Array signal processing method and device, equipment and storage medium

Abstract

The invention relates to an array signal processing method, device and equipment and a storage medium in the technical field of array signal processing, and the method comprises the steps: obtaining a sampling covariance matrix of an array signal; a conjugate symmetry constraint condition is applied to the sampling covariance matrix, and a CMSP-TNN optimization model is constructed; the CMSP-TNN optimization model is solved, and a low-rank matrix corresponding to the sampling covariance matrix is obtained; and carrying out direction of arrival estimation on the array signal based on the low-rank matrix. According to the method, the inherent conjugate symmetry characteristic of the signal covariance matrix is fused, the conjugate symmetry constraint condition is synchronously applied in the low-rank matrix recovery process, and the optimization model special for the signal processing scene is constructed, so that the recovered covariance matrix not only keeps the low-rank essence, but also more strictly conforms to the structural characteristic of the signal covariance matrix, and the signal processing efficiency is improved. The matrix recovery precision is significantly improved, and the DOA estimation robustness in a complex electromagnetic environment is improved.

Description

Technical Field

[0001] This application belongs to the field of array signal processing technology, and more specifically, relates to an array signal processing method, apparatus, device and storage medium. Background Technology

[0002] In the field of array signal processing, Direction of Arrival (DOA) estimation techniques based on subspace decomposition are widely used due to their super-resolution characteristics. General algorithms are all based on the theoretical foundation of eigenvalue decomposition of the received signal covariance matrix. These methods construct the orthogonality between the noise and signal subspaces of the ideal covariance matrix, build a spatial spectral function for peak search, and ultimately achieve DOA parameter estimation.

[0003] However, in practical engineering applications, there are two typical limiting scenarios: (1) when the distance between the signal source and the array is too far, resulting in a significant attenuation of the beamforming gain; and (2) in dynamic monitoring environments, when the effective number of snapshots is insufficient due to limitations in the equipment's sampling capability. In these two scenarios, the actual sampling covariance matrix of the received signal will deviate significantly from the statistical characteristics of the ideal mathematical model. Specifically, under finite sample conditions, the diffusion effect of matrix eigenvalues ​​is aggravated, the orthogonality between the noise subspace and the signal subspace is destroyed, leading to pseudo-peak phenomena and main lobe distortion in the spatial spectrum function.

[0004] Therefore, the accuracy of DOA estimation for array signals is currently difficult to guarantee. Summary of the Invention

[0005] The purpose of this application is to provide an array signal processing method, apparatus, device, and storage medium to improve the robustness of DOA estimation in complex electromagnetic environments.

[0006] A first aspect of this application provides an array signal processing method, including:

[0007] Obtain the sampling covariance matrix of the array signal;

[0008] A CMSP-TNN optimization model is constructed by imposing conjugate symmetry constraints on the sampling covariance matrix.

[0009] Solve the CMSP-TNN optimization model to obtain the low-rank matrix corresponding to the sampling covariance matrix;

[0010] Direction of arrival (DOA) estimation of array signals is performed based on a low-rank matrix.

[0011] In one embodiment, a conjugate symmetry constraint is imposed on the sampling covariance matrix, including:

[0012] Minimize the error between the low-rank matrix, the ideal matrix corresponding to the sampling covariance matrix, and the conjugate symmetry function of the sampling covariance matrix.

[0013] In one embodiment, a CMSP-TNN optimization model is constructed by imposing conjugate symmetry constraints on the sampling covariance matrix, including:

[0014] By imposing conjugate symmetry constraints on the sampling covariance matrix, an error matrix is ​​constructed.

[0015] The magnitude of the error matrix is ​​calculated using the l1 norm and added to the objective function of the TNN optimization model to obtain the appropriate CMSP-TNN optimization model.

[0016] In one embodiment, the CMSP-TNN optimization model is:

[0017]

[0018] stZ+E=X

[0019] In the formula All are complex matrices, Z is a low-rank matrix, ||Z|| * Let be the nuclear norm of matrix Z, E be a sparse matrix, ||E||1 be the l1 norm of matrix E, X be the sampling covariance matrix, λ and γ be regularization parameters, and tr(AZB) be the normalization parameter. H Let A be the trace of matrix X, and let A and B be the truncated left and right singular matrices of matrix X. N X * J N Let ||ZJ be the error matrix. N X * J N ||1 represents the l1 norm of the error matrix.

[0020] In one embodiment, solving the CMSP-TNN optimization model includes: solving the CMSP-TNN optimization model using an iterative method, further including:

[0021] In the first stage, fix matrices Z and E, and calculate matrices A and B;

[0022] In the second stage, with matrices A and B fixed, matrices Z and E are updated.

[0023] In one embodiment, during the l-th iteration, the first phase includes:

[0024] For a fixed Z l and E l Calculate matrix X l =Z l +E l For matrix Xl Perform singular value decomposition Among them U l =(u1,u2,...,u M V l =(v1,v2,...,v M );

[0025] From U l A is constructed by selecting the left singular vectors corresponding to the first r largest singular values. l From V l B is constructed by selecting the right singular vectors corresponding to the first r largest singular values. l .

[0026] In one embodiment, direction-of-arrival estimation of the array signal based on a low-rank matrix includes:

[0027] Based on the low-rank matrix, the direction of arrival (DOA) of the array signal is estimated using the MUSIC multi-signal classification algorithm or the ESPRIT rotation-invariant subspace algorithm.

[0028] A second aspect of this application provides an array signal processing apparatus, comprising:

[0029] The acquisition unit is used to acquire the sampling covariance matrix of the array signal;

[0030] The optimization model building unit is used to construct the CMSP-TNN optimization model by imposing conjugate symmetry constraints on the sampling covariance matrix;

[0031] The low-rank matrix acquisition unit is used to solve the CMSP-TNN optimization model and obtain the low-rank matrix corresponding to the sampling covariance matrix;

[0032] The direction-of-arrival (DOA) estimation unit is used to estimate the DOA of array signals based on a low-rank matrix.

[0033] A third aspect of this application provides an electronic device, including a memory, a processor, and a computer program stored in the memory and running on the processor, wherein the processor executes the computer program to implement the steps of a method.

[0034] A fourth aspect of this application provides a computer-readable storage medium storing a computer program, the steps of which are executed by a processor.

[0035] The beneficial effects of the array signal processing method, apparatus, device, and storage medium provided in this application embodiment are as follows:

[0036] This application, after obtaining the sampling covariance matrix of the array signal, constructs a CMSP-TNN optimization model by applying conjugate symmetry constraints to the sampling covariance matrix, solves the CMSP-TNN optimization model, and obtains the low-rank matrix corresponding to the sampling covariance matrix; based on the low-rank matrix, it performs direction-of-arrival (DOA) estimation on the array signal. This application, by integrating the inherent conjugate symmetry characteristics of the signal covariance matrix and simultaneously applying conjugate symmetry constraints during the low-rank matrix recovery process, and by constructing an optimization model specifically for signal processing scenarios, ensures that the recovered covariance matrix not only maintains its low-rank nature but also more strictly conforms to the structural characteristics of the signal covariance matrix, significantly improving matrix recovery accuracy and enhancing the robustness of DOA estimation in complex electromagnetic environments. Attached Figure Description

[0037] To more clearly illustrate the technical solutions in the embodiments of this application, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0038] Figure 1 A schematic flowchart of an array signal processing method provided in an embodiment of this application;

[0039] Figure 2 This is a structural block diagram of an array signal processing device provided in an embodiment of this application;

[0040] Figure 3 This is a schematic block diagram of an electronic device provided in an embodiment of this application. Detailed Implementation

[0041] In the following description, specific details such as particular system architectures and techniques are set forth for illustrative purposes and not for limitation, in order to provide a thorough understanding of the embodiments of this application. However, those skilled in the art will understand that this application may also be implemented in other embodiments without these specific details. In other instances, detailed descriptions of well-known systems, apparatuses, circuits, and methods have been omitted so as not to obscure the description of this application with unnecessary detail.

[0042] To make the objectives, technical solutions, and advantages of this application clearer, the following description will be provided in conjunction with the accompanying drawings and specific embodiments.

[0043] Please refer to Figure 1 , Figure 1 This is a flowchart illustrating an array signal processing method provided in an embodiment of this application, which can be executed by an electronic device. The method may include:

[0044] S101: Obtain the sampling covariance matrix of the array signal.

[0045] S102: Construct the CMSP-TNN optimization model by imposing conjugate symmetry constraints on the sampling covariance matrix.

[0046] In one embodiment, a conjugate symmetry constraint is imposed on the sampling covariance matrix, including:

[0047] Minimize the error between the low-rank matrix, the ideal matrix corresponding to the sampling covariance matrix, and the conjugate symmetry function of the sampling covariance matrix.

[0048] In one embodiment, a CMSP-TNN optimization model is constructed by imposing conjugate symmetry constraints on the sampling covariance matrix, including:

[0049] By imposing conjugate symmetry constraints on the sampling covariance matrix, an error matrix is ​​constructed.

[0050] The magnitude of the error matrix is ​​calculated using the l1 norm and added to the objective function of the TNN optimization model to obtain the appropriate CMSP-TNN optimization model.

[0051] The theoretical analysis is as follows:

[0052] In array signal processing, the covariance matrix of the received signal from a uniform array satisfies the Toeplitz structure and possesses a special property: two elements symmetric about the main diagonal are conjugates and equal. The specific structure can be represented as follows:

[0053]

[0054] The conjugate symmetry property of the array received signal covariance matrix is ​​expressed using the selection matrix.

[0055]

[0056] In the traditional TNN low-rank matrix recovery algorithm, the sparse matrix E is represented by E = XZ, where matrix X represents the sampling covariance matrix. Matrix E can be used to measure the difference between the recovered low-rank matrix Z and the sampling covariance matrix. The difference between them means minimizing the l1 norm of matrix E, which means making matrix Z as close as possible to the sampling covariance matrix while maintaining its low-rank property. because The covariance matrix R itself and the ideal covariance matrix xx There are errors between them, which may cause the optimized low-rank matrix Z to deviate from R. xx The error between them is larger. Considering the conjugate symmetric structure represented by equation (2), this invention adds a term to the objective function of the TNN model that is related to... The relevant l1 norm constraint is equivalent to imposing a constraint with a symmetric structure on matrix Z, such that matrix Z is related to R. xx and All of these are kept to the minimum error, making them closer to the ideal covariance matrix.

[0057] Based on the above analysis, a new error matrix is ​​constructed as follows:

[0058] W = ZJ N X * J N (3)

[0059] Using the l1 norm to calculate the size of the error matrix and adding it to the objective function of the TNN optimization model, we can obtain the objective optimization problem as follows:

[0060]

[0061] In the formula, Let σ be the truncated nuclear norm of matrix Z. i (Z) represents the i-th singular value of matrix Z in descending order, i = 1, 2, ..., M, where M is the number of antenna elements; λ and γ are regularization parameters. Since the first term of the optimization objective function, the truncated kernel norm, has been proven to be a non-convex problem, the truncated kernel norm can be rewritten as an optimization problem expressed in terms of the kernel norm and the trace function, i.e.

[0062]

[0063] In the formula All are complex matrices, Z is a low-rank matrix, ||Z|| * Let be the nuclear norm of matrix Z, E be a sparse matrix, ||E||1 be the l1 norm of matrix E, X be the sampling covariance matrix, λ and γ be regularization parameters, and tr(AZB) be the normalization parameter. H Let A be the trace of matrix X, and let A and B be the truncated left and right singular matrices of matrix X. N X * J N Let ||ZJ be the error matrix. N X * J N ||1 represents the l1 norm of the error matrix.

[0064] S103: Solve the CMSP-TNN optimization model to obtain the low-rank matrix corresponding to the sampling covariance matrix.

[0065] The optimization problem described by equation (5) is solved iteratively. The iterative process consists of two steps: first, matrices Z and E are fixed, and matrices A and B are calculated; then, the calculated matrices A and B are fixed, and matrices Z and E are updated. The algorithm alternates between these two stages. Taking the l-th iteration as an example, in the first stage of this iteration, for the fixed Z... l and E l Calculate matrix X l =Z l +E l For matrix X l Perform singular value decomposition Among them U l =(u1,u2,...,u M V l =(v1,v2,...,v M ), from U l A is constructed by selecting the left singular vectors corresponding to the first r largest singular values. l From V l B is constructed by selecting the right singular vectors corresponding to the first r largest singular values. l ,Right now

[0066]

[0067] In the second stage, for a fixed A l and B l The optimization problem that needs to be solved in updating Z and E is:

[0068]

[0069] Based on the above analysis, the methods for solving the CMSP-TNN optimization model include:

[0070] In the first stage, fix matrices Z and E, and calculate matrices A and B;

[0071] In the second stage, with matrices A and B fixed, matrices Z and E are updated.

[0072] This application improves the TNN optimization model by utilizing the conjugate symmetry property of the covariance matrix. The improved model is called the TNN model based on the covariance matrix symmetric prior (CMSP), namely the CMSP-TNN optimization model or the CMSP-TNN optimization algorithm. The solution process of this algorithm can be simply described as follows:

[0073] Table 1. Solution flow of CMSP-TNN optimization algorithm

[0074]

[0075] The second stage involves solving the optimization problem described by equation (7), and determining the norm ||ZJ||. N X * J N The error term in ||1 ​​is represented by the variable W, i.e.

[0076] W = W(Z) = ZJ N X * J N (8)

[0077] Using equation (8), the optimization problem can be re-expressed as

[0078]

[0079] Considering that the above optimization problem involves two variables, it can be solved using the Alternating Direction Method of Multipliers (ADMM). First, the augmented Lagrangian function of the optimization problem described by equation (9) is expressed as follows:

[0080]

[0081] In the formula, P and Q are Lagrange multipliers, μ is the penalty parameter and μ > 0, and the operator... Let the inner product of matrices be represented as follows: The inner product of matrices is related to the trace of the matrix as follows:<A,B> =tr(A T B), This represents the Frobenius norm of a matrix, or simply the F-norm.

[0082] Based on the principles of the ADMM algorithm, the above optimization problem can be solved by alternately updating the values ​​of variables Z, E, W, P, Q, and μ. When updating one variable, the other variables are kept constant. In the k-th update, the update method for each variable is as follows:

[0083]

[0084] (1) Variable Z k+1 The update method.

[0085] With variables E, W, P, Q, and μ fixed, the update method for variable Z is as follows:

[0086]

[0087] Substituting the error function represented by equation (8) into the optimization problem (12), we can obtain

[0088]

[0089] Equation (13) is expressed as the sum of the nuclear norm and two F norms. However, the objective function given by the singular value shrinkage algorithm for this type of problem is in the form of the sum of the nuclear norm and one F norm. Therefore, equation (13) cannot be directly solved using the singular value shrinkage algorithm. Next, we consider merging the two F norms in equation (13). First, for the form of... The expression can be expanded as

[0090]

[0091] Secondly, regarding the form as The expression can be expanded as

[0092]

[0093] Observing equations (14) and (15), the sum of the first three terms related to variable Z is the same, only the constant term unrelated to Z is different. However, when used as the objective function for optimization, the constant term can be ignored. Therefore, it is considered that the two equations above have the same effect in optimization and can be substituted for each other. Based on this, equation (13) can be further simplified to

[0094]

[0095] The minimization problem involving the nuclear norm and the F-norm can be solved using the singular value shrinkage algorithm, and the solution to equation (14) can be expressed as follows:

[0096]

[0097] In the formula Representing the singular value contraction operator, matrices U, V and vector σ are contracted through Γ(Z). k Γ is obtained by performing singular value decomposition. k =Udiag(σ)V H .

[0098] (2) Variable E k+1 The update method.

[0099] With variables Z, W, P, Q, and μ fixed, the update method for variable E is as follows:

[0100]

[0101] The solution to equation (16) is specifically expressed as follows:

[0102]

[0103] In the formula The soft thresholding (ST) operator is defined as follows:

[0104] ST τ (x)=sgn(x)(|x|-τ) (18)

[0105] For complex numbers, This represents the unit direction vector taking complex numbers, i.e.

[0106]

[0107] (3) Variable W k+1 Update method

[0108] With variables Z, E, P, Q, and μ fixed, the update method for variable W is as follows:

[0109]

[0110] Similar to equation (17), the solution to equation (20) can be obtained as follows:

[0111]

[0112] In summary, the specific process for solving the subproblem described by equation (7) is shown in the table.

[0113] The solution process for the subproblem described in Table 2 (7) is as follows:

[0114]

[0115]

[0116] The above solution process can recover the low-rank signal covariance matrix from the sampling covariance matrix obtained in step S101.

[0117] S104: Estimating the direction of arrival of array signals based on a low-rank matrix.

[0118] In one embodiment, direction-of-arrival estimation of the array signal based on a low-rank matrix includes:

[0119] Based on the low-rank matrix, the direction of arrival (DOA) of the array signal is estimated using the MUSIC multi-signal classification algorithm or the ESPRIT rotation-invariant subspace algorithm.

[0120] This application integrates the inherent conjugate symmetry properties of the signal covariance matrix and applies conjugate symmetry constraints simultaneously during the low-rank matrix recovery process. By constructing an optimization model specifically for signal processing scenarios, the recovered covariance matrix not only maintains its low-rank nature but also more strictly conforms to the structural characteristics of the signal covariance matrix, significantly improving matrix recovery accuracy and enhancing the robustness of DOA estimation in complex electromagnetic environments.

[0121] Corresponding to the array signal processing method in the above embodiments, Figure 2 This is a structural block diagram of an array signal processing apparatus provided according to an embodiment of this application. For ease of explanation, only the parts relevant to the embodiment of this application are shown. References Figure 2 The array signal processing device includes: an acquisition unit 201, an optimization model construction unit 202, a low-rank matrix acquisition unit 203, and a direction-of-arrival estimation unit 204, wherein...

[0122] Acquisition unit 201 is used to acquire the sampling covariance matrix of the array signal.

[0123] The optimization model building unit 202 is used to construct the CMSP-TNN optimization model by imposing conjugate symmetry constraints on the sampling covariance matrix.

[0124] The low-rank matrix acquisition unit 203 is used to solve the CMSP-TNN optimization model and obtain the low-rank matrix corresponding to the sampling covariance matrix.

[0125] The direction of arrival estimation unit 204 is used to estimate the direction of arrival of the array signal based on the low-rank matrix.

[0126] The specific functions and execution methods of the array signal processing device in this application are described in the section on array signal processing methods, and will not be repeated here.

[0127] See Figure 3 , Figure 3 This is a schematic block diagram of an electronic device provided according to an embodiment of this application. Figure 3 The electronic device 300 in this embodiment may include one or more processors 301, one or more input devices 302, one or more output devices 303, and one or more memories 304. The processors 301, input devices 302, output devices 303, and memories 304 communicate with each other via a communication bus 305. The memories 304 store computer programs, including program instructions. The processors 301 execute the program instructions stored in the memories 304. Specifically, the processors 301 are configured to invoke the program instructions to perform the functions of each module / unit in the above-described device embodiments, for example... Figure 2 The functions of the acquisition unit 201, the optimization model construction unit 202, the low-rank matrix acquisition unit 203, and the direction of arrival estimation unit 204 are shown.

[0128] It should be understood that, in the embodiments of this application, the processor 301 may be a central processing unit (CPU), but it may also be other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The general-purpose processor may be a microprocessor or any conventional processor.

[0129] Input device 302 may include a touchpad, a fingerprint sensor (for collecting the user's fingerprint information and fingerprint orientation information), a microphone, etc., and output device 303 may include a display (LCD, etc.), a speaker, etc.

[0130] The memory 304 may include read-only memory and random access memory, and provides instructions and data to the processor 301. A portion of the memory 304 may also include non-volatile random access memory. For example, the memory 304 may also store device type information.

[0131] In specific implementations, the processor 301, input device 302, and output device 303 described in the embodiments of this application can execute the implementation method described in the array signal processing method provided in the embodiments of this application, or they can execute the implementation method of the electronic device described in the embodiments of this application, which will not be repeated here.

[0132] In another embodiment of this application, a computer-readable storage medium is provided. This computer-readable storage medium stores a computer program, which includes program instructions. When executed by a processor, the program instructions implement all or part of the processes in the methods described above. Alternatively, the computer program can instruct related hardware to implement these processes. The computer program can be stored in a computer-readable storage medium, and when executed by a processor, it can implement the steps of the various method embodiments described above. The computer program includes computer program code, which can be in the form of source code, object code, executable files, or certain intermediate forms. The computer-readable medium can include any entity or device capable of carrying computer program code, a recording medium, a USB flash drive, a portable hard drive, a magnetic disk, an optical disk, a computer memory, a read-only memory (ROM), a random access memory (RAM), an electrical carrier signal, a telecommunication signal, and a software distribution medium, etc.

[0133] The computer-readable storage medium can be an internal storage unit of the electronic device in any of the foregoing embodiments, such as a hard disk or memory of the electronic device. The computer-readable storage medium can also be an external storage device of the electronic device, such as a plug-in hard disk, smart media card (SMC), secure digital card (SD), flash card, etc., equipped on the electronic device. Furthermore, the computer-readable storage medium can include both internal and external storage units of the electronic device. The computer-readable storage medium is used to store computer programs and other programs and data required by the electronic device. The computer-readable storage medium can also be used to temporarily store data that has been output or will be output.

[0134] This application provides a computer program product, which includes computer-executable instructions or a computer program. The computer-executable instructions or computer program are stored in a computer-readable storage medium. The processor of an electronic device reads the computer-executable instructions from the computer-readable storage medium and executes the computer-executable instructions, causing the electronic device to perform the array signal processing method described in this application embodiment.

[0135] Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, computer software, or a combination of both. To clearly illustrate the interchangeability of hardware and software, the components and steps of the various examples have been generally described in terms of functionality in the foregoing description. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementations should not be considered beyond the scope of this application.

[0136] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the specific working process of the electronic devices and units described above can be referred to the corresponding process in the foregoing method embodiments, and will not be repeated here.

[0137] In the several embodiments provided in this application, it should be understood that the disclosed electronic devices and methods can be implemented in other ways. For example, the device embodiments described above are merely illustrative; for instance, the division of units is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. In addition, the mutual coupling or direct coupling or communication connection shown or discussed may be indirect coupling or communication connection through some interfaces or units, or it may be an electrical, mechanical, or other form of connection.

[0138] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of the embodiments of this application, depending on actual needs.

[0139] Furthermore, the functional units in the various embodiments of this application can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit.

[0140] The above are merely specific embodiments of this application, but the scope of protection of this application is not limited thereto. Any person skilled in the art can easily conceive of various equivalent modifications or substitutions within the technical scope disclosed in this application, and these modifications or substitutions should all be covered within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. An array signal processing method, characterized in that, include: Obtain the sampling covariance matrix of the array signal; A CMSP-TNN optimization model is constructed by imposing conjugate symmetry constraints on the sampling covariance matrix. Solve the CMSP-TNN optimization model to obtain the low-rank matrix corresponding to the sampling covariance matrix; The direction of arrival (DOA) of the array signal is estimated based on the low-rank matrix.

2. The method as described in claim 1, characterized in that, The conjugate symmetry constraint applied to the sampling covariance matrix includes: Minimize the error between the low-rank matrix, the ideal matrix corresponding to the sampling covariance matrix, and the conjugate symmetry function of the sampling covariance matrix.

3. The method as described in claim 2, characterized in that, A CMSP-TNN optimization model is constructed by imposing conjugate symmetry constraints on the sampling covariance matrix, including: By applying conjugate symmetry constraints to the sampling covariance matrix, an error matrix is ​​constructed. The magnitude of the error matrix is ​​calculated using the l1 norm and added to the objective function of the TNN optimization model to obtain the appropriate CMSP-TNN optimization model.

4. The method as described in claim 1, characterized in that, The CMSP-TNN optimization model is as follows: In the formula All are complex matrices, Z is a low-rank matrix, ||Z|| * Let be the nuclear norm of matrix Z, E be a sparse matrix, ||E||1 be the l1 norm of matrix E, X be the sampling covariance matrix, λ and γ be regularization parameters, and tr(AZB) be the normalization parameter. H Let A be the trace of matrix X, and let A and B be the truncated left and right singular matrices of matrix X. N X * J N Let ||ZJ be the error matrix. N X * J N ||1 represents the l1 norm of the error matrix.

5. The method as described in claim 4, characterized in that, Solving the CMSP-TNN optimization model includes: solving the CMSP-TNN optimization model using an iterative method, and further includes: In the first stage, fix matrices Z and E, and calculate matrices A and B; In the second stage, with matrices A and B fixed, matrices Z and E are updated.

6. The method as described in claim 5, characterized in that, In the l-th iteration, the first stage includes: For a fixed Z l and E l Calculate matrix X l =Z l +E l For matrix X l Perform singular value decomposition X l =U l Σ l V l H U l =(u1,u2,...,u M V l =(v1,v2,...,v M ); From U l A is constructed by selecting the left singular vectors corresponding to the first r largest singular values. l From V l B is constructed by selecting the right singular vectors corresponding to the first r largest singular values. l .

7. The method as described in claim 1, characterized in that, The method of estimating the direction of arrival (DOA) of the array signal based on the low-rank matrix includes: Based on the low-rank matrix, the direction of arrival (DOA) of the array signal is estimated using either the MUSIC multi-signal classification algorithm or the ESPRIT rotation-invariant subspace algorithm.

8. An array signal processing device, characterized in that, include: The acquisition unit is used to acquire the sampling covariance matrix of the array signal; The optimization model building unit is used to construct a CMSP-TNN optimization model by applying conjugate symmetry constraints to the sampling covariance matrix; The low-rank matrix acquisition unit is used to solve the CMSP-TNN optimization model to obtain the low-rank matrix corresponding to the sampling covariance matrix. The direction-of-arrival (DOA) estimation unit is used to estimate the DOA of the array signal based on the low-rank matrix.

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

10. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by a processor, it implements the steps of the method as described in any one of claims 1 to 7.

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