Robust adaptive beamforming method based on cascaded sparse multi-polarized linear array

Abstract

The application discloses a kind of robust adaptive beamforming methods based on cascaded sparse multi-polarization linear array, mainly solve the problem of high complexity and limited degree of freedom of existing method calculation, its implementation steps are: constructing cascaded sparse multi-polarization linear array;The receiving signal modeling and multidimensional parameter decoupling are carried out to the array;The block representation is carried out to the received signal covariance matrix;Reconstruct virtual equivalent cascaded uniform multi-polarization linear array received signal covariance matrix;Based on the covariance matrix of reconstruction, one-dimensional wave direction and polarization parameter are solved;The sparse characteristics of expected signal and interference signal in space domain and polarization domain are used, and the robust adaptive beamformer weight vector is designed.The application is based on the multi-domain sparsity of signal space domain and polarization domain, provides feasible idea and effective solution for improving the calculation efficiency and degree of freedom of beamforming method, and can be used for wireless communication and radar anti-jamming.

Description

Technical Field

[0001] This invention belongs to the field of signal processing technology, and particularly relates to a beamforming method for sparse multi-polarization arrays. Specifically, it is a robust adaptive beamforming method based on cascaded sparse multi-polarization linear arrays, which can be used for wireless communication and radar anti-jamming. Background Technology

[0002] Beamforming technology enables signal enhancement and interference suppression, and has wide applications in radar, communications, sonar, and medical imaging. Classical methods include worst-case beamformers, minimum variance distortionless response (MVDR) beamformers, and interference covariance matrix reconstruction beamformers, typically employing uniform arrays. Compared to uniform arrays, sparse arrays can achieve larger array apertures with fewer physical elements, thereby improving beamforming performance. In recent years, sparse arrays with closed-form expressions for element positions, such as coprime arrays, nested arrays, and super-nested arrays, have attracted considerable attention. However, existing sparse array beamforming methods do not consider the polarization diversity of signals, and the prevalent polarization mismatch in practical applications leads to a decrease in beamformer output performance.

[0003] To avoid polarization mismatch and effectively utilize the parameter differences between the desired signal and interference in the spatial and polarization domains, a sparse multi-polarization array with signal polarization information processing capabilities can be designed. Based on the designed array, a joint-domain robust adaptive beamforming method in the spatial and polarization domains is proposed. However, existing joint-domain robust adaptive beamforming methods inevitably involve one-dimensional or multi-dimensional integration operations, resulting in high computational complexity; and they are all limited to uniform multi-polarization arrays, with degrees of freedom constrained by the number of physical array elements. Therefore, it is urgent to reduce the computational complexity of beamformers and optimize the array structure to achieve robust adaptive beamforming suitable for sparse multi-polarization arrays. Summary of the Invention

[0004] The purpose of this invention is to address the problems of high computational complexity and limited degrees of freedom in existing beamforming methods by proposing a robust adaptive beamforming method based on a cascaded sparse multi-polarization linear array. Based on the multi-domain sparsity of the signal spatial and polarization domains, this invention proposes a method for reconstructing the covariance matrix of interference and noise in the spatial and polarization domains, providing a feasible approach and effective solution for improving the computational efficiency and degrees of freedom of beamforming methods.

[0005] The objective of this invention is achieved through the following technical solution: a robust adaptive beamforming method based on a cascaded sparse multipolarized linear array, comprising the following steps:

[0006] (1) Constructing a cascaded sparse multipolar linear array: Constructing an array consisting of N p A cascaded sparse multipolar linear array is obtained by cascading sparse linear subarrays. The distance between adjacent subarrays is d. Each subarray consists of L0 magnetic rings or dipoles of the same polarization type. The normal direction of the magnetic rings is parallel to a certain coordinate axis, and the axial direction of the dipoles is parallel to a certain coordinate axis. Assume there are N subarrays in total. p′ For magnetic rings or dipoles with different polarization types, then 2 ≤ N p′ ≤N p This cascaded sparse multipolar linear array is composed of L = L0N p The above N array elements are composed of; p Each element of the subarray is arranged in the same sparse array manner; the number of virtual elements corresponding to each subarray is L. v The distance between adjacent virtual array elements is d;

[0007] (2) Assume the desired signal s0(t) and M interference signals. The incident signals to the designed cascaded sparse multipolarized linear array are all far-field narrowband signals and are uncorrelated; θ and φ represent the azimuth and elevation angles, respectively. When the elevation angle φ = 90°, the incident signal is located in the xy plane; the received signal x(t) of the designed cascaded sparse multipolarized linear array at time t is modeled as follows:

[0008]

[0009] Where s m (t) represents the waveform corresponding to the desired signal or the interference signal, and n(t) is a Gaussian white noise component with zero mean that is independent of each signal source. m = 0, 1, ..., M is the joint domain guidance vector of the spatial and polarization domains of the designed cascaded sparse multipolar linear array, expressed as:

[0010]

[0011] Where θ0 represents the azimuth angle of the desired signal, θ m m = 1, 2, ..., M, representing the azimuth angle of the m-th interference signal; γ0 and η0 represent the polarization auxiliary angle and polarization phase difference of the desired signal, respectively. m η m m = 1, 2, ..., M, representing the polarization auxiliary angle and polarization phase difference of the m-th interference signal, a h (θ m ), a v (θ m θ represents the horizontal polarization guidance vector and the vertical polarization guidance vector, respectively, corresponding to the direction of incoming wave. m The signal Let represent the polarization vector corresponding to the m-th signal, including the parameter cosγ corresponding to the horizontal and vertical polarization components. m and in [·] T This indicates the transpose operation, blkdiag[b s×t c p×q The brackets [] represent a diagonal block matrix constructed from the matrix within the brackets, i.e.:

[0012]

[0013] Where b s×t c p×q Let O represent s×t dimensional matrices and p×q dimensional matrices respectively. a×b Represents an a×b dimensional zero matrix;

[0014] To combine the spatial and polarimetric domains into a single domain guiding vector The pure spatial guidance vector and other factors related to the angle parameter sinθ m cosθ m and polarization vector Decoupled, the cascaded sparse multipolar linear array received signal can be further represented as:

[0015]

[0016] Where a s，m The purely spatial guidance vector for the designed cascaded sparse multipolar linear array, which is only related to spatial parameters:

[0017]

[0018] Where λ represents the signal wavelength, d l l = 1, 2, ..., L represents the distance between the l-th element and the origin, diag(a s，m ) indicates based on vector a s，m The elements in the matrix are used to generate a diagonal matrix, J, which is an L×6 dimensional selection matrix. Each row has exactly one element that is 1, and the rest are 0. J represents the selection of L antenna elements from three dipoles whose axes are parallel to the x, y, or z axes and three magnetic loop antennas whose normal directions are parallel to the x, y, or z axes. A 6×2 dimensional matrix representing the polarization type of each array element:

[0019]

[0020] After the above operations, the pure spatial guiding vector a s，m The angle parameters and polarization parameters related to the antenna polarization characteristics are decoupled, which facilitates the separate solution and estimation of the supporting multidimensional parameters of the proposed beamforming method.

[0021] (3) Based on the fact that the cascaded sparse multipolar linear array contains N p The array structure of the subarrays will guide the pure spatial vector a s，m The diagonal matrix form is represented as N p The diagonal matrix of each block:

[0022]

[0023] in The covariance matrix R of the received signal from the cascaded sparse multipolar linear array xx Represented as:

[0024]

[0025] in Indicates the power of the desired signal. m = 1, 2, ..., M, representing the power of the interference signal, σ 2 Indicates noise power, (·) H I represents the conjugate transpose operation. n Let ρ represent an n×n dimensional identity matrix. 11，m =δ 11，m , These represent variable factors related to the polarization type of the antenna elements in each subarray and the time delay difference between each subarray and the first subarray, respectively. [δ m ] m Represents vector δ m The nth element, (·) * Represents the conjugate operation; in practice, R xx It is approximately calculated based on K sample snapshots, that is:

[0026]

[0027] Where t k This represents the time corresponding to the k-th sampling snapshot;

[0028] According to R xx The data structure, R, facilitates joint smoothing operations in the spatial and polar domains. xx Indicated as common A block matrix related to spatial and polarization parameters:

[0029]

[0030] Each block matrix All have dimensions L0×L0, and p, q = 1, 2, ..., N p ; p = 1, 2, ..., N p This represents the autocorrelation of the received signal in the p-th subarray; p, q = 1, 2, ..., N p And p≠q indicates the cross-correlation between the received signals of the p-th subarray and the q-th subarray;

[0031] (4) To obtain the virtual signal corresponding to the virtual equivalent cascaded uniform multipolar linear array, firstly... p, q = 1, 2, ..., N p Vectorization operation is performed to obtain vector r. (pq) :

[0032]

[0033] in, Represents a matrix Vectorization operations, that is, transforming a matrix The columns in the vector are stacked sequentially to form a new vector. Represents the pure spatial domain guiding matrix. Denotes the Khatri-Rao product, σ (pq) =[ρ pq，0 , ρ pq，1 , ..., ρ pq，M ] T , This represents the vectorization of an L0×L0 dimensional identity matrix; since the positions of each subarray element correspond to a fully expandable sparse array, the vector r (pq) The corresponding virtual array can be represented as containing 2L V -1 uniform array of virtual continuous array elements Vector r (pq) The elements in the array are in a uniform array with virtual continuous array elements. The arrangement is reordered to correspond to The equivalent virtual signal λ (pq) :

[0034]

[0035] in For each subarray, a virtual uniform array The pure spatial guiding vector with polarization components removed. Indicates only at the Lth V A column vector in which one element is 1 and the rest are 0;

[0036] (5) To reconstruct the covariance matrix of the received signals of each subarray of the virtual equivalent cascaded uniform multipolar linear array, firstly, the virtual vector λ (pq) Decomposed into L in sequence V L V ×1 dimensional virtual subvector:

[0037]

[0038] in l″ = 1, 2, ..., L v ,but λ (pq) Middle 1 to L V A vector composed of elements λ (pq) Middle 2 to L V A vector consisting of +1 elements λ (pq) From L V To the 2nd L V A vector consisting of -1 elements; for L V indivual By performing column vector merging, we can obtain the autocorrelation / cross-correlation matrices corresponding to the received signals of each subarray of the virtual equivalent cascaded uniform multipolar linear array:

[0039]

[0040] in This represents the pure spatial guidance vector of the first subarray in the virtual equivalent cascaded uniform multipolar linear array; further, the covariance matrix of the received signal of the virtual equivalent cascaded uniform multipolar linear array can be obtained.

[0041]

[0042] in

[0043] (6) Solve for one-dimensional direction of arrival and polarization parameters based on the reconstructed covariance matrix;

[0044] (7) The interference plus noise covariance matrix is ​​expressed as follows: It can be seen that R i+n The reconstruction is mainly by The part related to noise power σ 2 I L Composition; Noise power estimation Depend on L V N p -M-1 smaller eigenvalues ​​are averaged to obtain the result. For R xx K-times of sampling The derived virtual reconstruction covariance matrix corresponds to the virtual equivalent cascaded uniform multipolar linear array. By solving the (M+1)×1 dimensional power distribution vector The corresponding matrix P = diag(p) ​​is obtained as follows:

[0045]

[0046] Among them ||·|| F Describing the Frobenius norm, In the above formula and For the estimated desired signal parameters, and m = 1, 2, ..., M are the estimated M interference signal parameters; based on the sparsity characteristics of the desired signal and the interference signal in the spatial and polarization domains, the closed-form solution of p is obtained as follows:

[0047] p = (B H B) -1 B H r,

[0048] in The reconstructed spatial and polarization domain joint domain interference plus noise covariance matrix It is expressed as follows:

[0049]

[0050] Therefore, by utilizing the joint domain sparsity of the desired signal and the interference signal in the spatial and polarization domains, the interference-noise covariance matrix is ​​reconstructed; and Substituting into the following equation, the robust adaptive beamformer weight vector in the joint spatial and polarization domains can be obtained:

[0051]

[0052] Then, by weighting the cascaded sparse multipolarized linear array with the designed beamformer weight vector, the array output can be obtained as y(t) = w H x(t).

[0053] Furthermore, in step (1), the cascaded sparse multipolar linear array is constructed, specifically by constructing an array composed of N... p An array consisting of N identical sparsely arranged arrays cascaded together. pThe sparse arrangement of the elements in each subarray is selected as a virtual domain difference array (Difference Co-array) with minimal redundancy (no holes), nested array, or super-nested array. Each subarray has the same antenna polarization characteristics and at least two different types of polarization antennas. The number of virtual elements corresponding to each subarray is L. v , nth p The positions of each element in the individual formation Represented as:

[0054]

[0055] Where n p =1,2,…,N p c is an L0×1 dimensional vector, representing the y-axis coordinates of the first to L0 elements in the first subarray.

[0056] Further, in step (2), the L×6 dimensional selection matrix J is constructed as follows: J(l, n) represents the element in the l-th row and n-th column of matrix J, where different columns of elements being 1 represent dipoles and magnetic rings with different polarization characteristics. Specifically, J(l, 1) = 1, l = 1, 2, ..., L indicates that the l-th element is a dipole with its axial direction parallel to the x-axis; J(l, 2) = 1, l = 1, 2, ..., L indicates that the l-th element is a dipole with its axial direction parallel to the y-axis. J(l,3)=1,l=1,2,…,L indicates that the l-th element is a dipole with its axial direction parallel to the z-axis; J(l,4)=1,l=1,2,…,L indicates that the l-th element is a magnetic ring with its normal direction parallel to the x-axis; J(l,5)=1,l=1,2,…,L indicates that the l-th element is a magnetic ring with its normal direction parallel to the y-axis; J(l,6)=1,l=1,2,…,L indicates that the l-th element is a magnetic ring with its normal direction parallel to the z-axis.

[0057] Further, in step (4), the vector r is... (pq) The elements in the array are in a uniform array with virtual continuous array elements. The arrangement is reordered to correspond to The equivalent virtual signal λ (pq) Specifically, this is achieved through a selection matrix: First, for p, q = 1, 2, ..., N p Vectorization operation is performed to obtain vector r. (pq) Then, define Dimensional selection matrix Δ:

[0058]

[0059] in Represents the l′ row of matrix Δ. Column elements, l′=1,…,2Lv -1, L0-1≥i1≥0, L0≥i2≥1, ω(l′-L V (i1, i2) represents l′-L V A function of i1 and i2, representing the combination of values ​​of i1 and i2 that satisfies The number of index combinations is used to determine the virtual signal vector λ corresponding to the autocorrelation / cross-correlation of the received signals in each subarray. (pq) Represented as:

[0060] λ (pq) =Δr (pq) .

[0061] Furthermore, the one-dimensional direction of arrival and polarization parameter estimation in step (6) is performed using the following methods: polarization multiple signal classification method, polarization subspace rotation invariant method, or polarization multiple signal classification root-finding method.

[0062] Furthermore, in step (6), a one-dimensional direction of arrival estimation is performed using the polarization multiple signal classification root-finding method, and then the polarization parameters are solved. Specifically, the polarization parameters are first determined by... Perform eigenvalue decomposition and sort the corresponding eigenvalues ​​from largest to smallest, then take the last L... V N p The subspace spanned by the eigenvectors corresponding to the -M-1 smaller eigenvalues ​​is denoted as the noise subspace U; according to From the expression for the virtual array guidance vector and the orthogonality between the virtual array guidance vector and the noise subspace U, we can see that:

[0063]

[0064] Furthermore, according to the principle of rank deficiency, it can be deduced that Where det(·) represents the determinant operation; when the constructed cascaded sparse multipolar linear array does not contain the six types of dipoles and magnetic rings with their axial or normal directions parallel to the three coordinate axes respectively, some column elements in matrix J are all zero, leading to The angle θ is zero for all angles; to avoid this situation, a column selection matrix is ​​defined. This ensures that no column in matrix JF is naturally zero; in this case, the following equation holds:

[0065] det.F H J H Λ H (z)UU H A(z)JF]=0,

[0066] in z is the independent variable, and the solution to the equation is: Then θ mThe closed-form solution is:

[0067] θ m =arcsin[λ(∠z)] m ) / 2πd],

[0068] Where ∠(·) represents the phase of the complex number; according to the subspace orthogonality principle, the estimated θ m Substitute into matrix And solve for the relationship between its minimum eigenvalue and... Parallel eigenvectors Where q m It is a non-zero constant; according to step (2) The polarization parameter γ can be obtained from the expression. m η m Closed-form solution:

[0069]

[0070]

[0071] Compared with the prior art, the present invention has the following advantages:

[0072] (1) Based on the polarization diversity of array antennas and the idea of ​​multi-subarray cascading, this invention constructs a novel cascaded sparse multi-polarization linear array. By rationally selecting the sparse arrangement and polarization type of each subarray, not only is the array aperture expanded, but the array also has polarization sensitive characteristics.

[0073] (2) This invention achieves the conversion of the covariance matrix of the received signal of the cascaded sparse multipolar linear array to the covariance matrix of the received signal of the virtual cascaded uniform multipolar linear array through multi-domain subarray smoothing processing, ensuring that the received data of the sparse multipolar array is compatible with the traditional root-finding method used for uniform multipolar arrays.

[0074] (3) Based on the multi-domain sparsity of the desired signal and the interference signal in the spatial domain and polarization domain, this invention calculates the closed-form solution of the signal power estimate and gives the closed-form expression of the robust adaptive beamformer, which effectively avoids the computationally complex multidimensional integration operation steps introduced in the design process of existing methods. Attached Figure Description

[0075] Figure 1 This is the overall flowchart of the present invention.

[0076] Figure 2 This is a schematic diagram of the structure of the cascaded sparse multipolar linear array proposed in this invention.

[0077] Figure 3 This is a schematic diagram of the virtual equivalent cascaded uniform multipolar linear array structure corresponding to the cascaded sparse multipolar linear array in this invention.

[0078] Figure 4 This is a curve showing the relationship between the output signal-to-interference-plus-noise ratio (SNR) and the input SNR of the method proposed in this invention and existing methods when the desired signal guidance vector is known.

[0079] Figure 5 This is a curve showing the relationship between the output signal-to-interference-plus-noise ratio and the number of sampling snapshots when the desired signal guidance vector is known, in the case of the method proposed in this invention and existing methods.

[0080] Figure 6 This is a curve showing the relationship between the output signal-to-interference-plus-noise ratio (SNR) and the input SNR of the method proposed in this invention and existing methods when there are fixed deviations in the desired signal angle parameters and polarization parameters.

[0081] Figure 7 This is a curve showing the relationship between the output signal-to-interference-plus-noise ratio and the number of sampling snapshots when the desired signal angle parameters and polarization parameters have fixed deviations. Detailed Implementation

[0082] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings.

[0083] To address the issues of high computational complexity and limited degrees of freedom in existing robust adaptive beamforming methods, this invention proposes a robust adaptive beamforming method based on a cascaded sparse multi-polarization linear array. This method leverages the multi-domain sparsity of the signal spatial and polarization domains, proposing a method for reconstructing the covariance matrix of interference and noise in the spatial and polarization domains, providing a feasible approach and effective solution for the design of robust adaptive beamformers. (Refer to...) Figure 1 The implementation steps of this invention are as follows:

[0084] Step 1: Construct a cascaded sparse multi-polarization linear array. To ensure the array's polarization information processing capability, and to expand the array aperture and reduce inter-element coupling while maintaining a fixed number of array elements, a cascaded sparse multi-polarization linear array is constructed. p A cascaded sparse multipolar linear array is composed of N sparse linear subarrays, with a distance d between adjacent subarrays. Each subarray consists of L0 magnetic rings (whose normal direction is parallel to a coordinate axis) or dipoles (whose axial direction is parallel to a coordinate axis) of the same polarization type. Assume there are N subarrays in total. p′ Given magnetic rings or dipoles of different polarization types, the cascaded sparse multipolar linear array is composed of L = L0N. p The array is composed of N array elements. The N in this cascaded sparse multipolar linear array... p Each subarray consists of at least two magnetic rings or dipoles with different polarization types, i.e., 2 ≤ N p′ ≤N p The above N pEach subarray has the same sparse array arrangement for its elements. A specific fully augmentable sparse array can be chosen, such as a minimum redundancy array, a nested array, or a super-nested array. The number of virtual elements corresponding to each subarray is L. v The distance between adjacent virtual array elements is d. Therefore, the nth... p The positions of each element in the individual formation It can be represented as:

[0085]

[0086] Where n p =1,2,…,N p Let c be an L0×1 dimensional vector representing the y-coordinate positions of the first to L0 elements in the first subarray. Given L0 = 3 and c = [0d 3d] T At that time, the constructed cascaded sparse multipolar linear array structure is as follows: Figure 2 As shown, [·] T This indicates the transpose operation.

[0087] Step 2: Modeling the received signal of the cascaded sparse multipolar linear array and decoupling multidimensional parameters. Assume the desired signal s0(t) and M interfering signals. The incident signal is projected onto the cascaded sparse multipolarized linear array designed in Step 1. Each signal is a far-field narrowband signal and is uncorrelated. Let θ and φ represent the azimuth and elevation angles, respectively. Without loss of generality, when the elevation angle φ = 90°, the incident signal lies in the xy-plane. The spatial and polarization domain joint domain guiding vector of the designed sparse multipolarized linear array is... m = 0, 1, ..., M can be represented as:

[0088]

[0089] Where θ0 represents the azimuth angle of the desired signal, θ m m = 1, 2, ..., M, representing the azimuth angle of the m-th interference signal; γ0 and η0 represent the polarization auxiliary angle and polarization phase difference of the desired signal, respectively. m η m m = 1, 2, ..., M, representing the polarization auxiliary angle and polarization phase difference of the m-th interference signal, a h (θ m ), a v (θ m θ represents the horizontal polarization guidance vector and the vertical polarization guidance vector, respectively, corresponding to the direction of incoming wave. m The signal This represents the polarization vector corresponding to the m-th signal (including the parameter cosγ corresponding to the horizontal and vertical polarization components). m and in ), blkdiag[b s×t c p×q The brackets [] represent a diagonal block matrix constructed from the matrix within the brackets, i.e.:

[0090]

[0091] Where b s×t c p×q Let O represent s×t dimensional matrices and p×q dimensional matrices respectively. a×b Let x(t) be an a×b dimensional zero matrix. Then, the received signal x(t) of the designed cascaded sparse multipolar linear array at time t can be modeled as:

[0092]

[0093] Where s m (t) represents the waveform corresponding to the desired signal or interference signal, and n(t) is a Gaussian white noise component with zero mean that is independent of each signal source.

[0094] To estimate the supporting multidimensional parameter azimuth θ of the proposed beamforming method m Polarization auxiliary angle γ m and polarization phase difference η m This requires decoupling the multidimensional parameters to facilitate their separate solution and estimation. First, the purely spatial guidance vector *a* of the designed cascaded sparse multipolar linear array, which is only related to the spatial parameters, is given. s，m :

[0095]

[0096] Where λ represents the signal wavelength, d l l = 1, 2, ..., L represents the distance between the l-th element and the origin.

[0097] To facilitate the joint domain guidance vector of the spatial and polarization domains The pure spatial guiding vector a s，m And other factors related to the angle parameter sinθ m cosθ m and polarization vector Decoupled, we define the following 6×2 dimensional matrix to represent the polarization type of each array element:

[0098]

[0099] The received signal of the cascaded sparse multipolar linear array can be further expressed as:

[0100]

[0101] Where diag(a)s，m ) indicates based on vector a s，m The diagonal matrix generated by the elements in the matrix, J, is an L×6 dimensional selection matrix (each row has exactly one element that is 1, and the rest are 0). It represents the selection of L antenna elements from three dipoles whose axes are parallel to the x, y, or z axes and three magnetic loop antennas whose normal directions are parallel to the x, y, or z axes. J(l,n) represents the element in the l-th row and n-th column of matrix J (different columns with elements of 1 represent dipoles and magnetic loops with different polarization characteristics). Specifically, J(l,1) = 1, l = 1, 2, ..., L indicates that the l-th element is a dipole whose axial direction is parallel to the x-axis; J(l,n) represents the element in the l-th row and n-th column of matrix J. 2) = 1, l = 1, 2, ..., L indicates that the l-th element is a dipole with its axial direction parallel to the y-axis; J(l, 3) = 1, l = 1, 2, ..., L indicates that the l-th element is a dipole with its axial direction parallel to the z-axis; J(l, 4) = 1, l = 1, 2, ..., L indicates that the l-th element is a magnetic ring with its normal direction parallel to the x-axis; J(l, 5) = 1, l = 1, 2, ..., L indicates that the l-th element is a magnetic ring with its normal direction parallel to the y-axis; J(l, 6) = 1, l = 1, 2, ..., L indicates that the l-th element is a magnetic ring with its normal direction parallel to the z-axis. For example, in Figure 1 Get N p =6, so J(1,1)=J(2,1)=J(3,1)=1, J(4,2)=J(5,2)=J(6,2)=1, ..., J(16,6)=J(17,6)=J(18,6)=1.

[0102] Due to the cascaded sparse multipolar linear array receiving signal The parameter diag(a) in s，m Only related to the spatial parameter θ m related, It is only related to the different polarization characteristics of the multi-polarization linear array antenna. It depends only on the polarization parameter; therefore, by defining the selection matrix J mentioned above, the pure spatial guiding vector a s，m This decouples the antenna from other angle parameters and polarization parameters that are related to its polarization characteristics.

[0103] Step 3: Represent the covariance matrix of the received signal from the cascaded sparse multi-polarized linear array in blocks. To facilitate subsequent joint smoothing operations in the spatial and polarization domains, and thus achieve the estimation of multi-dimensional support parameters in the designed beamforming method, it is necessary to first represent the covariance matrix of the received signal from the cascaded sparse multi-polarized linear array in blocks based on its multi-subarray structure. p The array structure of subarrays will guide the pure spatial vector a s，m The diagonal matrix form is represented as N p The diagonal matrix of each block:

[0104]

[0105] in The covariance matrix R of the received signal from the cascaded sparse multipolar linear array xx It can be represented as:

[0106]

[0107] in Indicates the power of the desired signal. m = 1, 2, ..., M, representing the power of the interference signal, σ 2 Indicates noise power, (·) H I represents the conjugate transpose operation. n Let ρ represent an n×n dimensional identity matrix. 11，m =δ 11，m , These represent variable factors related to the polarization type of the antenna elements in each subarray and the time delay difference between each subarray and the first subarray, respectively. Represents vector δ m The nth element, (·) * This indicates the conjugate operation. In practice, R... xx It can be approximately calculated based on K sample snapshots, that is:

[0108]

[0109] Where t k This represents the time corresponding to the k-th sampling snapshot.

[0110] From the above discussion, it can be seen that, according to R xx The data structure, R, facilitates joint smoothing operations in the spatial and polar domains. xx It can be represented as common A block matrix related to spatial and polarization parameters:

[0111]

[0112] Each block matrix All have dimensions L0×L0, and p, q = 1, 2, ..., N p . p = 1, 2, ..., N p This represents the autocorrelation of the received signal in the p-th subarray; p, q = 1, 2, ..., N pFurthermore, p≠q indicates the cross-correlation between the received signals of the p-th subarray and the q-th subarray. Since each subarray has a data structure similar to the covariance matrix of the received signals of each subarray that makes up the cascaded sparse multipolar linear array, it is very easy to implement the joint smoothing process of the spatial and polarization domains in a block-based manner.

[0113] Step 4: Perform joint spatial and polarization domain smoothing on each block submatrix of the proposed array covariance matrix to obtain the virtual signal vector corresponding to the autocorrelation / cross-correlation of the received signals of each subarray. First, [the text abruptly ends here]. p, q = 1, 2, ..., N p Vectorization operation is performed to obtain vector r. (pq) :

[0114]

[0115] in, Represents a matrix Vectorization operations, that is, transforming a matrix The columns in the vector are stacked sequentially to form a new vector. Represents the pure spatial domain guiding matrix. Denotes the Khatri-Rao product, σ (pq) =[ρ pq，0 , ρ pq，1 , ..., ρ pq，M ] T , Since the positions of each subarray element correspond to a fully expandable sparse array, the vector r (pq) The corresponding virtual array can be represented as containing 2L V -1 uniform array of virtual continuous array elements In order to convert vector r (pq) The elements in the array are in a uniform array with virtual continuous array elements. The arrangement is reordered to correspond to The equivalent virtual signal is defined. Dimensional selection matrix Δ:

[0116]

[0117] in Represents the l′ row of matrix Δ. Column elements, l′=1,…,2L v -1, L0-1≥i1≥0, L0≥i2≥1, ω(l′-L V (i1, i2) represents l′-L V The function of i1 and i2 (representing the combination of values ​​of i1 and i2 that satisfies) (The number of index combinations). Next, based on the selection matrix Δ, for vector r... (pq) The elements in the middle are reordered to correspond to The equivalent virtual signal λ (pq) :

[0118]

[0119] in For each subarray, a virtual uniform array The pure spatial guiding vector with polarization components removed. Indicates only at the Lth V A column vector with one element being 1 and the rest being 0.

[0120] Step 5: Based on the virtual signal vectors corresponding to the autocorrelation / cross-correlation of the received signals of each subarray, reconstruct the covariance matrix of the received signals of each subarray in the virtual equivalent cascaded uniform multipolar linear array. First, the virtual vector λ... (pq) Decomposed into L in sequence V L V ×1 dimensional virtual subvector:

[0121]

[0122] in l″ = 1, 2, ..., L v ,but λ (pq) Middle 1 to L V A vector composed of elements λ (pq) Middle 2 to L V A vector consisting of +1 elements λ (pq) From L V To the 2nd L V A vector consisting of -1 elements. For L V indivual By performing column vector merging, we can obtain the autocorrelation / cross-correlation matrices corresponding to the received signals of each subarray of the virtual equivalent cascaded uniform multipolar linear array:

[0123]

[0124] in This represents the spatial guidance vector of the first subarray in the virtual equivalent cascaded uniform multipolar linear array. Furthermore, the covariance matrix of the received signal from the virtual equivalent cascaded uniform multipolar linear array can be obtained.

[0125]

[0126] in Therefore, the covariance matrix R of the signal received by the cascaded sparse multipolar linear array xx It can be reconstructed as the covariance matrix of the received signal of its corresponding virtual equivalent uniform multipolar linear array. The covariance matrix The corresponding structure is Figure 3 The virtual equivalent cascaded uniform multipolar linear array is shown. The reconstructed covariance matrix... It includes data information on the decoupling of horizontal and vertical polarization parameters, as well as the parameter θ. m The data information, separated from the polarization parameters, facilitates the joint estimation of multidimensional parameters for the designed beamforming method.

[0127] Step Six: Solve for the one-dimensional direction of arrival (DOA) and polarization parameters based on the reconstructed covariance matrix. By introducing polarization multiple signal classification methods, polarization subspace rotation-invariant methods, or polarization multiple signal classification root-finding methods, the one-dimensional DOA and polarization parameter estimation results can be obtained. Taking the polarization multiple signal classification root-finding method as an example, firstly... Perform eigenvalue decomposition and sort the corresponding eigenvalues ​​from largest to smallest, then take the last L... V N p The subspace spanned by the eigenvectors corresponding to the -M-1 smaller eigenvalues ​​is denoted as the noise subspace U. According to... From the expression for the virtual array guidance vector and the orthogonality between the virtual array guidance vector and the noise subspace U, we can see that:

[0128]

[0129] Furthermore, according to the principle of rank deficiency, it can be deduced that Where `det(·)` represents the determinant operation. When the constructed cascaded sparse multipolar linear array does not contain the six types of dipoles and magnetic rings whose axial or normal directions are parallel to the three coordinate axes respectively, some column elements in matrix J are all zero, leading to... The angle θ is zero for all angles. To avoid this situation, a column selection matrix is ​​defined. This ensures that no columns in matrix JF are naturally zero (taking a cascaded sparse multipolar linear array composed of three types of dipoles with axes parallel to the three coordinate axes as an example, the corresponding selection matrix is...). At this point, we have the following equation:

[0130] det.F H J H Λ H (z)UU H Λ(z)JF]=0,

[0131] in Let z be a variable, and the solution to the equation is: Then θm The closed-form solution is:

[0132] θ m =arcsin[λ(∠z)] m ) / 2πd],

[0133] Where ∠(·) represents the phase of the complex number. According to the subspace orthogonality principle, the estimated θ... m Substitute into matrix And solve for the relationship between its minimum eigenvalue and... Parallel eigenvectors Where q m It is a non-zero constant. According to step two... The polarization parameter γ can be obtained from the expression. m η m Closed-form solution:

[0134]

[0135]

[0136] Step 7: Utilize the sparsity of the desired and interfering signals in the spatial and polarization domains to design the weight vector of the robust adaptive beamformer. The interference plus noise covariance matrix can be expressed as... It can be seen that R i+n The reconstruction is mainly by The part related to noise power σ 2 I L Composition. Noise power estimation. Depend on L V N p -M-1 smaller eigenvalues ​​are averaged to obtain the result. For R xx K-times of sampling The derived virtual reconstruction covariance matrix corresponds to the virtual equivalent concatenated uniform multipolar linear array. This can be achieved by solving the (M+1)×1 dimensional power distribution vector. The corresponding matrix P = diag(p) ​​is obtained as follows:

[0137]

[0138] Among them ||·|| F Describing the Frobenius norm, In the above formula and For the estimated desired signal parameters, and m = 1, 2, ..., M are the estimated M interference signal parameters. Based on the sparsity characteristics of the desired signal and the interference signal in the spatial and polarization domains, the closed-form solution of p is:

[0139] p = (B H B) -1 B H r,

[0140] in The reconstructed spatial and polarization joint domain interference plus noise covariance matrix It can be represented as follows:

[0141]

[0142] Therefore, by utilizing the joint domain sparsity of the desired signal and the interference signal in the spatial and polarimetric domains, the interference-noise covariance matrix can be reconstructed. and Substituting into the following equation, the robust adaptive beamformer weight vector in the joint spatial and polarization domains can be obtained:

[0143]

[0144] Then, by weighting the cascaded sparse multipolarized linear array with the designed beamformer weight vector, the array output can be obtained as y(t) = w H x(t).

[0145] The effects of the present invention will be further described below with reference to simulation examples.

[0146] Simulation Example: The proposed cascaded sparse multipolarized linear array is used to receive the incident signal, taking N... p =3, d=λ / 2, where the y-axis coordinates of each element in the first subarray are (0, 1, 2, 5, 8)d, then the y-axis coordinates of all elements are (0, 1, 2, 5, 8, 9, 10, 11, 14, 17, 18, 19, 20, 23, 26)d. For the selection matrix J, we have J(1, 1)=J(2, 1)=J(3, 1)=J(4, 1)=J(5, 1)=1, J(6, 2)=J(7, 2)=J(8, 2)=J(9, 2)=J(10, 2)=1, J(11, 3)=J(12, 3)=J(13, 3)=J(14, 3)=J(15, 3)=1, and the remaining elements are all 0. The parameters {θ0, γ0, η0} of the desired signal are {35°, 25°, 0°}; the parameters {θ0, γ0, η0} of the two interfering signals are... m γ m η mThe integral beamforming method (Integral-3D beamformer), which is compared with the beamforming method proposed in this invention, is a three-dimensional form of the M-dimensional beamforming method (Integral-MD beamformer). The integral intervals of the interference signal parameters (i.e., azimuth angle, polarization auxiliary angle, and polarization phase difference) are [θ...]. m -5°, θ m +5°],[γ m -5°, γ m +5°] and [η] m -5°, η m +5°]. Other beamforming methods compared to the beamforming method proposed in this invention include sample matrix inversion (SMI) beamforming, diagonal loading sample matrix inversion (DL-SMI) beamforming, and worst-case beamforming. The aforementioned existing beamforming methods did not initially consider the polarization diversity of the signal. For fair comparison, the simulation adopted beamforming methods that extend the aforementioned beamforming concept to the polarization domain, and all beamforming methods used for comparison employed the proposed cascaded sparse multi-polarization linear array. The diagonal loading factor of the diagonal loading sample matrix inversion beamforming method is 10σ. 2 The upper bound of the guidance vector error norm for the worst-case beamforming method is set to ε = 1. The desired signal, interference signal, and additive noise are all complex Gaussian white signals with zero mean. The interference-to-noise ratio (INR) is set to 30 dB for each antenna. When plotting the relationship between output INNR and input INNR, the number of sampling snapshots is set to 50; when plotting the relationship between output INNR and the number of sampling snapshots, the INNR is set to 20 dB. 500 Monte Carlo experiments are performed for each case, considering both the known guidance vector of the desired signal and the fixed deviations in the angle and polarization parameters of the desired signal.

[0147] First, consider the case where the desired signal guidance vector is known. Plot the relationship between the output signal-to-interference-plus-noise ratio (SNR) and the input SNR, as shown below. Figure 4 As shown; plot the relationship curve between the output signal-to-interference-plus-noise ratio and the number of sampling snapshots, as follows. Figure 5 As shown. From Figure 4 and Figure 5As can be seen, for a wide range of input signal-to-noise ratios, the output signal-to-interference-plus-noise ratio (SNR) of the beamforming method proposed in this invention is very close to the ideal value, which demonstrates the accurate reconstruction of the joint domain interference plus noise covariance matrix of the spatial and polarization domains. Since the three-dimensional integral beamforming method is sensitive to the estimation error of the noise subspace, it performs poorly under low input SNR conditions, while the method proposed in this invention is unaffected. Furthermore, the average simulation time of the beamforming method proposed in this invention is 32.10 milliseconds per experiment; while the three-dimensional integral beamforming method, due to its complex integration operations, has a significantly increased computational complexity, with an average simulation time of 2.28 seconds per experiment. The simulation platform used was MATLAB 2020a, and the central processing unit was an Intel(R) Core(TM) i7-10875H 2.30GHz. Figure 4 and Figure 5 As can be seen, under conditions of high input signal-to-noise ratio and all sampling snapshots, the beamforming method proposed in this invention performs better than existing methods. This is because the desired signal accounts for a larger proportion in the sampling covariance matrix used by the existing beamforming methods compared to this one, which leads to the self-cancellation of signals in the joint domain of the spatial and polarization domains.

[0148] Then, consider the case where the angle and polarization parameters of the desired signal have a fixed deviation. In each experiment, the angle and polarization parameters (θ) of the desired signal and the interference signal are... m γ m η m ), m = 0, 1, ..., M, for (θ m +0.5°, γ m +0.5°, η m +0.5°), meaning all parameters have a fixed deviation of 0.5°. When the estimated parameters exceed the 2.5° error range (especially at low input signal-to-noise ratios or with limited sampling snapshots), the assumed angle and polarization parameters of the desired and interfering signals are respectively in [θ m -2.5°, θ m +2.5°],[γ m -2.5°, γ m +2.5°] and [η m -2.5°, η m The value is randomly obtained from [+2.5°] as prior information. The relationship curve between the output signal-to-interference-plus-noise ratio (SNR) and the input SNR is plotted as follows: Figure 6 As shown; plot the relationship curve between the output signal-to-interference-plus-noise ratio and the number of sampling snapshots, as follows. Figure 7 As shown. Figure 6 and Figure 7 and Figure 4 and Figure 5By comparison, it can be found that the output performance of all beamforming methods is reduced due to the estimation bias of the parameters. Under higher input signal-to-noise ratios, the performance of the three-dimensional integral beamforming method is more severely degraded than that of the method proposed in this invention. This is because the three-dimensional integral beamforming method is less accurate in reconstructing the joint domain interference plus noise covariance matrix of the spatial and polarization domains.

[0149] In summary, this invention constructs a novel cascaded sparse multi-polarization linear array based on the polarization diversity of antennas and the concept of multi-subarray cascading. This increases the array's degrees of freedom and endows it with polarization-sensitive characteristics. Furthermore, based on multi-domain subarray smoothing technology, it achieves the transformation of the output covariance matrix of the cascaded sparse multi-polarization linear array to the output covariance matrix of the virtual cascaded uniform multi-polarization linear array. This makes the root-finding techniques traditionally used for uniform multi-polarization arrays applicable to sparse multi-polarization arrays as well. Moreover, based on the multi-domain sparsity of the signal spatial domain and polarization domain, a closed-form estimate of the signal power is obtained, and a closed-form expression for a robust adaptive beamformer is given. While ensuring superior performance, this invention effectively avoids the computationally complex multidimensional integration operations found in existing robust adaptive beamforming methods.

[0150] The above description is merely a preferred embodiment of one or more embodiments of this specification and is not intended to limit the scope of one or more embodiments of this specification. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of one or more embodiments of this specification should be included within the scope of protection of one or more embodiments of this specification.

Claims

1. A robust adaptive beamforming method based on a concatenated sparse multi-polarized linear array, characterized in that, Comprising the following steps: (1) Constructing a cascaded sparse multipolar linear array: Constructing an array consisting of N p A cascaded sparse multipolar linear array is obtained by cascading sparse linear subarrays. The distance between adjacent subarrays is d. Each subarray consists of L0 magnetic rings or dipoles of the same polarization type. The normal direction of the magnetic rings is parallel to a certain coordinate axis, and the axial direction of the dipoles is parallel to a certain coordinate axis. Assume there are N subarrays in total. p′ For magnetic rings or dipoles with different polarization types, then 2 ≤ N p′ ≤N p This cascaded sparse multipolar linear array is composed of L = L0N p The above N array elements are composed of; p Each element of the subarray is arranged in the same sparse array manner; the number of virtual elements corresponding to each subarray is L. v The distance between adjacent virtual array elements is d; (2) Assume that the desired signal s0(t) and M interference signals The incident signals are far-field narrowband signals and are mutually independent. θ and φ represent the azimuth angle and the elevation angle, respectively. When the elevation angle φ = 90°, the incident signal is located in the x-y plane. The received signal x(t) of the designed cascaded sparse multi-polarized linear array at time t is modeled as: where s m (t) represents the waveforms corresponding to the desired signal or the interference signal, n(t) is a Gaussian white noise component with zero mean and mutual independence with each signal source, is the joint spatial and polarization domain steering vector of the designed cascaded sparse multi-polarization linear array, which is expressed as where θ0denotes the azimuth angle of the desired signal, θ m , m = 1, 2, …, M, denotes the azimuth angle of the m-th interfering signal; γ0, η0denote the polarization auxiliary angle and polarization phase difference of the desired signal, γ m , η m , m = 1, 2, …, M, denote the polarization auxiliary angle and polarization phase difference of the m-th interfering signal, a h (θ m ), a v (θ m ) denote the horizontal polarization steering vector and the vertical polarization steering vector, respectively, corresponding to the signal with the direction of arrival θ m , denotes the polarization vector corresponding to the m-th signal, including the parameters cosγ m and where [·] T denotes the transpose operation, blkdiag[b s×t ,c p×q ] denotes the diagonal block matrix constructed by the matrices in the brackets, i.e.: where b s×t , c p×q denote s x t matrices and p x q matrices, respectively, O a×b denotes an a x b zero matrix; To decouple the pure spatial steering vector in the joint spatial and polarization domain steering vector and the rest of the angle parameter dependent factors sinθ m , cosθ m and polarization vector , the cascaded sparse multi-polarization linear array received signal is further expressed as: where a s,m is the pure spatial steering vector of the designed cascaded sparse multi-polarized linear array related only to the spatial parameters: where λ denotes the signal wavelength, d l , l = 1, 2, …, L denotes the distance between the lth array element and the coordinate origin, diag(a s,m ) denotes a diagonal matrix generated based on each element of the vector a s,m , J is an L x 6 selection matrix, each row has and only has one element of 1, and the rest of the elements are 0, which represents that L antenna units are selected from 3 axial dipoles parallel to the x, y or z axis and 3 normal direction magnetic loop antennas parallel to the x, y or z axis, is a 6 x 2 matrix representing the polarization type of each array element: After the above operation, the pure spatial steering vector a s,m And the rest of the angle parameters related to the antenna polarization characteristics and polarization parameters to achieve decoupling, facilitate the support of the proposed beamforming method to solve the respective estimation of multi-dimensional parameters; (3) According to the array structure of the cascade sparse multi-polarized linear array containing N p sub-arrays, the diagonal matrix form of the pure spatial steering vector a s,m is expressed as a diagonal matrix of N p blocks: wherein The covariance matrix R of the received signal of the concatenated sparse multi-polarized linear array xx is represented as: where denotes the power of the desired signal, denotes the power of the interference signal, σ 2 denotes the noise power, (·) H denotes the conjugate transpose operation, I n denotes the n x n identity matrix, p 11,m = δ 11,m , p 22,m = δ 22,m , denote the variable factors related to the polarization type of the antenna elements in each subarray and the time delay difference between each subarray and the first subarray, respectively, where [δ m ] n denotes the n-th element of the vector δ m , (·) * denotes the conjugate operation; in practice, R xx is calculated approximately from K sample snapshots, i.e.: where t k denotes the time instant corresponding to the k-th sampling snapshot; According to the data structure of R xx , in order to facilitate the joint smoothing processing operation of the spatial domain and the polarization domain, R xx is expressed as a common block matrix related to the spatial domain parameter and the polarization domain parameter: where each block matrix has dimensions L0x L0, and p, q = 1, 2,..., N p ; Rppdenotes the autocorrelation of the pthsubarray received signal; and p≠q denotes the cross-correlation of the pthand qthsubarray received signals; (4) To obtain the virtual signal corresponding to the virtual equivalent cascade uniform multi-polarization linear array, first, the vectorization operation is performed on the signals of the virtual equivalent cascade uniform multi-polarization linear array to obtain a vector r (pq) :​ in, Represents a matrix Vectorization operations, that is, transforming a matrix The columns in the vector are stacked sequentially to form a new vector. Represents the pure spatial domain guiding matrix. Denotes the Khatri-Rao product, σ (pq) =[ρ pq,0 ,ρ pq,1 ,…,ρ pq,M ] T , This represents the vectorization of an L0×L0 dimensional identity matrix; since the positions of each subarray element correspond to a fully expandable sparse array, the vector r (pq) The corresponding virtual array can be represented as containing 2L V -1 uniform array of virtual continuous array elements (-L V +2)d,…,-d,0,d,…,(L V -2)d,(L V -1)d]; will vector r (pq) The elements in the array are in a uniform array with virtual continuous array elements. The arrangement is reordered to correspond to The equivalent virtual signal λ (pq) : wherein is a virtual uniform array corresponding to each subarray a polarization component removed spatial-only steering vector, denotes a column vector with only the Lth V element being 1 and the rest being 0. (5) To reconstruct the covariance matrix of each subarray received signal of the virtual equivalent cascaded uniform multi-polarization linear array, first, the virtual vector λ (pq) is decomposed into L V virtual sub-vectors of L V ×1 dimension in turn: wherein then denotes λ (pq) a vector consisting of the first to the L V th elements in λ denotes λ (pq) a vector consisting of the second to the L V th elements in λ denotes λ (pq) a vector consisting of the L V th to the 2L V th elements in λ V ; and performing column vector merging operation on L V , the auto- / cross-correlation matrix corresponding to the received signals of each sub-array of the virtual equivalent cascaded uniform multiple polarization linear array can be obtained. wherein represents the pure spatial steering vector of the 1st subarray in the virtual equivalent cascaded uniform multiple-polarized linear array; and the received signal covariance matrix of the virtual equivalent cascaded uniform multiple-polarized linear array can be obtained wherein (6) Solving one-dimensional direction of arrival and polarization parameters based on the reconstructed covariance matrix; (7) The interference plus noise covariance matrix is denoted as It is known that R i+n The reconstruction of R is mainly composed of the signal power related part σ 2 I L and the noise power estimation The noise power estimation is obtained by averaging the L V N p (M+1) smallest eigenvalues of R The K snapshots of R xx are denoted as The virtual reconstructed covariance matrix of the virtual equivalent cascaded uniform multiple polarization linear array is derived as The power distribution vector p is obtained by solving the following equation The matrix P = diag(p) is obtained. where || · || F denotes the Frobenius norm, in the above equation and are estimated desired signal parameters, and are estimated M interference signal parameters; based on the sparse characteristics of the desired signal and interference signals in the spatial and polarization domains, the closed-form solution for p is: p = (B H B) -1 B H r, wherein The reconstructed spatial and polarization domain joint domain interference plus noise covariance matrix is represented as follows: Therefore, the interference plus noise covariance matrix is reconstructed by using the joint spatial and polarization domain sparsity of the desired signal and the interference signal; and and The robust adaptive beamformer weight vector of the joint spatial and polarization domain can be obtained by substituting the following formula: Then the array output of the cascaded sparse multi-polarized linear array with the designed beamformer weight vector weighting is y(t) = w H x(t).

2. The robust adaptive beamforming method based on the concatenated sparse multi-polarized linear array according to claim 1, characterized in that, In step (1), a cascaded sparse multi-polarized linear array is constructed, specifically: an array composed of N p sub-arrays with the same sparse arrangement mode is constructed, the sparse arrangement mode of each array element of the N p sub-arrays is selected from a minimum redundancy array without holes, a nested array or a super-nested array of a virtual domain difference hybrid array, the antenna polarization characteristics of each sub-array are the same, and at least two different types of polarized antennas exist; the number of virtual array elements corresponding to each sub-array is L v , and the position of each array element of the nth p sub-array is represented as: ​ where n p = 1, 2,..., N p , c is a L0x1 vector, representing the y-axis coordinate positions of the first to the L0th elements in the first sub-array.

3. The robust adaptive beamforming method based on the concatenated sparse multi-polarized linear array according to claim 1, characterized in that, In step (2), the forming mode of the Lx6-dimensional selection matrix J is specifically: J(l, n) represents the lth row and nth column element of the matrix J, and different column elements are 1, representing different polarization characteristics of the dipole and the magnetic ring. Specifically, J(l, 1) = 1, l = 1, 2, …, L, indicating that the lth array element is a dipole with an axial direction parallel to the x-axis; J(l, 2) = 1, l = 1, 2, …, L, indicating that the lth array element is a dipole with an axial direction parallel to the y-axis; J(l, 3) = 1, l = 1, 2, …, L, indicating that the lth array element is a dipole with an axial direction parallel to the z-axis; J(l, 4) = 1, l = 1, 2, …, L, indicating that the lth array element is a magnetic ring with a normal direction parallel to the x-axis; J(l, 5) = 1, l = 1, 2, …, L, indicating that the lth array element is a magnetic ring with a normal direction parallel to the y-axis; J(l, 6) = 1, l = 1, 2, …, L, indicating that the lth array element is a magnetic ring with a normal direction parallel to the z-axis.

4. The robust adaptive beamforming method based on the concatenated sparse multi-polarized linear array according to claim 1, characterized in that, In step (4), the vector r (pq) The elements in the array are in a uniform array with virtual continuous array elements. The arrangement is reordered to correspond to The equivalent virtual signal λ (pq) Specifically, this is achieved through a selection matrix: First, for Perform vectorization to obtain vector r (pq) Then, define Dimensional selection matrix Δ: wherein denotes the l'th column element of the matrix Δ, l' = 1,..., 2L v -1, L0-1≥i1≥0, L0≥i2≥1, ω(l'-L V ,i1,i2) denotes a function of l'-L V ,i1 and i2, representing the number of index combinations for which i1 and i2 take values satisfying The autocorrelation / cross-correlation corresponding to the virtual signal vector λ (pq) is denoted by:​ λ (pq) = Δr (pq) .

5. The robust adaptive beamforming method based on the concatenated sparse multi-polarized linear array according to claim 1, characterized in that, In step (6), the one-dimensional direction of arrival and polarization parameter estimation is performed by using the following methods: polarization multiple signal classification method, polarization subspace rotation invariant method or polarization multiple signal classification root method.

6. The robust adaptive beamforming method based on the concatenated sparse multi-polarized linear array according to claim 1, characterized in that, In step (6), one-dimensional DOA estimation is performed by using the polarized multiple signal classification root-finding method, and then the polarization parameters are solved. Specifically, first, the received signal matrix is subjected to eigenvalue decomposition, and the corresponding eigenvalues are arranged in descending order, and the last L eigenvalues are taken as the noise eigenvalues. V N p The subspace spanned by the eigenvectors corresponding to the L -M-1 smaller eigenvalues is denoted as the noise subspace U. According to the expression of the virtual array steering vector and the orthogonal relationship between the noise subspace U, it can be known that: Further, according to the rank deficiency principle, it can be deduced that where det(·) represents the determinant operation; when the constructed cascaded sparse multi-polarization linear array does not contain six dipoles and magnetic loops whose axial or normal directions are respectively parallel to the three coordinate axes, some column elements in the matrix J are all zeros, resulting in zero for all angles θ; in order to avoid the above situation, a column selection matrix so that some columns in the matrix JF are naturally zero; at this time, the following equation is obtained: det[F H J H Λ H (z)UU H Λ(z)JF] = 0, wherein z is the independent variable, the solution of the equation is then θ m The closed-form solution for is: θ m = arcsin [λ(∠z m ) / 2πd], where ∠(·) denotes the phase of a complex number; according to the subspace orthogonality principle, the estimated θ m is substituted into the matrix and its smallest eigenvalue corresponding to the eigenvector parallel to is solved, where q m is a nonzero constant; according to the expression of in step (2), the closed-form solutions of the polarization parameters γ m , η m are obtained:

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