Covert communication method suitable for multi-user random access scene

Abstract

The invention discloses a covert communication method suitable for a multi-user random access scene, and belongs to the technical field of wireless communication. The implementation method comprises the following steps: constructing a covert communication model in a multi-user random access scene based on a Gaussian mixture model, and deducing a total detection error probability of an eavesdropper and a covert communication judgment rule; and representing the detection error probability of the listener by using a total variation distance, further constraining the total variation distance by using a relative entropy, and deducing the limitation of a concealment constraint condition on the transmitting power of a user side. Besides, by deducing the expression of the average decoding error probability and the communication rate of a receiving end, the influence of mutual interference between users on the communication capacity and the communication reliability of the system is analyzed, an optimization model with the maximum covert communication capacity as the optimization target is established, the optimization model is solved to obtain the optimal transmitting power, and the optimal transmitting power is obtained. Therefore, the transmitting power of the user side is accurately controlled, and the communication capacity of the system is maximized while the communication concealment and reliability are ensured.

Description

Technical Field

[0001] The present invention relates to a covert communication method applicable to multi - user random access scenarios, belonging to the field of wireless communication technology. Background Art

[0002] With the advent of the information age, wireless communication technology has developed rapidly and is widely used in many fields such as military command, commercial transactions, and social communication. However, the openness of communication technology makes signals vulnerable to malicious detection and interception by third parties, which poses a serious threat to personal privacy protection and military security. Traditional wireless communication security mainly relies on encryption technology to protect data content, but this method cannot hide the communication behavior itself, and the leakage of communication behavior may also lead to privacy leakage and security risks. To solve this problem, covert communication technology has emerged, and its core goal is to ensure that the communication behavior itself is not detected by unauthorized third parties while protecting the communication content.

[0003] Existing covert communication methods mainly focus on single - user scenarios. For example, the covert communication method based on time characteristics hides information by adjusting the sending time interval of data packets. The sender can send data packets at specific time intervals, and the receiver decodes the covert information based on the changes in these intervals. In addition, the covert communication method based on rate change achieves covert transmission by changing the transmission rate of the signal. In wireless communication, the sender can dynamically adjust the transmission rate of the signal to embed the covert information without being easily detected. The covert communication method based on signal characteristics uses features such as the frequency and phase of the signal to hide information, such as embedding specific noise or interference in the signal to cover the existence of the true information. These methods have certain concealment and feasibility in single - user scenarios, but in multi - user scenarios, due to problems such as mutual interference and resource competition among users, their applications are restricted and it is difficult to directly expand and apply.

[0004] In a multi - user random access scenario, the communication behaviors and patterns of each user are difficult to predict and control, which makes it difficult to effectively guarantee communication concealment. Secondly, in a multi - user environment, multiple users share the same communication channel, and the mutual interference among users will increase the symbol error rate of signal transmission, thus reducing the communication quality and seriously affecting the reliability of covert communication. Existing research mainly improves communication concealment and reliability by adopting multi - antenna technology and beamforming. By adjusting the signal phase and amplitude of each unit in the antenna array, the signal is enhanced in the desired direction and weakened in other directions. In addition, researchers have also proposed methods such as introducing friendly interference to mislead enemy detection and using intelligent reflecting surfaces to optimize the wireless channel. However, existing research has not fully considered improving communication reliability and concealment by directly optimizing the transmission power of multiple users in a multi - user mutual interference environment. Therefore, in the face of large - scale and multi - node communication transmission scenarios in future wireless communications, such as the Internet of Things and mobile ad - hoc networks, it is of great practical significance to explore how to achieve an effective balance between interference and concealment among users through power control in a multi - user random access environment and maximize the communication capacity at the same time. Summary of the Invention

[0005] To solve the problem that it is difficult to effectively guarantee communication concealment and reliability in the scenario of uncontrollable user communication behaviors and severe multi - user interference, the object of the present invention is to provide a covert communication method applicable to a multi - user random access scenario. A covert communication model for a multi - user random access scenario is constructed based on the Gaussian mixture model. The detection error probability of the eavesdropper is expressed by the total variation distance, and then the total variation distance is constrained by the relative entropy, and the constraint condition of concealment on the transmission power of the user side is deduced. In addition, by deriving the expressions of the average decoding error probability and communication rate at the receiving end, analyzing the influence of mutual interference among users on the system communication capacity and communication reliability, an optimization problem is proposed, and then the transmission power of the user side is accurately controlled. While meeting the optimization conditions, the influence of interference among users is reduced, and the communication capacity of the system is maximized while ensuring communication concealment and reliability.

[0006] The object of the present invention is achieved by the following technical solutions.

[0007] A covert communication method applicable to a multi - user random access scenario, characterized in that:

[0008] Step S1: Construct a covert communication model for a multi - user random access scenario based on the Gaussian mixture model. Express the detection error probability of the eavesdropper by the total variation distance, and then constrain the total variation distance by the relative entropy, so as to deduce the total detection error probability of the eavesdropper and the judgment rule of covert communication;

[0009] Step S2: Based on the detection error probability and the covert communication judgment rule, calculate the transmit power constraint corresponding to the covert communication.

[0010] Step S3: When the user terminal satisfies the transmit power constraint, establish an optimization model with the goal of maximizing the covert communication capacity, solve the optimization model, obtain the optimal transmit power, and perform communication operations according to the optimal transmit power to achieve covert communication in the multi-user random access scenario.

[0011] Further, the implementation method of Step S1 is as follows:

[0012] Construct a multi-user covert communication system consisting of a user terminal, a receiver Bob, and a receiver Willie; the purpose of the user terminal is to communicate effectively with Bob, and Willie is the eavesdropping party, whose purpose is to monitor and determine whether there is a user communicating with Bob.

[0013] In a discrete-time Gaussian white noise channel, there are m users at the user terminal, and each user uses a single-antenna transmitter to transmit signals. They randomly send signals with fixed probabilities η 1 , η 2 ,..., η j ,..., η m-1 , η m (1 ≤ j ≤ m), and each signal vector has n real-valued symbols. Bob receives the vector where s j = 0 indicates that user j does not send a signal, and s j = 1 indicates that user j sends a signal. is independent and identically distributed Gaussian noise, satisfying a Gaussian distribution with a mean of 0 and a variance of ; Willie observes the vector where is independent and identically distributed Gaussian noise, satisfying a Gaussian distribution with a mean of 0 and a variance of .

[0014] The covert communication judgment rule is as follows: Willie uses a statistical hypothesis test on y w to determine whether there is a user communicating: The element of the signal vector received by Willie is expressed as:

[0015]

[0016] where H 0 is the null hypothesis in the binary hypothesis, indicating that there is no user communicating, and H 1is the alternative hypothesis, indicating the existence of user transmission, where \(i = 1,2,\cdots,n\); \(j = 1,2,\cdots,m\), and \(s\) j \(= 0,1\) indicates whether user \(j\) has sent a signal.

[0017] The detection efficiency of the eavesdropper is characterized by the detection probability \(P\) D When the prior probabilities of the transmitted signals are equally likely, this detection probability is defined as \(P\) D \(= 1-\xi\), and the total detection error probability \(\xi=\alpha+\beta\), where the false alarm probability represents the probability that Willie erroneously judges that there is communication activity when there is no signal transmission, that is, when \(H\) 0 holds; the missed detection probability represents the probability that when the user terminal sends a signal, that is, when \(H\) 1 holds, Willie fails to detect the communication activity and thus erroneously concludes that there is no communication; represents that Willie judges that communication behavior has occurred through detection, represents that Willie judges that no communication behavior has occurred through detection.

[0018] When \(\xi\geq1 - \varepsilon\) is satisfied, this communication is determined to be covert communication, where \(\varepsilon\) is the covert constraint, and the smaller the covert constraint, the higher the communication concealment.

[0019] Furthermore, the implementation method of step S2 is as follows:

[0020] The sum of the error probabilities of Willie's detection is expressed as where the total variation distance is the distribution of \(n\) noise readings observed by Willie under the null hypothesis and the distribution of the codewords of the user terminal transmission corrupted by noise observed under the alternative hypothesis The distance between them; for \(H\) 0 and \(H\) 1 each event is independent and identically distributed, so and are expressed as:

[0021]

[0022] where represents the distribution of \(n\) symbols in the codewords detected by Willie under the null hypothesis, represents the distribution of \(n\) symbols in the codewords detected by Willie under the alternative hypothesis. can be constructed as a Gaussian mixture model \(y\) k represents the \(k\)-th observed data, where \(k = 1,2,\cdots,M\), and \(M = 2\) mDenote the total number of possible signal situations that m users may send in an LPD channel observed by Willie. The parameter is the expectation, variance, and probability of occurrence in the Gaussian mixture model for each sub-model; is the sum of the average powers of the transmitted signals of all transmitted users in the k-th case, that is

[0023] The user side restricts the detection error probability of Willie by constraining the total variation distance to affect its detection performance.

[0024] According to Pinsker's inequality, transform the total variation distance into a relative entropy constraint for analysis, that is:

[0025]

[0026] Determine that the secrecy of communication can be guaranteed when the secrecy constraint condition in Equation (4) is satisfied.

[0027]

[0028] where represents the total transmit power of the user side when all users send signals simultaneously,

[0029] According to the relative entropy constraint and the secrecy constraint condition, calculate the power constraint of the user side:

[0030]

[0031] When the total transmit power of the user side satisfies Equation (6), it is determined that secure communication can be achieved.

[0032] Furthermore, the specific implementation method of step S3 is as follows:

[0033] Consider the average decoding error probability P of Bob over all possible codebooks e ; Bob uses a maximum likelihood decoder to process the signal vector unit received when a single user j sends a codeword At this time, it is necessary to consider the mutual interference between the signals of multiple communicating users among the m users, that is, when decoding the signal corresponding to user j, regard the signals sent by other users except user j as noise;

[0034] For each real-valued symbol in a signal vector sent by user j, the average decoding error probability of Bob is:

[0035]

[0036] Among them, R is the covert communication symbol rate, that is, the covert communication capacity, and its expression is as follows:

[0037]

[0038] When ρ < 1 is a constant, as n increases, the average decoding error probability of Bob on all codebooks of each user decays exponentially to zero.

[0039] The corresponding optimization problem of the covert communication capacity is:

[0040]

[0041] It is determined that when ξ = 1 - ε, the total transmission power of the user side reaches the maximum value, and the transmission power of a single user has a maximum value, realizing the maximization of the communication capacity of the system while ensuring the communication concealment and reliability.

[0042] Beneficial effects:

[0043] 1. A covert communication method applicable to the multi-user random access scenario disclosed by the present invention, by adopting a Gaussian mixture model, precisely controls the transmission power of each user at the user side, realizes covert communication in a multi-user random access network, and reduces the probability of the signal being detected by an eavesdropper. This beneficial effect can solve the problem of covert communication in a user-dense environment and provide a means of communication concealment for high-risk fields such as military operations and intelligence collection.

[0044] 2. A covert communication method applicable to the multi-user random access scenario disclosed by the present invention, by optimizing the signal transmission strategy at the user side, can maximize the communication transmission capacity on the premise of ensuring communication concealment, can provide reliable communication services for more users within limited spectrum resources, greatly improve the overall throughput of the wireless communication network, and help solve the problems of spectrum resource tension and network congestion.

[0045] 3. A covert communication method applicable to the multi-user random access scenario disclosed by the present invention, according to the theoretical decoding error probability at the receiving end, dynamically adjusts the symbol rate of each user at the user side to adapt to the change of the channel condition, and at the same time reduces the influence of mutual interference between users, significantly reducing the bit error rate of communication in a multi-user environment. The present invention can ensure the accurate transmission of key information, which is of great significance for improving the overall reliability and user experience of the communication system, especially in an environment with multi-user mutual interference and poor channel conditions. Description of the drawings

[0046] Figure 1 It is a flowchart of a method for realizing covert communication in a multi-user random access scenario of the present invention;

[0047] Figure 2This is the framework diagram of a covert communication system in a multi-user random access scenario according to the present invention;

[0048] Figure 3 This is the simulation result diagram of the symbol rate of covert communication varying with the codeword length and covert constraint in the example of the present invention;

[0049] Figure 4 This is the simulation result diagram of the symbol rate of covert communication varying with different numbers of users in the example of the present invention. Detailed implementation manners

[0050] The present invention will be described in detail below in conjunction with the drawings and embodiments, and at the same time, the technical problems solved by the technical solution of the present invention and the beneficial effects will be discussed. It should be noted that the described embodiments are only for facilitating the understanding of the present invention and do not impose any limitation on the present invention.

[0051] In view of the situation of multiple transmitters existing in the actual wireless communication environment, the present invention constructs a covert communication system model for multi-user random access under an additive white Gaussian noise channel. By calculating the upper bound of the relative entropy, the constraints of the maximum allowable detection probability and the signal power of the user when transmitting with Gaussian distributed signals are analyzed. Furthermore, the symbol rate expression of the covert communication system in a multi-user scenario is derived, and an optimization problem is constructed to maximize the capacity of the covert communication system.

[0052] To verify the feasibility of this method, a covert communication system under ideal multi-user random access is selected for simulation. Among them, the covertness constraint takes 0.01, 0.05, 0.1; the number of users varies from 1 to 100; the transmission probability η takes 0.5; the codeword length n takes 10 3 、10 4 、10 5 、10 6 、10 7 ; the number of transmitted symbols N is 10 4 ; the noise power at the receiving end is -110 dBm; the noise power at the eavesdropping end is -110 dBm.

[0053] As Figure 1 shown, a covert communication method applicable to a multi-user random access scenario disclosed in this embodiment is specifically implemented as follows:

[0054] Step S1: Construct a covert communication model for multi-user random access based on the Gaussian mixture model, represent the detection error probability of the eavesdropper by the total variation distance, and then constrain the total variation distance by the relative entropy, so as to derive the total detection error probability of the eavesdropper and the covert communication judgment rule;

[0055] Construct a multi - user covert communication system consisting of a client, a receiver Bob, and a receiver Willie, as shown in Figure 2 . The purpose of the client is to communicate effectively with Bob, and Willie is the eavesdropper, whose purpose is to monitor and determine whether there is communication between a user and Bob.

[0056] In a discrete - time Gaussian white - noise channel, there are m users at the client. Each user uses a single - antenna transmitter to send signals, and each signal is randomly sent with a fixed probability of 0.5. Each transmitted vector has n real - valued symbols. Bob receives the vector where s j = 0 indicates that user j does not send a signal, and s j = 1 indicates that user j sends a signal. The Gaussian noise is independent and identically distributed. Willie observes the vector where The Gaussian noise is independent and identically distributed. Willie uses a statistical hypothesis test on y w to determine whether there is a user communicating.

[0057] The unit for determining Willie's received signal vector is denoted as

[0058]

[0059] where H 0 is the null hypothesis in the binary hypothesis, indicating that there is no user communicating, and H 1 is the alternative hypothesis, indicating that there is a user transmitting. i = 1, 2..., n; j = 1, 2,..., m; s j = 0, 1 indicates whether user j has sent a signal.

[0060] It is determined that the eavesdropper will perform a statistical hypothesis test based on the received signal. The detection performance of the eavesdropper is characterized by the detection probability P D . When the prior probabilities of the transmitted signals are equally likely, this detection probability can be defined as P D = 1 - ξ. The total detection error probability is represented by the variable ξ, and ξ = α + β. Here, the false - alarm probability This probability describes the probability that Willie wrongly judges that there is communication activity when there is no signal transmission (i.e., when the null hypothesis H 0 holds); the miss - detection probability This probability describes the situation where the client actually sends a signal (i.e., the alternative hypothesis H 1The probability that Willie fails to detect communication activity when it occurs, thus wrongly concluding that no communication has taken place. and represent two possible outcomes of the detection, corresponding respectively to Willie's decisions of judging that communication has occurred and not occurred.

[0061] It is set that when ξ≥1 - ε, this communication is determined to be a covert communication, where ε is the covert constraint, and the smaller the covert constraint, the higher the communication concealment.

[0062] Step S2: Based on the detection error probability and the covert communication judgment rule, calculate the transmit power constraint corresponding to the covert communication for the user terminal.

[0063] When the eavesdropper Willie uses a detector that performs an optimal hypothesis test on his n channel readings. The sum of the error probabilities of Willie's detection is expressed as where the total variation distance is the distribution of the n noise readings that Willie expects to observe under the null hypothesis and the distribution of the codewords transmitted by the user terminal corrupted by noise between them. The user terminal can limit Willie's detection error probability by imposing a constraint on the total variation distance thereby affecting his detection performance.

[0064] For H 0 and H 1 each event is independent and identically distributed, so there is:

[0065]

[0066] For this Gaussian mixture model, y k represents the k - th observed data, k = 1, 2,..., M, and M = 2 m represents the total number of possible signal situations that m users may send in an LPD channel observed by Willie. The parameter is the expectation, variance, and probability of occurrence in the mixture model of each sub - model respectively. is the sum of the average powers of the transmitted signals of all the transmitted users in the k - th case, that is

[0067] According to Pinsker's inequality, the total variation distance is transformed into a relative entropy constraint for analysis, that is:

[0068]

[0069] Therefore, it is determined that when the covert constraint conditions are satisfied:

[0070]

[0071] When this is the case, the concealment of communication can be guaranteed.

[0072]

[0073] Among them,

[0074] According to the relative entropy constraint and the concealment constraint conditions, the power constraint of the user side is calculated as:

[0075]

[0076] When the total transmission power of the user side satisfies this constraint, it is determined that covert communication can be achieved.

[0077] Step S3: Establish an optimization model with the goal of maximizing the covert communication capacity when the transmission power of the sender satisfies the constraint, solve the optimization model to obtain the optimal transmission power, and perform communication work according to the optimal transmission power.

[0078] Consider the average probability of decoding error \(P\) of Bob over all possible codebooks e . Bob uses a maximum likelihood decoder to process the received vector when a single user transmits a codeword at this time At this time, the mutual interference between each user's signals needs to be considered, and the signals sent by other users can be regarded as noise.

[0079] For each real-valued symbol in a signal vector sent by user \(j\), the average probability of decoding error of Bob is:

[0080]

[0081] Among them, \(R\) is the covert communication symbol rate, that is, the covert communication capacity, and its expression is as follows:

[0082]

[0083] Taking \(\rho = 0.75\), as \(n\) increases, the average probability of decoding error of Bob over all codebooks of each user decays exponentially to zero.

[0084] Based on the above derivation, the corresponding optimization problem of the covert communication capacity is obtained:

[0085]

[0086] It is determined that when \(\xi = 1 - \varepsilon\), the total transmission power of the user side reaches the maximum value, and the transmission power of a single user has a maximum value.

[0087] Figure 3 It shows the influence of different maximum allowable detection probabilities ε and different codeword lengths n on the covert communication symbol rate R when the number of users m = 3: For all given ε values, the covert communication symbol rate R increases with the increase of the codeword length n. At the same time, as the given ε value increases, the covert communication capacity under the same codeword length also increases, indicating that under looser covertness constraints, this embodiment can achieve a higher communication capacity without significantly increasing the detection risk.

[0088] Figure 4 It shows the change of the covert communication capacity under different covertness constraints for different numbers of users. As the number of users m increases, the covert communication symbol rate R will decrease accordingly. This is due to the decrease in communication capacity caused by channel competition and interference in a multi-user environment. This indicates that in a multi-user environment, in order to maintain covertness, a certain amount of communication capacity needs to be sacrificed. This requires system designers to carefully consider the potential impact of the increase in the number of users on the system performance in a multi-user covert communication system, and make a balance between the covertness requirement and the communication capacity to achieve efficient and reliable communication in a multi-user environment.

[0089] The covert communication method in the multi-user random access scenario described in this example derives the limit of the transmit power at the user end under given covertness constraints based on the Gaussian mixture model. By setting the optimization objective and solving the optimization problem to obtain the optimization result, the transmit power at the user end can be accurately controlled, reducing the risk of the communication being detected by unauthorized users, ensuring that the user end can maximize the system communication capacity while meeting the covertness requirements, thus significantly improving the communication efficiency.

[0090] The above specific description further details the purpose, technical solution, and beneficial effects of the invention. It should be understood that the above is only a specific embodiment of the present invention and is not used to limit the protection scope of the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A covert communication method suitable for multi-user random access scenarios, characterized in that: Step S1, constructing a covert communication model in a multi-user random access scenario based on a Gaussian mixture model, expressing the detection error probability of the listener with the total variation distance, and then constraining the total variation distance with relative entropy, thereby deriving the total detection error probability of the eavesdropper and the covert communication judgment rule; Step S2: Calculate the user terminal transmission power constraint corresponding to the covert communication based on the detection error probability and the covert communication judgment rule; Step S3: Under the condition that the transmission power constraint is satisfied, the user terminal establishes an optimization model with the maximum covert communication capacity as the optimization goal, solves the optimization model to obtain the optimal transmission power, and performs communication according to the optimal transmission power to realize covert communication in a multi-user random access scenario.

2. A covert communication method suitable for multi-user random access scenarios as claimed in claim 1, characterized in that: The implementation method of step S1 is: Construct a multi-user covert communication system consisting of a user terminal, a receiver Bob and a receiver Willie; the user terminal aims to communicate effectively with Bob, and Willie is the listener, whose purpose is to monitor and determine whether there is a user communicating with Bob; In a discrete-time Gaussian white noise channel, there are m users at the user end, and each user uses a single antenna transmitter to transmit a signal with fixed probabilities η1, η2, ..., η j ,...,η m-1 ,η m (1≤j≤m) randomly sends signals, each signal vector has n real-valued symbols Bob receives the vector in s j = 0 means user j does not send a signal, s j =1 means user j sent a signal, is independent and identically distributed Gaussian noise with mean 0 and variance Gaussian distribution; Willie observed that the vector in is independent and identically distributed Gaussian noise with mean 0 and variance Gaussian distribution of The rules for determining covert communication are as follows: Willie uses y w A statistical hypothesis test is performed to determine whether there is a user communicating: Willie's received signal vector is represented by: Among them, H0 is the null hypothesis in the binary hypothesis, indicating that there is no user communication, H1 is the alternative hypothesis, indicating that there is user transmission, i = 1, 2..., n; j = 1, 2,..., m, s j =0,1 indicates whether user j has sent a signal; The detection efficiency of the listener is given by the detection probability P D Characterize, when the sent signal is equally likely a priori, the detection probability is defined as P D =1-ξ, total detection error probability ξ=α+β, false alarm probability Indicates the probability that Willie incorrectly judges that communication activity occurs when there is no signal transmission, that is, when H0 is established; the probability of missed detection It represents the probability that when the user sends a signal, i.e., H1 is established, Willie fails to detect the communication activity and thus incorrectly concludes that no communication occurs; It means that Willie has detected that communication has occurred. Indicates that Willie has determined through detection that no communication behavior has occurred; When ξ≥1-ε is satisfied, the communication is determined to be covert communication, where ε is the covert constraint. The smaller the covert constraint is, the higher the covertness of the communication is.

3. A covert communication method suitable for multi-user random access scenarios as claimed in claim 2, characterized in that: The implementation method of step S2 is: The sum of the error probabilities of Willie's test is expressed as Among them, the total variation distance is the distribution of n noise readings observed by Willie under the null hypothesis The observed distribution of codewords transmitted by the noise-corrupted client under the alternative hypothesis The distance between them; for H0 and H1, each event is independent and identically distributed, so and It is expressed as: in, represents the distribution of n symbols in the codeword that Willie hears under the null hypothesis, represents the distribution of n symbols in the codeword that Willie hears under the alternative hypothesis; Can be constructed as a Gaussian mixture model y k Represents the kth observation data, k = 1, 2, ..., M, M = 2 m represents the total number of possible signal situations that m users may send in an LPD channel observed by Willie, and the parameter is the expectation, variance and probability of each sub-model occurring in the Gaussian mixture model; is the sum of the average power of the transmitted signals of all users in the kth case, that is, The user constrains the total variation distance To limit Willie's detection error probability, thus affecting its detection performance; According to Pinsker inequality, the total variation distance is transformed into a relative entropy constraint for analysis, namely: Determine that the concealment of communication can be guaranteed when the concealment constraint condition as shown in formula (4) is met; in It represents the total transmission power of the user end when all users send signals at the same time. According to the relative entropy constraint and the hidden constraint, the power constraint of the user end is calculated: When the total transmission power of the user terminal satisfies equation (6), covert communication can be achieved.

4. A covert communication method suitable for multi-user random access scenarios as claimed in claim 3, characterized in that: The specific implementation method of step S3 is: Consider the average decoding error probability P of Bob on all possible codebooks e ; Bob uses the maximum likelihood decoder to process the codeword sent by a single user j The signal vector unit received at At this time, it is necessary to consider the mutual interference between the signals of multiple communication users among the m users, that is, when decoding the signal corresponding to user j, the signals sent by other users except user j are regarded as noise; For each real-valued symbol in a signal vector sent by user j, Bob's average decoding error probability is: Where R is the covert communication symbol rate, that is, the covert communication capacity, and its expression is as follows: When ρ<1 is a constant, as n increases, Bob's average decoding error probability on all codebooks of each user decays exponentially to zero; The corresponding optimization problem of covert communication capacity is: It is determined that when ξ=1-ε, the total transmission power of the user end reaches a maximum value, and the transmission power of a single user has a maximum value, so as to maximize the communication capacity of the system while ensuring the concealment and reliability of communication.

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