Intelligent covert communication method against probabilistic eavesdropping in cognitive radio system

Abstract

The application provides a kind of intelligent covert communication method of anti-probability wiretapping in cognitive radio system, belongs to wireless communication security technical field.The application deploys the covert communication system model between vice transmitter ST, vice receiver SR and K eavesdroppers Eve;Derives the AMDEP closed expression of eavesdropper in two modes of active-passive cooperative eavesdropping APCE and adaptive cooperative eavesdropping ACE and the closed expression of outage probability at SR;With the maximum SR covert rate as the target, with the covert constraint and outage constraint as the condition, a multi-discriminator generative adversarial network MGAN is constructed, the generator generates ST transmission power and decision threshold according to the environment state, multiple discriminators cooperatively judge whether there is covert communication, and the joint optimization of transmission power and decision threshold is realized through the adversarial game between generator and discriminator.The application effectively improves the covert communication rate under the threat of multiple eavesdroppers adaptive cooperative eavesdropping, improves the communication concealment and reliability.

Description

Technical Field

[0001] This invention relates to the field of visibility meters, and in particular to an intelligent covert communication method for cognitive radio systems that resists probabilistic eavesdropping. Background Technology

[0002] As wireless communication evolves from fifth-generation (5G) to sixth-generation (6G), cognitive radio (CR) technology, with its dynamic spectrum access capabilities, has become a key paradigm for solving spectrum resource shortages. CR allows secondary users to opportunistically occupy idle spectrum without causing harmful interference to primary users, significantly improving spectrum utilization. However, the open sensing nature of CR and the broadcast nature of wireless channels expose it to serious security threats, namely, the vulnerability of transmissions to illegal interception, and the potential for spectrum sensing activities to expose communication activities.

[0003] In existing technologies, cognitive network security primarily relies on Physical Layer Security (PLS) technology, which utilizes physical characteristics such as channel fading and noise to ensure the confidentiality of information content. However, PLS only focuses on encrypting the transmitted content and cannot conceal the existence of the communication event itself. As attackers' capabilities have improved, inferring whether communication has occurred by detecting spectrum occupancy patterns or energy changes has become a common tactic, rendering security mechanisms that rely solely on content encryption insufficient. Therefore, Covert Communication has emerged, with its core objective being to prevent communication activities from being detected by the surveillance party, extending security protection from "content protection" to "behavioral concealment."

[0004] In recent years, covert communication for cognitive radio networks has made initial progress, such as improving covert rates through joint optimization of UAV power and trajectory, or balancing security and covert transmission through robust alternating optimization. However, existing research still has significant shortcomings: First, it generally assumes that eavesdroppers adopt a fixed passive detection strategy, ignoring information interaction and adaptive cooperative eavesdropping among multiple eavesdroppers (eavesdroppers can dynamically switch between active interference and passive eavesdropping based on real-time channel conditions); second, optimization methods either rely on traditional convex optimization with limited online real-time performance, or only introduce single-discriminator generative adversarial networks, lacking the ability to collaboratively model multiple eavesdroppers and multiple detection strategies; third, most studies have not theoretically derived the average minimum false detection probability of eavesdroppers, making it difficult to accurately characterize the limiting performance of covert transmission. Summary of the Invention

[0005] The main objective of this invention is to provide an intelligent covert communication method for resisting probabilistic eavesdropping in cognitive radio systems, which solves the problems of insufficient adaptive and cooperative eavesdropping threat response, lack of multi-adversarial optimization modeling, low covert transmission performance, and low reliability in existing covert communication methods in cognitive radio networks.

[0006] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is: an intelligent covert communication method for resisting probabilistic eavesdropping in a cognitive radio system, comprising the following steps: The system deploys a pair of main transmitters PT and PR, a pair of secondary transmitters ST and SR, and multiple eavesdroppers Eve. ST acquires PT's spectrum by covering the spectrum and, under the surveillance of multiple Eve, secretly transmits confidential information to SR. The multiple Eves conduct coordinated eavesdropping. In each time slot, each Eve sends a pilot to estimate its own channel gain to ST and compares the obtained channel state information with a preset threshold. If it is greater than the preset threshold, Eve executes the active-passive coordinated eavesdropping APCE scheme, that is, Eve sends artificial noise interference SR while eavesdropping on information; otherwise, Eve executes the adaptive coordinated eavesdropping ACE scheme, that is, Eve adaptively switches between eavesdropping and interference according to the real-time environment. Construct an optimized model of a multi-discriminator generative adversarial network (MGAN). The MGAN includes a generator G and multiple discriminators D. The generator G generates the transmit power and decision threshold of ST based on the current environmental state, and the multiple discriminators determine whether covert communication exists. With the goal of maximizing the covert rate of SR, and under the premise of satisfying the covert constraints and interruption constraints, the MGAN is used to jointly optimize the transmit power and decision threshold of ST to obtain the optimal covert transmission strategy.

[0007] In the preferred scheme, the probability that Eve will perform the eavesdropping behavior is expressed as: ; in, The channel gain from ST to the i-th Eve is expressed as... , It follows an exponential distribution with a mean of . .

[0008] In the preferred scheme, the preset threshold is set by Eve based on the real-time environment; The received signal at SR under the APCE scheme is represented as follows: ; in, This indicates the transmit power of ST. express Transmission power, and They represent from ST and Channel gain to SR and These are concealed signals and artificial noise signals. It is additive Gaussian noise at SR; The received signal at SR under the ACE scheme is represented as follows: ; in, This indicates the number of passive eavesdropping sessions Eve chooses under this scheme.

[0009] In the preferred embodiment, the signal-to-interference-plus-noise ratio (SINR) of the SR under the APCE and ACE schemes are respectively expressed as: ; ; in, The noise power at SR is Channel gain from ST to SR In the preferred embodiment, the concealment rate of the SR under the APCE scheme and the ACE scheme are respectively expressed as: ; ; in, Indicates the ST spectrum sensing time. It is the false alarm probability of ST during the spectrum sensing phase.

[0010] In the preferred embodiment, the optimization objective is: ; The constraints include: ; ; in, and Let denoted by AMDEP, and let ε be the mean minimum false detection probability of Eve under the APCE and ACE schemes, respectively. Let ε be the concealment constraint parameter and β be the interruption constraint parameter. and These represent the interruption probabilities under the two schemes.

[0011] In the preferred scheme, based on the Newman-Pearson likelihood ratio energy detection criterion, the minimum error detection probability per slot under the APCE and ACE schemes is derived respectively. Combining channel statistics and noise uncertainty parameter ρ, the expected value of the instantaneous minimum error detection probability is taken to obtain the average minimum error detection probability under the two schemes, specifically: The average minimum error detection probability of Eve under the APCE scheme It is given by the following formula: ; in For noise uncertainty parameters, This is Eve's reference noise power. This represents the maximum transmit power of ST. For a complete gamma function, It is an incomplete gamma function; The average minimum error detection probability of Eve under the ACE scheme It is given by the following formula: ; in, This represents the number of Eves performing passive eavesdropping under the ACE scheme.

[0012] In the preferred embodiment, the interruption probability under the APCE scheme is expressed as: ; The interruption probability under the ACE scheme is expressed as: ; in, This is the minimum receive rate threshold for SR.

[0013] In the preferred embodiment, the MGAN optimization model includes: The input layer of the generator G adopts the current environment state: And random noise z, forming the input feature vector; The hidden layer uses the ReLU activation function, and the output layer generates the transmit power of ST. and decision threshold; Each discriminator Receive a two-dimensional feature vector, which corresponds to a real sample. Or generate samples [ The discriminator outputs its signal after passing through the hidden layer and then through the Sigmoid activation function. The outputs of multiple discriminators are weighted and averaged to obtain an overall discriminant value. The overall discriminant value is then compared with a predefined threshold to make a binary decision.

[0014] In the preferred embodiment, during the training process of the MGAN, the generator G and multiple discriminators... Engaging in adversarial game between them: Each discriminator evaluates the validity and security of the generated results, and the generator continuously updates its parameters based on the feedback from the discriminators.

[0015] This invention provides an intelligent covert communication method against probabilistic eavesdropping in cognitive radio systems. Addressing scenarios where multiple eavesdroppers in a cognitive radio network may employ two attack modes: Active-Passive Cooperative Eavesdropping (APCE) and Adaptive Cooperative Eavesdropping (ACE), a covert communication system model is established between a secondary transmitter (ST), a secondary receiver (SR), and K eavesdroppers (Eve). Closed-form expressions for the average minimum false detection probability (AMDEP) of the eavesdroppers and the interruption probability at SR are derived for both eavesdropping modes. With the goal of maximizing the covert rate of SR, and conditions including covertness and interruption constraints, a multi-discriminator generative adversarial network (MGAN) is constructed. The generator generates the ST transmit power and decision threshold based on the environmental state. Multiple discriminators collaboratively determine the existence of covert communication. Joint optimization of the transmit power and decision threshold is achieved through adversarial game theory between the generator and discriminators. This invention effectively improves the covert communication rate under the threat of adaptive cooperative eavesdropping by multiple eavesdroppers, enhancing communication covertness and reliability. Attached Figure Description

[0016] The present invention will be further described below with reference to the accompanying drawings and embodiments: Figure 1 This is a model diagram of a covert transmission system for coordinated eavesdropping by multiple eavesdroppers in a cognitive radio network according to the present invention. Figure 2 This is an experimental graph showing the variation of Eve's average minimum error detection probability with channel correlation ρ under different schemes of the present invention; Figure 3 This is a graph showing the variation of AMDEP of the ACE and APCE schemes under the influence of noise uncertainty parameter ρ in cooperative cognitive radio scenarios with different numbers of eavesdroppers K according to the present invention. Figure 4 This is a graph showing the relationship between the maximum concealment rate and the number of training iterations under different concealment constraints. Figure 5 This invention relates to the relationship between the generator and discriminator loss values ​​in MGAN and the number of training iterations at different training frequencies. Detailed Implementation

[0017] Example 1 like Figure 1-5 As shown, an intelligent covert communication method for resisting probabilistic eavesdropping in a cognitive radio system includes the following steps: Create a cooperative cognitive radio covert communication system, comprising: a pair of master transmitters PT and master receiver PR, a pair of slave transmitters ST and slave receiver SR, and multiple eavesdroppers Eve. ST acquires PT's spectrum by covering the spectrum and covertly transmits confidential information to SR under the surveillance of multiple Eve. All nodes operate in single-antenna half-duplex mode, each wireless channel follows Rayleigh fading, and the single-slot channel parameters are constant while the channel changes independently between time slots. Construct a multi-eavesdropper adaptive cooperative eavesdropping model: Multiple Eves conduct cooperative eavesdropping. In each time slot, each Eve sends a pilot to estimate its own channel gain to ST and compares the obtained channel state information with a preset threshold. If it is greater than the preset threshold, Eve executes the active-passive cooperative eavesdropping APCE scheme, that is, Eve sends artificial noise interference SR while eavesdropping on information; otherwise, Eve executes the adaptive cooperative eavesdropping ACE scheme, that is, Eve adaptively switches between eavesdropping and interference according to the real-time environment. Construct an optimized model for a multi-discriminator generative adversarial network (MGAN): MGAN consists of a generator G and multiple discriminators D. The generator G generates the transmit power and decision threshold of ST based on the current environmental state, and the multiple discriminators determine whether covert communication exists. Solving the optimization problem based on multi-discriminator generative adversarial network (MGAN): Taking maximizing the covert rate of SR as the optimization objective, under the premise of satisfying the covert constraints and interruption constraints, the MGAN is used to jointly optimize the transmit power and decision threshold of ST to obtain the optimal covert transmission strategy.

[0018] In this embodiment, by constructing an MGAN optimization framework that includes a generator and multiple discriminators, it can simultaneously address two attack modes that eavesdroppers may employ: Active-Passive Cooperative Eavesdropping (APCE) and Adaptive Cooperative Eavesdropping (ACE). Under the premise of satisfying concealment constraints and interruption constraints, it jointly optimizes the ST transmission power and decision threshold, thereby maximizing the concealment rate and dynamically adapting to changes in the cooperative strategies of multiple eavesdroppers, significantly improving the system's concealed transmission performance and robustness.

[0019] The following steps will be explained in detail.

[0020] Figure 1 A covert communication system in a cognitive radio network is presented, comprising a pair of primary users (primary transmitter PT and primary receiver PR), a pair of secondary users (secondary transmitter ST and secondary receiver SR), and K eavesdroppers (Eve). All nodes are uniformly configured with a single antenna and operate in half-duplex mode. In this embodiment, K=3 / 5 / 10.

[0021] In this embodiment, the distribution function parameter of each link is set to 1 (i.e., the mean parameter λ of the channel gain exponential distribution is 1), the noise power parameters at Eve and SR are set to 1, the concealment constraint parameter ε is set to 0.1, the minimum receive rate threshold R0 of SR is set to 0.5 bit / s / Hz, and the maximum transmit power of ST is set to... Set to 10dBm, Eve's transmit jamming power The noise uncertainty parameter ρ is set to 5 dBm and varies from 1.5 to 4.5 in the simulation. The adaptive eavesdropping threshold δ is generated by MGAN optimization. The time slot length T is normalized to 1, and the spectrum sensing time ratio μ is set to 0.1.

[0022] In the aforementioned system, ST acquires PT's spectrum through a spectrum coverage method and secretly transmits confidential information to SR under the surveillance of multiple eavesdroppers. Simultaneously, it is assumed that all wireless channels are modeled as Rayleigh fading, and that all channel parameters remain constant within each time slot but vary independently between different time slots. Furthermore, all nodes are assumed to operate in half-duplex mode and are equipped with a single antenna. Eve freely chooses her eavesdropping scheme: a combined active-passive eavesdropping scheme when eavesdropping link channel conditions are favorable, and an adaptive cooperative eavesdropping scheme when eavesdropping link channel conditions are unfavorable.

[0023] System links are divided into five categories: 1) Main link (yellow solid line): PT→PR, normal spectrum transmission for primary users; 2) Sensing Link (blue dashed line): ST→PT, ST energy detection senses the spectrum occupancy status of the primary user; 3) Secondary covert transmission link (solid black line): ST→SR, carrying confidential and covert information; 4) Eavesdropping link (red dotted line): Each Eve → ST, the eavesdropper collects the signal transmitted by ST; 5) Interference link (purple dotted line): Eve→SR does not meet the conditions for eavesdropping channel, and sends artificial noise AN to interfere with legitimate reception.

[0024] In this embodiment, multiple Eves can engage in active and passive collaborative eavesdropping and dynamically select eavesdropping schemes.

[0025] Specifically, at the beginning of each time slot, all K Eves transmit pilot signals, estimate their own channel gain to ST, compare the obtained channel state information (CSI) with a preset threshold δ, and calculate the probability of eavesdropping. If CSI is greater than δ, EveE initiates active-passive cooperative eavesdropping on APCE and collects ST signals for energy detection; otherwise, Eve switches to adaptive cooperative eavesdropping on ACE and transmits artificial noise to SR to interfere with legitimate reception. The threshold δ is set by Eve based on the real-time environment.

[0026] Under this adaptive eavesdropping scheme, the probability of Eve performing eavesdropping behavior is expressed as: ; in The channel gain from ST to the i-th Eve is expressed as... . It follows an exponential distribution with a mean of . .

[0027] In this embodiment, ST cannot obtain the instantaneous channel gain of any Eve by relying solely on channel statistics (CSI), and optimization is completed solely by global statistical parameters. In this embodiment, the threshold δ in adaptive collaborative eavesdropping is quantitatively correlated with channel statistical characteristics, enabling ST to pre-assess eavesdropping risks based on channel statistical information, thereby improving the accuracy of controlling its own transmission power and enhancing the precision and concealment of adjustments.

[0028] Furthermore, assume that ST opportunistically accesses the spectrum of PT through energy detection. Therefore, when ST detects that the spectrum of PT is idle, ST will covertly transmit its own information. Thus, under the APCE scheme, the received signal at SR can be expressed as: ; in, This indicates the transmit power of ST. express The transmission power; and They represent from ST and The channel gain to SR is expressed as follows: and , and They respectively follow the mean of and The exponential distribution; and These are the concealed signal and the AN signal, respectively, where t (t=1,2,...,N) is the index used for each channel. This is the total number of channels used, satisfying... and ; It is the additive Gaussian noise at SR, denoted as .

[0029] Under the ACE scheme, the received signal at SR can be expressed as: ; in This indicates the number of passive eavesdropping sessions Eve chooses under this scheme.

[0030] Furthermore, assuming ST's transmit power is in the range The above follows a uniform distribution, and its probability density function (PDF) is: ; The signal-to-interference ratio plus noise ratio (SINR) of SR under APCE and ACE schemes are expressed as follows: ; ; Therefore, the feasibility of SR under different schemes can be expressed as: ; ; in, Indicates the ST spectrum sensing time. It is the false alarm probability of ST during the spectrum sensing phase.

[0031] This embodiment uses the above formula to calculate the SR received signal, signal-to-interference-plus-noise ratio, and covert rate in real time, improving the accuracy of communication quality assessment in different eavesdropping scenarios. APCE mode: Single-channel Eve directional interference exists, the SR received signal contains single-channel artificial noise, and SINR only adds the interference power of a single eavesdropper. ACE mode: Multiple Eve units simultaneously transmit interference, and the interference power is summed. Under the same transmission power, the SR signal-to-interference-plus-noise ratio is lower than that in the APCE scenario. Concealment rate uniformly deducts spectrum sensing loss coefficient Spectrum sensing false alarm probability To obtain an effective transmission rate .

[0032] The objective of this embodiment is to maximize the concealment rate of SR while satisfying given concealment constraints. Therefore, the optimization problem is defined as follows: ; ; ; ; ; ; Among them, (9c) and (9d) are hidden constraints, and (9e) and (9f) are interruption constraints, which will be explained in detail below.

[0033] 1) Hidden constraints Theoretical derivation of the eavesdropper's average minimum false detection probability (AMDEP): During transmission, Eve uses collected information to perform hypothesis testing to determine whether ST has sent covert information. Considering a real-world intelligent Eve, it can adaptively switch between active / passive coordinated eavesdropping and adaptive coordinated eavesdropping strategies based on the CSI of the eavesdropping link. To satisfy the covert constraint, we first calculate Eve's average minimum false detection probability (MDEP) under the two attack modes, and take the smaller of the two as the minimum probability of Eve making an error during detection.

[0034] Assume Eves' sum of AWGN is , recorded as ,in This represents the total noise power and follows the interval... A uniform distribution on the surface. Then, the PDF is given by the following formula: ; consider This indicates that ST did not transmit any covert information. This indicates that ST transmitted covert information. Under both assumptions, the average power received by Eve in the active-passive cooperative eavesdropping mode is as follows: ; According to the Newman-Pearson criterion, Eve minimizes the probability of detection error through a likelihood ratio test. For a given transmission time slot, Eve determines the average received power as follows: ; in This indicates that Eve determined ST transmitted hidden information. This indicates that Eve determined ST did not transmit any covert information. This is the detection error threshold. Equation (10) means that when the average power received by Eve is greater than... Eve then determines that ST transmitted hidden information; if it is less than If so, it is determined that ST did not transmit any hidden information.

[0035] In the energy detection process, Eve's false detection probability consists of two parts: one is the false alarm probability, defined as... The other is the false negative probability, defined as... Then Eve's false detection probability is expressed as: ; When A hour, ; in, , , .

[0036] when hour, .

[0037] By taking the derivatives for each case, Eve's optimal detection threshold and minimum false detection probability are expressed as: ; .

[0038] When Eve uses the adaptive cooperative eavesdropping mode, under two assumptions, the average power received by Eve is as follows: .

[0039] Similar to the active-passive cooperative eavesdropping strategy, Eve minimizes the detection error probability through a likelihood ratio test, based on the Newman-Pearson criterion. The calculation process is also similar to that of active-passive cooperative eavesdropping; Eve's minimum false detection probability and optimal threshold in the adaptive cooperative eavesdropping mode are given by the following formula: ; .

[0040] Where D= .

[0041] Since ST does not know their instantaneous CSI to Eve, but only possesses the statistical state information of the channel, the average minimum error detection probability (AMDEP) is used to evaluate the stealth performance. The AMDEP for both modes is given by the following formula: ; Where B=A , It is a complete Gamma function. It is an incomplete Gamma function.

[0042] , In this embodiment, the closed-form expression of Eve's AMDEP under both APCE and ACE schemes reveals the influence of noise uncertainty parameter ρ, number of eavesdroppers K, and upper limit of transmission power on concealment performance, improving the stability of concealment. At the same time, it provides analytically calculable constraints for parameter optimization, significantly reducing the complexity of online optimization.

[0043] Therefore, in order to achieve covert transmission, the following covert constraint must be maintained: ; ; in It is an arbitrarily small positive integer.

[0044] In this embodiment, the optimization objective is defined as maximizing the minimum concealment rate under the two schemes. The optimization problem fully covers the key performance indicators of the system, ensuring the overall optimality of communication in combating intelligent eavesdroppers.

[0045] 2) No interruption constraint Outage probability is a key indicator for measuring communication reliability. By definition, outage probability refers to the probability that the receiver's concealment rate is less than a given threshold. Let the minimum receiving rate threshold for SR be... Therefore, based on equations (7) and (8), there are two possible interruption probabilities as follows: ; .

[0046] The primary consideration is the concealment performance under the conditions of satisfying concealment and interruption constraints. To address collaborative eavesdropping by multiple eavesdroppers in real-world scenarios, a multi-discriminator generative adversarial network (MGAN) is proposed to simulate these scenarios. This is achieved by adjusting the ST transmit power and threshold. Optimization was performed to maximize stealth rate and AMDEP under both schemes.

[0047] This embodiment clearly controls the risk of communication interruption, improves the reception reliability of SR, and achieves a balance between covert transmission and reliable transmission by combining channel statistical parameters and power allocation (the interruption probability is 0.06, which satisfies the constraint β=0.1).

[0048] In this embodiment, different covert transmission strategies are developed for multiple eavesdroppers in a cognitive radio network, namely, an active-passive cooperative eavesdropping strategy and an adaptive eavesdropping strategy. Specifically, while the ST and SR are communicating secretly, multiple eavesdroppers cooperate to send artificial noise to interfere with the SR's covert transmission while eavesdropping on information. At the same time, the ST dynamically controls its transmission power through the MGAN optimization algorithm to counter the eavesdropping and interference problems of colluding eavesdroppers.

[0049] For the hypothetical covert transmission involving multiple eavesdroppers collaborating in cognitive radio networks, three key performance indicators (KPIs) under the collaborative eavesdropping scenario were rigorously derived: Eves' mean minimum false detection probability, the covert rate at the SR (Search Stream), and the covert interruption probability (COP). Furthermore, the optimal maximum transmit power was obtained under covert constraints, and the maximum achievable covert rate of the system was determined.

[0050] In this embodiment, the eavesdropping capability is improved through the cooperation of multiple active eavesdroppers, and the resistance to cooperative active attacks by multiple eavesdroppers is enhanced.

[0051] like Figure 2 As shown, the MGAN multi-discriminator adversarial network solves for the optimization variables.

[0052] In this embodiment, the MGAN optimization framework consists of two modules: a generator. Generate transmit power and decision thresholds for ST; multiple discriminators This is used to determine whether hidden information exists. From the perspective of ST, MGAN transforms the entire optimization process into an adversarial game between a generator (ST) and multiple discriminators (Eves). Each discriminator receives a two-dimensional feature vector, which may correspond to a real sample. (From the training dataset) or generated samples (Generated by a generator), the input data passes through a hidden layer (using the ReLU activation function), and then the output layer (using the Sigmoid activation function) maps the output to the interval [0,1]. For the outputs of multiple discriminators, a weighted average is used to obtain the overall discriminant value, which is then compared with a predefined threshold D to make a binary decision: an output of 0 indicates that the ST did not transmit the secret information, while an output of 1 indicates that secret communication exists.

[0053] The generator's input layer takes the current environment state as its input. And random noise z, forming the input feature vector. The hidden layer uses the ReLU activation function, the same as the discriminator. In the output layer, the generator produces two key parameters: the emission power of ST. and decision threshold These outputs are then passed as input to each discriminator, which evaluates the validity and security of the generated results in the context of covert communication. Based on the discriminator's feedback, the generator continuously updates its parameters, thereby enhancing covertness while maintaining communication performance.

[0054] In this embodiment, channel state information is fully utilized to adaptively generate optimal parameters, and the multi-discriminator design improves the accuracy of fitting the joint decision of multiple eavesdroppers, thereby enhancing the accuracy and robustness of the optimization effect.

[0055] In this embodiment, the above technical solutions are simulated and analyzed.

[0056] like Figure 3 As shown, theoretical curves and simulation scatter plots of the AMDEP of APCE and ACE schemes as a function of the noise uncertainty parameter ρ are presented for different numbers of eavesdroppers K (K=3 and K=10). The theoretical and simulation results are in high agreement, verifying the accuracy of the established model: as... As the noise level increases, all curves monotonically rise and approach 1, indicating that the stronger the noise uncertainty, the higher Eve's detection error probability, and the more difficult it is to detect covert communication. At larger... In the same region, the performance gap between the two solutions gradually narrows. Under these conditions, the average MDEP of the APCE scheme is consistently higher than that of the ACE scheme, especially at low frequencies. The region indicates that, within the ACE mechanism, the ACE scheme, due to the eavesdropper's adaptive switching between interference and eavesdropping, makes Eve's detection capability relatively stronger and her stealth reduced. When When the number of eavesdroppers increases from 3 to 10, the AMDEP of both schemes decreases significantly, indicating that more eavesdroppers working together will reduce the stealth performance.

[0057] like Figure 4 As shown, the curves of the maximum concealment rate obtained by MGAN optimization as a function of the number of training iterations are displayed under different concealment constraints (ε=0.05, 0.1, 0.15). All curves rise rapidly in the first 500 iterations and then tend to plateau, indicating that the MGAN algorithm converges quickly and stably. Further comparison shows that the larger the ε value (i.e., the looser the concealment constraint), the higher the steady-state concealment rate after convergence. This is because a larger ε allows for a higher AMDEP, that is, a higher detection error probability for Eve, which allows ST to safely increase the transmission power, thereby increasing the rate and thus improving the concealment rate.

[0058] like Figure 5 As shown, the generator loss and discriminator loss vary with the number of training epochs under different discriminator update frequencies k (k=1,2,5). When k is fixed, the generator loss decreases rapidly and stabilizes at a low level, while the discriminator loss increases early and then converges, which is consistent with the theoretical expectation of adversarial training. A horizontal comparison shows that increasing k (increasing the discriminator training frequency) reduces the number of iterations required for convergence (accelerating convergence), but also leads to a slight increase in the steady-state loss of both the generator and discriminator, indicating a trade-off between convergence speed and optimization performance.

[0059] Based on the optimal transmit power and decision threshold obtained through MGAN optimization, this embodiment further statistically analyzes the system's average concealment rate, average AMDEP, and outage probability under the optimal strategy. In a typical scenario with ε=0.1, K=5, and ρ=3.0, the optimal... The impedance is approximately 6.8 dBm, and the optimal δ is approximately 0.32. At this point, the AMDEP of the APCE scheme is 0.93, and the AMDEP of the ACE scheme is 0.87. The average concealment rate reaches 0.82 bit / s / Hz, and the interruption probability is 0.06, all of which meet the constraints. This verifies the effectiveness of the method of the present invention in resisting probabilistic eavesdropping by multiple eavesdroppers.

[0060] This embodiment fully simulates the APCE / ACE adaptive eavesdropping scenario, improving the realism of the wireless security attack environment, increasing model credibility, improving balance convergence speed and optimization accuracy, achieving behavioral concealment solely based on physical layer channel characteristics, and reducing costs.

[0061] This embodiment takes a single ST-SR covert transmission link as an example, which can be extended to decentralized IoT multi-level user concurrent covert transmission scenarios; it only requires synchronously increasing the generator output dimension and expanding the number of discriminators to adapt to multi-user multi-eavesdropping game, which is still within the protection scope of this invention.

[0062] The above embodiments are merely preferred technical solutions of the present invention and should not be considered as limitations on the present invention. The scope of protection of the present invention should be limited to the technical solutions described in the claims, including equivalent substitutions of the technical features described in the claims. That is, equivalent substitutions and improvements within this scope are also within the scope of protection of the present invention.

Claims

1. A smart covert communication method for resisting probabilistic eavesdropping in a cognitive radio system, characterized in that, Includes the following steps: The system deploys a pair of main transmitters PT and PR, a pair of secondary transmitters ST and SR, and multiple eavesdroppers Eve. ST acquires PT's spectrum by covering the spectrum and, under the surveillance of multiple Eve, secretly transmits confidential information to SR. The multiple Eves conduct coordinated eavesdropping. In each time slot, each Eve sends a pilot to estimate its own channel gain to ST and compares the obtained channel state information with a preset threshold. If it is greater than the preset threshold, Eve executes the active-passive coordinated eavesdropping APCE scheme, that is, Eve sends artificial noise interference SR while eavesdropping on information; otherwise, Eve executes the adaptive coordinated eavesdropping ACE scheme, that is, Eve adaptively switches between eavesdropping and interference according to the real-time environment. Construct an optimized model of a multi-discriminator generative adversarial network (MGAN). The MGAN includes a generator G and multiple discriminators D. The generator G generates the transmit power and decision threshold of ST based on the current environmental state, and the multiple discriminators determine whether covert communication exists. With the goal of maximizing the covert rate of SR, and under the premise of satisfying the covert constraints and interruption constraints, the MGAN is used to jointly optimize the transmit power and decision threshold of ST to obtain the optimal covert transmission strategy.

2. The covert communication method against probabilistic eavesdropping in a cognitive radio system according to claim 1, characterized in that, The probability that Eve will engage in eavesdropping is expressed as: ； in, The channel gain from ST to the i-th Eve is expressed as... , It follows an exponential distribution with a mean of . .

3. The covert communication method against probabilistic eavesdropping in a cognitive radio system according to claim 1, characterized in that, The preset threshold is set by Eve based on the real-time environment; The received signal at SR under the APCE scheme is represented as follows: ； in, This indicates the transmit power of ST. express Transmission power, and They represent from ST and Channel gain to SR and These are concealed signals and artificial noise signals. It is additive Gaussian noise at SR; The received signal at SR under the ACE scheme is represented as follows: ； in, This indicates the number of passive eavesdropping sessions Eve chooses under this scheme.

4. The covert communication method against probabilistic eavesdropping in a cognitive radio system according to claim 1, characterized in that, The signal-to-interference-plus-noise ratio (SINR) of the SR under the APCE and ACE schemes are respectively expressed as follows: ； ； in, The noise power at SR is This represents the channel gain from ST to SR.

5. The covert communication method against probabilistic eavesdropping in a cognitive radio system according to claim 1, characterized in that, The concealment rates of SR under the APCE and ACE schemes are respectively expressed as: ； ； in, Indicates the ST spectrum sensing time. It is the false alarm probability of ST during the spectrum sensing phase.

6. The covert communication method against probabilistic eavesdropping in a cognitive radio system according to claim 1, characterized in that, The optimization objective is: ； The constraints include: ； ； in, and Let denoted by AMDEP, and let ε be the mean minimum false detection probability of Eve under the APCE and ACE schemes, respectively. Let ε be the concealment constraint parameter and β be the interruption constraint parameter. and These represent the interruption probabilities under the two schemes.

7. The covert communication method against probabilistic eavesdropping in a cognitive radio system according to claim 6, characterized in that, Based on the Newman-Pearson likelihood ratio energy detection criterion, the minimum error detection probability per slot under the APCE and ACE schemes is derived respectively. Combining channel statistics and the noise uncertainty parameter ρ, the expected value of the instantaneous minimum error detection probability is obtained, yielding the average minimum error detection probability for both schemes: The average minimum error detection probability of Eve under the APCE scheme It is given by the following formula: ； in For noise uncertainty parameters, This is Eve's reference noise power. This represents the maximum transmit power of ST. For a complete gamma function, It is an incomplete gamma function; The average minimum error detection probability of Eve under the ACE scheme It is given by the following formula: ； in, This represents the number of Eves performing passive eavesdropping under the ACE scheme.

8. The covert communication method against probabilistic eavesdropping in a cognitive radio system according to claim 6, characterized in that, The interruption probability under the APCE scheme is expressed as follows: ； The interruption probability under the ACE scheme is expressed as: ； in, This is the minimum receive rate threshold for SR.

9. The covert communication method against probabilistic eavesdropping in a cognitive radio system according to claim 1, characterized in that, In the MGAN optimization model: The input layer of the generator G adopts the current environment state: And random noise z, forming the input feature vector; The hidden layer uses the ReLU activation function, and the output layer generates the transmit power of ST. and decision threshold; Each discriminator Receive a two-dimensional feature vector, which corresponds to a real sample. Or generate samples The discriminator outputs its signal after passing through the hidden layer and then through the Sigmoid activation function. The outputs of multiple discriminators are weighted and averaged to obtain an overall discriminant value. The overall discriminant value is then compared with a predefined threshold to make a binary decision.

10. The covert communication method against probabilistic eavesdropping in a cognitive radio system according to claim 1, characterized in that, During the training process of the MGAN, the generator G and multiple discriminators... Engaging in adversarial game between them: Each discriminator evaluates the validity and security of the generated results, and the generator continuously updates its parameters based on the feedback from the discriminators.

Images