A method and system for joint cooperation of interference and relay selection for wireless covert communication

Abstract

The application discloses a wireless covert communication method and system of joint cooperation interference and relay selection, wherein a source node intends to send a message to its destination by means of selected relays, a detector intends to detect wireless transmission behaviors of the source node and the relay node, and meanwhile the source node selects some other idle relays as friendly forces to send interference signals to confuse the detector. To this end, two relay selection schemes, i.e. random relay selection and optimal relay selection, and a cooperation interference scheme are first proposed to ensure the concealment of the system. Then, a theoretical model of the concealment transmission performance is constructed in each relay selection scheme in combination with the cooperation interference, and the concealment rate is further optimized. Finally, extensive simulation and numerical analysis are given to verify the theoretical model, and through the results, the influence of various parameters on the system performance can be analyzed, and the joint cooperation interference technology can greatly improve the concealment transmission performance in the multi-relay scene.

Description

Technical Field

[0001] This invention belongs to the field of wireless communication technology, specifically relating to a wireless covert communication method and system with joint cooperative interference and relay selection. Background Technology

[0002] Wireless communication technology has fundamentally transformed our daily lives and promises to create a fully interconnected digital world in the upcoming sixth-generation (6G) era, where the Internet of Things will facilitate the unprecedented transmission of sensitive personal data over wireless channels. Due to the broadcast and open nature of wireless channels, wireless systems are highly vulnerable to security threats in both civilian and military applications. To address this threat, there is a strong desire to develop a promising security approach to provide robust protection for the many security-sensitive applications within 5G / 6G wireless systems.

[0003] Existing security methods primarily utilize encryption techniques implemented on top-layer protocols. These methods typically require significant computational power due to their complexity. However, many Internet of Things (IoT) devices have limited power. As a complement to encryption, Physical Layer Security (PLS) is emerging as a promising technology, leveraging interference and noise in the wireless channel to ensure confidentiality of communications. However, neither of these technologies can completely guarantee information security; once transmission is detected, it becomes vulnerable to various attacks.

[0004] The purpose of covert wireless communication is to secretly send messages to a receiver without being detected by a monitor, which greatly enhances security. In some application scenarios, the communication itself requires absolute security. A common covert communication model is as follows: the source node and the destination node want to communicate, and the monitor determines whether they are communicating. The purpose of covert communication is to achieve message transmission between the source node and the destination node without being detected by the monitor.

[0005] Existing research on covert communication primarily focuses on one-hop and two-hop wireless relay systems, where the source node attempts to secretly transmit information to the destination node with or without a relay. For single-hop wireless systems, current work has explored various scenarios, such as different channel models, channel uncertainty, noise uncertainty, channel inversion power control, delay constraints, jamming signals, and UAV scenarios. Covert performance has been further investigated in two recent wireless relay systems where one or more detectors attempt to detect the presence of wireless communication from the source node to the relay node and from the relay node to the destination node. Notably, cooperative jamming and relay selection are two key strategies for improving covert performance. Using cooperative jamming schemes, existing work utilizes jamming signals to confuse detectors, but neglects the significant interference these signals cause to legitimate relay nodes, which can lead to a substantial degrade in system performance.

[0006] Therefore, a problem arises: the need to design a cooperative jamming scheme that can interfere with the detector while minimizing interference with both relay and destination nodes. On the other hand, relay selection is crucial for improving stealth performance. Specifically, previous work has demonstrated the potential of relay selection in enhancing stealth. In fact, these schemes have a significant impact on stealth performance. However, due to the lack of joint research on cooperative jamming and relay selection, these effects remain an open question. Summary of the Invention

[0007] To address the problems existing in the prior art, this invention provides a wireless covert communication method based on joint cooperative interference and relay selection. It proposes a wireless covert communication scheme based on joint cooperative interference and relay selection, which effectively solves the relay selection problem in multi-relay scenarios and significantly improves the covert communication rate.

[0008] To achieve the above objectives, the technical solution adopted by this invention is: a wireless covert communication method involving joint cooperative interference and relay selection. A source node sends a message to its destination node via a selected relay node. A detector attempts to detect the existence of wireless transmission behavior between the source node and the relay node. Some other idle relay nodes are selected as friendly interference nodes to send interference signals, preventing the detector from detecting the transmission process. During cooperative interference, other relay nodes besides the selected relay node can act as interference nodes and generate artificial noise to confuse the detector. Simultaneously, based on random relay selection and optimal relay selection, interference to the selected relay node and the destination node is minimized as much as possible.

[0009] Random relay selection or optimal relay selection is adopted;

[0010] For random relay selection and joint cooperative interference transmission modes, the transmission strategy of the source node is designed, the detection error probability of the detector is determined, and the concealment rate is maximized through effective numerical search under given concealment requirements and interruption requirements.

[0011] The transmission strategy of the source node is designed for optimal relay selection and joint cooperative interference transmission mode. The detection error probability of the detector is determined, and the transmission power of the source node is optimized through numerical search to maximize the concealment rate under the constraint of concealment requirements.

[0012] When user resources are limited and the need for concealment is low, a random relay selection and joint cooperative interference transmission mode is adopted; when user resources are sufficient and the need for concealment is high, an optimal relay selection and joint cooperative interference transmission mode is adopted.

[0013] For the first transmission phase, from friendly relay J i Selecting some relays other than the transmission relay as interferers requires that the channel gain from the interferer to the selected transmission relay node is less than a threshold α, i.e., |h JiC | 2 <α,

[0014] Only when from a friendly relay J i The channel gain to the selected transmission relay node is less than the threshold α, i.e., |h JC | 2 <α, where J i When it is not the selected transmission relay node, any other relay J i Talent can be used as interference, for the second transmission phase, if from friendly jammer J i The channel gain to the destination node is less than α, i.e., |h JiB | 2 If <α, then the friendly disruptor J i Used as interference.

[0015] The detector attempts to determine whether the source node has sent a message. H0 indicates that the source node has not sent a message, and H1 indicates that it has sent a message. The detection error probability is the probability ζ that the detector mistakenly determines whether the source node has sent a message, which is equal to the false alarm probability P. FA and the probability of missed detection P MD The sum of these values ​​is as follows: a false alarm means that the detector judges H1 when it is actually H0, and a missed detection means that the detector judges H0 when it is actually H1. The covert rate is the achievable rate at which the source node can secretly send messages to the destination node while the detector maintains a high probability of detection errors.

[0016] A time-slot relay system is provided, in which quasi-static Rayleigh fading is used to model the wireless channel. Under fading conditions, all channel coefficients remain constant within a time slot and vary independently between different time slots. The channel fading coefficients follow a complex Gaussian distribution with zero mean and unit variance. Selected relay nodes operate in half-duplex mode, and the total system bandwidth is 1 MHz.

[0017] In the random relay selection and joint cooperative interference transmission modes, the signal y received by the detector from the source node / selected relay node is... W It is given by the following formula:

[0018]

[0019] Where x j It is a signal emitted by the interfering node, P J J is the transmit power used by the interfering node. i These are interfering nodes, where i ∈ [0, l], and l is the number of interfering nodes, P T It is the transmit power of the source node / relay node, x k It is a message signal sent by the source node / relay node. h is the channel coefficient from the interfering node to the detector. kW n represents the channel coefficients from the source node / relay node to the detector. W The noise near the detector follows a distribution.

[0020] During random relay selection and joint cooperative interference transmission, the detector uses the following optimal decision to minimize its detection error probability:

[0021]

[0022] Where Y is the power received by the detector, D0 and D1 represent the detector's judgments H0 and H1, and λ is the detector's detection threshold. If the signal received by the detector is greater than λ, the detector will determine that the source node is sending a message; otherwise, the detector will determine that the source node is not sending a message. Considering an infinite number of channels, Y can be written as:

[0023]

[0024] Among them, P J J is the transmit power used by the interfering node. i These are interfering nodes, where i ∈ [0, l], and l is the number of interfering nodes, P T It is the transmit power of the source node / relay node. For the channel gain from the interfering node to the detector, |h kW | 2The channel gain from the source node / relay node to the detector;

[0025] Maximizing the concealment rate R during random relay selection and joint cooperative interference transmission. AB Meanwhile, while maintaining a high probability of detection error by the detector; construct the following optimization problem:

[0026] Maximize R AB

[0027] st ζ * (P T )≥1-ε c ,

[0028] P T ≤P max ,

[0029] ε c ∈(0,1),

[0030] The optimization problem is solved using stochastic gradient descent to obtain the maximum transmit power of the source node / relay node under a given concealment requirement, thereby obtaining the maximum transmission rate R. AB .

[0031] During optimal relay selection and joint cooperative interference transmission, the signal y received by the detector from the source node / selected relay node. W as follows:

[0032]

[0033] Here, due to the different strategies for selecting relay nodes, the expression for Y is as follows:

[0034]

[0035] During optimal relay selection and joint cooperative interference transmission, the detector's detection error probability ζ is:

[0036]

[0037] in

[0038] when When ζ is found, the optimal detection threshold λ that minimizes ζ is obtained by taking the first derivative of ζ with respect to λ.

[0039] For optimal relay selection and joint cooperative interference transmission, the basic covert rate performance is simulated. First, the transmission interruption probability P from the source node to the destination node is determined. sto :

[0040]

[0041] Where z = θP J / P T ,

[0042] Obtain the concealment rate R′ from the source node to the destination node under the MMRS scheme. AB As shown below:

[0043] R′ AB =(1-P sto )min{R AC R CB},

[0044] The achievable concealment rate R from the source node to the selected relay node is... AC Represented as R AC =log2(1+SIR) AC The achievable rate R from the selected relay node to the destination node. CB Represented as R CB =log2(1+SIR) CB ); maximizing the concealment rate R′ when considering optimal relay selection and joint cooperative interference transmission. AB Meanwhile, while maintaining a high detection error probability for the detector, the following optimization problem is constructed:

[0045] Maximize R′ AB

[0046] st ζ * (P T )≥1-ε c ,

[0047] P T ≤P max ,

[0048] ε c ∈(0,1),

[0049] The optimization problem is solved using stochastic gradient descent to obtain the maximum transmit power P of the source node / selected relay node. T * .

[0050] A collaborative jamming and relay selection wireless covert communication system is also provided, comprising a source node, n potential relay nodes, a destination node, and a detector. The source node intends to covertly send messages to the destination node using relay nodes selected from all relays, while the detector attempts to detect whether the source node has sent a message. Potential relay nodes can also be selected as friendly jamming nodes, broadcasting jamming signals to confuse the detector. The source node and the selected relay nodes use the same covert transmission power P.T To send a message, the transmit power P of all friendly interference nodes. J Not exceeding the maximum power limit P max The source node, the selected relay node, the jammer, and the destination node are all equipped with a single antenna, and the transmission method described in this invention is used.

[0051] Compared with existing technologies, this invention has at least the following beneficial effects: Compared with existing multi-relay covert communication schemes, this scheme takes into account the potential impact of friendly interference nodes on the receiver and minimizes such impact. Furthermore, it allows for more flexible and rational selection of transmission relay schemes and adjustment of interference relay selection schemes according to user needs, achieving higher covert rates while considering transmission overhead. This provides more worthy perspectives for exploring current wireless covert communication technology research. This invention provides a relay selection scheme for multi-relay wireless communication systems and, through the design of selecting cooperative interference nodes, limits the impact of interference nodes on the receiver and maximizes interference detection, thereby improving the maximum covert rate. Attached Figure Description

[0052] Figure 1 This is a schematic diagram of a covert communication scenario.

[0053] Figure 2 Simulation results of communication interruption probability under RRS relay selection scheme, in conjunction with CJ;

[0054] Figure 3 Simulation results of communication interruption probability under the MMRS relay selection scheme, in conjunction with CJ;

[0055] Figure 4 To investigate the relationship between maximum covert communication rate and covert requirements under RRS relay selection schemes in conjunction with CJ.

[0056] Figure 5 To investigate the relationship between maximum covert communication rate and covert requirements under the MMRS relay selection scheme in conjunction with CJ.

[0057] Figure 6 The impact of cooperative interference on the maximum concealment rate. Detailed Implementation

[0058] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0059] This invention explores the problems of joint cooperative interference and relay selection, and develops a theoretical model describing the covert rate performance in wireless relay systems. The main contributions of this invention can be summarized as follows:

[0060] 1. Consider a wireless relay system consisting of a source node, multiple potential relays, a destination node, and a detector. In this case, the present invention proposes two relay selection schemes: Random Relay Selection (RRS) and Optimal Relay Selection (MMRS), along with corresponding Joint Cooperative Interference (CJ) schemes to ensure stealth.

[0061] 2. By applying a joint cooperative interference and random relay selection (RSS) scheme, the transmission strategy design of the source node is first given, and the detection error probability of the detector is determined. Then, the expressions for three performance indicators are derived: transmission interruption probability, detector error probability, and covert rate. Under given covert requirements and interruption requirements, the maximum covert rate is explored through effective numerical search.

[0062] 3. Further application of joint cooperative jamming and MMRS schemes. Under this scheme, the transmission strategy design of the source node is first given. Then, the detection error probability of the detector is derived, and the transmission power of the source node is optimized through effective numerical search to maximize the concealment rate under the constraint of concealment requirements;

[0063] 4. Finally, extensive simulation and numerical results are presented to validate our theoretical model and illustrate the covert rate performance of wireless communication systems under joint cooperative interference and relay selection.

[0064] System Model

[0065] 1. Network Model

[0066] like Figure 1 As shown, consider a wireless relay system consisting of a source node Alice (A), n potential relay nodes, a destination node Bob (B), and a detector Willie (W). Alice intends to covertly send a message to Bob using Carol (C), a relay node selected from these relays, while Willie tries to detect whether Alice has sent a message. Potential relay nodes can also be selected as friendly jamming nodes, broadcasting jamming signals to confuse Willie's detection. Alice and Carol use the same covert transmission power P. T To send a message, the transmit power P of all friendly interference nodes. J Not exceeding the maximum power limit P max Assume Alice, Carol, the jammer, and Bob are each equipped with a single antenna.

[0067] 2. Channel Model

[0068] This invention considers a time-slot relay system in which quasi-static Rayleigh fading is used to model the wireless channel, where, under fading conditions, all channel coefficients remain constant within a time slot and vary independently between different time slots. Alice and Carol, Alice and Willie, Carol and Bob, Carol and Willie, any friendly interferer (J i ) and Willie, J i And Carol, and J i The channel fading coefficients between Bob and [other individuals] are expressed as h. AC h AW h CB h CW h JiW h JiC and h JiB It follows a complex Gaussian distribution with zero mean and unit variance. ij | 2 It represents the corresponding channel gain, where ij∈{AC, AW, CB, CW, J} i C, J i W, J i B}. Using variance σ 2 The channel noise is modeled using AWGN (Additive White Gaussian Noise). It is assumed that Carol operates in half-duplex mode, with transmissions from Alice to Carol and from Carol to Bob occurring in different time slots. Without loss of generality, the total system bandwidth is assumed to be 1 MHz.

[0069] 3. Relay Selection Scheme

[0070] Under the Random Relay Selection (RRS) scheme: Alice randomly selects one from all potential relays, which will help Alice forward the message to Bob.

[0071] Under the Optimal Relay Selection (MMRS) scheme, a potential relay can be selected as Carol if the following conditions are met: |h AC | 2 and |h CB | 2 The maximum value of the minimum channel gain between them is equal to the maximum value among all minimum channel gains. Each minimum channel gain corresponds to |h| for any potential relay i. Ai | 2 and |h iB | 2 The minimum gain between the two conditions must be satisfied to ensure that no transmission interruption occurs.

[0072] 4. Cooperative Interference Scheme

[0073] Under each relay selection scheme, a corresponding Cooperative Jamming (CJ) scheme is further proposed to enhance concealment performance. In this scheme, relays other than Carol can be selected as jamming nodes to generate artificial noise to confuse the detector, while minimizing interference to Carol and Bob according to the following jamming node selection scheme. An interference threshold of α is set, and for the first transmission phase, interference is only generated from the friendly jammer J. i The channel gain to Carol is less than the threshold α, i.e., |h JiC | 2 <α, where J i When it's not Carol, any other relay J i Only then can it be used for interference. For the second transmission phase, if from a friendly jammer J... i The channel gain to Bob is less than α, i.e., |h JiB | 2 If <α, then the friendly disruptor J i Used as interference.

[0074] 5. Performance Indicators

[0075] The detector, Willie, attempts to determine whether Alice has sent a message. For this, two assumptions are made, H0 and H1: H0 indicates that the source node does not send a message, and H1 indicates that a message is sent. Then, the definitions of two performance metrics are given below.

[0076] The probability of a detection error is ζ, which is the probability that Willie mistakenly determines whether Alice has sent a message, and is equal to the false alarm probability P. FA and the probability of missed detection P MD The sum of these two factors indicates that a false alarm means Willie determines H1, but it is actually H0; a missed detection means Willie determines H0, but it is actually H1.

[0077] The stealth rate is the achievable rate at which Alice can secretly send messages to Bob while Willie maintains a high probability of detection errors.

[0078] I. Covert Rate of the Combined CJ and RRS Scheme

[0079] 1. Willie's detection mechanism

[0080] In one time slot, Willie attempts to determine whether Alice has sent a message. Based on the assumptions above, under the combined CJ and RRS scheme, the signal y that Willie receives from Alice / Carol... W It is given by the following formula:

[0081]

[0082] Where x j It is a signal emitted by the interfering node, x k It is the message signal sent by the source node / relay node, n W The noise near Willie follows a distribution

[0083] According to the Neiman Pearson criterion, Willie uses the following optimal decision to minimize his detection error probability:

[0084]

[0085] Where Y is the power received by Willie, D0 and D1 represent Willie's judgments of H0 and H1, and λ is Willie's detection threshold. If the signal received by Willie is greater than λ, Willie will determine that Alice is sending a message; otherwise, Willie will determine that Alice is not sending a message.

[0086] This invention considers an infinite number of channels, therefore Y can be written as:

[0087]

[0088] 2. Optimal detection threshold and minimum detection error probability

[0089] To determine the optimal detection threshold and the minimum detection error probability, we first derive the detection error probability at Willie. Under the CJ and RRS schemes, the detection error probability ζ at Willie can is:

[0090]

[0091] Where l represents the number of interfering nodes, and Γ(l) is the gamma function with the following probability density distribution:

[0092] Γ(l)=∫0 ∞ x (l-1) e -x dx.

[0093] Where x ~ Γ(l, a),

[0094] when When ζ is minimized, the optimal detection threshold λ can be obtained by taking the first derivative of ζ with respect to λ, i.e., ζ = λ / λ. * =ζ(λ * ).

[0095]

[0096] 3. Concealment Rate Model

[0097] To simulate basic covert rate performance, the transmission interruption probability from Alice to Bob is first determined. A transmission interruption means that the received signal strength at the receiver Carol / Bob is less than its required threshold θ, so the receiver cannot successfully recover the original message.

[0098] Use P to The probability of transmission interruption is expressed as follows:

[0099]

[0100] Where K = θP I / P T , and The background noise levels are for Carol and Bob, respectively.

[0101] Based on P to Obtain the concealment rate R from Alice to Bob. AB As shown below:

[0102] R AB =(1-P to )min{R AC R CB},

[0103] The achievable concealment rate R from Alice to Carol AC Represented as R AC =log2(1+SIR) AC The achievable rate R from Carol to Bob CB Represented as R CB =log2(1+SIR) CB ).

[0104] 4. Optimal concealment rate

[0105] The goal is to maximize the concealment rate R. AB While maintaining a high detection error probability in Willie, this can be expressed as the following optimization problem:

[0106] Maximize R AB

[0107] st ζ * (P T )≥1-ε c ,

[0108] P T ≤P max ,

[0109] ε c ∈(0,1),

[0110] This optimization problem can be solved using the stochastic gradient descent algorithm.

[0111] II. Covert Rate of the Combined CJ and MMRS Scheme

[0112] 1. Willie's detection mechanism

[0113] In one time slot, Willie attempts to determine whether Alice has sent a message. Based on the assumptions above, under the joint CJ and MMRS scheme, the signal y that Willie receives from Alice / Carol... W It is given by the following formula:

[0114]

[0115] Here, due to the different strategies for selecting relay nodes, the expression for Y is as follows:

[0116]

[0117] 2. Optimal detection threshold and minimum detection error probability

[0118] Under the combined CJ and MMRS scheme, Willie's detection error probability ζ can be determined as:

[0119]

[0120] in Therefore, when When ζ is minimized, the optimal detection threshold λ can be obtained by taking the first derivative of ζ with respect to λ, i.e., ζ = λ / λ. * =ζ(λ * ).

[0121]

[0122] 3. Concealment Rate Model

[0123] Similarly, to simulate basic covert rate performance, the transmission interruption probability P from Alice to Bob is first determined. sto :

[0124]

[0125] Where z = θP J / P T , Obtain the concealment rate R′ from Alice to Bob under the MMRS scheme. ABAs shown below:

[0126] R′ AB =(1-P sto )min{R AC R CB},

[0127] The achievable concealment rate R from Alice to Carol AC Represented as R AC =log2(1+SIR) AC The achievable rate R from Carol to Bob CB Represented as R CB =log2(1+SIR) CB ).

[0128] Although the selected link meets the condition of uninterrupted transmission before transmission, the covert transmission itself will not be interrupted. Instead, the threshold α affects the probability that the link meets the requirements in a time slot. It should be ensured that more time slots are sent to the covert message over a period of time. Therefore, the probability of covert transmission must be greater than a required threshold to give Alice more opportunities to send covert information.

[0129] 4. Optimal concealment rate

[0130] The goal is to maximize the concealment rate R′ AB At the same time, maintaining a high detection error probability in Willie can be expressed as the following optimization problem:

[0131] Maximize R′ AB

[0132] st ζ * (P T )≥1-ε c ,

[0133] P T ≤P max ,

[0134] ε c ∈(0,1),

[0135] The maximum transmit power of Alice / Carol can be obtained by solving the optimization problem using stochastic gradient descent.

[0136] refer to Figure 2 and Figure 3 In collaboration with CJ, a comparison of simulation results of communication interruption probability under two relay selection schemes, RRS and MMRS, was conducted: It is evident that the MMRS scheme reduces the communication interruption probability and can improve the communication rate.

[0137] refer to Figure 4 and Figure 5 In collaboration with CJ, a comparison was made between the maximum covert communication rate and covert requirements under the two relay selection schemes, RRS and MMRS: it is clear that the MMRS scheme can achieve a higher covert rate.

[0138] refer to Figure 6 The impact of cooperative interference on the maximum concealment rate: It is clear that the use of cooperative interference greatly improves the maximum concealment rate.

[0139] The simulation and numerical results above demonstrate that the method proposed in this invention has a good effect on improving the performance of covert communication.

[0140] The above content is only for illustrating the technical concept of the present invention and should not be construed as limiting the scope of protection of the present invention. Any modifications made to the technical solution based on the technical concept proposed in this invention shall fall within the scope of protection of the claims of this invention.

Claims

1. A method for covert wireless communication involving joint cooperative jamming and relay selection, characterized in that, The source node sends a message to its destination node with the help of the selected relay node. The detector attempts to detect the existence of the wireless transmission behavior of the source node and the relay node, and selects some other idle relay nodes as friendly interference nodes to send interference signals to prevent the detector from detecting the transmission process. In the case of cooperative interference, other relay nodes besides the selected relay node can act as interference nodes and generate artificial noise to confuse the detector. At the same time, the interference to the selected relay node and the destination node is reduced based on random relay selection and optimal relay selection. Random relay selection or optimal relay selection is adopted; For random relay selection and joint cooperative interference transmission modes, the transmission strategy of the source node is designed, the detection error probability of the detector is determined, and the concealment rate is maximized through effective numerical search under given concealment requirements and interruption requirements. The transmission strategy of the source node is designed for optimal relay selection and joint cooperative interference transmission mode. The detection error probability of the detector is determined, and the transmission power of the source node is optimized through numerical search to maximize the covert transmission rate under the constraint of covert requirements. When user resources are limited and the need for concealment is low, a random relay selection and joint cooperative interference transmission mode is adopted; when user resources are sufficient and the need for concealment is high, an optimal relay selection and joint cooperative interference transmission mode is adopted. During optimal relay selection and joint cooperative interference transmission, the signal received by the detector from the source node / selected relay node. as follows: Here, due to the different strategies for selecting relay nodes, the expression for Y is as follows: Where Y is the power received by the detector. It is a signal emitted by the interfering node. This is the transmission power used by the interfering nodes. These are interfering nodes, among which ,in It is the number of interfering nodes. It is the transmit power of the source node / relay node. It is the message signal sent by the source node / relay node, and the channel fading coefficient is a complex Gaussian random variable with zero mean and unit variance. The channel fading coefficient from the interfering node to the detector. The channel fading coefficient from the source node / relay node to the detector. The noise is additive white Gaussian noise near the detector, with a mean of 0 and a variance of . The complex Gaussian distribution: , h AC This represents the channel fading coefficient between the source node and the relay node. h AW The channel fading coefficient between the source node and the detector. This is the system transmission rate threshold; when the transmission rate is less than... The time indicates a transmission interruption. To relay J from the friendly i Channel gain to the selected relay node, It is the variance of the background additive white Gaussian noise at the selected transmission relay.

2. The wireless covert communication method for joint cooperative jamming and relay selection according to claim 1, characterized in that, For the first transmission phase, from friendly relay J i Selecting some relays other than the transmission relay as interferers requires that the channel gain from the interferer to the selected relay node is less than a threshold α, i.e., |h JiC | 2 <α, Only when relayed from a friendly J i The channel gain to the selected relay node is less than the threshold α, i.e., |h JiC | 2 <α, where J i When it is not the selected relay node, any other relay J i’ Talent can be used as interference, for the second transmission phase, if from friendly jammer J i’’ The channel gain to the destination node is less than α, i.e., |h Ji’’B | 2 <α, then the friendly disruptor J i’’ Used as interference.

3. The wireless covert communication method for joint cooperative jamming and relay selection according to claim 1, characterized in that, The detector attempts to determine whether the source node has sent a message. H0 indicates that the source node has not sent a message, and H1 indicates that it has sent a message. The detection error probability is the probability that the detector will incorrectly determine whether the source node has sent a message. , equal to the false alarm probability P FA and the probability of missed detection P MD The sum of these values ​​is as follows: a false alarm means that the detector judges H1 when it is actually H0, and a missed detection means that the detector judges H0 when it is actually H1. The covert rate is the achievable rate at which the source node can secretly send messages to the destination node while the detector maintains a high probability of detection errors.

4. The wireless covert communication method for joint cooperative jamming and relay selection according to claim 1, characterized in that, A time-slot relay system is provided, in which quasi-static Rayleigh fading is used to model the wireless channel. Under fading conditions, all channel coefficients remain constant within a time slot and vary independently between different time slots. The channel fading coefficients follow a complex Gaussian distribution with zero mean and unit variance. Selected relay nodes operate in half-duplex mode, and the total system bandwidth is 1 MHz.

5. The wireless covert communication method for joint cooperative jamming and relay selection according to claim 1, characterized in that, During random relay selection and joint cooperative interference transmission, the detector uses the following optimal decision to minimize its detection error probability: Where Y is the power received by the detector, and D0 and D1 represent the detector's judgments H0 and H1, respectively. It is the detector's detection threshold; if the signal power received by the detector is greater than... If the source node is not sending a message, the detector will determine that it is sending a message; otherwise, it will determine that it is not sending a message. Considering an infinite number of channels, Y can be written as: in, This is the transmission power used by the interfering nodes. These are interfering nodes, among which ,in It is the number of interfering nodes. It is the transmit power of the source node / relay node. The channel gain from the interfering node to the detector. The channel gain from the source node / relay node to the detector; Maximizing the covert transmission rate R during random relay selection and joint cooperative interference transmission. AB Meanwhile, while maintaining a high probability of detection error by the detector; construct the following optimization problem: The optimization problem is solved using stochastic gradient descent to obtain the maximum transmit power of the source node / relay node under a given concealment requirement, thereby obtaining the maximum concealed transmission rate. , It minimizes the detector's error probability. It is a hidden requirement, a constant between 0 and 1.

6. The wireless covert communication method for joint cooperative jamming and relay selection according to claim 5, characterized in that, For optimal relay selection and joint cooperative interference transmission, the basic covert rate performance is simulated. First, the transmission interruption probability P from the source node to the destination node is determined. sto : in ; Obtain the covert transmission rate from the source node to the destination node under the optimal relay selection scheme. As shown below: The achievable concealment rate R from the source node to the selected relay node is... AC Represented as R AC =log2(1+SIR) AC The achievable rate R from the selected relay node to the destination node. CB Represented as R CB =log2(1+SIR) CB ); to maximize the covert transmission rate when considering optimal relay selection and joint cooperative interference transmission. Meanwhile, while maintaining a high detection error probability for the detector, the following optimization problem is constructed: The optimization problem is solved using stochastic gradient descent to obtain the maximum transmit power of the source node / selected relay node. SIR CB SIR is the signal-to-noise ratio from the relay node to the destination node. AC α is the signal-to-noise ratio from the source node to the relay node, and α is the threshold.

7. The wireless covert communication method for joint cooperative jamming and relay selection according to claim 1, characterized in that, The probability of detection error by the detector during optimal relay selection and joint cooperative interference transmission. for: in , Meaningless; used to simplify calculations. when At that time, by seeking right The first derivative is obtained such that Minimum optimal detection threshold .

8. A wireless covert communication system with joint cooperative jamming and relay selection, characterized in that, The system consists of a source node, n potential relay nodes, a destination node, and a detector. The source node intends to covertly send a message to the destination node using relay nodes selected from all relays, while the detector attempts to detect whether the source node has sent a message. Potential relay nodes can also be selected as friendly jamming nodes, broadcasting jamming signals to confuse the detector. The source node and the selected relay nodes use the same covert transmission power P. T To send a message, the transmit power P of all friendly interference nodes. J Not exceeding the maximum power limit P max The source node, the selected relay node, the jammer, and the destination node are all equipped with a single antenna, and the wireless covert communication method of joint cooperative jamming and relay selection as described in any one of claims 1 to 5 is used, or the wireless covert communication method of joint cooperative jamming and relay selection as described in any one of claims 6 to 7 is used.

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