A passive hybrid covert communication method and system based on RIS

Abstract

The application relates to the technical field of wireless communication, and provides a kind of passive hybrid concealment communication method and system based on RIS, which includes the following steps: step one: constructing a multi-user concealment communication system;Step two: constructing the signal model of the main user and the secondary user, obtaining the signal-to-interference-and-noise ratio of the main user and the secondary user according to the signal model, and obtaining the user rate under the limited block length according to the signal-to-interference-and-noise ratio;Step three: constructing the signal model and binary hypothesis model of the eavesdropper Willie;Step four: establishing an optimization model with the optimization goal of maximizing the worst secondary user's concealment rate;Step five: introducing auxiliary variables, alternating optimization algorithm, semi-positive relaxation algorithm and Gaussian randomization method to convert the non-convex optimization problem into a convex optimization problem for solving, and using MM algorithm and alternating direction multiplier method (ADMM) to solve the problem with low complexity.The application can better guarantee the communication quality of the main user and the concealment transmission of the secondary user.

Description

Technical Field

[0001] This invention relates to the field of wireless communication technology, and more specifically, to a RIS-based active-passive hybrid covert communication method and system. Background Technology

[0002] As an emerging ultra-low-power communication paradigm, backscatter communication technology can absorb energy from radio frequency sources in the environment and adjust its own antenna reflection coefficient by switching antenna impedance. It then uses different reflection coefficients to reflect the incident signal and perform amplitude modulation for passive information transmission. However, due to the multiplicative fading effect, the backscattered signal received by the receiver is weak, limiting communication performance. In recent years, reconfigurable intelligent surfaces (RIS) have received widespread attention in the field of wireless communication. RIS can change the direction of the incident signal and perform passive beamforming through its numerous passive reflection elements, reshaping the wireless channel environment and bringing multipath gain. Due to the similar mechanism between backscattering and RIS, RIS-based backscattering technology (RIS-BackCom) uses RIS to replace the backscattering device (BD) in the original backscattering system. Because it can overcome the multiplicative fading effect and improve the backscattered signal strength through passive beamforming, it has been widely studied in recent years.

[0003] Both BackCom and RIS-BackCom, limited by device costs, can only perform simple signal tuning, failing to guarantee the security of information transmission and posing a significant risk of detection. Covert communication technology can achieve secure information transmission by concealing the information transmission itself. Common methods for achieving covert communication include beamforming, artificial scrambling, and signal masking. However, artificial scrambling degrades system communication performance and introduces additional power overhead, making it unsuitable for backscatter communication technologies designed for low-power communication. Therefore, increasing research is considering using beamforming and signal masking to achieve covert communication in backscatter communication systems.

[0004] For example, some scholars have considered jointly optimizing the base station beamforming vector and the passive beamforming of the reflector to achieve covert transmission of backscattered information. Others have considered partitioning the reflector, with one region reflecting the incident signal to serve a primary user, and another region tuning the incident signal for backscattering to serve a secondary user. Considering that base stations have stronger signal processing capabilities and can encrypt the signal before transmission, the base station signal serving the primary user can be used as a common signal to mask the backscattered signal and achieve covert information transmission. Still others have considered partitioning the reflector, with one passive region reflecting the incident signal to serve a primary user, and another active region backscattering to serve a secondary user, again using the base station signal as a common signal to mask the backscattered information transmission.

[0005] However, existing technologies still have the following drawbacks:

[0006] (1) The existing RIS-BackCom lacks a combination of active and passive beamforming and signal masking for covert communication. Using multiple applicable covert communication technologies in the system can further improve its covertness.

[0007] (2) Existing research on covert communication in RIS-BackCom lacks modeling and analysis in the case of multiple users. RIS contains a large number of reflection or modulation units that should serve as many users as possible to improve spectral efficiency. In addition, the richer spectral environment of multi-user systems can bring stronger signal masking to covert users. Summary of the Invention

[0008] The present invention provides a RIS-based active-passive hybrid covert communication method and system, which can overcome some or all of the defects of the prior art.

[0009] According to the present invention, a RIS-based active-passive hybrid covert communication method includes the following steps:

[0010] Step 1: Construct a multi-user covert communication system, which includes a multi-antenna transmitter Alice, RIS, K single-antenna master users PUs, M single-antenna slave users SUs, and an eavesdropper Willie;

[0011] Step 2: Construct signal models for the primary and secondary users, obtain the signal-to-interference-plus-noise ratio (SINR) for the primary and secondary users based on the signal models, and obtain the user rate under a finite block length based on the SINR.

[0012] Step 3: Construct the signal model and binary hypothesis model of the eavesdropper Willie. Consider the worst case, that is, Willie can achieve optimal detection every time according to the maximum likelihood ratio test. Calculate Willie's detection error probability and use KL divergence to find the lower bound of the detection error probability to construct a hidden constraint.

[0013] Step 4: Establish an optimization model with the goal of maximizing the covert rate of the worst secondary user. The constraints include Alice power constraints, primary user QoS constraints, secondary user covert constraints, and RIS constant mode constraints. By jointly optimizing the base station beamforming vector and RIS phase shift matrix, the covert rate of the worst secondary user is maximized, thus achieving covert communication for all secondary users.

[0014] Step 5: Introduce auxiliary variables, alternating optimization algorithm, positive semidefinite relaxation algorithm and Gaussian randomization method to transform the non-convex optimization problem into a convex optimization problem for solution. Use MM algorithm and alternating direction multiplier method ADMM to solve the problem with low complexity.

[0015] As a preferred embodiment, in step one, the multi-antenna transmitter Alice is used to actively transmit signals. The RIS transmits signals to the active user by reflecting Alice through cell division, and at the same time, it sends its own passive information, i.e., covert information, to the passive user using backscattering technology. The eavesdropper Willie judges whether the RIS is transmitting its own covert information by the power of the received signal.

[0016] Preferably, in step one, the multi-antenna transmitter Alice sends information to k master users using beamforming technology. The transmitted signal is represented as follows:

[0017]

[0018] Where x is the signal transmitted by transmitter Alice, l∈{1,…,L} represents the l-th signal observation, and L is the maximum number of signal observations allowed in a time slot; the signal of the k-th user is represented by... It means that among them This represents a complex Gaussian distribution with mean x and variance y; S represents the beamforming vector of the k-th user. t The number of transmitter antennas, Let K be a complex matrix space; K represents the total number of users.

[0019] As a preferred option, in step two, the signal model is:

[0020] All primary and secondary users will simultaneously receive the signal reflected by the RIS and the signal transmitted by the RIS via backscattering, both emitted by transmitter Alice. However, the direct link between the primary and secondary users and Alice is blocked by an obstacle. The signal y received by the k-th primary user... p,k [l] is represented as:

[0021]

[0022] Where PB This refers to the transmission power of the transmitter Alice. Let H be the Rayleigh channel response between RIS and the k-th primary user, and H denote the conjugate transpose operation. The Rayleigh channel response between Alice and RIS. For the noise received by the k-th primary user, This corresponds to the noise power; Let N be the RIS phase shift matrix and N be the total number of RIS units; in Let n be the reflection matrix. r This represents the number of RIS reflection units; Let n be the modulation matrix of the m-th sub-user, where n t The number of RIS modulation units serving each secondary user and n r +mn t =N, α is the reflection efficiency, C m The information bits corresponding to the m-th secondary user; the signal-to-interference-plus-noise ratio γ of the k-th primary user. p,k Represented as:

[0023]

[0024] in Considering the finite number of observations L, the achievable rate R of the k-th primary user is... p,k Represented as:

[0025]

[0026] Where δ>0 is the decoding error probability, Q -1 (.) represents the Gaussian Q-function;

[0027] The signal y received by the m-th secondary user s,m [l] is represented as:

[0028]

[0029] in For the noise received by the m-th secondary user, This corresponds to the noise power; Let be the Rayleigh channel response between RIS and the m-th sub-user; the signal-to-interference-plus-noise ratio (SINNR) of the m-th sub-user is expressed as:

[0030]

[0031] in The concealment rate R of the m-th sub-user s,m Represented as:

[0032]

[0033] As a preferred approach, in step three, the closed-form solution for detecting errors contains an incomplete gamma function. Therefore, the lower bound of the detection error probability is found using KL divergence, and a hidden constraint is constructed accordingly.

[0034] Preferably, in step three, Willie constructs a binary hypothesis model based on the received signal to determine whether RIS is transmitting covert information. The signal y received by Willie... w [l] is represented as:

[0035]

[0036] H0 indicates that RIS did not send covert information to the secondary user m; H1 indicates that RIS sent covert information to the secondary user m. For the noise received by Willie, This corresponds to the noise power; in Let H0 be the channel between the base station and Willie; based on the established signal model, the likelihood function under H1 is: in The false negative rate of eavesdroppers is expressed as The false alarm rate is expressed as For the eavesdropper's binary decision; among which The eavesdropper believed that the reflector was sending covert information to the secondary user m. Assuming the eavesdropper believes the reflector did not send any concealed information to the secondary user m, the total false detection probability ξ of the eavesdropper is obtained as follows:

[0037]

[0038] Where π0=π1=1 / 2 are the prior probabilities, and the assumption of equal probability is adopted; according to the Neyman-Pearson criterion, the eavesdropper uses the maximum likelihood ratio test to minimize the probability of detection error:

[0039]

[0040] Error detection probability P e The closed-form solution is obtained through calculation, thus constructing the hidden constraint P. e >1-∈, where ∈ is a preset value used to indicate the system's concealment; since P e The expression contains an incomplete gamma function, which complicates subsequent analysis and optimization. The lower bound of the hidden constraint is found using KL divergence as follows:

[0041]

[0042] in for arrive The KL divergence is used to construct a new hidden constraint.

[0043] As a preferred approach, in step four, for the RIS-based hybrid active-passive covert communication system, an optimization problem is constructed with the goal of maximizing the worst-case secondary user signal-to-noise ratio (SNR). The constraints include QoS constraints for the k primary users, power constraints for the transmitter Alice, covert constraints for the k secondary users, and constant-mode constraints for the reflector. By maximizing the worst-case secondary user SNR, effective reception by all secondary users in the multi-user communication system is guaranteed. Effective reception by all primary users is guaranteed by the primary user reachability rate constraint, effective transmission by the signal transmitter is guaranteed by the Alice power constraint, covert communication by the secondary user covert constraints, and signal reflection by the RIS constant-mode constraints. The final covert communication system optimization problem is shown below:

[0044]

[0045] |θ n |=1,n=1,…,N,

[0046] Constraint 1 is the primary user QoS constraint, R p,th The primary user rate threshold and constraint two are Alice power constraints, P max Given the maximum transmit power of transmitter Alice, constraint three is the secondary user concealment constraint, constraint four is the constant mode constraint of the reflector, and θ n The diagonal elements of Θ represent the phase shift of the nth RIS unit, where n∈{1,…,N}.

[0047] As a preferred option, the specific process in step five is as follows:

[0048] 1) Optimize the base station beamforming vector with a fixed phase shift matrix Θ. By introducing the auxiliary variable γ w Transform the max-min problem into a minimization problem and define... And for hidden constraints in exist Time about Monotonically increasing, therefore the hidden constraint is rewritten as an optimization problem, which is then rewritten as: Where η is the equation The solution is obtained by the bisection method; the final optimization problem is rewritten as:

[0049]

[0050] w H w≤P max ,

[0051]

[0052] in:

[0053]

[0054] Among them I K It is a K-dimensional identity matrix. For N t 3D identity matrix, e k For I K The k-th column vector, 1 K Let T be a K-dimensional unit column vector, and T denote the transpose operation. Since constraints one, two, and four are non-convex, consider using the MM method to transform the graph problem into a convex problem at fixed points, considering the following two functions:

[0055]

[0056] in Let represent the strictly positive real number space; find the convex upper bounds of the corresponding function at point x0 and (x0, y0) through a first-order Taylor expansion:

[0057]

[0058] in This represents the operation of taking the real part. Therefore, the optimization problem can be rewritten as:

[0059]

[0060] w H w≤P max ,

[0061]

[0062] At this point The optimization problem is a convex problem, which is solved by using a convex optimization toolkit.

[0063] 2) Fixed base station beamforming vector Optimize the phase shift matrix Θ by introducing the auxiliary variable -γ v The objective function max-min problem is transformed into a minimization problem, defined as v = diag(Θ). H The optimization problem is rewritten as follows:

[0064]

[0065] in:

[0066]

[0067] in The worst sub-user signal-to-interference-plus-noise ratio obtained after optimizing the base station beamforming vector;

[0068] Consider using the MM and ADMM optimization methods to decompose the optimization problem into a series of more manageable subproblems for iterative solution; by introducing auxiliary variables The augmented Lagrangian method is used to handle the constant modulus constraint, and the optimization problem is rewritten as follows:

[0069]

[0070] Fixed variables Optimization variables v, γ v Ignoring constraints and constant terms irrelevant to the optimization variables, the optimization problem can be written as:

[0071]

[0072] At a fixed point At this point, the optimization problem is a convex problem with respect to the variables;

[0073] Fixed variables With optimization results Optimize variables Ignoring constraints and constant terms irrelevant to the optimization variables, the optimization problem can be written as:

[0074]

[0075] The optimal solution to the optimization problem is directly obtained as Finally passed Update the dual variable μ.

[0076] This invention provides a RIS-based active-passive hybrid covert communication system, which employs the aforementioned RIS-based active-passive hybrid covert communication method.

[0077] The beneficial effects of this invention are as follows:

[0078] 1) This method proposes a hybrid active-passive covert communication method based on RIS. In a system with a multi-antenna transmitter Alice, multiple single-antenna master users, multiple single-antenna slave users, and a single eavesdropper Willie, covert communication is achieved using RIS. The objective is to maximize the minimum covert rate of the slave users. The constraints include Alice power constraints, master user QoS constraints, slave user covert constraints, and RIS constant mode constraints. By jointly optimizing the base station beamforming vector and the RIS phase shift matrix, the covert rate of the worst slave user is maximized, thus achieving covert communication for all slave users while ensuring the communication quality of the master user.

[0079] 2) This method considers user fairness. The constructed max-min optimization problem aims to maximize the minimum concealment rate of the secondary users, ensuring that all secondary users have a high concealment rate. Furthermore, considering the optimization of the complex non-convex problem, this method does not use the high-complexity semidefinite relaxation + Gaussian randomization method, but instead adopts a low-complexity optimization algorithm based on the MM algorithm and ADMM algorithm, effectively reducing the algorithm complexity.

[0080] 3) This method achieves covert information transmission between multiple secondary users by utilizing communication between multiple primary users in the system without incurring additional power overhead (such as using jammers), while ensuring communication security, low power consumption, and high spectral efficiency. Attached Figure Description

[0081] Figure 1 The flowchart in this example is an optimized version;

[0082] Figure 2 This is a schematic diagram illustrating the relationship between the maximum stealth rate achievable by the worst-case secondary user and the transmission power of the active transmitter Alice in the embodiment. Detailed Implementation

[0083] To further understand the content of this invention, a detailed description of the invention will be provided in conjunction with the accompanying drawings and embodiments. It should be understood that the embodiments are merely illustrative and not limiting of the invention.

[0084] Example

[0085] like Figure 1 As shown, this embodiment provides a RIS-based active-passive hybrid covert communication method, which includes the following steps:

[0086] Step 1: Construct a multi-user covert communication system. The system includes a multi-antenna transmitter Alice, RIS, K single-antenna primary users PUs, M single-antenna secondary users SUs, and an eavesdropper Willie. The multi-antenna transmitter Alice is used to actively transmit signals. RIS, through cell partitioning, reflects Alice's signals to the active users while simultaneously using backscattering technology to send its own passive information, i.e., covert information, to the passive users. The eavesdropper Willie determines whether RIS is transmitting its own covert information by the power of the received signal.

[0087] Alice, a multi-antenna transmitter, sends information to k primary users using beamforming technology. The transmitted signal is represented as follows:

[0088]

[0089] Where x is the signal transmitted by transmitter Alice, l∈{1,…,L} represents the l-th signal observation, and L is the maximum number of signal observations allowed in a time slot; the signal of the k-th user is represented by... It means that, among them This represents a complex Gaussian distribution with mean x and variance y; S represents the beamforming vector of the k-th user. t The number of transmitter antennas, Let K be a complex matrix space; K represents the total number of users.

[0090] Step 2: Construct signal models for the primary and secondary users, obtain the signal-to-interference-plus-noise ratio (SINR) for the primary and secondary users based on the signal models, and obtain the user rate under a finite block length based on the SINR.

[0091] The signal model is:

[0092] All primary and secondary users will simultaneously receive the signal reflected by the RIS and the signal transmitted by the RIS via backscattering, both emitted by transmitter Alice. However, the direct link between the primary and secondary users and Alice is blocked by an obstacle. The signal y received by the k-th primary user... p,k [l] is represented as:

[0093]

[0094] Where P B This refers to the transmission power of the transmitter Alice. Let H be the Rayleigh channel response between RIS and the k-th primary user, and H denote the conjugate transpose operation. The Rayleigh channel response between Alice and RIS. For the noise received by the k-th primary user, This corresponds to the noise power; Let N be the RIS phase shift matrix and N be the total number of RIS units; in Let n be the reflection matrix. r This represents the number of RIS reflection units; Let n be the modulation matrix of the m-th sub-user, where n t The number of RIS modulation units serving each secondary user and n r +mn t =N, α is the reflection efficiency, C m The information bits corresponding to the m-th secondary user; the signal-to-interference-plus-noise ratio γ of the k-th primary user. p,k Represented as:

[0095]

[0096] in Considering the finite number of observations L, the achievable rate R of the k-th primary user is... p,k Represented as:

[0097]

[0098] Where δ>0 is the decoding error probability, Q -1 (.) represents the Gaussian Q-function;

[0099] The signal y received by the m-th secondary user s,m [l] is represented as:

[0100]

[0101] in For the noise received by the m-th secondary user, This corresponds to the noise power; Let be the Rayleigh channel response between RIS and the m-th sub-user; the signal-to-interference-plus-noise ratio (SINNR) of the m-th sub-user is expressed as:

[0102]

[0103] in The concealment rate R of the m-th sub-user s,m Represented as:

[0104]

[0105] Step 3: Construct the signal model and binary hypothesis model of the eavesdropper Willie. Consider the worst case, that is, Willie can achieve optimal detection every time according to the maximum likelihood ratio test, and calculate Willie's detection error probability. The closed solution of the detection error contains an incomplete gamma function. Therefore, the upper bound of the detection error probability is found by using KL divergence, and the hidden constraint is constructed accordingly.

[0106] Willie constructs a binary hypothesis model based on the received signals to determine whether RIS is transmitting covert information. The signal Willie received is y. w [l] is represented as:

[0107]

[0108] H0 indicates that RIS did not send covert information to the secondary user m; H1 indicates that RIS sent covert information to the secondary user m. For the noise received by Willie, This corresponds to the noise power; in Let H0 be the channel between the base station and Willie; based on the established signal model, the likelihood function under H1 is: in The false negative rate of eavesdroppers is expressed as False alarm rate is expressed as For the eavesdropper's binary decision; among which The eavesdropper believed that the reflector was sending covert information to the secondary user m. Assuming the eavesdropper believes the reflector did not send any concealed information to the secondary user m, the total false detection probability ξ of the eavesdropper is obtained as follows:

[0109]

[0110] Where π0=π1=1 / 2 are the prior probabilities, and the assumption of equal probability is adopted; according to the Neyman-Pearson criterion, the eavesdropper uses the maximum likelihood ratio test to minimize the probability of detection error:

[0111]

[0112] Error detection probability P e The closed-form solution is obtained through calculation, thus constructing the hidden constraint P. e >1-∈, where ∈ is a preset value used to indicate the system's concealment; since P eThe expression contains an incomplete gamma function, which complicates subsequent analysis and optimization. The lower bound of the hidden constraint is found using KL divergence as follows:

[0113]

[0114] in for arrive The KL divergence is used to construct a new hidden constraint.

[0115] Step 4: Establish an optimization model with the goal of maximizing the covert rate of the worst secondary user. The constraints include Alice power constraints, primary user QoS constraints, secondary user covert constraints, and RIS constant mode constraints. By jointly optimizing the base station beamforming vector and RIS phase shift matrix, the covert rate of the worst secondary user is maximized, thus achieving covert communication for all secondary users and ensuring the communication quality of the primary user.

[0116] For a RIS-based hybrid active-passive covert communication system, an optimization problem is constructed with the goal of maximizing the worst-case signal-to-noise ratio (SNR) of the secondary users. Constraints include QoS constraints for k primary users, power constraints for the transmitter Alice, covert constraints for k secondary users, and constant-mode constraints for the reflector. By maximizing the worst-case SNR of the secondary users, effective reception by all secondary users in the multi-user communication system is guaranteed. Effective reception by all primary users is ensured by the primary user reachability constraint, effective transmission by the signal transmitter is guaranteed by the Alice power constraint, covert communication is guaranteed by the secondary user covert constraints, and signal reflection is guaranteed by the RIS constant-mode constraint. The final covert communication system optimization problem is shown below:

[0117]

[0118] |θ n |=1,n=1,…,N.

[0119] Constraint 1 is the primary user QoS constraint, R p,th The primary user rate threshold and constraint two are Alice power constraints, P max Given the maximum transmit power of transmitter Alice, constraint three is the secondary user concealment constraint, constraint four is the constant mode constraint of the reflector, and θ n The diagonal elements of Θ represent the phase shift of the nth RIS unit, where n∈{1,…,N}.

[0120] In step five, auxiliary variables, alternating optimization algorithm, positive semidefinite relaxation algorithm and Gaussian randomization method are introduced to transform the non-convex optimization problem into a convex optimization problem for solution. The MM algorithm and alternating direction multiplier method ADMM are used to solve the problem with low complexity.

[0121] The specific process is as follows:

[0122] 1) Optimize the base station beamforming vector with a fixed phase shift matrix Θ. By introducing the auxiliary variable γ w Transform the max-min problem into a minimization problem and define... And for hidden constraints in exist Time about Monotonically increasing, therefore the hidden constraint is rewritten as an optimization problem, which is then rewritten as: Where η is the equation The solution is obtained by the bisection method; the final optimization problem is rewritten as:

[0123]

[0124] w H w≤P max ,

[0125]

[0126] in:

[0127]

[0128] Where I K It is a K-dimensional identity matrix. For N t 3D identity matrix, e k For I K The k-th column vector, 1 K Let T be a K-dimensional unit column vector, and T denote the transpose operation. Since constraints one, two, and four are non-convex, consider using the MM method to transform the graph problem into a convex problem at fixed points, considering the following two functions:

[0129]

[0130] in Let represent the strictly positive real number space; find the convex upper bounds of the corresponding function at point x0 and (x0, y0) through a first-order Taylor expansion:

[0131]

[0132] in This represents the operation of taking the real part. Therefore, the optimization problem can be rewritten as:

[0133]

[0134] w H w≤P max ,

[0135]

[0136] At this point The optimization problem is a convex problem, which is solved by using a convex optimization toolkit.

[0137] 2) Fixed base station beamforming vector Optimize the phase shift matrix Θ by introducing the auxiliary variable -γ v The objective function max-min problem is transformed into a minimization problem, defined as v = diag(Θ). H The optimization problem is rewritten as follows:

[0138]

[0139] in:

[0140]

[0141] in The worst-case signal-to-interference-plus-noise ratio (SINR) for secondary users obtained after optimizing the base station beamforming vector;

[0142] Consider using the MM and ADMM optimization methods to decompose the optimization problem into a series of more manageable subproblems for iterative solution; by introducing auxiliary variables The augmented Lagrangian method is used to handle the constant modulus constraint, and the optimization problem is rewritten as follows:

[0143]

[0144] Fixed variables Optimize variables v, γ v Ignoring constraints and constant terms irrelevant to the optimization variables, the optimization problem can be written as:

[0145]

[0146] At a fixed point At this point, the optimization problem is a convex problem with respect to the variables;

[0147] Fixed variables With optimization results Optimize variables Ignoring constraints and constant terms irrelevant to the optimization variables, the optimization problem can be written as:

[0148]

[0149] The optimal solution to the optimization problem is directly obtained as Finally passed Update the dual variable μ. The optimization process flowchart is as follows: Figure 1 As shown.

[0150] This embodiment provides a RIS-based active-passive hybrid covert communication system, which adopts the above-mentioned RIS-based active-passive hybrid covert communication method.

[0151] This embodiment has the following advantages:

[0152] (i) This embodiment combines active and passive beamforming technology with common signal masking to further improve the system's stealth.

[0153] (ii) This embodiment has high spectrum utilization, and a single system can serve multiple primary and secondary users;

[0154] (III) This embodiment can solve the problem of multi-user network construction and multi-user collaborative optimization under resource constraints. This method proposes a hybrid active-passive covert communication method based on RIS. In a system with a multi-antenna transmitter Alice, multiple single-antenna primary users, multiple single-antenna secondary users, and a single eavesdropper Willie, covert communication is achieved using RIS. The objective is to maximize the lowest (worst) covert rate of the secondary users. The constraints include Alice power constraints, primary user QoS (Quality of Service) constraints, secondary user covert constraints, and RIS constant modulus constraints. By jointly optimizing the base station beamforming vector and the RIS phase shift matrix, the covert rate of the worst secondary user is maximized, thereby achieving covert communication for all secondary users and ensuring the communication quality of the primary user.

[0155] like Figure 2 The figure shows the trend of the worst-case achievable maximum stealth rate for the secondary user as the upper limit of the active transmitter Alice's transmit power changes, where: the optimization scheme adopted is:

[0156] The optimization scheme proposed in this embodiment maximizes the worst-case secondary user concealment rate by jointly optimizing the beamforming vector of the transmitter Alice and the RIS phase shift matrix.

[0157] Base station beamforming optimization: Only Alice beamforming is optimized, and RIS phase shift is randomly selected.

[0158] RIS phase shift optimization only: Only the RIS phase shift matrix is ​​optimized, and the Alice beam generation vector is randomly selected under the condition of satisfying the power constraint.

[0159] from Figure 2As can be seen from this, the optimization scheme proposed in this embodiment provides the best covert communication for secondary users.

[0160] The present invention and its embodiments have been described above illustratively. This description is not restrictive, and the figures shown are only one embodiment of the present invention; the actual structure is not limited thereto. Therefore, if those skilled in the art are inspired by this description and design similar structures and embodiments without departing from the spirit of the present invention, such designs should fall within the protection scope of the present invention.

Claims

1. A hybrid active-passive covert communication method based on RIS, characterized in that: Includes the following steps: Step 1: Construct a multi-user covert communication system, which includes a multi-antenna transmitter Alice, RIS, and K Single-antenna main user PUs, One single-antenna sub-user SUs and one eavesdropper Willie; Step 2: Construct signal models for the primary and secondary users, obtain the signal-to-interference-plus-noise ratio (SINR) for the primary and secondary users based on the signal models, and obtain the user rate under a finite block length based on the SINR. Step 3: Construct the signal model and binary hypothesis model of the eavesdropper Willie. Consider the worst case, that is, Willie can achieve optimal detection every time according to the maximum likelihood ratio test. Calculate Willie's detection error probability and use KL divergence to find the lower bound of the detection error probability to construct a hidden constraint. Step 4: Establish an optimization model with the goal of maximizing the covert rate of the worst secondary user. The constraints include Alice power constraints, primary user QoS constraints, secondary user covert constraints, and RIS constant mode constraints. By jointly optimizing the base station beamforming vector and RIS phase shift matrix, the covert rate of the worst secondary user is maximized, thus achieving covert communication for all secondary users. Step 5: Introduce auxiliary variables, alternating optimization algorithm, positive semidefinite relaxation algorithm and Gaussian randomization method to transform the non-convex optimization problem into a convex optimization problem for solution. Use MM algorithm and alternating direction multiplier method ADMM to solve the problem with low complexity.

2. The RIS-based active-passive hybrid covert communication method according to claim 1, characterized in that: In step one, the multi-antenna transmitter Alice is used to actively transmit signals. The RIS transmits signals to the active user by reflecting Alice through cell division, and at the same time, it sends its own passive information, i.e., covert information, to the passive user using backscattering technology. The eavesdropper Willie judges whether the RIS is transmitting its own covert information by the power of the received signal.

3. The RIS-based active-passive hybrid covert communication method according to claim 2, characterized in that: In step one, the multi-antenna transmitter Alice uses beamforming technology to transmit signals to… When a primary user sends a message, the signal sent is represented as follows: ； in The signal sent by transmitter Alice Indicates the first Secondary signal observation, The maximum number of signal observations allowed within a time slot; the first The signal of each user is used It means that among them The mean is The variance is The complex Gaussian distribution; Indicates the first Beamforming vectors for each user The number of transmitter antennas, It is a complex matrix space; This represents the total number of users.

4. The RIS-based active-passive hybrid covert communication method according to claim 3, characterized in that: In step two, the signal model is: All primary and secondary users will simultaneously receive the signal transmitted by transmitter Alice via RIS reflected signals and the signal transmitted by RIS via backscattering. However, the direct link between the primary and secondary users and Alice is blocked by an obstacle. Signals received by each main user Represented as: ； in This refers to the transmission power of the transmitter Alice. For RIS and the Rayleigh channel response between primary users This represents the conjugate transpose operation; The Rayleigh channel response between Alice and RIS. For the first Noise received by each primary user This corresponds to the noise power; The RIS phase shift matrix and This represents the total number of RIS units. ,in For the reflection matrix, This represents the number of RIS reflection units; ; For the first m The modulation matrices of the sub-users, where The number of RIS modulation units serving each secondary user and , For reflection efficiency, For the first m The information bits corresponding to the first secondary user; the first k Signal-to-interference-to-noise ratio of individual users Represented as: ； in , , Consider the number of observations Limited, the first The achievable rate for each primary user Represented as: ； in To decode the error probability, It is a Gaussian Q-function; No. m The signal received by the secondary user Represented as: ； in For the first m Noise received by each secondary user This corresponds to the noise power; For RIS and the m Rayleigh channel response between the secondary users; the first m The signal-to-interference-plus-noise ratio (SIR) of each secondary user is expressed as: ； in , ,;No. m The concealment rate of each secondary user Represented as:

5. The RIS-based active-passive hybrid covert communication method according to claim 4, characterized in that: In step three, the closed-form solution for detecting errors contains an incomplete gamma function. Therefore, the lower bound of the detection error probability is found using KL divergence, and a hidden constraint is constructed accordingly.

6. The RIS-based active-passive hybrid covert communication method according to claim 5, characterized in that: In step three, Willie constructs a binary hypothesis model based on the received signals to determine whether RIS is transmitting covert information. The signals Willie receives... Represented as: ； in RIS did not provide secondary users m Sending covert information; For RIS to secondary users m Sending covert information; For the noise received by Willie, This corresponds to the noise power; , ,in This is the channel between the base station and Willie; Based on the established signal model, we obtain... , The likelihood function under is , ;in , The false negative rate of eavesdroppers is expressed as The false alarm rate is expressed as , , For the eavesdropper's binary decision; among which The eavesdropper believed the reflector was pointing towards the secondary user. m Sending covert information, The eavesdropper believed that the reflector was not pointing towards the secondary user. m Sending covert information; This yields the total false detection probability of the eavesdropper. : ； in Assuming equal probability as the prior probability, the eavesdropper employs the maximum likelihood ratio test to minimize the probability of detection error, based on the Neyman-Pearson criterion. ； Error detection probability The closed-form solution is obtained through calculation, thus constructing the hidden constraints. ,in This is a preset value used to indicate the system's stealth; because The expression contains an incomplete gamma function, which complicates subsequent analysis and optimization. The lower bound of the hidden constraint is found using KL divergence as follows: ； for arrive The KL divergence is used to construct a new hidden constraint. .

7. The RIS-based active-passive hybrid covert communication method according to claim 6, characterized in that: In step four, for the RIS-based hybrid active-passive covert communication system, an optimization problem is constructed with the objective of maximizing the worst-case secondary user signal-to-noise ratio. The constraints include... QoS constraints for individual primary users, power constraints for the transmitter Alice. The optimization problem for the multi-user covert communication system is as follows: It addresses the concealment constraints of the secondary users and the constant mode constraints of the reflector. The optimization objective is to maximize the worst-case signal-to-interference-plus-noise ratio (SIR) of the secondary users, ensuring effective reception for all secondary users. The primary user reachability rate constraint ensures effective reception for all primary users, while the Alice power constraint ensures effective transmission by the signal transmitter. The covert communication system is further optimized by addressing the secondary user covert constraints and the RIS constant mode constraint, thus ensuring signal reflection. ； Constraint 1 is the primary user QoS constraint. The primary user rate threshold and constraint two are Alice power constraints. The maximum transmit power of the transmitter Alice is given by constraint 3, which is the concealment constraint for the secondary user, and constraint 4 is the constant mode constraint for the reflector surface. for Diagonal elements represent the first element. Phase shift of each RIS unit, .

8. The RIS-based active-passive hybrid covert communication method according to claim 7, characterized in that: Step five involves the following specific steps: 1) Fixed phase shift matrix Optimize base station beamforming vector ; By introducing auxiliary variables Transform the max-min problem into a minimization problem and define... And for hidden constraints ,in ,exist Time about Monotonically increasing, therefore the hidden constraint is rewritten as an optimization problem, which is then rewritten as: ;in For the equation The solution is obtained by the bisection method; the final optimization problem is rewritten as: ； in: ； in for 3D identity matrix for 3D identity matrix for The column vectors, for 1D unit column vector This represents the transpose operation; since constraints one, two, and four are non-convex, consider using the MM method to transform the graph problem into a convex problem at fixed points, considering the following two functions: ； in Represents the strictly positive real number space; find the corresponding function in the first-order Taylor expansion. Point and ( , The upper convex boundaries of the points are as follows: ； in (.) denotes the real part operation; therefore, the optimization problem can be rewritten as: ； At this point ( At point ), the optimization problem is a convex problem, which is solved using a convex optimization toolkit; 2) Fixed base station beamforming vector Optimize the phase shift matrix By introducing auxiliary variables Transform the max-min problem into a minimization problem and define... The optimization problem is rewritten as follows: ； in: ； in , , , The worst-case signal-to-interference-plus-noise ratio (SINR) for secondary users obtained after optimizing the base station beamforming vector; Consider using the MM and ADMM optimization methods to decompose the optimization problem into a series of more manageable subproblems for iterative solution; by introducing auxiliary variables The augmented Lagrangian method is used to handle the constant modulus constraint, and the optimization problem is rewritten as follows: ； Fixed variables , Optimize variables , Ignoring constraints and constant terms irrelevant to the optimization variables, the optimization problem can be written as: ； At a fixed point ( At point ), the optimization problem is a convex problem with respect to the variable; Fixed variables With optimization results , Optimize variables Ignoring constraints and constant terms irrelevant to the optimization variables, the optimization problem can be written as: ； The optimal solution to the optimization problem is directly obtained as Finally passed Update dual variables .

9. A RIS-based active-passive hybrid covert communication system, characterized in that: It employs a RIS-based active-passive hybrid covert communication method as described in any one of claims 1-8.

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