Design method of covert communication and perception integrated system based on intelligent reflecting surface

Abstract

The invention relates to a covert communication perception integrated system design method based on an intelligent reflecting surface, and the method comprises the following steps: building a covert communication perception integrated system model based on the intelligent reflecting surface, and building an optimization problem as an original problem, i.e., taking a Cramer-Rao bound estimated by a target response matrix as an optimization target function; solving an optimal solution by taking the beam forming vector of the base station and the gain of the active intelligent reflecting surface as optimization variables; splitting the original problem by adopting an alternative optimization mode to obtain an optimal solution of an optimization variable corresponding to each sub-problem; and alternately updating according to the optimal solutions of the two sub-problems to obtain the optimal solution of the original problem until the convergence of the target function is realized. According to the invention, a communication sensing integrated system based on an intelligent reflecting surface is combined with a covert communication scene, and system optimization is carried out for the covert communication scene, so that the system can better cope with eavesdropping threats in a communication process, and has the capability of sensing surrounding channel states 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 concealed communication and perception integrated system based on an intelligent reflective surface. Background Art

[0002] In wireless communication systems, with the surge in data transmission demand and the increasing complexity of communication environments, the reliability, security and concealment of communications have become one of the key issues affecting system performance. Traditional covert communication technologies, such as signal encryption, spectrum expansion, and low-power transmission, have been unable to meet the diverse communication needs in complex electromagnetic environments. These technologies usually rely on adjustments at the signal level, but cannot effectively deal with eavesdropping threats and interference from the physical layer, and it is difficult to balance concealment and communication efficiency.

[0003] As an emerging physical layer technology, active intelligent reflective surface (RIS) has received extensive attention in the field of wireless communications in recent years. By deploying a large number of passive controllable reflective units on its surface, active intelligent reflective surface (RIS) can dynamically adjust the amplitude, phase and direction of electromagnetic waves, thereby achieving precise control of the wireless propagation environment. This capability can not only significantly improve the communication quality, but also enhance the concealment of communication by controlling the propagation path and coverage of the signal. However, there are still limitations to relying solely on active intelligent reflective surface (RIS) to improve concealment, especially in complex dynamic environments, where the optimized configuration of active intelligent reflective surface (RIS) is difficult to quickly respond to system requirements. In addition, in order to better deal with the threat of eavesdropping during communication, the communication system must also have the ability to perceive the surrounding channel status and potential threats.

[0004] In recent years, ISAC, a technology integrating covert communication and perception, has been considered as a key direction to solve this problem. ISAC, a technology integrating covert communication and perception, realizes resource sharing and joint optimization of communication signals and perception signals by combining communication with radar perception functions. This technology can perceive the communication environment and threat information in real time, providing strong support for the dynamic optimization of covert communications. However, how to combine intelligent reflective surfaces with integrated perception systems and optimize the system for covert communication scenarios is still a research problem that has not been fully solved. 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 an intelligent reflecting surface, combine the communication perception integrated system based on an intelligent reflecting surface with a covert communication scenario, and optimize the system for the covert communication scenario, so that the system can better cope with the threat of eavesdropping during the communication process 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 of a covert communication perception integrated system based on an intelligent reflective surface, comprising the following steps: S1: Establish a concealed communication perception integrated system model based on an intelligent reflective surface, wherein 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, the active intelligent reflective 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 in the system scenario, the concealed communication signal model is used to establish a communication signal received by a concealed user and a public user, and the perception signal model is used to establish an echo signal containing target information received by the base station; S2: Based on the covert communication perception integrated system model, an optimization problem is established under system constraints as the original problem, that is, the Cramer-Rao bound estimated by the target response matrix 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; S3: Based on the optimization objective function and optimization variables, the original optimization problem established in S2 is split into two sub-problems by 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 only the active smart reflector is is a sub-problem of optimizing variables; solve the two sub-problems in sequence to obtain the optimal solution of the corresponding optimization variable of each sub-problem; S4: The optimal beamforming vector of the base station transmission waveform for the two sub-problems obtained in step S3 and the gain of the active smart reflector , and update alternately to obtain the optimal solution of the original problem of the optimization problem in S2 until the convergence of the objective function is achieved; the covert communication perception integrated system model is optimized with the optimal solution obtained.

[0007] Furthermore, the communication-aware 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 potentially hostile guardian Willie; the base station transmits a dual-function signal and is assisted by an active intelligent reflector. A single-antenna public user communicates with a single-antenna hidden user Bob, and at the same time perceives a potential hostile guardian Willie, who intends to monitor the communication of the hidden user;

[0008] The specific expression of the active intelligent reflector model is: ; ψ = [ a 1 e j f 1 ,..., a m e j f m ,..., a M e j f M ] T ; in, represents the gain vector of the active smart reflector, Indicates The amplitude of the coefficient, Indicates 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; 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, a channel from a dual-function base station to an 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 L symbols form a dual-function signal. The base station l The transmitted signal at the symbol is: { 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 ] ; in, ℋ 0 : x [ l ] Indicates that no covert signal is sent. l The transmitted signal at symbols is Indicates l Symbol No. k The corresponding beamforming vector of the user's signal is, s k [ l ] Indicates l Symbol No.k The signal of a user, x 0 [ l ] Indicates l The perceptual signal component dedicated to each symbol, ℋ 1 : x [ l ] Indicates when a covert signal is sent. l The transmitted signal at symbols is 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; No. k User in l The received signal at the symbol is: { 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 ] ; 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 when a covert signal is sent. k User in l The received signal at symbols is n k [ l ] Indicates l The symbol in k Additive Gaussian white noise at each user, z 0 [ l ] Indicates l Additive Gaussian white noise of 10 symbols at the active intelligent reflector; The covert system model includes the hostile guardian Willie in the l The hypothesis test and total error detection probability at the symbol are expressed as: { 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 ] ; ; in, ℋ 0 : r w [ l ] represents the hypothesis test that the base station transmission does not contain a hidden signal, It represents the composite channel between the communication and perception integrated base station and the hostile guardian through the active intelligent reflection surface. , z w [ l ] Indicates 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; The perception signal model includes the echo signal received by the base station, and the specific expression is: y r [ l ] = G T ΦH w ΦGx [ l ] + G T Φz 1 [ l ] + n r [ l ] ; 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 is 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.

[0009] Furthermore, 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 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; The original problem of the optimization problem is specifically described as: ; 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 nextk The signal-to-interference-noise ratio of each user is It represents the minimum signal-to-interference-noise ratio threshold to ensure the user communication quality. Represents the composite channel between the communication and perception integrated base station and the hostile guardian through the active intelligent reflection surface The conjugate transpose of express The solution of , where represents the concealment coefficient, L Indicates the communication symbol length, represents the Gaussian white noise power variance at the hostile guardian, represents 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.

[0010] Furthermore, 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 , and get the beam waveform vector of only the base station In order to optimize the subproblem of variables, the semi-positive definite relaxation method is used to transform the subproblem into a semi-positive definite 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 the active smart reflector The MM algorithm is used to solve the optimal solution of the active smart reflector gain. ; Optimize the gain 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.

[0011] Furthermore, in step S4, based on the optimization iterative algorithm and the optimal reflective element array obtained in step S3, an 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.

[0012] The beneficial effects of the present invention are: (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 the communication; when countering potential threats and interference, it can maintain low detectability in a complex environment and ensure the security of communication; (2) The present invention introduces covert communication into the integrated communication and perception system to construct a new scenario. Traditional covert communication methods usually rely on signal encryption or spectrum expansion technology, which is difficult to meet the needs 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

[0013] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings required for use in the embodiments will be briefly introduced below. 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 paying creative work.

[0014] Figure 1 is a flow chart of a method according to an embodiment of the present invention; Figure 2 It is a simulation verification diagram of the convergence result of the embodiment of the present invention; 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; Figure 4 Cramer-Rao bound CRB and number of smart reflector components of target response matrix estimation of objective function constructed for the method embodiment of the present invention with the assistance of active smart reflector and passive smart reflector Relationship simulation diagram. DETAILED DESCRIPTION

[0015] In order to more clearly understand the above-mentioned purpose, features and advantages of the present invention, the present invention is further described in detail below in conjunction with 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, but the present invention can also be implemented in other ways different from those described herein, and therefore, the present invention is not limited to the limitations of the specific embodiments disclosed below.

[0016] like Figure 1 As shown, an embodiment of the present invention provides a method for designing a covert communication perception integrated system based on an intelligent reflective surface, comprising the following steps: S1: Establish a concealed communication and perception integrated system model based on an intelligent reflecting surface, wherein the concealed 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 concealed 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 concealed communication signal model is used to establish the communication signal received by the concealed 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.

[0017] The communication-sensing 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 potentially hostile guardian Willie; the base station transmits a dual-function signal and is assisted by an active intelligent reflector. A single-antenna public user communicates with a single-antenna hidden user Bob, and at the same time perceives a potential hostile guardian Willie who intends to monitor the communication of the hidden user.

[0018] The specific expression of the active intelligent reflector model is: ; ψ = [ a 1 e j f 1 ,..., a m e j f m ,..., a M e j f M ] T ; in, represents the gain vector of the active smart reflector, Indicates The amplitude of the coefficient, Indicates 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.

[0019] The channel model includes a 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 a Rice channel, a channel from a dual-function base station to an active smart reflector. and the channel from the active intelligent reflector to the hostile guardian Willie The channel is modeled as a Rayleigh channel.

[0020] The concealed communication signal model includes the L symbols form a dual-function signal. The base station l The transmitted signal at the symbol is: { 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 ] ; in, ℋ 0 : x [ l ] Indicates that no covert signal is sent. l The transmitted signal at symbols is Indicates l Symbol No. k The corresponding beamforming vector of the user's signal is, s k [ l ] Indicates l The signal of the kth user at symbol, x 0 [ l ] Indicates l The perceptual signal component dedicated to each symbol, ℋ 1 : x [ l ] Indicates when a covert signal is sent. l The transmitted signal at symbols is 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.

[0021] No. k User in l The received signal at the symbol is: { 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 ] ; 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 when a covert signal is sent. k User in l The received signal of symbols is n k [ l ] Indicates l The symbol in k Additive Gaussian white noise at each user, z 0 [ l ] Indicates l Additive white Gaussian noise of 1 symbol at the active smart reflector.

[0022] make is the composite channel from user to base station, which can be expressed as , then the SINR of the public user can be expressed as: ; ; in, Indicates that the transmitted signal does not contain a hidden signal k The signal-to-interference-noise ratio of each user is represents the base station beamforming vector, Indicates the composite channel from user to base station The conjugate transpose of Indicates 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 smart reflector, Indicates 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-noise ratio of a user.

[0023] The covert system model includes the hostile guardian Willie in the l The hypothesis test and total error detection probability at the symbol are expressed as: { 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 ] ; ; in, ℋ 0 : r w [ l ] represents the hypothesis test that the base station transmission does not contain a hidden signal, It represents the composite channel between the communication and perception integrated base station and the hostile guardian through the active intelligent reflection surface. , z w [ l ] Indicates 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.

[0024] Therefore, the hidden constraints of the system can be expressed as: ; in, Represents a hidden constant.

[0025] The perception signal model includes the echo signal received by the base station, and the specific expression is: y r [ l ] = G T ΦH w ΦGx [ l ] + G T Φz 1 [ l ] + n r [ l ] ; 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 is 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.

[0026] S2: Based on the covert communication perception integrated system model, an optimization problem is established under system constraints as the original problem, that is, the Cramer-Rao bound estimated by the target response matrix 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.

[0027] 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 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.

[0028] The original problem of the optimization problem is specifically described as: ; 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-noise ratio of each user is It represents the minimum signal-to-interference-noise ratio threshold to ensure the user communication quality. Represents the composite channel between the communication and perception integrated base station and the hostile guardian through the active intelligent reflection surface The conjugate transpose of express The solution of , where represents the concealment coefficient, L Indicates the communication symbol length, represents the Gaussian white noise power variance at the hostile guardian, represents 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.

[0029] S3: Based on the optimization objective function and optimization variables, the original optimization problem established in S2 is split into two sub-problems by 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 only the active smart reflector is is a subproblem of optimizing variables; solve the two subproblems in sequence to obtain the optimal solution of the corresponding optimization variable of each subproblem.

[0030] The specific process of the alternating optimization is as follows: Initialize the base station's beam waveform vector , first fix the gain of the active smart reflector , and get the beam waveform vector of only the base station In order to optimize the subproblem of variables, the semi-positive definite relaxation method is used to transform the subproblem into a semi-positive definite 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: Initialize base station beam waveform vector , first fix the gain of the active smart reflector , transforming the optimization problem into subproblems : .

[0031] Introducing auxiliary variable t transforms the objective function into: .

[0032] because The C1 and C2 constraints in the form of the matrix inverse and trace function are included. 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: ; .

[0033] Then, the subproblem is transformed into a semi-definite programming problem using the semi-definite 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: .

[0034] make , which is a constant, where The C2 constraint in can be simplified to: .

[0035] By the S-program lemma, The C3 constraint in is transformed into: ; in, Represents the introduced auxiliary variables, .

[0036] For the problem The C4 constraint, Given by the following formula  ( 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 ; Among them, the definition is the target response matrix, , Indicates. , ,So It can be simplified to: ∑ 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 ; make , , , so the problem The C4 constraint can be simplified to: .

[0037] Ignoring the rank-one constraint, we can obtain a convex semidefinite programming problem , the above optimization problem can be equivalently written as: Among them, for The solution to the semidefinite programming problem is to The global solution of the semi-positive definite 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: right Perform eigenvalue decomposition: .

[0038] 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: ; in, express The conjugate transpose of . So we can get the subproblem The optimal solution .

[0039] Optimal solution for fixed transmit beam waveform vector , the MM algorithm is used to solve the optimal gain solution of the active smart reflector , the specific process is: After determining the beamforming vector of the transmit waveform, the gain of the active smart reflector The sub-problem can be expressed as .

[0040] For the subproblem, the optimal solution of the transmit beam waveform vector is used A similar simplification process can transform the subproblem into: ; in, represents the auxiliary variables introduced to process the objective function, Representation Matrix The dimension of Representation Matrix The dimension of 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 kth user, the i-th user obtains amplitude gain on the active intelligent reflection surface, Representation Matrix The conjugate matrix of It means that user k obtains amplitude gain on the active intelligent reflector. Defined as , It means taking the minimum eigenvalue of the matrix. Representation function The zero point, Defined as , Defined as , Defined as . Represents the unit matrix with dimension M. By solving the sub-problem, we can get the optimal gain solution of the active smart reflector. .

[0041] Optimize the gain 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.

[0042] 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 to 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 the 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.

[0043] The effect of the present invention is further illustrated by simulation below: (1) Simulation parameters 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 .

[0044] (2) Simulation results and data analysis Figure 2 Describes the CRB value estimated by the target response matrix with respect 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.

[0045] 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.

[0046] Figure 4 The relationship between the CRB estimated by the target response matrix of the covert communication and perception integrated system under different conditions and the number of reflective elements on the intelligent reflective surface is given. Figure 4 As shown, ARIS-radar-only means that the active intelligent reflective surface assisted covert communication perception integrated system only uses the radar function, ARIS-ISAC means that the active intelligent reflective surface assisted covert communication perception integrated system uses both communication and radar functions, and PRIS-ISAC means that the passive intelligent reflective surface assisted covert communication perception integrated system uses both communication and radar functions. Represents the maximum amplitude coefficient of the active intelligent reflector. The CRB performance of the target response matrix estimation is enhanced with the participation of the number of reflective elements of the intelligent reflector. This is because the number of reflective elements of the intelligent reflector can provide the system with a higher degree of freedom of radar. In addition, it can be observed that the covert communication perception integrated system assisted by the active intelligent reflector is better than the covert communication perception integrated system assisted by the passive intelligent reflector. And in the covert communication perception integrated system assisted by the active intelligent reflector, the larger the amplitude factor, the better the performance of the system.

[0047] 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.

[0048] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A design method for a concealed communication and perception integrated system based on an intelligent reflective surface, characterized in that: The steps include: S1: Establish a concealed communication perception integrated system model based on an intelligent reflective surface, wherein 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, the active intelligent reflective 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 in the system scenario, the concealed communication signal model is used to establish a communication signal received by a concealed user and a public user, and the perception signal model is used to establish an echo signal containing target information received by the base station; S2: Based on the covert communication perception integrated system model, an optimization problem is established under system constraints as the original problem, that is, the Cramer-Rao bound estimated by the target response matrix 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; S3: Based on the optimization objective function and optimization variables, the original optimization problem established in S2 is split into two sub-problems by 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 only the active smart reflector is is a sub-problem of optimizing variables; solve the two sub-problems in sequence to obtain the optimal solution of the corresponding optimization variable of each sub-problem; S4: The optimal beamforming vector of the base station transmission waveform for the two sub-problems obtained in step S3 and the gain of the active smart reflector , updated alternately to obtain the optimal solution of the original problem of the optimization problem in S2 until the convergence of the objective function is achieved; The covert communication perception integrated system model is optimized with the optimal solution obtained.

2. According to claim 1, a method for designing a covert communication and perception integrated system based on an intelligent reflective surface is characterized in that: The communication-sensing 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 potentially hostile guardian Willie; the base station transmits a dual-function signal and is assisted by an active intelligent reflector. A single-antenna public user communicates with a single-antenna hidden user Bob, and at the same time perceives a potential hostile guardian Willie, who intends to monitor the communication of the hidden user; The specific expression of the active intelligent reflector model is: ； ； in, represents the gain vector of the active smart reflector, Indicates The amplitude of the coefficient, Indicates The phase shift of the coefficients, M represents the number of components of the active smart reflector, diag {*} means extracting the vector elements in the brackets to form a diagonal matrix. j represents an imaginary unit; The channel model includes a dual-function base station to user k Channel , 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, a channel from a dual-function base station to an 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 L symbols form a dual-function signal. The base station l The transmitted signal at the symbol is: ； in, Indicates that no covert signal is sent. l The transmitted signal at symbols is Indicates l Symbol No. k The corresponding beamforming vector of the user's signal is, Indicates l Symbol No. k The signal of a user, Indicates l The perceptual signal component dedicated to each symbol, Indicates when a covert signal is sent. l The transmitted signal at symbols is represents the beamforming vector of the signal sent to the hidden user Bob, Represents the signal sent to the hidden user Bob; No. k User in l The received signal at the symbol is: ； in, Indicates that no covert signal is sent. k User in l The received signal at symbols is Indicates when a covert signal is sent. k User in l The received signal at symbols is Indicates l The symbol in k Additive Gaussian white noise at each user, Indicates l Additive Gaussian white noise of 10 symbols at the active intelligent reflector; The covert system model includes the hostile guardian Willie in the l The hypothesis test and total error detection probability at the symbol are expressed as: ； ； in, represents the hypothesis test that the base station transmission does not contain a hidden signal, It represents the composite channel between the communication and perception integrated base station and the hostile guardian through the active intelligent reflection surface. , Indicates l Gaussian white noise at symbols, 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 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, Indicates that the base station is l The transmitted signal at symbols is represents the Gaussian white noise at the active intelligent reflector, represents the Gaussian white noise of the entire channel.

3. According to claim 2, a method for designing a concealed communication and perception integrated system based on an intelligent reflective surface is characterized in that: 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 next k The signal-to-interference-noise ratio of each user is It represents the minimum signal-to-interference-noise ratio threshold to ensure the user communication quality. Represents the composite channel between the communication and perception integrated base station and the hostile guardian through the active intelligent reflector The conjugate transpose of express The solution of represents the concealment coefficient, L Indicates the communication symbol length, represents the Gaussian white noise power variance at the hostile guardian, represents 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.

4. According to claim 3, a method for designing a concealed communication and perception integrated system based on an intelligent reflective surface is 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 definite relaxation method is used to transform the subproblem into a semi-positive definite 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 the active smart reflector The MM algorithm is used to solve the optimal solution of the active smart reflector gain. ; Optimize the gain 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.

5. According to claim 4, a method for designing a covert communication and perception integrated system based on an intelligent reflective surface 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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