Unmanned aerial vehicle assisted covert communication method and system under cooperation of multiple monitoring nodes

Abstract

This invention discloses a UAV-assisted covert communication method and system under multi-monitoring node cooperation, belonging to the field of wireless communication technology. The UAV-assisted covert communication method under multi-monitoring node cooperation includes: establishing a legitimate link transmission model and a detection model for a fusion center to perform binary hypothesis testing on the legitimate transmitter's transmission behavior; deriving the minimum detection error probability of the fusion center; constructing a non-convex optimization problem of the amplification and forwarding coefficients of the monitoring nodes, equivalently transforming it into an optimization problem under unit norm constraints, and simplifying it into a one-dimensional search problem with a single variable, solving for the optimal amplification and forwarding coefficient direction; and optimizing the legitimate transmitter power to maximize the effective covert communication rate based on the monotonicity of detection performance with respect to the legitimate transmitter's transmission power. This invention achieves covert communication with low computational complexity, low resource consumption, and high effective rate, and reveals the saturation effect of the benefits of cooperative detection.

Description

Technical Field

[0001] This invention belongs to the field of wireless communication technology, specifically relating to a covert communication method and system assisted by unmanned aerial vehicles (UAVs) under the cooperation of multiple listening nodes. Background Technology

[0002] The statements herein provide only background information in relation to this invention and do not necessarily constitute prior art.

[0003] Existing research on covert communication largely focuses on single-monitoring node scenarios, improving concealment through methods such as UAV trajectory design and intelligent metasurface phase shift optimization. However, in practical applications, there are numerous spatially distributed multi-monitoring nodes. Their collaborative forwarding of observation information to a fusion center significantly enhances detection capabilities, becoming a core challenge for covert communication.

[0004] The inventors have discovered the following key problems and shortcomings in current research on covert communication involving multiple cooperative monitoring nodes: The detection model does not match reality. Existing research assumes that the fusion center aggregates information using simple methods such as equal-gain merging and maximum-ratio merging, failing to consider the actual scenario of monitoring nodes forwarding raw observations and the fusion center performing continuous-value radiometer soft information fusion, thus severely underestimating the detection capabilities of intelligent adversaries. Optimizing the amplification and forwarding coefficients of monitoring nodes is crucial to increasing the detection difficulty of the fusion center, but this optimization problem is non-convex, and existing technologies lack efficient low-complexity solution methods. Furthermore, existing technologies have not established a quantitative relationship between the detection performance of the fusion center and the legitimate link communication rate, making it impossible to maximize the effective covert communication rate while strictly satisfying covertness constraints. Summary of the Invention

[0005] The purpose of this invention is to overcome the shortcomings of the prior art and provide a covert communication method and system assisted by unmanned aerial vehicles under the cooperation of multiple listening nodes.

[0006] To achieve the above objectives, the present invention is implemented through the following technical solution: In a first aspect, the technical solution of the present invention provides a covert communication method assisted by unmanned aerial vehicles (UAVs) under the cooperation of multiple listening nodes, including: Define the channel model, power parameters and signal model between each monitoring node in a covert communication system with multiple monitoring nodes, and establish a legitimate link transmission model and a detection model for the fusion center to perform binary hypothesis testing on the legitimate transmitter transmission behavior; Based on the detection model, the minimum detection error probability when the fusion center performs optimal detection is derived. The minimum detection error probability is a function of the amplified forwarding coefficient vector of the listening node. With the goal of minimizing the minimum detection error probability, a non-convex optimization problem of the amplification and forwarding coefficient of the listening node is constructed. This problem is equivalently transformed into an optimization problem under the unit norm constraint, and then simplified into a one-dimensional search problem with a single variable. The optimal direction of the amplification and forwarding coefficient is obtained by solving this problem. Based on the monotonicity of the minimum detection error probability with respect to the transmit power of the legitimate transmitter, a transmit power optimization problem is constructed with the goal of maximizing the effective covert communication rate. Under the conditions of covertness constraints and power budget constraints, the optimal transmit power of the legitimate transmitter is obtained by solving the problem.

[0007] In at least one embodiment, the covert communication system with multiple listening nodes cooperating includes a legitimate transmitter, a legitimate receiver, multiple spatially distributed listening nodes, a friendly drone jammer, and a fusion center.

[0008] In at least one embodiment, defining the channel model between each monitoring node includes: The links between legitimate transmitter and legitimate receiver, legitimate transmitter and space-distributed listening node, and space-distributed listening node and fusion center are modeled as quasi-static Rayleigh flat fading channels, superimposed with large-scale path loss. The links between UAVs and space-distributed listening nodes, and between UAVs and legitimate receivers, are modeled as line-of-sight propagation channels. Define the artificial noise emission power of a drone as following an interval A continuous, uniform distribution is used to introduce power uncertainty and enhance the interference effect; among which, This represents the maximum artificial noise emission power of the drone.

[0009] In at least one embodiment, the fusion center employs a radiometer detector, and the decision criterion is: if the average received power sampled by the fusion center is greater than the detection threshold, it is determined to be a legitimate transmitter transmission; otherwise, it is determined to be a legitimate transmitter silence.

[0010] In at least one embodiment, the closed-loop expression for the minimum detection error probability is:

[0011] In the formula, To minimize the probability of detection error; The lower incomplete gamma function; It is a gamma function; , and All of these are model parameters.

[0012] In at least one embodiment, the optimization problem under the unity norm constraint is specifically expressed as:

[0013] In the formula, To minimize the probability of detection error; and These are model parameters; , , , This is the forwarding coefficient vector.

[0014] In at least one embodiment, the optimal transmit power of the legitimate transmitter is expressed as:

[0015] In the formula, The optimal transmission power for a legitimate transmitter; The minimum detection error probability of the fusion center; This is the concealment tolerance parameter; The transmission power of a legitimate transmitter; This represents the maximum transmission power of a legal transmitter.

[0016] Secondly, the technical solution of the present invention also provides a covert communication system assisted by unmanned aerial vehicles (UAVs) under the cooperation of multiple listening nodes, including: The model definition module is configured to: define the channel model, power parameters and signal model between each monitoring node in a covert communication system with multiple monitoring nodes cooperating; establish a legitimate link transmission model and a detection model for the fusion center to perform binary hypothesis testing on the legitimate transmitter transmission behavior. The derivation module is configured to: derive the minimum detection error probability when the fusion center performs optimal detection based on the detection model. The minimum detection error probability is a function of the amplified forwarding coefficient vector of the listening node. The optimization problem transformation module is configured to: construct a non-convex optimization problem of the amplification and forwarding coefficient of the listening node with the goal of minimizing the minimum detection error probability, convert it into an optimization problem under the unit norm constraint, and simplify it into a one-dimensional search problem with a single variable, and solve it to obtain the optimal direction of the amplification and forwarding coefficient; The optimization solution module is configured to: construct a transmission power optimization problem with the goal of maximizing the effective covert communication rate based on the monotonicity of the minimum detection error probability with respect to the transmission power of the legitimate transmitter; and solve for the optimal transmission power of the legitimate transmitter under the conditions of covertness constraints and power budget constraints.

[0017] Thirdly, the technical solution of the present invention also provides a computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements the steps in the UAV-assisted covert communication method under multi-listening node cooperation as described in the first aspect.

[0018] Fourthly, the present invention also provides a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, it implements the steps in the UAV-assisted covert communication method under multi-listening node cooperation as described in the first aspect.

[0019] The beneficial effects of the above-described technical solution of the present invention are as follows: 1) The UAV-assisted covert communication method under multi-monitoring node cooperation of the present invention is designed for soft information fusion scenarios in fusion centers. It derives closed-form analytical expressions for detection performance indicators such as minimum detection error probability and optimal transmission power of legitimate transmitters, breaking through the limitations of traditional simple merging models and providing a precise theoretical basis for covert strategy design.

[0020] 2) This invention transforms a non-convex optimization problem into a one-dimensional search problem by proving that the detection error probability is independent of the forwarding coefficient amplitude. This significantly reduces the computational complexity and activates only a small number of monitoring nodes with optimal channel conditions, saving more than 80% of forwarding resources and making it easy to implement in engineering.

[0021] 3) This invention establishes a quantitative relationship between detection performance and effective covert communication rate. By optimizing transmission power, the effective covert communication rate is maximized under the premise of strictly meeting covertness constraints.

[0022] 4) This invention uses randomized artificial noise from UAVs to interfere with power uncertainty, effectively interfering with the local observation of the monitoring node, effectively improving the probability of minimum detection error of the fusion center, meeting the high security level communication requirements in terms of concealment, and the UAV line-of-sight channel model fits the actual application scenario, making the solution highly feasible. Attached Figure Description

[0023] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an improper limitation of the invention.

[0024] Figure 1 This is a schematic diagram of the UAV-assisted covert communication method under multi-listening node cooperation disclosed in Embodiment 1 of the present invention; Figure 2 This is a schematic diagram of the curve showing the change of the minimum detection error probability of the fusion center with the number of monitoring nodes as disclosed in Embodiment 1 of the present invention; Figure 3 This is a schematic diagram of the effective covert communication rate as a function of the number of monitoring nodes, as disclosed in Embodiment 1 of the present invention. Detailed Implementation

[0025] It should be noted that the following detailed description is illustrative and intended to provide further explanation of the invention. Unless otherwise specified, all technical and scientific terms used in this invention have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.

[0026] As described in the background section, the purpose of this invention is to overcome the shortcomings of the prior art and provide a covert communication method and system assisted by unmanned aerial vehicles (UAVs) under the cooperation of multiple listening nodes.

[0027] Example 1 In a typical embodiment of the present invention, this embodiment discloses a UAV-assisted covert communication method under multi-monitoring node cooperation, specifically including the following steps: S1. Define the channel model, power parameters and signal model between each monitoring node in a covert communication system with multiple monitoring nodes, and establish a legitimate link transmission model and a detection model for the fusion center to perform binary hypothesis testing on the legitimate transmitter transmission behavior. S2. Based on the detection model, derive the minimum detection error probability when the fusion center performs optimal detection. The minimum detection error probability is a function of the amplified forwarding coefficient vector of the listening node. S3. With the goal of minimizing the minimum detection error probability, construct a non-convex optimization problem of the amplification and forwarding coefficient of the listening node, which is equivalently transformed into an optimization problem under the unit norm constraint, and simplified into a one-dimensional search problem with a single variable. Solve the problem to obtain the optimal direction of the amplification and forwarding coefficient. S4. Based on the monotonicity of the minimum detection error probability with respect to the transmit power of the legitimate transmitter, a transmit power optimization problem is constructed with the goal of maximizing the effective covert communication rate. Under the conditions of covertness constraints and power budget constraints, the optimal transmit power of the legitimate transmitter is obtained by solving the problem.

[0028] The following detailed description of the UAV-assisted covert communication method under multi-monitoring node cooperation, with specific implementation details, is provided below.

[0029] S1. Define the channel model, power parameters, and signal model among the monitoring nodes in a covert communication system with multiple monitoring nodes, and establish a legitimate link transmission model and a detection model for the fusion center to perform binary hypothesis testing on the legitimate transmitter transmission behavior.

[0030] S11. Construct a covert communication system with multiple listening nodes working together.

[0031] In this step, the covert communication system with multiple monitoring nodes refers to a single-antenna wireless communication system comprising a legitimate transmitter Alice, a legitimate receiver Bob, K spatially distributed monitoring nodes Willie, a friendly drone jammer, and a fusion center FC. In this covert communication system with multiple monitoring nodes, the legitimate transmitter Alice transmits confidential information to the legitimate receiver Bob. The K spatially distributed monitoring nodes Willie continuously monitor the channel and forward their local observation signals to the fusion center FC via a dedicated frequency band. The fusion center FC jointly processes the signals to determine whether the legitimate transmitter Alice should transmit. Simultaneously, the friendly drone emits randomized artificial noise (AN) to interfere with the local observations of the spatially distributed monitoring nodes Willie, increasing the decision error of the fusion center FC.

[0032] S12. Define the channel model, power parameters, and signal model.

[0033] In this step, the Alice-Bob, Alice-Willie, and Willie-FC links are modeled as quasi-static Rayleigh flat fading channels, superimposed with large-scale path loss. The channel coefficients are expressed as follows: , and The path loss function is specifically expressed as:

[0034] In the formula, The power gain is for a 1-meter reference channel. This refers to the node spacing; This is the path loss index.

[0035] The drone-Willie and drone-Bob links are modeled as line-of-sight (LoS) propagation channels, with the channel coefficients being respectively... and It is designed to fit the actual scenarios of drone-to-ground communication.

[0036] As a further implementation, the additive white Gaussian noises of Bob, Willie, and FC are independent of each other and their powers are known, and are respectively expressed as: , and .

[0037] When defining power parameters and signal models, set the artificial noise emission power of the UAV. Follow the interval A continuous, uniform distribution is used to introduce power uncertainty and enhance the interference effect; Alice's transmission power is set to... The amplification and forwarding gain of the Kth Willie is Furthermore, all Willie forwarding power satisfies the total power budget constraint, specifically expressed as follows:

[0038] In the formula, Forwarding coefficient vector; This is the power coefficient vector; For total power budget.

[0039] S13. Establish a legal link transmission model.

[0040] In this step, Alice sends a normalized complex Gaussian. The specific representation of the signal received by Bob is as follows:

[0041] In the formula, Artificial noise for drones; This is the additive white Gaussian noise for Bob.

[0042] The instantaneous channel capacity is defined as:

[0043] In the formula, Bob's received signal-to-interference-plus-noise ratio (SIN / N) is specifically expressed as follows:

[0044] When instantaneous channel capacity Less than the target transmission rate Transmission interruption occurs at a certain time, and the interruption probability is denoted as . .

[0045] Based on the interruption probability, the effective covert communication rate is defined as:

[0046] In the formula, This indicates the effective rate of covert communication.

[0047] S14. Establish a detection model for binary hypothesis testing of legitimate transmitter transmission behavior by the fusion center.

[0048] In this step, for Willie's local observations, the received signal of the k-th Willie follows a binary hypothesis test, specifically expressed as:

[0049] In the formula, This indicates that Alice is silent; Indicates Alice transmission; This is Willie's additive white Gaussian noise symbol.

[0050] For FC aggregated observations, when the number of observation symbols tending toward infinity (i.e.) ), number of forwarding symbols tending toward infinity (i.e.) When the fusion center performs binary hypothesis testing on legitimate transmitter transmission behavior, the detection model—FC sampled average received power model—is specifically as follows:

[0051] In the formula, The total power of the forwarding noise and the FC local noise is specifically expressed as follows:

[0052] The FC uses a radiometer detector, and the decision criterion is: ; In the formula, For the detection threshold, Alice was ordered to remain silent. The judgment was transmitted by Alice.

[0053] Based on the judgment result, the false alarm probability of FC is defined as:

[0054] The probability of a missed detection is:

[0055] The detection error probability is then expressed as:

[0056] The concealment constraint is:

[0057] In the formula, To minimize the probability of detection error; This is the concealment tolerance parameter.

[0058] S2. Based on the detection model, derive the minimum detection error probability when the fusion center performs optimal detection. The minimum detection error probability is a function of the amplified forwarding coefficient vector of the listening node.

[0059] S21. Derive the piecewise expression for the false alarm probability.

[0060] In this step, the piecewise expression for the false alarm probability is derived based on the FC sampling average received power model, which can be specifically expressed as:

[0061] In the formula, The detection threshold; The total power of forwarding noise and FC local noise; Specifically, it is expressed as follows:

[0062] In the formula, This represents the maximum artificial noise emission power of the drone.

[0063] By approximating the weighted sum of the observed signals under FC as a gamma distribution, the piecewise expression for the missed detection probability is derived, which can be specifically expressed as:

[0064] In the formula, Specifically, it is expressed as follows:

[0065] In the formula, The lower incomplete gamma function; It is a gamma function; Specifically, it is expressed as follows:

[0066] Specifically, it is expressed as follows:

[0067] In the formula, Specifically represented as ; The inverse of the Alice-Willie path loss function. .

[0068] S22. Derive the closed-form expression for the minimum detection error probability.

[0069] In this step, the detection error probability is determined. Regarding detection thresholds By taking the first derivative and analyzing its monotonicity, the optimal detection threshold is obtained, expressed as:

[0070] In the formula, The optimal detection threshold is [value].

[0071] Further derivation of the corresponding closed-form expression for the minimum detection error probability is as follows:

[0072] In the formula, To minimize the probability of detection error; The lower incomplete gamma function; It is a gamma function; Specifically, it is expressed as follows:

[0073] Specifically, it is expressed as follows:

[0074] In the formula, Specifically represented as ; The inverse of the Alice-Willie path loss function. .

[0075] S3. With the goal of minimizing the minimum detection error probability, construct a non-convex optimization problem of the amplification and forwarding coefficient of the listening node, which is equivalently transformed into an optimization problem under the unit norm constraint, and simplified into a one-dimensional search problem with a single variable. Solve the problem to obtain the optimal direction of the amplification and forwarding coefficient.

[0076] S31. Construct a non-convex optimization problem.

[0077] In this step, the minimum detection error probability of FC is minimized. To optimize the forwarding coefficient vector The constraint is the Willie total power budget constraint. This optimization problem is non-convex and difficult to solve directly.

[0078] S32. Equivalent transformation of non-convex optimization problems.

[0079] For a given vector Symmetric positive definite matrix and non-zero vectors definition and They are respectively:

[0080]

[0081] Then for any Consider the scaled vector The calculation yielded:

[0082]

[0083] visible, and It is about A zero-order homogeneous function whose value depends only on The direction, and with The length is irrelevant.

[0084] Furthermore, set For and If is a function of the independent variable, then by the above invariance, we can obtain:

[0085] That is, the minimum detection error probability Only with forwarding coefficient vector The direction is related, but the magnitude is independent. Therefore, the Willie total power budget constraint is replaced with a normalized constraint:

[0086] In the formula, It is a diagonal matrix. , .

[0087] Then, through variable transformation The non-convex optimization problem is equivalently transformed into an optimization problem under the unit norm constraint, expressed as:

[0088] S33. Multidimensional optimization is simplified into a one-dimensional search problem.

[0089] for and The identity of the incomplete gamma function is expressed as:

[0090] Therefore, the detection error probability can be rewritten as:

[0091] make Its probability density function is:

[0092] Define a non-negative and non-increasing function as:

[0093] Then the probability of detection error It can be represented as:

[0094] Detection error probability about Taking the partial derivative, we have:

[0095] Using Leibniz's law, and noting that the integrand in... If the value is zero, then:

[0096] Therefore about Strictly incremental.

[0097] For any Consider the likelihood ratio of the two gamma density functions:

[0098] because The ratio is about Strictly increasing. Therefore, the family of random variables about It possesses the monotonic likelihood ratio (MLR) property, that is, when As the likelihood ratio increases, the distribution tends to a larger value in order of likelihood ratio.

[0099] because about Non-increasing, therefore for non-decreasing functions have For non-increasing functions The inequality is reversed. Therefore:

[0100] Then we have:

[0101] therefore, about Strictly decreasing.

[0102] Based on the above minimum detection error probability about Strictly decreasing, regarding Strictly incremental, for Perform a one-dimensional binary search to find the probability that minimizes the detection error. Minimum optimal United and Solve the two inequalities according to Determine the optimal subset of active listening nodes (activate only a small number of Willie nodes with optimal channel conditions, and shut down the rest to improve resource utilization), and derive the optimal normalized vector. .

[0103] S34. Solve to obtain the optimal direction of the amplification and forwarding coefficient.

[0104] In this step, the optimal forwarding coefficient direction is obtained through inverse transformation, expressed as:

[0105] By linearly scaling it, we obtain the final optimal amplification and forwarding coefficient, expressed as:

[0106] In the formula, Scaling factor .

[0107] S4. Based on the monotonicity of the minimum detection error probability with respect to the transmit power of the legitimate transmitter, a transmit power optimization problem is constructed with the goal of maximizing the effective covert communication rate. Under the conditions of covertness constraints and power budget constraints, the optimal transmit power of the legitimate transmitter is obtained by solving the problem.

[0108] S41. Construct a power optimization problem.

[0109] In this step, the goal is to maximize the effective covert communication rate. Build Alice's transmit power for the target The optimization problem has constraints including concealment constraints and Alice's maximum transmission power constraints. The concealment constraints are expressed as follows:

[0110] Alice's maximum transmit power constraint is expressed as:

[0111] In the formula, This represents the minimum detection error probability for the fusion center.

[0112] S42. Use monotonicity to find the optimal solution.

[0113] Effective covert communication rate Regarding Alice's transmission power Strictly increasing, minimum detection error probability Regarding Alice's transmission power Strictly decreasing, Alice's transmission power will be reduced while satisfying the concealment constraint. Pushing it to the maximum will achieve an effective covert communication rate. Maximizing this, the optimal transmit power for a legal transmitter is obtained by solving the problem as follows:

[0114] In the formula, The optimal transmission power for a legitimate transmitter.

[0115] This embodiment also compares and verifies this method with the traditional gain combining (EGC) scheme. For example... Figure 2The diagram shows the curve of the minimum detection error probability of the fusion center as a function of the number of monitoring nodes. The x-axis represents the number of monitoring nodes K, and the y-axis represents the minimum detection error probability. The vertical axis represents the sum of the vertical and horizontal axes. The comparison results show that, compared to the EGC scheme, this method has significant advantages in improving the probability of detection errors and enhancing concealment.

[0116] like Figure 3 The diagram shows the effective covert communication rate as a function of the number of monitoring nodes (K), with the number of monitoring nodes (K) on the x-axis and the effective covert communication rate on the y-axis. The vertical axis represents the sum of the vertical and horizontal axes. The comparison results show that, compared to the EGC scheme, this method has a significant advantage in improving the effective detection rate, while also reflecting the saturation effect of collaborative detection benefits.

[0117] Example 2 In a typical embodiment of the present invention, this embodiment discloses a UAV-assisted covert communication system with multi-monitoring node cooperation, comprising: The model definition module is configured to: define the channel model, power parameters and signal model between each monitoring node in a covert communication system with multiple monitoring nodes cooperating; establish a legitimate link transmission model and a detection model for the fusion center to perform binary hypothesis testing on the legitimate transmitter transmission behavior. The derivation module is configured to: derive the minimum detection error probability when the fusion center performs optimal detection based on the detection model. The minimum detection error probability is a function of the amplified forwarding coefficient vector of the listening node. The optimization problem transformation module is configured to: construct a non-convex optimization problem of the amplification and forwarding coefficient of the listening node with the goal of minimizing the minimum detection error probability, convert it into an optimization problem under the unit norm constraint, and simplify it into a one-dimensional search problem with a single variable, and solve it to obtain the optimal direction of the amplification and forwarding coefficient; The optimization solution module is configured to: construct a transmission power optimization problem with the goal of maximizing the effective covert communication rate based on the monotonicity of the minimum detection error probability with respect to the transmission power of the legitimate transmitter; and solve for the optimal transmission power of the legitimate transmitter under the conditions of covertness constraints and power budget constraints.

[0118] Example 3 In a typical embodiment of the present invention, this embodiment provides a computer-readable storage medium storing a computer program thereon. When executed by a processor, the program implements the steps in the UAV-assisted covert communication method with multi-listening node cooperation as described in Embodiment 1. These steps include: S1. Define the channel model, power parameters and signal model between each monitoring node in a covert communication system with multiple monitoring nodes, and establish a legitimate link transmission model and a detection model for the fusion center to perform binary hypothesis testing on the legitimate transmitter transmission behavior. S2. Based on the detection model, derive the minimum detection error probability when the fusion center performs optimal detection. The minimum detection error probability is a function of the amplified forwarding coefficient vector of the listening node. S3. With the goal of minimizing the minimum detection error probability, construct a non-convex optimization problem of the amplification and forwarding coefficient of the listening node, which is equivalently transformed into an optimization problem under the unit norm constraint, and simplified into a one-dimensional search problem with a single variable. Solve the problem to obtain the optimal direction of the amplification and forwarding coefficient. S4. Based on the monotonicity of the minimum detection error probability with respect to the transmit power of the legitimate transmitter, a transmit power optimization problem is constructed with the goal of maximizing the effective covert communication rate. Under the conditions of covertness constraints and power budget constraints, the optimal transmit power of the legitimate transmitter is obtained by solving the problem.

[0119] Example 4 In a typical embodiment of the present invention, this embodiment provides a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, it implements the steps in the UAV-assisted covert communication method with multi-listening node cooperation as described in Embodiment 1. These steps include: S1. Define the channel model, power parameters and signal model between each monitoring node in a covert communication system with multiple monitoring nodes, and establish a legitimate link transmission model and a detection model for the fusion center to perform binary hypothesis testing on the legitimate transmitter transmission behavior. S2. Based on the detection model, derive the minimum detection error probability when the fusion center performs optimal detection. The minimum detection error probability is a function of the amplified forwarding coefficient vector of the listening node. S3. With the goal of minimizing the minimum detection error probability, construct a non-convex optimization problem of the amplification and forwarding coefficient of the listening node, which is equivalently transformed into an optimization problem under the unit norm constraint, and simplified into a one-dimensional search problem with a single variable. Solve the problem to obtain the optimal direction of the amplification and forwarding coefficient. S4. Based on the monotonicity of the minimum detection error probability with respect to the transmit power of the legitimate transmitter, a transmit power optimization problem is constructed with the goal of maximizing the effective covert communication rate. Under the conditions of covertness constraints and power budget constraints, the optimal transmit power of the legitimate transmitter is obtained by solving the problem.

[0120] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A UAV-assisted covert communication method with multi-monitoring node cooperation, characterized in that, include: Define the channel model, power parameters and signal model between each monitoring node in a covert communication system with multiple monitoring nodes, and establish a legitimate link transmission model and a detection model for the fusion center to perform binary hypothesis testing on the legitimate transmitter transmission behavior; Based on the detection model, the minimum detection error probability when the fusion center performs optimal detection is derived. The minimum detection error probability is a function of the amplified forwarding coefficient vector of the listening node. With the goal of minimizing the minimum detection error probability, a non-convex optimization problem of the amplification and forwarding coefficient of the listening node is constructed. This problem is equivalently transformed into an optimization problem under the unit norm constraint, and then simplified into a one-dimensional search problem with a single variable. The optimal direction of the amplification and forwarding coefficient is obtained by solving this problem. Based on the monotonicity of the minimum detection error probability with respect to the transmit power of the legitimate transmitter, a transmit power optimization problem is constructed with the goal of maximizing the effective covert communication rate. Under the conditions of covertness constraints and power budget constraints, the optimal transmit power of the legitimate transmitter is obtained by solving the problem.

2. The UAV-assisted covert communication method under multi-monitoring node cooperation as described in claim 1, characterized in that, A covert communication system with multiple listening nodes includes a legitimate transmitter, a legitimate receiver, multiple spatially distributed listening nodes, a friendly drone jammer, and a fusion center.

3. The UAV-assisted covert communication method under multi-monitoring node cooperation as described in claim 2, characterized in that, The channel model defined between each monitoring node includes: The links between legitimate transmitter and legitimate receiver, legitimate transmitter and space-distributed listening node, and space-distributed listening node and fusion center are modeled as quasi-static Rayleigh flat fading channels, superimposed with large-scale path loss. The links between UAVs and space-distributed listening nodes, and between UAVs and legitimate receivers, are modeled as line-of-sight propagation channels. Define the artificial noise emission power of a drone as following an interval A continuous, uniform distribution is used to introduce power uncertainty and enhance the interference effect; among which, This represents the maximum artificial noise emission power of the drone.

4. The UAV-assisted covert communication method under multi-monitoring node cooperation as described in claim 1, characterized in that, The fusion center uses a radiometer detector, and the decision criterion is: if the average received power sampled by the fusion center is greater than the detection threshold, it is determined to be a legitimate transmitter transmission; otherwise, it is determined to be a legitimate transmitter silence.

5. The UAV-assisted covert communication method under multi-monitoring node cooperation as described in claim 1, characterized in that, The closed-loop expression for the minimum detection error probability is: In the formula, To minimize the probability of detection error; The lower incomplete gamma function; It is a gamma function; , and All of these are model parameters.

6. The UAV-assisted covert communication method under multi-monitoring node cooperation as described in claim 1, characterized in that, The optimization problem under the unit norm constraint is specifically expressed as: In the formula, To minimize the probability of detection error; These are model parameters; , , , This is the forwarding coefficient vector.

7. The UAV-assisted covert communication method under multi-monitoring node cooperation as described in claim 1, characterized in that, The optimal transmit power of a legitimate transmitter is expressed as: In the formula, The optimal transmission power for a legitimate transmitter; The minimum detection error probability of the fusion center; This is the concealment tolerance parameter; The transmission power of a legitimate transmitter; This represents the maximum transmission power of a legal transmitter.

8. A covert communication system assisted by unmanned aerial vehicles (UAVs) with multi-monitoring node cooperation, characterized in that, include: The model definition module is configured to: define the channel model, power parameters and signal model between each monitoring node in a covert communication system with multiple monitoring nodes cooperating; establish a legitimate link transmission model and a detection model for the fusion center to perform binary hypothesis testing on the legitimate transmitter transmission behavior. The derivation module is configured to: derive the minimum detection error probability when the fusion center performs optimal detection based on the detection model. The minimum detection error probability is a function of the amplified forwarding coefficient vector of the listening node. The optimization problem transformation module is configured to: construct a non-convex optimization problem of the amplification and forwarding coefficient of the listening node with the goal of minimizing the minimum detection error probability, convert it into an optimization problem under the unit norm constraint, and simplify it into a one-dimensional search problem with a single variable, and solve it to obtain the optimal direction of the amplification and forwarding coefficient; The optimization solution module is configured to: construct a transmission power optimization problem with the goal of maximizing the effective covert communication rate based on the monotonicity of the minimum detection error probability with respect to the transmission power of the legitimate transmitter; and solve for the optimal transmission power of the legitimate transmitter under the conditions of covertness constraints and power budget constraints.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the program is executed by the processor, it implements the steps in the UAV-assisted covert communication method under multi-listening node cooperation as described in any one of claims 1-7.

10. A computer device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the steps in the UAV-assisted covert communication method under multi-listening node cooperation as described in any one of claims 1-7.

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