Mobile covert communication system and method based on mobility and noise uncertainty

Abstract

This invention discloses a mobile covert communication system and method based on mobility and noise uncertainty. The system includes a signal transmitter, a signal receiver, and a monitoring unit. The signal transmitter and monitoring unit are equipped with a single antenna, and the receiver is equipped with dual antennas. The signal transmitter is used to randomly transmit signals while moving at a constant speed along a circular trajectory. The signal receiver is used to receive signals while simultaneously transmitting artificial noise with randomly varying power in a stationary state. The monitoring unit is used to detect whether a communication transmission process exists between the signal transmitter and the signal receiver in a stationary state. The link between the signal transmitter and the signal receiver is a legitimate communication link, the link between the signal transmitter and the monitoring unit is a detection link, and the link between the signal receiver and the monitoring unit is an interference link.

Description

Technical Field

[0001] This invention relates to the field of wireless communication technology, and in particular to a mobile covert communication system and method based on mobility and noise uncertainty. Background Technology

[0002] Covert communication technology is a technology that can hide the existence of communication. This technology can use some technical means, such as cooperative interference, power control, and random transmission, to conceal the communication transmission process from potential malicious eavesdroppers, thereby ensuring communication security.

[0003] Traditional wireless communication security measures, such as cryptography and physical layer security, can only guarantee that the transmitted content will not be stolen to a certain extent. However, once the current wireless security transmission process is exposed, eavesdroppers can use the signal to locate the sender or launch targeted interference attacks, which can expose the sender's location or affect the performance of the secure transmission. Covert communication technology can address this problem by hiding the communication transmission process, making the communication process undetectable by the monitor, thereby providing a higher level of security.

[0004] Current research on covert communication focuses on achieving covert transmission at positive rates. The main approach utilizes inherent or artificially generated uncertainties in the system, such as noise uncertainty, channel uncertainty, and time uncertainty, to reduce the detection performance of eavesdroppers and thus improve covert communication performance. However, current research in this field focuses on achieving covert communication between static nodes, where the communicating nodes remain stationary throughout the communication process.

[0005] In fact, there are many situations in real-world scenarios where communication nodes are dynamic nodes, such as vehicle-to-vehicle communication, satellite-to-ground communication, and vehicle-to-base station communication. The mobility of nodes will cause changes in the channel model, distance, and connectivity between nodes. These factors make existing covert communication schemes unsuitable for covert transmission of mobile nodes. In the current research field, covert transmission schemes suitable for mobile nodes have not been studied. Summary of the Invention

[0006] Therefore, it is necessary to propose a mobile covert communication system and method based on mobility and noise uncertainty to address the above problems.

[0007] This invention provides a mobile covert communication system based on mobility and noise uncertainty, the system comprising: a signal transmitter, a signal receiver, and a monitoring unit;

[0008] The signal transmitter and the monitoring unit are equipped with a single antenna, and the receiver is equipped with dual antennas;

[0009] The signal transmitter is used to randomly transmit signals while moving at a constant speed along a circular trajectory in full-duplex mode.

[0010] The signal receiver is used to receive signals while simultaneously transmitting artificial noise with randomly varying power in a stationary state.

[0011] The monitoring device is used to detect whether there is a communication transmission process between the signal sender and the signal receiver in a static state;

[0012] The link between the signal sender and the signal receiver is a legitimate communication link, the link between the signal sender and the monitoring party is a detection link, and the link between the signal receiver and the monitoring party is an interference link.

[0013] In the above scheme, the signal receiver, while receiving the signal, models the self-interference signal as having a mean of 0 and a variance of γ. RSI A Gaussian distributed random variable.

[0014] In the above scheme, the movement trajectory of the signal transmitter is circular, with any point as the center and R as the radius, where R has a maximum value R_max.

[0015] In the above scheme, the artificial noise is transmitted by the signal receiver with randomly varying power, the power distribution is uniform, and the maximum value is P_max.

[0016] In the above scheme, the communication link channels between each node are modeled using a double Rayleigh fading channel model. The channel coefficients remain constant within a time slot and change randomly between time slots.

[0017] This invention also provides a method for utilizing a mobile covert communication system based on mobility and noise uncertainty, comprising the following steps:

[0018] The signal transmitter moves along a fixed trajectory and sends a concealed signal;

[0019] The signal receiver simultaneously transmits artificial noise with randomly varying power while receiving the signal;

[0020] The monitoring party uses an energy detection method to detect whether a communication transmission process exists;

[0021] Based on the detection results from the monitoring party, the performance of covert communication is analyzed and optimized to maximize the average covert transmission rate.

[0022] In the above scheme, the monitoring party detects the existence of a communication transmission process using an energy detection method. Specifically, the monitoring party continuously collects the received signals and calculates the average value Y of the received signal energy in each time slot. w The binary hypothesis test is used to compare it with a pre-set threshold γ; if Yw <γ, indicating no covert transmission between the signal sender and receiver, denoted by H0; if Y w >γ indicates that there is covert transmission between the signal sender and the signal receiver, denoted by H1;

[0023] According to the average value Y of the received signal energy in each time slot w Determine the probability of false alarms and the probability of missed detections;

[0024] When the probability of the signal transmitting party sending information or not sending information to the signal receiving party is equal, the detection error probability at the monitoring party is determined based on the false alarm probability and the missed detection probability.

[0025] Determine the optimal detection threshold and minimum detection error probability of the monitoring party;

[0026] Determine the average minimum detection error probability of the monitoring party.

[0027] In the above scheme, the average value Y of the received signal energy in each time slot is calculated. w Specifically, this includes: the k-th signal y received by the monitoring party within a time slot. w [k] is represented as:

[0028] Where v b [k] represents the artificial noise transmitted by the signal receiver, x a [k] represents the signal sent by the signal sender, which respectively satisfy... Where k = 1, 2, ..., n, represents the sequence number of the k-th signal received by the monitoring party within a time slot. It is v b The conjugate of [k] It is x a The conjugate of [k], E() denotes the mathematical expectation operation; P a The signal transmission power of the signal transmitter, P b The signal receiver's artificial noise transmission power is γ, and the path loss exponent is n. w [k] represents the environmental noise at the monitoring location;

[0029] according to Determine the average value Y w Where D1 and D0 represent the decisions to receive H1 and H0, respectively.

[0030] In the above scheme, the average value Y of the received signal energy in each time slot is... w Determining the probability of false alarms and false negatives specifically includes: based on Determine the false alarm probability, where

[0031] according to Determine the probability of missed detection, where d bw The distance between the signal receiver and the monitoring party is known to the monitoring party.

[0032] In the above scheme, determining the average minimum detection error probability of the monitoring party specifically includes: based on Confirmed, among which

[0033] The embodiments of the present invention have the following beneficial effects:

[0034] The mobile covert communication system of the present invention introduces uncertainty by having the signal sender transmit signals while moving and by having the full-duplex receiver transmit artificial noise while receiving signals. By using the uncertainty of node mobility and interference, the system interferes with the signal detection performance of the monitor, thereby achieving a covert transmission rate greater than zero while satisfying the covertness constraint. Attached Figure Description

[0035] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0036] in:

[0037] Figure 1 A network model diagram of a mobile covert communication system constructed for this invention;

[0038] Figure 2 This is a flowchart of the performance analysis process in this invention;

[0039] Figure 3 This is a flowchart of the detection error probability calculation in this invention;

[0040] Figure 4 This is a flowchart of the average covert transmission rate calculation in this invention;

[0041] Figure 5 This is a graph showing the relationship between the detection error probability and the radius of the moving trajectory in this invention;

[0042] Figure 6 This is a graph showing the relationship between the transmission interruption probability and the radius of the moving trajectory in this invention.

[0043] Figure 7 This is a graph showing the relationship between the covert transmission rate and the maximum power of the interference signal in this invention. Detailed Implementation

[0044] 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 embodiments of the present invention, and not all embodiments. 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.

[0045] Example 1

[0046] This invention provides a mobile covert communication system based on mobility and noise uncertainty, such as... Figure 1 As shown, the system includes: a signal transmitter, a signal receiver, and a monitoring unit;

[0047] The signal transmitter and the monitoring unit are equipped with a single antenna, and the receiver is equipped with dual antennas;

[0048] The signal transmitter is used to randomly transmit signals while moving at a constant speed along a circular trajectory in full-duplex mode.

[0049] The signal receiver is used to receive signals while simultaneously transmitting artificial noise with randomly varying power in a stationary state.

[0050] The monitoring device is used to detect whether a communication transmission process exists between the signal sender and the signal receiver in a static state.

[0051] The link between the signal sender and the signal receiver is a legitimate communication link, the link between the signal sender and the monitoring party is a detection link, and the link between the signal receiver and the monitoring party is an interference link.

[0052] In this invention, all communication link channels between nodes are modeled using a double Rayleigh fading channel model, and the channel coefficients remain constant within a time slot but vary randomly between time slots. The channel coefficient between node i and node j can be expressed as h. ij , where i∈{a,b}, j∈{b,w}; a, b, w represent the signal sender, the signal receiver, and the monitoring party, respectively.

[0053] Since all communication link channels are modeled using a dual Rayleigh fading channel, |h ij | 2 The probability density function (PDF) can be expressed as:

[0054]

[0055] Where K0 is the zeroth-order modified Bessel function of the second kind.

[0056] In this invention, it is assumed that the monitoring party knows the instantaneous channel state information of its link, i.e., h aw and h bw The signal transmitter and receiver know their respective channel distribution information (CDI); the ambient noise at the node signal receiver and monitoring point is n. b n w The mean is zero and the variance is . Gaussian white noise, i.e.

[0057] The received signal y in the k-th time slot at the signal receiver b [k] can be expressed by the following formula:

[0058]

[0059] Where I b To address the self-interference signal at the signal receiver, this invention employs self-interference cancellation technology at the signal receiver, thus allowing the self-interference signal to be modeled as having a mean of 0 and a variance of γ. RSI A Gaussian distributed random variable, i.e., I b ~CN(0,γ) RSI ),and This is the self-interference cancellation coefficient.

[0060] In addition, P a P b These represent the signal transmission power of the signal transmitter and the signal receiver, respectively, where Ptransmit is the signal transmission power of the signal transmitter and the signal receiver. a P is a fixed value and is known to other nodes. b Let be a random variable, following the parameter . The uniform distribution can randomly vary between different time slots, and its probability density function is:

[0061]

[0062] Due to equipment performance limitations, the signal transmission power of the signal receiver has a maximum value Ω, i.e.

[0063] In addition, the monitoring party knows the signal transmission power P of the signal receiver. b The distribution and probability density function of the denominator are known, but their exact values ​​are unknown.

[0064] Furthermore, in formula (2) x a[k] represents the signal sent by the signal sender, satisfying... Where k = 1, 2, ..., n, represents the sequence number of the k-th signal received by the signal receiver within a time slot. It is x a The conjugate of [k], E() represents the mathematical expectation operation, γ is the path loss exponent, and n b [k] represents the ambient noise at the signal receiver.

[0065] In this invention, the signal transmitter moves along a fixed circular trajectory with M as the center and r as the radius.

[0066] Use d ij Let i represent the distance between node i and node j. Then the distance between the signal sender and the monitor can be expressed as:

[0067]

[0068] Where d mw Let r be the distance between M and the monitoring party. Due to the limitation of the mobility of the signal transmitter, r has a maximum value Δ, that is, r≤Δ.

[0069] Depend on Figure 1 It can be seen that the distance d between the signal transmitter and the monitoring party is... aw ∈[d min ,d max ], where d min =d mw -r,d max =d mw +r. Let θ be the angle between the line connecting M and the signal transmitter and the line connecting M and the monitor. Since the signal transmitter randomly sends signals during its movement, the value of θ is random for the monitor at the moment the signal transmitter sends the signal. Therefore, θ can be modeled as a random variable following a uniform distribution with parameter 2π, and its probability density function can be expressed as:

[0070]

[0071] Example 2

[0072] In wireless communication networks, this invention utilizes the method of the mobile covert communication system based on mobility and noise uncertainty as described in the above embodiments, such as... Figure 2 As shown, the steps are as follows:

[0073] Step 1: Model the mobile covert communication system, including scene modeling, movement trajectory modeling, and channel modeling.

[0074] Step 2: Analyze the transmission performance of mobile covert communication. First, analyze the detection performance of the monitoring party and use this as a covert constraint; second, analyze the transmission interruption probability between the legitimate communication parties (signal sender and signal receiver); finally, considering the covert constraint, analyze the average covert transmission rate.

[0075] Specifically, step 2.1 involves analyzing the detection performance of the monitoring unit, the process of which is as follows: Figure 3 As shown.

[0076] (1) Design the monitoring method.

[0077] In this invention, the monitoring party uses energy detection to detect the presence of covert communication. In this method, the monitoring party continuously collects the received signals and calculates the average value Y of the received signal energy in each time slot. w The binary hypothesis test is used to compare it with a pre-set threshold γ.

[0078] If Y w <γ, indicating no covert transmission between the signal sender and receiver, denoted by H0; if Y w >γ indicates that there is covert transmission between the signal sender and the signal receiver, denoted by H1.

[0079] The specific process of using binary hypothesis testing to judge a signal is as follows:

[0080] Consider the k-th signal y received by the monitoring party within a time slot. w [k] is represented as:

[0081]

[0082] Where v b [k] represents the artificial noise transmitted by the signal receiver, x a [k] represents the signal sent by the signal sender, which respectively satisfy... Where k = 1, 2, ..., n, represents the sequence number of the k-th signal received by the monitoring party within a time slot. It is v b The conjugate of [k] It is x a The conjugate of [k], E() denotes the mathematical expectation operation; P a The signal transmission power of the signal transmitter, P b The signal receiver's artificial noise transmission power is γ, and the path loss exponent is n. w [k] represents the environmental noise at the monitoring location.

[0083] The monitoring party receives the average signal energy Y in each time slot. wThe comparison with a pre-set detection threshold can be expressed by the following formula:

[0084]

[0085] Where D1 and D0 represent the decisions to receive H1 and H0, respectively.

[0086] (2) Analyze the false alarm probability of the monitoring party. With the probability of missed detection The monitoring party uses energy detection to determine whether a concealed transmission signal exists. In this process, two types of errors can occur: false alarm error and missed detection error. False alarm error occurs when the monitoring party makes a D1 decision under condition H0, and missed detection error occurs when the monitoring party makes a D0 decision under condition H1.

[0087] As n→∞, according to the law of large numbers, the average energy value Y of the signal received by the monitoring party within one time slot is... w as follows:

[0088]

[0089] in For n w The variance of [k] is the environmental noise power at the monitoring location.

[0090] Calculate the false alarm probability and the missed detection probability separately.

[0091] The false alarm probability is:

[0092] in

[0093] The probability of a missed detection is:

[0094] in d bw Let be the distance between the signal receiver and the monitoring party, and the monitoring party is known. Due to the complexity of this integral, it cannot be solved using the Newton-Leibniz formula. Therefore, a rectangular approximation method is used to obtain an approximate solution, which can be expressed by the following piecewise formula:

[0095] When ρ2≤ρ3

[0096] When ρ2>ρ3

[0097] The parameters involved are as follows:

[0098]

[0099] (3) Analyze the minimum detection error probability and the optimal detection threshold at the monitoring point.

[0100] When the probability of the signal sender sending information or not sending information to the signal receiver is equal, the detection error probability at the monitoring point can be expressed as ξ = α + β.

[0101] Since the signal sender cannot know the energy detection threshold of the monitor, in order to ensure reliable covert transmission between the two parties, it is necessary to analyze the covert transmission performance of the two parties under the worst-case scenario, that is, when the monitor can use the optimal detection threshold. Therefore, it is necessary to analyze the monitor's optimal detection threshold and the minimum detection error probability.

[0102] The specific process is as follows:

[0103] The detection error probability at the monitoring point can be divided into two cases: ρ2≤ρ3 and ρ2>ρ3. Each case has multiple sub-cases, as detailed below:

[0104] Case 1: When ρ2≤ρ3, the false alarm rate is given by formula (9), and the false negative rate is given by formula (11). In this case, based on the relationship between ρ5, ρ1, and ρ2, the detection error probability can be divided into the following three sub-cases:

[0105] In sub-case 1.1, when ρ2 < ρ5 ≤ ρ3, the detection error probability is as follows:

[0106]

[0107] in

[0108] When the detection threshold When, the derivative of the detection error probability ξ with respect to τ

[0109] When the detection threshold τ∈[ρ2,ρ5], the derivative of the detection error probability ξ with respect to τ is...

[0110] When the detection threshold τ∈[ρ5,ρ4], the derivative of the detection error probability ξ with respect to τ is...

[0111] In summary, the optimal detection threshold τ under this condition is... * ∈[ρ2,ρ5], τ * Substituting B1+D1 yields the minimum detection error probability.

[0112] In sub-case 1.2, when ρ1 < ρ5 ≤ ρ2, the detection error probability is as follows:

[0113]

[0114] When the detection threshold When, the derivative of the detection error probability ξ with respect to τ When the detection threshold τ∈[ρ5,ρ4], the derivative of the detection error probability ξ with respect to τ is... In summary, the optimal detection threshold τ under this condition is... * =ρ5, τ * Substituting into A1 yields the minimum detection error probability.

[0115] In sub-case 1.3, when ρ5 ≤ ρ1, the detection error probability is as follows:

[0116]

[0117] In this case, the optimal detection threshold τ * ∈[ρ5,ρ1], the minimum detection error probability is 0.

[0118] Case 2: When ρ2 > ρ3, the false alarm rate is given by formula (9), and the false negative rate is given by formula (12). In this case, based on the relationship between ρ5 and ρ1, the detection error probability can be divided into the following two sub-cases:

[0119] Sub-case 2.1: When ρ1 < ρ5, the detection error probability is as follows:

[0120]

[0121] in When the detection threshold When, the derivative of the detection error probability ξ with respect to τ When the detection threshold τ∈[σ5,ρ4], the derivative of the detection error probability ξ with respect to τ

[0122] In summary, the optimal detection threshold τ under this condition is... * =ρ5, τ * Substituting into A1 yields the minimum detection error probability.

[0123] Sub-case 2.2: When ρ5≤ρ1, the detection error probability is as follows:

[0124]

[0125] In this case, the optimal detection threshold τ * ∈[ρ5,ρ1], the minimum detection error probability is 0.

[0126] In summary, under conditions 1 and 2, the optimal detection threshold and minimum detection error probability for the monitoring party are respectively:

[0127] Case 1: When ρ2≤ρ3

[0128]

[0129] in

[0130] Case 2: When ρ3 < ρ2

[0131]

[0132] (4) Analyze the average minimum detection error probability at the monitoring point.

[0133] After obtaining the optimal detection threshold and minimum detection error probability at the monitoring point, it is necessary to further analyze the average minimum detection error probability at the monitoring point and use this as a concealment constraint for both parties to communicate, which will then be introduced into the subsequent analysis of the concealed transmission performance of both parties to communicate.

[0134] The calculation process for the average minimum detection error probability at the monitoring location is as follows:

[0135]

[0136] in

[0137] Step 2.2, analyze the covert transmission performance of both communicating parties, the process is as follows: Figure 4 As shown.

[0138] (1) Analyze the probability of interruption of the covert communication link between the two parties.

[0139] According to formula (2), the signal-to-interference-plus-noise ratio (SINR) at the receiver is... b It can be expressed by the following formula:

[0140]

[0141] in Let C be the self-interference cancellation coefficient of the signal receiver. Therefore, the instantaneous channel capacity C of the link between the signal transmitter and the signal receiver can be expressed as C = log2(1 + SINR). b The probability of transmission interruption δ of this link can be given by the following formula:

[0142]

[0143] in It can be expressed by the following formula:

[0144]

[0145] Where K2 is a second-order modified Bessel function of the second kind.

[0146] (2) Analyze the average covert transmission rate between the two communicating parties. Average covert transmission rate The definition of is the covert transmission rate when no transmission interruption occurs, which can be expressed as the product of the ideal covert transmission rate R and the probability of no transmission interruption, i.e.:

[0147]

[0148] Substituting formula (24) into formula (26) yields the average covert transmission rate between the two communicating parties.

[0149] Step 3: Optimize the transmission performance of mobile covert communication.

[0150] Specifically, an optimization problem is constructed to maximize the average covert transmission rate of both communicating parties by optimizing the radius r of the signal sender's movement trajectory, while satisfying constraints. This problem can be represented by the following formula:

[0151]

[0152] in The maximum covert transmission rate; the first constraint is the covertness constraint, where The first constraint is to minimize the average detection error probability, where ε is the concealment coefficient, a sufficiently small positive number. The second constraint is the maximum value constraint of the trajectory radius r. Due to the limitation of the signal transmitter's mobility, r has a maximum value Δ. This invention uses a search algorithm to search for all r values ​​within the interval [0, Δ] to obtain the optimal value r. * This allows it to maximize its performance while satisfying the concealment constraint. To obtain the maximum covert transmission rate

[0153] Experimental data

[0154] To verify the performance of the covert communication system proposed in this invention, Monte Carlo simulation experiments were conducted. The experimental results are as follows: Figures 5 to 7 As shown, the experimental simulation environment is as follows: all communication links in the experiment are dual Rayleigh fading channels, and the ambient noise power at each node is [value missing]. Self-interference cancellation coefficient The distance between each node is d bw =10m,d mw =21m, and the path loss index is γ=2.

[0155] Figure 5 For the power P at the signal transmitter aThe simulation results show that the detection error probability ξ of the monitoring party varies with the radius r of the trajectory of the signal transmitter under different values. The analysis results show that the simulation results are consistent with the theoretical analysis results, verifying the accuracy of the approximation method used in the theoretical analysis. Furthermore, the detection error probability ξ first decreases to a minimum in the interval [0, 21] with respect to the trajectory radius r, and then increases in the interval [21, 40], where d... mw =r represents the case where the minimum value occurs. This applies to different transmitter signal power P. a With P a Decreasing P increases the probability of detection errors. Therefore, decreasing P... a The detection error probability ξ of the monitoring party can be increased, and the value of the trajectory radius r also affects the detection error probability. Therefore, the relationship between r and d should be avoided. mw The values ​​are consistent.

[0156] Figure 6 This diagram illustrates how the probability of transmission interruption δ varies with the radius r of the signal sender's trajectory under different values ​​of the ideal transmission rate R. Analysis of the results shows that the probability of transmission interruption δ increases with the increase of the trajectory radius r, indicating that a larger trajectory radius leads to a higher probability of transmission interruption. Furthermore, a higher ideal transmission rate results in an even higher probability of transmission interruption. Therefore, reducing the ideal transmission rate and the radius of the signal sender's trajectory can reduce the probability of transmission interruption between the two communicating parties.

[0157] Figure 7 To determine the average covert transmission rate between the communicating parties when the radius of the signal sender's movement trajectory varies. Maximum power of interference signal with the signal receiver The changes are shown in the graph. Analysis results show that the average covert transmission rate... along with The increase of initially remains at zero, then reaches a maximum value, and finally decreases towards zero. This is because when When the value is small, the concealment constraint cannot be met, causing the average concealed transmission rate to remain zero. As the rate continues to increase until the concealment constraint is met, the concealed transmission rate reaches its maximum average concealed transmission rate. And as... As the interference continues to increase, the impact of the interference signal on covert communication grows, leading to a continuous decrease in the average covert transmission rate. As shown in the graph, for different movement trajectory radii *r*, a larger *r* will result in a higher average covert transmission rate for both communicating parties. Larger.

[0158] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0159] The embodiments described above are merely illustrative of several implementation methods of this application, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of this patent application. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this patent application should be determined by the appended claims.

Claims

1. A method for mobile covert communication based on mobility and noise uncertainty, using a mobile covert communication system based on mobility and noise uncertainty, characterized in that, The method comprises the following steps: The signal sender moves along a fixed track and sends covert signals; The signal receiver sends artificial noise with randomly changed power while receiving signals; The monitoring party detects whether there is a communication transmission process through an energy detection method, specifically comprising: the monitoring party continuously collects received signals and calculates an average value Y of received signal energy in each time slot w , and compares the average value Y with a pre-set threshold value γ by using a binary hypothesis test w , specifically comprising: the monitoring party receives a kth signal in a time slot , and the kth signal is expressed as: ; wherein is an artificial noise sent by a signal receiving party, is a signal sent by a signal sending party, and respectively satisfies , , wherein k=1, 2,...n, represents a serial number of a kth signal received by the monitoring party in a time slot, is a conjugate of , is a conjugate of , and E() represents a mathematical expectation operation; P a is a signal sending power of the signal sending party, P b is an artificial noise sending power of the signal receiving party, and γ is a path loss index; is an environmental noise at the monitoring party; According to determining the average value Y w ; where D1 and D0 represent the decisions received for H1 and H0, respectively; If Y w < γ, indicates that there is no concealment transmission between the signal sender and the signal receiver, denoted as H0; if Y w > γ, indicates that there is concealment transmission between the signal sender and the signal receiver, denoted as H1; According to the average value Y of the received signal energy of each time slot w determining a false alarm probability and a miss probability; When the probability of the signal sender sending or not sending information to the signal receiver is equal, the false alarm probability and the missed detection probability are used to determine the detection error probability at the monitoring side; The optimal detection threshold and the minimum detection error probability of the monitoring side are determined; The average minimum detection error probability of the monitoring side is determined; The covert communication performance is analyzed and optimized according to the detection result of the monitoring side, and the average covert transmission rate is maximized.

2. The method according to claim 1, wherein, The average value Y of the energy of each time slot received signal w The false alarm probability and the miss detection probability are determined, specifically comprising: determining the false alarm probability and the miss detection probability according to determining a false alarm probability, wherein ; According to determining a probability of missing detection, wherein , d bw is a distance between the signal receiver and the monitoring party and is known by the monitoring party.

3. The method of claim 1, wherein, The system comprises a signal sender, a signal receiver and a monitoring side; The signal sender and the monitoring side are equipped with single antennas, and the signal receiver is equipped with double antennas; The signal sender is configured to send signals randomly in a full-duplex mode while moving at a constant speed along a circular track; The signal receiver is configured to send artificial noise with randomly changed power while receiving signals in a static state; The monitoring side is configured to detect whether there is a communication transmission process between the signal sender and the signal receiver in a static state; The link between the signal sender and the signal receiver is a legal communication link, the link between the signal sender and the monitoring side is a detection link, and the link between the signal receiver and the monitoring side is an interference link.

4. The method of claim 3, wherein, The signal receiver models the self-interference signal as a Gaussian-distributed random variable with mean 0 and variance while receiving the signal.

5. The method of claim 3, wherein, The moving track of the signal sender is a circle with an arbitrary point as the center and R as the radius, wherein R has a maximum value R_max.

6. The method of claim 5, wherein, The artificial noise is sent by the signal receiver with randomly changed power, and the distribution of the power is uniform distribution with a maximum value P_max.

7. The method of claim 6, wherein, The communication link channels between nodes are modeled by using a double-Rayleigh fading channel model, and the channel coefficients remain unchanged within a time slot and randomly change between time slots.

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