A method for realizing concealed information transmission in power line network

Abstract

The present application provides a method for realizing covert information transmission in a power line network, comprising the following steps: a transmitter prepares covert information to be transmitted to a receiver; the transmitter uses a determined transmission power to send the covert information to the receiver via the power line network; while receiving the transmitter signal, the receiver generates and transmits artificial noise to interfere with the eavesdropper's monitoring; the eavesdropper's false detection probability is evaluated to ensure that the eavesdropper cannot accurately determine whether the transmitter is transmitting information; on the premise of meeting the concealment requirements, the transmitter and receiver maximize the receiver's covert information reception rate by adjusting the transmission power; the covert interruption probability when the receiver receives the signal is analyzed and the concealment is evaluated, and based on the analysis and evaluation results, the system parameters are adjusted to optimize the covert transmission performance; the receiver decodes the received signal to recover the covert information sent by the transmitter; and the integrity and accuracy of the information received by the receiver are verified.

Description

Technical Field

[0001] The present invention relates to the technical field of covert communication, and in particular to a method for realizing covert information transmission in a power line network. Background Art

[0002] With the rapid development of domestic industry and the increasing demand for electricity, smart grids, as a new management technology, are gaining increasing attention and application worldwide. The internet connection of smart meters and household appliances extends the network boundary to the user side, raising concerns about the security of electricity usage information. The openness and accessibility of the power grid can lead to the injection of false data into grid control systems, disrupting normal operation and leaking user information, resulting in economic losses. Therefore, ensuring the secure transmission of data in smart grids is crucial.

[0003] Traditional data transmission security technologies encrypt transmission content above the network layer, making it more difficult for adversaries to decipher it. However, some encryption algorithms consume significant computing resources and increase system complexity, which, given the massive number of electricity users, could exceed the capacity of smart grids. While physical layer security (PLS) technologies do not rely on the computing power of transmission equipment, they share the same drawbacks as encryption technologies: they cannot fully protect user privacy, such as information about transmission time and location. In certain political and military fields, where secure transmission is more demanding, encryption and PLS technologies are far from sufficient. Against this backdrop, covert communication, a transmission technology offering enhanced security, has emerged.

[0004] Current encryption methods and devices require high computing resources, involve multiple hardware and software components, and have high initial investment and maintenance costs. As eavesdroppers' computing power increases, system security becomes compromised. Furthermore, existing encryption methods only protect the content of communications, not the actual communication itself. This poses risks to information transmission in smart grids. Summary of the Invention

[0005] The purpose of the present invention is to solve the technical problems in the above background and to propose a method for realizing covert information transmission in a power line network, comprising the following steps:

[0006] S1, the covert information that the transmitter is ready to transmit to the receiver;

[0007] S2, the transmitter uses the determined transmission power to send the covert information to the receiver via the power line network;

[0008] S3, while receiving the transmitter signal, the receiver generates and transmits artificial noise to interfere with the eavesdropper's monitoring;

[0009] S4, evaluating the false detection probability of an eavesdropper to ensure that the eavesdropper cannot accurately determine whether the transmitter is transmitting information;

[0010] According to the Newman-Pearson criterion, the eavesdropper minimizes the probability of detection error through the likelihood ratio test; for a given transmission time slot, the average power of the signal received by the eavesdropper is determined as follows:

[0011]

[0012] Where D1 indicates that the eavesdropper judges that the transmitter has transmitted covert information, and D0 indicates that the eavesdropper judges that the transmitter has not transmitted covert information. τ is the detection threshold. When the average power received by the eavesdropper is greater than τ, the eavesdropper judges that the transmitter has transmitted covert information. When the average power received by the eavesdropper is less than τ, the eavesdropper judges that the transmitter has not transmitted covert information.

[0013] In the energy detection process, the eavesdropper's false detection probability consists of two parts. One is the false alarm probability, which is defined as The other is the missed detection probability, defined as Then the false detection probability of the eavesdropper is expressed as:

[0014] ξ=P FA +P MD ;

[0015] S5. Under the premise of meeting the concealment requirements, the transmitter and receiver adjust the transmission power to maximize the receiver's concealed information reception rate;

[0016] S6. Analyze the probability of concealed interruption when the receiver receives the signal and evaluate the concealment performance. Based on the analysis and evaluation results, adjust the system parameters to optimize the concealed transmission performance.

[0017] S7, the receiver decodes the received signal to recover the hidden information sent by the transmitter;

[0018] S8. Verify the integrity and accuracy of the information received by the receiver.

[0019] In a preferred solution, the transmitter and the eavesdropper are in half-duplex mode, and the receiver is in full-duplex mode.

[0020] In a preferred solution, the power line includes a branch and a branch node o;

[0021] The location of the branch line affects the distance from the eavesdropper to the transmitter and receiver.

[0022] In a preferred solution, step S2 further includes the following steps: given a communication time slot, all channels remain unchanged within the communication time slot, but vary randomly between different communication time slots, and all channels are modeled using a log-normal distribution, that is, the channel gain from node u to node v is expressed as:

[0023]

[0024] Where u∈{a,b},v∈{b,w}, a is the transmitter, b is the receiver, w is the eavesdropper, A uv Represents the signal channel loss, expressed as:

[0025]

[0026] where d uv is the link distance between nodes u and v, f c is the power line carrier frequency; a0, a1 and κ are parameters measured from power line communication experiments; is a random variable that characterizes the statistical distribution characteristics of the channel. According to the properties of the lognormal distribution, Since the power line between nodes o and w is shared by the channel between the transmitter and the eavesdropper and the channel between the receiver and the eavesdropper, their channel correlation is set to ρ, and the joint distribution is

[0027] In a preferred solution, step S2 further includes the following steps: channel noise is modeled using Bernoulli-Gaussian distribution, and the total noise at node c is expressed as:

[0028] n c =n b +b i ·n i ,

[0029] where c∈{a,b,w}; n b is the background noise, expressed as n i is impulse noise, expressed as b i is a one-dimensional Bernoulli random variable, b i =1 indicates that impulse noise occurs with probability p I , b i =0 means that impulse noise does not occur, with a probability of 1-p I , the probability density function of the total channel noise at node c is expressed as:

[0030]

[0031] Where p1 = 1-p I, p2=p I ; represents the random variable n c Gaussian probability density function.

[0032] In a preferred solution, step S3 further includes the following steps:

[0033] When the transmitter sends a covert message, the signal received at the receiver is expressed as:

[0034]

[0035] Among them, P a and P b are the transmission powers of the transmitter and receiver respectively; h ab and h bb They represent the channel gains from the transmitter to the receiver and from the receiver to itself respectively; φ (0<φ≤1) represents the self-interference cancellation coefficient; x a and x bn They represent the covert signal sent by the transmitter and the artificial noise signal sent by the receiver, and their average powers are both 1, that is, n b represents the channel noise at the receiver, P b It obeys the uniform distribution, and its probability density function is expressed as:

[0036]

[0037] in is the maximum interference power transmitted by the receiver.

[0038] In a preferred solution, step S5 further includes the following steps:

[0039] Define the optimization problem:

[0040]

[0041] in is a hidden constraint;

[0042] During the transmission process, the eavesdropper will use the hypothesis test method to determine whether the transmitter has transmitted the hidden information based on the average energy of the received signal. In order to meet the given concealment constraints, the minimum probability of error in the eavesdropper's detection process must be calculated first. Indicates that the transmitter is not transmitting covert information, It means that the transmitter transmits hidden information, and the signal received by the eavesdropper is expressed as:

[0043]

[0044] where haw and h bw are the channel gains from transmitter to eavesdropper and from receiver to eavesdropper respectively; n w is the channel noise at the eavesdropper; according to Shannon's formula, in one information transmission process, that is, one communication time slot, the average power of the signal received by the eavesdropper is:

[0045]

[0046] In a preferred solution, step S4 further includes:

[0047] When e1≥e2,

[0048]

[0049] When e1<e2,

[0050]

[0051] in

[0052] By derivation analysis, the minimum false detection probability of the eavesdropper is and the optimal detection threshold τ * It is given by:

[0053]

[0054] The concealment performance is evaluated by the average minimum false detection probability, which is given by the following formula:

[0055]

[0056]

[0057] where f JP,LN (x,y0 is the probability density function of the joint lognormal distribution of x and y, expressed as:

[0058]

[0059] in ρ is and The correlation coefficient of ; using the Gauss-Chebyshev integration method, the approximate closed-form expression of the average minimum detection error probability is obtained:

[0060]

[0061] in,

[0062] N represents the complexity trade-off index;

[0063] In order to achieve covert transmission, the following covert constraints should be guaranteed to hold:

[0064]

[0065] Where ε is an arbitrarily small positive number used to evaluate the strength of the hidden constraint.

[0066] In a preferred solution, step S6 further includes the following steps: first analyzing the concealment constraints, then analyzing the optimal transmit power of the transmitter to maximize the concealment rate at the receiver, and finally analyzing the concealment outage probability of the system;

[0067] During a signal transmission process, the channel between node u (u∈{a,b}) and node v (v∈{b,w}) obeys the lognormal distribution, which is expressed as set up The approximate optimal solution is:

[0068]

[0069] in,

[0070]

[0071] Analyzing the receiver's covert interruption probability, the probability of interruption of covert communication between the transmitter and receiver is expressed as:

[0072]

[0073] where R b Indicates the rate requirement for covert communication between the transmitter and the receiver, set to R b =1bps / Hz; p j =p1 represents the probability that the channel noise at the receiver contains both background noise and impulse noise, p j =p2 represents the probability that the channel noise at the receiver consists only of background noise; The concealed outage probability of the receiver under two different channel noises is expressed by the following formula:

[0074]

[0075] in,

[0076]

[0077] Continuously apply the Gauss-Chebyshev integration method to obtain An approximate closed-form expression for :

[0078]

[0079] Finally, an approximate closed-form expression for the concealed outage probability of the receiver is obtained.

[0080] The beneficial effects of the present invention are:

[0081] 1) This paper develops a covert transmission strategy in power line networks using full-duplex artificial noise at the receiver. Specifically, while the transmitter and receiver are communicating covertly, the receiver transmits artificial noise through the full-duplex receiver to disrupt eavesdroppers, preventing them from determining whether covert information is being transmitted between the transmitter and receiver.

[0082] 2) This paper addresses the concept of covert transmission in power line networks and obtains an approximate closed-form expression for the average minimum false detection probability of an eavesdropper. Results show that communication distance and interference power significantly influence the eavesdropper's eavesdropping performance. Furthermore, we obtain an approximate closed-form expression for the optimal transmit power under covert constraints and determine the maximum achievable covert rate. Results indicate that the covert rate can be increased by adjusting the interference power and impulse noise.

[0083] 3) The present invention uses interference to enhance concealment performance and uses concealment rate and concealment interruption probability for evaluation. The results show that by setting a larger interference power and a better transmit signal-to-noise ratio, the concealment performance of the system can be significantly improved. BRIEF DESCRIPTION OF THE DRAWINGS

[0084] Figure 1 This is a model diagram of the hidden transmission system of the power line network;

[0085] Figure 2 This is an experimental graph showing the variation of Willie's minimum error detection probability with channel correlation ρ at different communication distances;

[0086] Figure 3 is the difference between Bob’s concealment rate and the maximum interference noise power under different impulse noise levels. Experimental diagram of changes;

[0087] Figure 4 This is an experimental graph showing how Bob's interruption probability changes with the input signal-to-noise ratio (SNR) under different impulse noise levels. DETAILED DESCRIPTION

[0088] like Figure 1As shown, the present invention considers a covert communication system in a power line network, which consists of a transmitter, a receiver, and a potential eavesdropper, corresponding to Alice (a), Bob (b), and Willie (w), respectively. Node o represents a branch node of the power line, and the access location of the branch affects the distance from Willie to Alice and Bob. In this system, Alice hopes to transmit secret information to Bob without Willie's knowledge, while Willie acts as a passive eavesdropper to detect whether Alice and Bob are communicating secretly. Alice and Willie are in half-duplex mode, while Bob is in full-duplex mode. That is, while receiving secret information, Bob transmits artificial noise to interfere with Willie's eavesdropping behavior.

[0089] The present invention focuses on a given information transmission time slot. All channels remain constant within this communication time slot, but vary randomly between different communication time slots. All channels are modeled using a log-normal distribution, i.e., the channel gain from node u to node v is expressed as:

[0090]

[0091] where u∈{a,b},v∈{b,w}, A uv represents the signal channel loss and can be expressed as:

[0092]

[0093] where d uv is the link distance between nodes u and v, f c is the power line carrier frequency; a0, a1 and κ are parameters measured from power line communication experiments; is a random variable that characterizes the statistical distribution characteristics of the channel. According to the properties of the lognormal distribution, In addition, since the power line between nodes o and w is shared by the channels of Alice-Willie and Bob-Willie, their channel correlation is set to ρ, and the joint distribution is

[0094] The channel noise is modeled using Bernoulli-Gaussian distribution, and the total noise at node c can be expressed as:

[0095] n c =n b +b i ·n i , (3) where c∈{a,b,w}; n b is the background noise, expressed as n i is impulse noise, expressed as b i is a one-dimensional Bernoulli random variable, b i =1 indicates that impulse noise occurs with probability p I , b i =0 means that impulse noise does not occur, with a probability of 1-p I Therefore, the probability density function of the total channel noise at node c can be expressed as:

[0096]

[0097] Where p1 = p I , p2=1-p I ; represents the random variable n c Gaussian probability density function.

[0098] Without loss of generality, assuming that when Alice sends a covert message, the signal received by Bob can be expressed as:

[0099]

[0100] Among them, P a and P b are the transmission powers of Alice and Bob respectively; h ab and h bb They represent the channel gains from Alice to Bob and from Bob to himself respectively; φ (0<φ≤1) represents the self-interference cancellation coefficient; x a and x bn They represent the covert signal sent by Alice and the artificial noise signal sent by Bob, and their average power is 1, that is, n b represents the channel noise at Bob. In order to confuse Willie’s eavesdropping and achieve covert transmission, we assume that P b It obeys the uniform distribution, and its probability density function can be expressed as:

[0101]

[0102] in is the maximum interference power sent by Bob.

[0103] 1. Optimization goals of the present invention

[0104] The goal of this invention is to maximize Bob's concealment rate while satisfying given concealment constraints. Therefore, the optimization problem is defined as follows:

[0105]

[0106] Where (7a) is a hidden constraint, which will be explained in detail below.

[0107] 1) Hidden constraints

[0108] During the transmission process, Willie will use the hypothesis test method to determine whether Alice has transmitted the hidden information based on the average energy of the received signal. In order to meet the given concealment constraints, we must first calculate Willie's minimum error detection probability (MDEP), that is, the minimum probability of error in Willie's detection process. Consider Indicates that Alice did not transmit any hidden information. Indicates that Alice transmits hidden information. Under the two assumptions, the signal received by Willie can be expressed as:

[0109]

[0110] where h aw and h bw are the channel gains from Alice to Willie and from Bob to Willie respectively; n w is the channel noise at Willie. According to Shannon’s formula, in one information transmission process, i.e., one communication time slot, the average power of the signal received by Willie is:

[0111]

[0112] Substituting (1) into (9) we can obtain:

[0113]

[0114] According to the Newman-Pearson criterion, Willie minimizes the probability of detection error through a likelihood ratio test. For a given transmission time slot, the average power of the signal received by Willie is determined as follows:

[0115]

[0116] Where D1 represents Willie's judgment that Alice has transmitted covert information, and D0 represents Willie's judgment that Alice has not transmitted covert information. τ is the detection threshold. Equation (11) means that when the average power received by Willie is greater than τ, Willie judges that Alice has transmitted covert information; if it is less than τ, then Alice is judged not to have transmitted covert information.

[0117] In the energy detection process, Willie's false detection probability consists of two parts. One is the false alarm probability, which is defined as The other is the missed detection probability, defined as Then Willie's false detection probability is expressed as:

[0118] ξ=P FA +P MD , (12)

[0119] When e1≥e2,

[0120]

[0121] When e1<e2,

[0122]

[0123] in

[0124] By derivation analysis and combining with formula (10), Willie's minimum error detection probability is and the optimal detection threshold τ * It is given by:

[0125]

[0126] Since Alice and Bob do not know the instantaneous channel state information (CSI) from their communication with Willie, but only know the statistical state information of the channel, we use the average minimum error detection probability (AMDEP) to evaluate the concealment performance. AMDEP is given by:

[0127]

[0128] where f JP,LN (x,y) is the probability density function of the joint lognormal distribution of x and y, which can be expressed as:

[0129]

[0130] in ρ is and Substituting (18) into (17), and then using the Gauss-Chebyshev integration method, we can obtain the approximate closed-form expression of AMDEP:

[0131]

[0132] in

[0133] N represents the complexity trade-off index. Simulation experiments show that when N is 10, the error between the approximate value and the actual value is very small.

[0134] Therefore, in order to achieve covert transmission, the following covert constraint should be guaranteed to hold:

[0135]

[0136] Where ε is an arbitrarily small positive number used to evaluate the strength of the hidden constraint.

[0137] 2. Problem Solving

[0138] The present invention focuses on the concealment performance without interruption under the conditions of meeting the concealment constraints. First, the concealment constraints are analyzed, then the optimal transmit power of Alice is analyzed to maximize the concealment rate at Bob, and finally the concealment interruption probability of the system is analyzed.

[0139] For the convenience of solving, we assume that during a signal transmission process, the channel between node u (u∈{a,b}) and node v (v∈{b,w}) obeys the lognormal distribution, which can be expressed as set up Therefore, we can obtain the approximate optimal solution of problem (7) as:

[0140]

[0141] in

[0142]

[0143] To ensure the reliability of covert communication between Alice and Bob, we next analyze Bob's covert interruption probability (CTOP). The probability of interruption of covert communication between Alice and Bob is expressed as:

[0144]

[0145] where R b The rate requirement for covert communication between Alice and Bob is set to R b =1bps / Hz; p j =p1 represents the probability that the channel noise at Bob contains both background noise and impulse noise, p j =p2 represents the probability that the channel noise at Bob consists only of background noise; The concealed outage probability of Bob under two different channel noise conditions can be expressed as follows:

[0146]

[0147] in

[0148]

[0149] Continuously use the Gauss-Chebyshev integration method to integrate equation (22a) and then substitute it into equation (22), we can get An approximate closed-form expression for :

[0150]

[0151] Substituting (23) into (22), we can obtain an approximate closed-form expression for Bob's CTOP.

[0152] Figure 1 An example of a full-duplex, artificial noise-assisted covert communication system in a power line network is presented. The mean and variance of the channel distribution function between any two nodes are set to 2 dB and 1 dB. Furthermore, since the Alice-Willie and Bob-Willie channels share the power line between node o and node w, the correlation between them is set to ρ (0 ≤ ρ ≤ 1).

[0153] like Figure 2 As shown in the figure, the average minimum error detection probability of Willie under different communication distances is The relationship between the channel correlation ρ. It can be seen that As ρ increases, it increases as the distance between Alice and Willie increases. This is because as the channel correlation ρ gradually increases from 0 to 1, the changes in the eavesdropping channel and the interference channel due to the change in the communication time slot have an impact on the minimum error detection probability. The impact is reduced, resulting in This indicates that channel correlation is beneficial for covert transmission. Furthermore, as Willie moves away from Alice and closer to Bob, the eavesdropping channel deteriorates while the interference channel improves, improving covert performance. This demonstrates that selecting the appropriate transmitting node, one that prevents Willie from eavesdropping at close range, effectively enables covert information transmission.

[0154] like Figure 3 As shown, under different impulse noise levels, Bob's concealment rate and maximum interference power It can be observed that as the interference power Increase, stealth speed will also increase, and the probability of impulse noise occurring p I Increase, stealth rate This is because the interference power The increase of will make the average minimum false detection probability Increase, under the same concealment requirements, we can appropriately increase Alice's transmission power P aTo obtain a higher stealth rate, although the interference transmitted by Bob will also cause interference to himself, the current self-interference elimination technology in the power line can reduce this interference to a very low level. Compared with the increase in P a Caused by The increase is much smaller, so overall along with In addition, the probability of impulse noise occurring p I As it increases, the total noise at Bob will increase, so the concealment rate Will reduce, in general, the interference power and the impulse noise level p I The combined effect on the stealth rate is significant.

[0155] like Figure 4 As shown in Figure 1, the relationship between the system's concealed outage probability CTOP and the input signal-to-noise ratio SNR under different impulse noise levels. We can see that the system's concealed outage probability CTOP decreases as the input signal-to-noise ratio SNR increases, while the probability of impulse noise appearing p I This is because the larger the input signal-to-noise ratio (SNR), the larger the received signal-to-noise ratio (SNR) at Bob’s output, the lower the interruption probability CTOP, and the probability of impulse noise occurring p I The larger the value, the lower the signal-to-noise ratio (SNR) Bob receives, and the higher the interruption probability (CTOP). Therefore, in order to ensure a more stable and covert transmission of information, we need to improve the quality of the transmitted signal as much as possible and create better transmission conditions to reduce the impulse noise level.

[0156] The above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit the same. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the various embodiments of the present invention.

Claims

1. A method for implementing covert information transmission in a power line network, characterized by: The following steps are involved: S1, the covert information that the transmitter is ready to transmit to the receiver; S2, the transmitter uses the determined transmission power to send the covert information to the receiver via the power line network; S3, while receiving the transmitter signal, the receiver generates and transmits artificial noise to interfere with the eavesdropper's monitoring; S4, evaluating the false detection probability of an eavesdropper to ensure that the eavesdropper cannot accurately determine whether the transmitter is transmitting information; According to the Newman-Pearson criterion, the eavesdropper minimizes the probability of detection error through the likelihood ratio test; for a given transmission time slot, the average power of the signal received by the eavesdropper is determined as follows: Where D1 means the eavesdropper judges that the transmitter has transmitted covert information, and D0 means the eavesdropper judges that the transmitter has not transmitted covert information; τ is the detection threshold; When the average power received by the eavesdropper is greater than τ, the eavesdropper determines that the transmitter has transmitted covert information. When the average power received by the eavesdropper is less than τ, the eavesdropper determines that the transmitter has not transmitted covert information. In the energy detection process, the eavesdropper's false detection probability consists of two parts. One is the false alarm probability, which is defined as The other is the missed detection probability, defined as Then the false detection probability of the eavesdropper is expressed as: ξ=P FA +P MD ; S5. Under the premise of meeting the concealment requirements, the transmitter and receiver adjust the transmission power to maximize the receiver's concealed information reception rate; S6. Analyze the probability of concealed interruption when the receiver receives the signal and evaluate the concealment performance. Based on the analysis and evaluation results, adjust the system parameters to optimize the concealed transmission performance. S7, the receiver decodes the received signal to recover the hidden information sent by the transmitter; S8. Verify the integrity and accuracy of the information received by the receiver.

2. The method for implementing covert information transmission in a power line network according to claim 1, wherein: The transmitter and the eavesdropper are in half-duplex mode, and the receiver is in full-duplex mode.

3. The method for implementing covert information transmission in a power line network according to claim 1, wherein: The power line includes branches and branch nodes o; The location of the branch line affects the distance from the eavesdropper to the transmitter and receiver.

4. The method for implementing covert information transmission in a power line network according to claim 1, wherein: Step S2 further includes the following steps: given a communication time slot, all channels remain unchanged within the communication time slot, but vary randomly between different communication time slots. All channels are modeled using a log-normal distribution, i.e., the channel gain from node u to node v is expressed as: Where u∈{a,b},v∈{b,w}, a is the transmitter, b is the receiver, w is the eavesdropper, A uv Represents the signal channel loss, expressed as: where d uv is the link distance between nodes u and v, f c is the power line carrier frequency; a0, a1 and κ are parameters measured from power line communication experiments; is a random variable that characterizes the statistical distribution characteristics of the channel. According to the properties of the lognormal distribution, Since the power line between nodes o and w is shared by the channel between the transmitter and the eavesdropper and the channel between the receiver and the eavesdropper, their channel correlation is set to ρ, and the joint distribution is 5. The method for implementing covert information transmission in a power line network according to claim 1, wherein: Step S2 further includes the following steps: channel noise is modeled using Bernoulli-Gaussian distribution, and the total noise at node c is expressed as: n c =n b +b i ·n i , where c∈{a,b,w}; n b is the background noise, expressed as n i is impulse noise, expressed as b i is a one-dimensional Bernoulli random variable, b i =1 indicates that impulse noise occurs with probability p I , b i =0 means that impulse noise does not occur, with a probability of 1-p I , the probability density function of the total channel noise at node c is expressed as: Where p1 = 1-p I , p2=p I ; represents the random variable n c Gaussian probability density function.

6. The method for implementing covert information transmission in a power line network according to claim 1, wherein: Step S3 further includes the following steps: When the transmitter sends a covert message, the signal received at the receiver is expressed as: Among them, P a and P b are the transmission powers of the transmitter and receiver respectively; h ab and h bb They represent the channel gains from the transmitter to the receiver and from the receiver to itself respectively; φ (0<φ≤1) represents the self-interference cancellation coefficient; x a and x bn They represent the covert signal sent by the transmitter and the artificial noise signal sent by the receiver, and their average powers are both 1, that is, n b represents the channel noise at the receiver, P b It obeys the uniform distribution, and its probability density function is expressed as: in is the maximum interference power transmitted by the receiver.

7. The method for implementing covert information transmission in a power line network according to claim 1, wherein: Step S5 further includes the following steps: Define the optimization problem: in is a hidden constraint; During the transmission process, the eavesdropper will use the hypothesis test method to determine whether the transmitter has transmitted the hidden information based on the average energy of the received signal. In order to meet the given concealment constraints, the minimum probability of error in the eavesdropper's detection process must be calculated first. Indicates that the transmitter is not transmitting covert information, It means that the transmitter transmits hidden information, and the signal received by the eavesdropper is expressed as: where h aw and h bw are the channel gains from transmitter to eavesdropper and from receiver to eavesdropper respectively; n w is the channel noise at the eavesdropper; according to Shannon's formula, in one information transmission process, that is, one communication time slot, the average power of the signal received by the eavesdropper is:

8. The method for implementing covert information transmission in a power line network according to claim 7, wherein: Step S4 further includes: When e1≥e2, When e1<e2, in By derivation analysis, the minimum false detection probability of the eavesdropper is and the optimal detection threshold τ * It is given by: The concealment performance is evaluated by the average minimum false detection probability, which is given by the following formula: where f JP,LN (x,y) is the joint lognormal distribution probability density function of x and y, expressed as: in ρ is and The correlation coefficient of ; using the Gauss-Chebyshev integration method, the approximate closed-form expression of the average minimum detection error probability is obtained: in, N represents the complexity trade-off index; In order to achieve covert transmission, the following covert constraints should be guaranteed to hold: Where ε is an arbitrarily small positive number used to evaluate the strength of the hidden constraint.

9. The method for implementing covert information transmission in a power line network according to claim 8, wherein: Step S6 also includes the following steps: first analyzing the concealment constraints, then analyzing the optimal transmit power of the transmitter to maximize the concealment rate at the receiver, and finally analyzing the concealment outage probability of the system; During a signal transmission process, the channel between node u (u∈{a,b}) and node v (v∈{b,w}) obeys the lognormal distribution, which is expressed as set up The approximate optimal solution is: in, Analyzing the receiver's covert interruption probability, the probability of interruption of covert communication between the transmitter and receiver is expressed as: where R b Indicates the rate requirement for covert communication between the transmitter and the receiver, set to R b =1bps / Hz; p j =p1 represents the probability that the channel noise at the receiver contains both background noise and impulse noise, p j =p2 represents the probability that the channel noise at the receiver consists only of background noise; The concealed outage probability of the receiver under two different channel noises is expressed by the following formula: in, Continuously apply the Gauss-Chebyshev integration method to obtain An approximate closed-form expression for : Finally, an approximate closed-form expression for the concealed outage probability of the receiver is obtained.

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