A method, device and system for federated edge learning gradient aggregation

Abstract

The present invention relates to a federated edge learning gradient aggregation method, device and system in the field of information and communication technology, comprising the following steps: obtaining a training symbol vector, and calculating a beamforming vector based on the training symbol vector; obtaining a transmitted signal in a wireless channel, and calculating a signal matrix based on the transmitted signal; calculating an aggregation gradient based on the beamforming vector and the signal matrix, and calculating a minimized global loss function; updating a global model based on the aggregation gradient and the minimized global loss function, and judging whether the updated global model converges, if converged, terminating, otherwise continuing to update the global model, thereby solving the problem of large communication overhead and loss of learning performance in air-based federated learning channel estimation.

Description

Technical Field

[0001] The present invention relates to the field of information and communication technology, and in particular to a federated edge learning gradient aggregation method, device and system. Background Art

[0002] With the booming development of communications and artificial intelligence (AI), the next generation of communications is expected to achieve native support for massive multiple access and ubiquitous intelligence. As a promising distributed learning paradigm, federated learning (FL) supports collaborative training on multiple edge devices. However, due to the conflict between limited communication resources and the explosively increasing number of edge devices, the communication between parameter servers (PS) and devices has become a key bottleneck for FL. Fortunately, the PS in FL only needs to aggregate gradients, usually the average of local gradients, rather than the local gradients of each device separately. Taking advantage of this feature of FL, over-the-air federated learning (OA-FL) was proposed. OA-FL uses the superposition characteristics of electromagnetic waves to upload gradients in wireless multiple access channels and complete local gradient aggregation in the air, which significantly reduces the communication cost of FL uploading local gradients.

[0003] Despite the above advantages of over-the-air federated learning, channel fading and channel noise still inevitably lead to communication errors in gradient aggregation, which deteriorates the learning performance of over-the-air federated learning models. Previous research works have attempted to mitigate the impact of fading channels, such as channel inversion at the transmitter end, where the transmitter adopts a precoder to compensate for the amplitude and phase distortion caused by the fading channel. However, channel inversion may amplify channel noise, especially when some devices are in deep fading. To overcome this disadvantage of channel inversion, joint optimization of the beamforming vectors of the transmitter and receiver can avoid strict channel inversion at the transmitter end, thereby alleviating the learning performance degradation caused by fading channels. Although the above channel equalization gradient aggregation method effectively mitigates the impact of fading channels, its main limitation is that it relies on perfect channel state information (CSI) obtained through channel estimation. Typically, the server estimates the CSI based on the pilot or training symbols sent by the device and feeds the estimated CSI back to the device in the downlink control channel. However, the inevitable errors in CSI estimation and feedback will impair the gradient aggregation performance of the channel equalization method based on perfect CSI, resulting in additional loss of learning performance. To deal with errors in CSI feedback, some gradient aggregation schemes that do not rely on CSI at the transmitter (CSIT-Free) have been proposed. However, CSIT-Free schemes still need to estimate CSI at the server side. In order to achieve a sufficiently small channel estimation error, the number of training symbols required for channel estimation is at least equal to the number of devices. This results in a huge communication overhead for sending training symbols, especially when the number of devices is large. Summary of the invention

[0004] In view of the shortcomings of the prior art, the present invention provides a method, device and system for federated edge learning gradient aggregation, which solves the problems of large communication overhead and learning performance loss in over-the-air computing federated learning channel estimation.

[0005] In order to solve the above technical problems, the present invention is solved by the following technical solutions:

[0006] A federated edge learning gradient aggregation method, comprising the following steps:

[0007] Acquire a training symbol vector, and calculate a beamforming vector based on the training symbol vector;

[0008] Acquire a transmission signal in a wireless channel, and calculate a signal matrix based on the transmission signal;

[0009] Calculating an aggregate gradient based on the beamforming vector and the signal matrix, and calculating a minimized global loss function;

[0010] The global model is updated based on the aggregated gradient and the minimized global loss function, and it is determined whether the updated global model converges. If so, the process ends; otherwise, the global model continues to be updated.

[0011] Optionally, calculating the beamforming vector comprises the following steps:

[0012] A training received signal is calculated based on the training symbol vector, and a beamforming vector is calculated based on the training received signal.

[0013] Optionally, the formula for calculating the training received signal is:

[0014] in, represents the channel information matrix of the tth training round, whose kth column represents the channel information vector from the kth user to the server, and K represents the number of edge devices; It means that in the tth training round, edge device k samples a training symbol vector of length M from the gradient distribution; represents the channel noise matrix, whose elements are distributed by independent and identically distributed complex Gaussian distribution Sampling obtained, represents the noise variance; N R ×M complex matrix, N R Indicates the number of antennas of the server;

[0015] The formula for calculating the beamforming vector is:

[0016] Among them, a=[A1 / A,…,A K / A] T represents the normalized device aggregation weight, represents the number of samples in the data set of the entire system, and T represents the maximum communication round of task training; (·) H is the conjugate transpose of the matrix.

[0017] Optionally, a calculation formula for calculating a signal matrix based on the transmitted signal is:

[0018] in, Indicates sending a signal.

[0019] Optionally, the formula for calculating the aggregation gradient is:

[0020]

[0021] Among them, ⊙ is the element-by-element product, To take the real part operation, To take the imaginary part operation, represents the beamforming vector; Y (t) represents the signal matrix; S represents the random flip vector.

[0022] Optionally, determining whether the updated global model has converged includes the following steps:

[0023] The updated global model is transmitted back to each edge device through an error-free broadcast channel;

[0024] Determine whether the communication round is greater than the maximum communication round. If so, it converges, otherwise it does not converge.

[0025] A federated edge learning gradient aggregation device, the federated edge learning gradient aggregation device performs any one of the federated edge learning gradient aggregation methods described above, including a parameter server, the parameter server performs the following steps:

[0026] After receiving the training symbol vector, a training received signal is calculated based on the training symbol vector, and a beamforming vector is calculated based on the training received signal;

[0027] Calculating a received signal matrix based on the synchronously transmitted transmit signal, and calculating a convergence gradient based on the signal matrix and a beamforming vector;

[0028] Update the global model based on the aggregated gradient and minimization of the global loss function, and determine whether the updated global model converges. If so, end the process, otherwise continue to update the global model.

[0029] Optionally, more than two groups of single-antenna edge devices are further included, and the more than two groups of single-antenna edge devices perform the following steps:

[0030] Each group of single-antenna edge devices synchronously sends a training symbol vector for the parameter server to calculate a beamforming vector;

[0031] Each group of single-antenna edge devices performs gradient descent processing, calculates local gradients, and sends signals based on the gradient calculation, which are then synchronously sent to the wireless channel for the parameter server to calculate the aggregated gradient and update the global model.

[0032] A federated edge learning gradient aggregation system, the system executing any one of the federated edge learning gradient aggregation methods described above, comprising a first computing unit, a second computing unit, a third computing unit and an update judgment unit;

[0033] The first calculation unit is used to obtain a training symbol vector and calculate a beamforming vector based on the training symbol vector;

[0034] The second calculation unit is used to obtain a transmission signal in the wireless channel and calculate a signal matrix based on the transmission signal;

[0035] The third calculation unit is used to calculate the aggregation gradient based on the beamforming vector and the signal matrix, and calculate the minimized global loss function;

[0036] The update judgment unit is used to update the global model based on the aggregated gradient and the minimized global loss function, and to judge whether the updated global model converges. If so, the update judgment unit ends, otherwise, the update of the global model continues.

[0037] A computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the federated edge learning gradient aggregation method described in any one of the above is implemented.

[0038] Compared with the prior art, the technical solution provided by the present invention has the following beneficial effects:

[0039] The receiving end beamforming vector is designed through a certain number of training symbol vectors, thereby avoiding channel estimation, reducing the channel estimation overhead and gradient aggregation error of air-computing federated learning, and solving the problems of large communication overhead and learning performance loss of channel estimation in air-computing federated learning. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

[0041] Figure 1 This is a curve showing the variation of the model aggregation error and learning accuracy with the number of training symbols proposed in the first embodiment;

[0042] Figure 2 This is a curve showing how the aggregation error and learning accuracy of the model proposed in the first embodiment vary with the number of receiving antennas;

[0043] Figure 3 This is the test accuracy and communication round number curve on the FMNIST dataset proposed in the first embodiment. DETAILED DESCRIPTION

[0044] The present invention is further described in detail below in conjunction with embodiments. The following embodiments are for explanation of the present invention but the present invention is not limited to the following embodiments.

[0045] Embodiment 1

[0046] First, this embodiment is applicable to an over-the-air computing federated learning (OA-FL) system consisting of a parameter server and K single-antenna edge devices, where the parameter server has N R Antenna. In this embodiment, an air computing federated learning system consisting of 100 edge devices and a parameter server is taken as an example. At this time, the edge devices are evenly distributed in a circle with a radius of 100m centered on the base station. The size of each training task data set is 60,000 samples, and there are 600 samples on each edge device. Then, based on the FMNIST data set, each device randomly selects two categories, and then randomly selects 300 samples from each selected category for training. Among them, the model of the federated learning task consists of a two-layer convolution layer (each layer contains a 5x5 convolution kernel, a 2x2 maximum pooling layer, a ReLU activation function and a batchnorm layer), a fully connected layer and a softmax output layer. The learning is set to 0.01, and the training communication round is set to T=200. After completing the above settings, the federated edge learning gradient aggregation can be started.

[0047] Furthermore, a federated edge learning gradient aggregation method includes the following steps: obtaining a training symbol vector, and calculating a beamforming vector based on the training symbol vector. Specifically, firstly, the maximum communication round of the federated learning task training is set to T. In the tth training round, the parameter server sends the global model parameter θ (t) Broadcast to each edge device, set the global model parameters received by each edge device to be error-free, then set the edge device and parameter server to share the information of gradient distribution, and the channel information is unknown on both the edge device and the server. At this time, since the channel information is unknown on both the edge device and the parameter server, in order to obtain the channel information, in the tth training round, the edge device k needs to sample a training symbol vector of length M from the gradient distribution, expressed as The training symbol matrix of K edge devices is expressed as (·)T is the matrix transpose, and then K edge devices synchronously send the training symbol vector to the parameter server

[0048] Next, the training received signal is calculated based on the training symbol vector, and the beamforming vector is calculated based on the training received signal, that is, in the tth training round, K edge devices synchronously send the training symbol vector to the parameter server, and the training received signal received by the parameter server is The calculation can be expressed as:

[0049] in, represents the channel information matrix of the tth training round, whose kth column represents the channel information vector from the kth user to the server, and K represents the number of edge devices; It means that in the tth training round, edge device k samples a training symbol vector of length M from the gradient distribution; represents the channel noise matrix, whose elements are distributed by independent and identically distributed complex Gaussian distribution Sampling obtained, represents the noise variance;

[0050] N R ×M complex matrix, N R Indicates the number of antennas of the server.

[0051] Since existing methods are often based on the received signal matrix and the training symbol matrix Estimated Channel Information Matrix II (t) , and to realize the channel information matrix H (t) For a more accurate estimation, the channel estimation algorithm often requires the number of training symbols M ≥ the number of devices K. Therefore, this embodiment obtains channel information for subsequent receiving end beamforming design to reduce the fading and noise of the wireless channel on the aggregation gradient The error introduced is based on the received signal matrix The beamforming vector at the receiving end is directly designed. Specifically, the parameter server receives the signal matrix containing the training symbols. Then, the beamforming vector at the receiving end is calculated according to the following formula, where the formula for calculating the beamforming vector is:

[0052] Among them, a=[A1 / A,…,A K / A] T represents the normalized device aggregation weight, represents the number of samples in the data set of the entire system, and T represents the maximum communication round of task training; (·) H is the conjugate transpose of the matrix.

[0053] Thus, the parameter server uses the beamforming vector Used to estimate the aggregate gradient in subsequent steps It should be noted that the algorithm proposed in this embodiment only requires that the number of training symbols M ≥ the number of receiving antennas N R When the number of devices K is large, the algorithm proposed in this embodiment can significantly reduce the demand for the number of training symbols M compared to the channel estimation algorithm, thereby reducing communication overhead.

[0054] Furthermore, the transmission signal in the wireless channel is obtained, and the signal matrix is ​​calculated based on the transmission signal. Specifically, each edge device performs local gradient descent processing on the background, and the calculation formula of the local gradient descent processing is: Among them, Q k (·) is the local loss function of device k, so as to obtain the local gradient set of each edge device

[0055] Then, in the tth round, each edge device k maps the gradient to a complex version, and then the edge device k calculates and sends a signal based on the complex version, where the mapping formula is: Where D is the gradient vector The dimension of C = D / 2; the calculation formula for sending the signal is: Among them, ⊙ is the element-by-element product, is the complex gradient The variance of is a random flip vector, each element of which is independently and uniformly drawn from {-1, +1}.

[0056] Then, K edge devices will send a signal set synchronously Send to the wireless channel and calculate the matrix signal. The calculation formula for calculating the signal matrix based on the sent signal is: in, Indicates sending a signal.

[0057] Then on the parameter server side, in the tth communication round, the cth channel usage, the signal received by the parameter server is It is given by the following formula:

[0058] in, Represents the transmitted signal matrix X (t) The cth column of represents the noise vector used by the c-th channel, whose elements are distributed by independent and identically distributed complex Gaussian distribution The signal matrix received by the parameter server in round t can be expressed as

[0059] Furthermore, the parameter server calculates the aggregate gradient based on the beamforming vector and the signal matrix, and calculates the minimized global loss function. Specifically, the formula for calculating the aggregate gradient is:

[0060]

[0061] Among them, ⊙ is the element-by-element product, To take the real part operation, To take the imaginary part operation, represents the beamforming vector; Y (t) represents the signal matrix; S represents the random flip vector.

[0062] When calculating the minimum global loss function, the global loss function is defined as: The number of samples in the dataset in the entire system, A k is the number of samples in the local data set of device k, is the network model parameter, D is the total number of model parameters, represents a real vector of dimension D×1. k (·) is the local loss function of device m, which is specifically expressed as: Among them, k，n represents the nth training data sample on device k, q(θ;ζ k，n ) is about sample ζ k，n The point-wise loss function of .

[0063] Finally, the global model is updated based on the aggregated gradient and the minimization of the global loss function, and it is determined whether the updated global model converges. If so, the process ends; otherwise, the global model continues to be updated. The process of determining whether the updated global model converges includes the following steps: transmitting the updated global model back to each edge device through an error-free broadcast channel; determining whether the communication round is greater than the maximum communication round. If so, the model converges; otherwise, the model does not converge.

[0064] Specifically, the parameter server obtains the estimated aggregate gradient according to the following formula: Among them, ⊙ is the element-by-element product, To take the real part operation, To take the imaginary part operation,

[0065] The parameter server then updates the model according to the following formula: Where η is the learning rate. The server then transmits the updated global model back to each device through an error-free broadcast channel. If the communication round t>T is reached, it means that the model converges and the model training ends. Otherwise, the global model continues to be updated.

[0066] Finally, if Figure 1 As shown, this embodiment studies the influence of the number of training symbols M on the gradient aggregation and learning performance of the proposed scheme, and the number of receiving antennas is set to N R =30, the research results are the average of 100 Monte Carlo experiments, Figure 1 (a) shows how the gradient aggregation least squares mean square error (MSE) changes with the number of training symbols, from Figure 1As can be seen from (a), as the number of training symbols gradually increases, the gradient aggregation MSE of the scheme in this embodiment gradually decreases, approaching the MSE of the gradient aggregation scheme based on perfect channel information; Figure 1 (b) shows how the test accuracy changes with the number of training symbols. Figure 1 (b) It can be seen that as the number of training symbols gradually increases, the test accuracy of the proposed scheme gradually increases, approaching the test accuracy based on the perfect channel information gradient aggregation scheme.

[0067] like Figure 2 As shown, this embodiment studies the number of receiving antennas N R The influence of gradient aggregation and learning performance of the proposed scheme, the number of training symbols is set to M = 70, and the research results are the average of 100 Monte Carlo experiments. Figure 2 (a) shows how the gradient aggregation MSE changes with the number of training symbols. Figure 2 (a) It can be seen that as the antenna gradually increases, the gradient aggregation MSE of the proposed scheme gradually increases; Figure 2 (b) shows how the test accuracy changes with the number of training symbols. Figure 2 (b) As can be seen, as the number of training symbols gradually increases, when 30≤N R When N ≤58, the test accuracy of the proposed scheme gradually increases, approaching the test accuracy of the scheme based on perfect channel information gradient aggregation. However, due to the insufficient number of training symbols, when N R When >58, the test accuracy of the proposed scheme decreases rapidly.

[0068] like Figure 3 As shown, this embodiment sets the number of receiving antennas to N by comparing the learning accuracy of various transmission schemes. R =50, and the number of training symbols is M=70. At this time, the learning accuracy obtained by the scheme proposed in this embodiment is similar to that of the gradient aggregation scheme based on perfect channel information, and is significantly better than other schemes, which clearly demonstrates the superiority of the scheme proposed in this embodiment.

[0069] Embodiment 2

[0070] A federated edge learning gradient aggregation device comprises a parameter server, which performs the following steps: after receiving a training symbol vector, calculating a training received signal based on the training symbol vector, and calculating a beamforming vector based on the training received signal; calculating a received signal matrix based on a synchronously transmitted transmission signal, and calculating an aggregation gradient based on the signal matrix and the beamforming vector; updating a global model based on the aggregation gradient and minimizing a global loss function, and judging whether the updated global model converges; if so, terminating the process, otherwise continuing to update the global model.

[0071] The federated edge learning gradient aggregation device also includes more than two groups of single-antenna edge devices, and the more than two groups of single-antenna edge devices perform the following steps: each group of single-antenna edge devices synchronously sends a training symbol vector for the parameter server to calculate the beamforming vector; each group of single-antenna edge devices performs gradient descent processing, calculates the local gradient, and sends a signal based on the gradient calculation, and then synchronously sends it to the wireless channel for the parameter server to calculate the aggregated gradient and update the global model.

[0072] Specifically, the steps performed by the federated edge learning gradient aggregation device are:

[0073] Each group of single-antenna edge devices synchronously sends a training symbol vector;

[0074] After receiving the training symbol vector, the parameter server calculates the training received signal based on the training symbol vector, and calculates the beamforming vector based on the training received signal; each group of single-antenna edge devices performs gradient descent processing, calculates the local gradient, and sends the signal based on the gradient calculation, and then sends it synchronously to the wireless channel;

[0075] The parameter server calculates a received signal matrix based on the synchronously transmitted transmit signal, and calculates an aggregate gradient based on the signal matrix and the beamforming vector;

[0076] The parameter server updates the global model based on the aggregated gradient and the minimization of the global loss function, and determines whether the updated global model converges. If so, the process ends; otherwise, the process continues to update the global model.

[0077] Since the federated edge learning gradient aggregation device executes the federated edge learning gradient aggregation method as described in Example 1, it is not repeated in this embodiment.

[0078] Embodiment 3

[0079] A federated edge learning gradient aggregation system, the system executes the federated edge learning gradient aggregation method as described in Example 1, including a first calculation unit, a second calculation unit, a third calculation unit and an update judgment unit; the first calculation unit is used to obtain a training symbol vector, and calculate a beamforming vector based on the training symbol vector; the second calculation unit is used to obtain a transmission signal in a wireless channel, and calculate a signal matrix based on the transmission signal; the third calculation unit is used to calculate an aggregation gradient based on the beamforming vector and the signal matrix, and calculate a minimized global loss function; the update judgment unit is used to update a global model based on the aggregation gradient and the minimized global loss function, and judge whether the updated global model converges, if converged, then end, otherwise continue to update the global model.

[0080] A computer-readable storage medium stores a computer program. When the computer program is executed by a processor, the federated edge learning gradient aggregation method described in Example 1 is implemented.

[0081] More specific examples of computer-readable storage media may include, but are not limited to, an electrical connection having one or more conductor segments, a portable computer disk, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), optical fiber, a portable compact disk-read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the foregoing.

[0082] In the present application, a computer-readable storage medium may be any tangible medium containing or storing a program that can be used by or in combination with an instruction execution system, apparatus, or device. In the present application, a computer-readable signal medium may include a data signal propagated in a baseband or as part of a carrier wave, which carries a computer-readable program code. Such propagated data signals may take a variety of forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination of the above. A computer-readable signal medium may also be any computer-readable medium other than a computer-readable storage medium, which may send, propagate, or transmit a program for use by or in combination with an instruction execution system, apparatus, or device. The program code contained on the computer-readable medium may be transmitted using any suitable medium, including but not limited to: wireless segments, wire segments, optical cables, RF, etc., or any suitable combination of the above.

[0083] In the several embodiments provided in this application, it should be understood that the disclosed devices and methods can be implemented in other ways. For example, the device embodiments described above are only schematic, for example, the division of the modules, modules or units is only a logical function division, and there may be other division methods in actual implementation, for example, multiple units, modules or components can be combined or integrated into another device, or some features can be ignored or not executed.

[0084] The units may or may not be physically separated, and the components displayed as units may be one physical unit or multiple physical units, that is, they may be located in one place or distributed in multiple different places. Some or all of the units may be selected according to actual needs to achieve the purpose of the present embodiment.

[0085] In addition, each functional unit in each embodiment of the present invention may be integrated into one processing unit, or each unit may exist physically separately, or two or more units may be integrated into one unit. The above-mentioned integrated unit may be implemented in the form of hardware or in the form of software functional units.

[0086] In particular, according to the embodiments disclosed in the present invention, the process described above with reference to the flowchart can be implemented as a computer software program. For example, the embodiments of the present disclosure include a computer program product, which includes a computer program carried on a computer-readable medium, and the computer program includes a program code for executing the method shown in the flowchart. In such an embodiment, the computer program can be downloaded and installed from the network through the communication part, and / or installed from a removable medium. When the computer program is executed by the central processing unit (CPU), the above-mentioned functions defined in the method of the present application are executed. It should be noted that the above-mentioned computer-readable medium of the present application can be a computer-readable signal medium or a computer-readable storage medium or any combination of the above two. The computer-readable storage medium can be, for example, but not limited to, a system, device or device of an electrical, magnetic, optical, electromagnetic, infrared segment, or semiconductor, or any combination of the above.

[0087] The flow chart and block diagram in the accompanying drawings illustrate the possible architecture, function and operation of the system, method and computer program product according to various embodiments of the present invention. In this regard, each square box in the flow chart or block diagram can represent a module, a program segment or a part of a code, and the module, the program segment or a part of the code contains one or more executable instructions for realizing the specified logical function. It should also be noted that in some alternative implementations, the functions marked in the square box can also occur in a sequence different from that marked in the accompanying drawings. For example, two square boxes represented in succession can actually be executed substantially in parallel, and they can sometimes be executed in the opposite order, depending on the functions involved. It should also be noted that each square box in the block diagram and / or flow chart, and the combination of the square boxes in the block diagram and / or flow chart can be implemented with a dedicated hardware-based system that performs the specified function or operation, or can be implemented with a combination of dedicated hardware and computer instructions.

[0088] The above is only a specific embodiment of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions within the technical scope disclosed by the present invention should be included in the protection scope of the present invention. Therefore, the protection scope of the present invention should be based on the protection scope of the claims.

Claims

1. A federated edge learning gradient aggregation method, characterized in that: The following steps are involved: A training symbol vector is obtained, and a beamforming vector is calculated based on the training symbol vector, wherein the beamforming vector is calculated, including the following steps: a training received signal is calculated based on the training symbol vector, and a beamforming vector is calculated based on the training received signal, and a formula for calculating the training received signal is: in, represents the channel information matrix of the tth training round, whose kth column represents the channel information vector from the kth user to the server, and K represents the number of edge devices; It means that in the tth training round, edge device k samples a training symbol vector of length M from the gradient distribution; represents the channel noise matrix, whose elements are distributed by independent and identically distributed complex Gaussian distribution Sampling obtained, represents the noise variance; Indicates M R ×M complex matrix, N R Represents the number of antennas of the server; the formula for calculating the beamforming vector is: Among them, a=[A1 / A,…,A K / A] T represents the normalized device aggregation weight, represents the number of samples in the data set of the entire system, and T represents the maximum communication round of task training; (·) H is the matrix conjugate transpose; Acquire a transmission signal in a wireless channel, and calculate a signal matrix based on the transmission signal; Calculating an aggregate gradient based on the beamforming vector and the signal matrix, and calculating a minimized global loss function; The global model is updated based on the aggregated gradient and the minimized global loss function, and it is determined whether the updated global model converges. If so, the process ends; otherwise, the global model continues to be updated.

2. A federated edge learning gradient aggregation method according to claim 1, characterized in that: The calculation formula for calculating the signal matrix based on the transmitted signal is: in, Indicates sending a signal.

3. A federated edge learning gradient aggregation method according to claim 1, characterized in that: The formula for calculating the aggregation gradient is: Among them, ⊙ is the element-by-element product, To take the real part operation, To take the imaginary part operation, in, is the complex gradient The variance of H is the matrix conjugate transpose, Where D is the gradient vector The dimension of C = D / 2, j is the imaginary number symbol, where Q k (·) is the local loss function of device k, θ (t) is the global model parameter; represents the beamforming vector; Y (t) represents the signal matrix; S represents the random flip vector.

4. A federated edge learning gradient aggregation method according to claim 1, characterized in that: Determining whether the updated global model has converged includes the following steps: The updated global model is transmitted back to each edge device through an error-free broadcast channel; Determine whether the communication round is greater than the maximum communication round. If so, it converges, otherwise it does not converge.

5. A federated edge learning gradient aggregation device, characterized in that: The federated edge learning gradient aggregation device performs the federated edge learning gradient aggregation method according to any one of claims 1 to 4, including a parameter server, and the parameter server performs the following steps: After receiving the training symbol vector, a training received signal is calculated based on the training symbol vector, and a beamforming vector is calculated based on the training received signal; Calculating a received signal matrix based on the synchronously transmitted transmit signal, and calculating a convergence gradient based on the signal matrix and a beamforming vector; Update the global model based on the aggregated gradient and minimization of the global loss function, and determine whether the updated global model converges. If so, end the process, otherwise continue to update the global model.

6. A federated edge learning gradient aggregation device according to claim 5, characterized in that: Also included are two or more groups of single-antenna edge devices, where the two or more groups of single-antenna edge devices perform the following steps: Each group of single-antenna edge devices synchronously sends a training symbol vector for the parameter server to calculate a beamforming vector; Each group of single-antenna edge devices performs gradient descent processing, calculates local gradients, and sends signals based on the gradient calculation, which are then synchronously sent to the wireless channel for the parameter server to calculate the aggregated gradient and update the global model.

7. A federated edge learning gradient aggregation system, characterized in that: The system executes the federated edge learning gradient aggregation method as described in any one of claims 1 to 4, comprising a first computing unit, a second computing unit, a third computing unit and an update judgment unit; The first calculation unit is used to obtain a training symbol vector and calculate a beamforming vector based on the training symbol vector; The second calculation unit is used to obtain a transmission signal in the wireless channel and calculate a signal matrix based on the transmission signal; The third calculation unit is used to calculate the aggregation gradient based on the beamforming vector and the signal matrix, and calculate the minimized global loss function; The update judgment unit is used to update the global model based on the aggregated gradient and the minimized global loss function, and to judge whether the updated global model converges. If so, the update judgment unit ends, otherwise, the update of the global model continues.

8. A computer-readable storage medium storing a computer program, characterized in that: When the computer program is executed by a processor, the federated edge learning gradient aggregation method described in any one of claims 1 to 4 is implemented.

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