Distributed cooperative interference management method for multi-task air federated learning system

Abstract

The invention discloses a distributed cooperative interference management method for a multi-task air federated learning system, and the method comprises the steps: firstly, obtaining channel information between each base station and associated edge equipment, and an interference temperature value between the base stations, so as to construct a communication parameter optimization model; secondly, calculating the optimal transmission power and the optimal noise reduction factor through interference temperature negotiation between paired base stations by adopting a distributed coordination mechanism; then, all base station pairs are traversed circularly, and collaborative optimization of power and noise reduction factors of the whole network is completed; and finally, the edge equipment executes air aggregation transmission of gradient signals based on the optimal transmission power, and the target base station completes signal processing and updates the cell model according to the optimal noise reduction factor of the target base station. According to the distributed cooperative interference management method, the cross-cell performance balance of a multi-task system can be remarkably improved, the communication and calculation burden can be effectively reduced, the network expansibility and stability are improved, and the distributed cooperative interference management method is more suitable for multi-task air federated learning in a large-scale network environment.

Description

Technical Field

[0001] The present invention belongs to the technical field of airborne federated learning, and in particular relates to a distributed collaborative interference management method for a multi-task airborne federated learning system. Background Art

[0002] Federated learning is a distributed machine learning method that distributes model training tasks to devices, eliminating the need to centrally transmit raw data and only requiring model parameters or gradient information to be uploaded. This effectively reduces the communication burden and enhances data security. However, despite its significant advantages in distributed learning and privacy protection, federated learning's deployment in wireless networks still faces the challenge of limited communication resources. Because edge devices frequently exchange high-dimensional parameters with servers to update information during model training, the communication load increases significantly. Traditional orthogonal multiple access methods treat signals from different devices as interference, resulting in a linear increase in wireless resource requirements with the number of devices. This makes it difficult to support federated learning tasks involving large-scale terminals simultaneously, severely restricting system scalability and actual deployment efficiency.

[0003] Over-the-air computing performs signal pre-processing at the transmitter and post-processing at the receiver. By leveraging the signal superposition characteristics of wireless multiple access channels, it enables parallel computation of required functions over the air, significantly alleviating the high latency associated with large-scale access and effectively reducing communication overhead. These characteristics make over-the-air computing a promising new over-the-air access solution. Its application in federated edge learning can achieve rapid model convergence. Consequently, over-the-air federated learning has garnered increasing attention in both academia and industry. Currently, most existing over-the-air federated learning approaches are based on single-task scenarios. However, with the continued growth of intelligent devices in edge networks, practical deployments of federated learning face emerging challenges such as uneven data distribution and task diversity. Single-task scenarios struggle to simultaneously meet the demands of multiple diverse tasks and heterogeneous data. Therefore, effectively deploying multi-task federated learning to better adapt to data heterogeneity and task personalization is becoming a crucial research issue for current and future edge intelligent networks.

[0004] Existing multi-task over-the-air federated learning primarily manages devices by categorizing them into cells, with each cell performing federated learning for its own task. Specifically, each cell has a base station that uses over-the-air computing technology to perform federated learning on multiple devices. Different cells are responsible for training different task models and learning in parallel. However, existing multi-cell multi-task over-the-air federated learning solutions also have drawbacks. Because multiple cells share limited spectrum resources, when multiple cells perform over-the-air computing simultaneously, different edge servers will interpret signals sent by devices in connected cells as inter-cell interference signals. This interference signal will be superimposed on the target signal, directly affecting the aggregation accuracy of the cell itself and leading to a decrease in model convergence performance. Therefore, these issues pose new challenges to multi-cell over-the-air federated learning. How to effectively manage inter-cell interference signals in a multi-cell environment to improve the training performance of multi-task over-the-air federated learning has become a key issue that needs to be addressed. Existing research generally adopts a centralized optimization architecture, which requires an additional central server to perform unified resource optimization and allocation to mitigate the impact of inter-cell interference. However, as the number of devices in edge networks continues to increase in the future, long-distance communication will lead to an increasing communication burden. If a centralized optimization framework is continued to be used, this will bring more communication overhead to the entire aerial federated learning, and there will be obvious limitations in scalability, stability, and other aspects. Summary of the Invention

[0005] In order to overcome the shortcomings of the existing technology, the present invention provides a distributed collaborative interference management method for a multi-task airborne federated learning system. The distributed collaborative interference management method can effectively improve the overall cross-cell performance balance and learning performance of the multi-task system, and can effectively reduce the communication and computing burden, improve network scalability and stability, and is more suitable for multi-task airborne federated learning in large-scale network environments.

[0006] The second object of the present invention is to provide a distributed collaborative interference management device for a multi-task airborne federated learning system.

[0007] The technical solution of the present invention to solve the above technical problems is:

[0008] A distributed collaborative interference management method for a multi-task airborne federated learning system includes the following steps:

[0009] Step S1: constructing a multi-cell multi-task air federated learning model, wherein each cell base station in the multi-cell multi-task air federated learning model broadcasts the corresponding cell model to the associated edge device;

[0010] Step S2: Obtain channel information between each cell base station and associated edge devices, as well as interference temperature values ​​between each cell base station;

[0011] Step S3: Based on the obtained channel information and interference temperature value, a communication parameter optimization model is constructed with minimizing the optimal gap as the optimization goal and the transmission power of the edge device and the noise reduction factor of the base station as the optimization variables;

[0012] Step S4: Select any pair of base stations, exchange information between them through a distributed coordination mechanism, and adopt a distributed power control optimization scheme based on interference temperature values. Through interference temperature negotiation between paired base stations, coordinate and update the interference temperature values ​​between the base stations. Based on the established communication parameter optimization model, calculate the optimal transmission power of the corresponding cell edge device and the optimal noise reduction factor of the base station.

[0013] Step S5: Repeat step S4 to loop through all base station pairs to complete the coordinated optimization of the transmission power of edge devices and the noise reduction factor of base stations across the entire network, so as to obtain the optimal transmission power of each cell edge device and the optimal noise reduction factor of each base station;

[0014] Step S6: The base station sends the optimal transmission power to the associated edge device. The gradient calculation module of the associated edge device calculates the device gradient signal based on the input of the cell model. The communication control module on all edge devices in each cell performs over-the-air aggregation and transmission of the device gradient signal to the target base station based on the received optimal transmission power through over-the-air calculation.

[0015] Step S7: The base station performs noise reduction processing on the received device gradient signal according to its own optimal noise reduction factor, and uses the cell model update module to update the cell model to obtain an updated cell model, and broadcasts the updated cell model to the associated edge devices.

[0016] A preferred solution of the present invention is that in step S1, the number of cells in the multi-cell multi-task air federated learning model is M, each cell is deployed with a base station, and each cell is deployed with K single-antenna edge devices, wherein the base station edge devices With the collaboration between edge devices and target base stations, each cell independently completes different learning tasks.

[0017] A preferred solution of the present invention is that, in step S2, the step of obtaining channel information between each cell base station and the associated edge device is:

[0018] Step S201: Using the stochastic gradient descent algorithm, calculate the local loss function gradient of the random data of each edge device

[0019]

[0020] Where: Represents the size of the local mini-batch training set data; x i With ξ i Respectively represent The i-th data in and its correct label value; Represents when the cell model in edge device k takes When , the local loss function gradient is obtained based on the data and its correct label value; n is the nth round of global iteration, N is the maximum number of global iterations;

[0021] Step S202: Calculate the local loss function gradient Perform normalization processing to obtain the normalized signal to be transmitted

[0022]

[0023] Where: is the mean of the local loss function gradient, C represents the dimension of the local loss function gradient, represents the standard deviation of the local loss function gradient, represent The c-th dimension signal of the vector;

[0024] Step S203: Obtaining a normalized signal The c-th dimension signal and precoding factor in , to achieve channel pre-compensation and obtain the signal received by base station m in the cth time slot

[0025]

[0026] Where: represents the transmission power of edge device k, represents the channel coefficient from edge device k to base station m, and the superscript H represents the conjugate transpose; represents the complex symmetric Gaussian white noise of base station m; Represents the inter-cell interference signal caused by simultaneous transmission of the same resource block;

[0027] Step S204: After receiving the signal, base station m responds to the signal of the cth time slot. Perform gradient linear estimation post-processing to obtain the scaled signal of base station m

[0028]

[0029] Where: represents the unbiased value of the cell gradient, represents the error in the gradient estimate, represents the noise reduction factor used by base station m for signal power alignment and noise power suppression;

[0030] Step S205: scaling signal of base station m Perform the real part operation to obtain the gradient estimate of the cell gradient And according to the gradient estimate Update the cell model, where:

[0031] Gradient estimate for:

[0032]

[0033] The updated cell model is:

[0034]

[0035] Where: is the real part operation; Here, the superscript T stands for ordinary transpose; represents the learning rate of base station m in the nth global iteration round;

[0036] The steps to obtain the interference temperature value between base stations in each cell are as follows:

[0037] Get the maximum interference power value of all edge devices associated with base station m to base station j as the interference temperature value Γ of base station j j,m ,in, Get the maximum interference power value of all edge devices associated with base station j to base station m as the interference temperature value Γ of base station m m,j .

[0038] A preferred solution of the present invention is that in step S3, the steps of constructing the communication parameter optimization model are:

[0039] Step S301: Based on the channel information from the edge device to the target base station, a first optimization problem is constructed with minimizing the optimal gap as the optimization goal and the transmission power of the edge device and the noise reduction factor of the base station as optimization variables;

[0040] Step S302: using the interference temperature value between base stations as an explicit constraint item of the first optimization problem to construct a second optimization problem;

[0041] Step S303: introducing an inverse noise reduction factor and defining auxiliary variables to convert the second optimization problem into a convex optimization problem, thereby obtaining the communication parameter optimization model.

[0042] A preferred solution of the present invention is that in step S301, the steps of constructing the first optimization problem are:

[0043] Step S301: Calculate the difference between the maximum global iteration round loss function and the optimal global iteration round loss function of base station m to obtain the optimal gap, and use the obtained optimal gap as the federated learning convergence performance indicator of base station m; wherein the upper bound of the optimal gap should meet the following conditions:

[0044]

[0045] Where: is the maximum global iteration round loss function of base station m; is the optimal global iteration round loss function of base station m; and satisfy

[0046] represents the gradient variance; L m Indicates the smoothness of the loss function;

[0047] Step S302: Represent the aggregation error in equation (8) Assume that the effective optimal gap needs to be optimized, and each round of global iteration is considered independent and can be optimized separately, omitting the superscript n of the global iteration round, so as to construct an optimization method with minimizing the optimal gap as the optimization goal and the transmission power p of the edge device as the optimization goal. k and the noise reduction factor θ of the base station m The first optimization problem for optimizing variables is:

[0048]

[0049] Where: The maximum power for each edge device.

[0050] A preferred solution of the present invention is that in step S302, the step of constructing the second optimization problem is:

[0051] The interference term in the first optimization problem Replace with Γ m,j , and define the edge device associated with base station m Interference channel to base station j This leads to the second optimization problem.

[0052] A preferred solution of the present invention is that, in step S303, the steps of constructing the convex optimization problem are:

[0053] Introducing the inverse noise reduction factor γ m =1 / θ m , and define auxiliary variables Rewrite the second optimization problem into a convex optimization problem:

[0054]

[0055] The convex optimization problem is the communication parameter optimization model.

[0056] A preferred solution of the present invention is that, in step S4, the Lagrange dual method is used to solve the obtained convex optimization problem to obtain the following closed-form solution:

[0057]

[0058] Where: and is the optimal solution to the convex optimization problem; and are the dual variables and optimal dual variables corresponding to the interference temperature constraint of base station j, respectively, where, and are the dual variable and optimal dual variable corresponding to the transmission power constraint of edge device k, respectively; and are the optimal solutions for the transmission power of the edge device associated with base station m and the noise reduction factor of base station m, respectively.

[0059] A preferred solution of the present invention is that, in step S4, the distributed power control optimization solution based on the interference temperature value is:

[0060] Step S401: Set the interference temperature vector Γ and the convergence precision ι, where Γ is a vector of size M(M-1)×1 containing all Γ j,m vector of

[0061] Step S402: Base station m and base station j solve the convex optimization problem respectively to obtain the optimal transmission power and the optimal noise reduction factor and the optimal dual variable

[0062] Step S403: According to equations (16) and (17), base station m and base station j each update T j,m The elements in , where

[0063]

[0064] Where: Γ m is a 2(M-1)×1 matrix containing all Γ j,m and Γ m,j vector of are the dual multipliers corresponding to the optimal interference temperature constraints of base station m and base station j respectively; Then they are the optimal inverse noise reduction factors corresponding to the optimal interference temperature value constraints of base station m and base station j respectively; For convex optimization problems at any given Γ m The optimal gap of base station m under the condition of; For convex optimization problems at any given Γ j The optimal gap of base station j under the condition of ;

[0065] Step S404: Base station m and base station j exchange their respective T j,m The elements in T are reconstructed according to formula (15) j,m , and calculate t by (19) j,m ;

[0066] [Γ′ j,m ,Γ′ m,j ] T =[Γ j,m ,Γ m,j ] T +δ j,m ·t j,m , (18)

[0067] make Then we have:

[0068] t j,m =sign(bc-ad)·[l j,m db,al j,m c] T , (19)

[0069] Where: δ j,m represents the step size parameter; t j,m To meet T j,m t j,m Vectors with l<0; j,m is the ratio parameter that controls the optimal gap reduction between base stations m and j; sign(·) represents the sign function;

[0070] Step S405: Base station m and base station j update their respective interference temperature values ​​according to formula (18) to obtain the updated interference temperature value Γ′ j,m ;

[0071] Step S406: Repeat steps S402 to S405 until |T j,m |>ι, and will satisfy |T j,m The optimal transmission power and optimal noise reduction factor when |>ι are taken as the final optimal transmission power and optimal noise reduction factor;

[0072] Step S407: After traversing all base station pairs, repeat steps S402 to S406 to output the optimal transmission power and optimal noise reduction factor of each cell.

[0073] An interference management device for a multi-task airborne federated learning system, comprising:

[0074] Channel information acquisition unit: used to obtain channel information between each cell base station and associated edge devices based on the constructed multi-cell multi-task air federated learning model;

[0075] Interference temperature value acquisition unit: used to obtain the interference temperature value between base stations in each cell based on the constructed multi-cell multi-task air federated learning model;

[0076] Communication parameter optimization unit: used to construct a communication parameter optimization model based on the obtained channel information and interference temperature value, with minimizing the optimal gap as the optimization goal and the transmission power of the edge device and the noise reduction factor of the base station as the optimization variables; and select any base station pair, conduct information exchange between base stations through a distributed collaborative mechanism, adopt a distributed power control optimization scheme based on the interference temperature value, coordinate and update the interference temperature value between base stations through interference temperature negotiation between paired base stations, and calculate the optimal transmission power of the corresponding cell edge device and the optimal noise reduction factor of the base station based on the constructed communication parameter optimization model; traverse all base station pairs in turn, complete the coordinated optimization of the transmission power of edge devices and the noise reduction factor of base stations within the entire network, and obtain the optimal transmission power of each cell edge device and the optimal noise reduction factor of the base station;

[0077] Communication control unit: used to send the calculated optimal transmission power to the corresponding edge device and the calculated optimal noise reduction factor to the corresponding base station, so as to prompt the edge device to use its optimal transmission power to aggregate the device gradient signal to the target base station by air calculation and prompt the target base station to perform noise reduction processing on the received device gradient signal according to its optimal noise reduction factor to generate a new cell model and broadcast it to the associated edge device.

[0078] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0079] 1. The distributed collaborative interference management method for the multi-task airborne federated learning system of the present invention utilizes air computing to perform parallel multi-task federated learning. When the same resource block is transmitted simultaneously to generate an interference signal, the interference temperature value between cells is effectively managed through a distributed power control optimization scheme based on interference temperature, thereby effectively improving the overall cross-cell performance balance and learning performance of the multi-task system. Compared with the existing centralized power control scheme, the interference management method of the present invention does not require the coordination of a central server (i.e., centralized control), thereby effectively reducing the communication and computing burden, improving network scalability and stability, and is more suitable for multi-task airborne federated learning in large-scale network environments.

[0080] 2. The distributed collaborative interference management method for the multi-task airborne federated learning system of the present invention is composed of a multi-cell scenario consisting of multiple base stations and multiple edge devices to perform multi-task federated learning. By defining the edge devices to aggregate device gradient information to the base station, the base station updates the cell model and broadcasts the new cell model to the associated edge devices as a global iteration. It also proposes a distributed power control optimization scheme based on interference temperature to optimize the transmission power and noise reduction factor of the edge devices, and perform interference management between cells, so that the multi-task airborne federated learning can reach the convergence state faster and improve the performance of model training. BRIEF DESCRIPTION OF THE DRAWINGS

[0081] Figure 1 This is a flow chart of the distributed collaborative interference management method for a multi-task airborne federated learning system of the present invention.

[0082] Figure 2 This is the architecture diagram of the multi-cell multi-task aerial federated learning model.

[0083] Figure 3 A schematic diagram of the Pareto frontier.

[0084] Figure 4 This is the simulation result of simulation 1 (optimal gap).

[0085] Figure 5 is the simulation result (prediction error) of simulation 1.

[0086] Figure 6 This is the simulation result of simulation 2 (the optimal gap interval can be achieved).

[0087] Figure 7 This is the simulation result of simulation 3 (convergence performance of the distributed power control optimization scheme proposed in the present invention). DETAILED DESCRIPTION

[0088] The present invention will be described in further detail below with reference to the embodiments and drawings, but the embodiments of the present invention are not limited thereto.

[0089] Example 1

[0090] See also Figure 1 and Figure 2 The distributed collaborative interference management method for a multi-task airborne federated learning system of the present invention comprises the following steps:

[0091] Step S1: constructing a multi-cell multi-task air federated learning model, wherein each cell base station in the multi-cell multi-task air federated learning model broadcasts the corresponding cell model to the associated edge device;

[0092] Step S2: Obtain channel information between each cell base station and associated edge devices, as well as interference temperature values ​​between each cell base station;

[0093] Step S3: Based on the obtained channel information and interference temperature value, a communication parameter optimization model is constructed with minimizing the optimal gap as the optimization goal and the transmission power of the edge device and the noise reduction factor of the base station as the optimization variables;

[0094] Step S4: Select any pair of base stations, exchange information between them through a distributed coordination mechanism, and adopt a distributed power control optimization scheme based on interference temperature values. Through interference temperature negotiation between paired base stations, coordinate and update the interference temperature values ​​between the base stations. Based on the established communication parameter optimization model, calculate the optimal transmission power of the corresponding cell edge device and the optimal noise reduction factor of the base station.

[0095] Step S5: Repeat step S4 to loop through all base station pairs to complete the coordinated optimization of the transmission power of edge devices and the noise reduction factor of base stations across the entire network, so as to obtain the optimal transmission power of each cell edge device and the optimal noise reduction factor of each base station;

[0096] Step S6: The base station sends the optimal transmission power to the associated edge device. The gradient calculation module of the associated edge device calculates the device gradient signal based on the input of the cell model. The communication control module on all edge devices in each cell performs over-the-air aggregation and transmission of the device gradient signal to the target base station based on the received optimal transmission power through over-the-air calculation.

[0097] Step S7: The base station performs noise reduction processing on the received device gradient signal according to its own optimal noise reduction factor, and uses the cell model update module to update the cell model to obtain an updated cell model, and broadcasts the updated cell model to the associated edge devices.

[0098] like Figure 2 As shown, Figure 2The architecture diagram of the multi-cell multi-task air federated learning model in the present invention is shown in FIG. 1 , wherein the number of cells in the multi-cell multi-task air federated learning model is M, each cell is deployed with a base station, and each cell is deployed with K single-antenna edge devices, wherein the base station edge devices With the collaboration between edge devices and target base stations, each cell independently completes different learning tasks, that is, each cell independently trains a different machine learning model; in the first round of global iteration, the base station broadcasts the initialized cell model to the edge devices connected to it. The edge devices use the gradient calculation module to calculate the device gradient signal based on the cell model. When the same resource block is transmitted simultaneously and an interference signal is generated, the transmission power optimized by the distributed control module is used for communication control, and the device gradient signal is aggregated to the base station through over-the-air calculation; the base station uses the noise reduction factor optimized by the distributed control module to reduce the noise of the received device gradient signal and update the cell model, and broadcasts the new cell model to the edge devices associated with it for the next round of global iteration. This global iteration will continue for N rounds.

[0099] The following selects a specific round of global iteration As research:

[0100] First, all devices use the stochastic gradient descent algorithm to calculate the local loss function gradient of random data

[0101]

[0102] Where: Represents the size of the local mini-batch training set data; x i With ξ i Respectively represent The i-th data in and its correct label value; Represents when the cell model in edge device k takes When , the local loss function gradient is obtained based on the data and its correct label value; n is the nth round of global iteration, N is the maximum number of global iterations;

[0103] In order to make the gradient unbiased, the edge device calculates the gradient of the local loss function Perform normalization processing to obtain the normalized signal to be transmitted

[0104]

[0105] Where: is the mean of the local loss function gradient, C represents the dimension of the local loss function gradient, represents the standard deviation of the local loss function gradient, represent The c-th dimension signal of the vector;

[0106] Before transmitting the signal, the edge device needs to pre-compensate the signal channel, that is, to obtain the normalized signal The c-th dimension signal and precoding factor in The product of is used to realize channel pre-compensation and obtain the signal received by base station m in the cth time slot.

[0107]

[0108] Where: represents the transmission power of edge device k, represents the channel coefficient from edge device k to base station m, and the superscript H represents the conjugate transpose; represents the complex symmetric Gaussian white noise of base station m; Represents the inter-cell interference signal caused by simultaneous transmission of the same resource block;

[0109] After receiving the signal, base station m responds to the signal of time slot c. Perform gradient linear estimation post-processing to obtain the scaled signal of base station m

[0110]

[0111] Where: represents the unbiased value of the cell gradient, Represents the error in the gradient estimate; represents the noise reduction factor used by base station m for signal power alignment and noise power suppression;

[0112] The scaled signal to base station m Perform the real part operation to obtain the gradient estimate of the cell gradient And according to the gradient estimate Update the cell model, where:

[0113] Gradient estimate for:

[0114]

[0115] The updated cell model is:

[0116]

[0117] Where: is the real part operation; Here, the superscript T stands for ordinary transpose; represents the learning rate of base station m in the nth global communication round;

[0118] The optimal gap is obtained by calculating the difference between the maximum global iteration round loss function and the optimal global iteration round loss function of base station m, and the obtained optimal gap is used as the federated learning convergence performance indicator of base station m;

[0119] The upper bound of the optimal gap should meet the following conditions:

[0120]

[0121] Where: is the maximum global iteration round loss function of base station m; is the optimal global iteration round loss function of base station m; and satisfy μ m is a constant, as determined by Polyak- The conditions are given, and represents the gradient variance, where is the upper limit of the variance of the stochastic gradient of edge device k, N is the number of samples per round; L m Indicates the smoothness of the loss function;

[0122] The aggregation error is represented as The optimization goal is to minimize the optimal gap and the transmission power p of the edge device is constructed. k and the noise reduction factor θ of the base station m The first optimization problem for optimizing variables is:

[0123]

[0124] Where: is the maximum power of each edge device;

[0125] When the first optimization problem is minimized, the optimal gap is also minimized. However, focusing solely on minimizing the optimal gap for each cell can cause severe interference across multiple cells, thereby impairing the learning performance of other cells. Therefore, to avoid performance imbalances between cells, the concept of the Pareto frontier is introduced below.

[0126] In order to achieve the balance of optimal gaps between different cells, the optimal gap interval is defined represents the optimal gap tuple that all cells can achieve simultaneously under given resource constraints (such as power budget), denoted as (Δ1, Δ2, ..., Δ M ), where Δ m represents the optimal gap of base station m. In particular, the optimal gap interval can be defined as:

[0127]

[0128] Where: represents the minimum optimal gap that can be achieved by base station m.

[0129] The lower left boundary of the optimal gap interval is defined as the Pareto frontier, and each point on the Pareto frontier is called the Pareto optimal point. M ) is Pareto optimal, indicating that there is no other optimal gap tuple that can reduce the optimal gap Δ of base station m without increasing the optimal gaps of other base stations. m , the overall performance of the system is balanced among the cells.

[0130] Furthermore, the Pareto frontier of system performance is characterized by the rate profile method. This method constructs an optimization problem of minimizing the sum of the optimal gaps of all cells by combining all base stations. Specifically, we first define κ = [κ1, κ2, ..., κ M ] is a set of given silhouette vectors, which are used to specify the performance weight relationship between different base stations. The optimal gap tuple on the Pareto frontier can be obtained by solving the following problem:

[0131]

[0132] Where: represents the sum of the optimal gaps of M cells;

[0133] Substituting the silhouette vector κ into the optimal gap tuple, the optimal gap tuple can be expressed as:

[0134] (Δ1,Δ2,...,Δ M )=(κ1Δ1,κ2Δ2,...,κ M Δ M ),

[0135] Where: κ m represents the ratio of the optimal gap that can be achieved by base station m to the total optimal gap. For any set of profile vectors satisfying

[0136] For a given vector κ, let is the optimal solution to problem (P1.1), then the corresponding optimal gap tuple is That is the Pareto optimal point, that is, the point set where the ray group with the silhouette vector κ as the direction intersects the Pareto frontier of the optimal gap interval. Therefore, by constantly changing the value of κ, we can obtain the Pareto frontier under the current resource allocation, such as Figure 2 shown.

[0137] However, the above-mentioned Pareto boundary can be characterized by the existing centralized power control scheme. However, considering that the centralized power control scheme in actual deployment has limitations such as large communication and coordination overhead and weak scalability, the present invention further proposes a distributed power control optimization scheme based on interference temperature to solve the problem of characterizing the Pareto boundary. The specific optimization process is described below.

[0138] The present invention introduces interference temperature technology to characterize the optimal gap interval and its Pareto frontier in a multi-cell multi-task airborne federated learning system. The interference temperature is used as an explicit constraint to limit the interference caused by each edge device to the adjacent cells, thereby achieving local power control optimization in each cell.

[0139] First, define Γ j,m is the interference temperature value, which is used to represent the maximum interference power value of all edge devices associated with base station m to base station j. Γ is defined as a M(M-1)×1 matrix containing all Γ j,m vector, define Γ m is a 2(M-1)×1 matrix containing all Γ j,m and Γ m,j vector of

[0140] Therefore, for base station m, the interference term in the first optimization problem (P1) is Replace with Γ m,j , and define the edge device associated with base station m Interference channel to base station j The second optimization problem is obtained, and the second optimization problem of minimizing the optimal gap can be implemented alone on the base station m, and the definition is and are the transmission power of the edge device connected to base station m and the optimal solution of the noise reduction factor of base station m. Since the transmission power p of the edge device k and the noise reduction factor θ m There is a complex coupling relationship in the objective function of the second optimization problem. Therefore, the second optimization problem presents a non-convex problem structure and is difficult to solve. Therefore, the inversion noise reduction factor γ is introduced. m =1 / θ m , and define auxiliary variables Convert the second optimization problem into a convex optimization problem (P1.2):

[0141]

[0142] Since the convex optimization problem (P1.2) is a standard convex optimization problem and satisfies the Slater condition, it can be solved using the Lagrangian dual method, specifically:

[0143] Using the KKT conditions, we can obtain the following closed-form solution:

[0144]

[0145] Where: and is the optimal solution to the convex optimization problem (P1.2), is the dual variable corresponding to the interference temperature constraint of base station j, where is the dual variable corresponding to the transmission power constraint of edge device k.

[0146] Then search for the optimal dual variable and Because it satisfies the complementary relaxation condition, it can be solved using the ellipsoid method, which is based on subgradient iteration; specifically, The subgradient is about The subgradient is After obtaining the optimal solution of the dual variable, the inverse operation is then performed. and That is, the optimal solution of the convex optimization problem (P1.2) or the second optimization problem can be obtained, namely:

[0147]

[0148] Where: and are the optimal solutions for the transmission power of the edge device associated with base station m and the noise reduction factor of base station m, respectively; is the optimal dual variable corresponding to the j-th interference temperature value constraint; is the optimal dual variable corresponding to the transmission power constraint of edge device k.

[0149] According to the above results, the transmission power of the edge device is affected by the maximum transmission power Restriction, when hour, Reaching the maximum power limit Otherwise, the transmission power adopts regularized inverse power transmission (the regularization term is ) ; noise reduction factor It is mainly determined by the interference temperature value between base stations and the maximum power constraint of all edge devices.

[0150] Thus, the optimal solution under the interference temperature constraint is obtained. However, the above result is only limited to the case where the interference temperature is a fixed value and cannot achieve Pareto optimality. Therefore, the present invention proposes an optimization update algorithm for the interference temperature value.

[0151] In order to achieve efficient distributed power control in a multi-cell, multi-task, airborne federated learning system, the present invention introduces the interference temperature value as a key coordination variable and constructs a distributed optimization framework driven by local information. On this basis, the present invention proposes an iterative collaborative algorithm that dynamically adjusts the interference temperature values ​​between base stations through point-to-point signaling interaction between base stations. In each round of global iteration, the system selects two base stations for local collaborative update. The update premise is that this adjustment will not increase the optimal gap of the local cell and will not weaken the performance of other cells, thereby ensuring non-inferiority improvement of the overall system performance. In order to implement this mechanism, it is assumed that there is basic backhaul link support between base stations to achieve necessary information sharing and interference parameter synchronization. However, under any interference temperature value, it is difficult to directly determine whether the system has reached Pareto optimality. To this end, the present invention proposes a lemma to characterize the necessary conditions for the interference temperature value and the optimal gap of the cell to meet the Pareto optimal condition, and based on this, provides a theoretical basis for subsequent algorithm design.

[0152] Lemma (necessary condition for Pareto optimality): For any given Γ, if the optimal gap of the convex optimization problem (P1.2) The Pareto optimal state has been reached, then any pair of base stations m and j must satisfy |T j,m |=0, where |T j,m | is a 2×2 matrix that satisfies the following conditions:

[0153]

[0154] Where: For the convex optimization problem (P1.2) at any given Γ m The optimal gap of base station m under the condition of; For the convex optimization problem (P1.2) at any given Γ j The optimal gap of base station j under the condition of ;

[0155] Based on any given Γ m By solving the optimal solution of the original problem and its corresponding dual problem respectively, we can deduce the optimal solution of |T j,m |Detailed expressions of each element:

[0156]

[0157] Where: are the dual multipliers corresponding to the optimal interference temperature constraints of base station m and base station j, Then they are the optimal inverse noise reduction factors corresponding to the optimal interference temperature value constraints of base station m and base station j respectively;

[0158] At the same time, you can also get:

[0159]

[0160] According to the above lemma, the present invention proposes an update optimization method for interference temperature as follows:

[0161] First, let Γ′ represent the updated interference temperature vector, and then each time only the mutual interference temperature Γ between a pair of selected base stations is calculated. j,m and Γ m,j Update, while the rest of the elements in Γ remain unchanged. The specific update method is:

[0162] [Γ′ j,m ,Γ′ m,j ] T =[Γ j,m ,Γ m,j ] T +δ j,m ·t j,m , (18)

[0163] Where: δ j,m represents a sufficiently small step size parameter; t j,m To meet T j,m t j,m Vectors with <0;

[0164] make Then t j,m A feasible solution is:

[0165] t j,m =sign(bc-ad)·[l j,m db,al j,m c] T , (19)

[0166] Where: l j,m is the ratio parameter that controls the optimal gap reduction between base stations m and j; sign(·) represents the sign function;

[0167] From the above analysis, we can see that by setting the control variable l j,m ≥1 to ensure that the optimal gap reduction achieved by base station m is larger than that achieved by base station j (when l j,m ≤1 is smaller); therefore, choose a sufficiently small step size parameter δ j,m , and by adding l j,mBy adjusting from 0 to infinity, we can find the intersection set of the optimal gaps between base stations m and j on the Pareto frontier.

[0168] Therefore, based on the above analysis, the steps of the distributed power control optimization solution based on interference temperature value of the present invention are as follows:

[0169] Step S401: setting the interference temperature vector Γ and the convergence accuracy ι;

[0170] Step S402: Base station m and base station j solve the convex optimization problem (P1.2) respectively to obtain the optimal transmission power and the optimal noise reduction factor and the optimal dual variable

[0171] Step S403: According to equations (16) and (17), base stations m and j each update T j,m Elements in

[0172] Step S404: Base station m and base station j exchange their respective T j,m The elements in T are reconstructed according to formula (15) j,m , and calculate t by (19) j,m ;

[0173] Step S405: Base station m and base station j update their respective interference temperature values ​​according to formula (18) to obtain the updated interference temperature value Γ′ j,m ;

[0174] Step S406: Repeat steps S402 to S405 until |T j,m |>ι, and will satisfy |T j,m The optimal transmission power and optimal noise reduction factor when |>ι are taken as the final optimal transmission power and optimal noise reduction factor;

[0175] Step S407: After traversing all base station pairs, repeat steps S402 to S406 to output the optimal transmission power and optimal noise reduction factor of each cell.

[0176] In essence, the distributed power control optimization scheme based on the interference temperature value of the present invention can gradually reduce the overall optimal gap of all base stations through pairwise interaction. Specifically, in each iteration, only a pair of selected base stations can adjust their interference temperature values ​​to reduce their respective optimal gaps while ensuring that the optimal gaps of other base stations are not adversely affected. Through this iterative update mechanism, the distributed power control optimization scheme of the present invention can gradually approach the Pareto frontier of the optimal gap interval, and the overall optimal gap is further optimized compared to the initial state (or the independent optimization scheme of a single cell). In addition, the distributed power control optimization scheme of the present invention can also encourage base stations to participate in collaboration, and even if some adjustments may involve a trade-off in their own interests, it can still promote the reduction of the optimal gap of the overall system.

[0177] The distributed collaborative interference management method for a multi-task airborne federated learning system of the present invention considers a parallel multi-task airborne federated learning scenario in which each cell independently performs training tasks, and utilizes a distributed power control optimization scheme based on interference temperature to improve the overall training performance of the system. First, the impact of the aggregation error of each cell on the learning performance of its local model is analyzed, and a communication parameter optimization model is constructed with the goal of minimizing the optimal gap of all cells. In order to characterize the performance balance between multiple tasks, the Pareto boundary theory is introduced for performance evaluation, and a distributed power control optimization scheme based on interference temperature is proposed. By decomposing the global coupling problem into local sub-problems that can be solved in parallel, each cell can independently adjust its power under the condition of relying only on local channel state information. In view of the non-convex characteristics of the second optimization problem, an analytical solution method based on Lagrangian duality theory is constructed, and combined with the dynamic update mechanism of interference temperature, an iterative approximation of the Pareto optimal boundary is achieved to effectively reduce the optimal gap of each cell, accelerate the model training process, and improve the overall cross-cell performance balance and learning performance of the multi-task system.

[0178] The following are specific simulation results of the jamming method of the multi-task airborne federated learning system of the present invention:

[0179] In the simulation, we consider the simplest multi-cell scenario with only two cells, where different federated learning tasks are performed between different cells. For the cell channel, we assume that the horizontal coordinates of the base station of the first cell are (0,0), and the horizontal coordinates of the base station of the second cell are (40,0), and the edge devices in each cell are randomly distributed in a circular area with a radius of 20 meters centered on the base station. For the channel between the edge device and the base station, the distance-based Rayleigh fading channel model is adopted, where the channel between the edge device in the cell and the connected base station is The interference channel between the edge device and the unconnected base station is where d m,k and dj,k represents the straight-line distance between edge device k and connected base station m and unconnected base station j, respectively. Parameter Ω0 = -60dB represents the path loss value at a reference distance of 10 meters. κ = 3 is the path loss exponent. The number of edge devices in each cell is K = 10, and the total number of edge devices is K tot =20, noise power at the base station Maximum power budget for edge devices Convergence accuracy ι=10 -9 , the optimal gap reduction ratio parameter l j,m =0.5, learning rate of cell 1 Learning rate of cell 2

[0180] In order to compare the performance and verify the effectiveness of the distributed power control optimization scheme proposed in this invention, the following three benchmark schemes are considered:

[0181] (1) Full transmission power scheme: Edge devices all use the maximum power budget for air calculation. This scheme does not require collecting any channel status and is the simplest power control scheme.

[0182] (2) Interference-ignoring power control scheme: Each base station only needs to obtain the channel state information of the edge devices in its own cell, does not cooperate with other base stations, and independently minimizes its own optimal gap while ignoring interference.

[0183] (3) No-over-the-air computing solution: The edge devices in each cell can losslessly transmit the device gradient signals of their local cell model and perform aggregate calculations directly on the corresponding target base station. This means that no over-the-air computing is involved in the entire communication process, and there is no inter-cell interference, thus ensuring the most ideal communication environment. This solution can quantify the optimal federated learning performance that can be achieved under ideal conditions with no communication loss and no inter-cell interference.

[0184] First, a multi-task ridge regression loss function is constructed in MATLAB. That is, the model parameters of each cell are independent and the data distribution is different. The sample loss function of cell m is defined as:

[0185]

[0186] The regularization hyperparameters are all set to ρ = 5 × 10 -5 ; Input sample vector for each cell Obey the independent and identically distributed Gaussian distribution, that is, The dimension of the federated learning model is set to C=20; the present invention distinguishes and generates labels for the two cells, and sets the correct labels of cell 1 and cell 2 as τ1=x1(2)+3x1(5)+0.2z and τ2=x2(3)+2x2(8)+4x2(10)+0.3z respectively; the data samples are evenly distributed among the edge devices, and the data volume of each edge device is Therefore, the total data volume of each cell The initial model of each cell is set to an all-zero vector; the performance evaluation indicators use the optimal gap and prediction error, where the prediction error represents the loss function value of the test set in machine learning.

[0187] Simulation 1 shows the optimal gap between two cells under different communication rounds N for different power control schemes (e.g. Figure 4 ) and prediction errors (as shown in Figure 5 The changing trend of .

[0188] As can be observed from the figure, as the number of communication rounds increases, the distributed power control optimization scheme proposed in the present invention shows a continuous downward trend in both indicators (i.e., optimal gap and prediction error), and the prediction error tends to converge in the high-round stage. This shows that: during the training process, the cell models of the two cells continuously approached the optimal solution on the training set, and ultimately showed good generalization performance on the test set; from the performance differences between different cells, cell 1 is always better than cell 2, both in terms of optimal gap and prediction error. This is mainly attributed to the simpler label of the cell 1 task itself and lower data noise, so lower optimal gap and prediction error can be achieved under the same training rounds.

[0189] Further comparison of the performance differences between the various power control schemes revealed that the distributed power control optimization scheme proposed in this invention significantly outperformed both the full power control scheme and the scheme that ignored inter-cell interference in both cells. Specifically, the distributed power control optimization scheme proposed in this invention not only reduced training error more quickly, bringing the model closer to the optimal model in the training set, but also demonstrated stronger generalization capabilities on the test set, manifested as smaller prediction errors. This advantage demonstrates the effectiveness of the distributed power control optimization scheme proposed in this invention in balancing training convergence speed with test generalization performance.

[0190] The figure also shows the upper bound of performance for the ideal, no-over-the-air computation scheme. At high communication rounds, the proposed distributed power control optimization scheme's prediction error is very close to the ideal benchmark, with only a slight difference. This demonstrates that even in the presence of real-world communication loss and interference, the proposed distributed power control optimization scheme can still approach optimal performance. In contrast, other comparison schemes still exhibit significant errors at high rounds, particularly the fixed power scheme, which exhibits slow error convergence and ultimately deviates from the ideal benchmark.

[0191] Simulation 2 depicts the optimal gap reachable interval between two cells when the communication round N = 100. By setting the profile variable of the existing centralized power control scheme to κ = [κ m ,1-κ m ], you can outline Figure 6 The Pareto frontier shown, where κ m =[0.001,0.01,0.1,0.3,0.4,0.5,0.6,0.7,0.9,0.99,0.999], and the lower left corner of the Pareto frontier is selected as the reference Pareto optimal point for the centralized solution.

[0192] From simulation 2, we can see that the no-over-the-air calculation scheme in the lower left corner represents the idealized learning performance, which is used to reflect the degree of closeness between the actual performance of each power control scheme and the ideal performance. It can be clearly observed that the distributed scheme proposed in this invention is closer to the Pareto optimal point than the scheme ignoring inter-cell interference and the full-power scheme, and the error with the Pareto optimal point is within 10 -4 This shows that the distributed power control optimization scheme proposed in the present invention can still stably approach the optimal performance of the centralized power control scheme without the need for coordination by an aggregation center (such as centralized control), thereby reflecting its practical application potential and engineering feasibility in communication resource-limited or cross-cell optimization. Relatively speaking, the scheme that ignores inter-cell interference only optimizes the performance of the cell and does not consider the impact of interference on neighboring cells. Therefore, its overall performance is inferior to the distributed power control optimization scheme proposed in the present invention. As the simplest fixed strategy, the full power control scheme does not perform any power regulation or interference management. Therefore, it does not achieve ideal results on both cell targets. It is the farthest from the Pareto frontier among all power control schemes and has the worst practicality.

[0193] Simulation 3 shows the convergence performance of the distributed power control optimization scheme proposed in this invention. Figure 7 FIG1 shows the changing trend of the optimal gap between cell 1 and cell 2 with the number of iteration rounds when the number of edge devices in the two cells is K=10 and K=20 respectively.

[0194] As can be seen from the figure, as the number of algorithm iterations increases, the four curves all show a monotonically decreasing trend, which indicates that the algorithm is constantly approaching the target optimal solution and reaches a stable state within about 30 rounds, with good convergence. From the comparison of different numbers of edge devices, it can be further observed that under the same rounds, the optimal gap when K=20 is significantly lower than that when K=10, indicating that more edge devices participating in the optimization can improve the overall performance of the system and make the final learning result closer to the optimal solution. This shows that the distributed power control optimization scheme proposed in the present invention has good scalability and can maintain performance advantages when the scale of edge devices is expanded. In addition, although the increase in the number of edge devices brings more complex collaborative computing and power regulation problems, resulting in a slight decrease in the convergence speed of the algorithm, it can still achieve stable convergence within a limited number of rounds. This phenomenon verifies the effectiveness and robustness of the distributed power control optimization scheme proposed in the present invention in complex multi-cell scenarios.

[0195] In summary, Simulation 3 effectively demonstrates that the distributed power control optimization scheme proposed in the present invention has good convergence characteristics and performance improvement capabilities under different edge device scales, which further confirms its applicability in coping with heterogeneous devices and scalability requirements in actual deployment.

[0196] Example 2

[0197] The jamming device of the multi-task airborne federated learning system of the present invention comprises:

[0198] Channel information acquisition unit: used to obtain channel information between each cell base station and associated edge devices based on the constructed multi-cell multi-task air federated learning model;

[0199] Interference temperature value acquisition unit: used to obtain the interference temperature value between base stations in each cell based on the constructed multi-cell multi-task air federated learning model;

[0200] Communication parameter optimization unit: used to construct a communication parameter optimization model based on the obtained channel information and interference temperature value, with minimizing the optimal gap as the optimization goal and the transmission power of the edge device and the noise reduction factor of the base station as the optimization variables; and select any base station pair, conduct information exchange between base stations through a distributed collaborative mechanism, adopt a distributed power control optimization scheme based on the interference temperature value, coordinate and update the interference temperature value between base stations through interference temperature negotiation between paired base stations, and calculate the optimal transmission power of the corresponding cell edge device and the optimal noise reduction factor of the base station based on the constructed communication parameter optimization model; traverse all base station pairs in turn, complete the coordinated optimization of the transmission power of edge devices and the noise reduction factor of base stations within the entire network, and obtain the optimal transmission power of each cell edge device and the optimal noise reduction factor of the base station;

[0201] Communication control unit: used to send the calculated optimal transmission power to the corresponding edge device and the calculated optimal noise reduction factor to the corresponding base station, so as to prompt the edge device to use its optimal transmission power to aggregate the device gradient signal to the target base station by air calculation and prompt the target base station to perform noise reduction processing on the received device gradient signal according to its optimal noise reduction factor to generate a new cell model and broadcast it to the associated edge device.

[0202] The above is a preferred embodiment of the present invention, but the embodiment of the present invention is not limited to the above content. Any other changes, modifications, substitutions, combinations, and simplifications that do not deviate from the spirit and principles of the present invention should be equivalent replacement methods and are included in the scope of protection of the present invention.

Claims

1. A distributed collaborative interference management method for a multi-task airborne federated learning system, characterized in that: The following steps are involved: Step S1: constructing a multi-cell multi-task air federated learning model, wherein each cell base station in the multi-cell multi-task air federated learning model broadcasts the corresponding cell model to the associated edge device; Step S2: Obtain channel information between each cell base station and associated edge devices, as well as interference temperature values ​​between each cell base station; Step S3: Based on the obtained channel information and interference temperature value, a communication parameter optimization model is constructed with minimizing the optimal gap as the optimization goal and the transmission power of the edge device and the noise reduction factor of the base station as the optimization variables; Step S4: Select any pair of base stations, exchange information between them through a distributed coordination mechanism, and adopt a distributed power control optimization scheme based on interference temperature values. Through interference temperature negotiation between paired base stations, coordinate and update the interference temperature values ​​between the base stations. Based on the established communication parameter optimization model, calculate the optimal transmission power of the corresponding cell edge device and the optimal noise reduction factor of the base station. Step S5: Repeat step S4 to loop through all base station pairs to complete the coordinated optimization of the transmission power of edge devices and the noise reduction factor of base stations across the entire network, so as to obtain the optimal transmission power of each cell edge device and the optimal noise reduction factor of each base station; Step S6: The base station sends the optimal transmission power to the associated edge device. The gradient calculation module of the associated edge device calculates the device gradient signal based on the input of the cell model. The communication control module on all edge devices in each cell performs over-the-air aggregation and transmission of the device gradient signal to the target base station based on the received optimal transmission power through over-the-air calculation. Step S7: The base station performs noise reduction processing on the received device gradient signal according to its own optimal noise reduction factor, and uses the cell model update module to update the cell model to obtain an updated cell model, and broadcasts the updated cell model to the associated edge devices.

2. The distributed collaborative interference management method for a multi-task airborne federated learning system according to claim 1, characterized in that: In step S1, the number of cells in the multi-cell multi-task air federated learning model is M, each cell is deployed with a base station, and each cell is deployed with K single-antenna edge devices, where the base station edge devices With the collaboration between edge devices and target base stations, each cell independently completes different learning tasks.

3. The distributed collaborative interference management method for a multi-task airborne federated learning system according to claim 2, characterized in that: In step S2, the steps of obtaining channel information between each cell base station and the associated edge device are: Step S201: Using the stochastic gradient descent algorithm, calculate the local loss function gradient of the random data of each edge device Where: Represents the size of the local mini-batch training set data; x i With ξ i Respectively represent The i-th data in and its correct label value; Represents when the cell model in edge device k takes When , the local loss function gradient is obtained based on the data and its correct label value; n is the nth round of global iteration, N is the maximum number of global iterations; Step S202: Calculate the local loss function gradient Perform normalization processing to obtain the normalized signal to be transmitted Where: is the mean of the local loss function gradient, C represents the dimension of the local loss function gradient, represents the standard deviation of the local loss function gradient, represent The c-th dimension signal of the vector; Step S203: Obtaining a normalized signal The c-th dimension signal and precoding factor in , to achieve channel pre-compensation and obtain the signal received by base station m in the cth time slot Where: represents the transmission power of edge device k, represents the channel coefficient from edge device k to base station m, and the superscript H represents the conjugate transpose; represents the complex symmetric Gaussian white noise of base station m; Represents the inter-cell interference signal caused by simultaneous transmission of the same resource block; Step S204: After receiving the signal, base station m responds to the signal of the cth time slot. Perform gradient linear estimation post-processing to obtain the scaled signal of base station m Where: represents the unbiased value of the cell gradient, represents the error in the gradient estimate, represents the noise reduction factor used by base station m for signal power alignment and noise power suppression; Step S205: scaling signal of base station m Perform the real part operation to obtain the gradient estimate of the cell gradient And according to the gradient estimate Update the cell model, where: Gradient estimate for: The updated cell model is: Where: is the real part operation; Here, the superscript T stands for ordinary transpose; represents the learning rate of base station m in the nth global iteration round; The steps to obtain the interference temperature value between base stations in each cell are as follows: Get the maximum interference power value of all edge devices associated with base station m to base station j as the interference temperature value Γ of base station j j,m ,in, Get the maximum interference power value of all edge devices associated with base station j to base station m as the interference temperature value Γ of base station m m,j .

4. The distributed collaborative interference management method for a multi-task airborne federated learning system according to claim 3, characterized in that: In step S3, the steps of constructing the communication parameter optimization model are: Step S301: Based on the channel information from the edge device to the target base station, a first optimization problem is constructed with minimizing the optimal gap as the optimization goal and the transmission power of the edge device and the noise reduction factor of the base station as optimization variables; Step S302: using the interference temperature value between base stations as an explicit constraint item of the first optimization problem to construct a second optimization problem; Step S303: introducing an inverse noise reduction factor and defining auxiliary variables to convert the second optimization problem into a convex optimization problem, thereby obtaining the communication parameter optimization model.

5. The distributed collaborative interference management method for a multi-task airborne federated learning system according to claim 4, characterized in that: In step S301, the steps of constructing the first optimization problem are: Step S301: Calculate the difference between the maximum global iteration round loss function and the optimal global iteration round loss function of base station m to obtain the optimal gap, and use the obtained optimal gap as the federated learning convergence performance indicator of base station m; wherein the upper bound of the optimal gap should meet the following conditions: Where: is the maximum global iteration round loss function of base station m; is the optimal global iteration round loss function of base station m; and satisfy represents the gradient variance; L m Indicates the smoothness of the loss function; Step S302: Represent the aggregation error in equation (8) Assume that the effective optimal gap needs to be optimized, and each round of global iteration is considered independent and can be optimized separately, omitting the superscript n of the global iteration round, so as to construct an optimization method with minimizing the optimal gap as the optimization goal and the transmission power p of the edge device as the optimization goal. k and the noise reduction factor θ of the base station m The first optimization problem for optimizing variables is: Where: The maximum power for each edge device.

6. The distributed collaborative interference management method for a multi-task airborne federated learning system according to claim 5, characterized in that: In step S302, the steps of constructing the second optimization problem are: The interference term in the first optimization problem Replace with Γ m,j , and define the edge device k associated with base station m, Interference channel to base station j This leads to the second optimization problem.

7. The distributed collaborative interference management method for a multi-task airborne federated learning system according to claim 6, characterized in that: In step S303, the steps for constructing the convex optimization problem are: Introducing the inverse noise reduction factor γ m =1 / θ m , and define auxiliary variables Rewrite the second optimization problem into a convex optimization problem: The convex optimization problem is the communication parameter optimization model.

8. The distributed collaborative interference management method for a multi-task airborne federated learning system according to claim 7, characterized in that: In step S4, the Lagrange dual method is used to solve the obtained convex optimization problem, and the following closed-form solution is obtained: Where: and is the optimal solution to the convex optimization problem; and are the dual variables and optimal dual variables corresponding to the interference temperature constraint of base station j, respectively, where, and are the dual variable and optimal dual variable corresponding to the transmission power constraint of edge device k, respectively; and are the optimal solutions for the transmission power of the edge device associated with base station m and the noise reduction factor of base station m, respectively.

9. The distributed collaborative interference management method for a multi-task airborne federated learning system according to claim 8, characterized in that: In step S4, the distributed power control optimization scheme based on the interference temperature value is: Step S401: Set the interference temperature vector Γ and the convergence precision ι, where Γ is a vector of size M(M-1)×1 containing all Γ j,m vector of Step S402: Base station m and base station j solve the convex optimization problem respectively to obtain the optimal transmission power and the optimal noise reduction factor and the optimal dual variable Step S403: According to equations (16) and (17), base station m and base station j each update T j,m The elements in , where Where: Γ m is a 2(M-1)×1 matrix containing all Γ j,m and Γ m,j vector of are the dual multipliers corresponding to the optimal interference temperature constraints of base station m and base station j respectively; Then they are the optimal inverse noise reduction factors corresponding to the optimal interference temperature value constraints of base station m and base station j respectively; For convex optimization problems at any given Γ m The optimal gap of base station m under the condition of ; For convex optimization problems at any given Γ j The optimal gap of base station j under the condition of ; Step S404: Base station m and base station j exchange their respective T j,m The elements in T are reconstructed according to formula (15) j,m , and calculate t by (19) j,m ; [C′ j,m ,C′ m,j ] T =[Γ j,m ,C m,j ] T +d j,m ·t j,m , (18) make Then we have: t j,m =sign(bc-ad)·[l j,m d-b,a-l j,m c] T , (19) Where: δ j,m represents the step size parameter; t j,m To meet T j,m t j,m Vectors with a value less than 0; e j,m is the ratio parameter that controls the optimal gap reduction between base stations m and j; sign(·) represents the sign function; Step S405: Base station m and base station j update their respective interference temperature values ​​according to formula (18) to obtain the updated interference temperature value Γ′ j,m ; Step S406: Repeat steps S402 to S405 until |T j,m |>ι, and will satisfy |T j,m The optimal transmission power and optimal noise reduction factor when |>ι are taken as the final optimal transmission power and optimal noise reduction factor; Step S407: After traversing all base station pairs, repeat steps S402 to S406 to output the optimal transmission power and optimal noise reduction factor of each cell.

10. A device for the distributed collaborative interference management method for a multi-task airborne federated learning system according to any one of claims 1 to 9, characterized in that: include: Channel information acquisition unit: used to obtain channel information between each cell base station and associated edge devices based on the constructed multi-cell multi-task air federated learning model; Interference temperature value acquisition unit: used to obtain the interference temperature value between base stations in each cell based on the constructed multi-cell multi-task air federated learning model; Communication parameter optimization unit: used to build a communication parameter optimization model based on the obtained channel information and interference temperature value, with minimizing the optimal gap as the optimization goal and the transmission power of the edge device and the noise reduction factor of the base station as the optimization variables; An arbitrary pair of base stations is selected, and information exchange between base stations is carried out through a distributed collaborative mechanism. A distributed power control optimization scheme based on interference temperature values ​​is adopted. Through interference temperature negotiation between paired base stations, the interference temperature values ​​between base stations are coordinated and updated. Based on the established communication parameter optimization model, the optimal transmission power of the corresponding cell edge device and the optimal noise reduction factor of the base station are calculated. All base station pairs are traversed in turn to complete the collaborative optimization of the transmission power of edge devices and the noise reduction factor of base stations across the entire network, so as to obtain the optimal transmission power of each cell edge device and the optimal noise reduction factor of the base station. Communication control unit: used to send the calculated optimal transmission power to the corresponding edge device and the calculated optimal noise reduction factor to the corresponding base station, so as to prompt the edge device to use its optimal transmission power to aggregate the device gradient signal to the target base station by air calculation and prompt the target base station to perform noise reduction processing on the received device gradient signal according to its optimal noise reduction factor to generate a new cell model and broadcast it to the associated edge device.

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