A hybrid power line-wireless communication system covert information probabilistic transmission method

Abstract

The application provides a mixed power line-wireless communication system covert information probability transmission method, channel state information of a power line and a wireless communication double link between legal transceiving nodes is acquired, and a probability transmission mechanism is used to send covert information when a preset condition is met. The uncertainty of impulse noise in the power line communication link and the uncertainty of background noise in the wireless communication link are fully utilized, information transmission can be dynamically and covertly performed according to the channel quality of the legal link, so that the probability that a eavesdropper detects the communication behavior is effectively reduced, and the strict covert constraint condition of the system is met.

Description

Technical Field

[0001] This invention relates to the field of covert communication technology, and more specifically to a method for covert information probabilistic transmission in a hybrid power line-wireless communication system. Background Technology

[0002] The hybrid architecture of power line communication (PLC) and wireless communication (WLC) is becoming increasingly prevalent, but this integration further expands the system's attack surface and complicates security boundaries. Currently, data security in hybrid communication systems primarily relies on encryption and physical layer security technologies. These traditional methods largely focus on protecting the content of communication while neglecting the privacy protection of the communication behavior itself. This makes the system's transmission behavior highly susceptible to detection by potential eavesdroppers in complex open communication environments, posing significant risks of privacy breaches and security vulnerabilities. To meet the enhanced security requirements of hybrid communication systems, there is an urgent need to introduce covert communication techniques to directly conceal communication activities. However, existing hybrid network transmission schemes mostly focus on improving communication performance or merely preventing information interception, failing to delve into the design from the perspective of covert communication. Therefore, how to fully utilize the inherent noise uncertainty characteristics of hybrid power line-wireless channels to dynamically and probabilistically transmit information based on link states, thereby effectively reducing the risk of communication activity exposure, has become a pressing problem to be solved in this field. Summary of the Invention

[0003] The purpose of this invention is to solve the technical problems mentioned above, and to propose a method for covert information probabilistic transmission in a hybrid power line-wireless communication system, comprising the following steps: Obtain channel state information for the power line communication link and wireless communication link between the legitimate sender and the legitimate receiver; Based on channel state information and employing a probabilistic transmission mechanism, when preset conditions are met, the legitimate sender transmits covert information to the legitimate receiver through power line communication links and wireless communication links. The transmission of covert information utilizes the uncertainty of impulse noise in power line communication links and the uncertainty of background noise in wireless communication links, while satisfying covert constraints.

[0004] In the preferred embodiment, a probabilistic transmission mechanism is adopted to send covert information when preset conditions are met. Specifically, this includes setting preset transmission thresholds for the power line communication link and the wireless communication link; when the channel gain of the power line communication link is greater than its corresponding preset transmission threshold, and the channel gain of the wireless communication link is greater than its corresponding preset transmission threshold, the legitimate sender initiates the transmission of covert information; otherwise, the legitimate sender remains silent.

[0005] In the preferred embodiment, the legitimate sender transmits covert information to the legitimate receiver through a power line communication link and a wireless communication link, including: allocating the legitimate sender's transmission power to the power line communication link and the wireless communication link respectively according to a set power allocation factor, and performing synchronous information transmission.

[0006] In the preferred embodiment, the concealment constraint is set based on the average minimum false detection probability of the eavesdropper; The average minimum false detection probability of an eavesdropper is evaluated using statistical channel state information obtained from long-term observations. The evaluation process is based on the uncertainty of the probability of impulse noise in power line communication links and the uncertainty of the actual noise power in wireless communication links.

[0007] In the preferred embodiment, when eavesdropping on communication activities, the eavesdropper uses hypothesis testing to determine whether the legitimate sender has transmitted hidden information based on the average energy of the received signal. The eavesdropper assesses the average received signal energy using a power detection method and formulates decision rules based on the Newman-Pearson criterion and likelihood ratio test, selecting the optimal detection threshold to minimize the overall detection error probability.

[0008] In a preferred embodiment, the method further includes: jointly optimizing the transmission parameters, with the optimization objective being to maximize the covert rate of the legitimate receiver while satisfying the given covert constraints.

[0009] In the preferred scheme, the transmission parameters for joint optimization include: The preset transmission threshold for the power line communication link, the preset transmission threshold for the wireless communication link, and the power allocation factor allocated to the two links.

[0010] In the preferred scheme, when optimizing the transmission parameters, the optimization problem is decomposed into two sub-problems and solved using an alternating optimization method. The specific steps include: With a fixed power allocation factor, the optimal preset transmission thresholds for the power line communication link and the wireless communication link are decoupled and calculated separately. The power allocation factor is optimized using a simulated annealing algorithm, ultimately maximizing the covert transmission rate at the legitimate receiver.

[0011] In the preferred embodiment, the channel models for the power line communication link and the wireless communication link respectively include: all wireless channels are modeled as Rayleigh fading, all power line channels follow a log-normal distribution; and each channel remains constant within each time slot and changes randomly and independently between different time slots, assuming that all nodes in the system operate in half-duplex mode.

[0012] A hybrid power line wireless communication system for implementing the above-mentioned method for covert information probabilistic transmission in a hybrid power line wireless communication system, comprising: a legitimate sender, a legitimate receiver, and a potential eavesdropper; The legitimate sender is configured to use a probabilistic transmission mechanism to send covert information to the legitimate receiver via power line communication links and wireless communication links; The system utilizes the uncertainty of impulse noise in power line communication links and the uncertainty of background noise in wireless communication links to transmit covert information probabilistically to legitimate receivers based on the channel quality of legitimate links, thereby reducing the probability that eavesdroppers in the system will successfully detect the communication behavior.

[0013] Compared with the prior art, the beneficial effects of the present invention are as follows: (1) This invention proposes a probabilistic transmission scheme based on channel state information to realize covert communication in a hybrid power line wireless communication system. Specifically, in the constructed HPWC model, by taking advantage of impulse noise uncertainty and background noise uncertainty, the transmitter can probabilistically transmit covert information to the legitimate receiver based on the channel quality of the legitimate link, thereby reducing the probability of eavesdroppers being detected in the system.

[0014] (2) This invention derives the optimal detection threshold and minimum detection error probability for eavesdroppers in the covert communication scheme of the HPWC system. In addition, by reasonably designing the transmission threshold and power allocation strategy of the two channels, the maximum covert rate of the system and the corresponding covert interruption probability are obtained.

[0015] (3) This invention utilizes probabilistic transmission, the uncertainty of PLC link impulse noise, and the uncertainty of WLC link background noise to enhance concealment performance, and evaluates it using concealment rate and concealment interruption probability. Results show that the degree of noise uncertainty and the transmission threshold jointly determine the dominant role of the medium in the eavesdropper's AMDEP. Compared with single-medium transmission and deterministic transmission schemes, the proposed scheme exhibits superior performance in both concealment and reliability. However, its concealment advantage gradually weakens when the transmission distance is too long. Attached Figure Description

[0016] Figure 1 This is a model diagram of a hybrid power line and wireless communication system.

[0017] Figure 2 This is an experimental graph showing the variation of Eve's average minimum detection error probability with the power allocation factor under different WLC link background noise uncertainties.

[0018] Figure 3 This is an experimental graph showing how Bob's hiding rate changes with the number of iterations for different distances between Alice and Bob.

[0019] Figure 4 This is an experimental graph showing the variation of Bob's concealment rate with the power allocation factor under different PLC and WLC link transmission thresholds. Detailed Implementation

[0020] Example 1 A method for probabilistic transmission of covert information in a hybrid power line-wireless communication system includes the following steps: Obtain channel state information for the power line communication link and wireless communication link between the legitimate sender and the legitimate receiver; Based on channel state information and employing a probabilistic transmission mechanism, when preset conditions are met, the legitimate sender transmits covert information to the legitimate receiver through power line communication links and wireless communication links. The transmission of covert information utilizes the uncertainty of impulse noise in power line communication links and the uncertainty of background noise in wireless communication links, while satisfying covert constraints.

[0021] Preferably, a probabilistic transmission mechanism is adopted to send covert information when preset conditions are met. Specifically, this includes setting preset transmission thresholds for the power line communication link and the wireless communication link; when the channel gain of the power line communication link is greater than its corresponding preset transmission threshold, and the channel gain of the wireless communication link is greater than its corresponding preset transmission threshold, the legitimate sender initiates the transmission of covert information; otherwise, the legitimate sender remains silent.

[0022] Preferably, the legitimate sender transmits covert information to the legitimate receiver through a power line communication link and a wireless communication link, including: allocating the legitimate sender's transmission power to the power line communication link and the wireless communication link respectively according to a set power allocation factor, and performing synchronous information transmission.

[0023] Preferably, the concealment constraint is set based on the average minimum false detection probability of the eavesdropper; The average minimum false detection probability of an eavesdropper is evaluated using statistical channel state information obtained from long-term observations. The evaluation process is based on the uncertainty of the probability of impulse noise in power line communication links and the uncertainty of the actual noise power in wireless communication links.

[0024] Preferably, when eavesdropping on communication activities, the eavesdropper uses hypothesis testing to determine whether the legitimate sender has transmitted concealed information based on the average energy of the received signal; The eavesdropper assesses the average received signal energy using a power detection method and formulates decision rules based on the Newman-Pearson criterion and likelihood ratio test, selecting the optimal detection threshold to minimize the overall detection error probability.

[0025] Preferably, it further includes: jointly optimizing the transmission parameters, with the optimization objective being to maximize the covert rate of the legitimate receiver while satisfying the given covert constraints.

[0026] Preferably, the transmission parameters for joint optimization include: The preset transmission threshold for the power line communication link, the preset transmission threshold for the wireless communication link, and the power allocation factor allocated to the two links.

[0027] Preferably, when optimizing the transmission parameters, the optimization problem is decomposed into two sub-problems and solved using an alternating optimization method. Specific steps include: With a fixed power allocation factor, the optimal preset transmission thresholds for the power line communication link and the wireless communication link are decoupled and calculated separately. The power allocation factor is optimized using a simulated annealing algorithm, ultimately maximizing the covert transmission rate at the legitimate receiver.

[0028] Preferably, the channel models for the power line communication link and the wireless communication link include: all wireless channels are modeled as Rayleigh fading, all power line channels follow a log-normal distribution; and each channel remains constant within each time slot and changes randomly and independently between different time slots, assuming that all nodes in the system operate in half-duplex mode.

[0029] A hybrid power line wireless communication system for implementing the above-mentioned method for covert information probabilistic transmission in a hybrid power line wireless communication system, comprising: a legitimate sender, a legitimate receiver, and a potential eavesdropper; The legitimate sender is configured to use a probabilistic transmission mechanism to send covert information to the legitimate receiver via power line communication links and wireless communication links; The system utilizes the uncertainty of impulse noise in power line communication links and the uncertainty of background noise in wireless communication links to transmit covert information probabilistically to legitimate receivers based on the channel quality of legitimate links, thereby reducing the probability that eavesdroppers in the system will successfully detect the communication behavior.

[0030] Example 2 like Figure 1As shown, this invention considers an HPWC system consisting of a legitimate sender (Alice), a legitimate receiver (Bob), and a potential eavesdropper (Eve). In this system, Alice sends covert information to Bob via a PLC link and a WLC link using a PT mechanism, while Eve listens for Alice's covert information transmission to Bob via the PLC and WLC links. This invention also considers the impact of uncertainties in impulse noise (IN) in the PLC link and background noise (BN) in the WLC link on Eve's eavesdropping. Under general assumptions, all wireless channels are modeled as Rayleigh fading, and all power line channels follow a log-normal distribution, with each channel remaining constant within each time slot and varying randomly and independently between different time slots. Furthermore, it is assumed that all nodes operate in half-duplex mode.

[0031] In this system, Alice employs a PT (Push-to-Shore) strategy for information transmission. Specifically, Alice will only initiate information transmission when the channel gains of both the PLC and WLC links are greater than a given threshold; otherwise, Alice remains silent. Subsequently, the transmission mechanisms for the PLC and WLC links will be introduced separately.

[0032] (1) Transmission on the PLC link Based on the above, the probability that the PLC link satisfies the conditions for covert information transmission is expressed as follows:

[0033]

[0034] in, The preset transmission threshold for the PLC link. The channel gain of the PLC link between Alice and Bob is denoted as . , ,in and Let represent the mean and variance, respectively. To ensure that the log-normal fading of the channel does not change the average signal power, assume... .

[0035] Therefore, once Alice begins transmitting information, the signal received on Bob's PLC link can be represented as:

[0036] in This indicates Alice's transmission power. It is the power allocation factor of the PLC link. Represents the path loss factor, where , and These are parameters measured in power line communication experiments. It is the carrier frequency of the signal. It is the distance from Alice to Bob. Representing hidden information, satisfying = 1. and These represent BN and IN on the Bob side, respectively. , . It is a Bernoulli random variable indicating whether IN exists at the Bob end.

[0037] (2) Transmission on WLC link Similarly, the probability that a WLC link satisfies the conditions for covert information transmission is expressed as:

[0038] in, This is the preset transmission threshold for the WLC link. The channel gain of the WLC link between Alice and Bob is denoted as . .therefore, The distribution follows the parameter. The exponential distribution.

[0039] Therefore, the signal received on Bob's WLC link can be represented as

[0040] in It is the path loss index. Let the additive white Gaussian noise (AWGN) at Bob be denoted as . .

[0041] Therefore, the probability that Alice can transmit covert information simultaneously on both the PLC link and the WLC link is:

[0042] The objective of this invention is to maximize Bob's concealment rate while satisfying given concealment constraints. Therefore, the optimization problem is defined as follows:

[0043]

[0044]

[0045]

[0046] Wherein, (6a) and (6b) represent the concealment constraints of the PLC link and WLC link, respectively. (6c) represents the feasible range of the power allocation factor.

[0047] Hidden constraints During transmission, Eve uses hypothesis testing based on the average energy of the received signal to determine whether Alice has transmitted hidden information. To satisfy the given concealment constraints, Willie's minimum false detection probability (MDEP) must first be calculated, which is the minimum probability that Willie will make an incorrect judgment during the detection process. Consider... This indicates that Alice did not transmit any hidden information. This indicates that Alice transmitted covert information. Under the two assumptions above, the signal received by Eve on the PLC link can be represented as:

[0048] in, and Let BN and IN represent the noise at Eve, respectively, satisfying and . It is a Bernoulli random variable representing the IN state at the Eve end. This indicates that impulse noise occurs with a probability of . , This indicates that impulse noise does not occur, with a probability of . . Represents the path loss factor, where This represents the distance from Alice to Eve. This represents the channel gain of the PLC link from Alice to Eve, and its distribution is as follows: Similarly, suppose .

[0049] Furthermore, this invention assumes that Eve is always in an observation state and that the number of observation samples tends to infinity. Therefore, under both assumptions, the average received signal energy can be expressed as:

[0050] in, . This represents the probability of impulse noise occurring at Eve. Meanwhile, IN is characterized by its short duration and high power spectral density, which can interfere with the detection of Eve. For ease of analysis, it is assumed that the probability of impulse noise occurring at Eve follows a uniform distribution, and its corresponding probability density function (PDF) can be expressed as:

[0051] in and These represent the standard probability and the actual probability of impulse noise occurring at Eve on the PLC link, respectively. This indicates the degree of uncertainty in the probability of impulse noise occurring.

[0052] Based on the Newman-Pearson criterion and likelihood ratio test, Eve evaluates the average received signal energy using a power detection method. The corresponding test rule is as follows:

[0053] in, This represents Eve's detection threshold for the PLC link. and These represent Eve's support. and The decision outcome.

[0054] According to the principles of hypothesis testing, Eve may make two types of errors during the hypothesis testing process, which respectively affect... False alarm probability and the probability of missed detection From Eve's perspective, selecting the optimal detection threshold minimizes the overall detection error probability. Therefore, the overall detection error probability is defined as...

[0055] when At that time, Eve's MDEP is zero. Therefore, this invention only considers... Under these conditions, the DEP of the PLC link can be represented as...

[0056] in , , , .

[0057] By differentiation, when Eve is performing detection on the PLC link, Willie's optimal detection threshold and corresponding MDEP are:

[0058]

[0059] Similarly, the signal received by Eve on the WLC link can be represented as

[0060] in It is Eve's AWGN, which satisfies . It is the channel gain of the WLC link between Alice and Eve, and .therefore, Follow the mean The exponential distribution.

[0061] Therefore, under both assumptions, the average signal energy at the Eve end of the WLC link can be expressed as:

[0062] Based on general assumptions, bounded noise uncertainty is considered on WLC links. Therefore, on WLC channels... The PDF is:

[0063] in, and These are the rated noise power and actual noise power at Eve on the WLC link, respectively. The degree of noise uncertainty.

[0064] Similarly,

[0065] in This represents Eve's detection threshold for the WLC link. and These represent Eve's support. and The decision outcome. Eve's goal is to minimize the overall detection error probability, which is defined as...

[0066] when At that time, Eve's MDEP is zero. Therefore, this invention only considers... Under these conditions, the overall detection error probability of the WLC link can be expressed as:

[0067] in , , , .

[0068] By differentiation, when Eve performs detection on the WLC link, Willie's optimal detection threshold and corresponding MDEP are:

[0069]

[0070] in .

[0071] Due to the passive nature of eavesdropping, Eve cannot obtain the instantaneous CSI of the eavesdropping channel, but can obtain the statistical CSI through long-term observation. Therefore, the mean minimum error probability (AMDEP) is used to evaluate the eavesdropper's detection performance. AMDEP is given by the following formula:

[0072]

[0073] in , .

[0074]

[0075] in, , , , , , , It is a complex trade-off index.

[0076] Therefore, in order to achieve covert transmission, the following covert constraint must be maintained:

[0077] Among them, (25) is equivalent to constraints (6a) and (6b). It is an arbitrarily small positive number used to evaluate the strength of hidden constraints.

[0078] This invention primarily considers the concealment performance without interruption under concealment constraints. First, the concealment constraints are analyzed; then, the optimal power allocation factor for Alice and the transmission threshold of the PLC-WLC link are analyzed to maximize the concealment rate at Bob's location; finally, the probability of concealment interruption in the system is analyzed.

[0079] Due to the complexity of solving the optimization problem, it is decomposed into two sub-problems: first, fix the power allocation factor, and then decouple... And find the optimal Then, a simulated annealing algorithm is used to optimize the power allocation factor. Through alternating optimization, the hidden transmission rate at Bob's location is ultimately maximized.

[0080] To ensure the reliability of covert communication between Alice and Bob, we will next analyze Bob's covert interruption probability (COP). The probability of covert communication between Alice and Bob being interrupted is expressed as:

[0081]

[0082]

[0083] in This is Bob's default stealth rate. , It is a composite trade-off index.

[0084] Now combined with the appendix Figure 1 The specific embodiments of the present invention are described as follows: Figure 1 An example of a covert communication system based on hybrid power line-wireless probabilistic transmission using channel state information is given. The local noise of the WLC link at Bob and Eve is set to 1, and the local noise of the PLC link at Bob and Eve is set to 10.

[0085] like Figure 2 The figure shows the relationship between AMDEP and the power allocation factor under different WLC link uncertainties. It can be seen that AMDEP first increases and then decreases with the increase of the power allocation factor. Simultaneously, it can be observed that when the factor is small, AMDEP increases with the increase of noise uncertainty; however, as the power allocation factor gradually increases, AMDEP is no longer affected by noise uncertainty. This is because when the power allocation factor is small, more power is allocated to the WLC link, making the impact of this link and its corresponding noise uncertainty on AMDEP more significant, thus leading to an increase in AMDEP. However, when the power allocation factor further increases, the power allocated to the PLC link gradually increases, significantly enhancing the signal strength of this link, reducing the difficulty of Eve detection, and thus gradually decreasing AMDEP. Furthermore, it can be observed that when the WLC link dominates Eve detection, the AMDEP of the PT scheme is significantly higher than that of the DT scheme. Therefore, it can be concluded that there exists an optimal power allocation scheme that maximizes AMDEP. AMDEP and the proposed probabilistic transmission scheme can significantly improve the system's stealth.

[0086] like Figure 3 The figure shows the convergence characteristics of the proposed algorithm under different distances between Alice and Bob. It can be seen that the algorithm converges quickly under different parameter conditions, indicating its good robustness. Furthermore, as Bob's distance from Alice increases... The CR also decreases accordingly. This is because when Bob moves away from Alice, the covert signal Bob receives weakens, leading to a decrease in CR. Therefore, it can be concluded that the proposed algorithm has good convergence and stability, ensuring the reliable implementation of covert communication.

[0087] like Figure 4 As shown, Bob's covert rate varies under different link transmission thresholds. The relationship between the power allocation factor and the power allocation factor is shown. The results indicate that as the power allocation factor increases, The rate initially increases and then decreases. This is because when the power allocation factor is small, Alice allocates more power to the WLC link. As the power allocation factor gradually increases, the power Alice allocates to the PLC and WLC links gradually converges, allowing Bob to achieve a rate response (CR) through both links, thus further increasing the rate. However, when the factor is large enough, only the PLC link can achieve a CR, leading to a decrease in rate. Furthermore, when the thresholds for the WLC and PLC links are sufficiently large, the impact of power allocation on the rate is negligible. Therefore, it can be concluded that by utilizing different channel media and setting appropriate thresholds, Bob's CR can be significantly improved.

[0088] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for covert information probabilistic transmission in a hybrid power line-wireless communication system, characterized in that, Includes the following steps: Obtain channel state information for the power line communication link and wireless communication link between the legitimate sender and the legitimate receiver; Based on channel state information and employing a probabilistic transmission mechanism, when preset conditions are met, the legitimate sender transmits covert information to the legitimate receiver through power line communication links and wireless communication links. The transmission of covert information utilizes the uncertainty of impulse noise in power line communication links and the uncertainty of background noise in wireless communication links, while satisfying covert constraints.

2. The method for covert information probabilistic transmission in a hybrid power line-wireless communication system according to claim 1, characterized in that, A probabilistic transmission mechanism is adopted to send covert information when preset conditions are met. Specifically, this includes setting preset transmission thresholds for the power line communication link and the wireless communication link; when the channel gain of the power line communication link is greater than its corresponding preset transmission threshold, and the channel gain of the wireless communication link is greater than its corresponding preset transmission threshold, the legitimate sender initiates the transmission of covert information; otherwise, the legitimate sender remains silent.

3. The method for covert information probabilistic transmission in a hybrid power line-wireless communication system according to claim 2, characterized in that, The legitimate sender transmits covert information to the legitimate receiver through power line communication links and wireless communication links, including: allocating the legitimate sender's transmission power to the power line communication links and wireless communication links respectively according to the set power allocation factor, and carrying out synchronous information transmission.

4. The method for covert information probabilistic transmission in a hybrid power line-wireless communication system according to claim 1, characterized in that, The concealment constraints are set based on the eavesdropper's average minimum false detection probability; The average minimum false detection probability of an eavesdropper is evaluated using statistical channel state information obtained from long-term observations. The evaluation process is based on the uncertainty of the probability of impulse noise in power line communication links and the uncertainty of the actual noise power in wireless communication links.

5. The method for covert information probabilistic transmission in a hybrid power line-wireless communication system according to claim 4, characterized in that, When eavesdroppers detect communication activities, they use hypothesis testing to determine whether a legitimate sender has transmitted hidden information based on the average energy of the received signal. The eavesdropper assesses the average received signal energy using a power detection method and formulates decision rules based on the Newman-Pearson criterion and likelihood ratio test, selecting the optimal detection threshold to minimize the overall detection error probability.

6. The method for covert information probabilistic transmission in a hybrid power line-wireless communication system according to claim 3, characterized in that, Also includes: The transmission parameters are jointly optimized, with the goal of maximizing the covert rate of the legitimate receiver while satisfying the given covert constraints.

7. A method for covert information probabilistic transmission in a hybrid power line-wireless communication system according to claim 6, characterized in that, The transmission parameters for joint optimization include: The preset transmission threshold for the power line communication link, the preset transmission threshold for the wireless communication link, and the power allocation factor allocated to the two links.

8. A method for covert information probabilistic transmission in a hybrid power line-wireless communication system according to claim 7, characterized in that, When optimizing transmission parameters, the optimization problem is decomposed into two sub-problems and solved using an alternating optimization method. The specific steps include: With a fixed power allocation factor, the optimal preset transmission thresholds for the power line communication link and the wireless communication link are decoupled and calculated separately. The power allocation factor is optimized using a simulated annealing algorithm, ultimately maximizing the covert transmission rate at the legitimate receiver.

9. A method for covert information probabilistic transmission in a hybrid power line-wireless communication system according to claim 1, characterized in that, The channel models for power line communication links and wireless communication links are as follows: all wireless channels are modeled as Rayleigh fading, all power line channels follow a log-normal distribution, and each channel remains constant within each time slot and changes randomly and independently between different time slots. It is assumed that all nodes in the system operate in half-duplex mode.

10. A hybrid power line-wireless communication system for implementing the covert information probabilistic transmission method of any one of claims 1 to 9, characterized in that, include: It consists of a legitimate sender, a legitimate receiver, and a potential eavesdropper; The legitimate sender is configured to use a probabilistic transmission mechanism to send covert information to the legitimate receiver via power line communication links and wireless communication links; The system utilizes the uncertainty of impulse noise in power line communication links and the uncertainty of background noise in wireless communication links to transmit covert information probabilistically to legitimate receivers based on the channel quality of legitimate links, thereby reducing the probability that eavesdroppers in the system will successfully detect the communication behavior.

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