A design method for covert communication and perception integrated system based on intelligent reflective surface

Abstract

The present application relates to a design method for a covert communication perception integrated system based on an intelligent reflecting surface, which includes the following steps: establishing a covert communication perception integrated system model based on an intelligent reflecting surface, and establishing an optimization problem as the original problem, that is, using the Cramer-Rao bound of the target response matrix estimation as the optimization objective function, and using the beamforming vector of the base station and the gain of the active intelligent reflecting surface as the optimization variables to solve the optimal solution; using an alternating optimization method to split the original problem and obtain the optimal solution of the corresponding optimization variable of each sub-problem; and alternately updating the optimal solution of the original problem according to the optimal solution of the two sub-problems until the convergence of the objective function is achieved. The present invention combines the communication perception integrated system based on the intelligent reflecting surface with the covert communication scenario, and performs system optimization for the covert communication scenario, so that the system can better deal with the threat of eavesdropping during the communication process and has the ability to perceive the surrounding channel status and potential threats.

Description

Technical Field

[0001] The present application relates to the field of wireless communication technology, and in particular to a design method for a covert communication and perception integrated system based on an intelligent reflective surface. Background Art

[0002] In wireless communication systems, with the surge in data transmission demands and the increasing complexity of communication environments, reliability, security, and confidentiality have become key issues affecting system performance. Traditional covert communication technologies, such as signal encryption, spectrum spreading, and low-power transmission, are no longer able to meet the diverse communication needs in complex electromagnetic environments. These technologies typically rely on signal-level adjustments but cannot effectively address eavesdropping and interference threats at the physical layer, making it difficult to strike a balance between confidentiality and communication efficiency.

[0003] Active smart reflectors (RIS), an emerging physical layer technology, have garnered widespread attention in the wireless communications field in recent years. By deploying a large number of passive, controllable reflective units on their surface, RIS can dynamically adjust the amplitude, phase, and direction of electromagnetic waves, thereby precisely controlling the wireless propagation environment. This capability not only significantly improves communication quality but also enhances communication stealth by controlling the signal propagation path and coverage. However, relying solely on RIS to improve stealth still has limitations. In particular, in complex and dynamic environments, the optimized configuration of RIS cannot quickly respond to system requirements. Furthermore, to better address eavesdropping threats during communications, communication systems must also be able to perceive surrounding channel conditions and potential threats.

[0004] In recent years, ISAC, a technology for integrated covert communication and perception, has been recognized as a key approach to addressing this issue. By integrating communication with radar sensing, ISAC enables resource sharing and joint optimization of communication and perception signals. This technology enables real-time perception of the communication environment and threat information, providing strong support for dynamic optimization of covert communications. However, integrating intelligent reflective surfaces with integrated perception systems and optimizing them for covert communication scenarios remains a challenging research challenge. Summary of the Invention

[0005] The purpose of the present invention is to provide a design method for a covert communication perception integrated system based on intelligent reflecting surfaces, combine the communication perception integrated system based on intelligent reflecting surfaces with covert communication scenarios, and optimize the system for covert communication scenarios, so that the system can better deal with eavesdropping threats during communication and have the ability to perceive the surrounding channel status and potential threats.

[0006] The technical solution adopted by the present invention is: a design method for a covert communication and perception integrated system based on an intelligent reflective surface, comprising the following steps:

[0007] S1: Establish a covert communication and perception integrated system model based on an intelligent reflecting surface, the covert communication and perception integrated system model including a communication and perception integrated base station model, an active intelligent reflecting surface model, a channel model, a covert communication signal model, and a perception signal model; the communication and perception integrated base station model is used to transmit a communication and perception dual-function signal waveform, the active intelligent reflecting surface model is used to overcome channel fading caused by non-line-of-sight channels and enhance dual-function signals, the channel model is used to establish a real communication channel in the system scenario, the covert communication signal model is used to establish communication signals received by concealed users and public users, and the perception signal model is used to establish an echo signal containing target information received by the base station;

[0008] S2: Based on the covert communication and perception integrated system model, an optimization problem is established as the original problem under system constraints, that is, the Cramer-Rao bound of the target response matrix estimation is used as the optimization objective function, and the beamforming vector of the base station is used as the optimization objective function. and the gain of the active smart reflector Find the optimal solution for the optimization variables;

[0009] S3: Based on the optimization objective function and optimization variables, the original optimization problem established in S2 is split into two sub-problems using an alternating optimization method; one of the sub-problems is to fix the gain of the active smart reflector. , and obtain the beamforming vector of the base station only To optimize the variable subproblem, another subproblem is to fix the beamforming vector of the base station , the gain of the active smart reflector is obtained is a sub-problem of optimizing variables; solve the two sub-problems in sequence to obtain the optimal solution of the corresponding optimization variables of each sub-problem;

[0010] S4: The optimal beamforming vector of the base station transmit waveform based on the two sub-problems obtained in step S3 and the gain of the active smart reflector , and alternately update to obtain the optimal solution of the original problem of the optimization problem in S2 until the convergence of the objective function is achieved; and the covert communication perception integrated system model is optimized with the optimal solution obtained.

[0011] Furthermore, the communication-aware integrated base station model includes a transmit antennas and A base station with receiving antennas, A single-antenna public user, a single-antenna hidden user and a potential hostile guardian Willie; the base station transmits dual-function signals through the active intelligent reflector to assist A single-antenna public user communicates with a single-antenna hidden user Bob, and simultaneously senses a potential hostile guardian Willie who intends to monitor the hidden user's communication.

[0012] The specific expression of the active intelligent reflector model is:

[0013] ;

[0014] ψ = [ a 1 e j f 1 ,..., a m e j f m ,..., a M e j f M ] T ;

[0015] in, represents the gain vector of the active smart reflector, Indicates the The amplitude of the coefficient, Indicates the The phase shift of the coefficients, M represents the number of components of the active smart reflector, diagnosis {*} means extracting the vector elements in the brackets to form a diagonal matrix. j represents an imaginary unit;

[0016] The channel model includes the channel from the dual-function base station to user k , active intelligent reflective surface to the user k Channel , Channel from dual-function base station to active intelligent reflector and the channel from the active intelligent reflector to the hostile guardian Willie ; Among them, dual-function base station to user k Channel and active intelligent reflective surface to the user k Channel The channel model is a Rice channel, the channel from the dual-function base station to the active smart reflector and the channel from the active intelligent reflector to the hostile guardian Willie The channel is modeled as a Rayleigh channel;

[0017] The concealed communication signal model includes the L symbols form a dual-function signal, and the base station l The transmitted signal at the symbol is:

[0018] { ℋ 0 : x [ l ] = ∑ k ∈  w k s k [ l ] + x 0 [ l ] ℋ 1 : x [ l ] = ∑ k ∈  w k s k [ l ] + x 0 [ l ] + w b s b [ l ] ;

[0019] in, ℋ 0 : x [ l ] Indicates that no covert signal is sent. l The transmitted signal at symbols, Indicates the l Symbol No. k The corresponding beamforming vector of the user's signal is, s k [ l ] Indicates the l Symbol No. k The user's signal, x 0 [ l ] Indicates the l The perceptual signal component dedicated to each symbol, ℋ 1 : x [ l ] Indicates the time when a covert signal is sent. l The transmitted signal at symbols, represents the beamforming vector of the signal sent to the hidden user Bob, s b [ l ] represents the signal sent to the hidden user Bob;

[0020] No. k User in l The received signal at the symbol is:

[0021] { ℋ 0 : y k [ l ] = ( h u , k + h r , k ΦG ) ℋ 0 : x [ l ] + h r , k F z 0 [ l ] + n k [ l ] ℋ 1 : y k [ l ] = ( h u , k + h r , k ΦG ) ℋ 1 : x [ l ] + h r , k F z 0 [ l ] + n k [ l ] ;

[0022] in, ℋ 0 : y k [ l ] Indicates that no covert signal is sent. k User in l The received signal at symbols is ℋ 1 : y k [ l ] Indicates the time when a covert signal is sent. k User in l The received signal at symbols is n k [ l ] Indicates the l The symbol in k Additive white Gaussian noise at each user, z 0 [ l ] Indicates the l Additive Gaussian white noise of symbols at the active intelligent reflector;

[0023] The covert system model includes the hostile guardian Willie in the l The hypothesis test and total error detection probability at symbols are expressed as follows:

[0024] { ℋ 0 : r w [ l ] = h w ( ∑ k ∈  w k s k [ l ] + x 0 [ l ] ) + z w [ l ] ℋ 1 : r w [ l ] = h w ( ∑ k ∈  w k s k [ l ] + x 0 [ l ] + w b s b [ l ] ) + z w [ l ] ;

[0025] ;

[0026] in, ℋ 0 : r w [ l ] represents the hypothesis test that the base station transmission does not contain a concealed signal, It represents the composite channel between the communication and perception integrated base station and the hostile guardian through the active intelligent reflector surface. , z w [ l ] Indicates the l Gaussian white noise at symbols, ℋ 1 : r w [ l ] represents the hypothesis test that the base station transmits a concealed signal, represents the total error detection probability, represents the probability of false alarm, represents the probability of missed detection;

[0027] The perception signal model includes the echo signal received by the base station, and the specific expression is:

[0028] y r [ l ] = G T ΦH w ΦGx [ l ] + G T Φz 1 [ l ] + n r [ l ] ;

[0029] in, y r [ l ] Indicates that the base station receives the l The echo signal of symbols, Indicates the channel from the dual-function base station to the active intelligent reflector The transpose of represents the target response matrix, x [ l ] Indicates that the base station is l The transmitted signal at symbols, z 1 [ l ] represents the Gaussian white noise at the active intelligent reflector, n r [ l ] represents the Gaussian white noise of the entire channel.

[0030] Furthermore, the specific expression of the optimization objective function is:

[0031] ;

[0032] in, represents the Cramer-Rao bound of the target response matrix, Indicates that the base station transmits a signal x [ l ] The covariance matrix of Indicates the channel from the dual-function base station to the active intelligent reflector The conjugate transpose of Indicates the gain of the active intelligent reflector The conjugate transpose of Indicates the gain of the active intelligent reflector The transpose of Indicates that there is no target response matrix The covariance matrix of Indicates the gain of the active intelligent reflector The conjugate matrix of , tr (*) means taking the trace of the matrix in brackets;

[0033] The original problem of the optimization problem is specifically described as:

[0034] ;

[0035] in, Denotes a dedicated perceptual signal component x 0 [ l ] The covariance matrix of Indicates the maximum power threshold of the base station. Represents a bivariate distribution The next k The signal-to-interference-and-noise ratio of each user, Indicates the minimum signal-to-interference-and-noise ratio threshold to ensure user communication quality, Represents a composite channel from a communication-aware integrated base station to a hostile guardian via an active intelligent reflector surface. The conjugate transpose of express The solution of , where represents the concealment coefficient, L Indicates the length of the communication symbol, represents the Gaussian white noise power variance at the hostile guardian, Indicates the power of the active smart reflector, Indicates the maximum power threshold of the active smart reflector. Indicates the maximum amplitude coefficient of the active smart reflector.

[0036] Furthermore, the specific process of the alternating optimization is:

[0037] Initialize the base station's beam waveform vector , first fix the gain of the active smart reflector , get the beam waveform vector of only the base station In order to optimize the subproblem of variables, the semi-positive relaxation method is used to transform the subproblem into a semi-positive programming problem to obtain the optimal solution of the subproblem, that is, to solve the optimal solution of the transmit beam waveform vector of the subproblem ;

[0038] The optimal solution of the base station transmit beam waveform vector is obtained Substituting into the original problem, we get the gain of only active smart reflector The MM algorithm is used to solve the optimal solution of the active smart reflector gain. ;

[0039] The optimal gain solution of the active smart reflector The optimal solution for the base station's transmit beam waveform vector The optimal reflection element array is formed and input into the optimization iterative algorithm.

[0040] Furthermore, in step S4, based on the optimization iterative algorithm and the optimal reflective element array obtained in step S3, an optimal solution to the original problem is obtained by iterative update. , the optimization iterative algorithm achieves the convergence of the objective function after r iterations.

[0041] The beneficial effects of the present invention are:

[0042] (1) The present invention introduces a communication system assisted by an active intelligent reflector (RIS), which can dynamically adjust the reflection angle, phase, and amplitude of the signal, effectively improving the concealment of communication. It can also maintain low detectability in complex environments to ensure communication security when countering potential threats and interference.

[0043] (2) The present invention introduces covert communication into the integrated communication and perception system to create a new scenario. Traditional covert communication methods usually rely on signal encryption or spectrum expansion technology, which is difficult to meet the requirements of communication efficiency and perception capabilities at the same time. The present invention combines communication with radar perception technology to form an integrated perception and communication ISAC, which can perceive the surrounding environment in real time, identify potential threats, and optimize communication strategies, thereby realizing resource sharing and joint optimization. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the following briefly introduces the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0045] Figure 1 is a flow chart of a method according to an embodiment of the present invention;

[0046] Figure 2 This is a simulation verification diagram of the convergence result of the embodiment of the present invention;

[0047] Figure 3 Cramer-Rao bound CRB and concealment coefficient of target response matrix estimation under different communication SINR constraints for the objective function constructed in the embodiment of the present invention Relationship simulation diagram;

[0048] Figure 4 Cramer-Rao bound CRB and number of smart reflector components of target response matrix estimation with the aid of active smart reflector and passive smart reflector for the objective function constructed in the embodiment of the method of the present invention Relationship simulation diagram. DETAILED DESCRIPTION

[0049] In order to more clearly understand the above-mentioned objects, features and advantages of the present invention, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments. In the following description, many specific details are set forth to facilitate a full understanding of the present invention. However, the present invention may also be implemented in other ways different from those described herein. Therefore, the present invention is not limited to the specific embodiments disclosed below.

[0050] like Figure 1 As shown, an embodiment of the present invention provides a method for designing a covert communication and perception integrated system based on an intelligent reflective surface, comprising the following steps:

[0051] S1: Establish a covert communication and perception integrated system model based on an intelligent reflecting surface, wherein the covert communication and perception integrated system model includes a communication and perception integrated base station model, an active intelligent reflecting surface model, a channel model, a covert communication signal model and a perception signal model; the communication and perception integrated base station model is used to transmit a communication and perception dual-function signal waveform, the active intelligent reflecting surface model is used to overcome the channel fading caused by the non-line-of-sight channel and enhance the dual-function signal, the channel model is used to establish a real communication channel under the system scenario, the covert communication signal model is used to establish the communication signal received by the covert user and the public user, and the perception signal model is used to establish the echo signal containing the target information received by the base station.

[0052] The communication-awareness integrated base station model includes transmit antennas and A base station with receiving antennas, A single-antenna public user, a single-antenna hidden user and a potential hostile guardian Willie; the base station transmits dual-function signals through the active intelligent reflector to assist A single-antenna public user communicates with a single-antenna covert user Bob, and at the same time perceives a potential hostile guardian Willie who intends to monitor the communication of the covert user.

[0053] The specific expression of the active intelligent reflector model is:

[0054] ;

[0055] ψ = [ a 1 e j f 1 ,..., a m e j f m ,..., a M e j f M ] T ;

[0056] in, represents the gain vector of the active smart reflector, Indicates the The amplitude of the coefficient, Indicates the The phase shift of the coefficients, M represents the number of components of the active smart reflector, diagnosis {*} means extracting the vector elements in the brackets to form a diagonal matrix. j Represents an imaginary unit.

[0057] The channel model includes dual-function base station to user k Channel , the channel from the active intelligent reflector to user k , Channel from dual-function base station to active intelligent reflector and the channel from the active intelligent reflector to the hostile guardian Willie ; Among them, dual-function base station to user k Channel and the channel from the active smart reflector to user k The channel model is Rice channel, the channel from the dual-function base station to the active smart reflector and the channel from the active intelligent reflector to the hostile guardian Willie The channel is modeled as a Rayleigh channel.

[0058] The concealed communication signal model includes the L symbols form a dual-function signal, and the base station l The transmitted signal at the symbol is:

[0059] { ℋ 0 : x [ l ] = ∑ k ∈  w k s k [ l ] + x 0 [ l ] ℋ 1 : x [ l ] = ∑ k ∈  w k s k [ l ] + x 0 [ l ] + w b s b [ l ] ;

[0060] in, ℋ 0 : x [ l ] Indicates that no covert signal is sent. l The transmitted signal at symbols, Indicates the l Symbol No. k The corresponding beamforming vector of the user's signal is, s k [ l ] Indicates the l The signal of the kth user at symbol, x 0 [ l ] Indicates the l The perceptual signal component dedicated to each symbol, ℋ 1 : x [ l ] Indicates the time when a covert signal is sent. lThe transmitted signal at symbols, represents the beamforming vector of the signal sent to the hidden user Bob, s b [ l ] Represents the signal sent to the hidden user Bob.

[0061] No. k User in l The received signal at the symbol is:

[0062] { ℋ 0 : y k [ l ] = ( h u , k + h r , k ΦG ) ℋ 0 : x [ l ] + h r , k F z 0 [ l ] + n k [ l ] ℋ 1 : y k [ l ] = ( h u , k + h r , k ΦG ) ℋ 1 : x [ l ] + h r , k F z 0 [ l ] + n k [ l ] ;

[0063] in, ℋ 0 : y k [ l ] Indicates that no covert signal is sent. k User in l The received signal at symbols is ℋ 1 : y k [ l ] Indicates the time when a covert signal is sent. k User in l The received signal of symbols, n k [ l ] Indicates the l The symbol in k Additive Gaussian white noise at each user, z 0 [ l ] Indicates the l Additive white Gaussian noise of 1 symbol at the active intelligent reflecting surface.

[0064] make is the composite channel from user to base station, which can be expressed as , then the signal-to-interference-plus-noise ratio (SINR) of the public user can be expressed as:

[0065] ;

[0066] ;

[0067] in, Indicates that the transmitted signal does not contain a hidden signal k The signal-to-interference-and-noise ratio of each user, represents the base station beamforming vector, Indicates the composite channel from user to base station The conjugate transpose of Indicates the l The perceptual signal component dedicated to each symbol x 0 [ l ] The covariance matrix of represents the Gaussian white noise power variance at the active intelligent reflector, Indicates the k The Gaussian white noise power variance at each user is: Indicates that the transmitted signal contains a hidden signal k The signal-to-interference-and-noise ratio of a user.

[0068] The covert system model includes the hostile guardian Willie in the l The hypothesis test and total error detection probability at symbols are expressed as follows:

[0069] { ℋ 0 : r w [ l ] = h w ( ∑ k ∈  w k s k [ l ] + x 0 [ l ] ) + z w [ l ] ℋ 1 : r w [ l ] = h w ( ∑ k ∈  w k s k [ l ] + x 0 [ l ] + w b s b [ l ] ) + z w [ l ] ;

[0070] ;

[0071] in, ℋ 0 : r w [ l ] represents the hypothesis test that the base station transmission does not contain a concealed signal, It represents the composite channel between the communication and perception integrated base station and the hostile guardian through the active intelligent reflector surface. , z w [ l ] Indicates the l Gaussian white noise at symbols, ℋ 1 : r w [ l ] represents the hypothesis test that the base station transmits a concealed signal, represents the total error detection probability, represents the probability of false alarm, represents the probability of missed detection.

[0072] Therefore, the hidden constraints of the system can be expressed as:

[0073] ;

[0074] in, Represents a hidden constant.

[0075] The perception signal model includes the echo signal received by the base station, and the specific expression is:

[0076] y r [ l ] = G T ΦH w ΦGx [ l ] + G T Φz 1 [ l ] + n r [ l ] ;

[0077] in, y r [ l ] Indicates that the base station receives the l The echo signal of symbols, Indicates the channel from the dual-function base station to the active intelligent reflector The transpose of represents the target response matrix, x [ l ] Indicates that the base station is l The transmitted signal at symbols, z 1 [ l ] represents the Gaussian white noise at the active intelligent reflector, n r [ l ] represents the Gaussian white noise of the entire channel.

[0078] S2: Based on the covert communication and perception integrated system model, an optimization problem is established as the original problem under system constraints, that is, the Cramer-Rao bound of the target response matrix estimation is used as the optimization objective function, and the beamforming vector of the base station is used as the optimization objective function. and the gain of the active smart reflector Find the optimal solution for the optimization variables.

[0079] The specific expression of the optimization objective function is:

[0080] ;

[0081] in, represents the Cramer-Rao bound of the target response matrix, Indicates that the base station transmits a signal x [ l ] The covariance matrix of Indicates the channel from the dual-function base station to the active intelligent reflector The conjugate transpose of Indicates the gain of the active intelligent reflector The conjugate transpose of Indicates the gain of the active intelligent reflector The transpose of Indicates that there is no target response matrix The covariance matrix of Indicates the gain of the active intelligent reflector The conjugate matrix of , tr(*) means taking the trace of the matrix in the brackets.

[0082] The original problem of the optimization problem is specifically described as:

[0083] ;

[0084] in, Denotes a dedicated perceptual signal component x 0 [ l ] The covariance matrix of Indicates the maximum power threshold of the base station. Represents a bivariate distribution The next k The signal-to-interference-and-noise ratio of each user, Indicates the minimum signal-to-interference-and-noise ratio threshold to ensure user communication quality, Represents a composite channel from a communication-aware integrated base station to a hostile guardian via an active intelligent reflector surface. The conjugate transpose of express The solution of , where represents the concealment coefficient, L Indicates the length of the communication symbol, represents the Gaussian white noise power variance at the hostile guardian, Indicates the power of the active smart reflector, Indicates the maximum power threshold of the active smart reflector. Indicates the maximum amplitude coefficient of the active smart reflector.

[0085] S3: Based on the optimization objective function and optimization variables, the original optimization problem established in S2 is split into two sub-problems using an alternating optimization method; one of the sub-problems is to fix the gain of the active smart reflector. , and obtain the beamforming vector of the base station only To optimize the variable subproblem, another subproblem is to fix the beamforming vector of the base station , the gain of the active smart reflector is obtained is a subproblem of optimizing variables; solve the two subproblems in sequence to obtain the optimal solution of the corresponding optimization variables of each subproblem.

[0086] The specific process of the alternating optimization is:

[0087] Initialize the base station's beam waveform vector , first fix the gain of the active smart reflector , get the beam waveform vector of only the base station In order to optimize the subproblem of variables, the semi-positive relaxation method is used to transform the subproblem into a semi-positive programming problem to obtain the optimal solution of the subproblem, that is, to find the optimal solution of the beam waveform vector of the base station that solves the subproblem. ; The specific method is:

[0088] Initialize base station beam waveform vector , first fix the gain of the active smart reflector , transforming the optimization problem into subproblems :

[0089] .

[0090] Introducing the auxiliary variable t transforms the objective function into:

[0091] .

[0092] because The form of the C1 constraint and C2 constraint in the formula contains the inverse and trace function of the matrix. To make these functions convex, the Schur complement lemma is used to convert The C1 and C2 constraints in are transformed into the following linear matrix inequalities:

[0093] ;

[0094] .

[0095] Then, the subproblem is transformed into a semidefinite programming problem using the semidefinite relaxation method to obtain the optimal solution of the subproblem. ,in and , ,in, represents the identity matrix, express The conjugate transpose of Representation matrix rank, represents a positive semidefinite matrix, The composite channel between the communication user and the base station can be expressed as , express The conjugate transpose of The C1 constraint in can be simplified as:

[0096] .

[0097] make , which is a constant, where The C2 constraint in can be simplified to:

[0098] .

[0099] By the S-program lemma, The C3 constraint in is transformed into:

[0100] ;

[0101] in, Represents the auxiliary variables introduced, .

[0102] For the problem The C4 constraint, Given by the following formula

[0103]  ( w k , F ) = ∑ k ∈  + 1 || ΦGw k || 2 2 + | | F G x 0 [ l ] | | 2 2 + 2 s z 2 | | F | | F 2 + ∑ k ∈  + 1 || ΦH w ΦGw k || 2 2 + || ΦH w ΦGx 0 [ l ]|| 2 2 ;

[0104] Among them, the definition is the target response matrix, , Indicates. , ,So It can be simplified to:

[0105] ∑ k ∈  + 1 W k ( G H F H ΦG ) + ∑ k ∈  + 1 W k ( G H F H H w H F H ΦH w ΦG ) + R 0 ( G H F H ΦG ) + R 0 ( G H F H H w H F H ΦH w ΦG ) + 2 s z 2 || F [ n ] || F 2 = ( ∑ k ∈  + 1 W k + R 0 ) ( G H F H ΦG ) + ( ∑ k ∈  + 1 W k + R 0 ) ( G H F H H w H F H ΦH w ΦG ) = ( ∑ k ∈  + 1 W k + R 0 ) ( G H F H ΦG + G H F H H w H F H ΦH w ΦG ) + 2 s z 2 || F [ n ] || F 2 ;

[0106] make , , , so the problem The C4 constraint can be simplified to:

[0107] .

[0108] Ignoring the rank-one constraint, we can obtain a convex semidefinite programming problem , the above optimization problem can be equivalently written as:

[0109]

[0110] Among them, for The solution to the semidefinite programming problem is to The global solution of the semidefinite programming problem is transformed into the problem A feasible solution can be found by using Gaussian random process to find the optimal approximation. The specific process is:

[0111] right Perform eigenvalue decomposition:

[0112] .

[0113] in, is the eigenvector matrix, is the eigenvalue matrix, is the eigenvector matrix The transpose of . From the standard Gaussian distribution Generate multiple random vectors in , then construct S candidate solutions , each candidate solution Substitute it into the objective function to calculate its value and select the solution that makes the objective function value optimal ,according to We can get:

[0114] ;

[0115] in, express The conjugate transpose of . Here we can get the sub-problem problem The optimal solution .

[0116] Optimal solution for fixed transmit beam waveform vector , using the MM algorithm to solve the optimal gain solution of the active smart reflector The specific process is:

[0117] After determining the beamforming vector of the transmit waveform, the gain of the active smart reflector The sub-problem can be expressed as

[0118] .

[0119] For the sub-problem, the optimal solution of the transmit beam waveform vector is used A similar simplification process can transform the subproblem into:

[0120] ;

[0121] in, Represents the auxiliary variables introduced to process the objective function, Representation matrix Dimensions, Representation matrix Dimensions, Representation matrix dimension. represents the gain vector of the active smart reflector, express The conjugate transpose of express The conjugate of Defined as ,in Defined as , represents the real part, Defined as , Indicates that in addition to the k-th user, the i-th user obtains amplitude gain on the active smart reflector. Representation matrix The conjugate matrix of Indicates that user k obtains amplitude gain on the active smart reflector, Defined as , It means taking the minimum eigenvalue of the matrix. Representation function Zero point, Defined as , Defined as , Defined as . Representing the unit matrix of dimension M, solving the subproblem can obtain the optimal gain solution of the active smart reflector .

[0122] The optimal gain solution of the active smart reflector The optimal solution for the transmit beam waveform vector The optimal reflective element array is formed and input into the subsequent optimization iterative algorithm.

[0123] S4: Beamforming vector based on the optimal base station transmit waveform and the gain of the active smart reflector , and update alternately to obtain the optimal solution of the original problem until the convergence of the objective function is achieved. The specific method is: based on the optimization iterative algorithm and the optimal reflective element array obtained in step S3 and , update alternately to obtain the optimal solution The optimization iterative algorithm achieves convergence of the objective function after r iterations. By optimizing the system through most of the methods in the embodiments of the present invention, the system can optimize the perception performance while ensuring covert communication, thereby ensuring the security and reliability of the communication system.

[0124] The effect of the present invention is further illustrated by simulation below:

[0125] (1) Simulation parameters

[0126] Assume that the ISAC base station is equipped with The transmitting antenna and The power budget of the base station is set to , the number of reflective elements of the active RIS is set to , the maximum power threshold of the active smart reflector is set to , the noise power variance is set to , the number of signal characters is set to , the hidden constant is set to .

[0127] (2) Simulation results and data analysis

[0128] Figure 2 Describes the CRB value of the target response matrix estimation relative to different user signal-to-interference-noise ratios and the hidden constant As the number of iterations increases, the CRB value of the target response matrix estimation gradually decreases, and converges with a very small number of iterations. It can be observed that under the same user signal to noise ratio Next, the hidden constant The higher the value, the smaller the convergence value of the objective function. Under the condition of user signal-to-interference-noise ratio The higher it is, the greater the value to which the objective function converges.

[0129] Figure 3 Describes the CRB value of the target response matrix estimation under different signal-to-interference-noise ratios Constrained and hidden coefficient It can be observed that the CRB value of the target response matrix estimate decreases as the threshold of the signal-to-interference-noise ratio decreases, and also decreases as the concealment constraint is relaxed.

[0130] Figure 4 The relationship between the target response matrix estimation CRB and the number of reflective elements of the intelligent reflective surface of the covert communication and perception integrated system under different conditions is given. Figure 4 As shown in the figure, ARIS-radar-only means that the active intelligent reflector assisted covert communication and perception integrated system only uses the radar function, ARIS-ISAC means that the active intelligent reflector assisted covert communication and perception integrated system uses both communication and radar functions, and PRIS-ISAC means that the passive intelligent reflector assisted covert communication and perception integrated system uses both communication and radar functions. represents the maximum amplitude coefficient of the active smart reflector. The CRB performance of target response matrix estimation improves with the number of reflective elements in the smart reflector. This is because the number of reflective elements in the smart reflector provides the system with higher radar degrees of freedom. Furthermore, it can be observed that the covert communication and perception integrated system assisted by active smart reflectors outperforms the covert communication and perception integrated system assisted by passive smart reflectors. Furthermore, in the covert communication and perception integrated system assisted by active smart reflectors, the larger the amplitude factor, the better the system performance.

[0131] The above simulation results show that adding intelligent reflective surface assistance to covert communication integration can effectively improve the security of the system and the communication quality of users.

[0132] The foregoing description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Those skilled in the art will readily appreciate that various modifications and variations of the present invention are possible. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of the present invention are intended to be within the scope of protection of the present invention.

Claims

1. A design method for a covert communication and perception integrated system based on intelligent reflective surfaces, characterized in that: The steps include: S1: Establish a concealed communication perception integrated system model based on an intelligent reflective surface, the concealed communication perception integrated system model includes a communication perception integrated base station model, an active intelligent reflective surface model, a channel model, a concealed communication signal model and a perception signal model; the communication perception integrated base station model is used to transmit a communication perception dual-function signal waveform, and is equipped with transmit antennas and A base station with receiving antennas, A single-antenna public user, a single-antenna hidden user and a potential hostile guardian Willie; the base station transmits dual-function signals through the active intelligent reflector to assist A single-antenna public user communicates with a single-antenna hidden user Bob, and simultaneously senses a potential hostile guardian Willie, who intends to monitor the communication of the hidden user. The active intelligent reflector model is used to overcome the channel fading caused by the non-line-of-sight channel and enhance the dual-function signal. The channel model is used to establish a real communication channel in the system scenario. The covert communication signal model is used to establish the communication signals received by the hidden user and the public user. The perception signal model is used to establish the echo signal containing target information received by the base station. S2: Based on the covert communication and perception integrated system model, an optimization problem is established as the original problem under system constraints, that is, the Cramer-Rao bound of the target response matrix estimation is used as the optimization objective function, and the beamforming vector of the base station is used as the optimization objective function. and the gain of the active smart reflector Find the optimal solution for the optimization variables; The specific expression of the optimization objective function is: ； in, represents the Cramer-Rao bound of the target response matrix, Indicates that the base station transmits a signal The covariance matrix of Indicates the channel from the dual-function base station to the active intelligent reflector The conjugate transpose of Indicates the gain of the active intelligent reflector The conjugate transpose of Indicates the gain of the active intelligent reflector The transpose of Indicates that there is no target response matrix The covariance matrix of Indicates the gain of the active intelligent reflector The conjugate matrix of , tr (*) means taking the trace of the matrix in brackets; The original problem of the optimization problem is specifically described as: ； in, Denotes a dedicated perceptual signal component The covariance matrix of Indicates the maximum power threshold of the base station. Represents a bivariate distribution The signal-to-interference-and-noise ratio of the kth user under Indicates the minimum signal-to-interference-and-noise ratio threshold to ensure user communication quality, Represents a composite channel from a communication-aware integrated base station to a hostile guardian via an active intelligent reflector surface. The conjugate transpose of express The solution of , where represents the concealment coefficient, L represents the communication symbol length, represents the Gaussian white noise power variance at the hostile guardian, Indicates the power of the active smart reflector, Indicates the maximum power threshold of the active smart reflector. Indicates the maximum amplitude coefficient of the active smart reflector, represents the beamforming vector of the signal sent to the hidden user Bob, represents the beamforming vector of the signal sent to the hidden user Bob The conjugate transpose of represents the beamforming vector corresponding to the signal of the kth user at the lth symbol, The beamforming vector corresponding to the signal of the kth user at the lth symbol is represented by The conjugate transpose of Indicates the The amplitude of the coefficient, Indicates the The phase shift of the coefficients; S3: Based on the optimization objective function and optimization variables, the original optimization problem established in S2 is split into two sub-problems using an alternating optimization method; one of the sub-problems is to fix the gain of the active smart reflector. , and obtain the beamforming vector of the base station only To optimize the variable subproblem, another subproblem is to fix the beamforming vector of the base station , the gain of the active smart reflector is obtained is a sub-problem of optimizing variables; solve the two sub-problems in sequence to obtain the optimal solution of the corresponding optimization variables of each sub-problem; S4: The optimal beamforming vector of the base station transmit waveform based on the two sub-problems obtained in step S3 and the gain of the active smart reflector , and alternately update to obtain the optimal solution of the original problem of the optimization problem in S2 until the convergence of the objective function is achieved; and the covert communication perception integrated system model is optimized with the optimal solution obtained.

2. The method for designing a covert communication and perception integrated system based on an intelligent reflective surface according to claim 1, characterized in that: The specific expression of the active intelligent reflector model is: ； ； in, represents the gain vector of the active smart reflector, Indicates the The amplitude of the coefficient, Indicates the The phase shift of the coefficients, M represents the number of components of the active smart reflector, diag{*} represents extracting the vector elements in the brackets to form a diagonal matrix, and j represents the imaginary unit; The channel model includes the channel from the dual-function base station to user k , the channel from the active intelligent reflector to user k , Channel from dual-function base station to active intelligent reflector and the channel from the active intelligent reflector to the hostile guardian Willie ; Among them, the channel from the dual-function base station to user k and the channel from the active smart reflector to user k The channel model is Rice channel, the channel from the dual-function base station to the active smart reflector and the channel from the active intelligent reflector to the hostile guardian Willie The channel is modeled as a Rayleigh channel; The concealed communication signal model includes the symbols form a dual-function signal, and the base station The transmitted signal at the symbol is: ； in, Indicates that no covert signal is sent. The transmitted signal at symbols, represents the beamforming vector corresponding to the signal of the kth user at the lth symbol, represents the signal of the kth user at the lth symbol, represents the perceptual signal component dedicated to the lth symbol, represents the transmitted signal at the lth symbol when sending the concealed signal, represents the beamforming vector of the signal sent to the hidden user Bob, represents the signal sent to the hidden user Bob; The received signal of the kth user at the lth symbol is: ； in, represents the received signal of the kth user at l symbols when no concealed signal is sent, represents the received signal of the kth user at l symbols when the concealed signal is sent, represents the additive white Gaussian noise of the lth symbol at the kth user, represents the additive white Gaussian noise of the lth symbol at the active intelligent reflector; The covert system model includes the hypothesis test and total error detection probability of the hostile guardian Willie at the lth symbol, which is specifically expressed as: ； ； in, represents the hypothesis test that the base station transmission does not contain a concealed signal, It represents the composite channel between the communication and perception integrated base station and the hostile guardian through the active intelligent reflector surface. , represents the Gaussian white noise at the lth symbol, represents the hypothesis test that the base station transmits a concealed signal, represents the total error detection probability, represents the probability of false alarm, represents the probability of missed detection; The perception signal model includes the echo signal received by the base station, and the specific expression is: ； in, Indicates that the base station receives the echo signal of the lth symbol, Indicates the channel from the dual-function base station to the active intelligent reflector The transpose of represents the target response matrix, represents the transmitted signal of the base station at the lth symbol, represents the Gaussian white noise at the active intelligent reflector, represents the Gaussian white noise of the entire channel.

3. The method for designing a covert communication and perception integrated system based on an intelligent reflective surface according to claim 2, characterized in that: The specific process of the alternating optimization is: Initialize the base station's beam waveform vector , first fix the gain of the active smart reflector , get the beam waveform vector of only the base station In order to optimize the subproblem of variables, the semi-positive relaxation method is used to transform the subproblem into a semi-positive programming problem to obtain the optimal solution of the subproblem, that is, to solve the optimal solution of the transmit beam waveform vector of the subproblem ; The optimal solution of the base station transmit beam waveform vector is obtained Substituting into the original problem, we get the gain of only active smart reflector The MM algorithm is used to solve the optimal solution of the active smart reflector gain. ; The optimal gain solution of the active smart reflector The optimal solution for the base station's transmit beam waveform vector The optimal reflection element array is formed and input into the optimization iterative algorithm.

4. The method for designing a covert communication and perception integrated system based on an intelligent reflective surface according to claim 3 is characterized in that: In step S4, based on the optimization iterative algorithm and the optimal reflective element array obtained in step S3, iterative update is performed to obtain the optimal solution to the original problem. , the optimization iterative algorithm achieves the convergence of the objective function after r iterations.

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