An OTFS signal super-resolution target parameter estimation method for synchronization error problem

Abstract

The application discloses an OTFS sensing integrated signal super-resolution target parameter estimation method for a synchronization error problem, which firstly establishes an OTFS time delay-Doppler domain sensing signal model considering timing offset and carrier frequency offset, and constructs a sparse observation model considering synchronization error; subsequently, a rough estimation of target time delay-Doppler parameters is completed through an ADMM algorithm, and the system synchronization error parameters are iteratively updated simultaneously by adopting an alternating minimization framework; then, multi-target interference cancellation is carried out based on the rough estimation result, and a Newton method is used to perform super-resolution fine estimation on target off-grid offset and synchronization error residual, so as to finally output fine parameters of target distance and velocity and a synchronization error estimation value. The application effectively solves the parameter estimation deviation problem caused by the synchronization error in the OTFS sensing system, and improves the estimation performance in the multi-target and closely adjacent target scene.

Description

Technical Field

[0001] This invention belongs to the field of communication and sensing integration technology, specifically relating to a super-resolution target parameter estimation method for OTFS communication and sensing integrated signals with synchronization error problem. Background Technology

[0002] The large-scale application of 5G technology is driving profound changes in the mobile communications field. The capabilities of wireless systems are expanding from a single communication link to a comprehensive system integrating communication, sensing, and computing capabilities. This trend stems from the ongoing demand for higher spectrum efficiency, lower latency, and stronger reliability, and is also driven by typical applications such as the Internet of Things (IoT), intelligent transportation, autonomous driving, and drone swarms. Integrated Sensing and Communication (ISAC) has thus become a key technological direction. Its basic idea is to reuse hardware platforms and spectrum resources, enabling the same signal to simultaneously handle both data transmission and environmental sensing tasks, thereby improving overall system efficiency under resource-constrained conditions.

[0003] In the high-frequency communication environment of 6G, millimeter wave and terahertz bands experience greater propagation loss and more complex scattering, with more significant Doppler spread and multipath fading. This challenges the robustness and processing complexity of traditional Orthogonal Frequency Division Multiplexing (OFDM) in high-dynamic scenarios. Against this backdrop, Orthogonal Time Frequency Space (OTFS) modulation has attracted attention due to its global joint modulation capability and its advantage in structurally representing time-varying channels, and is considered an important candidate system to support future sensing fusion. This technology maps information symbols to the Delay-Doppler (DD) domain and, through equivalent transformation, reshapes the rapidly changing channel in the Time Frequency (TF) domain into an approximately quasi-static expression in the DD domain. Compared to TF domain models, the DD domain often uses fewer parameters to characterize the propagation path, facilitating modeling and estimation using sparse structures. Simultaneously, delay and Doppler naturally correspond to distance and velocity in physical scenarios, providing a unified descriptive framework for communication channel characterization and sensing parameter extraction.

[0004] In 2019, Tiwari et al. designed a low-complexity Linear Minimum Mean Square Error (LMMSE) algorithm. This algorithm fully utilizes the sparsity and block ring structure of the matrix during demodulation to achieve log-linear complexity while maintaining good BER performance. In the same year, Thaj et al. redefined the Maximum Ratio Combining (MRC) method in the DD domain. By utilizing channel parameters in the DD domain grid, they reduced the impact of multipath fading on the received communication symbol data, thereby reducing the BER of the received signal. However, this method requires zeroing some symbols in the DD grid, resulting in some loss of communication performance. In 2020, Yuan et al. proposed the Variational Bayes (VB) method to reduce the receiver complexity of OTFS and address the factor graph loop problem that may occur in the Message Passing (MP) algorithm. Simulations showed that the proposed algorithm not only guarantees convergence to the global optimum of the Maximum a Posteriori (MAP) detection but also exhibits fast convergence. In 2024, Zhang et al. addressed the problem of excessive computational cost in the global two-dimensional search of the traditional WSF algorithm in the OTFS integrated radar communication system. They constructed an integrated OTFS echo model and proposed a target parameter estimation method combining sparse reconstruction preprocessing and WSF fine estimation, thereby reducing overall computational complexity while maintaining accuracy and resolution.

[0005] In multi-user scenarios, OTFS target parameter estimation technology has also been extensively studied. In 2022, Shang Xiaoke et al. analyzed the ambiguity function of OTFS signals and found that the uncorrelated characteristics of random communication information would reduce radar sensing performance. Therefore, they proposed a waveform optimization method that jointly suppresses peak sidelobe ratio and envelope peak-to-average power ratio. Simulation results show that the optimized signal exhibits good performance in radar target detection while also reducing the dynamic range of the system. In 2023, Hu Zelin et al. studied a multi-user OTFS integrated scheme based on frequency division multiple access. Addressing the issue that different subcarrier allocation methods in multi-user communication scenarios could lead to a decrease in radar ranging performance, they designed a suitable subcarrier allocation method to reduce the sidelobe level of radar range processing for each user, thereby effectively realizing the radar detection function for each user. In 2025, Sruti et al. constructed the OTFS multistatic ISAC system for V2I high-maneuver scenarios. They designed a Doppler ZC sequence that can distinguish waveforms in multi-transmitter scenarios and proposed to obtain the time delay-Doppler of each bistatic link in the time domain at the radar end and only transmit low-dimensional measurements back. Thus, in the fusion center, the association and localization of multi-target data are uniformly modeled as a sparse recovery problem and OMP is used to achieve low-complexity joint association and localization. At the same time, it is extended to fractional time delay-Doppler measurement to improve the localization and velocity measurement accuracy under narrowband conditions. Summary of the Invention

[0006] This invention discloses a super-resolution target parameter estimation method for OTFS integrated sensing signals with synchronization error problem. It can achieve high-precision and low-complexity joint estimation of target distance and radial velocity in non-ideal scenarios with timing offset and carrier frequency offset.

[0007] The technical solution to achieve the purpose of this invention is: a method for estimating super-resolution target parameters of OTFS integrated sensing signals with synchronization error, comprising the following steps:

[0008] Step 1: Construct an OTFS integrated sensing system model for a single base station. Based on the transmitter's DD-TF-time domain transformation, linear time-varying echo channel and receiver's Wigner transformation, and SFFT processing, establish the input-output relationship in the DD domain. At the same time, introduce system-level timing offset (TO) and carrier frequency offset (CFO) to construct a sparse observation model with synchronization error.

[0009] Step 2: Based on the sparse observation model, using the alternating minimization framework, fix the current synchronization error estimate, and solve the sparse vector using the ADMM algorithm to obtain the grid-level coarse estimate of the target time delay-Doppler parameters;

[0010] Step 3: Fix the sparse vector solution results, and based on the OTFS pilot structure, update the synchronization error parameters through Newton-type iteration to complete the joint coarse estimation of TO and CFO.

[0011] Step 4: Perform multi-target interference cancellation based on the coarse estimation results of time delay-Doppler parameters. Construct an extended parameter vector for the off-grid offset and synchronization error residual of each target. Perform local super-resolution fine estimation using Newton's method. Output the fine estimates of the distance and radial velocity of each target and the final estimate of the system synchronization error.

[0012] This invention also provides a super-resolution target parameter estimation system for OTFS integrated sensing signals with synchronization error problem, used to implement the above method, the system comprising:

[0013] The first module is used to construct the OTFS integrated sensing system model and the sparse observation model with synchronization error;

[0014] The second module is used to perform a grid-level coarse estimation of the target time delay-Doppler parameters based on the alternating minimization framework using the ADMM or UAMP algorithm;

[0015] The third module is used to perform joint estimation of system timing offset and carrier frequency offset through Newton-type iteration;

[0016] The fourth module is used to perform super-resolution fine estimation of target parameters and synchronization error residuals through multi-target interference cancellation and Newton iteration, and outputs the fine parameters of target distance and radial velocity and the final estimated value of synchronization error.

[0017] An electronic device includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the method described above.

[0018] A computer-readable storage medium having a computer program stored thereon that, when executed by a processor, implements the above-described method.

[0019] A computer program product includes a computer program that, when executed by a processor, implements the above-described method.

[0020] Compared with the prior art, the present invention has the following significant advantages: (1) The present invention introduces system-level timing offset and carrier frequency offset into the OTFS sensing model, constructs a sparse observation model with synchronization error, and realizes the joint estimation of target parameters and synchronization error through the alternating minimization framework, effectively eliminating the influence of synchronization error on target distance and velocity estimation, and greatly improving the robustness and estimation accuracy of the algorithm in non-ideal synchronization scenarios; (2) The present invention adopts a two-stage architecture of ADMM coarse estimation + Newton's method fine estimation. The coarse estimation stage realizes the rapid positioning of the target grid, and the fine estimation stage achieves the joint estimation of target grid level through multiple The target interference cancellation and the Newton iteration of the extended parameter vector, while correcting the target off-grid offset and synchronization error residual, effectively solve the grid mismatch problem, significantly improve the parameter estimation accuracy in multi-target and close-to-close target scenarios, and reduce the estimation threshold signal-to-noise ratio of the algorithm; (3) The algorithm of this invention has strong compatibility and is applicable to both ideal synchronization scenarios and non-ideal scenarios with timing offset and carrier frequency offset. It can maintain excellent detection performance and estimation accuracy in various scenarios such as single target, multi-target, and low signal-to-noise ratio, providing a feasible technical solution for the engineering implementation of the OTFS integrated sensing system.

[0021] The present invention will now be described in further detail with reference to the accompanying drawings. Attached Figure Description

[0022] Figure 1 This is the algorithm flowchart of the present invention.

[0023] Figure 2 This is a comparison chart of the estimation performance of the present invention in single-target, dual-target, and triple-target scenarios with synchronization error.

[0024] Figure 3 This is a comparison chart showing the root mean square error (RMSE) of distance and velocity estimation for different algorithms as a function of signal-to-noise ratio.

[0025] Figure 4 The graph shows the changes in RMSE (Reference Range Estimate) of the distance and velocity estimation algorithm of this invention with the signal-to-noise ratio under different combinations of M and N.

[0026] Figure 5 This is a graph showing the changes in the distance and velocity estimation RMSE of the algorithm of this invention with the signal-to-noise ratio under different numbers of targets.

[0027] Figure 6 This is a graph showing the changes in the signal-to-noise ratio (SNR) for distance and velocity estimation using the algorithm of this invention at different target distances. Detailed Implementation

[0028] The symbol duration of the OTFS integrated sensing signal in the DD domain is regarded as the pulse duration of a traditional pulse radar. The symbol matrix in the DD domain is equivalent to the range-Doppler matrix and contains target range and velocity information.

[0029] Combination Figure 1 This invention provides a method for estimating super-resolution target parameters of OTFS integrated sensing signals with synchronization error problems, comprising:

[0030] Step 1: Construct the OTFS sensing system model with synchronization error and the sparse observation model, specifically as follows:

[0031] Step 1-1: Set OTFS system parameters: Modulation symbol number is The number of subcarriers for each symbol is The duration of a single symbol is The length of the cyclic prefix CP is The subcarrier spacing is The system bandwidth is The DD field is represented as Integer delay-Doppler grid;

[0032] Steps 1-2: The DD-domain transmitted symbol matrix is ​​transformed to the TF-domain using ISFFT, and then a time-domain transmitted signal is generated using Heisenberg transform. The vectorized time-domain transmitted signal is represented as follows:

[0033]

[0034] in, For TF field information symbol matrix, For the DD field information symbol matrix, and These are the inverse discrete Fourier transform matrices at points M and N, respectively. It is an M-order identity matrix. This represents the operation of converting a matrix into a column vector. For Kronecker product;

[0035] Steps 1-3: Consider a linear time-varying channel with P resolvable echo paths, and introduce a system-level timing offset. and carrier frequency offset , No. The channel response of each path is represented as:

[0036]

[0037] in, For the first The reflection gain coefficient of the path, Indicates the total number of paths. For the first The delay of the path, The unit impulse function;

[0038] Steps 1-4: The received time-domain signal is mapped to the TF domain using Wigner transform, and then to the DD domain using SFFT transform to obtain the vectorized received signal, thus constructing a sparse observation model with synchronization error.

[0039]

[0040] in, This is a dictionary matrix with synchronization error. This is a set of path parameters and synchronization error parameters. Let w be a sparse coefficient vector, and let w be an additive white Gaussian noise vector. This is the channel matrix in the DD domain.

[0041] Step 2: Based on the sparse observation model, using the alternating minimization framework, and fixing the current synchronization error estimate, the sparse vector is solved using the ADMM algorithm to obtain the grid-level coarse estimate of the target delay-Doppler parameters:

[0042] Step 2-1: Based on the sparse observation model, construct a band Regularized robust sparse reconstruction optimization problem:

[0043]

[0044] in, for The estimated value, for The estimated value, It is a sparse vector. For synchronization error parameters, For a dictionary matrix with synchronization error, the regularization term... To promote sparsity of solutions, sparse solutions are encouraged to suppress irrelevant components, retaining only the non-zero coefficients corresponding to a small number of significant paths. Let be the denoting factor. .

[0045] Step 2-2: Introduce auxiliary variables And apply constraints The optimization problem is rewritten in a constrained form, and scaling dual variables are introduced. Construct the augmented Lagrange function:

[0046]

[0047] in, for Iteration number The value of the wheel, This is the penalty coefficient;

[0048] Steps 2-3: Perform ADMM iterative updates, completing them sequentially. -renew, -Update and dual variables -renew;

[0049] (a) -Update: Regarding the augmented Lagrange function Differentiate and set the gradient to zero, then solve the linear equation to obtain The iterative values ​​are obtained by using the conjugate gradient method to reduce the solution complexity:

[0050] No. The expression for the ADMM iteration is as follows:

[0051]

[0052] right Taking the derivative and setting the gradient to zero, we obtain the linear equation.

[0053]

[0054] (b) -Updated: Obtained through complex soft thresholding calculation Closed-form solution:

[0055] make

[0056]

[0057] The problem then becomes

[0058]

[0059] (c) Dual variables - Updated: Completed according to scaling duality. Iterative updates:

[0060] In the case of unscaled variables, the update of the standard dual variable is

[0061]

[0062] Transform it into a scaled dual form:

[0063]

[0064] Therefore, we obtain

[0065]

[0066] Steps 2-4: When the original residual and the dual residual satisfy the preset stopping criterion, the ADMM iteration converges, and the sparse coefficient vector under the current synchronization error is output. The estimated value is used to complete the grid-level coarse estimation of the target delay-Doppler parameters.

[0067] Step 3: With the sparse vector solution results fixed, based on the OTFS pilot structure, the synchronization error parameters are updated through Newton-type iteration to complete the joint coarse estimation of TO and CFO, specifically:

[0068] Step 3-1: Based on the OTFS pilot structure, extract the receive vector corresponding to the pilot symbol. Fixed sparse coefficient vector This reduces the optimization problem to minimizing data consistency terms:

[0069]

[0070] in, The equivalent dictionary matrix is ​​constructed from the known pilot structure and synchronization error. This represents the number of pilot samples participating in the synchronization estimation. This is the equivalent channel matrix of the communication link in the current iteration. This represents the dimension of the equivalent communication channel vector.

[0071] Step 3-2: Define the residual vector The gradient vector of the cost function with respect to the synchronization error parameter is calculated based on the chain rule, and the Hessian matrix is ​​approximated by Gauss-Newton.

[0072] Step 3-3: Use Newton-type iteration to update the synchronization error parameters; the formula in step 3-1 can be rewritten as follows:

[0073]

[0074] remember According to the chain rule, regarding The first derivative is

[0075]

[0076] in, This is a function that takes the real part.

[0077] The rigorous expression for the second derivative (Hessian) is:

[0078]

[0079] Considering The term is difficult to calculate precisely numerically, and when the residuals When the second term is relatively small, its influence is relatively weak, so the Gauss-Newton approximation can be used, ignoring the second term to obtain an approximate Hessian.

[0080]

[0081] in, To obtain the initial Hessian matrix, we first combine the two-dimensional first derivatives into a gradient vector, and then...

[0082]

[0083] Add step size damping factor To ensure numerical stability, the iterative formula is as follows:

[0084]

[0085] in, for The The iteration value of the wheel.

[0086] Steps 3-4: When the iteration satisfies the convergence criterion or reaches the maximum number of iterations, output a coarse estimate of the synchronization error parameter.

[0087] Step 4: Perform multi-target interference cancellation based on the coarse estimation results of time delay-Doppler parameters. Construct an extended parameter vector for the off-grid offset and synchronization error residual of each target. Perform local super-resolution fine estimation using Newton's method. Output the fine estimates of the distance and radial velocity of each target and the final estimate of the system synchronization error.

[0088] Step 4-1: Based on the coarse estimation results of the sparse coefficient vector, locate the time delay-Doppler grid index corresponding to each target, and perform multi-target interference cancellation on each target in sequence to construct the first... The residual signal of each target:

[0089]

[0090] in, for The estimated value, It is the first The echo vector generated by a target under the current parameter estimation.

[0091] Step 4-2, for the first For each target, a local continuous offset is introduced. and synchronization error residual Construct the extended parameter vector and the synchronization error residual, and then construct the extended parameter vector:

[0092]

[0093] Step 4-3: Calculate the gradient of the cost function with respect to the extended parameter vector and the Hessian matrix. Update the extended parameter vector through Newton iteration to complete the joint fine estimation of the target offset and the synchronization error residual.

[0094] Step 4-4: Based on the finely estimated time delay and Doppler parameters, the final fine estimates of the target distance and radial velocity are calculated through the linear mapping relationship between time delay-distance and Doppler-radial velocity. At the same time, the final estimate of the synchronization error is output.

[0095] Based on the same inventive concept, this invention also provides a super-resolution target parameter estimation system for OTFS integrated sensing signals with synchronization error problems, used to implement the above method. The system includes:

[0096] The first module is used to construct the OTFS integrated sensing system model and the sparse observation model with synchronization error;

[0097] The second module is used to perform a grid-level coarse estimation of the target time delay-Doppler parameters based on the alternating minimization framework using the ADMM or UAMP algorithm;

[0098] The third module is used to perform joint estimation of system timing offset and carrier frequency offset through Newton-type iteration;

[0099] The fourth module is used to perform super-resolution fine estimation of target parameters and synchronization error residuals through multi-target interference cancellation and Newton iteration, and outputs the fine parameters of target distance and radial velocity and the final estimated value of synchronization error.

[0100] The specific implementation methods of the first to fourth modules mentioned above are the same as those of the super-resolution target parameter estimation methods described above, and will not be repeated here.

[0101] The following is a detailed description with reference to the embodiments:

[0102] Example

[0103] Symbolic Number , the number of subcarriers The modulation scheme is QPSK, the carrier frequency is 24 GHz, the subcarrier spacing is 78.125 kHz, and the simulation environment is set to an additive white Gaussian noise (AWGN) channel. The three target groups are set as follows: , , .from Figure 2 As can be seen from this, the three sets of estimation results for the proposed scheme are as follows: , , The estimation results of the traditional ADMM+Newton scheme are... , , This clearly shows that the proposed solution can compensate for synchronization errors.

[0104] from Figure 3 The following conclusions can be drawn: First, under low SNR conditions, all methods are limited by noise, and the performance difference is not significant. The advantages and disadvantages of the algorithm structure only gradually become apparent after the threshold. Second, using only dictionary-based sparse reconstruction (ADMM, OMP) cannot break the limitation of raster resolution, while subspace methods (MUSIC, ESPRIT) can reduce RMSE to a certain extent through spectral interpolation, but there is still room for performance improvement. Third, after introducing Newton continuous optimization, ADMM+Newton achieved the minimum RMSE and the lowest error plateau in both distance and velocity dimensions, and significantly outperformed other algorithms in the medium-to-high SNR region, verifying the effectiveness of the proposed ADMM coarse estimation and Newton fine estimation joint structure in target parameter estimation of the OTFS integrated sensing system.

[0105] Figure 4 Curves showing the distance and velocity RMSE of the proposed ADMM+Newton algorithm as a function of signal-to-noise ratio under different time-frequency resource configurations are presented. The three curves correspond to... , and . Figure 4 Figure (a) shows that the distance RMSE is mainly determined by the delay grid quantization error caused by limited bandwidth and multi-target sidelobe interference, and the larger the total bandwidth, i.e., the larger M, the lower the error lower bound. Figure (b) shows that as N increases, the accuracy and threshold performance of velocity estimation are significantly improved. Combining the two figures, we can conclude that, under the premise of fixed subcarrier spacing, appropriately increasing N can improve the accuracy and threshold performance of velocity estimation. and In other words, extending the total bandwidth and coherent observation duration of the system can significantly improve the joint distance and velocity estimation performance of the ADMM+Newton algorithm, reducing both the minimum working SNR and effectively suppressing the error plateau under high signal-to-noise ratio.

[0106] Figure 5 Curves showing the distance and velocity RMSE as a function of signal-to-noise ratio for the proposed ADMM+Newton algorithm in three scenarios: single-target, dual-target, and triple-target. Figure 5 As can be seen, with a fixed system bandwidth, the ADMM+Newton method still performs well under the mutual interference between multiple targets.

[0107] Figure 6 The target spacing is given for three-target scenarios. , and The performance curves of the ADMM+Newton algorithm for distance RMSE and velocity RMSE as a function of SNR are shown. System parameters are fixed. The corresponding distance resolution is approximately Therefore, the first two spacing configurations both belong to adjacent target scenes that are much smaller than the distance resolution, only the degree of overlap is different.

[0108] comprehensive Figure 6 It can be seen that, under the premise of three fixed targets, the root mean square error is the smallest when the target distance interval is an integer multiple of the range resolution. When the target distance interval is 5m and 2m, the root mean square error increases. However, the velocity estimation accuracy of targets with closer distances is almost unaffected.

Claims

1. A method for estimating super-resolution target parameters of OTFS integrated sensing signals with synchronization error, characterized in that, Includes the following steps: Step 1: Construct an OTFS integrated sensing system model for a single base station. Based on the transmitter's DD-TF-time domain transformation, linear time-varying echo channel and receiver's Wigner transformation, and SFFT processing, establish the input-output relationship in the DD domain. At the same time, introduce system-level timing offset (TO) and carrier frequency offset (CFO) to construct a sparse observation model with synchronization error. Step 2: Based on the sparse observation model, using the alternating minimization framework, fix the current synchronization error estimate, and solve the sparse vector using the ADMM algorithm to obtain the grid-level coarse estimate of the target time delay-Doppler parameters; Step 3: Fix the sparse vector solution results, and based on the OTFS pilot structure, update the synchronization error parameters through Newton-type iteration to complete the joint coarse estimation of TO and CFO; Step 4: Perform multi-target interference cancellation based on the coarse estimation results of time delay-Doppler parameters. Construct an extended parameter vector for the off-grid offset and synchronization error residual of each target. Perform local super-resolution fine estimation using Newton's method. Output the fine estimates of the distance and radial velocity of each target and the final estimate of the system synchronization error.

2. The method for estimating super-resolution target parameters of OTFS integrated sensing signals with synchronization error problem according to claim 1, characterized in that, Step 1 involves constructing a sparse observation model with synchronization errors. The specific steps are as follows: Step 1-1: Set OTFS system parameters: Modulation symbol number is The number of subcarriers for each symbol is The duration of a single symbol is The length of the cyclic prefix CP is The subcarrier spacing is , The system bandwidth is The DD field is represented as Integer delay-Doppler grid; Steps 1-2: The DD-domain transmitted symbol matrix is ​​transformed to the TF-domain using ISFFT, and then a time-domain transmitted signal is generated using Heisenberg transform. The vectorized time-domain transmitted signal is represented as follows: ； in, For TF field information symbol matrix, For the DD field information symbol matrix, and These are the inverse discrete Fourier transform matrices at points M and N, respectively. It is an M-order identity matrix. This represents the operation of converting a matrix into a column vector. For Kronecker product; Steps 1-3: Consider a linear time-varying channel with P resolvable echo paths, and introduce a system-level timing offset. and carrier frequency offset , No. The channel response of each path is represented as: ； in, For the first The reflection gain coefficient of the path, Indicates the total number of paths. For the first The delay of the path, The unit impulse function; Steps 1-4: The received time-domain signal is mapped to the TF domain using Wigner transform, and then to the DD domain using SFFT transform to obtain the vectorized received signal, thus constructing a sparse observation model with synchronization error. ； in, This is a dictionary matrix with synchronization error. This is a set of path parameters and synchronization error parameters. Let w be a sparse coefficient vector, and let w be an additive white Gaussian noise vector. This is the channel matrix in the DD domain.

3. The OTFS integrated sensing target parameter estimation method according to claim 2, characterized in that, The specific steps for solving the sparse vector using the ADMM algorithm in step 2 are as follows: Step 2-1: Based on the sparse observation model, construct a band Regularized robust sparse reconstruction optimization problem: ； in, for The estimated value, for The estimated value, It is a sparse vector. For synchronization error parameters, For a dictionary matrix with synchronization error, the regularization term... To promote the sparsity of solutions, let be... ; Step 2-2: Introduce auxiliary variables And apply constraints The optimization problem is rewritten in a constrained form, and scaling dual variables are introduced. Construct the augmented Lagrange function: ； in, for Iteration number The value of the wheel, This is the penalty coefficient; Steps 2-3: Perform ADMM iterative updates, completing them sequentially. -renew, -Update and dual variables -renew; (a) -Update: Regarding the augmented Lagrange function Differentiate and set the gradient to zero, then solve the linear equation to obtain The iterative values ​​are obtained by using the conjugate gradient method to reduce the solution complexity; (b) -Updated: Obtained through complex soft thresholding calculation Closed-form solution; (c) Dual variables - Updated: Completed according to scaling duality. Iterative updates; Steps 2-4: When the original residual and the dual residual satisfy the preset stopping criterion, the ADMM iteration converges, and the sparse coefficient vector under the current synchronization error is output. The estimated value is used to complete the grid-level coarse estimation of the target delay-Doppler parameters.

4. The OTFS integrated sensing target parameter estimation method according to claim 3, characterized in that, The specific steps for iteratively updating the synchronization error parameters in step 3 are as follows: Step 3-1: Based on the OTFS pilot structure, extract the receive vector corresponding to the pilot symbol. Fixed sparse coefficient vector This reduces the optimization problem to minimizing data consistency terms: ； in, The equivalent dictionary matrix is ​​constructed from the known pilot structure and synchronization error. This represents the number of pilot samples participating in the synchronization estimation. The dimension of the equivalent communication channel vector; Step 3-2: Define the residual vector The gradient vector of the cost function with respect to the synchronization error parameter and the Hessian matrix approximated by Gauss-Newton are calculated based on the chain rule. Step 3-3: Update the synchronization error parameters using Newton-type iteration; add a step size damping factor. To ensure numerical stability, the iterative formula is as follows: ； in, for The The iteration value of the wheel; Steps 3-4: When the iteration satisfies the convergence criterion or reaches the maximum number of iterations, output a coarse estimate of the synchronization error parameter.

5. The OTFS integrated sensing target parameter estimation method according to claim 4, characterized in that, The specific steps of the super-resolution fine estimation in step 4 are as follows: Step 4-1: Based on the coarse estimation results of the sparse coefficient vector, locate the time delay-Doppler grid index corresponding to each target, and perform multi-target interference cancellation on each target in sequence to construct the first... The residual signal of each target: ； in, for The estimated value, It is the first The echo vector generated by each target under the current parameter estimation; Step 4-2, for the first For each target, a local continuous offset is introduced. and synchronization error residual Construct the extended parameter vector: ； Step 4-3: Calculate the gradient of the cost function with respect to the extended parameter vector and the Hessian matrix. Update the extended parameter vector through Newton iteration to complete the joint fine estimation of the target offset and the synchronization error residual. Step 4-4: Based on the finely estimated time delay and Doppler parameters, the final fine estimates of the target distance and radial velocity are calculated through the linear mapping relationship between time delay-distance and Doppler-radial velocity. At the same time, the final estimate of the synchronization error is output.

6. A super-resolution target parameter estimation system for OTFS integrated sensing signals with synchronization error problem, characterized in that, The system for implementing the method according to any one of claims 1 to 5 comprises: The first module is used to construct the OTFS integrated sensing system model and the sparse observation model with synchronization error; The second module is used to perform a grid-level coarse estimation of the target time delay-Doppler parameters based on the alternating minimization framework using the ADMM or UAMP algorithm; The third module is used to perform joint estimation of system timing offset and carrier frequency offset through Newton-type iteration; The fourth module is used to perform super-resolution fine estimation of target parameters and synchronization error residuals through multi-target interference cancellation and Newton iteration, and outputs the fine parameters of target distance and radial velocity and the final estimated value of synchronization error.

7. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the method as described in any one of claims 1 to 5.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the program is executed by the processor, it implements the method as described in any one of claims 1 to 5.

9. A computer program product, comprising a computer program, characterized in that, When executed by a processor, the computer program implements the method described in any one of claims 1 to 5.

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