A gridless DOA estimation method and device based on cross-grouping semi-positive definite programming

Abstract

The present application provides a gridless DOA estimation method and device based on cross-grouped semi-positive definite programming. The method provided by the present application includes: cross-grouping the MIMO signal matrix to obtain a cross-signal matrix; cross-grouping the first direction matrix and the second direction matrix to obtain a third direction matrix and a fourth direction matrix, respectively calculating the corresponding signal matrix based on the third direction matrix and the fourth direction matrix to obtain a cross-signal matrix; based on the vectorized cross-signal matrix, establishing and solving the atomic norm to obtain the optimal solution; performing eigendecomposition on the optimal solution, and determining the DOA estimation result based on the decomposition result. The method and device provided by the present application are used to adjust the gridless compressed sensing algorithm to adapt to the MIMO system, so as to realize the DOA estimation of the MIMO system.

Description

Technical Field

[0001] The present application relates to the technical field of array signal processing, and in particular to a gridless DOA estimation method and device based on cross-grouped semi-positive definite programming. Background Art

[0002] The classic beam direction of arrival (DOA) estimation algorithm has applications in satellite communications, target detection, voice positioning, sensor networks, etc., and is a research hotspot in the field of array signal processing. The Multiple-Input Multiple-Output (MIMO) system is also widely used in the field of array signal processing. It uses multiple antennas at the transmitter and receiver to greatly increase the system channel capacity to improve communication quality without increasing the channel bandwidth and transmission power. Therefore, it is necessary to perform DOA estimation on the MIMO system to achieve better applications.

[0003] At present, the main DOA estimation algorithms are based on the premise of gridding, and have good estimation performance under ideal conditions. However, in cases of low signal-to-noise ratio, insufficient number of snapshots, sparse signals, signal coupling, etc., there is a large deviation between the theoretical value and the actual value of DOA estimation, resulting in a significant decrease in the resolution of gridded DOA estimation. At the same time, there is also the phenomenon that the overall computational efficiency of gridded DOA estimation is too low. In response to the above problems, gridless DOA estimation algorithms have become an important iterative direction. Using compressed sensing to perform gridless DOA estimation is a current research hotspot. Compared with other gridless DOA estimation algorithms, compressed sensing has the highest resolution, and due to its own compressibility of the signal, the computational efficiency of compressed sensing algorithms is also considerable.

[0004] However, compressed sensing algorithms are only applicable to specific arrays and therefore cannot meet complex engineering requirements. For example, the CCM-ANM algorithm is only applicable to L-type arrays, and researchers need to adjust the algorithm according to the actual flow pattern of the array and the engineering environment. In addition, since the MIMO system itself is composed of multiple antenna elements, its actual flow pattern is more complex than other array systems. It is often necessary to consider both the transmitter and the receiver at the same time, and the coupling between the elements is more complex, with more complex engineering requirements. Therefore, there is an urgent need for a method to adjust the gridless compressed sensing algorithm to adapt to the MIMO system in order to achieve DOA estimation of the MIMO system. Summary of the invention

[0005] In view of this, the present application provides a gridless DOA estimation method and device based on cross-grouped semi-positive definite programming, which adjusts the gridless compressed sensing algorithm to adapt to the MIMO system to achieve DOA estimation of the MIMO system.

[0006] Specifically, the present application is implemented through the following technical solutions:

[0007] The first aspect of the present application provides a gridless DOA estimation method based on cross-grouping semi-positive definite programming, the method comprising:

[0008] Cross-grouping the MIMO signal matrix to obtain a cross signal matrix; wherein the MIMO signal matrix is ​​calculated by a MIMO direction matrix, and the MIMO direction matrix at least includes a first direction matrix of the transmitting array on the X-axis and the Y-axis and a second direction matrix of the receiving array on the X-axis and the Y-axis;

[0009] The first direction matrix and the second direction matrix are cross-grouped to obtain a third direction matrix and a fourth direction matrix, and corresponding signal matrices are calculated based on the third direction matrix and the fourth direction matrix to obtain a cross-signal matrix; the cross-signal matrix includes a first cross-signal matrix and a second cross-signal matrix, the first cross-signal matrix is ​​calculated by the third direction matrix, and the second cross-signal matrix is ​​calculated by the fourth direction matrix;

[0010] Based on the vectorized cross signal matrix, the atomic norm is established and solved to obtain the optimal solution;

[0011] The optimal solution is subjected to eigendecomposition, and an estimation result of the DOA is determined based on the decomposition result.

[0012] The second aspect of the present application provides a gridless DOA estimation device based on cross-grouping semi-positive definite programming, the device comprising a grouping module, a solving module and a determining module; wherein,

[0013] The grouping module is used to cross-group the MIMO signal matrix to obtain a cross signal matrix; wherein the MIMO signal matrix is ​​calculated by a MIMO direction matrix, and the MIMO direction matrix at least includes a first direction matrix of the transmitting array on the X-axis and the Y-axis and a second direction matrix of the receiving array on the X-axis and the Y-axis;

[0014] The first direction matrix and the second direction matrix are cross-grouped to obtain a third direction matrix and a fourth direction matrix, and corresponding signal matrices are calculated based on the third direction matrix and the fourth direction matrix to obtain a cross-signal matrix; the cross-signal matrix includes a first cross-signal matrix and a second cross-signal matrix, the first cross-signal matrix is ​​calculated by the third direction matrix, and the second cross-signal matrix is ​​calculated by the fourth direction matrix;

[0015] The solution module is used to establish and solve the atomic norm based on the vectorized cross signal matrix to obtain the optimal solution;

[0016] The determination module is used to perform eigendecomposition on the optimal solution and determine the DOA estimation result based on the decomposition result.

[0017] The gridless DOA estimation method and device based on cross-grouping semi-positive definite programming provided by the present application obtain a cross-signal matrix by cross-grouping the MIMO signal matrix; further, an atomic norm is established based on the vectorized cross-signal matrix, and the corresponding semi-positive definite programming formula is obtained by solving the atomic norm; further, the semi-positive definite programming formula is solved to obtain the optimal solution, and finally the optimal solution is characteristic decomposed, and the DOA estimation result is determined based on the decomposition result of the optimal solution. On the one hand, by cross-grouping the MIMO signal matrix, the data dimension of the processing can be effectively reduced, thereby reducing the computational complexity, simplifying the calculation steps of the algorithm, and making complex matrix operations more efficient. On the other hand, the cross-signal matrix after cross-grouping can more clearly distinguish the signal components from different signal sources, reduce the interference between signals, and improve the signal-to-noise ratio of the signal, thereby improving the signal processing performance. In addition, different grouping methods can improve the estimation accuracy of DOA, improve the resolution, reduce the error in matrix operations, and improve the accuracy and reliability of the estimation results. Thirdly, for high-dimensional MIMO signal matrices, cross-grouping allows large matrices to be decomposed into multiple smaller matrix blocks for processing, which not only reduces the computational complexity but also makes the processing of high-dimensional data more manageable. By performing local optimization and analysis on the grouped sub-matrices, it can provide higher flexibility and efficiency when processing large-scale data. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Figure 1 A flowchart of Embodiment 1 of a gridless DOA estimation method based on cross-grouping semi-positive definite programming provided in the present application;

[0019] Figure 2 This is a schematic diagram of an external model of a MIMO system shown in an exemplary embodiment of the present application;

[0020] Figure 3 A schematic diagram of a receiving array model shown as an exemplary embodiment of the present application;

[0021] Figure 4 A schematic diagram of an internal model of a MIMO system shown in an exemplary embodiment of the present application;

[0022] Figure 5 This is a structural diagram of Embodiment 1 of a gridless DOA estimation device based on cross-grouped semi-positive definite programming provided in the present application. DETAILED DESCRIPTION

[0023] Here, exemplary embodiments will be described in detail, and examples thereof are shown in the accompanying drawings. When the following description refers to the drawings, unless otherwise indicated, the same numbers in different drawings represent the same or similar elements. The implementations described in the following exemplary embodiments do not represent all implementations consistent with the present application.

[0024] The terms used in this application are only for the purpose of describing specific embodiments and are not intended to limit this application. The singular forms of "a", "said" and "the" used in this application are also intended to include plural forms, unless the context clearly indicates other meanings. It should also be understood that the term "and / or" used in this article refers to and includes any or all possible combinations of one or more associated listed items.

[0025] It should be understood that although the terms first, second, third, etc. may be used in the present application to describe various information, these information should not be limited to these terms. These terms are only used to distinguish the same type of information from each other. For example, without departing from the scope of the present application, the first information may also be referred to as the second information, and similarly, the second information may also be referred to as the first information. Depending on the context, the word "if" as used herein may be interpreted as "at the time of" or "when" or "in response to determining".

[0026] Specific embodiments are given below to introduce the technical solution of the present application in detail.

[0027] Figure 1 This is a flowchart of the first embodiment of the gridless DOA estimation method based on cross-grouping semi-positive definite programming provided by this application. Please refer to Figure 1 , the method provided in this embodiment may include:

[0028] S101. Cross-group a MIMO signal matrix to obtain a cross signal matrix; wherein the MIMO signal matrix is ​​calculated by a MIMO direction matrix, and the MIMO direction matrix at least includes a first direction matrix of a transmitting array on an X-axis and a Y-axis and a second direction matrix of a receiving array on an X-axis and a Y-axis.

[0029] The cross-grouping of the first direction matrix and the second direction matrix includes: detecting the linear array in the X-axis direction and the linear array in the Y-axis direction; extracting the pitch angle of the linear array in the X-axis direction; extracting the azimuth angle of the linear array in the Y-axis direction; calculating the comprehensive array element information based on the orthogonalization of the pitch angle and the azimuth angle; generating the first direction matrix and the second direction matrix based on the comprehensive array element information. For a plane array, the pitch angle signal of the orthogonalized linear array on the X-axis and the azimuth angle information of the linear array on the Y-axis can contain all the array element information of the plane array. After all the information is obtained, grouping processing is performed. On the one hand, the array element information of the plane array is obtained, which improves the comprehensiveness of the information. On the other hand, the array element information is grouped, which reduces the amount of calculation and improves the calculation efficiency.

[0030] Specifically, Figure 2 This is a schematic diagram of an external model of a MIMO system shown in an exemplary embodiment of the present application. Figure 2 , the MIMO system includes a transmitting array and a receiving array, and the transmitting array and the receiving array are symmetrical to each other. The signal is sent from the transmitting array, propagates through the wireless channel, and is received by the receiving array. The MIMO signal matrix represents the signal sent from the transmitting array and the signal received by the receiving array at a certain moment. The MIMO signal matrix is ​​calculated by the MIMO direction matrix. The MIMO direction matrix represents the propagation path of the signal between the transmitting array and the receiving array, which at least includes the first direction matrix of the transmitting array on the X-axis and the Y-axis and the second direction matrix of the receiving array on the X-axis and the Y-axis.

[0031] Optionally, the process of establishing the MIMO direction matrix includes:

[0032] (1) Based on the pitch angle and azimuth angle of the target signal source in the MIMO system, determine the direction vector of the target signal source on the X-axis and Y-axis.

[0033] Specifically, Figure 3 This is a schematic diagram of a receiving array model according to an exemplary embodiment of the present application. Figure 3 , the receiving array has a total of M×N array elements, and the spacing between adjacent array elements is set to , is the wavelength. When there are K signal sources incident on the receiving array, the direction of the target signal source can be expressed as ,in, represents the pitch angle of the target signal source, Represents the direction angle of the target signal source.

[0034] In specific implementation, based on the pitch angle and azimuth angle of the target signal source, the direction vectors of the target signal source on the X-axis and Y-axis are determined by calculating the components of the target signal source in the X-axis and Y-axis directions.

[0035] Furthermore, the direction vector of the target signal source on the X-axis can be expressed as:

[0036] ,

[0037] Among them, the For the The direction vector of the signal on the X-axis; is a complex number i, the square of which is -1; is the spacing between adjacent array elements; For the The pitch angle of the signal; For the The direction angle of the signal; is the wavelength; is the number of array elements on the X-axis.

[0038] The direction vector of the target signal source on the Y axis can be expressed as:

[0039] ,

[0040] Among them, the For the The direction vector of the signal on the Y axis; is a complex number i, the square of which is -1; is the spacing between adjacent array elements; For the The pitch angle of the signal; For the The direction angle of the signal; is the wavelength; is the number of array elements on the Y axis.

[0041] (2) Based on the direction vector of the target signal source on the X-axis and the Y-axis, determine a second direction matrix of the receiving array on the X-axis and the Y-axis.

[0042] In a specific implementation, based on the direction vector of the target signal source on the X-axis, all direction vectors are integrated to obtain a second direction matrix of the receiving array on the X-axis.

[0043] The second direction matrix of the receiving array on the X-axis can be expressed as:

[0044] ,

[0045] Among them, the is the second direction matrix of the receiving array on the X-axis; For the The direction vector of the signal on the X-axis.

[0046] In a specific implementation, based on the direction vector of the target signal source on the Y axis, all direction vectors are integrated to obtain a second direction matrix of the receiving array on the Y axis.

[0047] The second direction matrix of the receiving array on the Y axis can be expressed as:

[0048] ,

[0049] Among them, the is the second direction matrix of the receiving array on the Y axis; For the The direction vector of the signal on the Y axis.

[0050] (3) Based on the second direction matrix, a first direction matrix of the transmitting array on the X-axis and the Y-axis is obtained based on symmetry mapping.

[0051] Specifically, in combination with the above description, the transmitting array and the receiving array are symmetrical to each other. Therefore, the first direction matrix of the transmitting array on the X-axis and the Y-axis is the same as the second direction matrix of the receiving array on the X-axis and the Y-axis, that is, the first direction matrix of the transmitting array on the X-axis can be obtained by the second direction matrix of the receiving array on the X-axis, and the first direction matrix of the transmitting array on the Y-axis can be obtained by the second direction matrix of the receiving array on the Y-axis.

[0052] Further, based on the second direction matrix of the receiving array on the X-axis and the Y-axis, the signal matrix of the receiving array is calculated. The relevant calculation process will be described in the following embodiment and will not be repeated here. The signal matrix of the receiving array can be expressed as:

[0053] ,

[0054] Among them, the is a signal matrix of the receiving array; is the second direction matrix of the receiving array on the Y axis; is the second direction matrix of the receiving array on the X-axis; is a signal vector; is the noise matrix.

[0055] Figure 4 This is a schematic diagram of the internal model of a MIMO system shown in an exemplary embodiment of the present application. Figure 4, the MIMO system includes a transmitting array and a receiving array. The first direction matrix of the transmitting array on the X-axis is , the first direction matrix of the transmitting array on the Y axis is , the first direction matrix of the transmitting array can be expressed as:

[0056] ,

[0057] Among them, the is the first direction matrix of the transmitting array; is the first direction matrix of the transmitting array on the X-axis; It is the first direction matrix of the transmitting array on the Y axis.

[0058] Furthermore, the second direction matrix of the receiving array on the X-axis is , the second direction matrix of the receiving array on the Y axis is , the second direction matrix of the receiving array can be expressed as:

[0059] ,

[0060] Among them, the is the second direction matrix of the receiving array; is the second direction matrix of the receiving array on the X-axis; It is the second direction matrix of the receiving array on the Y axis.

[0061] Based on the first direction matrix of the transmitting array and the second direction matrix of the receiving array, combined with the calculation formula of the signal matrix of the receiving array, the MIMO signal matrix can be expressed as:

[0062] ,

[0063] Among them, the is a MIMO signal matrix; is the first direction matrix of the transmitting array; is the second direction matrix of the receiving array; is a signal vector; is the noise matrix; is the first direction matrix of the transmitting array on the X-axis; is the first direction matrix of the transmitting array on the Y axis; is the second direction matrix of the receiving array on the X-axis; It is the second direction matrix of the receiving array on the Y axis.

[0064] It should be noted that the structure of the MIMO signal matrix is ​​too complex, and it takes too long to establish the atomic norm based on the MIMO signal matrix and then solve the semi-positive definite programming. Therefore, it is necessary to cross-group the MIMO signal matrix and reduce the dimension to reduce the computational complexity of the solution.

[0065] Optionally, the first direction matrix and the second direction matrix are cross-grouped to obtain a third direction matrix and a fourth direction matrix, and corresponding signal matrices are calculated based on the third direction matrix and the fourth direction matrix, respectively, to obtain a cross-signal matrix; the cross-signal matrix includes a first cross-signal matrix and a second cross-signal matrix, the first cross-signal matrix is ​​calculated by the third direction matrix, and the second cross-signal matrix is ​​calculated by the fourth direction matrix.

[0066] In a specific implementation, cross-grouping the MIMO signal matrix to obtain a cross signal matrix includes:

[0067] (1) Determining array element information based on array element layouts of a transmitting array and a receiving array in a MIMO system; the array element information at least includes a response of each array element in different directions.

[0068] Specifically, the array element information refers to the specific data and attributes of each array element in the MIMO system, which usually includes the array element position, array type, array element characteristics, and the response of each array element in different directions. The array element information corresponds to the array element layout of the MIMO system.

[0069] In specific implementation, the coordinates of each array element are calculated based on the array element layout of the transmitting array and the receiving array in the MIMO system. The array element spacing is determined based on the design requirements, which is usually related to the wavelength of the signal. Based on the coordinates and type of the array element, a response matrix is ​​constructed. Based on the response matrix, the array element information of each array element is determined.

[0070] (2) Determining a first orthogonal object of a transmitting array and a second orthogonal object of a receiving array based on the array element information; the cross signal matrix is ​​calculated by the first orthogonal object and the second orthogonal object.

[0071] Specifically, the first orthogonal object of the transmitting array includes the first orthogonal object of the transmitting array on the X axis and the first orthogonal object on the Y axis, and the second orthogonal object of the receiving array includes the second orthogonal object of the receiving array on the X axis and the second orthogonal object on the Y axis.

[0072] In a specific implementation, the first orthogonal object of the transmitting array and the second orthogonal object of the receiving array are determined based on the response of each array element in different directions in the array element information.

[0073] (3) Cross-grouping the first orthogonal object and the second orthogonal object based on the response of each array element in different directions to obtain a third orthogonal object and a fourth orthogonal object; the third orthogonal object and the fourth orthogonal object each include part of the first orthogonal object and the second orthogonal object, and the third orthogonal object and the fourth orthogonal object have different contents.

[0074] Specifically, the third orthogonal object and the fourth orthogonal object combine the first orthogonal object and the second orthogonal object at the same time. Therefore, the third orthogonal object and the fourth orthogonal object both include part of the content of the first orthogonal object and the second orthogonal object, and the content of the third orthogonal object and the fourth orthogonal object are different.

[0075] In a specific implementation, cross-grouping the first orthogonal object and the second orthogonal object based on the response of each array element in different directions to obtain the third orthogonal object and the fourth orthogonal object includes:

[0076] (i) Based on the responses of each array element in different directions, the first orthogonal object and the second orthogonal object are split to obtain a first orthogonal object on the X axis, a first orthogonal object on the Y axis, a second orthogonal object on the X axis, and a second orthogonal object on the Y axis.

[0077] Specifically, in combination with the above description, the first orthogonal object includes a first orthogonal object on the X-axis and a first orthogonal object on the Y-axis. The first orthogonal object is split based on the response of each array element in the transmit array in different directions to obtain the first orthogonal object on the X-axis and the first orthogonal object on the Y-axis.

[0078] Similarly, the second orthogonal object includes a second orthogonal object on the X-axis and a second orthogonal object on the Y-axis. The second orthogonal object is split based on the response of each array element in the receiving array in different directions to obtain the second orthogonal object on the X-axis and the second orthogonal object on the Y-axis.

[0079] (ii) Based on the first orthogonal object on the X-axis and the second orthogonal object on the Y-axis, a third orthogonal object is obtained based on matrix operation.

[0080] In a specific implementation, a Khatri-Rao product operation is performed on the first orthogonal object on the X-axis and the second orthogonal object on the Y-axis to obtain a third orthogonal object. The third orthogonal object can be calculated based on the following formula:

[0081] ,

[0082] Among them, the is the third orthogonal object; is the first orthogonal object on the X-axis; is the second orthogonal object on the Y axis.

[0083] (iii) Based on the second orthogonal object on the X-axis and the first orthogonal object on the Y-axis, a fourth orthogonal object is obtained based on matrix operation.

[0084] In a specific implementation, a Khatri-Rao product operation is performed on the second orthogonal object on the X-axis and the first orthogonal object on the Y-axis to obtain a fourth orthogonal object. The fourth orthogonal object can be calculated based on the following formula:

[0085] ,

[0086] Among them, the is the fourth orthogonal object; is the second orthogonal object on the X-axis; is the first orthogonal object on the Y axis.

[0087] (4) Calculating a cross signal matrix based on the third orthogonal object and the fourth orthogonal object.

[0088] Specifically, the cross signal matrix includes a first cross signal matrix and a second cross signal matrix. The first cross signal matrix is ​​calculated from the third direction matrix, and the second cross signal matrix is ​​calculated from the fourth direction matrix.

[0089] In a specific implementation, the calculating of the cross signal matrix based on the third orthogonal object and the fourth orthogonal object includes:

[0090] (1) Determine a first intermediate matrix based on the product of the third orthogonal object and the signal vector.

[0091] Specifically, the first intermediate matrix can be determined based on the following formula:

[0092] ,

[0093] Among them, the is the first intermediate matrix; is the first orthogonal object on the X-axis; is the second orthogonal object on the Y axis; is the signal vector.

[0094] (2) Add the first intermediate matrix to the noise matrix to obtain a first cross signal matrix.

[0095] Specifically, the first cross signal matrix can be determined based on the following formula:

[0096] ,

[0097] Among them, the is a first cross signal matrix; is the first intermediate matrix; is the noise matrix; is the third orthogonal object; is the first orthogonal object on the X-axis; is the second orthogonal object on the Y axis; is the signal vector.

[0098] (3) Determine a second intermediate matrix based on the product of the fourth orthogonal object and the signal vector.

[0099] Specifically, the second intermediate matrix can be determined based on the following formula:

[0100] ,

[0101] Among them, the is the second intermediate matrix; is the fourth orthogonal object; is the second orthogonal object on the X-axis; is the first orthogonal object on the Y axis; is the signal vector.

[0102] (4) Add the second intermediate matrix to the noise matrix to obtain a second cross signal matrix.

[0103] Specifically, the second cross signal matrix can be determined according to the following formula:

[0104] ,

[0105] Among them, the is a second cross signal matrix; is the second intermediate matrix; is the fourth orthogonal object; is the noise matrix; is the second orthogonal object on the X-axis; is the first orthogonal object on the Y axis; is the signal vector.

[0106] The method provided in this embodiment can effectively reduce the dimension of the processed data by cross-grouping the MIMO signal matrix, thereby reducing the computational complexity, simplifying the calculation steps of the algorithm, and making complex matrix operations more efficient. In addition, the cross-signal matrix after cross-grouping can more clearly distinguish the signal components from different signal sources, reduce the interference between signals, and improve the signal-to-noise ratio of the signal, thereby improving the signal processing performance. Furthermore, different grouping methods can improve the estimation accuracy of DOA, improve the resolution, reduce the error in the matrix operation, and improve the accuracy and reliability of the estimation results. For high-dimensional MIMO signal matrices, cross-grouping allows large matrices to be decomposed into multiple smaller matrix blocks for processing, which not only reduces the computational complexity, but also makes the processing of high-dimensional data more manageable. By locally optimizing and analyzing the grouped sub-matrices, it can provide higher flexibility and efficiency when processing large-scale data.

[0107] S102. Based on the vectorized cross signal matrix, establish and solve the atomic norm to obtain the optimal solution.

[0108] In a specific implementation, the method establishes and solves the atomic norm based on the vectorized cross signal matrix to obtain the optimal solution, including: determining the optimization problem of the atomic norm based on the vectorized cross signal matrix; determining the convex hull and semi-positive definite matrix of the atomic set based on the optimization problem of the atomic norm; converting the optimization problem of the atomic norm into a semi-positive definite programming formula based on the convex hull and semi-positive definite matrix of the atomic set; and solving the semi-positive definite programming formula to obtain the optimal solution.

[0109] Specifically, the cross signal matrix is ​​vectorized and converted into a column vector. The atomic norm is established based on the vectorized cross signal matrix, and the atomic norm can be expressed as:

[0110] ,

[0111] Among them, the Represents a collection of atoms The norm of ; the t represents the objective function; the y represents the cross signal matrix.

[0112] Furthermore, based on the vectorized cross signal matrix, the optimization problem of the atomic norm (including the objective function and constraints) is determined. Based on the determined optimization problem of the atomic norm, the convex hull of the atomic set is determined. The objective function of the atomic norm is represented by a semi-positive definite matrix, and the atomic norm is relaxed based on the optimization problem of the atomic norm. The semi-positive definite matrix and the convex hull of the atomic set are introduced to convert the atomic norm into a convex semi-positive definite programming problem. The semi-positive definite programming formula corresponding to the first cross signal matrix can be expressed as:

[0113] ,

[0114] ,

[0115] Among them, the is the number of array elements of the cross signal matrix on the X-axis; is the number of array elements of the cross signal matrix on the Y axis; is the first group of column vectors of the Toeplitz matrix corresponding to the number of array elements of the first group of signals; is the first group of column vectors of the Toeplitz matrix corresponding to the number of snapshots of the first group of signals; is the first cross signal matrix.

[0116] The semi-positive definite programming formula corresponding to the second cross signal matrix can be expressed as:

[0117] ,

[0118] ,

[0119] Among them, the is the number of array elements of the cross signal matrix on the X-axis; is the number of array elements of the cross signal matrix on the Y axis; is the first group of column vectors of the Toeplitz matrix corresponding to the number of the second group of signal array elements; is the first group of column vectors of the Toeplitz matrix corresponding to the number of snapshots of the second group of signals; is the second cross signal matrix.

[0120] It should be noted that the above process does not take into account the actual noise situation. If the actual noise situation is taken into account, the semi-positive definite programming formula can be expressed as:

[0121] ,

[0122] Among them, the is the number of array elements of the cross signal matrix on the X-axis; is the number of array elements of the cross signal matrix on the Y axis; is the first group of column vectors of the Toeplitz matrix corresponding to the number of signal array elements; is the first group of column vectors of the Toeplitz matrix corresponding to the number of snapshots of the signal; is the regularization parameter; is the signal matrix considering the noise; is the cross signal matrix.

[0123] Furthermore, the optimization problem based on the atomic norm determines the solution method (such as the interior point method, ADMM) and the solution tool (such as MATLAB's CVX, MOSEK). Based on the solution method and solution tool, the semi-positive definite programming formula is solved to obtain the optimal solution. If the optimal solution is a continuous matrix, the matrix is ​​represented as a continuous function through conversion.

[0124] S103: Perform eigendecomposition on the optimal solution, and determine an estimation result of DOA based on the decomposition result.

[0125] In a specific implementation, the performing of characteristic decomposition on the optimal solution and determining the estimation result of DOA based on the decomposition result includes:

[0126] (1) Performing eigendecomposition on the optimal solution and establishing a spatial spectrum function based on the decomposition result.

[0127] In a specific implementation, the optimal solution is subjected to characteristic decomposition, and a spatial spectrum function is established based on the decomposition result, including:

[0128] (i) performing eigendecomposition on the optimal solution based on a Vandermonde determinant decomposition method to obtain a characteristic matrix; the characteristic matrix at least includes an eigenvector matrix of the noise subspace.

[0129] Specifically, the characteristic matrix includes an eigenvector matrix of the signal subspace, an eigenvalue diagonal matrix of the signal subspace, an eigenvector matrix of the noise subspace, and an eigenvalue diagonal matrix of the noise subspace.

[0130] In the specific implementation, the optimal solution is analyzed based on the Vandermonde determinant decomposition method, and the optimal solution is characteristic decomposed to obtain the eigenvector matrix and the eigenvalue diagonal matrix. The characteristic decomposition can be performed based on the following formula:

[0131] ,

[0132] Among them, the is the optimal solution; is the eigenvector matrix of the signal subspace; is the eigenvalue diagonal matrix of the signal subspace; is the eigenvector matrix of the noise subspace; is the diagonal matrix of eigenvalues ​​of the noise subspace;

[0133] ,

[0134] Among them, the is the optimal solution; is the eigenvector matrix of the signal subspace; is the eigenvalue diagonal matrix of the signal subspace; is the eigenvector matrix of the noise subspace; is the diagonal matrix of eigenvalues ​​of the noise subspace.

[0135] (ii) Establishing a spatial spectrum function based on the eigenvector matrix of the noise subspace and the cross signal matrix.

[0136] In specific implementation, the spatial spectrum function is established based on the following formula:

[0137] ,

[0138] Among them, the is the spatial spectrum function; is the eigenvector matrix of the noise subspace; is the first orthogonal object on the X-axis; is the second orthogonal object on the Y axis.

[0139] ,

[0140] Among them, the is the spatial spectrum function; is the eigenvector matrix of the noise subspace; is the second orthogonal object on the X-axis; is the first orthogonal object on the Y axis.

[0141] (2) A peak value in the spatial spectrum function is determined based on a peak search, and an estimation result of the DOA is determined based on the position of the peak value.

[0142] In specific implementation, a two-dimensional angle search is performed on each spatial spectrum function to determine a preset number (the preset number is set according to actual needs and is not limited in this embodiment) of peaks, and an estimated result of the DOA of each spatial spectrum function is obtained based on the positions of these peaks. All DOA estimation results are solved to obtain the final angle estimation value.

[0143] Furthermore, the final angle estimate can be expressed as:

[0144] ,

[0145] ,

[0146] Among them, the is the pitch angle; is the direction angle; is the pitch angle corresponding to the peak value of the spatial spectrum function; is the direction angle corresponding to the peak value of the spatial spectrum function.

[0147] The method provided in this embodiment, on the one hand, effectively reduces the dimension of calculation by performing characteristic decomposition on the optimal solution, thereby reducing the computational complexity of subsequent DOA estimation; on the other hand, the peak value is determined by peak searching, and then the DOA is determined by integrating the results of all DOA estimations. This can determine the possible signal source direction at a lower computational cost without having to conduct a comprehensive search of the entire high-dimensional space, thereby improving computational efficiency, enhancing the accuracy of DOA estimation, being able to process multi-source signals, and simplifying the optimization process.

[0148] The method provided in this embodiment, on the one hand, can effectively reduce the dimension of the processed data by cross-grouping the MIMO signal matrix, thereby reducing the computational complexity, simplifying the calculation steps of the algorithm, and making complex matrix operations more efficient. On the second hand, the cross-signal matrix after cross-grouping can more clearly distinguish the signal components from different signal sources, reduce the interference between signals, and improve the signal-to-noise ratio of the signal, thereby improving the signal processing performance. In addition, different grouping methods can improve the estimation accuracy of DOA, improve the resolution, reduce the error in the matrix operation, and improve the accuracy and reliability of the estimation results. On the third hand, for high-dimensional MIMO signal matrices, cross-grouping allows the large matrix to be decomposed into multiple smaller matrix blocks for processing, which not only reduces the computational complexity, but also makes the processing of high-dimensional data more manageable. By locally optimizing and analyzing the grouped sub-matrices, it can provide higher flexibility and efficiency when processing large-scale data. Fourthly, by determining the DOA through eigendecomposition and peak search of the optimal solution, the dimension of calculation is effectively reduced, the computational complexity of subsequent DOA estimation can be reduced, and the possible signal source direction can be determined at a lower computational cost without having to conduct a comprehensive search of the entire high-dimensional space. This improves computational efficiency, enhances the accuracy of DOA estimation, can process multi-source signals, and simplifies the optimization process.

[0149] Corresponding to the aforementioned embodiment of a gridless DOA estimation method based on cross-grouped semi-positive definite programming, the present application also provides an embodiment of a gridless DOA estimation device based on cross-grouped semi-positive definite programming.

[0150] Figure 5 This is a structural diagram of the first embodiment of the gridless DOA estimation device based on cross-grouping semi-positive definite programming provided by the present application. Figure 5 , the device provided in this embodiment includes a grouping module 510, a solving module 520 and a determining module 530; wherein,

[0151] The grouping module 510 is used to cross-group the MIMO signal matrix to obtain a cross signal matrix; wherein the MIMO signal matrix is ​​calculated by a MIMO direction matrix, and the MIMO direction matrix at least includes a first direction matrix of the transmitting array on the X-axis and the Y-axis and a second direction matrix of the receiving array on the X-axis and the Y-axis;

[0152] The first direction matrix and the second direction matrix are cross-grouped to obtain a third direction matrix and a fourth direction matrix, and corresponding signal matrices are calculated based on the third direction matrix and the fourth direction matrix to obtain a cross-signal matrix; the cross-signal matrix includes a first cross-signal matrix and a second cross-signal matrix, the first cross-signal matrix is ​​calculated by the third direction matrix, and the second cross-signal matrix is ​​calculated by the fourth direction matrix;

[0153] The solving module 520 is used to establish and solve the atomic norm based on the vectorized cross signal matrix to obtain the optimal solution;

[0154] The determination module 530 is used to perform eigendecomposition on the optimal solution and determine the DOA estimation result based on the decomposition result.

[0155] The device of this embodiment can be used to perform Figure 1 The steps, specific implementation principles and implementation processes of the method embodiment shown are similar and will not be repeated here.

[0156] The implementation process of the functions and effects of each unit in the above-mentioned device is specifically described in the implementation process of the corresponding steps in the above-mentioned method, and will not be repeated here.

[0157] For the device embodiment, since it basically corresponds to the method embodiment, the relevant parts can refer to the partial description of the method embodiment. The device embodiment described above is only schematic, wherein the units described as separate components may or may not be physically separated, and the components displayed as units may or may not be physical units, that is, they may be located in one place, or they may be distributed on multiple network units. Some or all of the modules may be selected according to actual needs to achieve the purpose of the present application scheme. A person of ordinary skill in the art can understand and implement it without paying any creative work.

[0158] The above description is only a preferred embodiment of the present application and is not intended to limit the present application. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present application shall be included in the scope of protection of the present application.

Claims

1. A gridless DOA estimation method based on cross-grouping semi-positive definite programming, characterized in that: The method comprises: Cross-grouping the MIMO signal matrix to obtain a cross signal matrix; wherein the MIMO signal matrix is ​​calculated by a MIMO direction matrix, and the MIMO direction matrix at least includes a first direction matrix of the transmitting array on the X-axis and the Y-axis and a second direction matrix of the receiving array on the X-axis and the Y-axis; The first direction matrix and the second direction matrix are cross-grouped to obtain a third direction matrix and a fourth direction matrix, and corresponding signal matrices are calculated based on the third direction matrix and the fourth direction matrix to obtain a cross-signal matrix; the cross-signal matrix includes a first cross-signal matrix and a second cross-signal matrix, the first cross-signal matrix is ​​calculated by the third direction matrix, and the second cross-signal matrix is ​​calculated by the fourth direction matrix; Wherein, based on the array element layout of the transmitting array and the receiving array in the MIMO system, the first orthogonal object on the X-axis and the first orthogonal object on the Y-axis of the first direction matrix are determined, and based on the array element layout, the second orthogonal object on the X-axis and the second orthogonal object on the Y-axis of the second direction matrix are determined; the first orthogonal object on the X-axis and the second orthogonal object on the Y-axis are subjected to a matrix operation to obtain a third orthogonal object, and the second orthogonal object on the X-axis and the first orthogonal object on the Y-axis are subjected to a matrix operation to obtain a fourth orthogonal object; the product of the third orthogonal object and the signal vector and the sum of the third orthogonal object and the noise matrix are determined as the first cross signal matrix, and the product of the fourth orthogonal object and the signal vector and the sum of the fourth orthogonal object and the noise matrix are determined as the second cross signal matrix; Based on the vectorized cross signal matrix, the atomic norm is established and solved to obtain the optimal solution; The optimal solution is subjected to Vandermonde determinant decomposition, and a peak search is performed on the decomposition result to determine the estimation result of the DOA.

2. The method according to claim 1, characterized in that The cross-grouping of the MIMO signal matrix to obtain a cross-signal matrix includes: Determine array element information based on the array element layout of the transmitting array and the receiving array in the MIMO system; the array element information at least includes the response of each array element in different directions; Determine a first orthogonal object of a transmitting array and a second orthogonal object of a receiving array based on the array element information; the cross signal matrix is ​​calculated by the first orthogonal object and the second orthogonal object; Cross-grouping the first orthogonal object and the second orthogonal object based on the response of each array element in different directions to obtain a third orthogonal object and a fourth orthogonal object; the third orthogonal object and the fourth orthogonal object each include part of the first orthogonal object and the second orthogonal object, and the third orthogonal object and the fourth orthogonal object have different contents; A cross signal matrix is ​​calculated based on the third and fourth orthogonal objects.

3. The method according to claim 2, characterized in that The cross-grouping of the first and second orthogonal objects based on the responses of each array element in different directions to obtain a third and fourth orthogonal objects includes: Based on the responses of each array element in different directions, the first orthogonal object and the second orthogonal object are split to obtain a first orthogonal object on the X axis, a first orthogonal object on the Y axis, a second orthogonal object on the X axis, and a second orthogonal object on the Y axis.

4. The method according to claim 1, characterized in that: The method of establishing and solving the atomic norm based on the vectorized cross signal matrix to obtain the optimal solution includes: Based on the vectorized cross-signal matrix, the optimization problem of the atomic norm is determined; Determine the convex hull and semi-positive definite matrix of the set of atoms based on the optimization problem of the atomic norm; Based on the convex hull and semi-positive definite matrix of the atomic set, converting the optimization problem of the atomic norm into a semi-positive definite programming formula; Solve the semi-positive definite programming formula to obtain the optimal solution.

5. The method according to claim 1, characterized in that The step of performing Vandermonde determinant decomposition on the optimal solution and performing peak search on the decomposition result to determine the DOA estimation result includes: Performing eigendecomposition on the optimal solution based on the Vandermonde determinant decomposition method to obtain a characteristic matrix; the characteristic matrix at least includes an eigenvector matrix of the noise subspace; Establishing a spatial spectrum function based on the eigenvector matrix of the noise subspace and the cross signal matrix; A peak value in the spatial spectrum function is determined based on a peak search, and an estimation result of the DOA is determined based on the position of the peak value.

6. The method according to claim 1, characterized in that The process of establishing the MIMO direction matrix includes: Based on the pitch angle and azimuth angle of the target signal source in the MIMO system, determining the direction vector of the target signal source on the X-axis and the Y-axis; Based on the direction vector of the target signal source on the X-axis and the Y-axis, determining a second direction matrix of the receiving array on the X-axis and the Y-axis; Based on the second direction matrix, a first direction matrix of the transmitting array on the X-axis and the Y-axis is obtained based on symmetry mapping.

7. The method according to claim 1, characterized in that The cross-grouping of the first direction matrix and the second direction matrix comprises: Detect the linear array in the X-axis direction and the linear array in the Y-axis direction; Extracting the pitch angle of the linear array in the X-axis direction; Extracting the direction angle of the linear array in the Y-axis direction; Orthogonal calculation of integrated array element information based on the pitch angle and the azimuth angle; The first direction matrix and the second direction matrix are generated based on the comprehensive array element information.

8. A gridless DOA estimation device based on cross-grouping semi-positive definite programming, characterized in that: The device comprises a grouping module, a solving module and a determining module; wherein, The grouping module is used to cross-group the MIMO signal matrix to obtain a cross signal matrix; wherein the MIMO signal matrix is ​​calculated by a MIMO direction matrix, and the MIMO direction matrix at least includes a first direction matrix of the transmitting array on the X-axis and the Y-axis and a second direction matrix of the receiving array on the X-axis and the Y-axis; The first direction matrix and the second direction matrix are cross-grouped to obtain a third direction matrix and a fourth direction matrix, and corresponding signal matrices are calculated based on the third direction matrix and the fourth direction matrix to obtain a cross-signal matrix; the cross-signal matrix includes a first cross-signal matrix and a second cross-signal matrix, the first cross-signal matrix is ​​calculated by the third direction matrix, and the second cross-signal matrix is ​​calculated by the fourth direction matrix; Wherein, based on the array element layout of the transmitting array and the receiving array in the MIMO system, the first orthogonal object on the X-axis and the first orthogonal object on the Y-axis of the first direction matrix are determined, and based on the array element layout, the second orthogonal object on the X-axis and the second orthogonal object on the Y-axis of the second direction matrix are determined; the first orthogonal object on the X-axis and the second orthogonal object on the Y-axis are subjected to a matrix operation to obtain a third orthogonal object, and the second orthogonal object on the X-axis and the first orthogonal object on the Y-axis are subjected to a matrix operation to obtain a fourth orthogonal object; the product of the third orthogonal object and the signal vector and the sum of the third orthogonal object and the noise matrix are determined as the first cross signal matrix, and the product of the fourth orthogonal object and the signal vector and the sum of the fourth orthogonal object and the noise matrix are determined as the second cross signal matrix; The solution module is used to establish and solve the atomic norm based on the vectorized cross signal matrix to obtain the optimal solution; The determination module is used to perform Vandermonde determinant decomposition on the optimal solution, and perform peak search on the decomposition result to determine the estimation result of DOA.

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