Robust adaptive beam forming method based on distance unit sparse modeling

Abstract

The invention discloses a robust adaptive beam forming method based on distance unit sparse modeling, which comprises the following steps of: independently carrying out angle domain sparse modeling and processing on an array observation signal corresponding to each distance unit by taking a radar distance unit as a basic processing granularity; an angle domain sparse coefficient vector reflecting energy distribution in each angle direction is obtained through an angle domain over-complete guide dictionary, and an equivalent space covariance matrix is constructed by using the angle domain sparse coefficient vector and the angle domain over-complete guide dictionary instead of constructing the equivalent space covariance matrix based on a sample statistical meaning of an array receiving signal. An interference dominant subspace is extracted on the basis of an equivalent space covariance matrix, an optimal array beam forming weight vector is calculated in combination with target direction constraint, and weighted synthesis is carried out, so that under the conditions of strong interference, few snapshots and array mismatch, effective suppression of interference signals can still be realized, and accurate pointing of a beam main lobe in the target direction is kept.

Description

Technical Field

[0001] This invention belongs to the field of array signal processing and radar signal processing technology, and specifically relates to a robust adaptive beamforming method based on sparse modeling of range cells. Background Technology

[0002] With the gradual opening of low-altitude airspace and the increasing number of targets such as UAVs and low-altitude aircraft, array radar systems based on ground base stations or fixed platforms are widely used in low-altitude target surveillance, airspace management, and security protection. Array radar, through spatial sampling and beamforming technologies, can enhance target-direction signals and suppress interference from non-target directions in the spatial domain, making it an important technical means for detecting weak low-altitude targets. However, in practical applications, radar systems often operate in complex electromagnetic environments, with multiple strong interference signals whose power is much higher than the target echo, severely affecting target detection and positioning performance.

[0003] Array radar primarily uses beamforming to weighted summation of the received signals from each array element, creating different gains for signals in different directions. However, this method lacks adaptability, making it difficult to effectively suppress interference when the interference power is strong or the interference direction changes. To improve anti-interference capabilities, Capon proposed the Minimum Variance Distortionless Response (MVDR) beamforming method, which achieves adaptive suppression of interference by minimizing the array output power while maintaining undistorted response in the target direction. Subsequently, Reed et al. proposed an adaptive array method based on Sample Matrix Inversion (SMI), enabling MVDR and its extended forms to be implemented in engineering systems. Building on this, Frost further extended the idea of ​​the MVDR criterion, proposing the Linearly Constrained Minimum Variance (LCMV) beamforming method. By introducing a constraint matrix, it can achieve signal enhancement or interference suppression in multiple directions, thus significantly improving beamforming performance. However, the aforementioned SMI-based MVDR or LCMV methods all rely on accurate estimation of the covariance matrix. When the number of snapshots is insufficient, the number of samples is limited, or interference changes rapidly, the sample covariance matrix often becomes ill-conditioned or distorted, resulting in a significant decrease in beamforming performance.

[0004] In practical systems, amplitude and phase errors are common among array elements due to manufacturing errors, channel inconsistencies, and other factors. These array amplitude and phase errors lead to a mismatch between the actual interference direction and the theoretical steering vector, causing performance degradation or even failure of traditional adaptive beamforming methods. Furthermore, in low-altitude detection scenarios, interference signals may have the same or similar modulation patterns as radar transmitted signals, further exacerbating the difficulty of interference suppression. In recent years, with the development of sparse signal processing theory, researchers have begun to introduce compressed sensing and sparse representation methods into the field of array signal processing. In most practical scenarios, only a few dominant signal sources exist in the spatial domain, and the array received signal exhibits sparse characteristics in the angular domain. Based on the idea of ​​angular domain sparsity, Malioutov et al. proposed a method for direction-of-arrival estimation using sparse reconstruction. Subsequently, Sparse Bayesian Learning (SBL) was introduced into the field of array processing. It achieves adaptive learning of sparse structures by introducing hyperparameters, offering advantages in noise resistance and robustness.

[0005] However, although the aforementioned existing technologies can achieve certain results in their respective application scenarios, their overall anti-interference performance is still constrained by factors such as the number of snapshots, array errors, and model mismatch. Furthermore, there is a lack of effective integration between different technical solutions, and a comprehensive solution that can simultaneously achieve both interference suppression and target direction pointing accuracy under conditions of strong interference, few snapshots, and array errors has not yet been formed. Summary of the Invention

[0006] To address the aforementioned problems in the existing technology, this invention provides a robust adaptive beamforming method based on sparse modeling of range cells. The technical problem to be solved by this invention is achieved through the following technical solution: This invention provides a robust adaptive beamforming method based on sparse range cell modeling, the robust adaptive beamforming method comprising: Acquire the array received signal, and divide the array received signal into range cells to obtain the array observation vector for each range cell; Based on the search angle range, an overcomplete directional dictionary for the angle domain is formed; For each range cell, the steps include: performing sparse reconstruction of the array observation vector of the range cell in the angle domain using the overcomplete directional dictionary in the angle domain to obtain the reconstruction result of the sparse coefficient vector in the angle domain of the range cell; constructing an angle domain power matrix based on the reconstruction result, and mapping the angle domain power matrix to a first equivalent spatial covariance matrix using the overcomplete directional dictionary in the angle domain; constructing an interference subspace basis matrix based on the first equivalent spatial covariance matrix, and projecting the first equivalent spatial covariance matrix using the interference subspace basis matrix to obtain a second equivalent spatial covariance matrix of the range cell; constructing a linearly constrained minimum variance beamforming model with respect to the array beamforming weight vector and the second equivalent spatial covariance matrix, and solving the linearly constrained minimum variance beamforming model to obtain the optimal array beamforming weight vector of the range cell; and weighting and synthesizing the array observation vector of the range cell using the optimal array beamforming weight vector to obtain the beamforming result of the range cell.

[0007] The beneficial effects of this invention are: The robust adaptive beamforming method based on sparse modeling of range cells proposed in this invention uses radar range cells as the basic processing granularity. For the array observation signal corresponding to each range cell, sparse modeling and processing in the angle domain are performed independently to avoid statistical distortion caused by the mixing of signals from different range cells. An angle-domain sparse coefficient vector reflecting the energy distribution in each angle direction is obtained through an overcomplete angle-domain steering dictionary. An equivalent spatial covariance matrix is ​​constructed using the angle-domain sparse coefficient vector and the overcomplete angle-domain steering dictionary, rather than constructing an equivalent spatial covariance matrix based on the sample statistical meaning of the array received signal. The interference-dominant subspace is extracted based on the equivalent spatial covariance matrix, and the optimal array beamforming weight vector is calculated and weighted in combination with the target direction constraint. Thus, even under conditions of strong interference, few snapshots, and array mismatch, it can still effectively suppress interference signals and maintain the accurate pointing of the main lobe of the beam in the target direction, avoiding the target pointing offset problem that occurs in unconstrained sparse recovery methods.

[0008] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0009] Figure 1 This is a flowchart illustrating a robust adaptive beamforming method based on sparse modeling of distance cells provided in an embodiment of the present invention. Figure 2 This is a schematic diagram comparing the radiation patterns of three existing algorithms and the method proposed in this invention under strong interference. Detailed Implementation

[0010] The present invention will be further described in detail below with reference to specific embodiments, but the implementation of the present invention is not limited thereto.

[0011] When array radar systems operate in complex electromagnetic environments, traditional adaptive beamforming methods based on sample covariance matrices are highly dependent on the number of snapshots. Under conditions of strong interference, few snapshots, and array amplitude and phase errors, covariance estimation distortion easily occurs, leading to decreased interference suppression capability and unstable beam main lobe pointing. Although existing sparse reconstruction methods can characterize the angular domain signal structure under conditions of few snapshots, most of them use sparse reconstruction for direction estimation or angular domain spectrum analysis, without taking into account the natural segmentation characteristics of radar signals in the range dimension. They are also difficult to directly use for stable covariance matrix construction and beamforming design.

[0012] Based on this research, please see Figure 1 This invention provides a robust adaptive beamforming method based on sparse modeling of range cells, specifically including the following steps: S10. Acquire the array received signal and divide the array received signal into range cells to obtain the array observation vector for each range cell.

[0013] This invention employs a uniform linear array as the array radar receiving structure. The array consists of M array elements with an element spacing of [missing information]. ,in Let be the operating carrier wavelength. Suppose that at a certain moment the array receives a superimposed signal from the target direction, multiple interference directions, and background noise. The array's received signal can be expressed as: ; in, express The array receives signals at each moment. Indicates the angle of incidence of the target signal. Indicates the first An angle of incidence of the interference signal. Q Indicates the number of interference signals. Indicates the array at the angle of incidence The array guide vector on, Indicates the array at the angle of incidence The array guide vector on, Indicates the target signal at The complex envelope of time, Indicates the first An interference signal The complex envelope of time, express The additive complex Gaussian white noise vector at time t.

[0014] In this embodiment of the invention, the array receives signals. After performing range-dimensional matched filtering or range processing, the array received signal is processed using the range cell as the basic processing object. The array is divided into multiple distance cells, and the corresponding array observation vector is extracted for each distance cell. For example, the first distance cell is divided into multiple distance cells. The array observation vector corresponding to each distance cell is denoted as . This serves as the input data for subsequent angular domain sparse modeling and adaptive beamforming processing.

[0015] S20. Based on the search angle range, form an angle domain overcomplete guide dictionary.

[0016] The embodiments of the present invention cover the search angle range where the target and interference may occur. Within this space, the angle space is uniformly discretized to form an angle set: ; in, This represents the boundary between the minimum and maximum possible angles of incidence for the target and interference. Represents the first in the set of angles k Angle components K This indicates the number of angle components in the angle domain, i.e., the number of discretized angles in the angle set. The angle grid used for discretization can be set according to actual requirements.

[0017] Based on the array's geometry, construct the array steering vectors corresponding to each angle: ; in, This indicates a transpose operation. All array guide vectors are combined column-wise to form an overcomplete guide dictionary in the angle domain: ; This dictionary is used to describe the sparse representation of the array received signals in the angular domain.

[0018] For each distance cell, the steps include: S30. Using the angle-domain overcomplete guide dictionary, the array observation vector of the distance cell is sparsely reconstructed in the angle domain to obtain the reconstruction result of the angle-domain sparse coefficient vector of the distance cell.

[0019] Under conditions of few or single snapshots, in order to stably extract the sparse structure of the array signal in the angle domain, this embodiment of the invention utilizes an overcomplete angle domain steering dictionary to perform angle domain sparse reconstruction of the array observation vector of the distance cell, obtaining the reconstruction result of the angle domain sparse coefficient vector of the distance cell, including: Based on the sparse Bayesian learning method, the array observation vector of the distance cell is sparsely reconstructed in the angle domain using an overcomplete directional dictionary in the angle domain, resulting in the reconstruction of the sparse coefficient vector in the angle domain of the distance cell.

[0020] Furthermore, based on the sparse Bayesian learning method, the array observation vector of the distance cell is sparsely reconstructed in the angle domain using an overcomplete directional dictionary in the angle domain, resulting in the reconstruction of the sparse coefficient vector in the angle domain of the distance cell, including: Based on the overcomplete directional dictionary in the angle domain and the array observation vector of the distance cell, an angle domain sparse coefficient vector representation model for the distance cell is constructed. The angle domain sparse coefficient vector follows a complex Gaussian prior distribution with a mean of 0 and a covariance equal to a hyperparameter diagonal matrix. Each diagonal element in the hyperparameter diagonal matrix represents the power parameter corresponding to the angle component. Using Bayesian inference principles, the posterior distribution probability of the angle domain sparse coefficient vector is calculated based on the angle domain sparse coefficient vector representation model, yielding the posterior mean vector and posterior covariance matrix of the distance cell. Based on the posterior mean vector and posterior covariance matrix, the hyperparameter diagonal matrix and noise variance of the distance cell are updated respectively. Using the updated hyperparameter diagonal matrix and noise variance, the steps of calculating the posterior distribution probability of the angle domain sparse coefficient vector based on the angle domain sparse coefficient vector representation model using Bayesian inference principles are returned until the iteration stopping condition is met. The posterior mean vector at this point is taken as the reconstruction result of the angle domain sparse coefficient vector of the distance cell. More specifically: The embodiments of the present invention are based on an already constructed overcomplete dictionary of the angle domain. and array observation vector Construct an angle-domain sparse coefficient vector representation model: ; in, Indicates the first The sparse coefficient vector in the angle domain corresponding to each distance cell Indicates the first The additive noise vector corresponding to each distance cell.

[0021] sparse coefficient vector in the angle domain Apply a sparse Bayesian prior, assuming it follows a zero-mean complex Gaussian distribution: ; in, Represents the sparse coefficient vector in the angle domain The prior probability density function, Indicates the first The hyperparameter diagonal matrix of distance cells, , Indicates the first The distance unit of the first k The power parameters of each angular component can be seen from its diagonal elements. Used to depict the first The distance unit of the first kThe power magnitude of each angular component. Meanwhile, it is assumed that the noise follows a zero mean and a variance of . The complex Gaussian distribution, Indicates the first The noise variance of each distance cell.

[0022] Given a hyperparameter diagonal matrix and noise variance Under these conditions, based on the Bayesian inference principle, the posterior distribution of the sparse coefficients in the angular domain is calculated, and its form remains a complex Gaussian distribution: ; in, Denotes the posterior probability density function. Indicates the first The posterior mean vector of distance units, Indicates the first The posterior covariance matrix of distance cells, This represents the complex Gaussian distribution operator.

[0023] Posterior mean vector The formula is expressed as: ; in, Values ​​range from 1 to , Indicates the number of distance units. , Indicates the first The distance unit of the first k The posterior mean vector of each angular component K Indicates the number of angle components in the angle domain. Indicates the first The noise variance of each distance cell, This indicates an overcomplete guided dictionary for the angle domain. , Indicates the first k Angle components Indicates the angular component Array guide vector in the direction, Indicates the number of array elements. express The conjugate operation, Indicates the first Array observation vectors of distance cells; Posterior covariance matrix The formula is expressed as: ; in, Indicates the first The posterior covariance matrix of distance cells, , Indicates the first The first hyperparameter in the diagonal matrix of the nth distance unit k Power parameters of each angular component. Indicates the first The hyperparameter diagonal matrix of distance cells, , Indicates the first The distance unit of the first k Power parameters of each angular component. This represents the operation of constructing a diagonal matrix. This indicates the inverse operation.

[0024] Based on the posterior distribution result, i.e., the posterior mean vector and posterior covariance matrix For the hyperparameter matrix Update each diagonal element in the table using the following formula: ; in, Indicates the updated number The distance unit of the first k Power parameters of each angular component. A sparse coefficient vector in the angle domain The k One portion, Indicates the first The distance unit of the first k The posterior mean vector of each angular component Indicates the first The first hyperparameter in the diagonal matrix of the nth distance unit k Power parameters of each angular component. This represents the operation of squaring after taking the modulus value. This indicates the expectation operation. This update process ensures that the angle corresponding to the no-signal angle... Gradually converge to a smaller value, while the target or interference direction corresponds to... It was retained.

[0025] Continue to adjust the noise variance based on the posterior distribution results. To further improve the model's adaptability, an update is performed, and the update format is as follows: ; in, Indicates the updated number The noise variance of each distance cell, Indicates the first The posterior mean vector of distance units, , Indicates the first The distance unit of the first k The posterior mean vector of each angular component This indicates an overcomplete guided dictionary for the angle domain. , Indicates the first k Angle components Indicates the angular component Array guide vector in the direction, Indicates the first The distance unit of the first k Power parameters of each angular component. express The inverse operation, Indicates the first The noise variance of each distance cell, Values ​​range from 1 to , Indicates the number of distance units. K Indicates the number of angle components in the angle domain. Indicates the number of array elements. This represents the square operation after finding the second normal form.

[0026] Returning to the steps of calculating the posterior distribution probability of the sparse coefficient vector in the angle domain based on the Bayesian inference principle and the sparse coefficient vector representation model in the angle domain, and using the updated... , Perform iterations until the posterior covariance matrix is ​​obtained. or posterior mean vector Convergence occurs when the number of iterations reaches a preset upper limit. After the iterations are complete, the posterior mean vector is... The reconstruction result as angular domain sparse coefficients: .

[0027] The reconstruction results of the sparse coefficients in the angular domain are used for subsequent construction of the equivalent space covariance matrix and extraction of the interference subspace.

[0028] S40. Construct the angle domain power matrix based on the reconstruction results, and use the angle domain overcomplete guiding dictionary to map the angle domain power matrix into the first equivalent spatial covariance matrix.

[0029] This invention utilizes the angle-domain power structure obtained through sparse Bayesian learning to construct the equivalent spatial covariance matrix of the array signal without relying on the statistical analysis of the array received signal samples. More specifically: The embodiments of the present invention construct based on the reconstruction results Power matrix of the angular domain: ; in, Indicates the first The angular domain power matrix of each distance cell. express The conjugate operation.

[0030] By utilizing the mapping relationship from the angular domain to the spatial domain, the first equivalent spatial covariance matrix of the array signal is reconstructed: ; in, Indicates the first The first equivalent spatial covariance matrix of distance cells. This equivalent spatial covariance matrix avoids estimation methods based directly on sample statistics and still has good numerical stability under conditions of few snapshots.

[0031] S50. Construct the interference subspace basis matrix based on the first equivalent spatial covariance matrix, and use the interference subspace basis matrix to project the first equivalent spatial covariance matrix to obtain the second equivalent spatial covariance matrix of the distance cell.

[0032] This invention embodiment constructs an interference subspace basis matrix based on a first equivalent spatial covariance matrix, including: performing eigenvalue decomposition on the first equivalent spatial covariance matrix; sorting all decomposed eigenvalues ​​from largest to smallest, selecting the top few eigenvalues ​​from the sorting result, and constructing the interference subspace basis matrix using the eigenvectors corresponding to all selected eigenvalues. The second equivalent spatial covariance matrix of the distance cell is obtained by projecting the first equivalent spatial covariance matrix using the interference subspace basis matrix, including: constructing a projection matrix using the interference subspace basis matrix; and projecting the first equivalent spatial covariance matrix using the projection matrix to obtain the second equivalent spatial covariance matrix of the distance cell. More specifically: In this embodiment of the invention, the first equivalent spatial covariance matrix is ​​eigenvalued to extract the interference-dominant subspace, and a projection matrix is ​​constructed based on the subspace to suppress noise and spurious components.

[0033] For the first equivalent space covariance matrix Perform eigenvalue decomposition: ; in, Represents the eigenvector matrix, , Indicates the first 1 eigenvector express The conjugate operation, Represents an eigenvalue diagonal matrix. , Indicates the first There are 10 eigenvalues, and the diagonal eigenvalues ​​are arranged in descending order.

[0034] Select the first corresponding larger eigenvalue The eigenvectors form the basis matrix of the interference subspace: ; in, Represents the basis matrix of the interference subspace. Indicates the selected first The eigenvectors corresponding to each eigenvalue.

[0035] Constructing the projection matrix based on the basis matrix of the interference subspace: ; in, Represents the projection matrix. express The conjugate operation.

[0036] Projecting the first equivalent spatial covariance matrix using the projection matrix: ; in, Indicates the first The second equivalent spatial covariance matrix of distance cells This represents the identity matrix. This step effectively suppresses noise and weak components while preserving the spatial structure information of the main interferences, thus improving the accuracy of interference subspace extraction.

[0037] S60. Construct a linearly constrained minimum variance beamforming model with respect to the array beamforming weight vector and the second equivalent spatial covariance matrix. Solve the linearly constrained minimum variance beamforming model to obtain the optimal array beamforming weight vector for the distance cell.

[0038] Let the angle of incidence of the target be... Its corresponding matrix steering vector is Based on subspace modeling, a linearly constrained minimum variance beamforming model is introduced to impose a preservation constraint on the target direction. This results in a linearly constrained minimum variance beamforming model with respect to the array beamforming weight vector and the second equivalent spatial covariance matrix, expressed as follows: ; in, Indicates the first The second equivalent spatial covariance matrix of distance cells Indicates the first The array beams of each range cell form a weight vector. express The conjugate operation, Indicates the angle of incidence of the target signal. Indicates the angle of incidence The array guidance vector in the direction. Constraints ensure that the target passes through without distortion.

[0039] Solve the linearly constrained minimum variance beamforming model using any algorithm to obtain the optimal array beamforming weight vector for the range cell, expressed by the formula: ; in, Indicates the first The optimal array beamforming weight vector for each range cell Indicates the first The second equivalent spatial covariance matrix of distance cells express The inverse operation, Indicates the angle of incidence of the target signal. Indicates the angle of incidence Array guide vector in the direction, express The conjugate operation. Due to the introduction of target direction constraints, even if there are errors in the subspace estimation, the target direction response can be guaranteed not to be destroyed, thereby avoiding the possible beam main lobe shift problem.

[0040] S70. The array observation vector of the range cell is weighted and synthesized using the optimal array beamforming weight vector to obtain the beamforming result of the range cell.

[0041] This invention utilizes the calculated optimal array beamforming weight vector. For the first Array observation vector corresponding to each distance cell Perform weighted synthesis.

[0042] After processing all range units, the final output signal is obtained with accurate target direction and effective suppression of interference.

[0043] To verify the effectiveness of the robust adaptive beamforming method based on sparse modeling of distance cells provided in this embodiment of the invention, the following experiments were conducted.

[0044] The specific simulation parameters are shown in Table 1. The array used is a uniform linear array.

[0045] Table 1. Specific Simulation Parameters for the Experiment

[0046] Figure 2This paper presents the beam patterns of three existing algorithms (ordinary beamforming under single-sample conditions, LCMV algorithm combined with beamforming under single-sample conditions, and LCMV-SBL algorithm combined with beamforming under single-sample conditions) and the proposed method under strong interference under single-sample conditions. Experimental results show that, under conditions of strong interference, non-negligible array amplitude and phase errors, and a limited number of available snapshots, the method in this embodiment can ensure that the main lobe of the formed beam stably points towards the target direction, while also forming a significant null in the direction of strong interference. Compared with traditional LCMV beamforming algorithms based on sample covariance matrices and unconstrained sparse reconstruction beamforming methods, it has significant advantages in target pointing and interference suppression.

[0047] In summary, the robust adaptive beamforming method based on sparse modeling of range cells proposed in this invention uses radar range cells as the basic processing granularity. For the array observation signal corresponding to each range cell, sparse modeling and processing in the angle domain are performed independently to avoid statistical distortion caused by the mixing of different range signals. An angle-domain sparse coefficient vector reflecting the energy distribution in each angle direction is obtained through an overcomplete angle-domain steering dictionary. An equivalent spatial covariance matrix is ​​constructed using the angle-domain sparse coefficient vector and the overcomplete angle-domain steering dictionary, rather than constructing an equivalent spatial covariance matrix based on the sample statistical meaning of the array received signal. The interference-dominant subspace is extracted based on the equivalent spatial covariance matrix, and the optimal array beamforming weight vector is calculated and weighted in combination with the target direction constraint. Thus, even under conditions of strong interference, few snapshots, and array mismatch, it can still effectively suppress interference signals and maintain the accurate pointing of the main lobe of the beam in the target direction, avoiding the target pointing offset problem that occurs in unconstrained sparse recovery methods.

[0048] In the description of this invention, it should be understood that the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Therefore, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of this invention, "a plurality of" means two or more, unless otherwise explicitly specified.

[0049] Although the invention has been described herein in conjunction with various embodiments, those skilled in the art, by reviewing the specification and accompanying drawings, will understand and implement other variations of the disclosed embodiments in carrying out the claimed invention. In the specification, the word "comprising" does not exclude other components or steps, and "a" or "an" does not exclude a plurality. While certain measures are described in different embodiments, this does not mean that these measures cannot be combined to produce good results.

[0050] The above description, in conjunction with specific preferred embodiments, provides a further detailed explanation of the present invention. It should not be construed that the specific implementation of the present invention is limited to these descriptions. For those skilled in the art, various simple deductions or substitutions can be made without departing from the concept of the present invention, and all such modifications and substitutions should be considered within the scope of protection of the present invention.

Claims

1. A robust adaptive beamforming method based on sparse modeling of range cells, characterized in that, The robust adaptive beamforming method includes: Acquire the array received signal, and divide the array received signal into range cells to obtain the array observation vector for each range cell; Based on the search angle range, an overcomplete directional dictionary for the angle domain is formed; For each range cell, the steps include: performing sparse reconstruction of the array observation vector of the range cell in the angle domain using the overcomplete directional dictionary in the angle domain to obtain the reconstruction result of the sparse coefficient vector in the angle domain of the range cell; constructing an angle domain power matrix based on the reconstruction result, and mapping the angle domain power matrix to a first equivalent spatial covariance matrix using the overcomplete directional dictionary in the angle domain; constructing an interference subspace basis matrix based on the first equivalent spatial covariance matrix, and projecting the first equivalent spatial covariance matrix using the interference subspace basis matrix to obtain a second equivalent spatial covariance matrix of the range cell; constructing a linearly constrained minimum variance beamforming model with respect to the array beamforming weight vector and the second equivalent spatial covariance matrix, and solving the linearly constrained minimum variance beamforming model to obtain the optimal array beamforming weight vector of the range cell; and weighting and synthesizing the array observation vector of the range cell using the optimal array beamforming weight vector to obtain the beamforming result of the range cell.

2. The robust adaptive beamforming method based on sparse modeling of distance cells according to claim 1, characterized in that, The angle-domain sparse reconstruction of the array observation vector of the distance cell is performed using the overcomplete directional dictionary in the angle domain, resulting in the reconstruction of the angle-domain sparse coefficient vector of the distance cell, including: Based on the sparse Bayesian learning method, the array observation vector of the distance cell is sparsely reconstructed in the angle domain using the angle-domain overcomplete guided dictionary, and the reconstruction result of the angle-domain sparse coefficient vector of the distance cell is obtained.

3. The robust adaptive beamforming method based on sparse modeling of distance cells according to claim 2, characterized in that, Based on the sparse Bayesian learning method, the array observation vector of the distance cell is sparsely reconstructed in the angle domain using the overcomplete directional dictionary in the angle domain, resulting in the reconstruction of the angle domain sparse coefficient vector of the distance cell, including: Based on the overcomplete directional dictionary in the angle domain and the array observation vector of the distance cell, an angle domain sparse coefficient vector representation model of the distance cell is constructed; wherein, the angle domain sparse coefficient vector follows a complex Gaussian prior distribution with a mean of 0 and a covariance of a hyperparameter diagonal matrix, and each diagonal element in the hyperparameter diagonal matrix represents the power parameter corresponding to the angle component; Using the Bayesian inference principle, the posterior distribution probability of the sparse coefficient vector in the angle domain is calculated based on the sparse coefficient vector representation model in the angle domain, thereby obtaining the posterior mean vector and posterior covariance matrix of the distance cell. Based on the posterior mean vector and the posterior covariance matrix, the hyperparameter diagonal matrix and noise variance of the distance cell are updated respectively. Using the updated hyperparameter diagonal matrix and noise variance, the process returns to the step of calculating the posterior distribution probability of the angular domain sparse coefficient vector based on the angular domain sparse coefficient vector representation model using the Bayesian inference principle, until the iteration stopping condition is met. The posterior mean vector at this point is then used as the reconstruction result of the angular domain sparse coefficient vector of the distance cell.

4. The robust adaptive beamforming method based on sparse modeling of range cells according to claim 3, characterized in that, The posterior mean vector of this distance cell is expressed by the formula: ； in, Indicates the first The posterior mean vector of distance units, Values ​​range from 1 to , Indicates the number of distance units. , Indicates the first The distance unit of the first k The posterior mean vector of each angular component K The number of angle components in the angle domain. Indicates the first The noise variance of each distance cell, This indicates an overcomplete guided dictionary for the angle domain. , Indicates the first k Angle components Indicates the angular component Array guide vector in the direction, Indicates the number of array elements. express The conjugate operation, Indicates the first Array observation vectors of distance cells; The posterior covariance matrix of this distance cell is expressed by the formula: ； in, Indicates the first The posterior covariance matrix of distance cells, , Indicates the first The first hyperparameter in the diagonal matrix of the nth distance unit k Power parameters of each angular component. Indicates the first The hyperparameter diagonal matrix of distance cells, , Indicates the first The distance unit of the first k Power parameters of each angular component. This represents the operation of constructing a diagonal matrix. This indicates the inverse operation.

5. The robust adaptive beamforming method based on sparse modeling of range cells according to claim 3, characterized in that, The hyperparameter diagonal matrix of this distance cell is updated using the following formula: ； in, Indicates the updated number The distance unit of the first k Power parameters of each angular component. Indicates the first The distance unit of the first k The posterior mean vector of each angular component Indicates the first The first hyperparameter in the diagonal matrix of the nth distance unit k Power parameters of each angular component. This indicates the operation of squaring the modulo value; The noise variance of this distance cell is updated using the following formula: ； in, Indicates the updated number The noise variance of each distance cell, Indicates the first The posterior mean vector of distance units, , Indicates the first The distance unit of the first k The posterior mean vector of each angular component This indicates an overcomplete guided dictionary for the angle domain. , Indicates the first k Angle components Indicates the angular component Array guide vector in the direction, Indicates the first The distance unit of the first k Power parameters of each angular component. express The inverse operation, Indicates the first The noise variance of each distance cell, Values ​​range from 1 to , Indicates the number of distance units. K Indicates the number of angle components in the angle domain. This indicates the number of array elements in the array.

6. The robust adaptive beamforming method based on sparse modeling of range cells according to claim 1, characterized in that, Based on the first equivalent space covariance matrix, construct the interference subspace basis matrix, including: Eigenvalue decomposition is performed on the first equivalent space covariance matrix; Sort all the eigenvalues ​​of the decomposition from largest to smallest, select the top few eigenvalues ​​from the sorting results, and construct the basis matrix of the interference subspace from the eigenvectors corresponding to all the selected eigenvalues.

7. The robust adaptive beamforming method based on sparse modeling of distance cells according to claim 1, characterized in that, The second equivalent spatial covariance matrix of the distance cell is obtained by projecting the first equivalent spatial covariance matrix onto the basis matrix of the interference subspace, including: Using the basis matrix of the interference subspace, construct the projection matrix; The second equivalent spatial covariance matrix of the distance cell is obtained by projecting the first equivalent spatial covariance matrix using the projection matrix.

8. The robust adaptive beamforming method based on sparse modeling of range cells according to claim 1, characterized in that, The constructed linearly constrained minimum variance beamforming model regarding the array beamforming weight vector and the second equivalent spatial covariance matrix is ​​expressed as follows: ； in, Indicates the first The second equivalent spatial covariance matrix of distance cells Indicates the first The array beams of each range cell form a weight vector. express The conjugate operation, Indicates the angle of incidence of the target signal. Indicates the angle of incidence Array guide vector in the direction.

9. The robust adaptive beamforming method based on sparse modeling of distance cells according to claim 1, characterized in that, The optimal array beamforming weight vector for this range cell is expressed by the formula: ； in, Indicates the first The optimal array beamforming weight vector for each range cell Indicates the first The second equivalent spatial covariance matrix of distance cells express The inverse operation, Indicates the angle of incidence of the target signal. Indicates the angle of incidence Array guide vector in the direction, express The conjugate operation.

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