A rank-minimizing coherent signal DOA estimation method based on sparse array

Abstract

The invention discloses a rank-minimized coherent signal DOA estimation method based on a sparse array. First, the covariance matrix of the array output vector is solved and the maximum eigenvalue and its corresponding eigenvector are found through eigendecomposition. Then, a selection matrix from a uniform array to a sparse array is constructed, and the selection matrix is ​​right-shifted by the least square method to obtain a reconstructed eigenvector. Then, the reconstructed eigenvector is rearranged to obtain a rearranged matrix, and the rank-minimized property of the rearranged matrix is ​​used to solve the matrix with the minimum rank. Finally, the MUSIC method is applied to the minimum rank matrix to obtain the DOA estimation value of the coherent signal. The method of the invention does not need to vectorize the covariance matrix of the sparse array, and can utilize the conversion relationship between the sparse array and the uniform array, and utilize the rank minimization method and the corresponding estimation method to obtain the DOA estimation value of the coherent signal. The method does not need additional physical hardware and is easy to implement in engineering and apply in practice.

Description

Technical Field

[0001] The present invention relates to the technical field of sparse array direction estimation, and in particular to a rank-minimizing coherent signal DOA estimation method based on a sparse array. Background Art

[0002] In the field of array signal processing, the use of sparse arrays to estimate the direction of incident signals has attracted much attention from the scientific research community and the industry. The reason is that compared with uniform arrays, sparse arrays have larger element spacing and larger array apertures when the number of array elements is the same, which can effectively reduce the mutual coupling effect between array elements and improve the accuracy and resolution of azimuth estimation. However, current research and applications on sparse arrays are mainly focused on scenarios where the incident signal is incoherent, while research on using sparse arrays to estimate the angle of arrival of coherent signals is not yet mature, which limits the application of sparse arrays in practice. Therefore, the problem of estimating the angle of arrival of coherent signals in sparse arrays needs to be solved urgently. Summary of the invention

[0003] The technical problem to be solved by the present invention is to provide a rank-minimized coherent signal DOA estimation method based on a sparse array in view of the defects involved in the background technology.

[0004] The present invention adopts the following technical solutions to solve the above technical problems:

[0005] A rank-minimized coherent signal DOA estimation method based on a sparse array, the method comprising:

[0006] Step 1), find the covariance matrix R of the received vector of the sparse array xx ;

[0007] The array element position set of the sparse array N is the total number of array elements, l 1 ,l 2 ,...,l N is the position of each element of the sparse array, d is the unit spacing of the element, which is set to half the half wavelength of the incident signal, the received signal vector of the array is x(t)=CAs(t)+n(t), C is the mutual coupling matrix, c l =c 1 e -j(l-1)π / 8 / l(l∈[2,4]) is the mutual coupling coefficient, c 1 =0.4, c 0 =1>c 1 >c 2 >... >c 4 >0;

[0008] K represents the number of coherent sources, λ is the wavelength of the incident signal, s(t) is the signal vector, and n(t) is the zero-mean Gaussian white noise vector;

[0009] The array receives the covariance matrix R of the vector xx =X(t)X H (t) = AR ss A H +δI,R ss is the covariance of the signal vector; δ is the noise energy, which is equal to R xx The minimum eigenvalue obtained after eigendecomposition; I is the identity matrix;

[0010] Step 2), for R xx Perform eigendecomposition to obtain the maximum eigenvalue γ and the corresponding eigenvector e 1 and the minimum eigenvalue σ 2 ;

[0011] Step 3), constructing a selection matrix T according to the positional relationship between the uniform linear array and the sparse array elements;

[0012] The element position set of the uniform linear array is

[0013] The number of rows of T is equal to the number of elements in the uniform linear array, the number of columns of T is equal to the number of elements in the sparse array, and only the lth element in the pth column of T p +1 row element is 1, the rest of the elements are 0, l p is the position of the pth array element in the sparse array, where p is a natural number greater than or equal to 1 and less than or equal to the number of array elements in the sparse array;

[0014] Step 4), using the least squares method, represents the direction matrix of the uniform linear array, for e 1 Left multiplication matrix (T H T-εI) -1 T H (γ-σ 2 ) is to obtain the reconstructed vector g, ε is a preset small constant and ε is a real number;

[0015] Step 5), add the qth to the lth N -v+q elements are arranged in a column as the column vector x of the matrix X q , l N is the position of the last element of the sparse array, For the rounding operation, q is a natural number greater than or equal to 1 and less than or equal to v. Finally, the matrix X = [x 1 ,x 2 ,...,x v ];

[0016] Step 6), minimize the rank of X and obtain the minimum rank matrix X m ;

[0017] Step 7) m As the covariance matrix of the signal, the MUSIC method is used to obtain the final angle estimate.

[0018] As a further optimization scheme of the rank minimization coherent signal DOA estimation method based on sparse array of the present invention, in step 2), R is calculated according to the following formula: xx Perform eigendecomposition:

[0019] R xx e 1 =γe 1 →AR ss A H e 1 =(γ-σ 2 ) 1 .

[0020] As a further optimization scheme of the rank-minimized coherent signal DOA estimation method based on a sparse array of the present invention, in step 6), the rank of X is minimized according to the following formula:

[0021]

[0022] subject to X m *S=X

[0023] Where S is a matrix with the same number of rows and columns as X. The value of the element in S that has the same position as the non-zero value in X is 1, and the value of the element in S that has the same position as the zero value in X is 0.

[0024] Compared with the prior art, the present invention adopts the above technical solution and has the following technical effects:

[0025] The method of the present invention does not need to vectorize the signal covariance matrix, and finds the maximum eigenvalue and its corresponding eigenvector through eigendecomposition; utilizes the conversion relationship between the dilute array and the uniform array, and uses the least squares method to obtain the reconstructed eigenvector; rearranges the eigenvectors, and uses the property of minimizing the rank of the rearranged matrix to solve the matrix with the minimum rank; applies the MUSIC method to the minimum rank matrix to obtain the DOA estimate of the coherent signal. The method of the present invention can accurately estimate the arrival angle of a fully coherent incident signal using a sparse array without adding physical array elements. It is suitable for scenes with coherent signals and can obtain the incident angle of the coherent signal with high precision. In addition, the method does not require additional physical hardware and is easy to implement in engineering and practical applications. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] Figure 1 It is a schematic diagram of the process of the present invention;

[0027] Figure 2 is the array element position of the sparse array of the present invention;

[0028] Figure 3 This is a performance diagram of angle estimation under different signal-to-noise ratios of the present invention;

[0029] Figure 4 This is a graph showing the angle estimation performance of the present invention as it changes with snapshots. DETAILED DESCRIPTION

[0030] The technical solution of the present invention is further described in detail below in conjunction with the accompanying drawings:

[0031] The present invention can be implemented in many different forms and should not be considered to be limited to the embodiments described herein. On the contrary, these embodiments are provided to make this disclosure thorough and complete, and will fully express the scope of the present invention to those skilled in the art. In the accompanying drawings, components are enlarged for clarity.

[0032] like Figure 1 As shown, the present invention discloses a rank-minimized coherent signal DOA estimation method based on a sparse array, the method comprising:

[0033] Step 1), find the covariance matrix R of the received vector of the sparse array xx ;

[0034] The array element position set of the sparse array N is the total number of array elements, l 1 ,l 2 ,...,l N is the position of each element of the sparse array, d is the unit spacing of the element, which is set to half the half wavelength of the incident signal, the received signal vector of the array is x(t)=CAs(t)+n(t), C is the mutual coupling matrix, c l =c 1 e -j(l-1)π / 8 / l(l∈[2,4]) is the mutual coupling coefficient, c 1 =0.4, c 0 =1>c 1 >c 2 >... >c 4 >0;

[0035] K represents the number of coherent sources, λ is the wavelength of the incident signal, s(t) is the signal vector, and n(t) is the zero-mean Gaussian white noise vector;

[0036] The array receives the covariance matrix R of the vector xx =X(t)X H (t) = AR ss A H +δI,R ss is the covariance of the signal vector; δ is the noise energy, which is equal to R xx The minimum eigenvalue obtained after eigendecomposition; I is the identity matrix;

[0037] Step 2), for R xx Perform eigendecomposition to obtain the maximum eigenvalue γ and the corresponding eigenvector e 1 and the minimum eigenvalue σ 2 , the formula for characteristic decomposition is as follows:

[0038] R xx e 1 =γe 1 →AR ss A H e 1 =(γ-σ 2 ) 1

[0039] Step 3), constructing a selection matrix T according to the positional relationship between the uniform linear array and the sparse array elements;

[0040] The element position set of the uniform linear array is

[0041] The number of rows of T is equal to the number of elements in the uniform linear array, the number of columns of T is equal to the number of elements in the sparse array, and only the lth element in the pth column of T p +1 row element is 1, the rest of the elements are 0, l p is the position of the pth array element in the sparse array, where p is a natural number greater than or equal to 1 and less than or equal to the number of array elements in the sparse array;

[0042] Step 4), using the least squares method, represents the direction matrix of the uniform linear array, for e 1 Left multiplication matrix (T H T-εI) -1 T H (γ-σ 2 ) is to obtain the reconstructed vector g, ε is a preset small constant and ε is a real number;

[0043] Step 5), add the qth to the lth N -v+q elements are arranged in a column as the column vector x of the matrix X q , l N is the position of the last element of the sparse array, For the rounding operation, q is a natural number greater than or equal to 1 and less than or equal to v. Finally, the matrix X = [x 1 ,x 2 ,...,x v ];

[0044] Step 6), minimize the rank of X and obtain the minimum rank matrix X m , the specific formula is as follows:

[0045]

[0046] subject to X m *S=X

[0047] Where S is a matrix with the same number of rows and columns as X. The value of the element in S that has the same position as the non-zero value in X is 1, and the value of the element in S that has the same position as the zero value in X is 0;

[0048] Step 7) m As the covariance matrix of the signal, the MUSIC method is used to obtain the final angle estimate.

[0049] In order to verify the correctness and advancement of the method in this embodiment, Figure 2 As shown in the figure, assume that the array element position set of the sparse array is {0,5,10,15,20,25,30,35,43,51,59,67}*0.5, the incident signal wavelength is set to 1, the unit element spacing is 0.5, and assume that there are two coherent signals incident on the array from angles of 10° and 40°, and perform a simulation experiment. Figure 3 As shown in Figure 1, compared with other methods, the array using this method has a higher DOA estimation accuracy, and as the signal-to-noise ratio changes, the estimation accuracy also improves. Figure 4 As shown in FIG. 1 , as the number of snapshots changes, the estimation performance of the method becomes better. Meanwhile, compared with other methods, the estimation performance of the method is also better.

[0050] In summary, the present invention proposes a rank-minimized coherent signal DOA estimation method based on a sparse array. In the scenario where the incident signal is a coherent signal, the present method can accurately estimate the incident angle of the coherent signal. The method of the present invention does not need to vectorize the signal covariance matrix. Through eigendecomposition, the maximum eigenvalue and its corresponding eigenvector are found; the conversion relationship between the dilute array and the uniform array is used to obtain the reconstructed eigenvector using the least squares method; the eigenvector is rearranged, and the rank minimization property of the rearranged matrix is ​​used to solve the matrix with the minimum rank; the MUSIC method is applied to the minimum rank matrix to obtain the DOA estimation value of the coherent signal; the method of the present invention is suitable for the scenario of coherent signals, and can obtain the incident angle of the coherent signal with high precision. The method does not require additional physical hardware and is easy to implement in engineering and practical application.

[0051] It will be understood by those skilled in the art that, unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as those generally understood by those skilled in the art in the art to which the present invention belongs. It should also be understood that terms such as those defined in common dictionaries should be understood to have meanings consistent with the meanings in the context of the prior art, and will not be interpreted with idealized or overly formal meanings unless defined as herein.

[0052] The specific implementation methods described above further illustrate the objectives, technical solutions and beneficial effects of the present invention in detail. It should be understood that the above description is only a specific implementation method of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A rank-minimizing coherent signal DOA estimation method based on sparse array, characterized in that: The method comprises: Step 1), find the covariance matrix R of the received vector of the sparse array xx ; The array element position set of the sparse array N is the total number of array elements, l1,l2,...,l N is the position of each element of the sparse array, d is the unit spacing of the element, which is set to half the half wavelength of the incident signal, the received signal vector of the array is x(t)=CAs(t)+n(t), C is the mutual coupling matrix, c l =c1e -j(l-1)π / 8 / l is the mutual coupling coefficient, where l∈[2,4], |c1|=0.4, c0=1>|c1|>|c2|>...>|c4|>0; k∈[1,2,...,K], K represents the number of coherent sources, λ is the wavelength of the incident signal, s(t) is the signal vector, and n(t) is the zero-mean Gaussian white noise vector; The array receives the covariance matrix R of the vector xx =X(t)X H (t) = AR ss A H +δI,R ss is the covariance of the signal vector; δ is the noise energy, which is equal to R xx The minimum eigenvalue obtained after eigendecomposition; I is the identity matrix; Step 2), for R xx Perform eigendecomposition to obtain the maximum eigenvalue γ and the corresponding eigenvector e1 and the minimum eigenvalue σ 2 ; Step 3), constructing a selection matrix T according to the positional relationship between the uniform linear array and the sparse array elements; The element position set of the uniform linear array is The number of rows of T is equal to the number of elements in the uniform linear array, the number of columns of T is equal to the number of elements in the sparse array, and only the lth element in the pth column of T p +1 row element is 1, the rest of the elements are 0, l p is the position of the pth array element in the sparse array, where p is a natural number greater than or equal to 1 and less than or equal to the number of array elements in the sparse array; Step 4), using the least squares method, Represents the direction matrix of the uniform linear array, multiply e1 by the matrix (T H T-εI) -1 T H (γ-σ 2 ) is to obtain the reconstructed vector g, ε is a preset small constant and ε is a real number; Step 5), add the qth to the lth N -v+q elements are arranged in a column as the column vector x of the matrix X q , l N is the position of the last element of the sparse array, is a rounding operation, q is a natural number greater than or equal to 1 and less than or equal to v, and the final matrix X = [x1, x2, ..., x v ]; Step 6), minimize the rank of X and obtain the minimum rank matrix X m ; Step 7) m As the covariance matrix of the signal, the MUSIC method is used to obtain the final angle estimate.

2. The rank-minimized coherent signal DOA estimation method based on sparse array according to claim 1, characterized in that: In step 2), R is calculated according to the following formula xx Perform eigendecomposition: R xx e1=γe1→AR ss From H e1=(γ-σ 2 )e1.

3. The rank-minimized coherent signal DOA estimation method based on sparse array according to claim 2, characterized in that: In step 6), the rank of X is minimized according to the following formula: subject to X m *S=X Where S is a matrix with the same number of rows and columns as X. The value of the element in S that has the same position as the non-zero value in X is 1, and the value of the element in S that has the same position as the zero value in X is 0.

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