A method and system for dual-task concurrent covert transmission for aerial computing

Abstract

The application provides a double-task concurrent covert transmission method and system for air computing, and belongs to the technical field of wireless communication. The method comprises the following steps: acquiring channel state information of each wireless user to a base station and a eavesdropping node; configuring a single-task mode to execute a first task and calculate a reference receiving power of the eavesdropping node; configuring a double-task mode to execute the first task and a second task simultaneously, and the base station receives superimposed signals containing two types of task signals; the base station adopts a successive interference cancellation mode, decodes the first task first, and then decodes the second task after eliminating the component of the first task; a concealment constraint is constructed, so that the deviation of the receiving power of the eavesdropping node in the double-task mode from the reference power does not exceed a preset threshold; and the power allocation of each user and the receiving scaling factor of the base station are jointly optimized with the minimum calculation error of the second task as the target. The application uses the first task to cover the second task, does not need to introduce artificial noise, and is suitable for air computing scenes such as wireless sensor networks and federated learning.

Description

Technical Field

[0001] This invention belongs to the field of wireless communication technology, specifically relating to a dual-task concurrent covert transmission method and system for over-the-air computing. Background Technology

[0002] With the development of sixth-generation mobile communication systems, wireless networks need to support tasks such as data acquisition, model training, distributed sensing, and edge intelligent computing for large-scale intelligent terminals under limited spectrum resources. Over-the-air computing technology utilizes the natural superposition characteristics of wireless multiple access channels, allowing signals transmitted by multiple users to be naturally superimposed within the wireless channel. The base station can then directly recover the required function values ​​from the superimposed signals, thereby achieving the integration of communication and computing. Compared to traditional per-user data upload methods, over-the-air computing can significantly reduce communication overhead and improve spectrum utilization efficiency, demonstrating broad application prospects in scenarios such as wireless sensor networks, federated learning, and distributed data fusion.

[0003] However, over-the-air computing systems typically operate in open wireless environments, where user signals are superimposed and transmitted in the air, making them vulnerable to eavesdropping by unauthorized nodes. Existing physical layer security methods usually protect transmitted content from eavesdropping by introducing artificial noise or using encryption. However, these methods have the following drawbacks: First, artificial noise does not carry valid information and consumes valuable transmission power and spectrum resources, reducing system energy efficiency. Second, even if the transmitted content is protected by encryption, eavesdropping nodes can still infer whether the system is performing privacy-related computing tasks by monitoring changes in the received signal power, leading to information leakage. For example, when the system enters a specific computing mode, changes in the distribution of user transmission power will cause corresponding changes in the received signal power on both the base station side and the eavesdropping node side. Such changes in physical layer characteristics are difficult to conceal through upper-layer encryption. Once an eavesdropping node can determine the existence of sensitive computing behavior through power detection, even if it cannot crack the specific data content, the system's task privacy has already been exposed. Summary of the Invention

[0004] To address the aforementioned problems, this invention provides a dual-task concurrent covert transmission method and system for over-the-air computing.

[0005] To achieve the above objectives, the present invention provides a dual-task concurrent covert transmission method for over-the-air computing, comprising: The system parameters of the target air system and the first mission signal components sent by each wireless user are acquired; the system parameters include the first channel state information from each wireless user to the base station and the second channel state information from each wireless user to the eavesdropping node.

[0006] Based on the system parameters, the reference received signal power of the eavesdropping node in single-task mode is determined. In dual-task mode, the base station receives the superimposed signal of the first task signal component and the second task signal component simultaneously transmitted by each wireless user. The first task signal component is the computational task that does not need to be hidden, and the second task signal component is the computational task that needs to be hidden. Based on the amplitude consistency of each first task signal component, the base station adopts a continuous interference cancellation method to first decode the first task signal from the superimposed signal and then decode the second task signal. Based on the transmission power allocated by each wireless user to the first task signal and the second task signal in dual-task mode, and the second channel state information, the eavesdropping received signal power of the eavesdropping node in dual-task mode is determined. Based on the reference received signal power and the eavesdropping received signal power, a transmission concealment constraint is constructed.

[0007] With minimizing the calculation error of the second task signal as the optimization objective, and with the transmission concealment constraint and the calculation error of the first task signal not exceeding a preset error threshold as constraints, a joint optimization problem is constructed, and the joint optimization problem is solved to obtain the optimal transmission scheme.

[0008] Preferably, the transmission concealment constraint specifically means that the absolute value of the difference between the received signal power of the eavesdropping node and the reference received signal power in dual-task mode is not greater than a preset concealment error threshold.

[0009] Preferably, the reference received signal power is determined based on the second channel state information and the transmit power of each wireless user in single-task mode.

[0010] The amplitude consistency of each first task signal component means that, in dual-task mode, the transmit power allocated to the first task signal by each wireless user, after being adjusted by the first channel state information, has the same equivalent receive amplitude at the base station.

[0011] Preferably, the calculation error of the first task signal is determined based on the amplitude alignment deviation of the first task signal at the base station, the interference caused by the decoding of the first task signal by the second task signal, and the base station noise; the calculation error of the second task signal is determined based on the amplitude alignment deviation of the second task signal at the base station and the base station noise.

[0012] Preferably, the optimal transmission scheme includes the optimal transmit power allocated by each wireless user to the first task signal, the optimal transmit power allocated to the second task signal, and the optimal receive scaling factor at the base station; the optimal receive scaling factor at the base station includes a first scaling factor when decoding the first task signal and a second scaling factor when decoding the second task signal; the first scaling factor is determined based on the amplitude alignment constant, the transmit power allocated by each wireless user to the second task signal, the channel state information from each wireless user to the base station, and the base station noise; the second scaling factor is determined based on the transmit power allocated by each wireless user to the second task signal, the channel state information from each wireless user to the base station, and the base station noise.

[0013] Preferably, solving the joint optimization problem specifically includes: first, introducing an auxiliary variable to take the square root of the power variable, transforming the original optimization problem into a fractional programming problem; then, using the Dinkelbach method to transform the fractional programming problem into a subtractive iterative subproblem; and in each iteration, using the successive convex approximation method to perform a first-order Taylor expansion approximation on the non-convex terms of the subtractive iterative subproblem, transforming it into a convex optimization subproblem for solution; and restoring the original power variable after the iteration converges.

[0014] This invention also provides a dual-task concurrent covert transmission system for over-the-air computing, comprising: The data acquisition module is used to acquire the system parameters of the target air system and the first mission signal components sent by each wireless user; the system parameters include the first channel state information from each wireless user to the base station and the second channel state information from each wireless user to the eavesdropping node.

[0015] A dual-task module is used to determine the reference received signal power of the eavesdropping node in single-task mode based on the system parameters. In dual-task mode, the base station receives the superimposed signal of the first task signal component and the second task signal component simultaneously transmitted by each wireless user. The first task signal component is a computational task that does not need to be hidden, and the second task signal component is a computational task that needs to be hidden. Based on the amplitude consistency of each first task signal component, the base station adopts a continuous interference cancellation method to first decode the first task signal from the superimposed signal and then decode the second task signal. Based on the transmission power allocated by each wireless user to the first task signal and the second task signal in dual-task mode, and the second channel state information, the eavesdropping received signal power of the eavesdropping node in dual-task mode is determined. Based on the reference received signal power and the eavesdropping received signal power, a transmission concealment constraint is constructed.

[0016] The calculation module is used to construct a joint optimization problem with the goal of minimizing the calculation error of the second task signal, and with the constraints of transmission concealment and the condition that the calculation error of the first task signal is not greater than a preset error threshold, and to solve the joint optimization problem to obtain the optimal transmission scheme.

[0017] The present invention also provides a computer device, including a memory, a processor, and a computer program stored in the memory, wherein the processor executes the computer program to implement any of the steps of the dual-task concurrent covert transmission method for over-the-air computing.

[0018] The present invention also provides a computer-readable storage medium storing a computer program that, when loaded by a processor, is capable of executing any of the steps in the dual-task concurrent covert transmission method for over-the-air computing.

[0019] This invention provides a dual-task concurrent covert transmission method for over-the-air computing, which has the following advantages: Traditional solutions fail because both encryption and noise addition alter the transmission power—a physical characteristic most easily detected by eavesdroppers. However, this invention does not attempt to hide the existence of sensitive signals; instead, it makes the transmission behavior of sensitive signals completely indistinguishable from the normal system state at the physical layer. This invention masks the sensitive task (second task) by superimposing it on a non-sensitive task (first task), transmitting them simultaneously on the same frequency, and jointly optimizing the power allocation of the two types of tasks. This ensures that the received power of the eavesdropping end remains consistent in both states with and without sensitive tasks, fundamentally cutting off the eavesdropper's basis for inferring the existence of tasks through power detection. Simultaneously, the base station utilizes amplitude consistency and continuous interference cancellation to effectively separate and accurately decode the two types of tasks, achieving concealment, resource utilization efficiency, and computational accuracy without relying on artificial noise or increasing spectrum overhead. Attached Figure Description

[0020] To more clearly illustrate the embodiments and design schemes of the present invention, the accompanying drawings required for this embodiment will be briefly described below. The drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0021] Figure 1 This is a flowchart illustrating a dual-task concurrent covert transmission method for over-the-air computing according to an embodiment of the present invention; Figure 2 This is a schematic diagram illustrating the variation of the mean square error in the calculation of non-sensitive and sensitive tasks under different signal-to-noise ratios and the number of users in an embodiment of the present invention. Figure 3This is a schematic diagram illustrating the variation of the optimal receiving scaling factor at the base station under different signal-to-noise ratios and numbers of users according to an embodiment of the present invention. Figure 4 This diagram illustrates the variation in the average number of iterations of the iterative algorithm described in this invention under different signal-to-noise ratio conditions according to an embodiment of the invention. Detailed Implementation

[0022] To enable those skilled in the art to better understand and implement the technical solutions of the present invention, the present invention will be described in detail below with reference to the accompanying drawings and specific embodiments. The following embodiments are only used to more clearly illustrate the technical solutions of the present invention and should not be construed as limiting the scope of protection of the present invention.

[0023] This invention provides a dual-task concurrent covert transmission method for over-the-air computing. Instead of relying on additional artificial noise to mask the sensitive task (second task), this invention utilizes the non-sensitive task (first task) itself as cover for the sensitive task. Specifically, in dual-task mode, the non-sensitive and sensitive tasks are transmitted simultaneously and superimposed in the air. The base station recovers both tasks sequentially using a continuous interference cancellation method; while the eavesdropping node can only observe the received power of the superimposed signal. By constructing power matching constraints, the power variation received by the eavesdropping node in single-task and dual-task modes is controlled within a preset error range, thereby achieving covert transmission of the sensitive task.

[0024] It should be noted that, for ease of description, this invention divides the computational tasks to be transmitted by each wireless user into a first task and a second task. The first task is a computational task that does not require hiding its existence from eavesdropping nodes, and is referred to herein as a non-sensitive task; the second task is a computational task that requires hiding its existence from eavesdropping nodes, and is referred to herein as a sensitive task. Both the first and second tasks are over-the-air computational tasks that each wireless user must complete; the only difference between them is whether or not their existence needs to be hidden from eavesdropping nodes. The first task signal corresponds to the data signal of the first task, and the second task signal corresponds to the data signal of the second task. In the following formula derivation, the superscripts 0 and 1 are used to identify the relevant variables of the first and second tasks, respectively, for example... This indicates the transmit power allocated to the first mission. This indicates the transmit power allocated to the second mission.

[0025] Based on this, the dual-task concurrent covert transmission method for over-the-air computing provided by this invention comprises 17 steps, in the following order: inputting parameters and establishing a system model; establishing a single-task mode; calculating the reference power of the eavesdropping end; establishing a dual-task mode; constructing non-sensitive task error constraints; constructing SIC amplitude alignment conditions; eliminating non-sensitive task components; constructing a sensitive task error model; establishing transmission covert constraints; establishing a joint optimization problem; analytically solving for the optimal scaling factor; variable substitution and transformation into fractional programming; Dinkelbach and SCA iterative solutions; determining convergence; restoring variables and outputting the optimal transmission scheme. Specifically, as follows... Figure 1 As shown, it includes the following steps:

[0026] S1. Data Acquisition and Initialization The target air system enters a dual-task concurrent covert air computing process, preparing to perform system parameter initialization, single-task mode baseline calculation, dual-task concurrent modeling, and subsequent power allocation optimization.

[0027] The system parameters of the target air system and the first mission signal components sent by each wireless user are acquired; the system parameters include the first channel state information from each wireless user to the base station and the second channel state information from each wireless user to the eavesdropping node.

[0028] S2. Establish an air system model Construct a system consisting of a base station, An airborne computing system (target airborne system) consisting of one wireless user and one eavesdropping node. Each wireless user transmits task signals to the base station via a wireless multiple access channel. The base station utilizes the wireless superposition characteristics of airborne computing to recover the aggregation function. The eavesdropping node, located within the wireless coverage area, can receive the wireless signals transmitted by the users and attempts to determine whether the system is currently performing a sensitive task based on changes in the received signal power.

[0029] System input parameters include the number of users. , No. Channel fading coefficient from user to base station (First channel state information), the Channel fading coefficient from user to eavesdropping node (Second channel state information), user transmit power in single-task mode User power constraints in dual-task mode Base station noise power , Eavesdropping node noise power Error threshold for non-sensitive tasks and hidden error threshold .

[0030] For ease of subsequent formula description, the following notation conventions are adopted in this embodiment: Let the user set be... ,in, Indicates the total number of users. Indicates the user ID, and In the formula This indicates summing the corresponding items for all users. Indicates all All users in this article are valid. Represents the modulus of a complex number. Indicates the first Channel fading coefficient from user to base station, No. Channel fading coefficient from a user to the eavesdropping node; Indicates the noise power at the base station. This represents the noise power at the eavesdropping node. (In this article...) and The superscripts 0 and 1 are used to distinguish between non-sensitive and sensitive tasks, respectively, and are not used for exponential operations; the text in this article includes superscripts. The variable represents the first The variable values ​​in the next iteration, where This is the numbering of the inner layer iterations for the successive convex approximation. It should be noted that... In the middle, superscript Indicates complex conjugation; in , , , , and In the middle, superscript This indicates the optimal value of the corresponding variable.

[0031] In the simulation implementation, the channel coefficient and The model is an independent, flat Rayleigh fading channel, following a circularly symmetric complex Gaussian distribution with zero mean and unit variance; the maximum transmit power for each user is set as follows: ; The error threshold for non-sensitive tasks is set as follows: ; The concealment error threshold is set as follows: ; The signal-to-noise ratio is adjusted by changing the noise variance setting, which ranges from: ; in, This indicates the signal-to-noise ratio, expressed in dB.

[0032] Figure 2 , Figure 3 and Figure 4 The main comparison is the number of users. and System performance at that time.

[0033] S3. Establish single-task mode In single-task mode, the system only performs non-sensitive task calculations. The superimposed signal received by the base station is represented as follows:

[0034] ; in, This indicates that the base station receives signals in single-task mode. For the first Each user sends a normalized first task signal. For the first Precoding factor for each user Additive white Gaussian noise is used at the base station. To compensate for channel fading between the user and the base station, the precoding factor can be set as follows:

[0035] ; in, Indicates the first task in single-task mode Transmit power of each user express The conjugate of . Substituting this, the base station received signal can be written as:

[0036] ; The base station further employs a receive scaling factor. Scaling of the received signal and by the number of users. Normalization is then performed. The baseband signal at the receiving end is now:

[0037] ; The ideal aggregation result is: ; The mean square error in single-task mode is: ; This step is used to obtain the baseline transmission mode and base station reception characteristics for non-sensitive tasks in single-task mode.

[0038] in, This represents the actual normalized aggregation result obtained at the base station. This represents the ideal aggregation result. This represents the base station receive scaling factor in single-task mode. This represents the calculated mean square error between the actual polymerization result and the ideal polymerization result.

[0039] S4. Calculate the reference power of the eavesdropping device. In single-task mode, the eavesdropping node receives the following signal: ; in, The noise received at the eavesdropping node. Substituting the precoding factor, we have:

[0040] ; Therefore, the received power of the eavesdropping node in single-task mode is: ; in, Let represent the noise power at the eavesdropping node. Since noise exists in both single-task and dual-task modes, subsequent transmission concealment constraints primarily control the variation in the received signal power of the eavesdropping node in both modes. For ease of representation, the baseline for the pure signal power received by the eavesdropping node in single-task mode is defined as:

[0041] ; It should be noted that, It is not an optimization variable in the dual-task mode of this invention, but rather a power allocation result obtained from an existing in-flight computational power control method in the single-task mode, which serves as a benchmark for covert matching in this invention.

[0042] in, This indicates that the eavesdropping node receives signals in single-task mode. This indicates that the eavesdropping node receives noise. This represents the total received power of the eavesdropping node in single-task mode. This represents the pure signal power reference received by the eavesdropping node in single-task mode.

[0043] S5. Establish dual-task mode In dual-task mode, the system executes both non-sensitive and sensitive tasks simultaneously. Non-sensitive tasks are denoted as:

[0044] ; Sensitive tasks are denoted as: ; in, This represents the target aggregation function for non-sensitive tasks. The target aggregation function represents the sensitive task. Indicates the first The first task signal for each user Indicates the first Sensitive task signals for each user. Each user divides the transmission power into two parts: For non-sensitive tasks, Used for sensitive tasks. Considering channel compensation and receiver noise, the base station received signal in dual-task mode is represented as:

[0045] ; in, This is the receiver scaling factor during the decoding phase of a non-sensitive task. This indicates the transmit power allocated to non-sensitive tasks. This indicates the transmit power allocated to sensitive missions. The superscripts 0 and 1 are only used to distinguish mission types and are not exponential.

[0046] S6. Constructing error constraints for non-sensitive tasks In dual-task mode, the base station first decodes the non-sensitive task. At this time, sensitive tasks and received noise This is considered an equivalent disturbance. The mean square error for non-sensitive tasks is:

[0047] To ensure that non-sensitive tasks can be reliably decoded, a computational error constraint for non-sensitive tasks is set: ; in, This represents the allowable computational error threshold for non-sensitive tasks. In the simulation implementation, Corresponding number of users hour Number of users hour .

[0048] S7. Constructing SIC amplitude alignment conditions To ensure that non-sensitive tasks can be completely removed from the received signal after decoding through continuous interference cancellation, the first task signals of all users need to have the same equivalent received amplitude at the base station. Therefore, the following amplitude alignment condition is set:

[0049] ; in, Let be the amplitude alignment constant. From this, we obtain:

[0050] ; This equation shows that the power allocated to non-sensitive tasks is determined by the amplitude alignment constant. This condition is determined by the channel gain from the user to the base station. It also forms the basis for subsequent variable elimination.

[0051] S8. Eliminate non-sensitive task components. In non-sensitive tasks After successful decoding, the base station removes non-sensitive task components from the received signal to obtain the remaining sensitive task signal: ; Combining the amplitude alignment condition in S7, the above equation can be further written as: ; In other words, after eliminating non-sensitive task components, the remaining signal at the base station mainly consists of sensitive task signals and received noise, providing a basis for subsequent sensitive task decoding.

[0052] S9. Constructing a sensitive task error model The base station uses a different receiver scaling factor. For sensitive tasks Decode the code. The mean square error of the sensitive task is expressed as:

[0053] in, This represents the receiver scaling factor during the sensitive task decoding phase. This represents the mean square error between the actual calculation result and the ideal aggregation result for the sensitive task.

[0054] This invention calculates the mean square error by minimizing the sensitive task. The goal is to improve the computational accuracy of sensitive tasks while meeting the requirements for covert and non-sensitive task decoding.

[0055] S10. Establish transmission concealment constraints In dual-task mode, the eavesdropping node receives the following signal: ; Its receiving power is: ; To prevent eavesdropping nodes from determining the presence of sensitive tasks through changes in received power, this invention requires that the received power of the eavesdropping node in dual-task mode remain close to that in single-task mode. Since both modes include eavesdropping noise power, the concealment constraint can be written as:

[0056] ; in, This represents the total power received by the eavesdropping node in dual-task mode. This indicates the permissible threshold for concealed power deviation.

[0057] In the simulation implementation, the concealment error threshold is set as follows: ; This constraint means that the difference in received power observed by the eavesdropping node in dual-task mode and single-task mode is limited to a small range, thereby reducing the likelihood of sensitive tasks being detected.

[0058] S11. Establishing a joint optimization problem Based on the above model, this invention establishes a joint transmit power allocation and receiver scaling factor optimization problem. The optimization variables include the power allocation variables for all users. , Receive scaling factor , and amplitude alignment constant The optimization objective is:

[0059] ; The constraints include: ; ; ; ; ; in, For the first The maximum transmit power for each user. In the simulation embodiment, the power limit for each user is set as follows:

[0060] ; S12. Analytical solution for the optimal scaling factor The variable in the upper right corner of this step It represents the optimal value of the corresponding variable, not the complex conjugate; complex conjugate only exists when... In use, according to the amplitude alignment condition in S7: ; Can Eliminate it from the optimization problem. Substitute it into... Afterwards, Taking the partial derivative and setting it to zero, we can obtain the optimal receive scaling factor for the decoding stage of the non-sensitive task:

[0061] ; Similarly, for In Optimization can be performed to obtain the optimal receive scaling factor for the sensitive task decoding stage: ; Furthermore, Substituting the non-sensitive task error constraints, we get: ; This expression must satisfy the following condition to be true. That is, the error threshold for non-sensitive tasks. The settings should meet .Will Substituting the sensitive task error expression, minimize It can be equivalently transformed into maximizing the subsequent fractional objective.

[0062] S13. Variable substitution and transformation into fractional programming. To facilitate the solution, auxiliary variables are introduced: ; in, Indicates the power of sensitive tasks The square root, Indicates amplitude alignment constant The square of.

[0063] but: ; The optimization objective can be transformed into: Meanwhile, the error constraint for non-sensitive tasks is transformed into: ; The implicit constraint is transformed into: The power constraint is transformed into: and: in: ; This represents the pure signal power reference received by the eavesdropping node in single-task mode.

[0064] S14, Dinkelbach and SCA iterative solutions definition: ; The original fractional objective can be expressed as: The Dinkelbach method is used, and auxiliary variables are introduced. The fractional programming problem is transformed into a series of subtraction subproblems: ; In each outer iteration, the fixed Solve the current subproblem and use the current optimal solution. renew: ; when When the value is less than the set threshold, the outer iteration terminates.

[0065] because Since the function is convex, directly maximizing a convex function would lead to a non-convex problem. Furthermore, the lower bound in the implicit constraints also contains a non-convex structure. Therefore, a successive convex approximation method is further employed. Given the ... Second inner iteration point ,right Construct its linear lower bound by performing a first-order Taylor approximation:

[0066] ; in: ; At the same time, Make a first-order linear approximation: ; Therefore, the original non-convex subproblem can be transformed into a convex quadratic constrained quadratic programming problem, and solved iteratively using convex optimization solvers such as CVX.

[0067] In the simulation embodiment, the termination condition of the outer Dinkelbach method is set as follows: ; Or, if the maximum number of iterations (10) is reached; the termination condition for the inner SCA method is set as follows: ; Or reach the maximum number of iterations, 20 times.

[0068] S15. Determine if convergence has occurred. After each round of joint Dinkelbach and SCA iterations, it is determined whether the current solution satisfies the outer and inner convergence conditions. If the convergence conditions are not met, the process returns to S14 and continues to update the Dinkelbach parameters. Find the SCA local linearization point and the solution to the convex optimization subproblem; if the convergence condition is met, proceed to S16, restore the original variables and output the results.

[0069] S16. In this step, the upper right corner This represents the optimal value obtained after the algorithm converges, restores the variables, and outputs the optimal transmission scheme: Once the algorithm converges, the optimal variables are obtained. and Further restore the original variables: ; ; in, Indicates the first The optimal sensitive task power square root variable for each user This represents the optimal magnitude-aligned squared variable. Indicates the first Optimal power allocated to sensitive tasks for each user. Indicates the first The optimal power allocated to non-sensitive tasks by each user.

[0070] And calculate the optimal receiver scaling factor according to the formula in S12: ; The final output is the optimal power allocation scheme for the dual-task concurrent covert aerial computing system: ; And the base station receiving scaling factor: ; S17. Complete the parameter solving and output of the optimal transmission scheme for the dual-task concurrent covert transmission method for over-the-air computing.

[0071] like Figure 2 As shown, this invention statistically analyzes the actual mean square error of calculations for non-sensitive and sensitive tasks under different signal-to-noise ratios (SNR) and user numbers. The SNR range in the simulation is set from 0 dB to 20 dB. The number of users is also compared. and The results show that as the signal-to-noise ratio increases, the mean square error of the sensitive task calculation also increases. Gradually reduce, and calculate mean square error for non-sensitive tasks. Basically maintained at the corresponding threshold Nearby. This indicates that in When the optimal condition is reached, the error constraint for non-sensitive tasks is... The system is typically in an active state, meaning it allocates more communication resources to sensitive tasks while ensuring that non-sensitive tasks are "just decodable," in order to reduce computational distortion in sensitive tasks.

[0072] like Figure 3 As shown, this invention further provides the optimal receive scaling factor under different signal-to-noise ratios and different numbers of users, including the non-sensitive task decoding stage. and the sensitive task decoding stage Simulation results show that the optimal receiver scaling factor generally decreases as the signal-to-noise ratio (SNR) increases. Under low SNR conditions, for example... At high signal-to-noise ratios (SNRs), received noise is the primary factor affecting calculation errors, thus requiring a larger receive scaling factor to reduce its impact. Under medium-to-high SNR conditions, the influence of received noise weakens, and a smaller receive scaling factor provides greater adjustment space for transmitter power allocation, thereby reducing errors caused by user amplitude mismatch. Meanwhile, under the same SNR conditions, Usually greater than This is because of solving At that time, the power of sensitive tasks is considered as additional interference in the decoding stage of non-sensitive tasks; while solving At that time, non-sensitive tasks have been removed through continuous interference cancellation, and the remaining interference at the receiver mainly comes from thermal noise.

[0073] like Figure 4 As shown, this invention statistically analyzes the average number of iterations of the iterative algorithm. Since this invention employs Dinkelbach outer iteration and successive convex approximation inner iteration, and utilizes CVX to solve the convex subproblems, the average number of iterations can be used as a measure of computational complexity. Simulation results show that, in to Within the specified signal-to-noise ratio range, both the outer Dinkelbach iteration and the inner SCA iteration maintain a low average number of iterations, converging to a stable point with acceptable complexity. However, the average number of iterations increases with increasing signal-to-noise ratio. This is because as noise power decreases, the stable term in the denominator of the fractional objective decreases, making the optimal ratio more sensitive to changes in the variable, requiring the outer Dinkelbach to search for more roots in S; simultaneously, lower noise expands the feasible region for transmit power, requiring the inner SCA to gradually approach the convergence point through a more refined local linear approximation.

[0074] In summary, this embodiment demonstrates that the present invention can effectively reduce the mean square error of sensitive task computation under the condition of strictly satisfying the concealment constraint and the non-sensitive task error constraint; at the same time, the proposed Dinkelbach and successive convex approximation joint iterative algorithm has a low average number of iterations and good engineering implementation feasibility.

[0075] This invention addresses the problem of sensitive tasks in over-the-air computing systems under open wireless environments being easily detected by eavesdropping nodes. It proposes a dual-task concurrent covert transmission method for over-the-air computing. This method utilizes the superposition characteristics of over-the-air computing signals to divide the system operation into single-task and dual-task modes. In single-task mode, the system executes only non-sensitive tasks; in dual-task mode, the system executes both non-sensitive and sensitive tasks simultaneously. By rationally designing the user transmit power and the base station receiver scaling factor, the signal power received by eavesdropping nodes remains similar in both modes, making it difficult for them to determine whether the system is executing a sensitive task.

[0076] In summary, this invention proposes a covert aerial computing scheme that combines over-the-air computing, dual-task concurrent transmission, and eavesdropping terminal received power matching constraints. The method includes steps such as system modeling, single-task mode transmission, dual-task mode transmission, continuous interference cancellation decoding, covertness constraint construction, and joint power allocation and receiver scaling factor optimization. In single-task mode, the system only computes non-sensitive tasks; in dual-task mode, the system computes both non-sensitive and sensitive tasks simultaneously. The base station uses continuous interference cancellation to first decode non-sensitive tasks, then eliminates non-sensitive task components, and further decodes sensitive tasks. To prevent eavesdropping nodes from determining the existence of sensitive tasks through changes in received power, this invention keeps the received power of the eavesdropping node in dual-task mode close to that in single-task mode, thereby achieving covert protection of sensitive computing behavior. Addressing the non-convexity and fractional objective structure in the joint power allocation and receiver scaling factor optimization problem, this invention solves the problem using variable elimination, fractional programming, Dinkelbach iteration, and successive convex approximation methods. This method does not require the introduction of additional artificial noise, and can reduce the mean square error of calculations for sensitive tasks while ensuring the accuracy of calculations for non-sensitive tasks, thereby improving the spectrum utilization, resource utilization efficiency, and physical layer security performance of the over-the-air computing system.

[0077] The present invention proposes a dual-task concurrent covert transmission method for over-the-air computing, which, compared with the traditional scheme of protecting over-the-air computing security through artificial noise, has the following technical advantages: First, this invention utilizes non-sensitive tasks as a natural cover for sensitive tasks, eliminating the need to send artificial noise that does not carry valid information, thereby improving the efficiency of communication resource utilization.

[0078] Secondly, by setting up single-task mode and dual-task mode, the present invention enables the system to execute sensitive tasks concurrently while performing non-sensitive tasks, thereby improving the spectrum utilization of the over-the-air computing system.

[0079] Third, by constructing a power matching constraint for the eavesdropping node, the present invention ensures that the power observed by the eavesdropping node in single-task mode and dual-task mode remains close, making it difficult to determine whether a sensitive task is being computed, thus achieving covert protection of the computation behavior of sensitive tasks.

[0080] Fourth, the present invention employs a continuous interference cancellation method at the base station end, first decoding non-sensitive tasks, then eliminating non-sensitive task components and decoding sensitive tasks, so that dual-task concurrent computation can be completed in the same radio resource.

[0081] Fifth, this invention optimizes the joint power allocation and receiver scaling factor through variable elimination, fractional programming, Dinkelbach iteration, and successive convex approximation methods, which can reduce the mean square error of computation for sensitive tasks while meeting the computational accuracy and concealment requirements of non-sensitive tasks.

[0082] Sixth, this invention is applicable to over-the-air computing scenarios that require balancing computational efficiency and privacy protection, such as large-scale wireless sensor networks, edge intelligence, federated learning, and distributed data fusion.

[0083] Based on the same inventive concept, this invention also provides a dual-task concurrent covert transmission system for over-the-air computing, comprising: The data acquisition module is used to acquire the system parameters of the target air system and the first mission signal components sent by each wireless user; the system parameters include the first channel state information from each wireless user to the base station and the second channel state information from each wireless user to the eavesdropping node.

[0084] A dual-task module is used to determine the reference received signal power of the eavesdropping node in single-task mode based on the system parameters. In dual-task mode, the base station receives the superimposed signal of the first task signal component and the second task signal component simultaneously transmitted by each wireless user. The first task signal component is a computational task that does not need to be hidden, and the second task signal component is a computational task that needs to be hidden. Based on the amplitude consistency of each first task signal component, the base station adopts a continuous interference cancellation method to first decode the first task signal from the superimposed signal and then decode the second task signal. Based on the transmission power allocated by each wireless user to the first task signal and the second task signal in dual-task mode, and the second channel state information, the eavesdropping received signal power of the eavesdropping node in dual-task mode is determined. Based on the reference received signal power and the eavesdropping received signal power, a transmission concealment constraint is constructed.

[0085] The calculation module is used to construct a joint optimization problem with the goal of minimizing the calculation error of the second task signal, and with the constraints of transmission concealment and the condition that the calculation error of the first task signal is not greater than a preset error threshold, and to solve the joint optimization problem to obtain the optimal transmission scheme.

[0086] This invention also provides a computer device, which, at the hardware level, includes a processor, an internal bus, a network interface, memory, and non-volatile storage, and may also include other hardware required for business operations. The processor reads the corresponding computer program from the non-volatile storage into the memory and then runs it to implement the above-mentioned dual-task concurrent covert transmission method for over-the-air computing.

[0087] The present invention also provides a computer-readable storage medium storing a computer program that can be used to execute the above-described dual-task concurrent covert transmission method for over-the-air computing.

[0088] Specific limitations on the computing system for the dual-task concurrent covert transmission method for over-the-air computing can be found in the limitations described above for the dual-task concurrent covert transmission method for over-the-air computing, and will not be repeated here. Each module in the aforementioned dual-task concurrent covert transmission system for over-the-air computing can be implemented entirely or partially through software, hardware, or a combination thereof. These modules can be embedded in or independent of the processor in the computer device, or stored in the memory of the computer device as software, so that the processor can call and execute the corresponding operations of each module.

[0089] The technical features of the above embodiments can be combined arbitrarily. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as the combination of these technical features does not contradict each other, it should be considered within the scope of this specification. Furthermore, the above embodiments only illustrate several implementation methods of this application, and their descriptions are relatively specific and detailed, but they should not be construed as limiting the scope of the invention patent. It should be noted that those skilled in the art can make several modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this patent application should be determined by the appended claims.

Claims

1. A dual-task concurrent covert transmission method for over-the-air computing, characterized in that, Includes the following steps: Acquire the system parameters of the target air system and the first mission signal components transmitted by each wireless user; the system parameters include the first channel state information from each wireless user to the base station and the second channel state information from each wireless user to the eavesdropping node. Based on the system parameters, determine the reference received signal power of the eavesdropping node in single-task mode; In dual-task mode, the base station receives the superimposed signal of the first task signal component and the second task signal component simultaneously transmitted by each wireless user; the first task signal component is the computation task that does not need to be hidden, and the second task signal component is the computation task that needs to be hidden; based on the amplitude consistency of each first task signal component, the base station adopts a continuous interference cancellation method to first decode the first task signal from the superimposed signal, and then decode the second task signal; based on the transmission power allocated by each wireless user to the first task signal and the second task signal in dual-task mode, and the second channel state information, the eavesdropping received signal power of the eavesdropping node in dual-task mode is determined; based on the reference received signal power and the eavesdropping received signal power, a transmission concealment constraint is constructed; With minimizing the calculation error of the second task signal as the optimization objective, and with the transmission concealment constraint and the calculation error of the first task signal not exceeding a preset error threshold as constraints, a joint optimization problem is constructed, and the joint optimization problem is solved to obtain the optimal transmission scheme.

2. The dual-task concurrent covert transmission method for over-the-air computing according to claim 1, characterized in that, The transmission concealment constraint is specifically defined as follows: the absolute value of the difference between the received signal power of the eavesdropping node and the reference received signal power in dual-task mode is not greater than a preset concealment error threshold.

3. The dual-task concurrent covert transmission method for over-the-air computing according to claim 1, characterized in that, The reference received signal power is determined based on the second channel state information and the transmit power of each wireless user in single-task mode.

4. The dual-task concurrent covert transmission method for over-the-air computing according to claim 1, characterized in that, The amplitude consistency of each first task signal component means that, in dual-task mode, the transmit power allocated to the first task signal by each wireless user, after being adjusted by the first channel state information, has the same equivalent receive amplitude at the base station.

5. The dual-task concurrent covert transmission method for over-the-air computing according to claim 1, characterized in that, The calculation error of the first task signal is determined by the amplitude alignment deviation of the first task signal at the base station, the interference caused by the decoding of the first task signal by the second task signal, and the base station noise. The calculation error of the second task signal is determined by the amplitude alignment deviation of the second task signal at the base station and the base station noise.

6. The dual-task concurrent covert transmission method for over-the-air computing according to claim 1, characterized in that, The optimal transmission scheme includes the optimal transmit power allocated by each wireless user to the first task signal, the optimal transmit power allocated to the second task signal, and the optimal receive scaling factor at the base station. The optimal receive scaling factor at the base station includes a first scaling factor when decoding the first task signal and a second scaling factor when decoding the second task signal. The first scaling factor is determined based on the amplitude alignment constant, the transmit power allocated by each wireless user to the second task signal, the channel state information from each wireless user to the base station, and the base station noise. The second scaling factor is determined based on the transmit power allocated by each wireless user to the second task signal, the channel state information from each wireless user to the base station, and the base station noise.

7. A dual-task concurrent covert transmission method for over-the-air computing according to claim 1, characterized in that, Solving the joint optimization problem specifically includes: first, introducing auxiliary variables to take the square root of the power variable, transforming the original optimization problem into a fractional programming problem; then, using the Dinkelbach method to transform the fractional programming problem into a subtractive iterative subproblem; and in each iteration, using the successive convex approximation method to perform a first-order Taylor expansion approximation on the non-convex terms of the subtractive iterative subproblem, transforming it into a convex optimization subproblem for solution; and restoring the original power variable after the iteration converges.

8. A dual-task concurrent covert transmission system for over-the-air computing, characterized in that, include: The data acquisition module is used to acquire the system parameters of the target air system and the first mission signal components sent by each radio user; The system parameters include the first channel status information from each wireless user to the base station and the second channel status information from each wireless user to the eavesdropping node. The dual-task module is used to determine the reference received signal power of the eavesdropping node in single-task mode based on the system parameters. In dual-task mode, the base station receives the superimposed signal of the first task signal component and the second task signal component simultaneously transmitted by each wireless user; the first task signal component is the computation task that does not need to be hidden, and the second task signal component is the computation task that needs to be hidden; based on the amplitude consistency of each first task signal component, the base station adopts a continuous interference cancellation method to first decode the first task signal from the superimposed signal, and then decode the second task signal; based on the transmission power allocated by each wireless user to the first task signal and the second task signal in dual-task mode, and the second channel state information, the eavesdropping received signal power of the eavesdropping node in dual-task mode is determined. Based on the reference received signal power and the eavesdropped received signal power, a transmission concealment constraint is constructed; The calculation module is used to construct a joint optimization problem with the goal of minimizing the calculation error of the second task signal, and with the constraints of transmission concealment and the condition that the calculation error of the first task signal is not greater than a preset error threshold, and to solve the joint optimization problem to obtain the optimal transmission scheme.

9. A computer device, comprising a memory, a processor, and a computer program stored in the memory, characterized in that, The processor executes the computer program to implement the steps of the method according to any one of claims 1 to 7.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is loaded by the processor, it is able to perform the steps of the method according to any one of claims 1 to 7.

Images