A Method for Optimizing Transmit Power and Time Slots in a Covert Communication System with Imperfect Prior Information

Abstract

The present invention discloses a method for optimizing the transmission power and time slots of a covert communication system under imperfect prior information. First, the scenario where malicious monitoring nodes in the covert communication network do not have prior information about the transmission power of covert users is described and modeled. Then, based on the premise of imperfect prior information, a detection framework based on the generalized likelihood ratio test is constructed, and based on this, a detection model using the observation results of the current time slot and a detection model using the observations of all past time slots are constructed. Finally, a joint optimization model for the transmission power and time slots of the covert communication system is proposed to obtain the optimized transmission power and time slots of the covert communication system. The present invention derives the optimal detection theory of malicious detection nodes in the case of unknown prior information, redesigns the transmission power and time slot strategies of the covert communication system, obtains the optimal solution, and completes the optimization of the transmission power and time slots of the covert communication system under the condition that the malicious detection nodes do not have prior information about the transmission power.

Description

Technical Field

[0001] The present invention belongs to the field of covert communication strategies, and in particular relates to a method for optimizing transmission power and time slots of a covert communication system under imperfect priori information. Background Art

[0002] Due to the openness and complexity of wireless channels, information leakage in wireless communications poses a serious threat, placing higher demands on security. Covert communication, also known as low-probability-of-detection communication, is a technology that conceals signals, minimizing the likelihood of detection by malicious detection nodes. Unlike encryption and physical-layer security technologies, which only protect information content, covert communication secures transmission at the physical signal level. Therefore, covert communication is considered to offer greater security. Steganography and spread spectrum technology were two of the first widely used covert communication techniques.

[0003] The square root law of covert communication reveals that the concealment rate tends to zero as the number of channels used increases. Therefore, how to improve the concealment rate has attracted widespread attention from researchers. Related research shows that creating incomplete information about the transmission or environment at the malicious detection node is an effective way to achieve covert communication. Current research generally believes that the malicious detection node has prior information about the transmitter power or the probability density function of the transmitter power. When the malicious detection node knows the specific device used by the transmitter, the above assumption is feasible. However, in many cases, since the malicious detection node is an external malicious node, it is difficult to obtain prior knowledge of the transmitter. Therefore, how the malicious detection node constructs the optimal detector under incomplete transmitter power prior information and designs the corresponding covert communication strategy remains to be studied.

[0004] Related research focuses on two main areas: one is the design of optimal detectors for malicious detection nodes. Due to the presence of unknown power information in detection, the problem of estimating transmit power is coupled with the detection problem. Existing detectors under perfect information conditions cannot achieve optimal detection performance. Therefore, it is necessary to study how to use historical observation data to reduce the uncertainty of unknown parameters. Previous research on covert communications has not addressed the problem of joint detection and estimation. The second is the design of covert transmission strategies. While rapidly changing transmit power can help improve covert performance, it can also lead to decoding errors at the receiver and requires sharing additional prior knowledge with the receiver. When the malicious detection node has non-ideal prior knowledge, the transmitter does not need to change power frequently, because it takes some time for the warden to accurately estimate the unknown power. Therefore, it is necessary to redesign the covert transmission strategy that jointly considers transmit power and time slots. Summary of the Invention

[0005] In view of the above problems, the object of the present invention is to provide a method for optimizing the transmission power and time slot of a covert communication system under imperfect prior information.

[0006] The specific technical solution for achieving the object of the present invention is as follows:

[0007] A method for optimizing the transmission power and time slots of a covert communication system under imperfect prior information, comprising the following steps:

[0008] Step 1: Describe and construct a model for the scenario where the malicious monitoring nodes in the covert communication network have no prior information about the transmission power of the covert users;

[0009] Step 2: Construct a detection framework based on the generalized likelihood ratio test on the premise of imperfect prior information;

[0010] Step 3: Based on the detection framework in Step 2, construct a detection model using the observation results of the current time slot;

[0011] Step 4: Based on the detection framework in Step 2 and the detection model in Step 3, construct a detection model using the observations of all past time slots;

[0012] Step 5: Based on the detection models in Step 3 and Step 4, propose a joint optimization model for the transmission power and time slots of the covert communication system, and obtain the optimized transmission power and time slots of the covert communication system.

[0013] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0014] The solution of the present invention is based on the scenario where the malicious monitoring nodes in the covert communication network have no prior information about the transmission power of the covert users, constructs a detection framework based on the generalized likelihood ratio test, deduces the optimal detection theory of the malicious detection nodes in the case of unknown prior information, designs two detectors based on the observation vectors of the current time slot and the historical time slots under this framework, and based on this joint optimization model of the transmission power and time slots of the covert communication system, redesigns the transmission power and time slot strategies of the covert communication system and obtains the optimal solution, completing the optimization of the transmission power and time slots of the covert communication system when the malicious detection nodes do not know the prior information of the transmission power. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] Figure 1 It is a flowchart of the steps of the method for optimizing the transmission power and time slots of the covert communication system under imperfect prior information of the present invention.

[0016] Figure 2 It is a schematic diagram of the detection models using the observation results of the current time slot and using the observations of all past time slots in the embodiments of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0017] Embodiment

[0018] Combined with Figure 1 and Figure 2A method for optimizing transmit power and time slot of a covert communication system under imperfect prior information comprises the following steps:

[0019] Step 1: Describe and build a model for the scenario where a malicious monitoring node in a covert communication network does not have prior information about the transmit power of the covert user:

[0020] In a covert communication system, the hidden user sends a node with a transmission power P A Communicate with the receiving node and hope not to be detected by the malicious detection node;

[0021] Considering a classic additive white Gaussian noise channel, the time slots between all nodes are fully synchronized, and all nodes operate in single-antenna half-duplex mode. Because Gaussian signals maximize the mutual information between transmitted and received signals, the transmitting node uses an independent and identically distributed Gaussian codebook and shares the secret codebook with the receiving node, but keeps it secret from the malicious detection node.

[0022] At time slot t, if the sending node transmits information, it will map the information into a standard complex Gaussian random variable symbol sequence:

[0023] x(t)=[x(t)[1],x(t)[2],…,x(t)[N]]

[0024] Where N is the codeword length of one time slot;

[0025] There is additive Gaussian white noise in the system. The noise at the malicious monitoring node and the receiving node can be modeled as a set of zero-mean complex Gaussian random variable sequences: the noise power is n w (t)=[n w (t)[1],n w (t)[2],…,n w (t)[N]] and n b (t)=[n b (t)[1],n b (t)[2],…,n b (t)[N]];

[0026] Assume that the signal vector observed by the malicious monitoring node at time slot t is:

[0027] y w (t) = [y w (t)[1],y w (t)[2],…,y w (t)[N]]

[0028]

[0029] Similarly, the signal vector y received by the receiving node b (t) = [y b (t)[1], y b (t)[2], …, y b (t)[N]] is:

[0030]

[0031] where H1 represents that the transmitting node transmits information in this time slot, H0 represents that the transmitting node does not transmit information in this time slot, P A represents the transmission power, and n w (t) represents the noise vector sequence at the malicious monitoring node, representing the noise power of the noise;

[0032] In each time slot, the decision of the malicious detection node on whether the transmitting node transmits is a binary hypothesis test. Correspondingly, there are two types of detection errors of the malicious detection node: false alarm and missed detection. A false alarm is that the malicious detection node believes that there is a transmission under the hypothesis of H0, and a missed detection is that the malicious detection node believes that there is no transmission under the hypothesis of H1. Assume that the false alarm probability is P FA , and the missed detection probability is P MD . Generally, it is considered that the probabilities of the two hypotheses H0 and H1 are equal, that is equals The total detection error probability of the malicious detection node can be expressed as ξ = P FA + P MD . The malicious detection node wants to construct an optimal detector to minimize the detection error probability, while the goal of the covert user sender is to ensure covert transmission in the worst case. In view of this, for any small ε, the covertness constraint can be expressed as ξ ≥ 1 - ε, meaning that the sender can hide its transmission with a probability of 1 - ε.

[0033] When the malicious monitoring node has prior information about the user's transmission power, the signal it receives follows a Gaussian distribution, and the probability density functions under H0 and H1 are respectively:

[0034]

[0035]

[0036] Step 2: On the premise of imperfect prior information, construct a detection framework based on the generalized likelihood ratio test:

[0037] This patent considers the actual scenario that the malicious detection node does not know the prior information of the transmission power, but this does not mean that a malicious detection node has weak capabilities, because it can estimate the unknown transmission power by observing the signal. Different from the detection under perfect prior information, the malicious detection node does not know f(y w (t)|H1) Because P A is unknown; therefore, the likelihood ratio:

[0038]

[0039] It is also unknown and the likelihood ratio detector cannot be used. This scheme proposes a detector based on generalized likelihood ratio detection, which has been proved to be the optimal detector under finite samples;

[0040] Given a finite number of observation vectors Y, assume that the unknown parameters θ0 and θ1 under H0 and H1 satisfy:

[0041]

[0042] Under the Neyman-Pearson criterion, the optimal test for binary hypothesis testing is the generalized likelihood ratio test:

[0043]

[0044] The estimated values of the unknown parameters are:

[0045]

[0046] As can be seen from the above formula, the generalized likelihood ratio test first estimates the unknown parameters using the maximum likelihood estimation criterion, and then replaces the location parameters with estimated values in the probability density function before making a judgment.

[0047] Under imperfect prior information, the detection framework of generalized likelihood ratio detection is:

[0048]

[0049] in, is an estimate of the transmit power, which is a function of the observation vector.

[0050] Step 3: Based on the detection framework of step 2, a detection model is constructed using the observation results of the current time slot. Specifically:

[0051] Based on the generalized likelihood ratio test framework, the observation vector y in the current time slot w (t), build a detection model using the observation results of the current time slot:

[0052]

[0053] in is the estimated value of the transmission power based on the observation vector y of the current time slot. To simplify the mathematical form of this detector, it is necessary to first calculate w (t). According to the definition of the generalized likelihood ratio test, is the maximum likelihood estimate that maximizes the probability density function. It is necessary to first calculate f(y (t)|H1) with respect to P w The derivative is: A Let the derivative be zero, that is

[0054]

[0055] We can get the value of :

[0056]

[0057] Considering that the transmission power is positive, the estimated value is corrected to:

[0058]

[0059] Substitute the obtained back into , and the generalized likelihood ratio detection model can be obtained as:

[0060]

[0061] It is easy to prove that this formula can be written in the form of , indicating that this detector is equivalent to the energy detector;

[0062] Among them, by comparing the average received power P w with the decision threshold β C , a conclusion on whether to transmit is drawn, that is, the noise power of the malicious detection node, and the estimated value of the transmission power is the part of the received power that exceeds the noise power:

[0063]

[0064] The error detection probability of the generalized likelihood ratio detection model based on the existing time slot observation vector is:

[0065]

[0066] [[ID=A]]This result can also be used as a criterion for evaluating the concealment of the sender because the parameters in the formula are completely known to the sender.

[0067] Step 4: Based on the detection framework in Step 2 and the detection model in Step 3, construct a detection model that utilizes all past time slot observations, specifically:

[0068] Since the malicious detection node is uncertain whether the sender transmits in the current time slot and also uncertain about the information sequence transmitted by the sender, the estimation of the transmit power is inaccurate. In the detection model proposed in step 3, only the current observed data is used for estimation. Moreover, the detection models in most works are also based on the current observation. As can be seen from the previous analysis, the maximum likelihood estimate is a function of the samples, and increasing the sample size will make the estimate closer to the true value. In practice, the malicious detection node has made long-term observations and has all the historical observed data. If more samples can be mined, the uncertainty of the transmission can be reduced, thus making the estimation more accurate. Therefore, we further consider a powerful Willie who can use all the historical observed data to estimate the unknown parameters and perform detection in the case of prior unknown.

[0069] Similar to the current observation-based detection vector model, we first calculate the estimated value of the unknown transmit power under the historical observations;

[0070] Define all the historical observed vectors of the malicious detection node in T time slots:

[0071]

[0072] Also based on the generalized likelihood ratio detection framework, under the observed vectors of all historical time slots The detection model that uses the observations of all past time slots is:

[0073]

[0074] is The maximum likelihood estimate value of P under A which uses the observed data of all historical time slots. Note that the detection of the current observed value is a binary hypothesis test, while the historical observed data is the observed vectors of multiple time slots, where the sending node only transmits in a part of the time slots during this period. Therefore, the probability density distribution form of all the historical observed vectors is different from that of the observed vector y of a single time slot w (t). Since the malicious detection node does not know whether the transmitting node transmits in each time slot, the probability density function of the observed vector on a single time slot y w (t) (1 ≤ t ≤ T) can be modeled as the weighted sum of the probability density functions of the observed vectors under H0 and H1

[0075]

[0076] where the prior probabilities and serve as the weights of the probability density functions. Since the observed vectors of all time slots are independent and identically distributed, so The probability density function of can be modeled as the product of the probability density functions of each time slot:

[0077]

[0078] From this, we can calculate the estimated value of the transmission power. For the sake of simplicity, we take The logarithm of the probability density function is denoted as L. L is about P A The first-order derivative of is:

[0079]

[0080] where γ t1 for y w The probability of (t) under the assumption H1, that is, the probability of the sending node transmitting in time slot t, is:

[0081]

[0082] make Equal to zero, that is Equal to 0, the maximum likelihood estimate of the transmit power can be obtained for

[0083]

[0084] To see is the historical observation vector and γ t1 function, but γ t1 Again and The two are coupled, making it difficult to obtain an estimated value A closed-form expression for . A feasible method for solving highly coupled variables in this equation is the expectation-maximization algorithm. Specifically, an iterative approach is used to approximate the optimal solution, with each iteration consisting of two steps. The first, the E-step, calculates the expectation of the likelihood function based on the parameters estimated in the previous iteration. The second, the M-step, updates the parameters to maximize the likelihood function. Because the algorithm ensures that the likelihood function increases after each iteration, the function eventually converges, resulting in an estimated value.

[0085] The estimated value obtained by the expected maximum algorithm Bringing it into generalized likelihood detection, we can get the optimal detector which is equivalent to energy detection;

[0086] The optimal threshold at time T of the detection model using all past time slot observations is:

[0087]

[0088] Accordingly, the error detection probability of the malicious detection node is:

[0089]

[0090] It can be seen that ν H (T) is and a function of. However, the transmitter does not know and the values of, and cannot directly use the error detection probability ξ H (T) to measure the concealment of transmission. Note that the expected maximum value algorithm is an iterative method that can be iterated to approach the optimal solution, rather than the optimal solution. Here, we consider the worst-case scenario where the malicious detection node can obtain the optimal solution. When the error detection probability contains unknown variables, the expected error detection probability can be used to evaluate the concealment performance. The expected detection probability can be expressed as

[0091]

[0092] where is the probability density function of the estimated value. We have obtained that is a function of the historical observation vector , but it is difficult to obtain a closed-form expression, is even more difficult to obtain. Here, we draw on the asymptotic properties of maximum likelihood estimation and can obtain where I(P A ) for the Fisher information of the transmission power can be expressed as:

[0093] T

[0094] Its value can be achieved through numerical integration. Substituting it into the average error detection probability gives:

[0095]

[0096] Step 5. Based on the detection models in Steps 3 and 4, a joint optimization model of the transmission power and time slots of the covert communication system is proposed, and the optimized transmission power and time slots of the covert communication system are obtained, specifically:

[0097] At a finite block length, the decoding error probability of the receiver cannot be ignored. For a fixed decoding error probability δ, the transmission rate C is approximately:

[0098]

[0099] where Q -1 (·) is the Q inverse function. The total transmission throughput within T time slots can be expressed as Ψ = TC

[0100] And the concealment within T time slots is defined as:

[0101]

[0102] Maximize the total transmission throughput under the covert constraint by optimizing the transmit power and time slots. The optimization model is as follows:

[0103]

[0104]

[0105]

[0106] T > 0 and is an integer.

[0107] where is the maximum power that the sender can transmit, corresponds to the transmission power required for the minimum transmission rate, and C represents the transmission rate corresponding to the fixed decoding error probability δ.

[0108] Since the number of time slots is an integer, this optimization problem is a mixed-integer programming problem, where the covert constraint has a complex form and it is difficult to obtain a closed-form solution for the average error detection probability. An effective method is to ignore the integer constraint and solve the corresponding relaxed problem. Next, we will analyze the monotonicity of A with respect to T and P.

[0109] Since is the mean of , their monotonicities with respect to P A are the same. Therefore, we first calculate the derivative of with respect to P A :

[0110]

[0111] where is

[0112]

[0113]

[0114] The inequality in (30) is due to when x ≥ 1. Taking the approximation The derivative of I(P A ) with respect to P A can be written as

[0115]

[0116] When x ≥ 1, From this, we can obtain Combined with the previous form, Can be written as

[0117]

[0118] From the above formula we can get therefore About P A Monotonically decreasing.

[0119] The following calculation Derivative with respect to T:

[0120]

[0121] Its value is less than zero. Therefore It is also monotonically decreasing with respect to T.

[0122] According to the above conclusion, when the hidden constraint is just satisfied, the optimization objective reaches the maximum. Therefore, T can be expressed as P A Since the specific closed-form function is difficult to calculate, define an implicit function between the two.

[0123]

[0124] Then, the relaxation problem corresponding to the optimization problem can be written as

[0125]

[0126]

[0127] Contains only one optimization variable P A Ψ About P A The derivative of

[0128]

[0129] in for

[0130]

[0131] Another key is calculation According to the implicit function derivation rule, the formula can be written as

[0132]

[0133] according to Can get

[0134]

[0135] Therefore, the optimal transmission power P of this optimization problem is Aand the number of time slots T are and This conclusion shows that the total concealment rate is the largest when the transmission power is the smallest, which guides the design of concealment strategy.

[0136] A system for optimizing transmit power and time slots of a covert communication system under imperfect prior information, characterized by comprising the following modules:

[0137] Scenario description module: used to describe and build a model for scenarios in which malicious monitoring nodes in a covert communication network do not have prior information on the transmit power of covert users;

[0138] Detection framework construction module: used to build a detection framework based on generalized likelihood ratio test under the premise of imperfect prior information;

[0139] Current time slot detection model building module: used for the detection framework to build a detection model using the current time slot observation results;

[0140] Past time slot detection model building module: used to build a detection model using all past time slot observations;

[0141] Transmission power and time slot joint optimization module: used to build a joint optimization model of transmission power and time slot of covert communication system to obtain the optimized transmission power and time slot of covert communication system.

[0142] A computer device comprises a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the computer program, the following steps are implemented:

[0143] Step 1: Describe and build a model for the scenario where a malicious monitoring node in a covert communication network does not have prior information about the transmit power of the covert user;

[0144] Step 2: Under the premise of imperfect prior information, a detection framework based on the generalized likelihood ratio test is constructed;

[0145] Step 3: Based on the detection framework of step 2, a detection model using the observation results of the current time slot is constructed;

[0146] Step 4: Based on the detection framework in step 2 and the detection model in step 3, a detection model is constructed that utilizes all past time slot observations.

[0147] Step 5: Based on the detection models of steps 3 and 4, a joint optimization model of the covert communication system transmission power and time slot is proposed to obtain the optimized covert communication system transmission power and time slot.

[0148] A computer storable medium storing a computer program, wherein a processor implements the following steps on the computer program:

[0149] Step 1: Describe and construct a model for the scenario where malicious monitoring nodes in the covert communication network do not have prior information on the transmitted power of covert users.

[0150] Step 2: Construct a detection framework based on the generalized likelihood ratio test under the premise of imperfect prior information.

[0151] Step 3: Based on the detection framework in Step 2, construct a detection model that utilizes the observation results of the current time slot.

[0152] Step 4: Based on the detection framework in Step 2 and the detection model in Step 3, construct a detection model that utilizes the observations of all past time slots.

[0153] Step 5: Based on the detection models in Steps 3 and 4, propose a joint optimization model for the transmitted power and time slot of the covert communication system, and obtain the optimized transmitted power and time slot of the covert communication system.

[0154] The present invention derives the optimal detection theory for malicious detection nodes in the case of unknown prior information, designs two detectors based on the observation vectors of the current time slot and historical time slots within this framework, and based on this joint optimization model of the transmitted power and time slot of the covert communication system, redesigns the transmitted power and time slot strategies of the covert communication system and obtains the optimal solution, completing the optimization of the transmitted power and time slot of the covert communication system when the malicious detection node does not have prior information on the transmitted power.

[0155] The above embodiments illustrate and describe the basic principles and main features of the present invention. Those skilled in the art should understand that the present invention is not limited by the above embodiments. What is described in the above embodiments and the specification only illustrates the principles of the present invention. Without departing from the spirit and scope of the present invention, the present invention will have various changes and improvements, and these changes and improvements all fall within the scope of the present invention claimed.

Claims

1. A method for optimizing the transmission power and time slots of a covert communication system under imperfect prior information, characterized in that It includes the following steps: Step 1: Describe and build a model for the scenario where malicious monitoring nodes in the covert communication network have no prior information on the transmitted power of covert users: The signal vector observed by the malicious monitoring node at the t-th time slot is: y w (t) = [y w (t)[1], y w (t)[2],..., y w (t)[N]] x(t) = [x(t)[1], x(t)[2],..., x(t)[N]] n w (t) = [n w (t)[1], n w (t)[2],..., n w (t)[N]] Among them, \(x(t)\) is the symbol sequence of standard complex Gaussian random variables mapped by the transmitting node to transmit information, \(N\) is the codeword length of one time slot, \(H_1\) represents that the transmitting node transmits information in this time slot, \(H_0\) represents that the transmitting node does not transmit information in this time slot, \(P\) A represents the transmission power, \(n\) w (t) represents the noise vector sequence at the malicious monitoring node, and represents the noise power of this noise; The signal vector received by the receiving node at the t-th time slot is: y b (t) = [y b (t)[1], y b (t)[2],..., y b (t)[N] 0 n b (t) = [n b (t)[1], n b (t)[2],..., n b (t)[N]] where n b (t0 represents the noise vector sequence at the receiving node, represents the noise power of the noise; When the malicious monitoring node has prior information on the transmitted power of the user, the signal it receives follows a Gaussian distribution, and the probability density functions under H0 and H1 are respectively: Step 2: Based on the premise of imperfect prior information, build a detection framework based on the generalized likelihood ratio test; Step 3: Based on the detection framework in Step 2, build a detection model that utilizes the observation results of the current time slot; Step 4: Based on the detection framework in Step 2 and the detection model in Step 3, build a detection model that utilizes the observations of all past time slots; Step 5: Based on the detection models in Step 3 and Step 4, propose a joint optimization model for the transmitted power and time slots of the covert communication system, and obtain the optimized transmitted power and time slots of the covert communication system.

2. The method for optimizing the transmission power and time slots of the covert communication system under imperfect prior information according to claim 1, characterized in that The detection framework based on the generalized likelihood ratio test in Step 2 is specifically: Under imperfect prior information, the detection framework of the generalized likelihood ratio detection is: Among them, is the estimated value of the transmission power and is a function of the observation vector.

3. The method for optimizing the transmission power and time slot of a covert communication system under imperfect prior information according to claim 1, wherein The building of the detection model that utilizes the observation results of the current time slot in Step 3 is specifically: Based on the generalized likelihood ratio test detection framework, under the current time slot observation vector y w (t), construct a detection model that utilizes the observation results of the current time slot: Among them, by comparing the average received power P w with the decision threshold β C a conclusion on whether to transmit is obtained: The error detection probability of this detection model is:

4. The method for optimizing the transmission power and time slot of the covert communication system under imperfect prior information according to claim 3, characterized in that The building of the detection model that utilizes the observations of all past time slots in Step 4 is specifically: Define all historical observation vectors of the malicious detection node in T time slots: Observation vectors for all historical time slots Under this condition, the detection model using observations from all past time slots is as follows: Let Then: Among them, is the maximum likelihood estimate of P A , which utilizes the observed data of all historical time slots, and γ t1 is the probability of y w (t) under the hypothesis H1, that is, the probability that the transmitting node transmits in the t-th time slot; The optimal threshold at T time slots of the detection model that utilizes the observations of all past time slots is: The error detection probability of the malicious detection node is:

5. The method for optimizing the transmission power and time slots of a covert communication system under imperfect prior information according to claim 4, wherein The joint optimization model for the transmitted power and time slots of the covert communication system in Step 5 is specifically: By optimizing the transmitted power and time slots, maximize the total transmission throughput under the covert constraint. This optimization model is: T > 0 and is an integer. Among them, among them is the maximum power that the sender can transmit, corresponds to the transmission power required for the minimum transmission rate, and C represents the transmission rate corresponding to the fixed decoding error probability δ.

6. A transmission power and time slot optimization system for a covert communication system under imperfect prior information, characterized in that, It includes the following modules: Scenario description module: Used to describe and build a model for the scenario where malicious monitoring nodes in the covert communication network have no prior information on the transmitted power of covert users: Among them, the signal vector observed by the malicious monitoring node at the t-th time slot is: y w (t) = [y w (t)[1], y w (t)[2],..., y w (t)[N]] x(t) = [x(t)[1], x(t)[2],..., x(t)[N]] n w (t) = [n w (t)[1], n w (t)[2],..., n w (t)[N]] Among them, \(x(t)\) is the symbol sequence of standard complex Gaussian random variables mapped by the transmitting node to transmit information, \(N\) is the codeword length of a time slot, \(H_1\) represents that the transmitting node transmits information in this time slot, \(H_0\) represents that the transmitting node does not transmit information in this time slot, \(P\) A represents the transmission power, \(n\) w (t) represents the noise vector sequence at the malicious monitoring node, represents the noise power of this noise; The signal vector received by the receiving node at the t-th time slot is: y b y(t) = [y b (t)[1], y b (t)[2],..., y b (t)[N]] n b (t) = [n b (t)[1], n b (t)[2],..., n b (t)[N]] where n b (t) represents the noise vector sequence at the receiving node, represents the noise power of the noise; When the malicious monitoring node has prior information on the transmitted power of the user, the signal it receives follows a Gaussian distribution, and the probability density functions under H0 and H1 are respectively: Detection framework building module: Used to build a detection framework based on the generalized likelihood ratio test on the premise of imperfect prior information; Current time slot detection model building module: Used for the detection framework to build a detection model that utilizes the observation results of the current time slot; Past time slot detection model building module: Used to build a detection model that utilizes the observations of all past time slots; Transmitted power and time slot joint optimization module: Used to build a joint optimization model for the transmitted power and time slots of the covert communication system, and obtain the optimized transmitted power and time slots of the covert communication system.

7. A computer device, comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the method steps specified in any one of claims 1 to 5.

8. A computer-readable storage medium storing a computer program, characterized in that, On the computer program, the processor implements the method steps specified in any one of claims 1 to 5 as described above.

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