Two-way relay-based covert communication method and system for power monitoring network

Abstract

The invention discloses a two-way relay-based covert communication method and system for a power monitoring network, and the method comprises the steps: constructing a transmission model and a communication scheme of a two-way relay covert communication system, and enabling nodes in the transmission model to comprise two legal information sources S1 and S2, a relay R and a covert user B; according to the transmission model and the communication scheme, obtaining a necessary condition for uninterrupted communication and a necessary condition for the relay to carry out covert communication; a joint detection mechanism is determined, and in covert communication, two legal information sources jointly serve as detectors and are independently detected; jointly making a judgment result according to the respective detection results of the two legal information sources; and determining a two-way relay-based covert communication performance evaluation method, and determining the total detection error probability of the system and the effective covert transmission rate of the covert user under the condition of meeting the covert constraint condition. The method can be used for realizing the positive hidden transmission rate under the two-way relay network.

Description

Technical Field

[0001] The present invention belongs to the field of wireless communication, relates to the wireless communication of a power monitoring network, and particularly relates to a method and system for covert communication based on two-way relay in a power monitoring network. Background Art

[0002] With the rapid development of information technology, security and privacy are crucial in existing and future wireless networks, because a large amount of confidential information (such as location, credit card information, physiological information of electronic health) is transmitted through open wireless media. The security of information transmission faces unprecedented challenges. On the one hand, the openness and popularity of the network make it extremely easy for information to be intercepted, stolen or tampered with by a third party during the transmission process. For example, in the military field, the enemy may obtain key information such as our military deployment and combat plan by eavesdropping on communication channels, thus gaining the initiative in the war. On the other hand, in the civilian field, personal privacy data, enterprise business secrets, etc. are also at risk of being leaked. For example, personal information in social networks, account passwords in financial transactions, etc. Once leaked, it will cause serious losses to individuals and enterprises. Against this background, traditional cryptography and information theory secrecy technologies have been developed to gradually provide a higher level of security by protecting the content of messages from being eavesdropped.

[0003] However, these technologies cannot reduce the threat of the existence of communication to the security and privacy of users. How to ensure the security of the transmission process itself is also very important. Covert communication aims to ensure the normal information transmission between legitimate users, and at the same time reduce the probability of successful detection by illegal detectors by introducing uncertainty, so as to achieve a certain positive rate of covert transmission. Covert communication technology is widely used in fields such as medical, military, smart grid and Internet of Things. For example, in the Internet of Things cloud system for digital power monitoring, the transmission security of data is crucial. Covert communication can ensure that data is not stolen or tampered with during the transmission process, and ensure the stable operation of the power monitoring system. It can hide the transmission path of data, prevent lawbreakers from obtaining sensitive information, and maintain the normal operation of the system.

[0004] The existing relay-based covert communication mainly targets unidirectional relay transmission networks, and its channel utilization rate is lower than that of two-way relay networks. At present, there is still a lack of relevant technologies for covert communication in two-way relay transmission networks. Summary of the Invention

[0005] Object of the Invention: In order to overcome the deficiencies in the prior art, a method and system for covert communication based on two-way relay in a power monitoring network are provided, which can be used to achieve a positive covert transmission rate in a two-way relay network.

[0006] Technical solution: To achieve the above object, the present invention provides a method for covert communication based on two-way relay in a power monitoring network, including the following steps:

[0007] S1: Construct a transmission model and a communication scheme for the two-way relay covert communication system. The nodes in the transmission model include two legitimate sources S 1 and S 2 , a relay R, and a covert user B;

[0008] S2: Obtain the necessary conditions for non-interrupted communication and the necessary conditions for the relay to conduct covert communication according to the transmission model and the communication scheme;

[0009] S3: Determine a joint detection mechanism. In covert communication, the two legitimate sources jointly act as detectors and detect independently; make a determination result jointly according to the respective detection results of the two legitimate sources;

[0010] S4: Based on the determination result of step S3, determine the performance evaluation method for covert communication based on two-way relay, determine the total detection error probability of the system, and the effective covert transmission rate of the covert user under the condition of meeting the covert constraint conditions.

[0011] Furthermore, the communication process in the communication scheme of step S1 is as follows:

[0012] The transmission is divided into two phases. In the first phase, S 1 and S 2 simultaneously send their legitimate messages x 1 and x 2 to R; in the second phase, R forwards the legitimate messages x 1 and x 2 to S 2 and S 1 , while R takes the opportunity to forward its covert message x C to the covert user B; the system resources allocated to R are used to transmit messages for legitimate users. However, R may also intend to use these resources to send its own messages to B; considering fixed-rate transmission, in the first phase, S 1 transmits messages to R at a fixed rate R 1 , and S 2 transmits messages to R at a fixed rate R 2 .

[0013] Furthermore, the received signal of the relay R in the transmission model of step S1 is:

[0014]

[0015] where P 1 and P 2 are respectively S 1and S 2 The transmit power of is the channel coefficient between S 1 and relay R, is the channel coefficient between S 2 and relay R, n R (i) is the additive white Gaussian noise with variance and mean 0 at R, x 1 (i) is the transmitted signal of S 1 , x 2 (i) is the transmitted signal of S 2 , i = 1,..., n, where n is the finite block length of this transmission.

[0016] Furthermore, the necessary condition for non - interruption of communication in step S2 depends on the relay being able to successfully decode x 1 and x 2 and both sources being able to successfully decode each other's data, that is:

[0017]

[0018] Denote the non - interruption condition of communication as:

[0019]

[0020] where j ∈ {1, 2} corresponds to S 1 and S 2 two sources respectively, γ thj is the signal - to - noise ratio threshold at S j , P M is the maximum transmit power of R;

[0021] When the relay does not send a covert message, the received signal at the source is:

[0022]

[0023] In the formula, is the transmit power when R does not send a covert message, x R (i) is the forwarded message of R, is the additive white Gaussian noise with variance and mean 0 at the source; with fixed - rate transmission, the transmit power when R does not send a covert message is:

[0024]

[0025] When the relay sends a covert message, the received signal at the source is:

[0026]

[0027] In the formula, Forwarded by R carrying the source information x R (i)'s transmission power, P C is the transmission of the covert message x by R C (i)'s transmission power; source decoding of x R when (i), taking x C (i) as interference, according to fixed-rate transmission, it is obtained that is:

[0028]

[0029] Considering the maximum power constraint at R, that is, The necessary condition for R to perform covert communication is

[0030] Furthermore, the joint detection mechanism in step S3 is as follows: The two sources jointly act as detectors and detect independently. The detectors perform binary hypothesis testing based on the received signals, and obtain the expressions of the two detection error probabilities and the total detection error probability expression for each detector according to the power detector and the corresponding decision rules. Then, a determination result is jointly made based on their respective detection results, that is, as long as one detector detects that the relay is transmitting a covert message, the system determines that the relay is sending a covert message.

[0031] Furthermore, when each detector in step S3 detects independently and the detector performs binary hypothesis testing based on the received signal, the detector has two detection error cases H 0 and H 1 , H 0 is the null hypothesis, indicating that the detector believes that the relay is not transmitting a covert message, and H 1 is the alternative hypothesis, indicating that the detector believes that the relay has transmitted a covert message. Then, the received signal of the detector is as follows:

[0032]

[0033] The detector uses a power detector to judge the behavior of the relay, and the received power of the detector is:

[0034]

[0035] The decision rule for an independent single detector is:

[0036] The decision rule of detector S 1 is expressed as:

[0037] The decision rule of detector S 2 is expressed as: where τ jis the detection threshold of the detector, D 0 and D 1 respectively represent the decisions made by the detector under the assumptions that H 0 and H 1 hold; then at this time, the false alarm probability of the detector S j is expressed as:

[0038]

[0039] The miss detection probability is expressed as:

[0040]

[0041] Since the mathematical processing of the above formula is very difficult, a more stringent decoding condition is set here, expressed as:

[0042]

[0043] Then the condition for the communication not to be interrupted is expressed as:

[0044]

[0045] Let R transmit the message with a larger power, and is expressed as:

[0046]

[0047] Considering the maximum power constraint at R, that is, Then the necessary condition for R to perform covert transmission is expressed as:

[0048]

[0049] Furthermore, the specific step S4 is as follows:

[0050] Since the channel coefficients between nodes are independent of each other and then and The distribution functions of are as follows:

[0051]

[0052] Then The distribution function of is as follows:

[0053]

[0054] Then at this time, the false alarm probability of the detector S j is expressed as:

[0055] The detector S jThe probability of missed detection is expressed as:

[0056]

[0057] where

[0058] The prior probability that the relay sends a covert message is expressed as:

[0059]

[0060] where ρ is the probability that the relay sends a covert message, then the prior probability that the relay does not send a covert message is

[0061] Pr(H 0 ) = 1 - Pr(H 1 ) = 1 - β

[0062] S j The total detection error probability is expressed as:

[0063]

[0064] Determine the initial constraints of P C and the bounds of τ j such that S j Set the value of τ j to minimize ξ j :

[0065] S j The total detection error probability is divided into two cases: when t 1j < t 2j , that is, P C > P Δ where the value of P Δ is S j The total detection error probability is as follows:

[0066]

[0067] This indicates that when P C > P Δ , S j can simply set τ j ∈[t 1j , t 2j to ensure ξ j = 0, that is to say, S j can detect covert transmission with probability 1; therefore, P C should satisfy P C ≤P Δ to ensure ξ j > 0;

[0068] When t 1j ≥ t 2j , that is, P C ≤ P Δ , the total detection error probability of S j is as follows:

[0069]

[0070] Analyzing the above formula, the optimal detection threshold range at S j is as follows: Within this range, the particle swarm algorithm can be used to search for an optimal τ j that minimizes the total detection error probability of S j , and the corresponding minimum detection error probability is as follows:

[0071]

[0072] According to the joint detection mechanism, the false alarm probability of the system is as follows:

[0073]

[0074] The miss detection probability of the system is as follows:

[0075]

[0076] The total detection error probability of the system is as follows:

[0077] ξ = (1 - β)P FA + βP MD

[0078] According to the relay's forwarding signal, the received signal at the covert user B, and the decoding of the covert message x C , the signal-to-noise ratios are respectively:

[0079]

[0080] The covert transmission rate is defined as R C = log(1 + γ C ), then the effective covert transmission rate is as follows:

[0081]

[0082] The present invention also provides a covert communication system for a power monitoring network based on two-way relay. The system includes a network interface, a memory, and a processor; wherein,

[0083] The network interface is used to receive and send signals during the process of receiving and sending information with other external network elements;

[0084] The memory is used to store computer program instructions that can run on the processor;

[0085] The processor is used to execute the steps of a covert communication method based on two-way relay in a power monitoring network when running the computer program instructions.

[0086] The present invention provides a covert communication method and system based on two-way relay in a power monitoring network, including two legitimate sources, one relay, and one covert user. The two source nodes forward each other's messages with the assistance of the relay, and the relay opportunistically transmits its own message to the secret user. At this time, the two sources simultaneously act as detectors to detect whether the relay sends a covert message.

[0087] Advantageous effects: Compared with the prior art, the present invention has the following advantages:

[0088] 1. Since the two-way relay can simultaneously receive and forward the information of two-way users, its channel utilization rate is higher than that of the one-way relay. The present invention provides an effective covert communication method and system for a two-way relay network configured with greedy relay nodes.

[0089] 2. For a two-way relay network configured with greedy relay nodes, the present invention gives a method for determining the optimal detection threshold that minimizes the detection error probability, and proves that a positive covert transmission rate can be achieved in this network.

[0090] 3. For a two-way relay network configured with greedy relay nodes, the present invention gives a method for quickly and accurately evaluating the performance of covert communication. Description of the Drawings

[0091] Figure 1 It is a covert communication model diagram based on two-way relay provided by the present invention;

[0092] Figure 2 It is a relationship curve diagram between the total detection error probability of the system and the power of the relay sending covert messages;

[0093] Figure 3 It is a relationship curve diagram between the total detection error probability of the system and the large-scale fading degree of the legitimate channel under different fixed transmission rates;

[0094] Figure 4 It is a relationship curve diagram between the effective covert transmission rate and the fixed transmission rate. Detailed Embodiment

[0095] The present invention will be further illustrated below in conjunction with the accompanying drawings and specific embodiments. It should be understood that these embodiments are only used to illustrate the present invention and not to limit the scope of the present invention. After reading the present invention, those skilled in the art's various equivalent modifications of the present invention all fall within the scope defined by the appended claims of this application.

[0096] Embodiment 1:

[0097] This embodiment provides a method for covert communication based on two-way relay in a power monitoring network, including the following steps:

[0098] S1: Construct a transmission model and a communication scheme for the two-way relay covert communication system;

[0099] As Figure 1 shown, there are four roles in the system, namely two source nodes (S 1 (detector 1) and S 2 (detector 2)), a relay (R), and a covert user (B);

[0100] The channel model in the communication scheme is:

[0101] Assume that the wireless channel is affected by independent quasi-static Rayleigh fading. The channel coefficient from node i to node j is represented by h ij (i, j ∈ {S 1 , S 2 , R, B}), which is an independent, zero-mean, circularly symmetric complex Gaussian random variable with a variance of

[0102] In addition, the noise at each node follows With being the additive white Gaussian noise with the corresponding position variance, where is the noise variance at the two source nodes. Each node is equipped with one antenna. Assume that R knows h RB , S 1 only knows S 2 only knows B only knows h BR .

[0103] The communication process in the communication scheme is:

[0104] The transmission is divided into two phases. In the first phase, S 1 and S 2 simultaneously send their legitimate messages x 1 and x 2 to R; in the second phase, R forwards the legitimate messages x 1 and x 2 to S2 and S 1 , while R takes the opportunity to forward its covert message x C to the covert user B; the system resources allocated to R are used to transmit messages for legitimate users. However, R may also intend to use these resources to send its own message to B; considering fixed-rate transmission, in the first phase, S 1 transmits a message to R at a fixed rate R 1 to R, and S 2 transmits a message to R at a fixed rate R 2 to R.

[0105] The received signal at the relay R is:

[0106]

[0107] where P 1 and P 2 are the transmission powers of S 1 and S 2 respectively, is the channel coefficient between S 1 and the relay R, is the channel coefficient between S 2 and the relay R, n R (i) is the additive white Gaussian noise with variance and mean 0 at R, x 1 (i) is the transmitted signal of S 1 , and x 2 (i) is the transmitted signal of S 2 , i = 1,..., n, and n is the finite block length of this transmission.

[0108] S2: Obtain the necessary conditions for non-interrupted communication and the necessary conditions for the relay to perform covert communication according to the transmission model and communication scheme;

[0109] The necessary conditions for non-interrupted communication depend on the relay being able to successfully decode x 1 and x 2 and the two sources being able to successfully decode each other's data, that is:

[0110]

[0111] Denote the non-interrupted communication condition as:

[0112]

[0113] where j ∈ {1, 2} corresponds to the two sources S 1 and S 2 respectively, γ thj is the signal-to-noise ratio threshold at S j , PM is the maximum transmission power of R;

[0114] When the relay does not send the covert message, the received signal at the source is:

[0115]

[0116] In the formula, is the transmission power when R does not send the covert message, and x R (i) is the forwarding message of R, is the additive white Gaussian noise with zero mean and variance at the source; with fixed-rate transmission, the transmission power when R does not send the covert message is:

[0117]

[0118] When the relay sends the covert message, the received signal at the source is:

[0119]

[0120] In the formula, is the transmission power for R to forward the source information x R (i), and P C is the transmission power for R to send the covert message x C (i); when the source decodes x R (i), it takes x C (i) as interference, and according to fixed-rate transmission, it is obtained that is:

[0121]

[0122] Considering the maximum power constraint at R, that is, The necessary condition for R to perform covert communication is

[0123] S3: Determine a joint detection mechanism. In covert communication, two legitimate sources jointly act as detectors and detect independently; make a decision result jointly according to the respective detection results of the two legitimate sources;

[0124] The joint detection mechanism is: Two sources jointly act as detectors and detect independently. The detectors perform binary hypothesis testing based on the received signals, and obtain two detection error probability expressions and the total detection error probability expression for each detector according to the power detector and the corresponding decision rules, and then make a decision result jointly according to their respective detection results, that is, as long as one detector detects that the relay is transmitting a covert message, the system determines that the relay is sending a covert message.

[0125] Each detector conducts the detection independently. When the detector performs binary hypothesis testing based on the received signal, there are two types of detection errors for the detector, H 0 and H 1 ; H 0 is the null hypothesis, indicating that the detector believes the relay has not sent a covert message, and H 1 is the alternative hypothesis, indicating that the detector believes the relay has sent a covert message. Then the received signal of the detector is as follows:

[0126]

[0127] The detector uses a power detector to judge the behavior of the relay, and the received power of the detector is:

[0128]

[0129] The decision rule for an independent single detector is:

[0130] The decision rule of detector S 1 is expressed as:

[0131] The decision rule of detector S 2 is expressed as: where τ j is the detection threshold of the detector, and D 0 and D 1 represent the decisions made by the detector when the hypotheses H 0 and H 1 hold, respectively. Then the false alarm probability of detector S j is expressed as:

[0132]

[0133] The miss detection probability is expressed as:

[0134]

[0135] Since the mathematical processing of the above formula is very difficult, a more stringent decoding condition is set here, expressed as:

[0136]

[0137] Then the condition for non - interruption of communication is expressed as:

[0138]

[0139] Let R transmit the message with a larger power, and is expressed as:

[0140]

[0141] Considering the maximum power constraint at R, i.e., The necessary condition for R to perform covert transmission is expressed as:

[0142]

[0143] S4: Based on the determination result of step S3, determine the performance evaluation method of covert communication based on two-way relaying, determine the total detection error probability of the system, and the effective covert transmission rate of the covert user under the condition of satisfying the covert constraint;

[0144] Since the channel coefficients between nodes are independent of each other and Then And The distribution functions of are as follows:

[0145]

[0146] Then The distribution function of is as follows:

[0147]

[0148] Then at this time, the detector S j The false alarm probability is expressed as:

[0149] The detector S j The miss detection probability is expressed as:

[0150]

[0151] Where

[0152] The prior probability that the relay sends a covert message is expressed as:

[0153]

[0154] Where ρ is the probability that the relay sends a covert message, then the prior probability that the relay does not send a covert message is

[0155] Pr(H 0 ) = 1 - Pr(H 1 ) = 1 - β

[0156] S j The total detection error probability is expressed as:

[0157]

[0158] Determine P C 's preliminary constraints and τ j 's bounds such that S j Set the value of τ j to minimize ξ j :

[0159] S j The total detection error probability is divided into two cases: when t 1j < t 2j , that is, P C > P Δ where the value of P Δ is S j The total detection error probability is as follows:

[0160]

[0161] This indicates that when P C > P Δ , S j can simply set τ j ∈ [t 1j , t 2j to ensure ξ j = 0, that is to say, S j can detect the covert transmission with probability 1; therefore, P C should satisfy P C ≤ P Δ to ensure ξ j > 0;

[0162] When t 1j ≥ t 2j , that is, P C ≤ P Δ , S j The total detection error probability is as follows:

[0163]

[0164] Analyzing the above formula, the optimal detection threshold range at S j is Within this range, the particle swarm optimization algorithm can be used to search for an optimal τ j that minimizes the total detection error probability of S j , and the corresponding minimum detection error probability is as follows:

[0165]

[0166] According to the joint detection mechanism, the false alarm probability of the system is as follows:

[0167]

[0168] The missed detection probability of the system is as follows:

[0169]

[0170] The total detection error probability of the system is as follows:

[0171] ξ = (1 - β)P FA + βP MD

[0172] According to the relayed signal, the received signal at the covert user B, and decoding the covert message x C The signal-to-noise ratios are respectively:

[0173]

[0174] The covert transmission rate is defined as R C = log(1 + γ C ), then the effective covert transmission rate is as follows:

[0175]

[0176] Example 2:

[0177] For the method provided in Example 1, this example also provides a covert communication system for a power monitoring network based on two-way relaying. The system includes a network interface, a memory, and a processor. Among them, the network interface is used to receive and send signals during the process of receiving and sending information with other external network elements; the memory is used to store computer program instructions that can run on the processor; the processor is used to execute the steps of the above consensus method when running the computer program instructions.

[0178] This embodiment also provides a computer storage medium which stores a computer program. When the processor executes the computer program, the above-described method can be implemented. The computer-readable medium can be considered tangible and non-transitory. Non-limiting examples of non-transitory tangible computer-readable media include non-volatile memory circuits (such as flash memory circuits, erasable programmable read-only memory circuits, or mask read-only memory circuits), volatile memory circuits (such as static random access memory circuits or dynamic random access memory circuits), magnetic storage media (such as analog or digital magnetic tapes or hard disk drives), and optical storage media (such as CDs, DVDs, or Blu-ray discs), etc. The computer program includes processor-executable instructions stored on at least one non-transitory tangible computer-readable medium. The computer program may also include or rely on stored data. The computer program may include a basic input / output system (BIOS) that interacts with the hardware of a dedicated computer, device drivers that interact with specific devices of a dedicated computer, one or more operating systems, user applications, background services, background applications, etc.

[0179] Those skilled in the art should understand that the embodiments of the present application can be provided as a method, a system, or a computer program product. Therefore, the present application can take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware aspects. Moreover, the present application can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0180] The present application is described with reference to the flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each flow and / or block in the flowchart and / or block diagram, and the combination of flows and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to the processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing devices to generate a machine, such that the instructions executed by the processor of the computer or other programmable data processing devices generate a means for implementing the functions specified in Figure 1 one flow or multiple flows and / or blocks Figure 1 one block or multiple blocks.

[0181] Embodiment 3:

[0182] Based on Embodiments 1 and 2, in order to verify the effectiveness and effects of the present invention, this embodiment analyzes the influence of system parameters on the system detection error probability and the effective concealment rate through simulation experiments, specifically as follows:

[0183] Figure 2 It is the relationship curve between the total system detection error probability and the power of the relay sending the covert message. It can be observed that as P C increases, the total system detection error probability decreases monotonically. From this, it can be observed that the total system detection error probability increases as P M increases.

[0184] Figure 3 It is the relationship curve between the total system detection error probability and the large-scale fading degree of the legitimate channel under different fixed transmission rates. It can be observed that when the fixed rate is 1 bit, the total system detection error probability is insensitive to the value change, while when the fixed transmission rate is low, the total system detection error probability decreases as increases.

[0185] Figure 4 It is the relationship curve between the effective covert transmission rate and the fixed transmission rate. It can be observed that the effective covert transmission rate decreases as the fixed transmission rate increases and increases as increases.

Claims

1. A covert communication method based on two-way relay for power monitoring network, characterized in that: The steps include: S1: Construct a transmission model and communication scheme for a two-way relay covert communication system. The nodes in the transmission model include two legitimate information sources S1 and S2, a relay R and a covert user B; S2: Based on the transmission model and communication scheme, the necessary conditions for uninterrupted communication and the necessary conditions for relays to conduct covert communication are obtained; S3: Determine a joint detection mechanism, in which two legitimate sources act as detectors together and detect independently in covert communication; make a joint decision based on the detection results of the two legitimate sources; S4: Based on the determination result of step S3, determine the performance evaluation method of covert communication based on two-way relay, determine the total detection error probability of the system, and the effective covert transmission rate of the covert user under the covert constraint condition.

2. According to claim 1, a covert communication method based on two-way relay in a power monitoring network is characterized in that: The communication process in the communication scheme of step S1 is: The transmission is divided into two stages. In the first stage, S1 and S2 send their legitimate messages x1 and x2 to R at the same time. In the second stage, R forwards the legitimate messages x1 and x2 to S2 and S1, and R takes the opportunity to send its own hidden message x C Forwarded to hidden user B; the system resources allocated to R are used to transmit messages for legitimate users, however, R may also intend to use these resources to send its own messages to B; considering fixed rate transmission, in the first stage, S1 transmits messages to R at a fixed rate R1, and S2 transmits messages to R at a fixed rate R2.

3. A covert communication method based on two-way relay in a power monitoring network according to claim 2, characterized in that: The received signal of relay R in the transmission model of step S1 is: Among them, P1 and P2 are the transmission power of S1 and S2 respectively. is the channel coefficient between S1 and relay R, is the channel coefficient between S2 and relay R, n R (i) is the variance at R Additive Gaussian white noise with mean 0, x1(i) is the transmitted signal of S1, x2(i) is the transmitted signal of S2, i=1,…,n, n is the finite block length of this transmission.

4. According to claim 1, a covert communication method based on two-way relay in a power monitoring network is characterized in that: The necessary condition for uninterrupted communication in step S2 depends on the relay being able to successfully decode x1 and x2 and the two sources being able to successfully decode each other's data, that is: The communication uninterrupted condition is recorded as: Among them, j∈{1,2} corresponds to the two information sources S1 and S2 respectively, γ thj YesS j The signal-to-noise ratio threshold at M is the maximum transmit power of R; When the relay does not send a covert message, the received signal of the source is: In the formula, is the transmission power when R does not send a covert message, x R (i) is the forwarding message of R, The source prescription error is Additive Gaussian white noise with a mean of 0; using fixed rate transmission, the transmission power when R does not send a covert message is: When the relay sends a covert message, the receiving signal of the source is: In the formula, Forwarding the source information x for R R (i) The transmission power, P C R sends a covert message x C (i) Transmit power; source decoding x R (i) When x C (i) As interference, according to fixed rate transmission, we get for: Consider the maximum power constraint at R, that is, The necessary condition for R to conduct covert communication is 5. A covert communication method based on two-way relay in a power monitoring network according to claim 4, characterized in that: The joint detection mechanism in step S3 is as follows: two information sources jointly act as detectors and perform independent detection respectively. The detectors perform binary hypothesis tests based on the received signals. Two detection error probability expressions for each detector and a total detection error probability expression are obtained based on the power detector and the corresponding decision rules. A determination result is then made jointly based on the respective detection results. That is, as long as one detector detects that the relay is transmitting a covert message, the system determines that the relay is sending a covert message.

6. A covert communication method based on two-way relay in a power monitoring network according to claim 5, characterized in that: In step S3, each detector conducts independent detection. When the detector performs binary hypothesis test based on the received signal, the detector has two detection error conditions H0 and H1. H0 is the null hypothesis, indicating that the detector believes that the relay does not send a covert message. H1 is the alternative hypothesis, indicating that the detector believes that the relay sends a covert message. The received signal of the detector is as follows: The detector uses a power detector to determine the behavior of the relay. The detector's receiving power is: The decision rule for an independent single detector is: Among them, τ j is the detection threshold of the detector, D0 and D1 represent the decisions made by the detector under the assumptions H0 and H1 respectively; then the detector S j The false alarm probability is expressed as: The missed detection probability is expressed as:

7. A covert communication method based on two-way relay in a power monitoring network according to claim 6, characterized in that: In step S3, a decoding condition is set for the processing of the decision rule, which is expressed as: The condition for uninterrupted communication is expressed as: Let R use more power to transmit the message, and It is expressed as: Consider the maximum power constraint at R, that is, Then the necessary condition for R to perform covert transmission is expressed as:

8. A covert communication method based on two-way relay in a power monitoring network according to claim 7, characterized in that: The step S4 is specifically as follows: Since the channel coefficients between nodes are independent of each other and but and The distribution functions are as follows: but The distribution function of is as follows: Then the detector S j The false alarm probability is expressed as: Detector S j The probability of missed detection is expressed as: in The prior probability of a relay sending a covert message is expressed as: Where ρ is the probability that the relay sends a covert message, then the prior probability that the relay does not send a covert message is Pr(H0)=1-Pr(H1)=1-β S j The total detection error probability is expressed as: Determine P C The initial constraints and τ j The limit of S j Setting τ j to minimize the value of ξ j ; According to the joint detection mechanism, the false alarm probability of the system is as follows: The system's missed detection probability is as follows: The total detection error probability of the system is as follows: ξ=(1-β)P FA +βP MD According to the relayed signal, conceal the received signal at user B and decode the concealed message x C The signal-to-noise ratios are: The covert transmission rate is defined as R C =log(1+γ C ), then the effective covert transmission rate is as follows:

9. A covert communication method based on two-way relay in a power monitoring network according to claim 8, characterized in that: In step S4, P is determined C The initial constraints and τ j The limit of S j Setting τ j to minimize the value of ξ j The specific method is: S j The total probability of detection error is divided into two cases: when t 1j <t 2j , that is, P C >P Δ When P Δ The value of S j The total probability of detection error is as follows: This shows that when P C >P Δ When S j You can simply set τ j ∈[t 1j ,t 2j ] to ensure j =0, that is, S j Covert transmissions can be detected with probability 1; therefore, P C Should satisfy P C ≤P Δ To ensure j >0; When t 1j ≥t 2j , that is, P C ≤P Δ When S j The total probability of detection error is as follows: Analyzing the above formula, we can see that S j The optimal detection threshold range is In this range, we can use the particle swarm algorithm to search for a j The optimal τ with the minimum total probability of detection error j , the corresponding minimum detection error probability is as follows:

10. A covert communication system based on two-way relay for power monitoring network, characterized in that: The system comprises a network interface, a memory and a processor; wherein, The network interface is used to receive and send signals during the process of sending and receiving information with other external network elements; The memory is used to store computer program instructions that can be executed on the processor; The processor is used to execute the steps of a covert communication method based on two-way relay in a power monitoring network according to any one of claims 1 to 9 when running the computer program instructions.

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