A signal transmission method and system for two-way relay collaborative secure air computing

Abstract

The present invention relates to the field of over-the-air computing technology, and more specifically to a signal transmission method and system for bidirectional relay-coordinated secure over-the-air computing. The method comprises: in a first time slot, a sensor sends its pre-processed sensor data to a relay, while a target user simultaneously sends a multicast signal with a beamformer to the relay, and a friendly interference node sends an interference signal to the relay and an eavesdropper; in a second time slot, the relay broadcasts a received signal multiplied by a beamforming matrix and sends it to the target user and sensor; under the constraints that the eavesdropper's minimum computational distortion is greater than a given threshold and that the transmit power of all nodes cannot exceed their budget, the computational distortion of the target user is minimized. The present invention enables the target user to receive an accurate aggregated signal, ensuring the secure transmission of multicast signals based on over-the-air computing.

Description

Technical Field

[0001] The present invention relates to the field of airborne computing technology, and in particular to a signal transmission method and system for bidirectional relay collaborative secure airborne computing. Background Art

[0002] By utilizing the characteristics of wireless signals on multiple access channels, air computing technology achieves efficient integration of sensor data distributed in the Internet of Things network, significantly improves the efficiency of spectrum resource utilization, and greatly reduces data transmission latency.

[0003] In traditional wireless communications, relay technology focuses on data decoding, improving confidentiality, and ensuring communication reliability. However, in airborne computing networks, its role is to ensure the secure aggregation of sensor data, which is directly linked to the degree of distortion in the calculation results at the receiving end. However, traditional relay-assisted communications require decoding each data source. When data from multiple sensors is aggregated or processed at the relay, it may be eavesdropped or tampered with by eavesdroppers. In practical applications, although the data can be decoded, the quality and accuracy of the received data cannot be guaranteed, which makes it unsuitable for some applications with high data accuracy requirements. Summary of the Invention

[0004] In order to solve the above technical problems, the purpose of the present invention is to provide a signal transmission method and system for bidirectional relay collaborative secure over-the-air computing. The technical solutions adopted are as follows:

[0005] In a first aspect, the present invention provides a signal transmission method for bidirectional relay collaborative secure over-the-air computing, comprising:

[0006] In the first time slot, the sensor sends the pre-processed sensing data to the relay, the target node sends the signal data with the beamformer to the relay, and the interference node sends the interference signal data to the relay and the eavesdropper;

[0007] In the second time slot, the relay sends the received data in combination with the beamforming matrix to the target node and sensor, and the eavesdropper receives the interfered superposition signal;

[0008] When the deviation between the interfered superimposed signal received by the eavesdropper and the original signal data sent by the target node or sensor meets the threshold requirement, an optimization problem is solved; the optimization problem is to minimize the deviation between the signal received by the target node and the original signal sent by optimizing the allocated power of each sensor, target node, relay and interfering node.

[0009] Preferably, in the first time slot, the superimposed signal received by the relay is:

[0010]

[0011] Among them, y R represents the superimposed signal received by the relay, K represents the total number of sensors, b k represents the emission coefficient of the kth sensor, s k represents the sensor data with zero mean and unit variable sent by the kth sensor to the relay, s B represents the signal data transmitted by the target node to the relay, w represents the beamforming vector of the target node; s J represents the interference signal data transmitted by the interference node to the relay, V represents the beamforming vector of the interference node; h kR 、h BR and h JR denote the channel coefficients from the kth sensor, target node and interference node to the relay, n R Represents the additional noise signal relayed out; R represents the relay, B represents the target node, and J represents the interference node.

[0012] Preferably, in the second time slot, after the target node receives the signal sent by the relay, it eliminates the self-interference signal and the interference signal of the interfering node to obtain the transmission signal of the target node, specifically:

[0013]

[0014] Among them, y B ′ represents the transmission signal of the target node, F represents the beamforming matrix of the relay, n B represents the additional noise of the target node.

[0015] Preferably, the interfered superimposed signal received by the eavesdropper is specifically represented as:

[0016]

[0017] Among them, y E represents the interfered superposition signal received by the eavesdropper, E represents the eavesdropper, h RE represents the channel coefficient from the relay to the eavesdropper, n E represents the additional noise of the eavesdropper.

[0018] Preferably, the mean square error of the target node is expressed as:

[0019]

[0020] Among them, MSE B represents the mean square error of the target node, represents the arithmetic sum of sensor data; Indicates the value of the beamforming vector d aggregate received by the target node, represents the conjugate transpose of the beamforming vector d, Represents conjugate transpose, which is used to adjust the change of signal phase; represents the variance of the noise at the relay, represents the variance of the noise at the target user, Represents the expected value operation.

[0021] Preferably, the mean square error of the eavesdropper is expressed as:

[0022]

[0023] Among them, MSE E represents the mean square error of the eavesdropper, represents the value aggregated by the received beamforming vector a at the eavesdropper, represents the conjugate transpose of the beamforming vector a; represents the variance of the noise at the eavesdropper.

[0024] Preferably, when the mean square error of the eavesdropper meets the threshold requirement, the transmission power of all nodes does not exceed the corresponding transmission power, specifically including:

[0025]

[0026] |b k | 2 ≤P k ,k=1,...K

[0027] |w| 2 ≤P B

[0028] |V| 2 ≤P J

[0029]

[0030] Among them, ξ E Indicates the minimum calculated distortion threshold of the eavesdropper, P k represents the transmission power of the kth sensor, P B represents the transmission power of the target node, P J represents the transmission power of the interfering node, P R Indicates the transmission power of the relay.

[0031] In the second aspect, the present invention provides a signal transmission system for bidirectional relay collaborative secure air computing, which includes a multi-antenna bidirectional relay, an interference node, multiple sensors and a multi-antenna target user; the secure signal transmission system is used to implement the steps of a signal transmission method for bidirectional relay collaborative secure air computing.

[0032] The embodiments of the present invention have at least the following beneficial effects:

[0033] The present invention achieves bidirectional signal transmission through trusted bidirectional relays and the assistance of friendly interfering nodes. Since the interference signals sent by the friendly interfering nodes are pre-agreed, and under perfect CSI conditions, the target user can completely eliminate the interference signals from both the self-interference signals and those sent by the interfering nodes. If the target user's transmit power is sufficiently high, the sensor can simultaneously identify the strongest signal using a method similar to the first step of serial interference cancellation (SIC). After recovering the target user's signal, the sensor subtracts this signal from the total received signal. Next, the serial interference cancellation (SIC) method is used to eliminate other interference signals, retaining only the useful signal sent by the target user. The transmission variables of all nodes and the aggregated variables sent by the relay and received by the target user and the eavesdropper are jointly optimized. Under the constraint that the transmit power of all nodes cannot exceed their budgets, the eavesdropper's minimum computational distortion is set to exceed a given threshold, thereby preventing the eavesdropper from obtaining an accurate transmission signal. Ultimately, the computational distortion of the target user is minimized, allowing the target user to receive an accurate aggregated signal, thereby ensuring the secure transmission of multicast signals based on over-the-air computation. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] In order to more clearly illustrate the technical solutions and advantages of the embodiments of the present invention or the prior art, the following briefly introduces the drawings required for use in the embodiments or the prior art descriptions. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0035] Figure 1 This is a flowchart of the steps of a signal transmission method for bidirectional relay cooperative secure air computing provided by the present invention;

[0036] Figure 2 It is a model schematic diagram of a signal transmission system for bidirectional relay cooperative secure air computing provided by the present invention. DETAILED DESCRIPTION

[0037] To further illustrate the technical means and effectiveness of the present invention to achieve its intended purpose, the following, in conjunction with the accompanying drawings and preferred embodiments, describes in detail the specific implementation, structure, features, and effectiveness of a signal transmission method and system for bidirectional relay cooperative secure over-the-air computing proposed by the present invention. In the following description, different references to "one embodiment" or "another embodiment" do not necessarily refer to the same embodiment. Furthermore, specific features, structures, or characteristics of one or more embodiments may be combined in any suitable manner.

[0038] Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs.

[0039] The following describes in detail a signal transmission method and system for bidirectional relay cooperative secure over-the-air computing provided by the present invention with reference to the accompanying drawings.

[0040] See also Figure 1 , which shows a flowchart of a signal transmission method for bidirectional relay cooperative secure over-the-air computing provided by one embodiment of the present invention, the method comprising the following steps:

[0041] Step S100: In the first time slot, the sensor sends the pre-processed sensing data to the relay, the target node sends the signal data with the beamformer to the relay, and the interference node sends the interference signal data to the relay and the eavesdropper.

[0042] First, it should be noted that the relay and friendly interference nodes are configured with multiple antennas, while the sensors and target user B are configured with single antennas. Target user B has two task requirements: one is to send a multicast signal, such as updating the sensor status, to K sensors, and the other is that target node B needs to obtain the aggregated results of the sensor data transmitted by the K sensors.

[0043] Based on this, in this embodiment, K sensors are set in the scene, and the value of K needs to be set by the implementer according to the specific implementation scenario. Among them, the distance between each node in the scene is set to the position with the best effect under known conditions.

[0044] In the first time slot, K sensors, target user B, and friendly interference nodes send signals simultaneously, and the superimposed signal received by the relay is:

[0045]

[0046] Among them, y R represents the superimposed signal received by the relay, K represents the total number of sensors, b k represents the emission coefficient of the kth sensor, s krepresents the sensor data with zero mean and unit variable sent by the kth sensor to the relay, s B represents the signal data transmitted by the target node to the relay, w represents the beamforming vector of the target node; s J represents the interference signal data transmitted by the interference node to the relay, V represents the beamforming vector of the interference node; h kR 、h BR and h JR denote the channel coefficients from the kth sensor, target node and interference node to the relay, n R Represents the additional noise signal relayed out; R represents the relay, B represents the target node, and J represents the interference node.

[0047] Step S200: In the second time slot, the relay sends the received data in combination with the beamforming matrix to the target node and the sensor, and the eavesdropper receives the interfered superposition signal.

[0048] It should be noted that the relay broadcasts the superimposed signals received in the first time slot from target node B, K sensors, and interfering node J. The interference signal sent by the interfering node is pre-agreed and known to target node B and K sensors. After receiving the signal, the target node B and K sensors can completely eliminate the self-interference signal and the interference signal sent by the interfering node. Based on this, the interference signal sent by the interfering node only increases the computational distortion at the eavesdropper without affecting the computational distortion of target user B, thus providing an effective computational security method while not interfering with target user B's data aggregation.

[0049] Furthermore, in the second time slot, the signal received at the relay is multiplied by the beamforming matrix F and then forwarded to the K sensors and the target user B. Due to the perfect CSI, the target user B can completely remove the self-interference signal and the interference signal sent by the friendly interfering node. After the target node receives the signal sent by the relay, it eliminates the self-interference signal and the interference signal of the interfering node to obtain the target node's transmission signal. Specifically,

[0050]

[0051] Among them, y B ′ represents the transmission signal of the target node, F represents the beamforming matrix of the relay, n B represents the additional noise of the target node.

[0052] Since the eavesdropper is unaware of the interference signal and cannot eliminate it, the interfered superimposed signal received by the eavesdropper is specifically expressed as:

[0053]

[0054] Among them, y E represents the interfered superposition signal received by the eavesdropper, E represents the eavesdropper, h RE represents the channel coefficient from the relay to the eavesdropper, n E represents the additional noise of the eavesdropper.

[0055] Step S300, when the deviation between the interfered superimposed signal received by the eavesdropper and the original signal data sent by the target node or sensor meets the threshold requirement, solve the optimization problem; the optimization problem is to minimize the deviation between the signal received by the target node and the original signal sent by optimizing the allocated power of each sensor, target node, relay and interfering node.

[0056] Under perfect channel state information (CSI), target user B can completely eliminate the self-interference signal and the interference signal of the agreed friendly interfering node after receiving the signal, and finally obtain the accurate transmission signal. When the transmission power of target user B is large enough, K sensors can simultaneously use a method similar to the first step of serial interference cancellation (SIC) to first identify the strongest signal. After recovering the signal of target user B, the sensor subtracts the signal from the total received signal and then uses the serial interference cancellation (SIC) method to eliminate other interference signals, retaining only the useful signal sent by target user B. However, the eavesdropper cannot eliminate the interference signal and obtain the accurate transmission signal because it cannot obtain accurate channel state information and information about the interference signal.

[0057] It should be noted that the relay sends the beamforming matrix while transmitting the signal to the target user B and K sensors. The target user B aggregates the data using the corresponding beamforming vector and finally obtains the arithmetic sum of the K sensor data. Among them, the kth sensor can use the known data s sent by itself in the first time slot to obtain the arithmetic sum of the K sensor data. k To eliminate the interference of its own signal on the received signal, if the target user B's transmit power is sufficiently high, the K sensors can simultaneously use a method similar to the first step of Successive Interference Cancellation (SIC) to first identify and recover the strongest signal. After recovering the target user B's signal, the sensor subtracts the recovered target user B signal from the received superimposed signal to obtain the remaining signal, and then begins to perform Successive Interference Cancellation (SIC). First, the sensor sorts the other interfering signals according to their power. Then, starting with the signal with the highest power, it demodulates each one and subtracts the demodulated signal from the remaining signal. Ultimately, only the useful signal sent by target user B is retained, resulting in accurate sensor status update information.

[0058] In this embodiment, the arithmetic sum of the sensor data is The target user B aggregates the value of s using the received beamforming vector d to be: The mean square error of the arithmetic sum of the estimated sensor data of the corresponding target user B can be expressed as:

[0059]

[0060] Among them, MSE B represents the mean square error of the target node, represents the arithmetic sum of sensor data; Indicates the value of the beamforming vector d aggregate received by the target node, represents the conjugate transpose of the beamforming vector d, Represents conjugate transpose, which is used to adjust the change of signal phase; represents the variance of the noise at the relay, represents the variance of the noise at the target user, Represents the expected value operation.

[0061] Preferably, the mean square error of the eavesdropper is expressed as:

[0062]

[0063] Among them, MSE E represents the mean square error of the eavesdropper, represents the value aggregated by the received beamforming vector a at the eavesdropper, represents the conjugate transpose of the beamforming vector a; represents the variance of the noise at the eavesdropper.

[0064] Furthermore, to achieve secure over-the-air computation, the minimum computational distortion measured by the mean squared error (MSE) at the eavesdropper should be larger than a given threshold, so that the eavesdropper cannot compute the aggregation of sensor data accurately enough, and the transmit power of all nodes cannot exceed their budget.

[0065] Specifically, when the mean square error of the eavesdropper meets the threshold requirement, the transmission power of all nodes does not exceed the corresponding transmission power, specifically including:

[0066]

[0067] |b k | 2 ≤P k ,k=1,...K

[0068] |w| 2 ≤P B

[0069] |V| 2 ≤P J

[0070]

[0071] Among them, ξ E Indicates the minimum calculated distortion threshold of the eavesdropper, P k represents the transmission power of the kth sensor, P B represents the transmission power of the target node, P J represents the transmission power of the interfering node, P R Represents the transmission power of the relay. Each sensor uses the same time and frequency resources at a specific transmission power to send sensor data to the target user B through the relay in a non-orthogonal manner.

[0072] Furthermore, assuming that {h kR} and {h Rk} is perfect, the kth sensor can eliminate its own data s in the received signal k , and when the target user B's transmission power is large enough, K sensors can simultaneously identify the strongest signal through a method similar to the first step of serial interference cancellation (SIC). After recovering the signal of target user B, the sensor subtracts the signal from the total received signal, and then uses the serial interference cancellation (SIC) method to eliminate other interference signals, retaining only the useful signal sent by target user B to ensure reliable multicast; given the corresponding required variables, optimize the aggregation variables {d, a}, the relay beamforming matrix F, and the transmission variables {V, w, b} respectively. k}.

[0073] Specifically, given the variables {F, V, w, b k}, solve the optimization problem of the aggregate vector {d, a}; given the variables {d, a, V, w, b k}, solve the optimization problem of the relay beamforming matrix F; bring the optimal solution of a into the corresponding solution formula and give other variables to solve the transmission variables {V, w, b k} related optimization issues.

[0074] Based on this, after optimizing all variables to obtain the optimal solution, the optimal solution of the optimization target can be obtained, that is, the minimum value of the calculation distortion of the target user B. That is, the deviation between the signal received by the target node and the original signal sent is minimized.

[0075] It can be understood that the transmission variables of all nodes and the aggregated variables sent by the relay received by the target user B and the eavesdropper are jointly optimized to minimize the computational distortion of the target user B under the constraints that the minimum computational distortion of the eavesdropper is greater than a given threshold and the transmission power of all nodes cannot exceed their budget.

[0076] The calculated distortion needs to be within a certain range, and the transmission power of each node does not exceed its budget. When the eavesdropper's calculated distortion meets the requirements, that is, when it is greater than the threshold, the optimal allocated power P is solved. k 、P B 、P J 、P R , minimizing the objective function (the mean squared error of target user B). The above optimization problem can be solved using a variety of methods, and its numerical solution is easily obtained using the MATLAB Optimization Toolbox. Its closed-form solution can also be obtained using classical convex optimization theory after appropriate transformation, which will not be discussed here.

[0077] In summary, the present invention can achieve bidirectional signal transmission through trusted bidirectional relays and the assistance of friendly interfering nodes. Since the interference signals sent by friendly interfering nodes are pre-agreed, and under perfect CSI conditions, target user B can completely eliminate the interference signals from both itself and the interfering nodes. If the transmit power of target user B is sufficiently high, K sensors can simultaneously identify the strongest signal using a method similar to the first step of serial interference cancellation (SIC). After recovering the target user B signal, the sensors subtract it from the total received signal. Next, serial interference cancellation (SIC) is used to eliminate other interference signals, retaining only the useful signal sent by target user B. The transmission variables of all nodes and the aggregated variables sent by the relay and received by target user B and the eavesdropper are jointly optimized. Under the constraint that the transmit power of all nodes cannot exceed their budgets, the eavesdropper's minimum computational distortion is set to a threshold, thereby preventing the eavesdropper from obtaining an accurate transmission signal. Ultimately, the computational distortion of target user B is minimized, allowing target user B to receive an accurate aggregated signal, thus ensuring the secure transmission of multicast signals based on over-the-air computation.

[0078] like Figure 2 As shown, the present invention also provides a signal transmission system for two-way relay collaborative secure air computing, which includes a multi-antenna two-way relay, an interference node, multiple sensors and a multi-antenna target user; the sensor, target user, two-way relay and friendly interference node cooperate with each other to interfere with the eavesdropper's eavesdropping process, and the secure signal transmission system is used to implement the steps of a signal transmission method for two-way relay collaborative secure air computing.

[0079] The above-described embodiments are only used to illustrate the technical solutions of the present application, rather than to limit them. Although the present application has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. These modifications or replacements do not deviate the essence of the corresponding technical solutions from the scope of the technical solutions of the embodiments of the present application, and should all be included in the scope of protection of the present application.

Claims

1. A signal transmission method for two-way relay collaborative secure over-the-air computing, characterized in that: The method comprises the following steps: In the first time slot, the sensor sends the pre-processed sensing data to the relay, the target node sends the signal data with the beamformer to the relay, and the interference node sends the interference signal data to the relay and the eavesdropper; In the second time slot, the relay sends the received data in combination with the beamforming matrix to the target node and sensor, and the eavesdropper, and the eavesdropper receives the interfered superposition signal; When the deviation between the jammed superimposed signal received by the eavesdropper and the original signal data sent by the target node or sensor meets the threshold requirement, an optimization problem is solved; the optimization problem is to minimize the deviation between the signal received by the target node and the original signal sent by optimizing the allocated power of each sensor, target node, relay and interfering node; The mean square error of the eavesdropper is expressed as: in, represents the mean square error of the eavesdropper, , represents the beamforming vector received at the eavesdropper The aggregated value, represents the beamforming vector The conjugate transpose of represents the variance of the noise at the eavesdropper; represents the beamforming matrix of the relay, represents the emission coefficient of the kth sensor, represents the channel coefficient relayed to the eavesdropper, 、 and denote the channel coefficients from the kth sensor, target node and interference node to the relay, respectively, represents the beamforming vector of the target node, represents the beamforming vector of the interfering node, represents the variance of the noise at the relay, K represents the total number of sensors, represents the expected value operation, , represents the arithmetic sum of sensor data, represents the sensor data with zero mean and unit variable sent by the kth sensor to the relay; When the mean square error of the eavesdropper meets the threshold requirement, the transmission power of all nodes does not exceed the corresponding transmission power, specifically including: in, Indicates the minimum calculated distortion threshold of the eavesdropper, represents the transmission power of the kth sensor, represents the transmission power of the target node, represents the transmission power of the interfering node, Indicates the transmission power of the relay.

2. A signal transmission method for bidirectional relay cooperative secure over-the-air computing according to claim 1, characterized in that: In the first time slot, the superimposed signal received by the relay is: in, represents the superimposed signal received by the relay, K represents the total number of sensors, represents the emission coefficient of the kth sensor, represents the sensor data with zero mean and unit variable sent by the kth sensor to the relay, Indicates the signal data transmitted by the target node to the relay, The vector representing the beamforming of the target node; Represents the interference signal data transmitted by the interference node to the relay, The vector representing the beamforming of the interfering node; 、 and denote the channel coefficients from the kth sensor, target node and interference node to the relay, respectively, represents the additional noise signal at the relay; R represents the relay, B represents the target node, and J represents the interference node.

3. The signal transmission method for bidirectional relay cooperative secure over-the-air computing according to claim 2, characterized in that: In the second time slot, after receiving the signal sent by the relay, the target node eliminates the self-interference signal and the interference signal of the interfering node to obtain the transmission signal of the target node, specifically: in, represents the transmission signal of the target node, represents the beamforming matrix of the relay, represents the additional noise of the target node.

4. The signal transmission method for bidirectional relay cooperative secure over-the-air computing according to claim 3, characterized in that: The interfered superposition signal received by the eavesdropper is specifically expressed as: in, represents the interfered superposition signal received by the eavesdropper, E represents the eavesdropper, represents the channel coefficient relayed to the eavesdropper, represents the additional noise of the eavesdropper.

5. The signal transmission method for bidirectional relay cooperative secure over-the-air computing according to claim 3, characterized in that: The mean square error of the target node is expressed as: in, represents the mean square error of the target node, , represents the arithmetic sum of sensor data; , Indicates that the target node receives the beamforming vector The aggregated value, represents the beamforming vector The conjugate transpose of Represents conjugate transpose, which is used to adjust the change of signal phase; represents the variance of the noise at the relay, represents the variance of the noise at the target node, Represents the expected value operation.

6. A signal transmission system for two-way relay collaborative secure air computing, characterized in that: The system includes a multi-antenna bidirectional relay, an interference node, multiple sensors and a multi-antenna target node; the signal transmission system is used to implement the steps of a signal transmission method for bidirectional relay collaborative secure air computing as described in any one of claims 1-5.

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