A covert transmission method in a multi-eavesdropper joint detection environment

Abstract

The application discloses a covert transmission method in a multi-eavesdropper joint detection environment, comprising the following steps: establishing a wireless covert communication network model; detecting whether a sending node sends a message by an eavesdropping node and calculating a minimum detection error probability of the eavesdropping node; sending an interference signal by a destination node to resist the eavesdropping node; in the case that a given covert constraint and the minimum detection error probability of the eavesdropping node are satisfied, maximizing a covert transmission rate of the system by power distribution and selecting the most suitable interference node transmission power to obtain an optimal covert transmission rate of the system; and comprehensively considering the covertness and reliability constraints of the system by the destination node to solve a maximum effective rate of the sending node. The application improves the detection performance, effectively resists the case of double-detecting cooperation detection, and significantly improves the covert transmission rate.

Description

Technical Field

[0001] This invention belongs to the field of covert communication technology, specifically relating to a covert transmission method in a multi-eavesdropper joint detection environment. Background Technology

[0002] With the rapid development of mobile communication technologies, represented by 5G, and the extension of human activities into space and the deep sea, modern wireless communication technologies that utilize electromagnetic waves, sound waves, and light as information transmission media have become the primary communication methods in various scenarios. Among these, radio communication is currently the most widely used communication method. Due to the open nature of radio media, communication signals can be easily intercepted and eavesdropped on by third parties, leading to the leakage of communication content or the exposure of communication intentions. Therefore, ensuring the security of information transmitted through wireless links is crucial for consumer, industrial, and military applications.

[0003] Data transmitted in wireless networks typically employs various encryption methods and key exchange protocols to prevent interception by eavesdroppers. While traditional cryptography-based encryption promises to ensure the integrity of any transmitted information, its security depends on the difficulty of certain number theory problems. However, quantum computing, with its powerful computational capabilities, can effectively solve these complex mathematical problems that traditional computers struggle with, thereby breaking most public-key systems and jeopardizing modern communications. With ongoing research, physical layer security has emerged as a supplementary and significantly enhanced technology for wireless network communication security, offering a reliable alternative. However, both encryption and physical layer security technologies focus on preventing information theft and cannot completely address privacy issues. The wireless transmission process itself may expose the user's source location information or be used by eavesdroppers for reverse attacks, which is extremely dangerous in military conflicts. Therefore, we need to first prevent transmission detection through covert communication. Covert communication (also known as low-probability-of-detection communication, LPD) is emerging as a new technology for achieving robust security and privacy in wireless communication. Covert communication aims to achieve the hidden transmission of information between the communicating parties. In addition to protecting the content of the communication, it emphasizes ensuring that the transmission is difficult for non-cooperative eavesdroppers to detect, that is, it is not easy to attract the attention of eavesdroppers during the transmission process.

[0004] In the field of covert communication, artificial noise is often used to introduce uncertainty, making it impossible for the detector / eavesdropper to determine whether a covert transmission exists. In many existing covert communication networks, there is usually only one detector; however, in reality, eavesdroppers are ubiquitous. Therefore, in a planar scenario, we consider eavesdroppers to be uniformly distributed; in this scenario, we consider two eavesdroppers for detection. Summary of the Invention

[0005] The purpose of this invention is to propose a covert transmission method in a multi-eavesdropper joint detection environment.

[0006] The technical solution to achieve the purpose of this invention is: a covert transmission method in a multi-eavesdropper joint detection environment, the specific steps of which are:

[0007] (10) Establish a wireless covert communication network model, which includes a sending node, a legitimate receiving destination node, and two eavesdropping nodes. The sending node transmits covertly to the destination node, that is, the sending node generates a random signal with a certain probability and sends it to the destination node.

[0008] (20) The eavesdropping node detects whether the sending node has sent a message and calculates the minimum test error probability of the eavesdropping node;

[0009] (30) The target node sends jamming signals to counter the eavesdropping node;

[0010] (40) Under the condition of satisfying the given concealment constraints and minimizing the detection error probability of the eavesdropping node, the concealed transmission rate of the system is maximized by power allocation and selecting the most suitable interference node transmission power, so as to obtain the optimal concealed transmission rate of the system.

[0011] (50) The destination node comprehensively considers the system's concealment and reliability constraints to solve for the maximum effective rate of the sending node.

[0012] Preferably, the specific method by which the eavesdropping node detects whether the sending node has sent a message is as follows:

[0013] The two eavesdropping nodes each use a radiometer to detect the energy of the received signal to determine whether a transmission signal exists.

[0014] A joint decision scheme is used to detect whether a sending node has sent a message. There are two joint decision schemes, as shown in the table below:

[0015]

[0016] Option 1: If any eavesdropping node detects the transmission, it determines that the sending node has sent confidential information. Option 2: Only when both eavesdropping nodes detect the transmission is it determined that the sending node has sent a confidential message. Y0 indicates that the sending node has not sent any information, and Y1 indicates that the sending node has sent information. This indicates that the sending node did not send any information, Y1 (i) This indicates that the sending node has sent information, i = 1, 2.

[0017] Preferably, the method for the two eavesdropping nodes to determine whether a transmission signal exists is as follows:

[0018]

[0019] In the formula, Indicates the eavesdropping node w i Average received power, τ i For w i The threshold for judgment, This indicates that the sending node did not send any information, Y1 (i) This indicates that the sending node has sent information.

[0020] Preferably, the method for calculating the minimum test error probability of the eavesdropping node is as follows:

[0021] The false negative rate and false positive rate of the testers are expressed as follows:

[0022]

[0023]

[0024] i = 1 indicates scheme one, and i = 2 indicates scheme two;

[0025] Assuming the probability of the sending node transmitting confidential information is Pr{H1}=Pr{H0}=1 / 2, then the detection error probability ξ of the eavesdropping node is:

[0026]

[0027] Calculate the error probability based on Scheme 1:

[0028] When using Scheme 1, the false negative rate and false positive rate of the eavesdropping node are:

[0029]

[0030]

[0031] When the system satisfies (where subscript a represents Alice, subscript b represents Bob, and subscript w represents Alice) i The eavesdropping node is Willie(i), where the index i of w is 1, representing eavesdropping node 1, and 2, representing eavesdropping node 2; P a Send signal power to the transmitting node Alice; For P b Maximum transmit power; Let Alice be the channel coefficient from Willie(i). Let |·| be the channel coefficient from Bob to the eavesdropping node Willie(i); 2 This represents the square of the modulus; This represents the path loss coefficient from the sending node Alice to the eavesdropping node Willie(i); Let w1 represent the path loss coefficient from destination node Bob to Willie(i), and let w2 be the optimal decision threshold. and in For P b Maximum transmit power; Here are the channel coefficients from Bob to Willie(i); |·| 2 This represents the square of the modulus; This represents the path loss coefficient from Bob to Willie(i); Given the Gaussian white noise power, the minimum probability of detection error is obtained. for:

[0032]

[0033] Where subscript a represents Alice, subscript b represents Bob, and subscript w... i Let W represent Willie(i), where the index i of w is 1 for Willie1 and 2 for Willie2; P a Send signal power to the transmitting node Alice; For P b Maximum transmit power; Let these be the channel coefficients from Alice to Willie(i). Similarly, Here are the channel coefficients from Bob to Willie(i); |·| 2 This represents the square of the modulus; This represents the path loss coefficient from Alice to Willie(i); This represents the path loss coefficient from Bob to Willie(i);

[0034] When using Scheme 2, the false negative rate and false positive rate of the eavesdropping node are:

[0035]

[0036]

[0037] When the system satisfies (where subscript a represents Alice, subscript b represents Bob, and subscript w represents Alice) i Let W represent Willie(i), where the index i of w is 1 for Willie1 and 2 for Willie2; P a Send signal power to the transmitting node Alice; For P b Maximum transmit power; Let these be the channel coefficients from Alice to Willie(i). Similarly, Here are the channel coefficients from Bob to Willie(i); |·| 2 This represents the square of the modulus; This represents the path loss coefficient from Alice to Willie(i); Let w1 represent the path loss coefficient from Bob to Willie(i), and let w2 be the optimal decision threshold. and Where P a Send signal power to the transmitting node Alice; Here are the channel coefficients from Alice to Willie(i); |·| 2 This represents the square of the modulus; This represents the path loss coefficient from Alice to Willie(i); Given the Gaussian white noise power, the minimum probability of detection error is obtained. for:

[0038]

[0039] Where subscript a represents Alice, subscript b represents Bob, and subscript w... i Let W represent Willie(i), where the index i of w is 1 for Willie1 and 2 for Willie2; P a Send signal power to the transmitting node Alice; For P b Maximum transmit power; Let these be the channel coefficients from Alice to Willie(i). Similarly, Here are the channel coefficients from Bob to Willie(i); |·| 2 This represents the square of the modulus; This represents the path loss coefficient from Alice to Willie(i); This represents the path loss coefficient from Bob to Willie(i).

[0040] Preferably, when the destination node sends jamming signals to counter eavesdropping nodes, the process of determining the capacity expression and the covert transmission rate expression is as follows:

[0041] In a network of multiple eavesdropping nodes, the sending node performs covert transmission; the received signal at the legitimate receiving destination node is:

[0042]

[0043] Among them, P a P represents the transmit power of the transmitting node. b To legally receive the noise transmission power of the destination node; h represents the path loss coefficient from Alice to Bob. a,b h represents the channel coefficients from Alice to Bob. b,b x is the channel coefficient between Bob's transmitting antenna and Bob's receiving antenna; a (k) is the covert signal sent by Alice; x b (k) represents the artificial noise at Bob, satisfying E[|x b (k)| 2 ] = 1; n b (k) represents the noise at Bob, satisfying... φ (0 < φ ≤ 1) is the interference cancellation coefficient; k = 1, 2, ..., n represents the kth symbol in the time slot;

[0044] P b obey Uniform distribution For P b Maximum transmit power, probability density function for:

[0045]

[0046] The signal-to-interference-plus-noise ratio γ at the destination node b for:

[0047]

[0048] Where P a P represents the transmit power of the transmitting node. b To legally receive the noise transmission power of the destination node; h represents the path loss coefficient from Alice to Bob. a,b h represents the channel coefficients from Alice to Bob. b,b Here is the channel coefficient between Bob's transmitting antenna and Bob's receiving antenna; |·| 2 This represents the square of the modulus; φ (0 < φ ≤ 1) is the interference cancellation coefficient;

[0049] The transmission rate formula, also known as the capacity expression C, is... a,b for:

[0050] C a,b =log2(1+γ) b )

[0051] Given a system target transmission rate of R s System security interruption probability P out for:

[0052] P out =Pr{C a,b <R s}=Pr{log2(1+γ b ) < R s}

[0053] Connection probability O a,b =1-P out The system's covert transmission rate is π1 represents the probability that Alice sends a hidden message, assuming that Alice sends messages with equal probability.

[0054] Preferably, under the given concealment constraints and minimizing the detection error probability of the eavesdropping nodes, the specific process of maximizing the concealed transmission rate of the system by power allocation and selecting the most suitable interference node's transmission power to obtain the optimal concealed transmission rate of the system is as follows:

[0055] (41) Set the required detection error probability threshold ε;

[0056] (42) Establish constraints: Based on the minimum detection error probability of the system, the error probability of the eavesdropping node must not be lower than the set error threshold, that is, it must be required that...

[0057] (43) Formulating the optimization content: Combine the capacity expression with the constraints to obtain the optimization content, which requires that the covert transmission rate R is satisfied under the given constraints, given that the error probability of the eavesdropping node detection is satisfied. c maximum:

[0058]

[0059]

[0060] Preferably, the specific method for solving the maximum effective rate of the transmitting node is as follows:

[0061] Let the total transmit power of the system be P, and let the transmit power of the transmitting node and the destination node be...

[0062] Solving for the total transmitted power P of the system, the range of values ​​for P when the concealment condition constraint is satisfied is:

[0063]

[0064] Because of R c It is an increasing function of P. Based on the range of values ​​for P, the optimal transmit power of the system is:

[0065]

[0066] in,

[0067]

[0068] in Let Alice be the channel coefficient from Willie(i). Here are the channel coefficients from Bob to Willie(i); |·| 2 This represents the square of the modulus; This represents the path loss coefficient from Alice to Willie(i); This represents the path loss coefficient from Bob to Willie(i).

[0069] Compared with the prior art, the significant advantages of this invention are:

[0070] In this invention, when both detectors perform detection and the two detection results are combined for a decision, two joint detection decision criteria are designed. The expressions for the minimum test error probability under the two detection schemes are analyzed and derived. Based on this, the interference node group selects the optimal interference to interfere with the detector. Then, under the condition that the minimum test error probability satisfies the given concealment constraint, the maximum concealed transmission rate is obtained by finding the optimal total transmission power and interference nodes. This invention uses joint detection by two detectors to reduce the test error probability at the detector. Through joint detection, the detector can improve its detection performance, effectively counter the situation of cooperative detection by two detectors, and significantly improve the concealed transmission rate.

[0071] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments. Attached Figure Description

[0072] Figure 1 This is a model diagram of a covert transmission method in a multi-eavesdropper joint detection environment according to the present invention.

[0073] Figure 2 It is a method and process for countering covert communication by multiple eavesdroppers.

[0074] Figure 3 This invention presents a method for covert transmission in a multi-eavesdropper joint detection environment, which compares the performance of two joint detection methods with that of a single detector – a comparison chart of the missed detection rate of eavesdropping nodes.

[0075] Figure 4 This invention presents a method for covert transmission in a multi-eavesdropper joint detection environment, which compares the performance of two joint detection methods with that of a single detector—a comparison chart of the false detection rate of eavesdropping nodes. Detailed Implementation

[0076] A covert transmission method for multi-eavesdropper joint detection is proposed. A system model with two eavesdroppers is presented. Under joint detection by the two eavesdroppers, the method optimizes the power allocation between the transmitting node and artificial noise, yielding the minimum detection error probability and the optimal covert transmission rate of the system. The specific steps are as follows:

[0077] (10) Establish a multi-eavesdropper wireless covert communication network model: This model includes one transmitting node Alice, one legitimate receiving node Bob, and two eavesdropping nodes Willie1 and Willie2. Both the transmitting and eavesdropping nodes are equipped with one antenna, while the legitimate receiving nodes are equipped with two omnidirectional antennas: one for receiving signals and the other for transmitting artificial noise. The transmitting node Alice randomly sends a covert signal x to the receiving nodes. a (k), k=1,...,n, the receiving node sends artificial interference noise to the outside world to interfere with the detection of the eavesdropping node. The sending node Alice encodes the covert information and completes the transmission of n symbols in each time slot. The signal satisfies the condition that the average power is 1, i.e., E[|x a (k)| 2 =1. The channel fading coefficient from any node x to another node y is represented by h. x,y It means that h x,y It satisfies the condition that the mean is 0 and the variance is g. x,y The cyclically symmetric Gaussian distribution, i.e. All receiver noise is independent zero-mean additive white Gaussian noise with a power of [value missing].

[0078] (20) The eavesdropping node detects whether the sending node has sent a message:

[0079] H0 indicates that the sending node Alice did not communicate with the receiving node Bob. In this case, the signal received by the eavesdropping node Willie(1,2) only contains artificial noise and Gaussian noise. H1 indicates that the sending node Alice sent a signal to the receiving node Bob. The signal received by the eavesdropping node Willie(1,2) includes the signal from the sending node Alice and other noise.

[0080] (21) The eavesdropping node eavesdrops on the signal of the transmitting node, and the eavesdropped signal... Specifically

[0081]

[0082] Subscript a represents Alice, subscript b represents Bob, and subscript w represents... i Let w represent Willie(i), where i = 1 represents Willie1, and i = 2 represents Willie2; n wiP represents the noise at Willie(i); a Send signal power to the transmitting node Alice; P b Send artificial noise power to the destination node Bob; x a (k) represents the transmission signal from the transmitting node Alice; x b (k) represents the artificial noise signal of the destination node Bob; This represents the path loss coefficient from node x to node y.

[0083] Two eavesdropping nodes perform separate detection: each node uses a radiometer to detect the energy of the received signal to determine the presence of a transmission signal. Each node then makes a judgment on the covert communication. Eavesdropping nodes w1 and w2 use the Neyman-Pearson criterion to determine whether confidential information has been sent; the judgment formula is as follows:

[0084]

[0085] In the formula, i represents 1 or 2, and T wi Indicates the eavesdropping node w i Average received power, τ i For w i The threshold for judgment. and For eavesdropping node w i Judgment regarding the information transmission situation: This indicates that the sending node has not sent any information. This indicates that the sending node has been identified as sending information.

[0086] (23) Joint Detection Scheme for Eavesdropping Nodes: Based on the detection results of both parties, a joint decision scheme is adopted to obtain the detection result of whether covert transmission exists. Two decision schemes are proposed here: In Scheme 1, if any eavesdropping node detects the existence of transmission, the eavesdropping node determines that the sending node has sent confidential information; while in Scheme 2, the sending node is determined to have sent confidential information only when both eavesdropping nodes detect the existence of transmission. Y0 and Y1 are the joint decision results of the two eavesdropping nodes on the information transmission status: Y0 indicates that the sending node has not sent information, and Y1 indicates that the sending node has sent information.

[0087] Table 1 Joint Detection and Judgment Scheme for Eavesdropping Nodes

[0088]

[0089] (24) Calculate the detection error probability of the eavesdropping node. When the eavesdropping node detects covert transmission behavior, the detection result may have two types of errors: missed detection and false detection. Missed detection is defined as when the sending node sends confidential information (H1 case), the eavesdropping node determines that the sending node did not send confidential information. False detection is defined as when the sending node does not send confidential information (H0 case), the eavesdropping node determines that the sending node sent confidential information. Based on the definitions of missed detection and false detection, the missed detection rate and false detection rate of the detector are further expressed as follows: i = 1 represents Scheme 1, i = 2 represents Scheme 2:

[0090]

[0091] Assuming the probability of the sending node transmitting confidential information is Pr{H1}=Pr{H0}=1 / 2, then the detection error probability ξ of the eavesdropping node is:

[0092]

[0093] (241) Calculate the error probability according to Scheme 1 in the table.

[0094] When using Scheme 1, the false negative rate and false positive rate of the eavesdropping node are:

[0095]

[0096]

[0097] When the system satisfies (where subscript a represents Alice, subscript b represents Bob, and subscript w represents Alice) i Let W represent Willie(i), where the index i of w is 1 for Willie1 and 2 for Willie2; P a Send signal power to the transmitting node Alice; For P b Maximum transmit power; Let these be the channel coefficients from Alice to Willie(i). Similarly, Here are the channel coefficients from Bob to Willie(i); |·| 2 This represents the square of the modulus; This represents the path loss coefficient from Alice to Willie(i); (where w1 represents the path loss coefficient from Bob to Willie(i), and the optimal decision thresholds for w1 and w2 are respectively...) and (in For P b Maximum transmit power; Here are the channel coefficients from Bob to Willie(i); |·|2 This represents the square of the modulus; This represents the path loss coefficient from Bob to Willie(i); (Given the Gaussian white noise power) This represents the minimum probability of error that the system can achieve. for:

[0098]

[0099] Where subscript a represents Alice, subscript b represents Bob, and subscript w... i Let W represent Willie(i), where the index i of w is 1 for Willie1 and 2 for Willie2; P a Send signal power to the transmitting node Alice; For P b Maximum transmit power; Let these be the channel coefficients from Alice to Willie(i). Similarly, Here are the channel coefficients from Bob to Willie(i); |·| 2 This represents the square of the modulus; This represents the path loss coefficient from Alice to Willie(i); This represents the path loss coefficient from Bob to Willie(i);

[0100] (242) Scheme 2 is adopted: the false negative rate and false positive rate of the eavesdropping node are:

[0101]

[0102]

[0103] When the system satisfies (where subscript a represents Alice, subscript b represents Bob, and subscript w represents Alice) i Let W represent Willie(i), where the index i of w is 1 for Willie1 and 2 for Willie2; P a Send signal power to the transmitting node Alice; For P b Maximum transmit power; Let these be the channel coefficients from Alice to Willie(i). Similarly, Here are the channel coefficients from Bob to Willie(i); |·| 2 This represents the square of the modulus; This represents the path loss coefficient from Alice to Willie(i); (where w1 represents the path loss coefficient from Bob to Willie(i), and the optimal decision thresholds for w1 and w2 are respectively...) and (where P) a Send signal power to the transmitting node Alice; Here are the channel coefficients from Alice to Willie(i); |·| 2 This represents the square of the modulus; This represents the path loss coefficient from Alice to Willie(i); (Given the Gaussian white noise power) This represents the minimum probability of error that the system can achieve. for:

[0104]

[0105] Where subscript a represents Alice, subscript b represents Bob, and subscript w... i Let W represent Willie(i), where the index i of w is 1 for Willie1 and 2 for Willie2; P a Send signal power to the transmitting node Alice; For P b Maximum transmit power; Let these be the channel coefficients from Alice to Willie(i). Similarly, Here are the channel coefficients from Bob to Willie(i); |·| 2 This represents the square of the modulus; This represents the path loss coefficient from Alice to Willie(i); This represents the path loss coefficient from Bob to Willie(i);

[0106] This shows that when the system meets the conditions for covert communication, although the two decision schemes are different, the minimum error probability of the two schemes is equal when the probability of sending and not sending confidential information is equal. However, when the system does not meet the conditions for covert communication, the error probability is 0, and legitimate nodes cannot perform covert transmission of information.

[0107] when At that time, the minimum detection error probability of the system is

[0108]

[0109] This is equivalent to the eavesdropping node randomly guessing the situation of the covert transmission.

[0110] (30) At the destination node, the full-duplex receiver Bob transmits interference signals to counter the eavesdropping node and reduce its detection performance. Bob uses self-interference cancellation technology, meaning that AN has no effect on Bob.

[0111] In a network of multiple eavesdropping nodes, the sending node Alice performs covert transmission; the received signal at the legitimate receiver Bob is...

[0112]

[0113] Among them, P a P represents the transmit power of the transmitting node. b To legally receive the noise transmission power of the destination node; h represents the path loss coefficient from Alice to Bob. a,b h represents the channel coefficients from Alice to Bob. b,b x is the channel coefficient between Bob's transmitting antenna and Bob's receiving antenna; a (k) is the covert signal sent by Alice; x b (k) represents the artificial noise at Bob, satisfying E[|x b (k)| 2 ] = 1; n b (k) represents the noise at Bob, satisfying... φ (0<φ≤1) is the interference cancellation coefficient; k=1,2,……,n represents the kth symbol in the time slot.

[0114] P b obey Uniform distribution For P b Maximum transmission power, its probability density function for

[0115]

[0116] Then the signal-to-interference-plus-noise ratio γ at Bob b for

[0117]

[0118] Where P a P represents the transmit power of the transmitting node. b To legally receive the noise transmission power of the destination node; h represents the path loss coefficient from Alice to Bob. a,b h represents the channel coefficients from Alice to Bob. b,b The channel coefficient between Bob's transmitting antenna and Bob's receiving antenna; |·| 2 φ represents the square of the modulus; φ (0 < φ ≤ 1) is the interference cancellation coefficient.

[0119] Transmission rate formula, capacity expression C a,b For: C a,b =log2(1+γ) bSubstituting (14) into equation (14) yields...

[0120]

[0121] System covert transmission rate: Given the system target transmission rate as R s System security interruption probability P out For: P out =Pr{C a,b <R s Substituting (15) into equation (15) yields...

[0122]

[0123] Where g b,b for h b,b Channel variance; φ (0 < φ ≤ 1) is the interference cancellation coefficient; For P b Maximum transmit power; For noise variance; g a,b for h a,b Channel variance; P a This refers to the transmit power of the transmitting node; This represents the path loss coefficient from Alice to Bob.

[0124] Connection probability O a,b =1-P out Substituting into (16) gives

[0125]

[0126] The system's covert transmission rate is Substituting (17) gives

[0127]

[0128] Where π1 represents the probability that Alice sends a hidden message, assuming that Alice sends messages with equal probability.

[0129] (40) Establish the optimization problem: Under the given concealment constraints and the condition of minimizing the detection error probability of the eavesdropper, the power allocation of the transmission power and noise power is performed to maximize the concealed transmission rate of the system and obtain the optimal concealed transmission rate of the system.

[0130] (41) Set the required detection error probability threshold: This value is designed according to the system requirements. For example, if Wille needs to have a 90% (i.e. 1-ε) probability of not being able to detect Alice and Bob's communication, then ε = 0.1.

[0131] (42) Establish constraints: For the given condition (41) combined with the minimum detection error probability of the system (Equation 11), the error probability of the eavesdropping node must not be lower than the set error threshold, that is, the system must...

[0132] (43) Forming the optimized content: Combining the capacity expression (18) with the constraints proposed in (42), the optimized content is obtained. The requirement is that the covert transmission rate R is achieved under the given constraints, provided that the error probability of the eavesdropping node detection satisfies the given constraints. c maximum.

[0133]

[0134] (50) Considering the system's concealment and reliability constraints, the destination node solves for the maximum effective rate R of the transmitting node. c .

[0135] Let the total transmit power of the system be P, and let the transmit power of the transmitting node and the destination node be... Furthermore, it can be seen from equation (18) that the influence of R c The only variable of size is P, and R c It is an increasing function of P. Solving for P, when the implicit condition constraint of formula (19) is satisfied, the range of values ​​for P is:

[0136]

[0137] Because of R c It is an increasing function of P. Based on the range of values ​​for P, the optimal transmit power of the system is obtained as follows:

[0138]

[0139] in

[0140] in Let these be the channel coefficients from Alice to Willie(i). Similarly, Here are the channel coefficients from Bob to Willie(i); |·| 2 This represents the square of the modulus; This represents the path loss coefficient from Alice to Willie(i); This represents the path loss coefficient from Bob to Willie(i).

[0141] At this point, R is obtained. c This is the optimal solution. It shows that the sending node can find an optimal transmission power that allows it to send covert messages at a certain rate even under joint detection by multiple eavesdroppers.

Claims

1. A method for covert transmission in a multi-eavesdropper joint detection environment, characterized in that, The specific steps are as follows: (10) Establish a wireless covert communication network model, which includes a sending node, a legitimate receiving destination node, and two eavesdropping nodes. The sending node transmits covertly to the destination node, that is, the sending node generates a random signal with a certain probability and sends it to the destination node. (20) The eavesdropping node detects whether the sending node has sent a message and calculates the minimum test error probability of the eavesdropping node; (30) The target node sends jamming signals to counter the eavesdropping node; (40) Under the given concealment constraints and the minimum detection error probability of the eavesdropping node, the concealed transmission rate of the system is maximized by power allocation and selection of the most suitable target node transmission power, so as to obtain the optimal concealed transmission rate of the system. (50) Considering the system's concealment and reliability constraints, the destination node calculates the maximum effective rate of the sending node using the following method: Let the total transmit power of the system be Set the transmit power of the sending node and the destination node. ; Total transmit power of the system To solve this problem, when the hidden condition constraints are met, The range of values ​​for is: ； In the formula, To set a threshold for the probability of detecting errors; The maximum transmit power of the destination node; because It is about The increasing function, according to Given the range of values ​​for , the optimal transmit power of the system is obtained as follows: ； in, , ； in Let Alice be the channel coefficient from Willie(i). Let be the channel coefficients from Bob to Willie(i); This represents the square of the modulus; This represents the path loss coefficient from Alice to Willie(i); The subscript represents the path loss coefficient from Bob to Willie(i). Represents the eavesdropping node Willie(i), subscript A value of 1 represents eavesdropping node 1, and a value of 2 represents eavesdropping node 2.

2. The covert transmission method in a multi-eavesdropper joint detection environment according to claim 1, characterized in that, The specific method by which an eavesdropping node detects whether a sending node has sent a message is as follows: The two eavesdropping nodes each use a radiometer to detect the energy of the received signal to determine whether a transmission signal exists. A joint decision scheme is used to detect whether a sending node has sent a message. There are two joint decision schemes, as shown in the table below: ； Option 1: If any eavesdropping node detects the existence of transmission, the eavesdropping node determines that the sending node has sent confidential information; Option 2: Only when both eavesdropping nodes detect the existence of transmission will the sending node determine that it has sent confidential information. This indicates that the sending node has not sent any information. This indicates that the sending node has sent information. This indicates that the sending node has not sent any information. This indicates that the sending node has sent information, i=1,2.

3. The covert transmission method in a multi-eavesdropper joint detection environment according to claim 2, characterized in that, The methods used by the two eavesdropping nodes to determine whether a transmission signal exists are as follows: ； In the formula, Indicates eavesdropping node Average received power, for The threshold for judgment, This indicates that the sending node has not sent any information. This indicates that the sending node has sent information.

4. The covert transmission method in a multi-eavesdropper joint detection environment according to claim 3, characterized in that, The method for calculating the minimum test error probability of an eavesdropping node is as follows: The false negative rate and false positive rate of the testers are expressed as follows: ； A value of 1 represents Option 1, and a value of 2 represents Option 2. This indicates that the sending node Alice sent a signal to the destination node Bob. This indicates that the sending node Alice is not communicating with the destination node Bob; Assume the probability of a sending node sending confidential information is... The probability of a detection error by the eavesdropping node is... for: ； Calculate the error probability based on Scheme 1: When using Scheme 1, the false negative rate and false positive rate of the eavesdropping node are: ； ； When the system satisfies , subscript Represents Alice, subscript Represents Bob, subscript The eavesdropping node Willie(i) subscript A value of 1 represents eavesdropping node 1, and a value of 2 represents eavesdropping node 2; The transmit power of the transmitting node Alice; for Maximum transmit power; Let Alice be the channel coefficient from Willie(i). Let be the channel coefficients from Bob to the eavesdropping node Willie(i); This represents the square of the modulus; This represents the path loss coefficient from the sending node Alice to the eavesdropping node Willie(i); Let represent the path loss coefficient from destination node Bob to Willie(i), and and The optimal decision thresholds are respectively and ,in for Maximum transmit power; Let be the channel coefficients from Bob to Willie(i); This represents the square of the modulus; This represents the path loss coefficient from Bob to Willie(i); Given the Gaussian white noise power, the minimum probability of detection error is obtained. for: ； Subscript Represents Alice, subscript Represents Bob, subscript Represents Willie(i), subscript A value of 1 represents Willie1, and a value of 2 represents Willie2; The transmit power of the transmitting node Alice; for Maximum transmit power; Let these be the channel coefficients from Alice to Willie(i). Similarly, Let be the channel coefficients from Bob to Willie(i); This represents the square of the modulus; This represents the path loss coefficient from Alice to Willie(i); This represents the path loss coefficient from Bob to Willie(i); When using Scheme 2, the false negative rate and false positive rate of the eavesdropping node are: ； ； When the system satisfies , subscript Represents Alice, subscript Represents Bob, subscript Represents Willie(i), subscript A value of 1 represents Willie1, and a value of 2 represents Willie2; The transmit power of the transmitting node Alice; Let these be the channel coefficients from Alice to Willie(i). Similarly, Let be the channel coefficients from Bob to Willie(i); This represents the square of the modulus; This represents the path loss coefficient from Alice to Willie(i); Let represent the path loss coefficient from Bob to Willie(i), and and The optimal decision thresholds are respectively and , This represents the square of the modulus; This represents the path loss coefficient from Alice to Willie(i); Given the Gaussian white noise power, the minimum probability of detection error is obtained. for: ； Subscript Represents Alice, subscript Represents Bob, subscript Represents Willie(i), subscript A value of 1 represents Willie1, and a value of 2 represents Willie2; This represents the square of the modulus; This represents the path loss coefficient from Alice to Willie(i); This represents the path loss coefficient from Bob to Willie(i).

5. The covert transmission method in a multi-eavesdropper joint detection environment according to claim 1, characterized in that, When the destination node sends jamming signals to counter eavesdropping nodes, the process of determining the capacity expression and the covert transmission rate expression is as follows: In a network of multiple eavesdropping nodes, the sending node transmits data covertly; the legitimate receiving node receives the signal. for: ； in, This refers to the transmit power of the transmitting node; To legally receive the noise transmission power of the destination node; This represents the path loss coefficient from Alice to Bob; Here are the channel coefficients from Alice to Bob; The channel coefficients between Bob's transmitting antenna and Bob's receiving antenna; A covert signal sent to Alice; Artificial noise at Bob's location, satisfying ; For the noise at Bob, satisfying ; This is the interference cancellation coefficient. ; Indicates the first time slot A symbol, This indicates that the sending node Alice sent a signal to the destination node Bob; obey Uniform distribution for Maximum transmit power, probability density function for: ； Signal-to-interference-plus-noise ratio at the destination node for: ； in This refers to the transmit power of the transmitting node; To legally receive the noise transmission power of the destination node; This represents the path loss coefficient from Alice to Bob; Here are the channel coefficients from Alice to Bob; The channel coefficients between Bob's transmitting antenna and Bob's receiving antenna; This represents the square of the modulus; Transmission rate formula, i.e., capacity expression for: ； Given the target transmission rate of the system is System security interruption probability for: ； Connection probability The system's covert transmission rate is , The probability of Alice sending a covert message, assuming Alice sends it with equal probability. .

6. The covert transmission method in a multi-eavesdropper joint detection environment according to claim 4, characterized in that, Given the concealment constraints and minimizing the detection error probability of the eavesdropping nodes, the specific process of maximizing the system's concealed transmission rate through power allocation and selecting the most suitable target node's transmit power is as follows: (41) Set the required detection error probability threshold ; (42) Establish constraints: Based on the minimum detection error probability of the system, the error probability of the eavesdropping node must not be lower than the set error threshold, that is, it is required that... ; (43) Forming the optimization content: Combine the capacity expression with the constraints to obtain the optimization content, which requires that the covert transmission rate meets the given constraints under the condition that the error probability of the eavesdropping node detection satisfies the constraints. maximum: 。

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