Secure transmission method for improving sensing performance of ISAC system for active RIS scene

Abstract

The invention discloses a secure transmission method for improving the sensing performance of an ISAC system for an active RIS scene, and the method constructs an ISAC system based on the assistance of an active RIS to complete communication and sensing tasks at the same time. When the active RIS assists the system in safe communication, the active RIS can effectively overcome serious multiplicative interference caused by the four-hop radar, so that the sensing performance of the system is improved. Considering that the active RIS has inevitable thermal noise, the Cramer-Rao lower bound (CRLB) of system perception under thermal noise interference is deduced. In order to efficiently solve the constructed non-convex optimization problem, the constructed non-convex optimization problem is divided into two sub-problems to be optimized and solved respectively. Through a block coordinate descent method, a minimization-maximization algorithm (MM), a positive semidefinite relaxation method (SDR) and a Taylor approximation method, a BS emission beam forming matrix and a gain phase shift joint matrix of an active RIS are solved respectively. According to the invention, the beamforming and active RIS reflection design is combined, so that the comprehensive performance of system perception and safety is effectively improved.

Description

Technical Field

[0001] The present invention relates to a secure transmission method for improving ISAC system perception performance in an active RIS scenario, and belongs to the technical field of wireless communication. Background Art

[0002] In recent years, driven by the demand for precise applications, the industry has been committed to building integrated network systems that fuse perception and communication functions, spurring the innovation and development of integrated synaesthesia (ISAC) technology. Based on differences in core design concepts, ISAC systems are primarily categorized into three architecture types: Communication-centric (C&C) designs integrate perception functions within the communication platform, prioritizing communication performance; Radar-centric (R&C) designs prioritize perception, embedding communication information into perception waveforms to achieve limited data transmission; and Joint Waveform Designs overcome the limitations of the first two by innovatively constructing new waveforms independent of traditional communication / radar signals, achieving a dynamic balance between perception and communication within a spectrum-sharing framework. This design paradigm not only empowers the system with greater freedom but also significantly improves spectrum efficiency, energy utilization, and hardware reuse through functional synergy, while creating integration gains unattainable with traditional discrete systems.

[0003] While ISAC technology demonstrates significant advantages, data security issues arising from its broadcast transmission characteristics and signal superposition characteristics require urgent resolution. Current physical layer security (PLS) technologies primarily rely on channel differences between base stations and legitimate users / eavesdroppers, exploiting these differences through techniques such as beamforming and cooperative jamming. However, the widespread use of active jammers leads to a surge in energy consumption and limits security enhancements in complex channel environments. Notably, breakthroughs in reconfigurable smart surfaces (RIS) offer a new approach. By deploying passive reflector arrays with programmable phase shifting, RIS precisely controls the direction of electromagnetic wave propagation, enabling reflective signals to constructively superimpose at the target receiver while simultaneously generating destructive interference at the eavesdropping end. This passive control mechanism effectively avoids the high energy consumption and high costs of traditional solutions while ensuring security, opening up a new path for enhancing the security of ISAC systems.

[0004] The perception performance of an ISAC system is typically structured as a threshold constraint. However, in some applications with high perception performance requirements, the system's perception performance is expected to be as strong as possible. If the system's secure transmission performance is also considered, using a RIS to facilitate communication will severely degrade the system's perception performance if the direct link between the base station and the user is disrupted. This is because the system's perception function relies on the virtual link established by the RIS, and its perception model can be modeled as a four-hop radar. The severe multiplicative fading of a four-hop radar can severely degrade the system's perception performance. Some literature addresses this issue by deploying sensors at the RIS, reducing the number of hops for the perception signal by one to mitigate severe multiplicative fading. However, this solution stores the perception data at the RIS. For applications where base stations require perception data for communication, this solution requires additional consideration of the communication between the RIS and the base station. Alternatively, enhancing signal strength at the RIS can also overcome the severe multiplicative fading of four-hop radars. The base station can then directly receive the target's sensing echo, thereby extracting sensing data. However, no research has yet focused on improving sensing performance while using an active RIS to address the severe multiplicative fading caused by four-hop radars in ISAC systems. Summary of the Invention

[0005] The present invention addresses the shortcomings and deficiencies of the aforementioned prior art by proposing a secure transmission method for improving the ISAC system's perception performance in active RIS scenarios. This method leverages the gain provided by active RIS for reflected signals to increase the signal-to-noise ratio (SNR) of the echo received by the base station, thereby improving the system's perception performance. This method also exploits the channel differences between the user and the eavesdropper and adjusts the reflection coefficient of the active RIS to improve the user's received SNR and reduce the eavesdropper's SNR, achieving secure transmission.

[0006] The technical solution adopted by the present invention to solve the technical problem is: a secure transmission method for improving the ISAC system perception performance in an active RIS scenario, the method comprising the following steps:

[0007] Step 1: Build a system model that includes the BS, active RIS, users, and sensing targets (potential eavesdroppers). The direct link between the BS and the user is blocked by an obstacle, and only the active RIS is used to complete the communication and sensing tasks simultaneously.

[0008] Step 2: To overcome the severe multiplicative path loss of the four-hop radar, the system uses an active RIS that amplifies the signal during reflection. The Cramer-Rao lower bound (CRLB) of the system perception is derived taking into account the inevitable thermal noise of the active RIS.

[0009] Step 3: Construct a BS-associated transmit beamforming matrix and the associated optimization problem of the active RIS gain and phase shift to maximize the system's safe rate and the weighted sum of the Cramér-Rao lower bound (CRLB) while simultaneously satisfying the system's target detection requirements, the BS transmit power budget, the active RIS transmit power budget, and the active RIS maximum gain constraint.

[0010] Step 4: Consider the distance between the perceived target and the active RIS. When the distance between the two is close enough, the perceived target cannot be treated as just a point. Therefore, the perceived target is modeled as an extended target, and a similar optimization problem is established accordingly.

[0011] Step 5: Based on the fact that the channel between the BS and the active RIS is a line-of-sight channel, the BS transmit beamforming matrix is solved using the minimization-maximization algorithm (MM) and the semidefinite relaxation method (SDR).

[0012] Step 6: Based on the optimal solution of the BS transmit beamforming matrix obtained in step 5 above, continue to use the SDR-MM method and adopt the Taylor approximation method to solve the joint gain and phase shift matrix of the active RIS;

[0013] Step 7: Based on the BS transmit beamforming matrix obtained in step 5 and the joint gain and phase shift matrix of the active RIS obtained in step 6, the block coordinate descent (BCD) method is used to iteratively update the BS transmit beamforming matrix and the joint gain and phase shift matrix of the active RIS until they converge to achieve the optimal system perception and security performance.

[0014] Furthermore, in step 1 above, the present invention establishes an ISAC system consisting of an ISAC BS with M transmit and receive antennas, an N-element active RIS, a single-antenna user, and a sensing target considered a potential eavesdropper. Assume that the direct path from the BS to the ground node is blocked due to the complex urban environment. The active RIS is used to establish an additional link to assist the BS in achieving both communication and sensing functions. The dual-function signal transmitted by the BS in the first time slot of the system model of the present invention is:

[0015]

[0016] in is the communication symbol to be transmitted, is a dedicated sensing signal. Assume that d is a pseudo-random sequence that satisfies and It is known a priori by the BS, users and eavesdroppers. It is assumed that the communication signal is independent of the sensing signal. and Define a joint signal vector for the sensing signal beamforming matrix and the communication signal beamforming vector respectively and a joint beamforming matrix where w i is the i-th column of the joint beamforming matrix W.

[0017] Give the channel coefficients and Denote the channels from the BS to the RIS, from the RIS to the user, and from the RIS to the eavesdropper, respectively. It is assumed that the CSI of the aforementioned channels is fully known at the BS by applying low-complexity channel estimation methods. It is worth noting that we assume that the eavesdropper eavesdrops on the communication signals by actively attacking the system. Specifically, the eavesdropper can mislead the BS by sending pilot signals during the channel estimation phase and impersonate the legitimate user. Therefore, the BS can obtain the CSI of the user and the eavesdropper during the channel estimation process.

[0018] In addition, due to the severe multiplicative path loss, we can ignore the signal reflected more than twice by the active RIS. Based on this, the signals received by the user and the eavesdropper are given as:

[0019]

[0020] in, Represents AWGN. Φ=dia g(φ1,φ2,…,φ N ) is the diagonalized matrix of reflection coefficients, is the i-th reflection coefficient, where β i ≥0,

[0021] Compared with the traditional passive RIS, the components of the active RIS are equipped with a reflective amplifier, which consumes extra power to amplify the incident signal. Therefore, the thermal noise of the active RIS cannot be ignored. i >1 is the maximum gain of the amplifier, so there is naturally β i ≤η i .definition is the thermal noise of the active RIS.

[0022] It is assumed that the potential target is located in the NLoS region of the BS due to occlusion, and the virtual LoS channel created by the active RIS is much stronger than the NLoS channel. Therefore, the impact of the NLoS channel between the BS and the perceived target is negligible. In addition, it is assumed that the location of the active RIS is carefully designed with few obstacles.

[0023] If the spatial range of the target is narrow (point-shaped target), the perceived target can be regarded as a single scatterer, and the reflected echo signal consists of only one path. In this case, the round-trip target response matrix from the active RIS to the target and back to the active RIS can be expressed as:

[0024]

[0025] This is based on a clutter-free model (assuming there are no obstacles around the target that could interfere with the RIS). β represents the complex path loss coefficient of the response channel, and θ is the departure angle from the active RIS to the sensing target. In this case, the complex coefficient β and the target DoAθ are unknown parameters to be estimated.

[0026] If the target is close enough to the active RIS, the target cannot be simply perceived as a single scatterer, but rather as a collection of several scatterers whose reflected echo signals contain paths at multiple angles. Therefore, the sensor at the active RIS needs to estimate the complete target response matrix, i.e. It can describe the combined effect of all scatterers. In this case, the complete target response matrix is an unknown parameter to be estimated.

[0027] Then consider the radar signal received by the BS. Since the communication signal and the sensor signal can be used to illuminate the sensor target at the same time, the radar echo signal received by the BS is given as:

[0028]

[0029] in, They represent the dynamic thermal noise of the active RIS and the receiving noise of the BS in the RIS-BS uplink, respectively.

[0030] Note that the reflection coefficients of the two reflections during the transmission are considered to be the same, because the active RIS cannot switch its components during the time interval between the two reflections. This means that the distance between the active RIS and the target is not sufficient for the RIS to switch its components during the propagation interval. In addition, it should be noted that the radar echo signal is the direct reflection of the RIS. It is considered interference because it has no information about the target.

[0031] Finally, the active RIS reflects the transmitted signal to the user, eavesdropper, and target. The signal received during this process is called the first reflected signal. The active RIS reflects the target's echo signal. The signal received by the active RIS at this time is called the second reflected signal. The formula is as follows

[0032]

[0033] Based on the above transmission model, the SNR of the user and the eavesdropper are given as:

[0034]

[0035] Note that the user and the eavesdropper are assumed to be able to eliminate the perceptual interference by the prior knowledge of the sensing signal. Therefore, the achievable transmission rate (nat / s / Hz) of the user and the eavesdropper can be written as

[0036] R U =ln(1+ξ U ),R E =ln(1+ξ E )

[0037] Then the safe rate from user to BS is given as:

[0038] S=[R U -R E ] +

[0039] For radar sensing, it is important to note that the BS receiver has full knowledge of the transmitted signal x, so it can exploit the communication waveform as well as the sensing signal in the radar echo. The following performance metrics are defined:

[0040]

[0041] Then, the SINR of the radar echo received by the BS is expressed as ξ R =tr(ARA H J s -1 ),

[0042] Among them, J s represents the interference plus noise covariance matrix, which is given by s =BRB H +N, where

[0043] In addition, the transmission power of BS is given Give the energy consumption of active RIS in the first and second reflections

[0044]

[0045] Furthermore, the above step 2 of the present invention provides a specific derivation process for estimating unknown parameters of CRB, and uses it as the lower bound of the variance of any unbiased estimate. First, consider a point target, expand the transmitted signal in time to become L time slots, and re-express the received echo signal

[0046]

[0047] Expand the target response matrix

[0048]

[0049] Establish an estimated parameter space for the target parameter to be estimated

[0050] χ=[θ,β] T

[0051] β=[Re{β},Im{β}]

[0052] Then, the echo signal is vectorized

[0053]

[0054] Then, write the information matrix FIM of the estimated parameter space,

[0055]

[0056] Restate the information matrix FIM, First write the partial derivatives with respect to the two parameters,

[0057]

[0058]

[0059] Expand the partial derivatives of the target response matrix

[0060]

[0061] Give the expression of each element in the FIM matrix

[0062]

[0063] Since the CRBs for estimating the two parameters have similar forms, this patent focuses on estimating DoA.

[0064]

[0065] There are the following identity transformations,

[0066] tr(a T (θ)ΦH BR )=tr(v T diag(a(θ))H BR )

[0067] v=[φ1,φ2,…,φ N ] T

[0068] Then we have:

[0069]

[0070] A=diag(a(θ))

[0071] In addition, there are:

[0072]

[0073] tr(a(θ)a H (θ))=N

[0074] Then, expand the partial derivative of Z with respect to θ in the above expression and substitute it into the expression of CRB:

[0075]

[0076] in,

[0077]

[0078] Furthermore, the CRB under the extended target is derived. The echo signal received by the sensor is vectored:

[0079]

[0080] Find the partial derivative:

[0081]

[0082] The estimated parameters Split into real and imaginary parts. Rewrite FIM

[0083]

[0084] According to the above formula, CRB can be obtained.

[0085]

[0086] In addition, only when M≥rank(R)≥N≥rank(H BR )hour, Bounded and estimable.

[0087] Furthermore, in step 3 of the present invention, a problem is established to maximize the weighted sum of the system safety rate and the Cramér-Rao lower bound (CRLB), while simultaneously satisfying the system target detection requirements, BS transmit power budget, active RIS transmit power budget and active RIS maximum gain constraints.

[0088]

[0089]

[0090] The objective function represents the normalized weighted sum of the system safety rate and the target arrival angle CRB, ρ∈(0,1) is the weighting factor, Qs ,Q c are the normalized parameters of the system safety rate and target arrival angle CRB, which are the values of the objective function when ρ = 1 and ρ = 0, respectively. Solving the optimization problem posed by these two parameters is two special cases of P1, so the solution method is the same; constraint C1 represents the constraint on the radar echo signal-to-noise ratio; constraint C2 represents the constraint on the total BS transmission power; constraint C3 represents the constraint on the total power of the two reflections of the active RIS; constraint C4 represents the constraint on the maximum gain of the active RIS.

[0091] The two performance metrics have different units and scales, solving the CRB minimization problem and the confidentiality rate maximization problem, respectively. The optimal solution then generates a lower bound on the CRB and an upper bound on the confidentiality rate, which are defined as normalization constants, namely Qc and Qs.

[0092] Furthermore, in the above step 4 of the present invention, the point-like target of P1 is changed to an extended target, and a similar optimization problem P2 is obtained:

[0093]

[0094] Furthermore, in step 5 of the present invention, based on the fact that the channel between the BS and the active RIS is a line-of-sight channel, the BS transmit beamforming matrix is solved using the minimization-maximization algorithm (MM) and the semidefinite relaxation method (SDR). Since the channel between the BS and the active RIS is a line-of-sight channel, the BS transmit beamforming matrix needs to be adjusted to perform beamforming so that the BS transmitted signal is reflected by the active RIS as much as possible, reducing the loss of useful signals. Specifically,

[0095] Fix the joint vector v of the gain and phase shift of the active RIS, expand the safety rate and define new variables. Non-convexity exists in the radar SINR constraint and the objective function. For the radar SINR constraint, Proposition 1 is given, according to which ξ can be found R A convex approximation of is used. For the safe rate, the MM algorithm is used. Proposition 2 is applied to obtain an upper convex surrogate function, which is then solved iteratively. For the CRB, expansion is performed and slack variables are introduced to solve the problem. Furthermore, the SDR method is applied to transform the problem into an SDP problem.

[0096] Specifically, we first deal with the radar SINR constraint:

[0097] Given Proposition 1, given X (k) and J (k) , that is, the values of X and J at the kth iteration, then:

[0098]

[0099] This gives tr(X H J -1X), so let X = AW, then:

[0100]

[0101] Among them, w i(k) represents w i The kth iteration of is a constant, and substituting it into the radar SINR constraint, we get

[0102]

[0103] Next, we deal with the safe rate: Given Proposition 2, for any convex function f(X), we have:

[0104]

[0105] Applying Lemma 2 to the safe rate, we obtain:

[0106]

[0107] Next, process CRB: expand it,

[0108]

[0109] Finally, applying the SDR method, let And by introducing slack variables, we get a convex problem that can be solved directly:

[0110]

[0111]

[0112] Furthermore, to solve the optimization problem under the extended objective, we only need to solve the non-convexity of the CRB. However, the CRB is already convex and does not need to be transformed.

[0113] Furthermore, in step 6 of the present invention, based on the optimal solution for the BS transmit beamforming matrix obtained, the SDR-MM method is continued, and the Taylor approximation method is employed to solve the joint gain-phase shift matrix of the active RIS. The active RIS constructs N virtual channels, reflecting the signals transmitted from the BS to the user and the eavesdropper respectively. The active RIS utilizes the channel differences between the two channels to adjust the joint gain-phase shift matrix of the active RIS, thereby increasing the user's received signal-to-noise ratio and reducing the eavesdropper's eavesdropping signal-to-noise ratio. Specifically,

[0114] The optimal solution W for the BS transmit beamforming matrix is fixed. The non-convexity of the problem is reflected in the radar SINR constraint, the active RIS reflected power constraint, and the objective function. For the radar SINR constraint, Proposition 1 is used to obtain a lower bound for the radar SINR constraint. To address the cubic term associated with the phase shift, Proposition 3 is introduced. For the active RIS reflected power constraint, the problem is transformed into an SDP problem by defining new symbols. For the secure rate, the MM algorithm is used, using a first-order Taylor approximation at a given point. For the CRB, slack variables are introduced and the problem is transformed into an SDP problem.

[0115] Specifically, we first solve the radar SINR constraint: Similarly, applying Proposition 1, we get the lower bound of the radar SINR constraint

[0116]

[0117] Using the formula tr(A H B)=(vec(A)) H vec(B) and Rewrite the first two terms of the above equation,

[0118]

[0119] Expanding the third term J yields a quartic expression for phase shift, which consists of a quartic term, a cubic term, a quadratic term, and a constant term.

[0120] Apply the formula The quartic term can be transformed into

[0121]

[0122] in, Similarly, the quadratic term can be transformed into

[0123]

[0124] in, To solve the cubic term, we introduce Proposition 3: Given K (l) , L (l) , then

[0125]

[0126] From this we can get

[0127]

[0128] in,

[0129]

[0130] Thus, we obtain a tractable lower bound

[0131]

[0132] Next, we deal with the active RIS reflected power constraint and convert the active RIS transmit power expression into the quadratic form of V

[0133]

[0134] Next, we deal with the safety rate, at a given point Using the first-order Taylor approximation,

[0135]

[0136] Next, solve CRB and expand it.

[0137]

[0138] Finally, by introducing slack variables, we obtain the convex problem that can be solved directly

[0139]

[0140]

[0141] in,

[0142] Finally, because the SDR method is used and the rank-one solution is ignored, the eigenvalue decomposition and Gaussian randomization methods are applied to recover the rank-one solution from the obtained solution.

[0143] Furthermore, to solve the optimization problem under the extended objective, we only need to solve the non-convexity of CRB. We can convert CRB into a convex matrix by defining a new notation:

[0144]

[0145] in,

[0146] Furthermore, in step 7 of the present invention, based on the BS transmit beamforming matrix obtained in step 5 and the joint gain and phase shift matrix of the active RIS obtained in step 6, the BS transmit beamforming matrix and the joint gain and phase shift matrix of the active RIS are iteratively updated through the block coordinate descent method (BCD) until the joint gain and phase shift matrix of the BS transmit beamforming matrix and the active RIS converge, thereby achieving a balance between secure transmission and accurate radar parameter estimation, and obtaining optimal system perception and safety comprehensive performance.

[0147] Beneficial effects:

[0148] 1. The present invention fully utilizes the characteristics of active RIS, improves the signal-to-noise ratio of the echo received by the base station, effectively overcomes the serious multiplicative path loss caused by the four-hop radar, and thus improves the perception performance of the system.

[0149] 2. The present invention utilizes the channel difference between the user and the eavesdropper and exacerbates this channel difference through the virtual channel constructed by active RIS, thereby improving the user's receiving signal-to-noise ratio and reducing the eavesdropper's eavesdropping signal-to-noise ratio, thereby improving the security performance of the system.

[0150] 3. The weighted optimization problem constructed in the present invention can adapt to scenarios with different emphasis on the system's perception performance and safety performance by simply adjusting the value of the weighting factor.

[0151] 2. The present invention finds a suitable solution for the base station transmit beamforming matrix and the active RIS gain and phase shift matrix. BRIEF DESCRIPTION OF THE DRAWINGS

[0152] Figure 1 A diagram of a secure ISAC system model for improving system perception performance in an active RIS scenario provided by the present invention.

[0153] Figure 2 This is a flow chart of a secure ISAC system optimization method for improving system perception performance in an active RIS scenario provided by the present invention. DETAILED DESCRIPTION

[0154] In order to make the purpose, technical solutions and advantages of the present invention more clear, the present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

[0155] This paper proposes a secure transmission method for improving the perception performance of an ISAC system in an active RIS scenario. This method is applicable to scenarios where the direct link between the base station (BS) and the user is blocked by obstacles, requiring the active RIS to simultaneously perform both communication and perception tasks, and where an eavesdropper is present. In an ISAC system consisting of an ISAC BS with M transmit and receive antennas, an N-element active RIS, a single-antenna user, and a perceived target considered a potential eavesdropper, assume that the direct path from the BS to the ground node is blocked due to a complex urban environment. The active RIS is used to establish an additional link to assist the BS in achieving both communication and perception. The BS's transmit beamforming matrix affects the active RIS's reflection of useful signals, which in turn affects the received signal-to-noise ratio (SNR) of the user and eavesdropper, as well as the SNR of the BS's received echo, impacting the system's security and perception performance. The active RIS's joint gain and phase shift matrix affects the gain of the constructed virtual channel, further impacting the system's security and perception performance. Based on this premise, a compromise between the system's security and perception performance is achieved by adjusting the BS's transmit beamforming matrix and the active RIS's joint gain and phase shift matrix.

[0156] like Figure 1 As shown, the system of the present invention includes an ISAC BS with M transmit and receive antennas, an N-element active RIS, a single-antenna user, and a sensing target considered a potential eavesdropper. Assume that the direct path from the BS to the ground node is blocked due to the complex urban environment. The active RIS is used to build additional links to assist the BS in simultaneously achieving communication and sensing functions. Due to the characteristics of wireless transmission, information can be easily eavesdropped by eavesdroppers during the process of being transmitted from the BS to the user. It is necessary to suppress eavesdropping and improve the security performance of the system by adjusting the joint gain and phase shift matrix of the active RIS. At the same time, it is noted that in some scenarios where the accuracy of perception parameters is emphasized, the signal-to-noise ratio of the BS received echo can be improved by adjusting the BS's transmit beamforming matrix and the joint gain and phase shift matrix of the active RIS, thereby improving the system's perception performance. This achieves a compromise between the system's security and perception performance while meeting the system's target detection requirements.

[0157] Figure 2 The present invention provides a flow chart of a secure transmission method for improving ISAC system perception performance in an active RIS scenario. The method includes the following steps:

[0158] Step 1: Establish a system model that includes a base station (BS), an active RIS, a user, and a sensing target (potential eavesdropper). The direct link between the BS and the user is blocked by an obstacle, and only the active RIS is used to simultaneously complete the communication and sensing tasks. Specifically, this involves establishing an ISAC system consisting of an ISAC BS with M transmit and receive antennas, an N-element active RIS, a single-antenna user, and a sensing target considered a potential eavesdropper. Assume that due to the complex urban environment, the direct path from the BS to the ground node is blocked. The active RIS is used to build additional links to assist the BS in simultaneously achieving communication and sensing functions. The dual-function signal transmitted by the BS in the first time slot of the system model of the present invention is:

[0159]

[0160] in is the communication symbol to be transmitted, is a dedicated sensing signal. Assume that d is a pseudo-random sequence that satisfies and It is known a priori by the BS, users and eavesdroppers. It is assumed that the communication signal is independent of the sensing signal. and Define a joint signal vector for the sensing signal beamforming matrix and the communication signal beamforming vector respectively and a joint beamforming matrix where w i is the i-th column of the joint beamforming matrix W.

[0161] Give the channel coefficients and Denote the channels from the BS to the RIS, from the RIS to the user, and from the RIS to the eavesdropper, respectively. It is assumed that the CSI of the aforementioned channels is fully known at the BS by applying low-complexity channel estimation methods. It is worth noting that we assume that the eavesdropper eavesdrops on the communication signals by actively attacking the system. Specifically, the eavesdropper can mislead the BS by sending pilot signals during the channel estimation phase and impersonate the legitimate user. Therefore, the BS can obtain the CSI of the user and the eavesdropper during the channel estimation process.

[0162] In addition, due to the severe multiplicative path loss, we can ignore the signal reflected more than twice by the active RIS. Based on this, the signals received by the user and the eavesdropper are given as

[0163]

[0164] in, Represents AWGN. Φ=diag(φ1,φ2,…,φ N ) is the diagonalized matrix of reflection coefficients, is the i-th reflection coefficient, where β i ≥0,

[0165] Performance comparison:

[0166] Compared with the traditional passive RIS, the active RIS of the present invention is equipped with a reflective amplifier. The amplifier consumes extra power to amplify the incident signal. Therefore, the thermal noise of the active RIS cannot be ignored. i >1 is the maximum gain of the amplifier, so there is naturally β i ≤η i .definition is the thermal noise of the active RIS.

[0167] It is assumed that the potential target is located in the NLoS region of the BS due to occlusion, and the virtual LoS channel created by the active RIS is much stronger than the NLoS channel. Therefore, the impact of the NLoS channel between the BS and the perceived target is negligible. In addition, it is assumed that the location of the active RIS is carefully designed with few obstacles.

[0168] If the spatial range of the target is narrow (point target), the perceived target can be regarded as a single scatterer, and the reflected echo signal consists of only one path. In this case, the round-trip target response matrix from the active RIS to the target and back to the active RIS can be expressed as

[0169]

[0170] This is based on a clutter-free model (assuming there are no obstacles around the target that could interfere with the RIS). β represents the complex path loss coefficient of the response channel, and θ is the departure angle from the active RIS to the sensing target. In this case, the complex coefficient β and the target DoAθ are unknown parameters to be estimated.

[0171] If the target is close enough to the active RIS, the target cannot be simply perceived as a single scatterer, but rather as a collection of several scatterers whose reflected echo signals contain paths at multiple angles. Therefore, the sensor at the active RIS needs to estimate the complete target response matrix, i.e. It can describe the combined effect of all scatterers. In this case, the complete target response matrix is an unknown parameter to be estimated.

[0172] Then consider the radar signal received by the BS. Since the communication signal and the sensor signal can be used to illuminate the sensor target at the same time, the radar echo signal received by the BS is given accordingly.

[0173]

[0174] in, They represent the dynamic thermal noise of the active RIS and the receiving noise of the BS in the RIS-BS uplink, respectively.

[0175] Note that the reflection coefficients of the two reflections during the transmission are considered to be the same, because the active RIS cannot switch its components during the time interval between the two reflections. This means that the distance between the active RIS and the target is not sufficient for the RIS to switch its components during the propagation interval. In addition, it should be noted that the radar echo signal is the direct reflection of the RIS. It is considered interference because it has no information about the target.

[0176] Finally, the active RIS reflects the transmitted signal to the user, eavesdropper, and target. The signal received during this process is called the first reflected signal. The active RIS reflects the target's echo signal. The signal received by the active RIS at this time is called the second reflected signal. The formula is as follows

[0177]

[0178] Based on the above transmission model, the SNR of the user and the eavesdropper are given as:

[0179]

[0180] Note that the user and the eavesdropper are assumed to be able to eliminate the perceptual interference by the prior knowledge of the sensing signal. Therefore, the achievable transmission rate (nat / s / Hz) of the user and the eavesdropper can be written as

[0181] R U =ln(1+ξ U ),R E =ln(1+ξ E )

[0182] Then the safe rate from user to BS is given as:

[0183] S=[R U -R E ] +

[0184] For radar sensing, it is important to note that the BS receiver has full knowledge of the transmitted signal x, and can therefore exploit the communication waveform as well as the sensing signal in the radar echo. The following performance metrics are defined:

[0185]

[0186] Then, the SINR of the radar echo received by the BS is expressed as ξ R =tr(ARA H J s -1 ),

[0187] Among them, J s represents the interference plus noise covariance matrix, which is given by s =BRB H +N, where

[0188] In addition, the transmission power of BS is given Give the energy consumption of active RIS in the first and second reflections

[0189]

[0190] Step 2: To overcome the severe multiplicative path loss of the four-hop radar, the system uses an active RIS that can amplify the signal during reflection. The Cramer-Rao lower bound (CRLB) of the system perception is derived taking into account the inevitable thermal noise of the active RIS. Specifically, the system first considers a point target, expands the transmitted signal in time to become L time slots, and reformulates the received echo signal.

[0191]

[0192] Expand the target response matrix

[0193]

[0194] Establish an estimated parameter space for the target parameter to be estimated

[0195] χ=[θ,β] T

[0196] β=[Re{β},Im{β}]

[0197] Then, the echo signal is vectorized

[0198]

[0199] Then, write the information matrix FIM of the estimated parameter space,

[0200]

[0201] Restate the information matrix FIM, First write the partial derivatives with respect to the two parameters,

[0202]

[0203] Expand the partial derivatives of the target response matrix

[0204]

[0205] Λ N =diag(0,1,…,N-1)

[0206] Give the expression of each element in the FIM matrix

[0207]

[0208] Since the CRBs for estimating the two parameters have similar forms, this patent focuses on estimating DoA.

[0209]

[0210] There are the following identity transformations,

[0211] tr(a T (θ)ΦH BR )=tr(v T diag(a(θ))H BR )

[0212] v=[φ1,φ2,…,φ N ] T

[0213] Then there is

[0214]

[0215] A=diag(a(θ))

[0216] In addition, there are:

[0217]

[0218] tr(a(θ)a H (θ))=N

[0219] Then, expand the partial derivative of Z with respect to θ in the above expression and substitute it into the expression of CRB:

[0220]

[0221] in,

[0222]

[0223] Furthermore, the CRB under the extended target is derived. The echo signal received by the sensor is vectored:

[0224]

[0225] Find partial derivatives

[0226]

[0227] The estimated parameters Split into real and imaginary parts. Rewrite FIM

[0228]

[0229] According to the above formula, CRB can be obtained.

[0230]

[0231] In addition, only when M≥rank(R)≥N≥rank(H BR )hour, Bounded and estimable.

[0232] Step 3: Construct a transmit beamforming matrix associated with the BS, and the associated optimization problem of the active RIS gain and phase shift to maximize the system safety rate and the weighted sum of the Cramér-Rao lower bound (CRLB), while simultaneously satisfying the system target detection requirements, the BS transmit power budget, the active RIS transmit power budget, and the active RIS maximum gain constraint: The specific expression is:

[0233]

[0234] The objective function represents the normalized weighted sum of the system safety rate and the target arrival angle CRB, ρ∈(0,1) is the weighting factor, Q s ,Q c are the normalized parameters of the system safety rate and target arrival angle CRB, which are the values of the objective function when ρ = 1 and ρ = 0, respectively. Solving the optimization problem posed by these two parameters is two special cases of P1, so the solution method is the same; constraint C1 represents the constraint on the radar echo signal-to-noise ratio; constraint C2 represents the constraint on the total BS transmission power; constraint C3 represents the constraint on the total power of the two reflections of the active RIS; constraint C4 represents the constraint on the maximum gain of the active RIS.

[0235] The two performance metrics have different units and scales, solving the CRB minimization problem and the confidentiality rate maximization problem, respectively. The optimal solution then generates a lower bound on the CRB and an upper bound on the confidentiality rate, which are defined as normalization constants, namely Qc and Qs.

[0236] Step 4: Consider the distance between the perceived target and the active RIS. When the distance between the two is close enough, the perceived target cannot be treated as just a point. Therefore, the perceived target is modeled as an extended target, and a similar optimization problem is established accordingly: the specific expression is:

[0237]

[0238] Step 5: Based on the fact that the channel between the BS and the active RIS is a line-of-sight channel, the minimization-maximization algorithm (MM) and the semidefinite relaxation method (SDR) are used to solve the BS transmit beamforming matrix. Specifically, since the channel between the BS and the active RIS is a line-of-sight channel, the BS transmit beamforming matrix needs to be adjusted to perform beamforming so that the BS transmitted signal is reflected by the active RIS as much as possible, reducing the loss of useful signals. Specifically:

[0239] Fix the joint vector v of the gain and phase shift of the active RIS, expand the safety rate and define new variables. Non-convexity exists in the radar SINR constraint and the objective function. For the radar SINR constraint, Proposition 1 is given, according to which ξ can be found R A convex approximation of is used. For the safe rate, the MM algorithm is used. Proposition 2 is applied to obtain an upper convex surrogate function, which is then solved iteratively. For the CRB, expansion is performed and slack variables are introduced to solve the problem. Furthermore, the SDR method is applied to transform the problem into an SDP problem.

[0240] Specifically, we first deal with the radar SINR constraint:

[0241] Given Proposition 1, given X (k) and J (k) , that is, the values of X and J at the kth iteration, then:

[0242]

[0243] This gives tr(X H J -1 X), so let X = AW, then:

[0244]

[0245] Among them, w i(k) Indicates w i The kth iteration of is a constant, and substituting it into the radar SINR constraint, we get

[0246]

[0247] Next, we deal with the safe rate: Given Proposition 2, for any convex function f(X), we have:

[0248]

[0249] Applying Lemma 2 to the safe rate, we obtain:

[0250]

[0251] Next, process CRB: expand it,

[0252]

[0253] Finally, applying the SDR method, let And by introducing slack variables, we get a convex problem that can be solved directly:

[0254]

[0255] Furthermore, to solve the optimization problem under the extended objective, we only need to solve the non-convexity of the CRB. However, the CRB is already convex and does not need to be transformed.

[0256] Step 6: Based on the obtained optimal solution for the BS transmit beamforming matrix, continue to use the SDR-MM method and adopt the Taylor approximation method to solve the joint gain and phase shift matrix of the active RIS: Specifically, the active RIS constructs N virtual channels, reflects the signal transmitted from the BS to the user and the eavesdropper respectively, and uses the channel difference between the two to adjust the joint gain and phase shift matrix of the active RIS to increase the user's received signal-to-noise ratio and reduce the eavesdropper's eavesdropping signal-to-noise ratio. Specifically:

[0257] The optimal solution W for the BS transmit beamforming matrix is fixed. The non-convexity of the problem is reflected in the radar SINR constraint, the active RIS reflected power constraint, and the objective function. For the radar SINR constraint, Proposition 1 is used to obtain a lower bound for the radar SINR constraint. To address the cubic term associated with the phase shift, Proposition 3 is introduced. For the active RIS reflected power constraint, the problem is transformed into an SDP problem by defining new symbols. For the secure rate, the MM algorithm is used, using a first-order Taylor approximation at a given point. For the CRB, slack variables are introduced and the problem is transformed into an SDP problem.

[0258] Specifically, we first solve the radar SINR constraint: Similarly, applying Proposition 1, we get the lower bound of the radar SINR constraint

[0259]

[0260] Using the formula tr(A H B)=(vec(A)) H vec(B) and Rewrite the first two terms of the above equation,

[0261]

[0262] Expanding the third term J yields a quartic expression for phase shift, which consists of a quartic term, a cubic term, a quadratic term, and a constant term.

[0263] Apply the formula The quartic term can be transformed into:

[0264]

[0265] in,

[0266] Similarly, the quadratic term can be transformed into:

[0267]

[0268] in,

[0269] To solve the cubic term, we introduce Proposition 3: Given K (l) , L (l) , then:

[0270]

[0271] From this we can get:

[0272]

[0273] in,

[0274]

[0275]

[0276] Thus, a tractable lower bound is obtained:

[0277]

[0278] Next, we deal with the active RIS reflected power constraint and convert the active RIS transmit power expression into the quadratic form of V:

[0279]

[0280] Next, we deal with the safety rate, at a given point Using the first-order Taylor approximation,

[0281]

[0282] Next, solve CRB and expand it:

[0283]

[0284] Finally, by introducing slack variables, we obtain a convex problem that can be solved directly:

[0285]

[0286] in,

[0287] Finally, because the SDR method is used and the rank-one solution is ignored, the eigenvalue decomposition and Gaussian randomization methods are applied to recover the rank-one solution from the obtained solution.

[0288] Furthermore, to solve the optimization problem under the extended objective, we only need to solve the non-convexity of CRB. We can convert CRB into a convex matrix by defining a new notation:

[0289]

[0290] in,

[0291] Step 7: Based on the BS transmit beamforming matrix obtained in step 5 and the joint gain and phase shift matrix of the active RIS obtained in step 6, the block coordinate descent (BCD) method is used to iteratively update the BS transmit beamforming matrix and the joint gain and phase shift matrix of the active RIS until they converge. This method strikes a balance between secure transmission and accurate radar parameter estimation, achieving optimal system perception and safety performance.

[0292] The preferred embodiments of the present invention have been specifically described above, but the present invention is not limited to the described embodiments. Those skilled in the art may make various equivalent modifications or substitutions without departing from the spirit of the present invention. These equivalent modifications or substitutions are all included in the scope defined by the claims of this application.

Claims

1. A secure transmission method for improving ISAC system perception performance in active RIS scenarios, characterized in that: The method comprises the following steps: Step 1: Build a system model that includes the BS, active RIS, users, and sensing targets (potential eavesdroppers). The direct link between the BS and the user is blocked by an obstacle, and only the active RIS is used to complete the communication and sensing tasks simultaneously. Step 2: To overcome the severe multiplicative path loss of the four-hop radar, the system uses an active RIS that amplifies the signal during reflection. The Cramer-Rao lower bound (CRLB) of the system perception is derived taking into account the inevitable thermal noise of the active RIS. Step 3: Construct a BS-associated transmit beamforming matrix and the associated optimization problem of the active RIS gain and phase shift to maximize the system's safe rate and the weighted sum of the Cramér-Rao lower bound (CRLB) while simultaneously satisfying the system's target detection requirements, the BS transmit power budget, the active RIS transmit power budget, and the active RIS maximum gain constraint. Step 4: Consider the distance between the perceived target and the active RIS. When the distance between the two is close enough, the perceived target cannot be treated as just a point. Therefore, the perceived target is modeled as an extended target, and a similar optimization problem is established accordingly. Step 5: Based on the fact that the channel between the BS and the active RIS is a line-of-sight channel, the BS transmit beamforming matrix is solved using the minimization-maximization algorithm (MM) and the semidefinite relaxation method (SDR). Step 6: Based on the optimal solution of the BS transmit beamforming matrix obtained in step 5 above, continue to use the SDR-MM method and adopt the Taylor approximation method to solve the joint gain and phase shift matrix of the active RIS; Step 7: Based on the BS transmit beamforming matrix obtained in step 5 and the joint gain and phase shift matrix of the active RIS obtained in step 6, the block coordinate descent (BCD) method is used to iteratively update the BS transmit beamforming matrix and the joint gain and phase shift matrix of the active RIS until they converge to achieve the optimal system perception and security performance.

2. A secure transmission method for improving ISAC system perception performance in active RIS scenarios according to claim 1, characterized in that: The dual-function signal transmitted by the BS of the system model in the lth time slot is: in is the communication symbol to be transmitted, Assume that d is a pseudo-random sequence that satisfies and and is known a priori by the BS, user, and eavesdropper. Assuming that the communication signal is independent of the sensor signal, and Define a joint signal vector for the sensing signal beamforming matrix and the communication signal beamforming vector respectively and a joint beamforming matrix where w i is the i-th column of the joint beamforming matrix W; Under the system model, the safe rate of the system can be expressed as follows: in They represent the channels from the base station to the active RIS, from the active RIS to the user and the eavesdropper, respectively. The phase shift matrix Φ = diag(φ1, φ2, ..., φ N ),in And β i ≥0,θ i ∈[0,2π), and are the additive white Gaussian noise generated during communication and eavesdropping signal reception, It is the thermal noise generated by the reflection of the signal through the active RIS in the downlink channel; Under the system model, the radar echo signal-to-noise ratio ξ received by the system R ξ R =tr(ARA H I s -1 ) in, is the covariance matrix of the transmitted signal, J s =BRB H +N represents the interference plus noise covariance matrix, and the definition symbol To simplify expressions; Under the system model, the power consumed by the active RIS during two reflections is in, is the thermal noise generated by the reflection of the signal through the active RIS in the uplink channel. is the response matrix from the active RIS to the target. When the perceived target is modeled as a point target, it is considered that the reflected echo signal consists of only one path, so there is a more specific expression: Where β is the complex loss coefficient, is the target-oriented vector.

3. The secure transmission method for improving ISAC system perception performance in active RIS scenarios according to claim 1, characterized in that: In step 2, the thermal noise introduced by active RIS is considered, and the Cramer-Rao lower bound (CRLB) is derived for modeling the perceived target as a point target and an extended target respectively: in, is the additive white Gaussian noise generated in the process of receiving radar echo, T is the number of time slots divided by a transmission symbol, Λ N =diag(0,1,…,N-1), In addition, only when M≥rank(R)≥N≥rank(H BR )hour, Bounded and estimable.

4. The secure transmission method for improving ISAC system perception performance in active RIS scenarios according to claim 1, characterized in that: In step 3, a transmit beamforming matrix associated with the BS and an associated optimization problem of the active RIS phase shift are constructed to maximize the system safety rate and the weighted sum of the Cramér-Rao lower bound (CRLB), while simultaneously satisfying the system target detection requirements, the BS transmit power budget, the active RIS transmit power budget, and the active RIS maximum gain constraint: P1: st.C1:ξ R ≥γ r C2:P t ≤P0 C3： C4:|Φ [i,i] |≤η i ,i=1,2,…,N The objective function represents the normalized weighted sum of the system safety rate and the target arrival angle CRB, ρ∈(0,1) is the weighting factor, Q s ,Q c are the normalized parameters of the system safety rate and target arrival angle CRB, which are the values of the objective function when ρ = 1 and ρ = 0, respectively. Solving the optimization problem posed by these two parameters is two special cases of P1, so the solution method is the same; constraint C1 represents the constraint on the radar echo signal-to-noise ratio; constraint C2 represents the constraint on the total BS transmission power; constraint C3 represents the constraint on the total power of the two reflections of the active RIS; constraint C4 represents the constraint on the maximum gain of the active RIS.

5. The secure transmission method for improving ISAC system perception performance in active RIS scenarios according to claim 1, characterized in that: In step 4, the perception target is modeled as an extended target, and an optimization problem P2 similar to P1 is established: P2： st.C1:ξ R ≥γ r C2:P t ≤P0 C3： C4:|Φ [i,i] |≤η i ,i=1,2,…,N。 6. The secure transmission method for improving ISAC system perception performance in active RIS scenarios according to claim 1, characterized in that: In step 5, since the variables in the objective function are coupled with each other and the constraints are non-convex, the objective problem is non-convex, so it is divided into two sub-problems and optimized and solved separately; Assuming the channel between the BS and the active RIS is a line-of-sight channel, the BS transmit beamforming matrix is solved using the minimization-maximization (MM) algorithm and the semidefinite relaxation (SDR) method: Since the channel between the BS and the active RIS is a line-of-sight channel, it is necessary to adjust the BS transmit beamforming matrix to perform beamforming so that the BS transmitted signal is reflected by the active RIS as much as possible to reduce the loss of useful signals; In addition, there is non-convexity in the optimization problem, which exists in the objective function and C1 constraint, and needs to be solved after convexification; Given Proposition 1, we can find ξ R Convex approximation of Proposition 1: Given X (k) and J s(k) , that is, X and J s The value of the kth iteration is: Next, using the SDR method and MM algorithm, the conversion system safety rate of Proposition 2 is given; Proposition 2: For any convex function f(X), we have: For CRLB, slack variables are introduced to solve its non-convex problem. The final sub-optimization problem is as follows: f1(W i )-k2≥κ1 κ1≥0 κ2≥f2(W i ) In addition, since the rank-one constraint was previously omitted, it is necessary to use the eigenvalue decomposition and Gaussian randomization methods to construct a rank-one solution; For P2: its only difference from P1 is the CRB in the optimization variables. It only needs to solve the non-convexity of CRB: CRB is already convex, so the solution is the same as before.

7. The secure transmission method for improving ISAC system perception performance in active RIS scenarios according to claim 1, characterized in that: In step 6, based on the obtained optimal solution of the BS transmit beamforming matrix, the SDR-MM method is continued to be used, and the Taylor approximation method is adopted to solve the gain and phase shift joint matrix of the active RIS: Active RIS constructs a virtual channel to reflect the signal transmitted from the BS to the user and the eavesdropper respectively. The channel difference between the two is used to adjust the joint gain and phase shift matrix of the active RIS to increase the user's received signal-to-noise ratio and reduce the eavesdropper's eavesdropping signal-to-noise ratio. Next, the non-convex terms in the optimization problem are made convex: Continuing to use the SDR-MM method, when dealing with the C1 constraint, in order to solve the cubic term of phase shift generated, Proposition 3 is given; Proposition 3: Given K (l) ,L (l) , then: When dealing with safe rates, at a given point The first-order Taylor approximation is used at , and slack variables are introduced to solve CRB. The final sub-optimization problem is as follows: Similarly, since the rank-one constraint was previously omitted, it is necessary to use the eigenvalue decomposition and Gaussian randomization methods to construct a rank-one solution; For P2: its only difference from P1 is the CRB in the optimization variables. It only needs to solve the non-convexity of CRB: Define new symbols to transform CRB into SDP problem:

8. The secure transmission method for improving ISAC system perception performance in active RIS scenarios according to claim 1, characterized in that: In step 7, based on the BS transmit beamforming matrix obtained in step 5 and the gain and phase shift joint matrix of the active RIS obtained in step 6, the block coordinate descent method (BCD) is used to iteratively update the BS transmit beamforming matrix and the gain and phase shift joint matrix of the active RIS until they converge, thereby obtaining the optimal system perception and safety comprehensive performance.

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