Covert communication active detection method based on full duplex detector

Abstract

The invention discloses a covert communication active detection method based on a full duplex detector, and belongs to the field of information security and wireless communication systems. According to the method, a full duplex detector adopts energy detection to detect covert communication and sends artificial noise to interfere communication so as to solve the problems of communication detection and countering in a high-level data security and data protection scene; the method specifically comprises the steps that the transmitting power of artificial noise is optimized, and the communication throughput is minimized under the constraint conditions of the detection capacity and the maximum transmitting power of the artificial noise. According to the method, throughput minimization is put forward, monotonicity of a target and a constraint function is analyzed, the optimal artificial noise transmitting power is found, and communication throughput minimization is achieved; according to the method, an effective active detection and countering means can be provided in scenes with high requirements on data security and data protection, such as prevention of potential Internet of Things information leakage and guarantee of industrial Internet privacy protection.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of wireless communication, secure communication, etc., in particular to a covert communication active detection method based on a full-duplex detector. BACKGROUND

[0002] In the current high-speed development of wireless communication technology, signal detection, as the core link of the communication system, undertakes key tasks such as spectrum resource management, interference identification, and information security protection. The core goal of the detector is to accurately determine whether there is a target signal in a complex electromagnetic environment, which directly affects the reliability of the communication system and the level of information security protection. Under the traditional detection framework, energy detection, with its advantages of not requiring prior knowledge of the signal, low computational complexity, and theoretical optimality, has become the optimal detection method for the existence of unknown signals, and is widely used in cognitive radio, Internet of Things device monitoring, and wireless environment monitoring scenarios. For example, in a cognitive radio network, secondary users use energy detection to sense the existence of primary user signals to avoid interference, and the detection performance directly determines the effectiveness of spectrum sharing; in the scenario of massive device access in the Internet of Things, the signal detection of low-power devices relies on the efficiency of energy detection to reduce the terminal computing overhead.

[0003] However, with the development of communication technology, the detector faces unprecedented technical challenges. On the one hand, the popularity of low-power communication technology leads to a high detection error probability caused by the low signal-to-noise ratio of the detection channel. For example, in industrial Internet of Things, sensors use power control technology to reduce signal power to near or even below the noise floor to prolong device endurance. On the other hand, the rise of covert communication technology poses a fundamental challenge to detection theory. It is worth noting that traditional network security communication protocols, including various Internet of Things security communication protocols and industrial Internet security communication protocols, aim to protect the transmission content from eavesdropping and tampering, but cannot hide the communication behavior itself. Covert communication can ensure that the detection probability of two legitimate users at the detector is negligible, thus hiding the existence of the transmission itself. Such technology, as a new information security technology, has been widely studied in military anti-interception communication, privacy-sensitive data transmission, Internet of Things privacy protection, data security, and data protection scenarios. For example, in industrial Internet of Things applications, by hiding communication in background noise, sensitive data and behavior patterns can be effectively protected from malicious detection, thereby preventing information leakage in industrial Internet of Things, and the transmission of critical instructions such as production control can also be protected by covert communication technology to achieve industrial Internet privacy protection. In addition, such covert communication technology has been widely used in military anti-interception communication and privacy-sensitive data transmission. Therefore, it is of great significance to analyze and improve the detection ability of the detector from the perspective of the detector.

[0004] The present application considers a practical application scenario, i.e., detecting and interfering with the covert communication of the enemy in a military scenario; specifically, the unit of our side detects whether the enemy is communicating and sends artificial noise to interfere with the communication of the enemy. Specifically, the full-duplex detector detects the communication behavior and sends artificial noise to interfere with the enemy's communication to minimize the throughput of the enemy's communication; considering that both detecting and interfering with the communication behavior play an important role in military operations, it is very valuable for a unit to simultaneously complete the detection and interference of the enemy's communication. For the full-duplex detector, sending artificial noise will cause self-interference, thereby reducing the probability of detecting the enemy's communication; this means that there is a contradiction between the communication detection capability and the interference capability, and it is necessary to weigh between detection and interference, therefore, it is of great significance to study the method of detecting and interfering with the legal communication of the full-duplex detector. SUMMARY

[0005] In view of the deficiencies of the prior art, the present application provides a covert communication active detection method based on a full-duplex detector, the present application calculates the probabilities of false detection and missed detection from the perspective of the detector, and then deduces the upper limit of the detection error probability to analyze the detection capability, so that it is less than a small value to guarantee its detection capability; the signal-to-interference-and-noise ratio and the decoding error probability are calculated from the perspective of the receiving end, and then the throughput is deduced to evaluate the performance of the communication; under the constraints of the detection performance and the transmission power, the throughput minimization optimization problem is proposed; by optimizing the artificial noise transmission power of the detector, the proposed throughput minimization problem is solved under the condition of ensuring a certain degree of detection capability.

[0006] In order to realize the above technical scheme, the specific steps are as follows: S1, constructing a wireless communication system; establishing three nodes and three channel links; The construction method is: taking the sender Alice, the receiver Bob and the detector Willie as the three nodes, and constructing the three channel links of the communication link, the detection link and the interference link, to complete the construction of the wireless communication system; The wireless communication system model constructed by the present application is as follows Figure 2As shown, the present application considers a wireless communication scenario; the model is composed of an enemy signal sender Alice, an enemy receiver Bob, and a friendly detector Willie; in the system model, Alice and Bob carry out covert communication, Willie detects the sending signal of Alice and sends artificial noise to interfere with the communication; Willie configured with separate transmitting antennas and receiving antennas in a full-duplex architecture, together with the transmitting antennas of Alice and the receiving antennas of Bob to form the system antennas; the wireless communication system model of the present application includes a communication link from Alice to Bob, a detection link from Alice to Willie, and an interference link from Willie to Bob, and the three channel links adopt additive white Gaussian noise channels; the communication system uses three channel links, and the communication block length of the three channel links is set to N , N is a preset threshold.

[0007] S2, obtaining the detection error probability of the detector Willie according to the received signal of the detector Willie and the detection strategy of the detector Willie; The obtaining of the detection error probability of the detector Willie specifically includes the following steps: S2.1, establishing a received signal model: using the parameters of the wireless communication model, the Gaussian distribution of the received signal is obtained through the received signal formula calculation, and the received signal model is established; The parameters of the wireless communication model include: the self-interference coefficient of Willie, the noise power at Willie, the noise power at Bob, the communication block length, the maximum transmission power of the artificial noise of Willie and the fixed transmission power of the signal, the detection requirement value and the set fixed transmission rate of the communication from Alice to Bob; In order to obtain the detection error probability of the detector Willie to analyze the detection performance, the present application first gives the formula of the received signal of the detector Willie in the channel using the first i signal sample as follows: Wherein, represents that the sender Alice does not transmit a signal, represents that Alice transmits a signal, is the self-interference coefficient of Willie, is the transmission power of the artificial noise of Willie, is the sending signal of Willie, is the complex Gaussian noise at Willie, is the noise power at Willie, ​a fixed transmit power for the Alice communication signal, a transmit signal for the Alice; S2.2, input a received signal model, and obtain an expression of a detection error probability of the Willie through likelihood ratio detection; The present application sets and with equal prior probabilities, the Willie makes a binary decision, and is respectively denoted as and to determine whether the Alice exists transmission behavior. Therefore, the detection error probability of the Willie is defined as: wherein, is the detection error probability of the Willie, is the false detection probability of the Willie, is the missed detection probability of the Willie; As a preferred embodiment of the present application, the optimal energy detection of the Willie is the likelihood ratio detection, and an expression of a detection strategy of the Willie is: wherein, and are respectively the Willie in and Let the likelihood function of a received signal be and are respectively the Willie in and Assume the probability density function of a received signal is i is a signal sample, N is a communication block length; according to equation (1), and can be expressed as: According to the likelihood ratio statistical detection of the Willie, the detection error probability of the Willie can be further expressed as: wherein, is the total variation distance between and

[0008] S3, an upper limit of the detection error probability of the Willie is derived according to the detection error probability of the Willie, and a detection capability constraint is obtained according to the upper limit of the detection error probability; ​The derivation process of the detection capability constraint is as follows: The present application is based on the relationship between the total variation distance and the Hellinger distance, and the following inequality exists, and the expression is: Among them, The total variation distance between and , The square of the Hellinger distance between and , According to the definition of the Hellinger distance and formula (3), formula (4) and formula (5), It can be derived as: Among them, Is the support set of and , x Is the possible value of Willie's received signal, Is the differential of Willie's received signal; Substitute formula (7) into formula (6), the upper limit of the detection error probability Can be obtained, and the expression is: Set To represent the detection index of Willie, the smaller T is, the smaller the detection error probability is, and the stronger the detection capability is; make T less than a small fixed value set , which means that the detection error probability of Willie will not exceed , Indicates the detection requirement value, so the detection capability constraint is: S4, according to the signal-to-interference ratio of the receiver Bob, the communication throughput from the sender Alice to the receiver Bob is obtained; The derivation method of the communication throughput from the sender Alice to the receiver Bob is as follows: In order to obtain the communication throughput from Alice to the receiver Bob, first give the expression of the signal-to-interference ratio At Bob: Among them, Is the noise power of the complex Gaussian noise at Bob; For finite block length communication, the decoding error probability cannot be ignored; the present application sets the fixed transmission rate of the communication from Alice to BobR with the communication block length N , the decoding error probability can be approximated as: where is Q a function, Q the inverse CDF of the standard normal distribution; therefore, the expression of the communication throughput from the sender Alice to the receiver Bob is: The communication throughput from the sender Alice to the receiver Bob represents the number of bits that can be effectively transmitted in the wireless communication, and in order to minimize the throughput under the Willie interference, the throughput is used as the performance index of the communication.

[0009] S5, by optimizing the transmission power of the artificial noise of the detector Willie, an optimization problem of minimizing the communication throughput from Alice to Bob is proposed, and the optimization problem is solved according to the monotonicity of the target and the constraint function, and the method is completed; The solving of the optimization problem according to the monotonicity of the target and the constraint function specifically includes the following steps: S5.1, the minimization of the communication throughput from Alice to Bob under the Willie interference is expressed as an optimization problem constrained by the detection capability and the artificial noise transmission power; The expression of the optimization problem is: wherein, is the maximum transmission power constraint of the artificial noise of Willie, is the maximum transmission power of the artificial noise of Willie; is the detection capability constraint, is the detection requirement reflecting the detection capability level; S5.2, the monotonicity of the communication throughput with respect to the transmission power of the artificial noise of Willie is analyzed; In order to solve the optimization equation, the monotonicity of the target and the constraint function needs to be analyzed; first, the monotonicity of the communication throughput from Alice to Bob with respect to the transmission power of the artificial noise of Willie is analyzed; the whole item in the function bracket in formula (13) is expressed as Q , the communication throughput is derived with respect to the signal-to-interference-and-noise ratio at Bob: ​​​ where is with respect to , is given by Notice that and , so , plugging into equation (15) gives which means that the communication throughput monotonically increases with the signal-to-interference-plus-noise ratio at Bob Then, we notice that according to equation (11), the signal-to-interference-plus-noise ratio at Bob is a monotonically decreasing function of the transmission power of Willie's artificial noise , so the communication throughput monotonically decreases with the increase of the transmission power of Willie's artificial noise ; S5.3, analyze the monotonicity of the detection metric with respect to the transmission power of the artificial noise of the detector Willie; According to equation (10), the detection metric is monotonically increasing with the transmission power of Willie's artificial noise , which is the same as with respect to , take the derivative of the transmission power of Willie's artificial noise : Therefore, the detection metric monotonically increases with the increase of the transmission power of Willie's artificial noise ; S5.4, according to the monotonicity of the target and constraint functions, obtain the optimal transmission power expression of Willie's artificial noise, so as to obtain the minimum communication throughput from Alice to Bob, and the optimization equation is solved; According to the present application, the communication throughput monotonically decreases with the increase of the transmission power of Willie's artificial noise and the detection metric monotonically increases with the increase of the transmission power of Willie's artificial noise , so the optimal transmission power of Willie's artificial noise, denoted as , should be the minimum value in the upper bound of the transmission power of Willie's artificial noise determined by the maximum transmission power constraint and the detection capability constraint, which can be expressed as: where, is the root of equation , the analytical solution of can be obtained by solving the equation as: The optimal Willie artificial noise transmission power is brought into formula (11) to obtain the signal-to-interference ratio at the optimal Bob , and is brought into formula (13) to obtain the minimum communication throughput , so that the optimization equation is solved; the signal-to-interference ratio at the optimal Bob and the minimum communication throughput are specifically expressed as: Compared with the prior art, the present application provides a covert communication active detection method based on a full-duplex detector, which has the following beneficial effects: 1. The present application establishes a novel detection capability constraint based on the upper limit of the detection error probability of the detector to ensure a certain degree of detection capability.

[0010] 2. The present application designs a full-duplex detector that can simultaneously receive signals and transmit artificial noise, thereby simultaneously meeting the requirements of detecting communication and interfering communication, and achieving a trade-off between detection capability and interference.

[0011] 3. The present application optimizes the resources of the detector based on the angle of the detector to achieve the goals of detection and interference. BRIEF DESCRIPTION OF DRAWINGS

[0012] Figure 1 is the step flow chart of the present application; Figure 2 is the wireless communication system model diagram of the present application; Figure 3 is the minimum communication throughput under different Alice transmission powers of the present application; with the change of the transmission power of Willie artificial noise ; Figure 4 is the detection index under different Alice transmission powers of the present application; with the change of the transmission power of Willie artificial noise ; Figure 5 is the minimum communication throughput under different Alice transmission powers of the present application; with the detection capability requirement a change graph of the minimum communication throughput Figure 6 different Alice transmit power the minimum communication throughput the maximum transmit power of Willie artificial noise a change graph. DETAILED DESCRIPTION

[0013] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only some of the embodiments of the present application, but not all the embodiments. The present application can be widely applied to power facility inspection, strong edge fixed defense, emergency communication, forest fire prevention, disaster rescue, mineral resource exploration, traffic monitoring, city security, cross-border logistics, agricultural monitoring and major event security, etc. in key industries and public safety fields. The present application is based on the application scene of detecting and interfering wireless communication, considering the additive white Gaussian noise channel model, under the condition of ensuring a certain degree of detection ability of the detector, realizing the minimization of communication throughput after interference.

[0014] As shown in Figure 1 , the specific steps of a covert communication active detection method based on a full-duplex detector are as follows: S1, constructing a wireless communication system; establishing three nodes and three channel links; The construction method is: taking the sender Alice, the receiver Bob and the detector Willie as the three nodes, and constructing the three channel links of the communication link, the detection link and the interference link, to complete the construction of the wireless communication system; The wireless communication system model constructed by the present application is shown in Figure 2 , the present application considers a wireless communication scene; the model is composed of an enemy signal sender Alice, an enemy receiver Bob and a our detector Willie; in the system model, Alice and Bob carry out covert communication, Willie detects the sending signal of Alice and sends artificial noise to interfere with the communication; the Willie adopting the full-duplex architecture is configured with separate transmitting antennas and receiving antennas, which together with the transmitting antennas of Alice and the receiving antennas of Bob form the system antennas; the wireless communication system model of the present application includes the communication link from Alice to Bob, the detection link from Alice to Willie and the interference link from Willie to Bob, and the three channel links all adopt additive white Gaussian noise channel; the communication system uses the three channel links, and the communication block length of the three channel links is set to N, N is a preset threshold.

[0015] S2, obtaining the detection error probability of the detector Willie according to the received signal of the detector Willie and the detection strategy of the detector Willie; The obtaining of the detection error probability of the detector Willie specifically comprises the following steps: S2.1, establishing a received signal model: using the parameters of the wireless communication model, the Gaussian distribution of the received signal is obtained through a received signal formula calculation, and the received signal model is established; The parameters of the wireless communication model include: the self-interference coefficient of Willie, the noise power at Willie, the noise power at Bob, the communication block length, the maximum transmission power of the artificial noise of Willie and the fixed transmission power of the signal, the detection requirement value and the fixed transmission rate of the Alice-to-Bob communication set; In order to obtain the detection error probability of the detector Willie to analyze the detection performance, the detector Willie uses the received signal formula in the channel at the first i signal sample is as follows: Among them, represents that the sender Alice does not transmit a signal, represents that Alice transmits a signal, is the self-interference coefficient of Willie, is the transmission power of the artificial noise of Willie, is the transmission signal of Willie, is the complex Gaussian noise at Willie, is the noise power at Willie, is the fixed transmission power of the Alice communication signal, is the transmission signal of Alice; S2.2, inputting the received signal model, obtaining the expression of the detection error probability of Willie through likelihood ratio detection; The present application sets and have equal prior probabilities, Willie makes a binary decision, and is respectively recorded as and to determine whether Alice exists transmission behavior. Therefore, the detection error probability of Willie is defined as: Among them, is the detection error probability of Willie, is the false detection probability of Willie, ​is the probability of missed detection of Willie; As a preferred embodiment of the present application, the optimal energy detection of Willie is the likelihood ratio detection, and the expression of the detection strategy is: wherein, and are the probabilities of missed detection of Willie under the assumption that the received signal is and the likelihood function of the received signal under the assumption that the received signal is and the probability density function of the received signal under the assumption that the received signal is and i is the signal sample, N is the communication block length; according to equation (1), and can be expressed as: According to the likelihood ratio statistical detection of Willie, the detection error probability of Willie can be further expressed as: wherein, is the total variation distance between and In order to facilitate those skilled in the art to understand the specific implementation of the present application, the following examples, simulation parameters and numerical results are provided; the simulation is performed using MATLAB, and the simulation parameters are shown in Table 1: Table 1: System simulation parameters S3, the upper limit of the detection error probability is derived according to the detection error probability of the detector Willie, and the detection capability constraint is obtained according to the upper limit; The derivation process of obtaining the detection capability constraint is as follows: According to the relationship between the total variation distance and the Hellinger distance, the following inequality exists, and the expression is: wherein, is the total variation distance between and is the square of the Hellinger distance between and ; according to the definition of the Hellinger distance and equations (3), (4) and (5), ​​​The detection error probability can be derived as: wherein, is and the support set of x is the possible value of the Willie received signal, is the differential of the Willie received signal; Substitute formula (7) into formula (6), the upper limit of the detection error probability can be obtained, and the expression is: Set to represent the detection index of Willie, and the smaller the T is, the smaller the detection error probability is, and the stronger the detection capability is; make T less than a small fixed value set , which means that the detection error probability of Willie will not exceed , represent the detection requirement value, so that the detection capability constraint is obtained as: S4, according to the signal-to-interference-and-noise ratio of the receiver Bob, the communication throughput of the sender Alice to the receiver Bob is obtained; The derivation method of the communication throughput of the sender Alice to the receiver Bob obtained by the application is as follows: In order to obtain the communication throughput of Alice to the receiver Bob, first, the expression of the signal-to-interference-and-noise ratio at Bob is given as: wherein, is the noise power of the complex Gaussian noise at Bob; For a finite block length communication, the decoding error probability cannot be ignored; in the case that the fixed transmission rate of the communication from Alice to Bob R and the communication block length N are set, the decoding error probability can be approximated as: wherein is Q a function, Q the function is the right tail function of the standard normal distribution; therefore, the expression of the communication throughput of the sender Alice to the receiver Bob is: The communication throughput from sender Alice to receiver Bob represents the number of bits that can be effectively transmitted in wireless communication. In order to minimize the throughput under Willie interference, throughput is used as a performance indicator of communication.

[0016] S5. By optimizing the transmission power of the artificial noise of the detector Willie, an optimization problem of minimizing the communication throughput from Alice to Bob is proposed, and the optimization problem is solved based on the monotonicity of the objective and constraint functions, thus completing the method. Solving the optimization problem based on the monotonicity of the objective and constraint functions specifically includes the following steps: S5.1 Minimizing the communication throughput from Alice to Bob under Willie interference is expressed as an optimization problem constrained by detection capability and artificial noise transmission power. The optimization problem is expressed as follows: in, This is the maximum transmit power constraint for Willie artificial noise. That is the maximum emission power of Willie's artificial noise; It is a constraint on detection capability. It reflects the level of testing capabilities; S5.2 Analyze the monotonicity of communication throughput relative to the transmit power of Willie artificial noise; This invention aims to solve the optimization equations, which requires analyzing the monotonicity of the objective and constraint functions. First, it analyzes the communication throughput from Alice to Bob. The emission power relative to Willie's artificial noise The monotonicity of; in equation (13) Q The whole term in parentheses of the function is represented as Communication throughput Signal-to-interference-plus-noise ratio at Bob Differentiate: in yes Compared to The first derivative is given by the following equation: Note and ,therefore Substituting into equation (15) yields This means communication throughput Signal-to-interference-to-noise ratio at Bob monotonically increases. Then, we notice that according to equation (11), the signal-to-interference-and-noise ratio at Bob is a monotonically decreasing function of the transmission power of Willie's artificial noise , so the communication throughput monotonically decreases with the increase of the transmission power of Willie's artificial noise ; S5.3, analyze the monotonicity of the detection metric with respect to the transmission power of Willie's artificial noise; According to equation (10), the detection metric is monotonically increasing with respect to the transmission power of Willie's artificial noise , and is monotonically decreasing with respect to , take the derivative of the transmission power of Willie's artificial noise : Therefore, the detection metric monotonically increases with the increase of the transmission power of Willie's artificial noise ; S5.4, according to the monotonicity of the objective and constraint functions, obtain the optimal transmission power of Willie's artificial noise, so as to obtain the minimum communication throughput from Alice to Bob, and the optimization equation is solved; According to the fact that the communication throughput monotonically decreases with the increase of the transmission power of Willie's artificial noise and the detection metric monotonically increases with the increase of the transmission power of Willie's artificial noise , the optimal transmission power of Willie's artificial noise should be the minimum value in the upper bound of the transmission power of Willie's artificial noise determined by the maximum transmission power constraint and the detection capability constraint, which can be expressed as: wherein, is the root of the equation , and the analytical solution of can be obtained by solving the equation as: Put the optimal transmission power of Willie's artificial noise into equation (11) to obtain the optimal signal-to-interference-and-noise ratio at Bob , and then put into equation (13) to obtain the minimum communication throughput Thus, the equation is optimized to obtain the solution; the signal-to-interference-plus-noise ratio at the optimal Bob position. and minimum communication throughput Specifically, it is expressed as follows: The simulation results are now explained; Figure 3 Showing different Alice transmit powers Communication throughput With Willie artificial noise emission power Changes; from Figure 3 With Willie's artificial noise emission power The increase in communication throughput It decreases accordingly; this is because The larger the value, the stronger Willie's ability to interfere with communication, thus reducing communication throughput; Figure 4 Showing different Alice transmit powers Lower detection indicators With Willie artificial noise emission power Changes; from Figure 4 With Willie's artificial noise emission power The increase in detection indicators The value increases accordingly, note that The higher the value, the weaker the detection capability, so as As the number of [unspecified elements] increases, the corresponding detection capacity decreases; this is because... The larger the value, the stronger Willie's self-interference, increasing its own detection error probability and thus reducing its detection capability; combined with Figure 3 and Figure 4 It can be observed that for full-duplex detectors, there is a trade-off between interference capability and detection capability. Furthermore, it can be observed that as Alice's transmission power increases... Increase, communication throughput Consequently, the number of detection indicators increased. It then decreases. This is because the larger... This means Alice sends more signals, increasing communication throughput and making the communication easier to detect.

[0017] Figure 5 Showing different Alice transmit powers Minimum Communication Throughput As the demand for testing capacity increases The change can be observed. The increase in minimum communication throughput first decreases, and then remains constant. The reason is as follows. As increases, the detection capability requirement is relaxed, and when is relatively small, the detection capability constraint is too tight to be satisfied, and Willie is considered to fail to detect the communication. As increases, the detection capability requirement is relaxed, and Willie transmits artificial noise to interfere with the communication with the optimal artificial noise transmit power that is in equation (18) with , increasing as increases, while the communication throughput is a monotonic decreasing function of the artificial noise transmit power, so the minimum communication throughput decreases. When further increases, the optimal artificial noise transmit power is in equation (18) with being a constant, so the minimum communication throughput remains constant. In addition, it can be found that as Alice's transmit power increases, the corresponding to the same minimum communication throughput decreases. This is because a larger means that the communication can be more easily detected, which means that the relatively tighter detection capability requirement can be satisfied when is relatively large.

[0018] Figure 6 shows the minimum communication throughput as a function of the maximum artificial noise transmit power for different Alice transmit powers . It can be observed that as increases, the minimum communication throughput first decreases and then remains constant. This is because when is relatively small, the optimal artificial noise transmit power is , so the minimum communication throughput decreases as increases. When increases beyond , the optimal artificial noise transmit power will remain at , so the minimum communication throughput It remains unchanged. In addition, it can be observed that as Alice's transmission power... Increase, same minimum communication throughput Corresponding The increase is due to the larger [the number of elements]. Allowing Willie to interfere with communications with more powerful artificial noise means that as As the magnitude increases, the interference intensity must also increase accordingly.

[0019] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A covert communication active detection method based on full-duplex detector, characterized in that, The method comprises the following steps: S1, constructing a wireless communication system, comprising establishing a three-party node and three channel links; The three-party node comprises a sender Alice, a receiver Bob and a detector Willie; The three channel links comprise a communication link, a detection link and an interference link; S2, obtaining the detection error probability of the detector Willie according to the received signal of the detector Willie and the detection strategy of the detector Willie; S3, deriving the upper limit of the detection error probability according to the detection error probability of the detector Willie, and obtaining the detection capability constraint according to the upper limit of the detection error probability; S4, obtaining the communication throughput from the sender Alice to the receiver Bob according to the signal-to-interference ratio of the receiver Bob; S5, by optimizing the transmission power of the artificial noise of the detector Willie, an optimization problem of minimizing the communication throughput from Alice to Bob is proposed, and the optimization problem is solved according to the monotonicity of the optimization objective and the constraint function, and the construction of the method is completed; The optimization objective is to minimize the communication throughput from Alice to Bob; The constraint function is obtained by the detection capability constraint.

2. The method of claim 1, wherein, The three channel links include a communication link, a detection link and an interference link, and the communication block length of the three channel links is set as N , N is a preset threshold.

3. The method of claim 1, wherein, The detection error probability of the detector Willie is obtained according to the received signal of the detector Willie and the detection strategy of the detector Willie, and the specific steps comprise: S2.1, establishing a received signal model: using the parameters of the wireless communication model, the Gaussian distribution of the received signal is obtained by the received signal formula calculation, the received signal model is established, and the expression is as follows: wherein, represents that the sender Alice does not transmit a signal, represents that Alice transmits a signal, is a self-interference coefficient of Willie, is a transmission power of artificial noise of Willie, is a transmission signal of Willie, is a complex Gaussian noise at Willie, is a noise power at Willie, is a fixed transmission power of the Alice communication signal, is a transmission signal of Alice; S2.2, input the received signal model, and obtain the expression of the detection error probability of Willie by likelihood ratio detection.

4. The method of claim 3, wherein, The expression of the detection error probability of Willie is obtained by inputting the received signal model and performing likelihood ratio detection. wherein is the probability of detection error for Willie, is the likelihood function of receiving a signal when no signal was transmitted by the sender Alice, is the likelihood function of receiving a signal when a signal was transmitted by the sender Alice, is the total variation distance between and the total variation distance between 5. The method of claim 1, wherein, In the step of deriving the upper limit of the detection error probability according to the detection error probability of the detector Willie, and obtaining the detection capability constraint according to the upper limit of the detection error probability, the expression of the detection capability constraint is: wherein is a predetermined Willie detection metric, is a Willie self-interference coefficient, is a Willie artificial noise transmit power, is a noise power at Willie, is a fixed transmit power of Alice's communication signal, N is a communication block length, is a detection requirement value.

6. The covert communication active detection method based on full-duplex detector according to claim 1, wherein, In the step of obtaining the communication throughput from the sender Alice to the receiver Bob according to the signal-to-interference ratio of the receiver Bob, the expression of the communication throughput is: wherein is the communication throughput from a sender Alice to a receiver Bob, N is the communication block length, R is the fixed transmission rate, is the decoding error probability, is the right tail function of the standard normal distribution, is the signal-to-noise ratio.

7. The method of claim 1, wherein, In the step of proposing an optimization problem of minimizing the communication throughput from Alice to Bob by optimizing the transmission power of the artificial noise of the detector Willie, the expression of minimizing the communication throughput from Alice to Bob is: wherein is the minimum communication throughput from Alice to Bob, is the optimal signal-to-interference-and-noise ratio at Bob, N is the communication block length, R is the fixed transmission rate, is the right tail function of the standard normal distribution.

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