Secrecy capacity and low detection probability joint optimization method and system based on RIS

Abstract

The invention discloses an RIS-based secrecy capacity and low detection probability joint optimization method and system. The method comprises the steps of 1, constructing an RIS-based secrecy capacity and low detection probability joint communication system model; step 2, determining channel statistical information of each link in the model based on the joint communication system model in the step 1; 3, analyzing the secrecy capacity and the error detection probability, and deriving an analytic expression of the average secrecy capacity and the average error detection probability; step 4, taking the total power of the sending end and the jammer as a constraint condition, taking power distribution as an optimization variable, and constructing an optimization problem of maximizing the safety communication rate in the covert communication system; and 5, solving an optimization target by adopting a mode of combining a generation diffusion model GDM and deep reinforcement learning DRL. According to the method, the performance optimization of the covert communication system under the imperfect CSI condition is considered, the secrecy capacity of the system is increased while the link concealment is enhanced, and dual assurance is provided for the system.

Description

Technical Field

[0001] The present invention belongs to the technical field of wireless communications, and in particular relates to a method and system for jointly optimizing confidentiality capacity and low detection probability based on RIS (Reconfigurable Intelligent Surface). Background Art

[0002] At present, the research on the physical layer security of wireless communication systems mainly focuses on two aspects: one is information theory security based on Shannon's basic principles of information theory. Its core idea is to use the characteristics of wireless channels for channel coding to prevent eavesdroppers from decoding communication signals. In order to measure the security performance of the system, Wyner and others first proposed the concept of confidentiality capacity. Confidentiality capacity refers to the maximum transmission rate that can be achieved under the premise that the eavesdropper cannot decode any information. Its value is the difference in channel capacity between the legitimate link and the eavesdropping link. The second is the concept of low detection probability communication, namely covert communication, which was first mentioned by Simon in the spread spectrum communication system. Covert communication aims to hide the existence of the transmission signal. In essence, it reduces the difference between the signal and the background noise by reducing the signal transmission power and controlling the signal waveform characteristics, thereby reducing the probability of the eavesdropper detecting the signal transmission.

[0003] However, both aspects have their own advantages and limitations: Information security research focuses on the confidentiality capacity limit of communication systems in hostile environments, but this cannot completely prevent the enemy from detecting the existence of transmission signals. Similarly, although covert communication can effectively hide communication activities, it may limit its transmission efficiency by ignoring the physical characteristics of the communication channel.

[0004] Therefore, it is more realistic to study how to combine the advantages of both to achieve dual protection of communication systems at the content level and behavior level.

[0005] With the development of the sixth generation of mobile communication technology, RIS provides new possibilities for improving both confidentiality capacity and communication concealment by relying on its ability to dynamically adjust and optimize the wireless propagation environment. On the one hand, RIS can optimize the channel gap between legitimate users and eavesdroppers by adjusting the phase shift and amplitude of the intelligent reflection unit. On the other hand, RIS can control the electromagnetic properties and reflection path of the signal, thereby reducing the probability of the signal being detected. In addition, as a passive reflection element, RIS is controlled by the central processor and has better security than active relay nodes. This makes RIS highly applicable in the physical layer security of wireless communications.

[0006] At present, in the existing wireless communication security schemes, the research on covert communication optimization methods that take into account both confidentiality capacity and low detection probability is still in its infancy. In addition, the existing methods all assume that the legitimate system has perfect CSI (Channel State Information), but in actual situations, it is often difficult to measure the instantaneous CSI of the eavesdropping channel. Therefore, it is urgent to propose a joint optimization scheme of confidentiality capacity and low detection probability based on RIS to achieve dual security protection of the physical layer of wireless communication under imperfect channel conditions. Summary of the invention

[0007] In view of the above problems existing in the prior art, the present invention proposes a RIS-based joint optimization method and system for confidentiality capacity and low detection probability, so as to achieve double security protection of the physical layer of wireless communication under imperfect channel conditions.

[0008] To achieve the above object, the present invention adopts the following technical solutions:

[0009] A joint optimization method of confidentiality capacity and low detection probability based on RIS is applicable to a covert communication system including a transmitter, a jammer, a RIS, a receiver and an eavesdropper. The optimization method comprises the following steps:

[0010] Step 1: Construct a joint communication system model based on RIS with confidentiality capacity and low detection probability;

[0011] Step 2: Based on the system model in step 1, determine the channel statistics of each link in the model;

[0012] Step 3: Based on step 1 and step 2, analyze the confidentiality capacity and the false detection probability, and derive the analytical formulas of the average confidentiality capacity and the average false detection probability;

[0013] Step 4: Taking the total power of the transmitter and the jammer as the constraint and the power allocation as the optimization variable, construct an optimization problem to maximize the secure communication rate in the covert communication system;

[0014] Step 5: Since the optimization problem is non-convex, the optimization objective is solved by combining GDM (Generative Diffusion Model) and DRL (Deep Reinforcement Learning).

[0015] Preferably, step 1 is specifically implemented as follows:

[0016] A joint communication system model with confidentiality capacity and low detection probability based on RIS is constructed, which specifically includes three parts: mathematical model of RIS reflection matrix, channel model and signal model.

[0017] RIS consists of N reflection units, and each reflection unit is independent. Therefore, the reflection coefficient matrix of RIS can be expressed as a diagonal matrix in the form of:

[0018]

[0019] Among them, β n ∈[0,1] is the amplitude reflection coefficient of the nth element, θ n ∈[0, 2π) is the phase shift variable of the nth element.

[0020] For the channel model, the fading coefficients between the transmitter, jammer, receiver, eavesdropper, and RIS are expressed as h AR 、h JR 、h RB 、h RW , the fading coefficient vector shape is N×1, and both follow the Nakagami-m fading model. The path loss exponents are expressed as α AR , α JR , α RB , α RW For the two links of sender-RIS-receiver and jammer-RIS-receiver, the sender can obtain its instantaneous CSI. However, for the RIS-eavesdropper link, considering the actual situation, the sender can only obtain its statistical CSI, and the eavesdropper has its instantaneous CSI.

[0021] For the signal model, the signal sent by the transmitter and the signal sent by the jammer are modeled as:

[0022]

[0023] Among them, P A and P J are the transmit power of the transmitter and the jammer respectively, s A (k)(E(|s A (k)| 2 )=1) is the information sent by the sender to the receiver, s J (k)(E(|s J (k)| 2 )=1) is the interference information sent by the jammer, s A (k) and s J (k) are all unit power signals, and their average power E(|S A (k)| 2 ) and E(|S J (k)| 2 ) are all equal to 1. J It obeys uniform distribution, and its probability density function is:

[0024]

[0025] Combining the channel fading coefficient, path loss and RIS reflection coefficient matrix, the expression of the received signal at the receiving end can be obtained:

[0026]

[0027] in, represents the path loss. And

[0028] in d χ represents the distance, α χ is the path loss index, and χ∈{AR, JR, RB, RW}. B (k) is the additive white Gaussian noise at the receiving end.

[0029] According to formula (4), the SINR (Signal to Interference Plus Noise Ratio) at the receiving end is expressed as:

[0030]

[0031] in, is the variance of the additive white Gaussian noise at the receiving end, and ρ∈[0, 1] represents the self-interference elimination coefficient.

[0032] The eavesdropper faces a binary detection problem: 1) Testing the hypothesis Indicates that there is no communication between the sender and the receiver; 2) Alternative hypothesis Indicates that the sender is sending a message to the receiver.

[0033] Under the two assumptions, the received signal is modeled as:

[0034]

[0035] in, m W (k) is the additive Gaussian white noise of the eavesdropper. When the alternative hypothesis When established, the eavesdropper's SINR is expressed as:

[0036]

[0037] Based on formulas (6) and (7), the eavesdropper will calculate the average power received Perform binary detection, and the decision rules are:

[0038]

[0039] Where τ is the binary detection threshold, and Respectively, it is beneficial to and judgment.

[0040] Assume that the eavesdropper performs binary detection on an infinite number of signal samples, that is, K→∞. Therefore, there is no uncertainty in sending signals and receiving noise. The average power of the eavesdropper is given by:

[0041]

[0042] in, in, is Gaussian white noise.

[0043] Preferably, step 2 is specifically implemented as follows:

[0044] Step 2-1: For the transmitter-RIS-receiver link, adjust the RIS parameters to provide the best channel quality for the receiver. The channel gain of the transmitter-RIS-receiver link is as follows:

[0045]

[0046] Among them, h RB，n and h AR，n h RB and h AR The nth element of .

[0047] By adjusting all phase shift variables θ n (n=1,2,...,N), the channel gain can be maximized. The determined generalized solution can make the phases of the various channel gain terms consistent, thereby maximizing the overall channel gain, where is an arbitrary constant in the range [0, 2π). Set the optimal phase shift After that, we get the following formula:

[0048]

[0049] in, Without loss of generality, assuming that the fading coefficient of the transmitter-RIS-receiver link follows the Nakagami-m distribution, when the number of reflection elements N is large enough, the variable Follows non-central chi-square distribution in Its probability density function and distribution function are expressed as:

[0050]

[0051] and

[0052]

[0053] Step 2-2: For the transmitter-RIS-eavesdropper, jammer-RIS-receiver, and jammer-RIS-eavesdropper links, the phase shift of the RIS is considered random. Therefore, when N is large enough and {θ n} Random, variable and tends to be a complex Gaussian random variable with mean zero and variance N, and follows the distribution Thus, the variable The probability density function and distribution function of are expressed as:

[0054]

[0055] and

[0056]

[0057] Preferably, step 3 is specifically implemented as follows:

[0058] Step 3-1, the eavesdropper's DEP (Detection Error Probility) is expressed as:

[0059]

[0060] in, is the false alarm probability, is the probability of missed detection. Furthermore, ξ = 0 indicates that the eavesdropper can completely detect the covert communication, and ξ = 1 indicates that the covert communication is completely random to the eavesdropper.

[0061] According to equations (9) and (10), under a fixed detection threshold τ, the expressions of false alarm probability and missed detection probability can be obtained as follows:

[0062]

[0063] and

[0064]

[0065] Furthermore, by substituting formula (3) into formula (18) and formula (19), we can obtain their specific expressions, which are:

[0066]

[0067] and

[0068]

[0069] Among them, τ1=ζ2, τ3=ζ3,

[0070] According to equations (20) and (21), we can get the expression of DEP under a fixed threshold, which can be divided into two cases. When τ2≤τ3, we have:

[0071]

[0072] When τ2>τ3, we have:

[0073]

[0074] The above DEP is derived based on a fixed threshold. However, eavesdroppers usually adjust the threshold to achieve the minimum DEP, and it is necessary to analyze the system performance in the worst case. The minimum DEP in the two cases can be obtained from equations (22) and (23), namely:

[0075]

[0076] Step 3-2: The confidentiality capacity is the difference in channel capacity between the receiver and the eavesdropper. According to Shannon's theorem, the confidentiality capacity of the system can be obtained as:

[0077] R C =[R B -R W ] + =[log2(1+ψ B )-log2(1+ψ W )] + (25)

[0078] Since RIS provides the maximum channel gain for the receiver and the gains of each channel are independent of each other, the probability that the SINR of the receiver is less than the SINR of the eavesdropper is close to zero, so the average confidentiality capacity can be approximated as:

[0079]

[0080] Since the jammer is controlled by the transmitter, the effect of the jammer on the receiver can be ignored, that is, ρ = 0, and the ergodic rate of the receiver can be expressed as:

[0081]

[0082] in, Substituting equation (13) into equation (27) and combining it with Gauss-Laguerre numerical integration, we can obtain:

[0083]

[0084] Where u1 is the order of the Gauss-Laguerre polynomial, x 1，l is the Laguerre polynomial The lth root of is the lth weight, Φ1 is the integrand, that is:

[0085]

[0086] The traversal rate of the eavesdropper under the alternative hypothesis can be expressed as:

[0087]

[0088] in, Substituting equation (3) and equation (15) into equation (30) and combining with Gauss-Laguerre numerical integration, we can obtain:

[0089]

[0090] in, u2 is the order of the Gauss-Laguerre polynomial, x 2，l is the Laguerre polynomial The lth root of is the lth weight, Φ2 is the integrand, that is:

[0091]

[0092] in,

[0093] Substituting equation (28) and equation (31) into equation (26), the average confidentiality capacity can be approximated as:

[0094]

[0095] Step 3-3: Based on the above, the definition of secure communication rate is further given. The secure communication rate, that is, the sum of the communication rates within the confidentiality capacity or outside the confidentiality capacity but concealed, can be expressed as:

[0096] R S =R C +ξ * R W (34)

[0097] Among them, ξ * R W =ξ * (R B -R C ). The average secure communication rate expression is as follows:

[0098]

[0099] in,

[0100] Preferably, step 4 is specifically implemented as follows:

[0101] The optimization goal is to maximize the average secure communication rate by optimizing the power distribution between the transmitter and the jammer's transmission power. The optimization problem can be constructed as follows:

[0102]

[0103] Among them, P max is the total power limit.

[0104] Since the average secure communication rate increases with P A As it increases, the average secure communication rate can be maximized only when the constraint equation holds. Therefore, equation (36) can be transformed as follows:

[0105]

[0106] in, is the power allocation coefficient.

[0107] Preferably, step 5 is specifically implemented as follows:

[0108] The closed-form expression of the average secure communication rate is relatively complex, and it is difficult to directly obtain the optimal solution under the constraints. Therefore, it is considered to use a combination of GDM and DRL to solve the optimization objective. The Markov decision process model of the optimization objective is represented by a triple To describe, is the state space, is the action space, is the reward function.

[0109] For each step t (t = 1, 2, ..., T), the state s t By Collection Composition, where P max is the total power, are path losses.

[0110] The action space in each time slot is represented as a t =κ, where κ is the power allocation coefficient.

[0111] The reward in a time slot is Indicates the average secure communication rate.

[0112] The process of generating the optimal power allocation solution is as follows:

[0113] DRL adopts the PPO (Proximal Policy Optimization) strategy, and GDM replaces the action network in DRL. GDM generates the optimal power allocation plan by denoising the initial distribution. In the training phase, the denoising network and the evaluation network are initialized. For each round, GDM uses Gaussian noise as input, samples actions in the denoising network, denoises the input, and generates an initial power allocation plan. The generated power allocation plan is rewarded, and the parameters of the denoising network and the evaluation network are updated to complete a training. This iteration is repeated. When the difference between the output results of the denoising network and the evaluation network is close to 0, it means that the denoising network has converged. In the inference phase, the trained denoising network is used to generate the optimal power allocation for a given initial state to maximize the average secure communication rate.

[0114] The deep reinforcement learning method combined with GDM is to maximize the value of the generated solution output by training the denoising network. GDM is better at incorporating conditional information into the denoising process, such as wireless environment information such as path loss and small-scale fading channel parameters. After sufficient training, the denoising network can generate the optimal solution under any dynamic wireless environment conditions.

[0115] The present invention also discloses a RIS-based confidentiality capacity and low detection probability joint optimization system for executing the above method. The optimization system includes the following modules:

[0116] Joint communication system model building module: build a joint communication system model based on RIS confidentiality capacity and low detection probability;

[0117] Channel statistical information determination module: based on the constructed joint communication system model, determine the channel statistical information of each link in the model;

[0118] Analytical formula derivation module: analyzes the confidentiality capacity and the false detection probability, and derives the analytical formula of the average confidentiality capacity and the average false detection probability;

[0119] Optimization problem construction module: Taking the total power of the transmitter and the jammer as the constraint condition and the power allocation as the optimization variable, the optimization problem of maximizing the secure communication rate in the covert communication system is constructed;

[0120] Optimization target solving module: The optimization target is solved by combining the generative diffusion model GDM with deep reinforcement learning DRL.

[0121] Compared with the prior art, the present invention has the following beneficial effects:

[0122] Aiming at the joint optimization problem of confidentiality capacity and low detection probability, the present invention considers the performance optimization of the covert communication system under imperfect CSI conditions, increases the confidentiality capacity of the system while enhancing the link concealment, and provides double protection for system security. BRIEF DESCRIPTION OF THE DRAWINGS

[0123] Figure 1 It is a schematic diagram of a system model involved in a preferred embodiment of the present invention.

[0124] Figure 2 It is a schematic diagram of the variation of the receiving end rate, eavesdropper rate and confidentiality capacity with the transmitting end power when the maximum power of the fixed jammer is 10dBm provided by the preferred embodiment of the present invention.

[0125] Figure 3 It is a schematic diagram of the variation of the receiving end rate, the eavesdropper rate and the confidentiality capacity with the total power when the fixed power allocation coefficient is 0.5 provided by the preferred embodiment of the present invention.

[0126] Figure 4 It is a schematic diagram of the changes of the receiving end rate, the eavesdropper rate and the confidentiality capacity with the power allocation coefficient under a fixed total power of 10dBm provided by the preferred embodiment of the present invention.

[0127] Figure 5 It is a block diagram of a confidentiality capacity and low detection probability joint optimization system based on RIS according to a preferred embodiment of the present invention. DETAILED DESCRIPTION

[0128] The preferred embodiments of the present invention are described in detail below with reference to the accompanying drawings.

[0129] like Figure 1 As shown, the present embodiment is a joint optimization method of confidentiality capacity and low detection probability based on RIS, which is applicable to a covert communication system including a transmitter, a jammer, a RIS, a receiver and an eavesdropper. The optimization method includes the following steps:

[0130] Step 1: Construct a joint communication system model based on RIS with confidentiality capacity and low detection probability;

[0131] Step 2: Based on the system model in step 1, determine the channel statistics of each link in the model;

[0132] Step 3: Based on step 1 and step 2, analyze the confidentiality capacity and the false detection probability, and derive the analytical formulas of the average confidentiality capacity and the average false detection probability;

[0133] Step 4: Taking the total power of the transmitter and the jammer as the constraint and the power allocation as the optimization variable, construct an optimization problem to maximize the secure communication rate in the covert communication system;

[0134] Step 5: Since the optimization problem is non-convex, the optimization objective is solved by combining GDM (Generative Diffusion Model) and DRL (Deep Reinforcement Learning).

[0135] In this embodiment, step 1 is specifically implemented as follows:

[0136] A joint communication system model with confidentiality capacity and low detection probability based on RIS is constructed, which specifically includes three parts: mathematical model of RIS reflection matrix, channel model and signal model.

[0137] RIS consists of N reflection units, and each reflection unit is independent. Therefore, the reflection coefficient matrix of RIS can be expressed as a diagonal matrix in the form of:

[0138]

[0139] Among them, β n ∈[0,1] is the amplitude reflection coefficient of the nth element, θ n ∈[0, 2π) is the phase shift variable of the nth element.

[0140] For the channel model, the fading coefficients between the transmitter, jammer, receiver, eavesdropper, and RIS are expressed as h AR 、h JR 、h RB 、h RW , the fading coefficient vector shape is N×1, and both follow the Nakagami-m fading model. The path loss exponents are expressed as α AR , α JR , α RB , α RW For the two links of sender-RIS-receiver and jammer-RIS-receiver, the sender can obtain its instantaneous CSI. However, for the RIS-eavesdropper link, considering the actual situation, the sender can only obtain its statistical CSI, and the eavesdropper has its instantaneous CSI.

[0141] For the signal model, the signal sent by the transmitter and the signal sent by the jammer are modeled as:

[0142]

[0143] Among them, P A and P J are the transmit power of the transmitter and the jammer respectively, s A (k)(E(|s A (k)| 2)=1) is the information sent by the sender to the receiver, s J (k)(E(|s J (k)| 2 )=1) is the interference information sent by the jammer. J It obeys uniform distribution, and its probability density function is:

[0144]

[0145] Combining the channel fading coefficient, path loss and RIS reflection coefficient matrix, the expression of the received signal at the receiving end can be obtained:

[0146]

[0147] in, represents the path loss. And

[0148] in d χ represents the distance, α χ is the path loss index, and χ∈{AR, JR, RB, RW}, AR, JR, RB, RW are specific paths, such as Figure 1 Example shown. AR is the sender-RIS path, JR is the jammer-RIS path, RB is the RIS-receiver path, and RW is the RIS-eavesdropper path. B (k) is the additive white Gaussian noise at the receiving end.

[0149] According to formula (4), the SINR (Signal to Interference Plus Noise Ratio) at the receiving end is expressed as:

[0150]

[0151] Wherein, ρ∈[0, 1] represents the self-interference cancellation coefficient.

[0152] The eavesdropper faces a binary detection problem: 1) Testing the hypothesis Indicates that there is no communication between the sender and the receiver; 2) Alternative hypothesis Indicates that the sender is sending a message to the receiver.

[0153] Under the two assumptions, the received signal is modeled as:

[0154]

[0155] in, n W(k) is the additive Gaussian white noise of the eavesdropper. When the alternative hypothesis When established, the eavesdropper's SINR is expressed as:

[0156]

[0157] Based on formulas (6) and (7), the eavesdropper will calculate the average power received Perform binary detection, and the decision rules are:

[0158]

[0159] Where τ is the binary detection threshold, and Respectively, it is beneficial to and judgment.

[0160] Assume that the eavesdropper performs binary detection on an infinite number of signal samples, that is, K→∞. Therefore, there is no uncertainty in sending signals and receiving noise. The average power of the eavesdropper is given by:

[0161]

[0162] in, in, is Gaussian white noise.

[0163] In this embodiment, step 2 is specifically implemented as follows:

[0164] Step 2-1: For the transmitter-RIS-receiver link, adjust the RIS parameters to provide the best channel quality for the receiver. The channel gain of the transmitter-RIS-receiver link is as follows:

[0165]

[0166] Among them, h RB，n and h AR，n h RB and h AR The nth element of .

[0167] By adjusting all phase shift variables θ n =(n=1, 2, ..., N), the channel gain can be maximized. There is a The determined generalized solution can make the phases of the various channel gain terms consistent, thereby maximizing the overall channel gain, where is an arbitrary constant in the range [0, 2π). Set the optimal phase shift After that, we get the following formula:

[0168]

[0169] in, Without loss of generality, assuming that the fading coefficient of the transmitter-RIS-receiver link follows the Nakagami-m distribution, when the number of reflection elements N is large enough, the variable Follows non-central chi-square distribution in Its probability density function and distribution function are expressed as:

[0170]

[0171] and

[0172]

[0173] Step 2-2: For the transmitter-RIS-eavesdropper, jammer-RIS-receiver, and jammer-RIS-eavesdropper links, the phase shift of the RIS is considered random. Therefore, when N is large enough and {θ n} Random, variable and tends to be a complex Gaussian random variable with mean zero and variance N, and follows the distribution Thus, the variable The probability density function and distribution function of are expressed as:

[0174]

[0175] and

[0176]

[0177] In this embodiment, step 3 is specifically implemented as follows:

[0178] Step 3-1, the eavesdropper's DEP (Detection Error Probility) is expressed as:

[0179]

[0180] in, is the false alarm probability, is the probability of missed detection. Furthermore, ξ = 0 indicates that the eavesdropper can completely detect the covert communication, and ξ = 1 indicates that the covert communication is completely random to the eavesdropper.

[0181] According to equations (9) and (10), under a fixed detection threshold τ, the expressions of false alarm probability and missed detection probability can be obtained as follows:

[0182]

[0183] and

[0184]

[0185] Furthermore, by substituting formula (3) into formula (18) and formula (19), we can obtain their specific expressions, which are:

[0186]

[0187] and

[0188]

[0189] Among them, τ1=ζ2, τ3=ζ3,

[0190] According to equations (20) and (21), we can get the expression of DEP under a fixed threshold, which can be divided into two cases. When τ2≤τ3, we have:

[0191]

[0192] When τ2>τ3, we have:

[0193]

[0194] The above DEP is derived based on a fixed threshold. However, eavesdroppers usually adjust the threshold to achieve the minimum DEP, and it is necessary to analyze the system performance in the worst case. The minimum DEP in the two cases can be obtained from equations (22) and (23), namely:

[0195]

[0196] Step 3-2: The confidentiality capacity is the difference in channel capacity between the receiver and the eavesdropper. According to Shannon's theorem, the confidentiality capacity of the system can be obtained as:

[0197] R C =[R B -R W ] + =[log2(1+ψ B )-log2(1+ψ W )] + (25)

[0198] Since RIS provides the maximum channel gain for the receiver and the gains of each channel are independent of each other, the probability that the SINR of the receiver is less than the SINR of the eavesdropper is close to zero, so the average confidentiality capacity can be approximated as:

[0199]

[0200] Since the jammer is controlled by the transmitter, the effect of the jammer on the receiver can be ignored, that is, ρ = 0, and the ergodic rate of the receiver can be expressed as:

[0201]

[0202] in, Substituting equation (13) into equation (27) and combining it with Gauss-Laguerre numerical integration, we can obtain:

[0203]

[0204] Where u1 is the order of the Gauss-Laguerre polynomial, x 1，l is the Laguerre polynomial The lth root of is the lth weight, Φ1 is the integrand, that is:

[0205]

[0206] The traversal rate of the eavesdropper under the alternative hypothesis can be expressed as:

[0207]

[0208] in, Substituting equation (3) and equation (15) into equation (30) and combining with Gauss-Laguerre numerical integration, we can obtain:

[0209]

[0210] in, u2 is the order of the Gauss-Laguerre polynomial, x 2，l is the Laguerre polynomial The lth root of is the lth weight, Φ2 is the integrand, that is:

[0211]

[0212] in,

[0213] Substituting equation (28) and equation (31) into equation (26), the average confidentiality capacity can be approximated as:

[0214]

[0215] Step 3-3: Based on the above, the definition of secure communication rate is further given. The secure communication rate, that is, the sum of the communication rates within the confidentiality capacity or outside the confidentiality capacity but concealed, can be expressed as:

[0216] R S =R C +ξ * R W (34)

[0217] Among them, ξ * R W =ξ * (R B -R C ). The average secure communication rate expression is as follows:

[0218]

[0219] in,

[0220] In this embodiment, step 4 is specifically implemented as follows:

[0221] The optimization goal is to maximize the average secure communication rate by optimizing the power distribution between the transmitter and the jammer's transmission power. The optimization problem can be constructed as follows:

[0222]

[0223] Among them, P max is the total power limit.

[0224] Since the average secure communication rate increases with P A As it increases, the average secure communication rate can be maximized only when the constraint equation holds. Therefore, equation (36) can be transformed as follows:

[0225]

[0226] in, is the power allocation coefficient.

[0227] In this embodiment, step 5 is specifically implemented as follows:

[0228] The closed-form expression of the average secure communication rate is relatively complex, and it is difficult to directly obtain the optimal solution under the constraints. Therefore, it is considered to use a combination of GDM and DRL to solve the optimization objective. The Markov decision process model of the optimization objective is represented by a triple To describe, is the state space, is the action space, is the reward function.

[0229] For each step t (t = 1, 2, ..., T), the state s t By Collection Composition, among which is the average secure communication rate.

[0230] The action space in each time slot is represented as a t =κ, where κ is the power allocation coefficient.

[0231] The reward in a time slot is Indicates the average secure communication rate.

[0232] The process of generating the optimal power allocation solution is as follows:

[0233] DRL adopts the PPO (Proximal Policy Optimization) strategy, and GDM replaces the action network in DRL. GDM generates the optimal power allocation plan by denoising the initial distribution. In the training phase, the denoising network and the evaluation network are initialized. For each round, GDM uses Gaussian noise as input, samples actions in the denoising network, denoises the input, and generates an initial power allocation plan. The generated power allocation plan is rewarded, and the parameters of the denoising network and the evaluation network are updated to complete a training. This iteration is repeated. When the difference between the output results of the denoising network and the evaluation network is close to 0, it means that the denoising network has converged. In the inference phase, the trained denoising network is used to generate the optimal power allocation for a given initial state to maximize the average secure communication rate.

[0234] The deep reinforcement learning method combined with GDM is to maximize the value of the generated solution output by training the denoising network. GDM is better at incorporating conditional information into the denoising process, such as wireless environment information such as path loss and small-scale fading channel parameters. After sufficient training, the denoising network can generate the optimal solution under any dynamic wireless environment conditions.

[0235] Figure 2 These are the simulation results and analysis results of equations (28), (31), and (33) when the jammer power is fixed at 10 dBm. The simulation results fit the analysis results well.

[0236] Figure 3 These are the simulation results and analysis results of equations (28), (31), and (33) when the power allocation coefficient is fixed at 0.5. The simulation results fit the analysis results well.

[0237] Figure 4 These are the simulation results and analysis results of equations (28), (31), and (33) at a fixed total power of 10 dBm. The simulation results fit the analysis results well.

[0238] like Figure 5As shown, this embodiment discloses a RIS-based confidentiality capacity and low detection probability joint optimization system, which is used to execute the above method embodiment, and includes the following modules:

[0239] Joint communication system model building module: build a joint communication system model based on RIS confidentiality capacity and low detection probability;

[0240] Channel statistical information determination module: based on the constructed joint communication system model, determine the channel statistical information of each link in the model;

[0241] Analytical formula derivation module: analyzes the confidentiality capacity and the false detection probability, and derives the analytical formula of the average confidentiality capacity and the average false detection probability;

[0242] Optimization problem construction module: Taking the total power of the transmitter and the jammer as the constraint condition and the power allocation as the optimization variable, the optimization problem of maximizing the secure communication rate in the covert communication system is constructed;

[0243] Optimization target solving module: The optimization target is solved by combining the generative diffusion model GDM with deep reinforcement learning DRL.

[0244] For other contents of this embodiment, please refer to the above method embodiment.

[0245] The preferred embodiments and principles of the present invention are described in detail above. For those skilled in the art, according to the ideas provided by the present invention, there may be changes in the specific implementation methods, and these changes should also be regarded as the protection scope of the present invention.

Claims

1. A joint optimization method of confidentiality capacity and low detection probability based on RIS is applicable to a covert communication system including a transmitter, a jammer, a RIS, a receiver and an eavesdropper, and is characterized in that: The optimization method comprises the following steps: Step 1: Construct a joint communication system model based on RIS's confidentiality capacity and low detection probability; Step 2: Based on the joint communication system model of step 1, determine the channel statistics of each link in the model; Step 3: Analyze the confidentiality capacity and the false detection probability, and derive the analytical formulas of the average confidentiality capacity and the average false detection probability; Step 4: Taking the total power of the transmitter and the jammer as the constraint condition and the power allocation as the optimization variable, an optimization problem of maximizing the secure communication rate in the covert communication system is constructed; Step 5: Use the generative diffusion model GDM combined with deep reinforcement learning DRL to solve the optimization objective.

2. The RIS-based joint optimization method for confidentiality capacity and low detection probability as claimed in claim 1, characterized in that: Step 1 is as follows: A joint communication system model based on RIS confidentiality capacity and low detection probability is constructed, which includes three parts: mathematical model of RIS reflection matrix, channel model and signal model; RIS consists of N reflection units, and each reflection unit is independent; therefore, the reflection coefficient matrix of RIS is expressed as a diagonal matrix in the form of: Among them, e is a natural constant, β n ∈[0,1] is the amplitude reflection coefficient of the nth element, θ n ∈[0,2π] is the phase shift variable of the nth element; For the channel model, the fading coefficients between the transmitter, jammer, receiver, eavesdropper, and RIS are expressed as h AR 、h JR 、h RB 、h RW , the fading coefficient vector shape is N×1, and both follow the Nakagami-m fading model. The path loss exponents are expressed as α AR , α JR , α RB , α RW ; For the two links of sender-RIS-receiver and jammer-RIS-receiver, the sender obtains the instantaneous channel state information CSI; for the RIS-eavesdropper link, the sender can only obtain the statistical CSI, and the eavesdropper has the instantaneous CSI; For the signal model, the signal sent by the transmitter and the signal sent by the jammer are modeled as: Among them, K is the number of signal samples, P A and P J are the transmit power of the transmitter and the jammer respectively, s A (k)(E(|s A (k)| 2 )=1) is the information sent by the sender to the receiver, s J (k)(E(|s J (k)| 2 )=1) is the interference information sent by the jammer; P J It obeys uniform distribution, and the probability density function is: Where x is the probability density function The independent variable; is the upper limit of uniform distribution, that is, the maximum value that the jammer power can reach; Combining the channel fading coefficient, path loss and RIS reflection coefficient matrix, the expression of the received signal at the receiving end is obtained: in, represents the path loss; and in d χ represents the distance, α χ is the path loss index, and χ∈{AR, JR, RB, RW}; n B (k) is the additive white Gaussian noise at the receiving end; According to formula (4), the signal to interference and noise ratio SINR at the receiving end is expressed as: in, is the variance of the additive Gaussian white noise at the receiving end, ρ∈[0,1] represents the self-interference elimination coefficient; The eavesdropper faces a binary detection problem: 1) Test the hypothesis Indicates that there is no communication between the sender and the receiver; 2) Alternative hypothesis Indicates that the sender is sending a message to the receiver; based on the two assumptions, the received signal is modeled as: in, n W (k) is the additive Gaussian white noise of the eavesdropper; when the alternative hypothesis When established, the eavesdropper's SINR is expressed as: Based on formulas (6) and (7), the eavesdropper can calculate the average power received For binary detection, the decision rule is: Where τ is the binary detection threshold, and Respectively, it is beneficial to and judgment; Assume that the eavesdropper performs binary detection on an infinite number of signal samples, that is, K→∞; the average power of the eavesdropper is given by the following formula: in, in, is Gaussian white noise.

3. The RIS-based joint optimization method for confidentiality capacity and low detection probability as claimed in claim 2, characterized in that: Step 2 is as follows: Step 2-1: The channel gain of the transmitter-RIS-receiver link is as follows: Among them, h RB，n and h AR，n h RB and h AR The nth element of ; By adjusting all phase shift variables θ n , n=1,2,...,N, to maximize the channel gain; there exists a The generalized solution determined by the algorithm makes the phases of the channel gain terms consistent, thereby maximizing the overall channel gain, where is any constant in the range [0, 2π); sets the optimal phase shift After that, we get the following formula: in, Without loss of generality, assume that the fading coefficient of the transmitter-RIS-receiver link follows the Nakagami-m distribution. When the number of reflection elements N is large enough, the variable Follows non-central chi-square distribution in m AB and m RB are the parameters of Nakagami-m distribution on path AR and path RB respectively; the probability density function and distribution function are expressed as: and Where Γ is the gamma function, i is the subscript of the summation symbol, and x is the function variable; Step 2-2: When N is large enough and {θ n } Random, variable and tends to be a complex Gaussian random variable with mean zero and variance N, and follows the distribution variable The probability density function and distribution function of are expressed as: and 4. The RIS-based joint optimization method for confidentiality capacity and low detection probability as claimed in claim 3, characterized in that: Step 3 is as follows: Step 3-1, the detection error probability DEP of the eavesdropper is expressed as: in, is the false alarm probability, is the probability of missed detection; ξ = 0 means that the eavesdropper can completely detect the covert communication, and ξ = 1 means that the covert communication is completely random to the eavesdropper; According to equations (9) and (10), under a fixed detection threshold τ, the expressions of false alarm probability and missed detection probability are obtained as follows: and Substituting formula (3) into formula (18) and formula (19), we can obtain their specific expressions, which are: and Among them, τ1=ζ2, τ3=ζ3, According to equations (20) and (21), the expression of DEP under a fixed threshold is obtained, which can be divided into two cases. When τ2≤τ3, we have: When τ2>τ3, we have: The minimum DEP in the two cases is obtained from equations (22) and (23), namely: Step 3-2: The confidentiality capacity is the difference between the channel capacity of the receiving end and the eavesdropper. According to Shannon's theorem, the confidentiality capacity of the system is: R C =[R B -R W ]+=[log2(+ψ B )-log2(1+ψ W )] + (25) Among them, R B =log2(1+ψ B ) is the channel capacity at the receiving end, R W =log2(1+ψ W ) is the channel capacity of the eavesdropper; The average confidentiality capacity is approximately: ρ=0, then the traversal rate at the receiving end is expressed as: in, Substituting equation (13) into equation (27) and combining it with Gauss-Laguerre numerical integration, we can obtain: Where u1 is the order of the Gauss-Laguerre polynomial, x 1，l is the Laguerre polynomial The lth root of is the lth weight, Φ1 is the integrand, that is: The ergodic rate of the eavesdropper under the alternative hypothesis is expressed as: in, Substituting equation (3) and equation (15) into equation (30), and combining with Gauss-Laguerre numerical integration, we obtain: in, u2 is the order of the Gauss-Laguerre polynomial, x 2,l is the Laguerre polynomial The lth root of is the lth weight, φ2 is the integrand, that is: in, Substituting equations (28) and (31) into equation (26), the average confidentiality capacity is approximated as: Step 3-3: The secure communication rate, i.e., the sum of the communication rates within the confidentiality capacity or outside the confidentiality capacity but concealed, is expressed as: R S =R C +ξ*R W (34) Among them, ξ * R W =ξ * (R B -R C ); the average secure communication rate expression is as follows: in, 5. The RIS-based joint optimization method for confidentiality capacity and low detection probability as claimed in claim 4, characterized in that: Step 4 is as follows: The optimization problem is formulated as follows: Among them, P max is the total power limit; Transform formula (36) as follows: in, is the power allocation coefficient.

6. The RIS-based joint optimization method for confidentiality capacity and low detection probability as claimed in claim 5, characterized in that: Step 5 is as follows: The Markov decision process model of the optimization objective is constructed through a triple To describe, is the state space, is the action space, is the reward function; For each step t (t = 1, 2, ..., T), the state s t By Collection Composition, where P max is the total power, All are path losses; The action space in each time slot is represented as a t =k, where k is the power allocation coefficient; The reward in a time slot is represents the average secure communication rate; The process of generating the optimal power allocation solution is as follows: GDM generates the best power allocation plan by denoising the initial distribution. In the training phase, the denoising network and the evaluation network are initialized. For each round, GDM uses Gaussian noise as input, samples actions in the denoising network, denoises the input, and generates an initial power allocation plan. The generated power allocation plan is rewarded, and the parameters of the denoising network and the evaluation network are updated to complete a training. This is repeated iteratively. When the difference between the output results of the denoising network and the evaluation network is close to 0, it means that the denoising network has converged. In the inference phase, the trained denoising network is used to generate the best power allocation for a given initial state to maximize the average secure communication rate. The deep reinforcement learning method combined with GDM maximizes the value of the generated solution output by training the denoising network.

7. A RIS-based joint optimization system for confidentiality capacity and low detection probability, used to execute the method according to any one of claims 1 to 6, characterized in that: The optimization system includes the following modules: Joint communication system model building module: build a joint communication system model based on RIS confidentiality capacity and low detection probability; Channel statistical information determination module: based on the constructed joint communication system model, determine the channel statistical information of each link in the model; Analytical formula derivation module: analyzes the confidentiality capacity and the false detection probability, and derives the analytical formula of the average confidentiality capacity and the average false detection probability; Optimization problem construction module: Taking the total power of the transmitter and the jammer as the constraint condition and the power allocation as the optimization variable, the optimization problem of maximizing the secure communication rate in the covert communication system is constructed; Optimization target solving module: The optimization target is solved by combining the generative diffusion model GDM with deep reinforcement learning DRL.

Images