilities pose serious challenges to smart IoT relying on traditional ML.

[0003] While Federated Learning (FL) can significantly reduce the communication overhead and training time of traditional Centralized Learning (CL), its distributed nature can compromise model training accuracy. Furthermore, a key difference between FL and CL is that the powerful computing resources of base stations are not readily used for model training in FL; user data is stored locally, and all nodes perform model training on their local devices. However, this is unacceptable in large-scale wireless IoT scenarios. Due to the heterogeneous computing capabilities of devices, less powerful devices struggle to collaborate with more powerful devices to train shared models. These limitations of the IoT render existing machine learning paradigms (such as CL and FL) inefficient when directly combined with traditional communication technologies. Therefore, there is an urgent need to develop novel learning-oriented network technologies for efficient model training in wireless IoT.

[0004] At the same time, it's important to recognize that communication and computation within the system require considerable energy, and IoT devices with limited battery capacity struggle to support the long-term operation of distributed systems. Furthermore, some devices may be deployed in inaccessible or hazardous locations, making periodic charging extremely difficult. Therefore, designing an efficient power control strategy is crucial for extending the lifespan of wireless IoT networks. Summary of the Invention

[0005] This invention addresses the performance degradation at the network edge caused by heterogeneous device computing capabilities and resource constraints in existing smart IoT scenarios. It proposes a wireless federated learning method based on next-generation multiple access technology. By integrating centralized learning (CL) and federated learning (FL), it enables devices with weaker computing capabilities to participate in the training of the global model. Furthermore, it deploys a Simultaneously Transmitting And Reflecting Reconfigurable Intelligent Surface (STAR-RIS) to dynamically alter the channel environment, allowing the system to meet the diverse task requirements of heterogeneous users. This supports parallel data transmission on the same time-frequency resources for communication-centric CL users and computation-centric FL users, avoiding data resource waste and enriching the base station's data acquisition, thus improving the accuracy of the global model. Simultaneously, the proposed method integrates a joint optimization strategy of user power allocation and STAR-RIS configuration to reduce the total uplink transmission power consumption and extend the lifecycle of the smart IoT network.

[0006] To achieve the above objectives, the present invention provides the following technical solution:

[0007] This invention provides a wireless federation learning method based on next-generation multiple access technology, comprising the following steps:

[0008] S1: The user sends a status information report to the base station; the status information includes instantaneous channel status information and available CPU frequency status information;

[0009] S2: After receiving the status information report, the base station divides the user into two categories based on the computing power of the user's local device: CL users who are communication-centric and FL users who are computing-centric. After the classification is completed, the base station broadcasts the classification results to all users.

[0010] S3: Each FL user trains a local model on the local dataset based on the global model w obtained in the previous round, and calculates the local gradient g. k Each CL user prepares the local dataset to be uploaded to the base station.

[0011] S4: Encode the local dataset of the CL user into communication symbols {s n}, process the gradient of the local model trained by the FL user into the computation symbol {s k All users use NGMA technology combined with smart metasurfaces that can simultaneously reflect and refract to send their information-bearing symbols to the base station;

[0012] S5: The base station receives superimposed signals from two types of users. First, it decodes the local dataset from the CL user to perform centralized training and obtain the average gradient. Then, it aggregates the model gradients from the FL user and finally uses the obtained gradients to perform global model aggregation.

[0013] S6: After each round of communication, the base station will update the global model. Broadcast to all FL users so that they can perform gradient calculations in the next round;

[0014] S7: Repeat the above steps until convergence or the maximum number of communication rounds is reached.

[0015] Furthermore, the NGMA technology described in step S4 provides services to all users in a non-orthogonal manner within the same frequency band, enabling all users to communicate in parallel on the same time-frequency resources.

[0016] Furthermore, the smart metasurface deployed in step S4, capable of both reflecting and refracting, reshapes the wireless propagation environment by modifying the amplitude and phase of the incident signal, thereby adjusting the channel gain for different users.

[0017] Furthermore, the specific operation process of the base station in step S5 is as follows:

[0018] S51: The base station uses serial interference cancellation technology to detect the communication output of each CL user. n}, decode and further generate training samples for centralized learning. Then, the model is trained using gradient descent to obtain the average gradient of CL users. for:

[0019]

[0020] Where N is the number of CL users, This represents the gradient calculated by the base station for the nth CL user. It is used to train model parameters The objective function, It is the model for the i-th sample of the n-th CL user. The loss function;

[0021] S52: Assuming all symbols from the CL user were successfully decoded in S51, the base station subtracts the CL user's signal from the received superimposed signal to obtain a residual signal containing the FL user's signal. The residual signal of the FL user signal is averaged and calculated from the symbol {s} k The local gradient of the FL user is recovered in} kFinally, the base station obtains the average gradient estimate of FL users as follows:

[0022]

[0023] Where K is the number of FL users. σ represents the noise vector at the base station. 2 Noise power;

[0024] S53: Base station collects gradients Then, the global gradient is updated as follows:

[0025]

[0026] Then through Perform a global model update, where λ > 0 is the learning rate.

[0027] Furthermore, before each round of communication, with the goal of minimizing the total transmit power consumption of this round, the user transmit power allocation and STAR-RIS configuration are jointly optimized. The optimization problem and constraints are as follows:

[0028]

[0029]

[0030]

[0031] MSE({p k},{Θ k})≤E0,

[0032]

[0033] in Represents the set of all users. Represents the CL user set, Let p represent the set of FL users. u Θ represents the transmit power of the u-th user. u This represents the coefficient matrix of STAR-RIS for user u. For the joint channel of base station-STAR-RIS-user, For the feasible set of refractive and reflectance coefficients of STAR-RIS, and Let R represent the amplitude and phase shift of the m-th element in the χ∈{R,T} mode, respectively. min To meet the minimum data transmission rate required by CL users for QoS, E0 is the maximum computational distortion that FL users can tolerate, and R... n ({p u},{Θu}) represents the data transmission rate of CL user n, MSE({p k},{Θ k}) indicates the computational distortion of FL user k.

[0034] Furthermore, the optimization problem is decoupled into two sub-problems, namely, the user's transmit power {p}. u} and the user's STAR-RIS configuration {Θ u Alternate optimization is performed.

[0035] Furthermore, in the alternating optimization method, for a fixed {Θ} u In the case of {p}, u Subproblem, using the uplink communication rate expression for CL users. The computational distortion expression for FL users Rewrite the constraints to express an equivalent subproblem of user power allocation;

[0036] For the transformed expression, first fix the power allocation {p} for FL users. k The optimal power allocation for CL users is derived using mathematical induction. Closed expression:

[0037]

[0038] Then fix the power allocation for CL users {p n},make Reorganize the optimization problem and use the Lagrange duality method to find the optimal power allocation for FL users. Closed expression:

[0039]

[0040] in and These are the optimal dual variables related to QoS and MSE constraints, respectively.

[0041] Furthermore, in the alternating optimization method, for a fixed {p} u In the case of}, {Θ u The subproblem is a feasibility verification problem, represented as:

[0042] find{Θ u}

[0043]

[0044]

[0045] MSE({p k},{Θ k})≤E0,

[0046]

[0047] Introduction Rewrite the joint uplink channel coefficients to further represent the subproblem, where... Diag(Q u )=β u And there exists a non-convex rank-1 constraint rank(Q) u =1, and the transformed expression still has a binary variable;

[0048] For nonconvex rank-one constraints and binary variables, introduce and They are transformed into penalty terms in the objective function. Since the penalty terms are non-convex, a first-order Taylor expansion is then used in the l-th iteration to obtain the convex upper bound of the penalty terms:

[0049]

[0050]

[0051] Introducing it into the objective function as a penalty function yields a convex semidefinite programming problem.

[0052] Furthermore, the solution method for convex semidefinite programming problems is as follows: continuously update the penalty factors η1 and η2 of the penalty term, and then use the iterative method to solve the semidefinite programming problem until the penalty term satisfies the predefined maximum violation amount or the outer iteration reaches the predefined maximum number of iterations.

[0053] Furthermore, the method for alternately optimizing the aforementioned user power allocation and STAR-RIS configuration sub-problems specifically involves initializing {p u [0]},{Q u [0]},{β u [0]} and preset precision ∈3; set the current iteration index l3=0, given {Q u [l3]} and {β u [l3]}, calculate {p} using the closed-form expression for optimal user power allocation. u [l3+1]}, followed by {p u [l3+1]}, update {Q} using a penalty-based continuous convex approximation method. u [l3+1]} and {β u [l3+1]}, update l3=l3+1, repeat the above process until the value of the objective function is reduced to the preset precision or the preset maximum number of iterations L3 has been reached.

[0054] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0055] This invention proposes a wireless federated learning method based on next-generation multiple access technology. By integrating centralized learning and federated learning, it enables devices with weaker computing power to participate in the training of the global model. During uplink transmission, it utilizes a smart metasurface that can simultaneously reflect and refract to flexibly adjust the user's channel conditions and dynamically change the channel environment. This allows the system to meet the different task requirements of heterogeneous users and supports parallel data transmission on the same time-frequency resources for CL users with weak local computing power (communication-centric) and FL users with strong local computing power (computation-centric). This avoids the waste of data resources, enriches the data acquisition of the base station, and helps improve the accuracy of the global model.

[0056] In large-scale wireless IoT scenarios, underlying devices may face the dilemma of limited battery capacity and inconvenience in periodic charging, which will seriously affect the life cycle of the entire system. To address this issue, this invention aims to minimize user transmit power consumption and constructs a hybrid integer nonlinear programming problem that jointly optimizes power allocation and STAR-RIS configuration. The proposed nonconvex optimization problem can be decoupled into two subproblems. For the user power allocation subproblem, a closed-form expression for optimal power allocation can be derived using mathematical induction and Lagrange duality. For the STAR-RIS configuration subproblem, the original feasibility verification problem can be transformed into a convex semidefinite programming problem using the penalty function method and continuous convex approximation method, which can then be solved using CVX tools. In summary, the method proposed in this invention, which integrates user power allocation and STAR-RIS configuration joint optimization strategies to reduce the total uplink transmission power consumption of the system, extends the life cycle of the intelligent IoT network. Attached Figure Description

[0057] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments recorded in this invention. For those skilled in the art, other drawings can be obtained based on these drawings.

[0058] Figure 1 A flowchart of a wireless federation learning method based on next-generation multiple access technology provided in an embodiment of the present invention.

[0059] Figure 2 This is an architecture diagram of a wireless federated learning method based on next-generation multiple access technology provided in an embodiment of the present invention.

[0060] Figure 3 This is an application structure diagram of the wireless federated learning method based on next-generation multiple access technology provided in an embodiment of the present invention.

[0061] Figure 4 This is a schematic diagram of the STAR-RIS-assisted NGMA technology provided in an embodiment of the present invention. Detailed Implementation

[0062] This invention proposes a wireless federated learning method (SemiFL) based on next-generation multiple access technology. By integrating centralized learning and federated learning, it enables devices with lower computing power in large-scale wireless IoT scenarios to participate in the training of the global model. During uplink transmission, by utilizing STAR-RIS to flexibly adjust the user's channel environment, it allows CL users with weaker computing power and FL users with stronger computing power to communicate in parallel on shared time-frequency resources. Then, this invention investigates how to minimize the total power consumption of user transmissions, constructing a mixed-integer nonlinear programming problem that jointly optimizes user power allocation and STAR-RIS configuration, using an alternating optimization method to obtain the optimal suboptimal solution. Specifically, for the user power allocation subproblem, mathematical induction and Lagrange duality are used to directly obtain the closed-form expression for the optimal power; for the STAR-RIS configuration subproblem, the feasibility verification problem needs to be transformed into a convex semidefinite programming problem using the penalty function method and continuous convex approximation method.

[0063] To better understand this technical solution, the method of the present invention will be described in detail below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0064] Please see Figure 1 and Figure 2 This invention provides a wireless federated learning method based on next-generation multiple access technology, enabling all users to participate in global model training and allowing all users to transmit data in parallel on shared time-frequency resources. The method includes the following steps:

[0065] S1: Before each round of communication begins, all local users estimate their instantaneous channel state information (CSI) and available CPU frequency, and then report the state information to the base station.

[0066] S2: After receiving the status report, the base station divides the user into two categories based on the computing power of the user's local device: CL users who are communication-centric and FL users who are computing-centric. After the classification is completed, the base station needs to broadcast the classification results to all users.

[0067] Consider a STAR-RIS assisted wireless network that supports collaborative learning among heterogeneous users. See [link to relevant documentation]. Figure 3 Based on the differences in computing power of users' local devices, the entire heterogeneous user set is... Users are divided into CL users (with weaker computing power and primarily focused on communication) and FL users (with stronger computing power and primarily focused on computing), denoted as . and The STAR-RIS system has M passive reflective / refractive elements. Each element relays (refracts or reflects) the incident signal to the desired direction. To avoid energy leakage and facilitate synchronous communication for all users, STAR-RIS relies on a mode switching protocol, selecting a subset of elements to operate in total refraction mode (T mode) and the remaining elements in total reflection mode (R mode). Let... Let x represent the reflection (χ = R) and refraction (χ = T) vectors, where and Let x and y represent the amplitude and phase shift of the m-th element in the χ∈{R,T} mode, respectively. Since each element can only operate in one mode within a specific time slot, the constraint regarding mode switching is:

[0068] The channel gain of a wireless link can be obtained by multiplying the path loss by the small-scale fading. Specifically, the link distance from STAR-RIS to the base station and the user is expressed as... Where u = 0 represents a base station. Representing users. Large-scale fading is caused by... Give, The path loss is defined as the reference distance of 1m, where α≥2 is the path loss exponent. For small-scale fading, this invention assumes that the channel between the user and base station follows Rayleigh fading due to congestion and widespread scattering; since the STAR-RIS is deployed at a relatively high location, it can be assumed that all links associated with RIS follow Ricean fading. Therefore, this invention can express the channel coefficients of all links associated with RIS:

[0069]

[0070] Where κ is the Rice factor, It is a deterministic line-of-sight channel component. Let be the Rayleigh fading channel component. STAR-RIS divides the effective coverage area of ​​the base station into refraction space and reflection space. In a system with STAR-RIS deployed, the joint channel coefficients of the uplink from the u-th user to the base station are:

[0071]

[0072] in This represents the direct link from the u-th user to the base station. The dual-fading reflection / refraction link provided for STAR-RIS. Specifically, if the u-th user is located in the reflection space, then Θ u =diag(q) R If the u-th user is located in the refracted space, then Θ u =diag(q) T This invention assumes that instantaneous channel state information for all channels is available at the base station.

[0073] S3: Each FL user calculates their local gradient g based on the model w obtained in the previous round. k Each CL user needs to prepare a local dataset to upload to the base station.

[0074] S4: Encode the local dataset of the CL user into communication symbols {s n}, process the gradient of the local model trained by the FL user into the computation symbol {s k All users use NGMA technology to send their information bearer symbols to the base station;

[0075] Please see Figure 4 Utilizing the superposition characteristics of signals in wireless channels, this invention designs an NGMA technology that integrates NOMA and AirComp technologies. By using a STAR-RIS-assisted multiple access channel, it provides wireless access services to both CL and FL users simultaneously, enabling the uplink communication of the CL user's original dataset and the over-the-air computation of the FL user's model parameters (such as gradient information) to be multiplexed in the same frequency band.

[0076] In each round of communication, the CL user and the FL user first transfer their local dataset {d} n} and gradient {g k} are respectively mapped to communication symbols {s n} and computation symbol {s k}. NGMA technology provides services to all users in a non-orthogonal manner within the same frequency band, enabling concurrent uplink communication. The communication symbol {s} n Transmitted via power domain NOMA technology, the symbol {s} is calculated. k Transmitted via AirComp technology. Therefore, the superimposed signal received by the base station is:

[0077]

[0078] Where p n (p k Let be the transmit power of the nth (k)th user. This is additive white Gaussian noise (AWGN) at the base station. This invention assumes that all symbols {s}u}={s n}∪{s k} Statistically independent and having zero mean and standardized variance, i.e. and

[0079] With the help of STAR-RIS, parallel communication between the two user groups can be guaranteed even if some direct links between the base station and the user are blocked. CL users and FL users have different communication goals and performance metrics. For example, CL users, who are communication-centric, expect their local datasets sent to the base station to be perfectly decoded by the base station while maximizing data transmission rate; while FL users, who are computation-centric, expect their local model parameters sent to the base station to be carefully aggregated by the base station while minimizing computational distortion (MSE). Considering the multiple objectives involved in NGMA, this invention aims to improve the throughput of CL users by suppressing interference, while simultaneously utilizing channel superposition characteristics to perform weighted calculations of FL user model parameters. Therefore, a cooperative transmission mechanism with efficient interference management capabilities needs to be designed within this joint communication and learning framework.

[0080] Based on different path losses, heterogeneous users are divided into strong and weak categories. By using Successive Interference Cancellation (SIC) at the base station to separate the superimposed signals, the signal from the strong user can be perfectly decoded. Then, the strong signal is remodulated and subtracted from the received composite signal y to obtain the signal from the weak user. This operation leaves a weak signal for over-the-air collaborative computing. To achieve the above process, this invention needs to use STAR-RIS to modify the amplitude and phase of the incident signal to reshape the wireless propagation environment, thereby adjusting the channel gain of the two groups of users in the following order:

[0081]

[0082] Specifically, by using STAR-RIS to adjust the channel coefficients, all CL users are assigned as strong users for message decoding, and all FL users are assigned as weak users for model aggregation. Based on the superimposed signals and decoding order, the uplink communication rate of the nth CL user is:

[0083]

[0084] Where B is the system's available bandwidth.

[0085] Communication symbols sent by CL user {s n The signal can be decoded and remodulated at the base station, and then subtracted from the superimposed signal y received from the base station to obtain a residual signal containing gradient information of the FL user model. For the aggregation operation of the FL model, the linear computation output estimated at the base station is:

[0086]

[0087] Its computational distortion can be quantified by mean squared error (MSE):

[0088]

[0089] S5: The base station receives superimposed signals from two groups of users. First, it decodes the local dataset from the CL user to perform centralized training and obtain the average gradient. Then, it aggregates the model gradients from the FL user and finally uses the obtained gradients to perform global model aggregation.

[0090] For details, please refer to Figure 4 The base station first uses SIC to detect the communication output {s} of each CL user. n}, decode and further generate training samples for CL. Then, the model is trained using gradient descent to obtain the average gradient of CL users. for:

[0091]

[0092] Where N is the number of CL users, This represents the gradient calculated by the base station for the nth CL user. It is used to train model parameters The objective function, It is the model for the i-th sample of the n-th CL user. The loss function.

[0093] Next, the base station subtracts the decoded CL user information symbols from the received superimposed signal to obtain a residual signal containing FL user model information. Perform an average operation on it and calculate the symbol {s} k The local gradient of the FL user is recovered in} k The final average gradient estimate of FL users obtained by the base station is as follows:

[0094]

[0095] Where K is the number of FL users. σ represents the noise vector at the base station. 2 This represents noise power.

[0096] Finally, the base station collects the gradients. Then, the global gradient is updated as follows:

[0097]

[0098] and through Perform a global model update, where λ > 0 is the learning rate.

[0099] S6: After each round of communication, the base station will update the global model. Broadcast to all FL users so that they can perform gradient calculations in the next round;

[0100] S7: Repeat the above steps until convergence or the maximum number of communication rounds is reached.

[0101] The wireless federated learning method based on NGMA technology proposed in this invention also considers reducing the total uplink power consumption while meeting the computational distortion tolerance of FL users and the data transmission rate requirements of CL users. Specifically, before each round of communication, an optimization problem and constraints are constructed with the goal of minimizing the total transmission power consumption of this round, and the user transmission power allocation and STAR-RIS configuration are jointly optimized through alternating optimization methods.

[0102] The objective of this invention is to minimize the total transmit power consumption in each communication round by jointly optimizing the uplink power allocation for all users and the STAR-RIS configuration. Considering the QoS requirements of CL users and the computational distortion tolerance of FL users, the optimization problem can be formulated as follows:

[0103]

[0104]

[0105]

[0106] MSE({p k},{Θ k})≤E0,

[0107]

[0108] in R is the feasible set of refractive and reflectance coefficients of STAR-RIS. min Minimum data transfer rate to meet the needs of CL users. Constraints This indicates the decoding order that ensures successful separation of communication and computation symbols. (Constraint) This refers to the QoS requirements of CL users. The constraint MSE({p k},{Θ k The condition})≤E0 guarantees that the computational distortion of FL users does not exceed E0<1 / K.

[0109] Due to the non-convexity of the constraints, directly solving the constructed optimization problem faces the following difficulties: First, the optimization of the STAR-RIS configuration is more complex than that of the traditional RIS with only reflection coefficients. Second, discrete variables... The coexistence of the variable {p} with other continuous variables makes the optimization problem a mixed-integer programming problem. It is difficult to find highly coupled variables {p} within polynomial time complexity. u} and {Θ u The optimal solution to the problem is found in the following paper. To effectively solve the proposed problem, this invention decouples it into two sub-problems: a power allocation sub-problem and a STAR-RIS configuration sub-problem, and performs alternating optimization on the two sub-problems.

[0110] Given a STAR-RIS configuration, by rewriting the relevant constraints using the expression for the uplink communication rate of CL users and the expression for the distortion MSE of FL users, the power allocation subproblem in the previous optimization problem can be equivalently expressed as:

[0111]

[0112]

[0113]

[0114] in This is a constant. This invention uses analytical structures and the Lagrange duality method to derive the optimal solution to this problem. The final optimal transmit power for CL and FL users is obtained. and The closed expressions are as follows:

[0115]

[0116]

[0117] in and These are the optimal dual variables related to QoS and MSE constraints, respectively.

[0118] Regarding the optimal transmission power and The specific proof process is as follows:

[0119] Transmit power {p u The solution to} is provided by CL user {p n} and FL users {p k It consists of two parts;

[0120] First, given {p k Then the power allocator subproblem degenerates into:

[0121]

[0122]

[0123] Based on the analytical structure of this problem, it can be proved by contradiction. It is an effective constraint at the optimal solution that achieves the minimum QoS requirement. Therefore, given {p k The optimal transmit power for the Nth CL user can be written as:

[0124]

[0125] The optimal transmit power for the (N-1)th CL user can be written as:

[0126]

[0127] Where (e) can be achieved by... Substitute the expression The expression is derived using some simple algebraic operations. Similarly, for the (N-2)th CL user, the optimal transmit power is:

[0128]

[0129] In summary, by using induction, we can obtain The closed-form solution.

[0130] Next, for a given {p n},make The power distribution problem can be rearranged as follows:

[0131]

[0132]

[0133]

[0134] in

[0135] Let τ1≥0 and τ2≥0 denote the Lagrange multipliers, then the Lagrange function of the transformed subproblem is:

[0136]

[0137] Its dual function is:

[0138]

[0139] Therefore, the dual problem of the transformed subproblem is:

[0140]

[0141] Given dual variables τ1 and τ2, find the solution that satisfies The extreme points of the dual function can be directly obtained by finding the optimal solution of the dual function. Substituting this optimal solution into the expression for the dual function yields the dual function. For the proposed dual problem, the optimal Lagrange multiplier can be found by applying the subgradient descent method. and Right now:

[0142]

[0143]

[0144] Where l is the index of the iteration number, This is the step size, which is a constant. (The rest of the text is missing.) In the expression, {τ1,τ2} is replaced with the obtained optimal dual variables. Then use recover The optimal transmit power for FL users can then be obtained.

[0145] The proof is complete.

[0146] Given the user's transmit power, since the objective function in the optimization problem is independent of {Θ} u Therefore, the STAR-RIS configuration subproblem is a feasibility verification problem, which can be equivalently expressed as:

[0147] find{Θ u}

[0148]

[0149]

[0150] MSE({p k},{Θ k})≤E0,

[0151]

[0152] This invention further defines Then there is If the u-th user is located in the reflection space, then q u =q R If the u-th user is located in the refracted space, then q u =q T Accordingly, the present invention can obtain

[0153]

[0154] in It can be found definition Need to meet rank(Q u ) = 1 and Diag(Q) u )=β u Vector Diag(Q) u ) represents from matrix Q u The elements extracted from the main diagonal. If the u-th user is located in the reflection space, then otherwise Then, the joint uplink channel coefficients can be further simplified as follows:

[0155]

[0156] Similarly, define and Therefore, the present invention can yield:

[0157]

[0158] Based on the above transformation, the first three non-convex constraints in the STAR-RIS configuration subproblem can be re-expressed as:

[0159]

[0160]

[0161]

[0162] Based on the above approximation, the STAR-RIS configuration subproblem can be approximately expressed as:

[0163] find{Q u},{β u}

[0164]

[0165]

[0166]

[0167]

[0168]

[0169]

[0170]

[0171]

[0172] This invention can equivalently transform the non-convex rank-one constraints and binary constraints in the above problem into the following form:

[0173]

[0174]

[0175] Among them ||·|| * and ||·||2 represent the nuclear norm and spectral norm, respectively.

[0176] Next, this invention adds the above two equations to the objective function of the transformed subproblem as a penalty term, thus obtaining the following problem:

[0177]

[0178]

[0179]

[0180]

[0181]

[0182]

[0183]

[0184] Where η1 and η2 are two non-negative penalty factors, if {Q u} Rank not equal to 1 or These terms are not binary and will penalize the objective function. However, these penalty terms make the objective function of the above problem non-convex. This invention employs the Successive Convex Approximation (SCA) method to obtain a suboptimal solution through iterative solving. Specifically, in the l-th iteration, this invention applies a first-order Taylor expansion using a fixed point Q. u [l] and Q u ||2 and Linearization, i.e.:

[0185]

[0186]

[0187] Then, the non-convex penalty term from the l-th iteration is replaced with the calculated convex upper bound. The transformed problem is a convex semidefinite programming problem, which can be efficiently solved using CVX. The penalty-based SCA algorithm proposed for solving the STAR-RIS placement subproblem consists of two loops: the inner loop iteratively solves the approximate SDP problem of the placement subproblem, and the outer loop continuously updates the penalty factor and determines whether the iteration termination condition is met, where the constraint violation is defined as:

[0188]

[0189] Details are given in the algorithm below.

[0190] Specifically, first initialize {Q u [0]} and {β u [0]}, penalty factors η1 and η2, and corresponding scaling factors and The preset precision values ​​are ∈1 and ∈2. The outer iteration index l1 = 0 is set, and the constraint violation value is calculated. Set the inner iteration index l2 = 0. Calculate the objective function value E of the approximate semidefinite programming problem of the STAR-RIS homeostasis subproblem. tot [l2]. Update l2 = l2 + 1, and update Q by solving the approximate semidefinite programming problem. u [l2] and β u [l2], then update the objective function E tot The value of [l2] is used to repeat the above process until... Or, the number of inner iterations l2 ≥ L2. Update l1 = l1 + 1, update Q. u [l1]=Q u [2], β u [l1]=β u [2], update constraint violation quantity renew Repeat the above process until Or l1≥L1.

[0191] This invention proposes an alternating optimization algorithm to jointly optimize user power allocation and STAR-RIS configuration to minimize total uplink transmission power consumption;

[0192] Specifically, initialize {p u [0]},{Q u [0]},{β u [0]} and preset precision ∈3. Set the current iteration index l3=0, given {Q} u [l3]} and {β u [l3]}, calculate {p} using the closed-form expression for optimal user power allocation.u [l3+1]}, followed by {p u [l3+1]}, update {Q} using the penalty-based SCA algorithm. u [l3+1]} and {β u [l3+1]}, update l3=l3+1, repeat the above process until the value of the objective function is reduced to the preset precision or the preset maximum number of iterations L3 has been reached.

[0193] Since the total transmit power decreases with increasing iterations in the alternating optimization algorithm and is subject to a lower bound constraint, the proposed alternating optimization algorithm is guaranteed to converge. In each iteration, the computational complexity of the algorithm mainly depends on solving the approximate semidefinite programming problem, with a complexity of O(n log n). Where L o =min{L1,log(1 / ∈1)} and L i =min{L2,log(1 / ∈2)} represents the number of external and internal iterations required for the penalty-based SCA algorithm to converge, respectively.

[0194] Simulation results show that the method proposed in this invention can effectively reduce communication overhead and transmission latency compared with centralized learning, and can improve learning accuracy compared with federated learning.

[0195] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit them. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. However, these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A wireless federated learning method based on next-generation multiple access technology, characterized in that, Includes the following steps: S1: The user sends a status information report to the base station; the status information includes instantaneous channel status information and available CPU frequency status information; S2: After receiving the status information report, the base station divides the user into two categories based on the computing power of the user's local device: CL users who are communication-centric and FL users who are computing-centric. After the classification is completed, the base station broadcasts the classification results to all users. S3: Each FL user is based on the global model obtained in the previous round. Train the model locally on the local dataset and compute the local gradient. Each CL user prepares the local dataset to be uploaded to the base station. ; S4: Encode the CL user's local dataset into communication symbols The gradients of the local model trained by the FL user are processed into computational symbols. All users use next-generation multiple access technology combined with smart metasurfaces that can simultaneously reflect and refract to send their information-bearing symbols to the base station; S5: The base station receives superimposed signals from two types of users. First, it decodes the local dataset from the CL user to perform centralized training and obtain the average gradient. Then, it aggregates the model gradients from the FL user and finally uses the obtained gradients to perform global model aggregation. S6: After each round of communication, the base station will update the global model. Broadcast to all FL users so that they can perform gradient calculations in the next round; S7: Repeat the above steps until convergence or the maximum number of communication rounds is reached; Before each round of communication, with the goal of minimizing the total transmit power consumption of this round, the user transmit power allocation and STAR-RIS configuration are jointly optimized. The optimization problem and constraints are as follows: in Represents the set of all users. Represents the CL user set, Represents the FL user set. Indicates the first Transmit power of each user Indicates user The coefficient matrix of STAR-RIS For the joint channel of base station-STAR-RIS-user, For the feasible set of refractive and reflectance coefficients of STAR-RIS, and They represent the first Each component Amplitude and phase shift in the mode, To meet the minimum data transmission rate required for CL users' QoS requirements, The maximum computational distortion that FL users can tolerate. Indicates CL user Data transmission rate, Indicates FL user Calculation distortion; The optimization problem is decoupled into two sub-problems, namely, the user's transmit power. and the user's STAR-RIS configuration Perform alternating optimization.

2. The wireless federated learning method based on next-generation multiple access technology according to claim 1, characterized in that, The next-generation multiple access technology described in step S4 provides services to all users in a non-orthogonal manner within the same frequency band, enabling all users to communicate in parallel on the same time-frequency resources.

3. The wireless federated learning method based on next-generation multiple access technology according to claim 1, characterized in that, The smart metasurface deployed in step S4, which can simultaneously reflect and refract, reshapes the wireless propagation environment by modifying the amplitude and phase of the incident signal, thereby adjusting the channel gain for different users.

4. The wireless federated learning method based on next-generation multiple access technology according to claim 1, characterized in that, The specific operation process of the base station in step S5 is as follows: S51: The base station uses serial interference cancellation technology to detect the communication output of each CL user. This involves decoding and further generating training samples for centralized learning. Then, the model is trained using gradient descent to obtain the average gradient of CL users. for: in, It is the number of CL users. Representing the The gradient for each CL user is calculated by the base station. It is used to train model parameters The objective function, Is the model about the first The first CL user Sample The loss function; S52: Assuming all symbols from the CL user were successfully decoded in S51, the base station subtracts the CL user's signal from the received superimposed signal to obtain a residual signal containing the FL user's signal. The residual signal of the FL user signal is averaged and calculated from the symbol. Recover the local gradient of the FL user Finally, the base station obtains the average gradient estimate of FL users as follows: in It is the number of FL users. This represents the noise vector at the base station. Noise power; S53: Base station collects gradients Then, the global gradient is updated as follows: Then through Perform a global model update, where This is the learning rate.

5. The wireless federated learning method based on next-generation multiple access technology according to claim 1, characterized in that, In the alternating optimization method, for a fixed In this situation, in response to Subproblem, using the uplink communication rate expression for CL users. The computational distortion expression for FL users Rewrite the constraints to express an equivalent subproblem of user power allocation; For the transformed expression, first fix the power allocation for FL users. The optimal power allocation for CL users is derived using mathematical induction. Closed expression: Then fix the power allocation for CL users ,make The optimization problem was reorganized, and the optimal power allocation for FL users was found using the Lagrange duality method. Closed expression: in and These are the optimal dual variables related to QoS and MSE constraints, respectively.

6. The wireless federated learning method based on next-generation multiple access technology according to claim 1, characterized in that, In the alternating optimization method, for a fixed In this situation, The subproblem is a feasibility testing problem, represented as: Introduction , , Rewrite the joint uplink channel coefficients to further represent the subproblem, where... , And there exists a non-convex rank-1 constraint. The transformed expression also has binary variables; For nonconvex rank-one constraints and binary variables, introduce , and They are each transformed into penalty terms in the objective function. Since the penalty terms are non-convex, then in the... In the next iteration, the convex upper bound of the penalty term is obtained using a first-order Taylor expansion: Introducing it into the objective function as a penalty function yields a convex semidefinite programming problem.

7. The wireless federated learning method based on next-generation multiple access technology according to claim 6, characterized in that, The solution method for convex semidefinite programming problems is to continuously update the penalty factor of the penalty term. and Then, the semidefinite programming problem is solved using an iterative method until the penalty term meets the predefined maximum violation amount or the outer iteration reaches the predefined maximum number of iterations.

8. The wireless federated learning method based on next-generation multiple access technology according to claim 1, characterized in that, The method for alternately optimizing the user power allocation and STAR-RIS configuration subproblems specifically involves initialization. , , And preset precision ∈ 3; set the current iteration index. Given and Calculate using a closed-form expression for optimal user power allocation Then given Update using a penalty-based continuous convex approximation method and ,renew Repeat the above process until the value of the objective function decreases to the preset precision or the preset maximum number of iterations has been reached. .

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