Flexible antenna array aided isac system channel estimation method

Abstract

This invention discloses a channel estimation method for a flexible antenna array-assisted ISAC system. It constructs a multidimensional tensor channel model that integrates antenna rotation parameters. The received signals are then stacked into a tensor form with a Vandermonde structure. A two-stage parameter estimation framework is employed: the first stage utilizes the translation invariance of the tensor in the time delay dimension to achieve initial estimation of time delay and Doppler shift using the ESPRIT algorithm; the second stage performs tensor normalized multilinear decomposition within a Bayesian probabilistic framework, introduces hierarchical sparse priors to adaptively determine the model rank, and performs joint fine estimation of multidimensional channel parameters such as angle of arrival, departure angle, time delay, Doppler shift, and reflection coefficient. Simulation results show that this invention has higher estimation accuracy and stability under complex channel and low signal-to-noise ratio conditions, and is suitable for broadband large-scale ISAC systems assisted by flexible antenna arrays.

Description

Technical Field

[0001] This invention relates to the field of integrated sensing and communication (ISAC) technology, and is particularly applicable to broadband massive MIMO systems with integrated flexible antenna arrays (FAA). Background Technology

[0002] In 6G networks, ISAC systems simultaneously achieve communication and sensing functions by sharing physical infrastructure. Flexible antenna arrays (FAAs) provide additional spatial degrees of freedom to ISAC systems by rotating to adjust the beam direction. However, FAAs simultaneously change the antenna element positions and gains, leading to geometry-mode coupling and rendering traditional static array models ineffective. Furthermore, the number of propagation paths (equivalent to tensor rank) varies with the environment, and incorrect specification can cause component loss or overfitting.

[0003] Existing ISAC parameter estimation methods based on tensor decomposition have the following limitations: 1. Model mismatch: Traditional methods treat the FAA as a static array, ignoring the influence of its geometric rotation on the guide vector; 2. Rank dependence: The rank Q needs to be specified in advance, which can easily lead to overfitting or underfitting in complex scenarios; 3. High computational complexity: The ALS algorithm for unstructured CP decomposition has a complexity of O(n log n). This makes it difficult to meet real-time requirements. Summary of the Invention

[0004] This invention aims to address the geometry-mode coupling challenge introduced by the FAA, and provides a geometrically constrained third-order tensor modeling method and a Bayesian adaptive rank estimation framework to achieve high-precision joint estimation of AoA, AoD, time delay, Doppler frequency shift and reflection coefficient.

[0005] To address the above problems, this invention provides a channel estimation method for a flexible antenna array-assisted ISAC system. The flexible antenna array-assisted ISAC system mainly includes the following functional modules: Module 1: Base Station Flexible Antenna Array Module The base station is equipped with a rotatable or reconfigurable flexible antenna array module for simultaneously transmitting communication signals and sensing waveforms. This module achieves adaptive optimization of the beam direction and array geometry by adjusting the spatial position and rotation angle of the antenna array. Module 2: Flexible Antenna Array Module for Receiver The receiver is equipped with a flexible antenna array for sensing echo signals, which can receive echo signals from multiple propagation paths under different array orientations and output multi-dimensional time-frequency domain sampling data. Module 3: Signal Acquisition and Preprocessing Module It is used to perform down-conversion, sampling and pilot separation processing on the received signal, and to organize the data in the time domain, frequency domain and symbol dimension to provide basic input for subsequent tensor modeling; Module 4: Multidimensional Tensor Construction Module This is used to stack the preprocessed received signals according to the symbol dimension, subcarrier dimension and array observation dimension to construct a multidimensional tensor model containing angle, time delay, Doppler and array rotation information; Module 5: Channel Parameter Estimation Module Based on the constructed tensor model, a two-stage parameter estimation algorithm is executed, including ESPRIT initialization and Bayesian tensor decomposition, to extract multidimensional channel parameters. Module 6: Parameter Output and Application Module The estimated angle of arrival, angle of departure, time delay, Doppler shift, and reflection coefficient are output and used for communication beamforming, target sensing and localization, or system resource optimization. The method includes the following steps: Step S1: Construct a third-order tensor model The observation samples at the receiver are rearranged and stacked in the array dimension (space), OFDM symbol dimension (time), and subcarrier dimension (frequency) to construct a third-order observation tensor. ,in For spatial observation dimension (equivalent array element number / channel number). To train the OFDM symbol count, The number of training subcarriers. Its canonical multilinear decomposition (CPD) is expressed as: Equivalent to: in: , The elevation / azimuth angle of this path. FAA rotation angle (around the z-axis) (This is the spatial modulus factor matrix). ( (This is the time modulus factor matrix). , , Vandermonde steering vector ( (where E is the frequency modulus factor matrix and E is the noise tensor).

[0006] (1) Rotation update of array element coordinates (geometric approach): After array rotation, the coordinates of the (m,n)th array element can be written as And order .

[0007] (2) Rotational steering vector (phase term included): Let the wave vector (unit direction vector) be used. carrier wavelength The unified array response under FAA rotation is then... in For Hadamard products, This indicates that the radiation pattern shifts angularly with rotation (electromagnetic input).

[0008] Note: If the direction chart item is ignored during implementation, it can be set as follows: ,but Still through array element coordinates Enter the phase term.

[0009] Step S2: ESPRIT Initialization (Phase 1) The tensor is expanded along both the frequency dimension (subcarrier dimension) and the time dimension (symbol dimension). Utilizing the translation invariance of the signal subspace, ESPRIT is applied to the frequency dimension to obtain initial estimates of the path delay; ESPRIT is applied to the time dimension to obtain initial estimates of the Doppler frequency shift of each path, providing prior information for subsequent Bayesian inference.

[0010] (1) Delay initialization (frequency dimension ESPRIT) Expanding the tensor according to its frequency modulus yields... SVD is performed on it to obtain the signal subspace. Construct the selection matrix. Establish shift-invariant relation right Eigenvalues ​​are obtained through eigenvalue decomposition The initial time delay is obtained from its phase. (2) Doppler initialization (time dimension ESPRIT) Expanding the tensor along the time modulus yields... , for its SVD .structure And calculate Eigendecomposition yields The initial value of its phase Doppler Step S3: Bayesian CP decomposition (second stage) Inference of the CP model is performed within a Bayesian probabilistic framework. The observation likelihood is set to complex Gaussian noise (which can be applied to the entire sample set or the observation set). definition): in For noise accuracy, Indicates the CP model for the first... Prediction of the multilinear inner product of tensor elements.

[0011] To achieve automatic rank determination, a shared column sparsity (ARD) prior is introduced, which allows the same rank component of the three modulo factor matrices to share the same precision hyperparameter. ,Right now and take , .when As the value increases, the r-th column will shrink and be pruned synchronously across the three moduli, thereby achieving automatic rank determination.

[0012] Mean field variational inference is used, and CAVI is used for iterative updates: via ELBO Monitoring convergence; satisfying the following conditions during the iteration process. The portion was pruned.

[0013] Step S4: Physical parameter extraction (1) Time delay and Doppler From frequency modulus factor Phase slope estimation (or use) (Initialization and refinement after Bayesian convergence); by time modulus factor Phase advance estimation (Similarly, further details are provided).

[0014] (2) AoA / AoD (angle parameters, including FAA rotation compensation) From spatial modulus factor With FAA Rotary Guide Vector The angle obtained by matching: in The unified expression of "rotation coordinates + phase term + (optional) pattern translation" from step S1 is adopted; thus, the FAA rotation angle is expressed through... and Explicit entry angle estimation for both paths.

[0015] If the spatial modulus includes both the transmitter and receiver array responses, the spatial factors can be rearranged according to the transmitter / receiver dimensions and matched to obtain AoD / AoA respectively.

[0016] (3) Reflection coefficient / path gain For each r, let Then the reflection coefficient vector It can be obtained by least squares Thus, the reflection coefficients of each path are obtained. .

[0017] Finally, the final channel parameter estimation results are output by the result output module, which can be further used for communication beam design, target sensing, and system performance optimization in the ISAC system.

[0018] This invention addresses the geometry-mode coupling problem introduced by the rotation or displacement of flexible antenna arrays, as well as the model order uncertainty caused by the unknown number of channel paths. It constructs a multidimensional tensor channel model that integrates antenna rotation parameters. By stacking the received signals into a tensor form with a Vandermonde structure, a two-stage parameter estimation framework is adopted: the first stage (steps S1 and S2) utilizes the translation invariance of the tensor in the time delay dimension to achieve initial estimation of time delay and Doppler shift using the ESPRIT algorithm; the second stage (steps S3 and S4) performs tensor normalized multilinear decomposition within a Bayesian probabilistic framework, introduces hierarchical sparse priors to adaptively determine the model rank, and performs joint fine estimation of multidimensional channel parameters such as angle of arrival, departure angle, time delay, Doppler shift, and reflection coefficient. Simulation results show that this invention has higher estimation accuracy and stability under complex channel and low signal-to-noise ratio conditions, and is suitable for broadband large-scale ISAC systems assisted by flexible antenna arrays. This invention can be further extended to higher-dimensional tensor modeling and parameter estimation scenarios. In mobile antenna communication systems, by further incorporating the displacement and rotation parameters of the antenna array into a multidimensional steering vector, a high-dimensional tensor channel model encompassing time, space, frequency, and array motion states can be constructed. In this extended scenario, the described Bayesian probabilistic framework and variational inference algorithm are equally applicable, enabling joint probabilistic estimation of multidimensional angular parameters such as horizontal and elevation angles at both the transmitter and receiver. By fusing the channel response changes caused by antenna motion and expressing them as structured constraints in tensor decomposition, the method of this invention maintains high-precision parameter estimation capabilities in complex communication scenarios such as MIMO and OFDM, significantly improving estimation robustness and system adaptability under low signal-to-noise ratio conditions. Attached Figure Description

[0019] Figure 1This is a diagram of the flexible antenna array-assisted ISAC system architecture of the present invention; Figure 1 The image shows the base station FAA, user equipment FAA, and radar receiver array; Figure 2 This is the overall design block diagram of the present invention; Figure 3 , Figure 4 , Figure 5 , Figure 6 , Figure 7 , Figure 8 The above are simulation results of the present invention. Figure 3 —— Figure 8 The angle, time delay, and Doppler estimation RMSE comparison of the present invention are shown, where the SNR ranges from 0 dB to 30 dB; Figure 9 This is a scatter plot of the MS-side two-dimensional angle estimation performance in Embodiment 1 of the present invention; Figure 10 This is a diagram illustrating the objective function optimization process in Embodiment 1 of the present invention. Figure 10 This illustrates the impact of FAA rotation angle on communication-sensing performance; Figure 11 This is the posterior analysis diagram of Bayesian automatic rank estimation in Embodiment 1 of the present invention; Figure 11 The ELBO convergence, component suppression, and noise estimation are shown. Detailed Implementation

[0020] The specific embodiments of the present invention will be further described below with reference to the accompanying drawings.

[0021] like Figure 2 As can be seen, the flexible antenna array-assisted ISAC system of the present invention includes the following modules: Module 1: Base Station Flexible Antenna Array Module The base station is equipped with a rotatable or reconfigurable flexible antenna array module for simultaneously transmitting communication signals and sensing waveforms. This module achieves adaptive optimization of the beam direction and array geometry by adjusting the spatial position and rotation angle of the antenna array.

[0022] Module 2: Flexible Antenna Array Module for Receiver The receiver is equipped with a flexible antenna array for sensing echo signals, which can receive echo signals from multiple propagation paths under different array orientations and output multi-dimensional time-frequency domain sampling data.

[0023] Module 3: Signal Acquisition and Preprocessing Module It is used to perform down-conversion, sampling and pilot separation processing on the received signal, and to organize the data in the time domain, frequency domain and symbol dimension to provide basic input for subsequent tensor modeling.

[0024] Module 4, Multidimensional Tensor Construction Module This is used to stack the preprocessed received signals according to the symbol dimension, subcarrier dimension, and array observation dimension to construct a multidimensional tensor model containing angle, time delay, Doppler, and array rotation information.

[0025] Module 5, Channel Parameter Estimation Module Based on the constructed tensor model, a two-stage parameter estimation algorithm is executed, including ESPRIT initialization and Bayesian tensor decomposition, to extract multidimensional channel parameters.

[0026] Module 6, Parameter Output and Application Module The estimated angle of arrival, angle of departure, time delay, Doppler shift, and reflection coefficient are output and used for communication beamforming, target sensing and localization, or system resource optimization.

[0027] like Figure 2 As can be seen, the flexible antenna array-assisted ISAC system channel estimation method of the present invention includes the following steps: Step S1: Tensor Modeling The received signals are sorted and stacked to construct a multidimensional tensor model that integrates the rotation parameters of the flexible antenna array, and a steering vector with a Vandermonde structure is explicitly introduced.

[0028] Step S2: ESPRIT Initialization Module The tensor is expanded along the time delay dimension. By utilizing the translation invariance of the signal subspace, the initial estimates of time delay and Doppler frequency shift are obtained through the ESPRIT algorithm, providing prior information for subsequent Bayesian inference.

[0029] Step S3: Bayesian Tensor Decomposition Module Within the Bayesian probabilistic framework, a normalized multilinear decomposition of the tensor model is performed, a hierarchical sparse prior is introduced to achieve automatic rank determination, and the posterior distribution of the factor matrix is ​​iteratively optimized through a coordinate ascending variational inference algorithm.

[0030] Step S4: Physical Parameter Extraction Module Based on the estimated factor matrix, the receiver angle, transmitter angle, Doppler frequency shift, time delay, and reflection coefficient are extracted by spatial correlation matching, joint optimization, and least squares methods, respectively.

[0031] Output results: Output the final channel parameter estimation results, which can be further used for communication beam design, target sensing and system performance optimization in the ISAC system. Example 1 This embodiment is used to illustrate the algorithm flow of the present invention.

[0033] This embodiment provides a FAA-ISAC channel parameter estimation algorithm based on Bayesian tensor decomposition, such as... Figure 2 As can be seen, this embodiment mainly includes the following steps: Input: Received signal , , Initial Doppler Number of iterations Output: Parameter estimation 1. ESPRIT initialization (step S2): (1) Calculation (2) Estimate 2. Bayesian CP decomposition (step S3): (1) Initialization Set hyperparameters (2) Optimization through CAVI iteration until ELBO converges 3. Parameter extraction (step S4): For each : a. estimate b. Alternating optimization and ( Second-rate) c. estimate 4. Output: Estimated values ​​of all parameters Experimental simulation analysis To verify the effectiveness and stability of the FAA-assisted ISAC channel parameter estimation method based on Bayesian tensor decomposition proposed in this invention, this embodiment conducts a systematic simulation experiment in a millimeter-wave broadband massive MIMO-ISAC scenario, using the root mean square error (RMSE) as the main performance indicator. The system parameters are set as follows: 64 transmit antennas for the base station (BS), and 16 antennas each for the sensing receiver and user equipment (UE); carrier frequency of 28 GHz, system bandwidth of 100 MHz, number of subcarriers of 128, and cyclic prefix duration of [missing information]. Channel path delay at The target is uniformly distributed within the target area, and both the number of targets (Q) and the number of paths (L) are set to 4; the reflection coefficient and path gain follow (CN(0,1)); the azimuth angle (AoA / AoD) is within the range of... Independently and uniformly distributed within, with an elevation angle of... Internal sampling; target velocity exist Uniformly distributed within, among which Corresponding to maximum Doppler frequency shift kHz; the elements of the training code matrix are sampled independently on the unit circle.

[0034] To ensure fairness and representativeness in the comparison, the baseline algorithms include Alternating Least Squares (ALS), Nonlinear Least Squares (NLS), and MUSIC. Both ALS and NLS are used for unstructured CP decomposition and minimizing the same least squares criterion; the difference lies only in the optimizer: ALS uses block least squares alternating updates, while NLS uses Gauss–Newton / Levenberg–Marquardt type nonlinear least squares optimization implemented in the TensorLab toolbox. Unless otherwise specified, ALS and NLS use the same rank (L) and consistent stopping criteria / maximum number of iterations to ensure fair comparison.

[0035] 1. Angle estimation performance analysis Figures 3 to 6 The comparison results of the RMSE estimates for azimuth and elevation angles on the MS and BS sides as a function of SNR are presented. The results show that the method of this invention consistently achieves the lowest RMSE throughout the entire SNR evaluation range, and exhibits a clear monotonically decreasing trend with increasing SNR, demonstrating good noise resistance and scalability. In the unstructured tensor decomposition baseline, the NLS curve is generally superior to the ALS curve; that is, under the same rank and the same stopping rule, using a stronger nonlinear least squares optimizer helps improve the CP fitting quality and the subsequent accuracy of physical parameter recovery.

[0036] In contrast, the MUSIC method, due to its failure to fully utilize the multilinear structure of multidimensional tensors, exhibits significantly larger errors and is less sensitive to SNR improvement. In summary, this invention, based on structured probabilistic modeling and prior regularization, can more effectively suppress noise and coupling effects; while ALS / NLS, as an unstructured decomposition method, lacks explicit physical manifold and factor structure constraints, making it susceptible to limitations in parameter distinguishability and residual coupling errors.

[0037] 2. Performance Analysis of Distance and Velocity Estimation Figure 7 The results demonstrate the effect of distance (or equivalent time delay) estimation RMSE on SNR. The error of the method in this invention decreases rapidly with increasing SNR and gradually approaches the Cramér-Rao bound (CRB) in the high SNR region, exhibiting near-efficient estimation characteristics. Compared with matched filtering (MF) that does not utilize tensor structures, both ALS and NLS can significantly reduce distance estimation error by leveraging tensor models; and NLS typically outperforms ALS further, consistent with the improved fitting quality brought about by its nonlinear least squares optimization.

[0038] Figure 8 The RMSE of velocity (Doppler) estimation was compared. The method of this invention maintains the best accuracy across the entire SNR range and can continue to improve with SNR. Meanwhile, simulations show that in the medium-to-high SNR region, ALS is more prone to a significant error margin; while NLS continues to decrease with increasing SNR and achieves a lower RMSE than ALS. This indicates that in non-convex optimization problems with unstructured CP fitting, NLS is less likely to stagnate at suboptimal stagnation points than ALS, thus improving the stability of velocity recovery.

[0039] 3. Angle estimation visualization analysis Figure 9 A visualization comparison of the scatter points of the two-dimensional angle estimation on the MS side is presented. The estimated points of the method of this invention almost coincide with the true values, demonstrating stability and reliability at the single-experiment level; ALS exhibits systematic bias in areas such as oblique incidence angles; the MUSIC estimation points are scattered and deviate most significantly from the true values, resulting in the largest estimation error. This visualization result is consistent with the RMSE statistical conclusions, further illustrating the advantages of this invention in terms of statistical accuracy and reliability of individual experiments.

[0040] 4. FAA Rotation Optimization Verification Figure 10 The relationship between the FAA rotation angle and the joint objective function obtained using Bayesian optimization (BO) is illustrated. As shown in the figure, the joint objective function first increases and then decreases with the rotation angle, exhibiting a clear global maximum at the optimal rotation angle. This indicates that FAA rotation can affect both communication and sensing performance simultaneously by influencing the coupled channel response. Furthermore, the curve exhibits a smooth, single-peak shape, demonstrating that the proposed BO framework can effectively characterize the nonlinear dependence of the joint performance index on the rotation angle and can stably converge to the global optimum, thus possessing engineering-feasible closed-loop optimization characteristics.

[0041] 5. Bayesian Automatic Rank Determination Verification Figure 11 This demonstrates the effectiveness of the Bayesian ARD mechanism of this invention in automatic rank determination and adaptive noise modeling in FAA-assisted ISAC models: First, the posterior magnitude index of the potential tensor components shows that redundant components are gradually suppressed under the hierarchical sparse prior constraint, while the components that maintain significant posterior strength correspond to the intrinsic effective rank, thus automatically identifying the effective model order without the need for multiple manual trials.

[0042] Secondly, the lower bound of evidence (ELBO) increases monotonically with iteration and stabilizes after a finite number of iterations, indicating that the variational inference process has good numerical convergence.

[0043] Third, noise accuracy parameters The posterior distribution shows that the model can adaptively estimate the noise level and can explicitly characterize uncertainty in low SNR or time-varying environments, thereby improving robustness. Example 2 like Figure 1 As can be seen, this embodiment demonstrates a method for closed-loop parameter estimation and beam / FAA joint configuration in a high-speed mobile vehicle-to-everything (V2X) scenario, as an application scenario.

[0045] After analyzing the simulation results above, to further illustrate the feasibility of the method of the present invention in high-speed mobile scenarios of vehicle-to-everything (V2X) networks, the following application examples are provided. It should be understood that these examples are for illustrative purposes only and do not constitute a limitation on the scope of protection of the present invention.

[0046] 1. Scenarios and System Parameters In one embodiment, the system carrier frequency may be in the millimeter-wave band (e.g., 28 GHz), with a bandwidth of, for example, 100 MHz, and the number of subcarriers, for example, 128; the vehicle / terminal is in a high-speed moving state (e.g., on the order of approximately 120 km / h). The system consists of a base station, a terminal, and an FAA (Field Application Array). The FAA can be configured as a linear array or an equivalent programmable reflective / transmittive element array, and its phase configuration can be updated according to the target / vehicle orientation to form multi-view observations.

[0047] 2. Processing Flow In this embodiment, the method of the present invention can be performed according to the following steps: S401: Observation Acquisition and Tensor Construction.

[0048] Within frame (t), the base station transmits a signal containing the training sequence, and the receiver obtains observation data at each subcarrier and symbol time. The observation data is then rearranged according to the array dimension, frequency domain dimension, and time domain dimension to construct the observation tensor. .

[0049] S402: Establish a physically parameterized tensor decomposition model.

[0050] Will It is represented as a superposition of several rank-one outer product terms, each outer product term corresponding to an effective propagation path / target echo; among them, the angle factor is related to the array steering vector, the time delay factor is related to the frequency domain phase advance, and the Doppler factor is related to the time domain phase advance.

[0051] S403: Bayesian tensor decomposition joint inference.

[0052] Prior distributions are introduced for path coefficients, noise accuracy, and factor matrices, and variational Bayesian inference is used for iterative updates to obtain posterior estimates of parameters such as angle, time delay, and Doppler. During the inference process, hierarchical sparse priors can be used to adaptively suppress weak paths, thereby maintaining robust convergence under conditions of high-speed motion and noise uncertainty.

[0053] S404: Physical quantity recovery and closed-loop update.

[0054] AoA / AoD is recovered from the angle factor, distance is converted from the time delay factor, and velocity is converted from the Doppler factor. Based on the estimation results, communication precoding / merging and sensing beam pointing are performed, and the phase configuration of the FAA is updated synchronously, so that the next frame observation can obtain higher effective gain and stronger identification in the main target direction.

[0055] S405: Online tracking.

[0056] The estimation result of frame (t) is used as the initialization or prior center of frame (t+1). S401 to S404 are executed in a loop to reduce iteration overhead and improve tracking stability in high-speed dynamic scenes.

[0057] 3. Effect Description Under the aforementioned high-speed movement conditions, the method of this invention demonstrates a stable error reduction trend while improving SNR, and exhibits significant advantages over ALS tensor decomposition and subspace methods such as MUSIC in angle and velocity estimation; simultaneously, closed-loop updates allow both communication and sensing performance to benefit. These effects are consistent with those described above. Figures 3-11 The simulation trends shown are consistent. Example 3 like Figure 1 As can be seen, this embodiment demonstrates a robust joint estimation and adaptive configuration optimization method in an indoor low-speed, high-precision scenario, as another application scenario.

[0059] To further illustrate the feasibility of the present invention in indoor low-speed, strong direct path dominant scenarios, and where weak multipath and occlusion may exist, the following application examples are provided.

[0060] 1. Scenarios and System Parameters In one embodiment, the system may operate in the mid-to-low frequency band or the centimeter-wave band (e.g., 5.8 GHz), with a bandwidth of, for example, 20 MHz and a number of subcarriers of, for example, 64; the terminal is in a low-speed movement state (e.g., on the order of 5 km / h), with high-precision angle / position perception as the primary objective. The FAA may be configured as a planar array or an equivalent two-dimensional programmable cell array, and rotation / attitude or equivalent geometric configuration optimization may be enabled to enhance the effective aperture and angular resolution.

[0061] 2. Processing Flow In this embodiment, the method of the present invention can be performed according to the following steps: S501: Multi-target / multipath uncertainty modeling and missing observation handling.

[0062] To address potential occlusion or missing observations in indoor environments, a mask model is introduced into the observation tensor, performing likelihood calculations only for valid observations. Simultaneously, a sparsity hierarchical prior is introduced into the path components, enabling the weak multipath components to adaptively shrink during iterations, achieving robust modeling without needing to pre-define the number of valid paths.

[0063] S502: Bayesian Tensor Decomposition Inference and Parameter Recovery.

[0064] Variational Bayesian inference is used to iteratively update the posterior of each factor and recover parameters such as angle, time delay / distance; noise accuracy parameters can be adaptively estimated during inference to adapt to changes in environmental noise.

[0065] S503: FAA Configuration and Beam Co-optimization.

[0066] Based on the estimated angle / distance information, a joint objective function for communication and sensing is constructed. The FAA rotation angle or equivalent configuration parameters are searched and updated using black-box optimization methods such as Bayesian optimization, so that the joint objective function reaches a better value at the optimal configuration and maintains stable convergence in subsequent frames.

[0067] 3. Effect Description In the aforementioned low-speed, high-precision scenarios, the method of this invention can fully utilize tensor structures and Bayesian priors to achieve weak multipath suppression, and combine FAA configuration optimization to enhance angular resolution, ensuring that angle / distance estimation maintains a stable convergence trend under different SNRs. Simultaneously, the joint objective function exhibits optimizable unimodal or approximately unimodal characteristics depending on the configuration parameters, which is beneficial for stable optimization. The above effects are consistent with those described earlier. Figure 10-11 The trends shown are consistent.

[0068] Beneficial effects: Compared with the prior art, the present invention has at least the following beneficial effects: 1) Precision and trend advantages: This invention achieves joint estimation of multi-dimensional parameters such as angle, distance (time delay) and velocity (Doppler) under the unified Bayesian tensor decomposition framework. The RMSE shows a monotonically decreasing trend with the increase of SNR and approaches the theoretical limit (such as CRB) in the high SNR region, reflecting the near-effective estimation characteristics.

[0069] 2) The comparative advantages are more convincing: Compared with subspace methods such as MUSIC, the present invention has lower error across the entire SNR range and more reasonable SNR dependence; compared with the unstructured tensor decomposition baseline, the present invention is superior to ALS and NLS overall, and even achieves lower RMSE under the premise that ALS and NLS have the same objective function and only the optimizer is different, which reflects the substantial gains brought by structured probabilistic modeling and prior regularization.

[0070] 3) Optimizable and loop-closed: The FAA rotation angle is searched and updated by BO. The joint objective function has a smooth single peak and reaches the global maximum value at the optimal rotation angle, which facilitates stable optimization and realizes the synergistic gain of communication and sensing.

[0071] 4) Model Adaptation and Robustness Enhancement: The effective rank / number of effective paths can be automatically determined through the ARD hierarchical sparse prior; ELBO monotonically increases and stabilizes, and the noise accuracy parameter can be adaptively estimated, thereby improving the robustness and usability under low SNR and noise variation conditions.

[0072] in conclusion This invention proposes a channel estimation method for flexible antenna array-assisted ISAC systems. Essentially, it is a Bayesian tensor decomposition joint parameter estimation method for FAA-assisted broadband massive MIMO-ISAC systems. It can uniformly model and jointly infer key parameters such as angle, time delay, Doppler, and reflection coefficient, and adaptively determine the effective rank through the ARD mechanism, reducing the manual dependence on model order selection and enhancing robustness in complex noise environments. Simulation results show that this invention achieves the best overall accuracy and stability within the evaluated SNR range, outperforming representative baselines such as ALS, NLS, MUSIC, and MF. Specifically, when minimizing the same unstructured CP least squares objective function with only different optimizers, this invention still achieves lower RMSE and exhibits stronger robustness; the RMSE curve monotonically decreases with SNR and approaches the theoretical limit in the high SNR region. By integrating array reconstruction, Bayesian inference, and resource optimization, this invention establishes a scalable and physically consistent framework, laying a solid foundation for the realization of high-performance ISACs in massive MIMO systems. This framework not only effectively solves the model order uncertainty and geometric coupling problem in FAA-assisted ISAC systems, but also achieves dynamic coordination of communication and sensing performance through adaptive FAA rotation, providing practical guidance for 6G system design and resource optimization.

Claims

1. A channel estimation method for a flexible antenna array-assisted ISAC system, wherein the flexible antenna array-assisted ISAC system mainly includes the following functional modules: Module 1: Base Station Flexible Antenna Array Module The base station is equipped with a rotatable or reconfigurable flexible antenna array module for simultaneously transmitting communication signals and sensing waveforms. This module achieves adaptive optimization of the beam direction and array geometry by adjusting the spatial position and rotation angle of the antenna array. Module 2: Flexible Antenna Array Module for Receiver The receiver is equipped with a flexible antenna array for sensing echo signals, which can receive echo signals from multiple propagation paths under different array orientations and output multi-dimensional time-frequency domain sampling data. Module 3: Signal Acquisition and Preprocessing Module It is used to perform down-conversion, sampling and pilot separation processing on the received signal, and to organize the data in the time domain, frequency domain and symbol dimension to provide basic input for subsequent tensor modeling; Module 4: Multidimensional Tensor Construction Module This is used to stack the preprocessed received signals according to the symbol dimension, subcarrier dimension and array observation dimension to construct a multidimensional tensor model containing angle, time delay, Doppler and array rotation information; Module 5: Channel Parameter Estimation Module Based on the constructed tensor model, a two-stage parameter estimation algorithm is executed, including ESPRIT initialization and Bayesian tensor decomposition, to extract multidimensional channel parameters. Module 6: Parameter Output and Application Module The estimated angle of arrival, angle of departure, time delay, Doppler shift, and reflection coefficient are output and used for communication beamforming, target sensing and localization, or system resource optimization. Its features are, The flexible antenna array-assisted ISAC system channel estimation method includes the following steps: Step S1: Construct a third-order tensor model: The multidimensional tensor construction module stacks the received signals into a third-order tensor. Its canonical multilinear decomposition is ， in , ， ； Step S2: Utilize the ESPRIT algorithm Delaying the Vandermonde structure and Doppler shift Initialization; Step S3: Automatic rank estimation and parameter refinement using the Bayesian CP decomposition framework: Introducing hierarchical Bayesian priors. and ;Optimize the variational posterior distribution through coordinate ascending variational inference (CAVI); Step S4: Extract physical parameters: AoA and of the receiver. pass Spatial correlation function estimation; AoA at the transmitter and With Doppler frequency shift Through joint optimization Estimate; Delay With reflection coefficient pass estimate; Output results.

2. The channel estimation method for a flexible antenna array-assisted ISAC system according to claim 1, characterized in that: In step S1 ; in The guide vector conforming to the Vandermonde structure.

3. The channel estimation method for a flexible antenna array-assisted ISAC system according to claim 1, characterized in that: In step S3, the hierarchical prior of the Bayesian CP decomposition achieves automatic rank estimation: when When it is larger, the first Each rank-1 component is pruned, effectively suppressing redundant components.

4. The channel estimation method for a flexible antenna array-assisted ISAC system according to claim 1, characterized in that: In step S4, the angle Estimate using the following formula: 。 5. The channel estimation method for a flexible antenna array-assisted ISAC system according to claim 1, characterized in that: In step S4, the angle of the receiving end With Doppler The following formula is used for joint estimation: ， 。 6. The channel estimation method for a flexible antenna array-assisted ISAC system according to claim 1, characterized in that: In step S4, the reflection coefficient Estimate using the following formula: 。 7. The channel estimation method for a flexible antenna array-assisted ISAC system according to claim 1, characterized in that: In step S3, the Bayesian CP decomposition framework is implemented using the Coordinate Ascending Variational Inference (CAVI) algorithm, and its lower bound of evidence (ELBO) is: ， in .

8. The channel estimation method for a flexible antenna array-assisted ISAC system according to claim 1, characterized in that: In step S2, the ESPRIT initialization algorithm is implemented through the following steps: (1) Construct the selection matrix form ; (2) To Perform singular value decomposition and estimate using translation invariance. Vandermondgen; (3) Obtain the time delay by normalizing the phase. and Doppler .

9. The channel estimation method for a flexible antenna array-assisted ISAC system according to claim 1, characterized in that: In step S3, Bayesian automatic rank estimation is achieved through the following steps: (1) Initialization Set hyperparameters ; (2) Optimization through CAVI iteration until ELBO converges; (3) For each r, if If the threshold is reached, retain the component; otherwise, prune redundant components.

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