Active ris-aided isac network transmission method based on hardware impairment and imperfect channel

Abstract

The application belongs to the technical field of wireless communication, and particularly relates to an active RIS assisted ISAC network transmission method based on hardware impairment and imperfect channel, which comprises the following steps: constructing an ISAC network system model based on active RIS assistance; based on the ISAC network system model, combining user signal-to-noise ratio constraints, eavesdropper signal-to-noise ratio constraints, ARIS amplitude constraints, base station transmission power constraints and ARIS power constraints, establishing a target perceptual beamforming gain maximization model; solving the target perceptual beamforming gain maximization model, obtaining an optimal transmission scheme and executing data transmission; and the application realizes maximum perceptual beam gain under the premise of considering HWIs and imperfect CSI.

Description

Technical Field

[0001] This invention belongs to the field of wireless communication technology, specifically relating to an active RIS-assisted ISAC network transmission method based on hardware impairments and imperfect channels. Background Technology

[0002] After decades of independent development, wireless communication and radar sensing technologies are now rapidly moving towards a new stage of deep integration. Faced with multiple challenges such as increasingly scarce spectrum resources, high hardware costs, and persistently low system energy efficiency, Integrated Sensing and Communication (ISAC), as an emerging system architecture, has been widely regarded as a key enabling technology for sixth-generation mobile communication (6G) and future intelligent networks. Compared to traditional discrete system solutions, ISAC can significantly improve the system's spectral efficiency, energy efficiency, and hardware utilization through shared spectrum resources, a unified hardware platform, and integrated waveform design. However, its performance inevitably degrades in harsh propagation environments. To address this challenge posed by complex electromagnetic environments, the rapidly developing Reconfigurable Intelligent Surface (RIS) technology offers a highly promising and transformative approach to solving these problems. Traditional passive RIS consists of a large number of low-cost, reconfigurable passive reflective units, each of which can independently control the phase of the incident signal; while active RIS integrates an amplification module on the basis of passive reflective units, which can not only control the phase, but also actively compensate for path loss and fading during signal propagation, thereby reshaping the wireless propagation environment more efficiently and further improving spectrum utilization efficiency and system robustness.

[0003] Introducing active RIS into ISAC systems has significant research value and broad application prospects. Active RIS can not only enhance signal quality between the base station and users or sensing targets, but also improve sensing performance while enhancing physical layer security transmission capabilities through precise beamforming and active gain compensation. For example, existing research has explored using active RIS to assist ISAC systems to optimize multi-user communication quality while meeting target sensing signal-to-noise ratio or estimation error constraints; or, in cases of imperfect channel state information, to improve sensing accuracy and secure transmission performance through joint design of active beamforming and active RIS-based active beamforming. These works have initially revealed the enormous potential of active RIS in synergistically enhancing communication and sensing capabilities in ISAC systems.

[0004] However, most current research is based on idealized assumptions and has not fully considered the impact of hardware impairments (HWIs) and imperfect channel state information (CSI) prevalent in real-world systems. Hardware impairments such as transceiver nonlinear distortion and phase noise, as well as CSI uncertainties caused by channel estimation errors, user mobility, and environmental time-varying factors, severely restrict beamforming accuracy and thus weaken overall system performance, especially secure transmission capabilities. Although a few studies have begun to focus on robust design in active RIS-assisted communication systems, there is still a lack of work on incorporating both hardware impairments and imperfect CSI into the active RIS-assisted ISAC secure transmission framework and conducting joint optimization. Therefore, exploring the secure transmission mechanism of active RIS-assisted ISAC systems under conditions closer to real-world systems has significant theoretical and practical value. Summary of the Invention

[0005] To address the above problems, this invention provides an active RIS-assisted ISAC network transmission method based on hardware impairments and imperfect channels, comprising the following steps:

[0006] S1. Construct an ISAC network system model based on active RIS assistance;

[0007] S2. Based on the ISAC network system model, and combining user signal-to-noise ratio constraints, eavesdropper signal-to-noise ratio constraints, ARIS amplitude constraints, base station transmit power constraints, and ARIS power constraints, a target sensing beamforming gain maximization model is established.

[0008] S3. Solve the target-aware beamforming gain maximization model, obtain the optimal transmission scheme, and execute data transmission.

[0009] The beneficial effects of this invention are:

[0010] This invention proposes a robust and secure transmission method for an active RIS-assisted ISAC system under non-ideal conditions, which has the following advantages compared to existing technologies:

[0011] (1) Active RIS amplification effectively compensates for path loss and significantly improves sensing beam gain.

[0012] This invention integrates amplification modules into each reflection unit of the RIS (Radio Reflection Array), allowing the reflection coefficient amplitude to be adjusted to be greater than or equal to one. Compared to traditional passive RIS, which can only passively reflect signals, active RIS can actively compensate for product path fading in the two-hop links between the base station and the RIS, as well as between the RIS and the target. By jointly optimizing the base station's transmit beamforming matrix and the ARIS reflection matrix under the ARIS power budget constraint, the beam gain in the target direction is maximized, effectively improving the radar sensing signal-to-noise ratio and target detection probability, especially suitable for scenarios where the target is located in a strongly obstructed area or propagates over long distances.

[0013] (2) Robust reconstruction based on ellipsoidal outer wrapping ensures that the communication quality of legitimate users still meets the requirements under the worst case of channel error.

[0014] This invention addresses the real-world scenario where estimation errors exist simultaneously in the ARIS-to-user channel and the base station-to-user direct connection channel. It constructs a joint ellipsoidal error set, enclosing the constraints of two independent spheres into a single ellipsoid. Based on this, an S-procedure is used to transform the user signal-to-noise ratio (SNR) requirements under all possible channel errors into solvable linear matrix inequality constraints. This ensures that the jointly designed beamforming matrix and ARIS reflection matrix strictly satisfy the user communication SNR threshold under all channel implementations that meet the error bounds, fundamentally avoiding the risk of user service quality collapse under channel estimation errors in traditional non-robust schemes.

[0015] (3) It is immune to the uncertainty of the eavesdropping channel, ensuring the secure transmission of the physical layer.

[0016] This invention addresses the practical constraint that eavesdroppers cannot actively communicate with base stations, making it difficult to accurately obtain their channel state information. Under the condition that only an estimated channel from the eavesdropper can be obtained, an eavesdropping channel error ellipsoid is established, and an S-procedure is used to transform the eavesdropper's signal-to-noise ratio constraint into a linear matrix inequality constraint. This constraint ensures that for all possible channels of the eavesdropper, their ability to intercept target user information is suppressed below a preset security threshold, effectively resisting eavesdropping channel fluctuations caused by random walks of the eavesdropper or changes in the electromagnetic environment, and achieving physical layer security protection for legitimate user information.

[0017] (4) Joint modeling of various hardware defects yields a solution that is engineering feasible.

[0018] This invention differs from existing idealized assumptions by modeling three types of real-world hardware impairments: base station transmitter distortion noise, user receiver distortion noise, and random phase error in the ARIS reflector unit, where phase jitter follows a uniform distribution. These non-ideal factors are rigorously embedded into the denominator of the signal-to-noise ratio expression for legitimate users and eavesdroppers. This ensures that the optimized beamforming and RIS configuration maintain stable performance even when faced with the non-ideal characteristics of commercial devices, reducing reliance on expensive, high-precision hardware and providing direct engineering deployment value.

[0019] (5) The solution framework combines alternating optimization and convex relaxation to ensure that the algorithm is efficient and solvable.

[0020] This invention decouples the original non-convex joint optimization problem into two convex subproblems. When the ARIS phase shift is fixed, the base station beamforming subproblem is solved by rank-one recovery through semidefinite relaxation combined with singular value decomposition. When the base station beam is fixed, the ARIS reflection coefficient subproblem is transformed into a linear function by introducing augmented variables and then into a standard semidefinite programming problem by linearizing the ARIS power constraint. Each step of the algorithm calls the standard convex optimization toolbox, avoiding exhaustive search or heuristic parameter tuning, and can obtain high-quality local optima in polynomial time, exhibiting good scalability for large-scale ARIS deployments.

[0021] (6) The conservative design is controllable, leaving room for flexible adjustment in the project.

[0022] When dealing with constraints where two independent spheres are enclosed by a single ellipsoid, this invention constructs an enclosing ellipsoid that strictly contains the original set of independent spheres, ensuring that any channel error satisfying the original constraints falls within the range of the enclosing ellipsoid. The conservatism of this design can be flexibly adjusted through a channel error upper limit threshold, providing engineers with a controllable trade-off between optimal sensing performance and communication security margins, adapting to the differentiated reliability requirements of different application scenarios. Attached Figure Description

[0023] Figure 1 This is a flowchart of the RIS-assisted ISAC network transmission method based on hardware impairment and imperfect channels in this invention.

[0024] Figure 2 This is a model diagram of the active RIS-assisted ISAC network system based on hardware impairments and imperfect channels in this invention.

[0025] Figure 3 This is an algorithm iteration diagram of the active RIS-assisted ISAC system based on hardware impairment and imperfect channels in this invention. Detailed Implementation

[0026] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0027] Please see Figures 1-2 This invention provides an active RIS-assisted ISAC network transmission method based on hardware impairments and imperfect channels, comprising the following steps:

[0028] S1. Construct an ISAC network system model based on active RIS assistance.

[0029] In some embodiments, the present invention is constructed as follows Figure 2 The illustrated ISAC network system model includes a base station (BS) equipped with M antennas, an active RIS (ARIS) equipped with N reflector elements, and K single-antenna users (i.e., legitimate users), with an eavesdropper as the target. In this ISAC network system model, the channels from BS to users, BS to ARIS, ARIS to users, ARIS to the eavesdropper, and ARIS to the target are defined as follows: , , , , .

[0030] This invention comprehensively incorporates two key non-ideal factors in its modeling process: hardware impairments (HWIs) and imperfect channel state information (ICSI). Regarding HWIs, hardware impairments from the base station, legitimate users, and ARIS are considered. Specifically, ARIS hardware impairments mainly manifest as N random phase errors caused by reflector hardware defects or inaccurate channel estimation, and are modeled as a random diagonal phase error matrix. Furthermore, although the linear thermal noise of ARIS does not fall under the category of HWIs, it is modeled separately as additive noise.

[0031] Based on this, considering that the eavesdropper, as a sensing target, simultaneously assumes the dual role of being sensed by radar and having its communication information eavesdropped, this invention, in order to further distinguish the impact of ARIS hardware damage and noise on different functional links and thus more realistically reflect the actual transmission quality of each link, splits the channel between ARIS and the eavesdropper into two independent links—a sensing channel and an eavesdropping channel—for modeling.

[0032] Since the position (or orientation) information of the sensed target can be obtained from the target tracking process of the previous sensing cycle, it is assumed that the propagation link between the ARIS and the sensed target is dominated by the line-of-sight (LoS) component. Let θ and φ be the azimuth and elevation angles from the ARIS to the sensed target, respectively. Based on this assumption, the channel from the ARIS towards the sensed target in the direction (θ, φ) can be expressed as:

[0033]

[0034] In the formula, Represents the large-scale fading coefficient. and λ represents the number of reflective elements in the ARIS along the x-axis and z-axis, respectively, λ represents the wavelength, and d represents the spacing between two adjacent reflective elements.

[0035] S2. Based on the ISAC network system model, and combining user signal-to-noise ratio constraints, eavesdropper signal-to-noise ratio constraints, ARIS amplitude constraints, base station transmit power constraints, and ARIS power constraints, a target sensing beamforming gain maximization model is established.

[0036] In some embodiments, the target-aware beamforming gain maximization model is expressed as:

[0037] ,

[0038] ,

[0039] ,

[0040] ,

[0041] ,

[0042] ,

[0043] In the formula, the diagonal complex matrix of the reflection coefficients of ARIS is expressed as: . This represents the complex reflection coefficient of the nth reflecting unit. The magnitude of the amplification factor represents the signal amplification factor; and These represent the amplitude and phase of the nth reflecting unit, respectively. This invention assumes that the amplitude and phase can vary continuously within an interval; accordingly, , This indicates the maximum adjustable amplitude of each reflection unit in ARIS. This represents the equivalent ISAC transmit beamforming matrix. Represents the communication beamforming matrix. This represents the communication beam assignment vector for the k-th single-antenna user. Represents the radar beamforming matrix. This represents the sensing beamforming vector of the m-th antenna of the base station; This indicates that the HWIs of ARIS are modeled as random diagonal phase error matrices. , This represents the nth random phase error caused by a hardware defect in the reflector or inaccurate channel estimation. This random phase error is uniformly distributed in the interval [-π / 2, π / 2). This represents the signal-to-noise ratio (SNR) of the k-th single-antenna user. This represents the minimum signal-to-noise ratio for the k-th single-antenna user. This represents the signal-to-noise ratio (SNR) of the eavesdropper decoding the signal of the k-th single-antenna user. The matrix represents the maximum signal-to-noise ratio (SNR) of the eavesdropper on the k-th single-antenna user signal. ; Represents the trace of a matrix. Indicates the noise of ARIS. Indicates the maximum power allowed by ARIS. This indicates the maximum allowable transmit power for the base station;

[0044] Furthermore, the signal-to-noise ratio (SNR) for the k-th single-antenna user is calculated as follows:

[0045] ,

[0046] ,

[0047] ,

[0048] ,

[0049] ,

[0050] In the formula, This indicates a composite channel from the base station to the user. This indicates interference with irrelevant signals from the k-th single-antenna user. This represents the base station hardware noise for the k-th single-antenna user. This represents the noise variance of the k-th single-antenna user; This represents the ratio of distortion noise power to the actual received signal power. It represents the ratio of distorted noise power to undistorted received signal power; Indicates user hardware noise; Represents the communication beam assignment vector for the i-th single-antenna user; This means transforming matrix R into a diagonal matrix;

[0051] The formula for calculating the signal-to-noise ratio (SNR) of the decoded signal of the k-th single-antenna user signal by the eavesdropper is:

[0052] ,

[0053] ,

[0054] ,

[0055] In the formula, This indicates interference with irrelevant signals from the eavesdropper. This indicates the base station hardware noise of the eavesdropper. This represents the noise variance corresponding to the eavesdropper.

[0056] S3. Solve the target-aware beamforming gain maximization model, obtain the optimal transmission scheme, and execute data transmission.

[0057] In some embodiments, step S3 of solving the target sensing beamforming gain maximization model includes:

[0058] S31. Construct a composite channel uncertainty model.

[0059] Specifically, this invention considers that channel uncertainty is unavoidable in practical applications. Traditional channel estimation methods can obtain channel state information between the base station and the smart reflector. However, due to user mobility and the complexity of the electromagnetic environment, accurately obtaining channel state information between the smart reflector and the user faces significant challenges. Furthermore, eavesdroppers cannot actively communicate with the base station, making it difficult for the base station to obtain channel state information between the eavesdropper and the smart reflector. To address these problems, this invention constructs a composite channel uncertainty model based on a finite uncertainty model, as follows:

[0060] ,

[0061] ,

[0062] ,

[0063] In the formula, This represents the ideal channel from ARIS to the k-th single-antenna user. This represents the channel estimation error from ARIS to the k-th single-antenna user. This represents the ideal channel from ARIS to the eavesdropper. This represents the channel estimation error from ARIS to the eavesdropper. This represents the ideal channel from the base station to the k-th single-antenna user. This represents the channel estimation error from the base station to the k-th single-antenna user. This represents the set of ARIS and user channel errors. This represents the set of channel errors between ARIS and the eavesdropper. This represents the set of k users at the base station, ||·|| F Describing the Frobenius norm, This represents the estimated upper channel limit from ARIS to the k-th single-antenna user. This represents the eavesdropper's estimated channel upper limit. This represents the estimated upper channel limit from the base station to the k-th single-antenna user.

[0064] Since the S-Procedure is needed to handle robust constraints, and the S-Procedure requires that the uncertainty be represented in the form of a single ellipsoid, the two independent channels are... and The sets of uncertainties are merged into a single joint ellipsoidal set of uncertainties:

[0065] ,

[0066] In the formula, express and The real channel set, express and The ideal set of channels, express and The set of error channels.

[0067] Accordingly, the joint ellipsoid error set is defined. , I N Represents the identity matrix. This represents the construction of a block diagonal matrix. However, this circumscribed ellipsoid is not equivalent to the original set of independent spheres because the former expands the boundary of the uncertain parameters. Therefore, subsequent robust designs based on this ellipsoid are conservative approximations; that is, while the obtained solution necessarily satisfies the robustness constraints of the original system, it may sacrifice some feasible region and optimality.

[0068] S32. Based on the composite channel uncertainty model, auxiliary variables are introduced to reconstruct the user signal-to-noise ratio constraint and the eavesdropper signal-to-noise ratio constraint, and the reconstruction objective function is obtained.

[0069] In some embodiments, for user signal-to-noise ratio constraints, the present invention introduces auxiliary variables. satisfy Therefore, the user signal-to-noise ratio constraint is equivalent to

[0070] ,

[0071] ,

[0072] In the formula, , , , ;definition This represents the covariance matrix of the transmitted signal allocated by the base station to the k-th communication user. The covariance matrix represents the radar sensing beamforming vector. , , , ,but ; Represents the identity matrix.

[0073] Further substitution The rewritten user signal-to-noise ratio constraint is equivalent to:

[0074] ,

[0075] .

[0076] Similarly, an auxiliary variable is introduced to constrain the signal-to-noise ratio of the eavesdropper. satisfy Then the signal-to-noise ratio constraint for the eavesdropper is equivalent to:

[0077] ,

[0078] ,

[0079] Further substitution The rewritten eavesdropper signal-to-noise ratio constraint is equivalent to:

[0080] ,

[0081] ,

[0082] in, , , , .

[0083] In some embodiments, a robust constraint is defined as follows:

[0084] ,

[0085] Then, the S-Procedure can be used to transform it into the following form.

[0086] ,

[0087] Based on the above transformation, the two inequalities in the user signal-to-noise ratio constraint can be further rewritten as follows:

[0088] ,

[0089] ,

[0090] In the formula, , , , It is a non-negative slack variable.

[0091] S33. After completing step S32, the channel estimation error is separated according to the S-procedure lemma, and the reconstructed sensing beamforming gain maximization model is obtained.

[0092] In some embodiments, the S-procedure lemma can be expressed as: defining a quadratic function ,in, , , ,and If there exists a point x0 such that g1(x0) < 0 (Slater's condition holds), then the condition... The necessary and sufficient condition for its validity is that a scalar exists if and only if such a scalar exists. Makes the following linear matrix inequalities hold:

[0093] .

[0094] Using the S-procedure lemma described above, the channel error in the target-aware beamforming gain maximization model is separated, and the target-aware beamforming gain maximization model is rewritten, defining non-negative relaxation variables. , The target-aware beamforming gain maximization model can be transformed into:

[0095] ,

[0096] st ,

[0097] ,

[0098] ,

[0099] ,

[0100] ,

[0101] ,

[0102] ,

[0103] ,

[0104] In the formula, Rank() represents the rank, and I represents the identity matrix.

[0105] S34. Based on the reconstructed sensing beam gain shaping gain maximization model, the optimal transmission scheme is obtained by using the alternating optimization method.

[0106] In some embodiments, the process of solving using the alternating optimization method includes:

[0107] S341. Introducing a semi-definite relaxation algorithm, fixing the reflection phase of ARIS, and constructing a base station transmit beamforming optimization problem, expressed as:

[0108] ,

[0109] st ,

[0110] ,

[0111] ,

[0112] ,

[0113] ,

[0114] ;

[0115] When solving the above model, if the obtained solution satisfies the first-order optimality condition, then the singular value decomposition method can be used to directly obtain the solution. , The exact optimal solution can be obtained. Conversely, if this condition cannot be met, an approximate solution can be obtained using Gaussian randomization.

[0116] S342. Substituting the solution from step S341 into the equation, and fixing the base station transmit beamforming, construct the ARIS reflection phase optimization problem, expressed as:

[0117] ,

[0118] st ,

[0119] ,

[0120] ,

[0121] ,

[0122] ,

[0123] ;

[0124] Since the aforementioned constraint function remains non-convex, and handling the non-convex constraint Φ remains challenging, this invention employs a semi-definite relaxation (SDR) technique for solution. First, augmented variables are introduced.

[0125] ,

[0126] And add the following constraints:

[0127] ,

[0128] At this point, all quadratic terms involving the ARIS reflection coefficient can be transformed into terms relating to... The linear matrix function. Therefore, the original problem can be restated as:

[0129] ,

[0130] ,

[0131] ,

[0132] ,

[0133] ,

[0134] ,

[0135] ,

[0136] ,

[0137] in, , , , , They are respectively for , , , middle The result after linearization Let represent the Hadamard product. The ARIS power constraint in the above equation is still non-convex. Next, we will further convexify it by transforming the left side of the ARIS power constraint inequality to obtain...

[0138] ,

[0139] in The ultimate goal is to become

[0140] ,

[0141] ,

[0142] ,

[0143] ,

[0144] ,

[0145] ,

[0146] ,

[0147] ;

[0148] When the rank-one constraint is relaxed, the global problem can be transformed into a problem with respect to linear constraints. This involves a semidefinite programming problem (SDP). The optimal solution to the relaxation problem is obtained using the CVX tool. Finally, we use Gaussian randomization or eigenvalue decomposition to construct the solution Φ* that satisfies the rank-one condition.

[0149] In one embodiment, the system parameters are set as follows: number of base station antennas M=6, number of ARIS units N=30, and number of users K=3. The path loss exponents from the base station to the ARIS, from the ARIS to the user, and from the ARIS to the eavesdropper are all 2.2. The hardware impairment coefficients for the base station and the user end are set to... = =0.03. The maximum amplitude of the ARIS reflection coefficient is set to 0.03. =3, ARIS's maximum power consumption is The base station's maximum transmit power is 12W. The base station's location is set to (0,0,0), and the distance d between the base station and ARIS is... b,r =40m, Angle of arrival of ARIS relative to the base station The distance d between ARIS and the target r,t =8m, the target's azimuth and elevation angles relative to ARIS are θ=π / 4 and φ=π / 6, respectively. The distance d between ARIS and the user. r,k =6m. The maximum number of iterations is set to N. max =100.

[0150] Figure 3Iterative curves of the proposed method and comparative scheme in terms of sensing beam gain are shown, verifying the robustness of the proposed method under different conditions.

[0151] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. An active RIS-assisted ISAC network transmission method based on hardware impairments and imperfect channels, characterized in that, Includes the following steps: S1. Construct an ISAC network system model based on active RIS assistance, which includes a base station equipped with M antennas, an ARIS equipped with N reflector units, K single-antenna users, and an eavesdropper as the sensing target. The channels from base station to user, base station to ARIS, ARIS to user, ARIS to eavesdropper, and ARIS to the target are set as follows: , , , ; S2. Based on the ISAC network system model, and combining user signal-to-noise ratio constraints, eavesdropper signal-to-noise ratio constraints, ARIS amplitude constraints, base station transmit power constraints, and ARIS power constraints, a target sensing beamforming gain maximization model is established, expressed as: ， ， ， ， ， ， In the formula, Let ARIS be a diagonal complex matrix of reflection coefficients, where This represents the complex reflection coefficient of the nth reflecting unit. and These represent the amplitude and phase of the nth reflecting unit, respectively. ; This represents the equivalent ISAC transmit beamforming matrix. Represents the communication beamforming matrix. This represents the communication beam assignment vector for the k-th single-antenna user. Represents the radar beamforming matrix. This represents the sensing beamforming vector of the m-th antenna of the base station; , This represents the random diagonal phase error matrix. , This represents the nth random phase error caused by a hardware defect in the reflector or inaccurate channel estimation. This random phase error is uniformly distributed in the interval [-π / 2, π / 2). This represents the signal-to-noise ratio (SNR) of the k-th single-antenna user. This represents the minimum signal-to-noise ratio for the k-th single-antenna user. This represents the signal-to-noise ratio (SNR) of the eavesdropper decoding the signal of the k-th single-antenna user. The matrix represents the maximum decoding signal-to-noise ratio of the k-th single-antenna user signal by the eavesdropper. ; Represents the trace of a matrix. Indicates the noise of ARIS. Indicates the maximum power allowed by ARIS. This indicates the maximum allowable transmission power of the base station. This represents the reflection phase vector of ARIS. This indicates the maximum adjustable amplitude of each reflective unit in the ARIS; S3. Solve the target-sensing beamforming gain maximization model to obtain the optimal transmission scheme and execute data transmission; the solution process includes: S31. Construct a composite channel uncertainty model; S32. Based on the composite channel uncertainty model, auxiliary variables are introduced to reconstruct the user signal-to-noise ratio constraint and the eavesdropper signal-to-noise ratio constraint; S33. After completing step S32, the channel estimation error is separated according to the S-procedure lemma, and the reconstruction sensing beamforming gain maximization model is obtained. S34. Based on the reconstructed sensing beam gain shaping gain maximization model, the optimal transmission scheme is obtained by using the alternating optimization method.

2. The active RIS-assisted ISAC network transmission method based on hardware impairments and imperfect channels according to claim 1, characterized in that, The formula for calculating the signal-to-noise ratio of the kth single-antenna user is: ， ， ， In the formula, This refers to a composite channel for base station-to-user communication. This indicates interference with irrelevant signals from the k-th single-antenna user. This represents the base station hardware noise for the k-th single-antenna user. This represents the noise variance of the k-th single-antenna user; This represents the ratio of distortion noise power to the actual received signal power. It represents the ratio of distorted noise power to undistorted received signal power; Indicates user hardware noise; R represents the communication beamforming vector for the i-th single-antenna user; R represents joint beamforming. This means transforming matrix R into a diagonal matrix; The formula for calculating the signal-to-noise ratio (SNR) of the decoded signal of the k-th single-antenna user signal by the eavesdropper is: ， ， ， In the formula, This indicates interference with irrelevant signals from the eavesdropper. This indicates the base station hardware noise of the eavesdropper. This represents the noise variance corresponding to the eavesdropper.

3. The active RIS-assisted ISAC network transmission method based on hardware impairments and imperfect channels according to claim 1, characterized in that, The composite channel uncertainty model is represented as follows: ， ， ， In the formula, This represents the ideal channel from ARIS to the k-th single-antenna user. This represents the channel estimation error from ARIS to the k-th single-antenna user. This represents the ideal channel from ARIS to the eavesdropper. This represents the channel estimation error from ARIS to the eavesdropper. This represents the ideal channel from the base station to the k-th single-antenna user. This represents the channel estimation error from the base station to the k-th single-antenna user. This represents the set of ARIS and user channel errors. This represents the set of channel errors between ARIS and the eavesdropper. This represents the set of k users at the base station, ||·|| F Describing the Frobenius norm, This represents the estimated upper channel limit from ARIS to the k-th single-antenna user. This represents the eavesdropper's estimated channel upper limit. This represents the estimated upper channel limit from the base station to the k-th single-antenna user; Channel and The uncertainties are merged into a joint ellipsoidal uncertainty set. ， In the formula, express and The real channel set, express and The ideal set of channels, express and The set of error channels.

4. The active RIS-assisted ISAC network transmission method based on hardware impairments and imperfect channels according to claim 3, characterized in that, Introducing auxiliary variables to constrain user signal-to-noise ratio and substitute The reconstructed user signal-to-noise ratio constraint is: , , In the formula, , , , ; This represents the ratio of distortion noise power to the actual received signal power. It represents the ratio of distorted noise power to undistorted received signal power; Represents the identity matrix; definition This represents the covariance matrix of the transmitted signal allocated by the base station to the k-th communication user. The covariance matrix represents the radar sensing beamforming vector. , , , , ; Introducing auxiliary variables to constrain the signal-to-noise ratio of eavesdroppers and substitute The signal-to-noise ratio constraint for the reconstructed eavesdropper is: ， ， in, , , , , This represents the noise variance corresponding to the eavesdropper.

5. The active RIS-assisted ISAC network transmission method based on hardware impairments and imperfect channels according to claim 4, characterized in that, Using S-Procedure, the reconstructed user signal-to-noise ratio constraint is further transformed into: ， ， In the formula, , , , It is a non-negative slack variable. This represents the noise variance of the k-th single-antenna user. I N Represents the identity matrix. This indicates the construction of a block diagonal matrix.

6. The active RIS-assisted ISAC network transmission method based on hardware impairments and imperfect channels according to claim 5, characterized in that, Based on the reconstructed user signal-to-noise ratio constraints and eavesdropper signal-to-noise ratio constraints, define non-negative slack variables. , Using the S-procedure lemma, the model for maximizing the reconstructed sensing beamforming gain is as follows: ， s.t. , ， ， ， ， ， ， ， In the formula, , , , Let represent a nonnegative slack variable, Rank() represent the rank, and I represent the identity matrix.

7. The active RIS-assisted ISAC network transmission method based on hardware impairments and imperfect channels according to claim 1, characterized in that, Step S34 includes: S341. Introduce a semi-definite relaxation algorithm, fix the reflection phase of ARIS, construct and solve the base station transmit beamforming optimization problem; S342. Substitute the solution result from step S341 into the solution, fix the base station transmit beamforming, construct the ARIS reflection phase optimization problem, and solve it.

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