Complex scene DOA estimation method based on matrix reconstruction

Abstract

The invention belongs to the technical field of signal processing. The invention provides a complex scene DOA estimation method based on matrix reconstruction. The method comprises the following steps: acquiring a received signal, and obtaining a signal covariance matrix of the received signal according to the received signal; performing eigenvalue decomposition on the signal covariance matrix to obtain a signal eigenvector corresponding to the signal subspace; extracting a maximum signal feature vector corresponding to a maximum feature value of the signal feature vectors, and performing element rearrangement on the maximum signal feature vector to obtain a reconstruction matrix; and performing DOA estimation based on the reconstruction matrix in combination with a Root-MUSIC algorithm based on polynomial reconstruction so as to obtain a DOA estimation value. According to the embodiment of the invention, the correction matrix is a square matrix, and DOA estimation in a complex scene can be realized only through eigenvalue decomposition. Moreover, the method is high in success probability, is lower in signal-to-noise ratio threshold, and is good in estimation performance.

Description

Technical Field

[0001] The disclosed embodiments relate to the field of signal processing technology, and in particular to a complex scene DOA estimation method based on matrix reconstruction. Background Art

[0002] In a complex electromagnetic environment, radar targets, multipath effects, coherent decoys and other independent radiation sources coexist. When the signals are strongly correlated or completely coherent, subspace entanglement will occur. The performance of the traditional subspace-based algorithm for estimating the direction of arrival (DOA) of the source will drop sharply or even fail in the presence of coherent or highly correlated signals. Spatial smoothing algorithms and matrix reconstruction algorithms based on decomposition can effectively estimate coherent sources. Although the performance of matrix reconstruction algorithms is better than that of spatial smoothing algorithms, their corrected covariance matrix is ​​a rectangular matrix and needs to be decomposed by singular value. The maximum likelihood method has a good decoherence effect, but the implementation process is complicated and requires multi-dimensional search, and the DOA direction finding is greatly affected by the initial value. Although sparse reconstruction algorithms based on compressed sensing theory or spatial sparsity concepts are not sensitive to the coherent source environment, the extremely large amount of computation of the algorithm hinders its engineering practical application.

[0003] Therefore, it is necessary to improve one or more problems existing in the above-mentioned related technical solutions.

[0004] It should be noted that this section is intended to provide background or context for the technical solutions of the present disclosure stated in the claims. The description herein is not admitted to be prior art by virtue of being included in this section. Summary of the invention

[0005] The purpose of the embodiments of the present disclosure is to provide a complex scene DOA estimation method based on matrix reconstruction, thereby overcoming one or more problems caused by the limitations and defects of related technologies at least to a certain extent.

[0006] According to an embodiment of the present disclosure, a complex scene DOA estimation method based on matrix reconstruction is provided, the method comprising:

[0007] Acquire a received signal, and obtain a signal covariance matrix of the received signal based on the received signal;

[0008] Performing eigenvalue decomposition on the signal covariance matrix to obtain a signal eigenvector corresponding to the signal subspace;

[0009] Extracting a maximum signal feature vector corresponding to a maximum eigenvalue of the signal feature vector, and rearranging elements of the maximum signal feature vector to obtain a reconstruction matrix;

[0010] Based on the reconstruction matrix, the DOA estimation is performed in combination with the Root-MUSIC algorithm based on polynomial reconstruction to obtain a DOA estimation value.

[0011] Further, the step of obtaining a received signal and obtaining a signal covariance matrix of the received signal based on the received signal includes:

[0012] Acquire the received signal using a uniform linear array receiving array having N array elements and d array element spacing;

[0013] The received signal is solved using a covariance matrix equation of the array received signal to obtain the signal covariance matrix of the received signal.

[0014] Furthermore, the expression of the received signal is:

[0015]

[0016] Where s0(t) is the complex envelope of the desired signal, a(θ0) is the steering vector of the desired signal, and s l (t) is the composite envelope of the desired signal multipath, a(θ l ),l=1,2,…,L is the steering vector of the desired signal multipath, s l (t) = β l s0(t),β l is the composite envelope s of the lth desired signal multipath l (t) is the attenuation factor of the complex envelope s0(t) of the desired signal, g v is the composite envelope of the incoherent interference signal, a(θ v ) is the steering vector of the incoherent interference signal, and N(t) is the noise;

[0017] The expression of the signal covariance matrix is:

[0018]

[0019] Where E{} represents the mathematical expectation operation, H is the transposed conjugate, σ0 is the expected signal noise power, σ l is the multipath coherent signal noise power, σ v is the incoherent interference noise power, R N is the noise covariance matrix;

[0020] Using the covariance matrix under K snapshots Instead of the signal covariance matrix R x ,get:

[0021]

[0022] Wherein, X(k) is the received data vector of the kth snapshot number.

[0023] Further, the step of performing eigenvalue decomposition on the signal covariance matrix to obtain a signal eigenvector corresponding to the signal subspace includes:

[0024] Based on the signal covariance matrix, solve the eigenvalue λ, λ = λ1, ... λ i ,…λ N ;

[0025] For each eigenvalue λ i , and obtain its corresponding first eigenvector u i ;

[0026] Sort all the first feature vectors from large to small to obtain a first feature vector group u1, u2, ... u N ;

[0027] Using u1,u2,…u N The first Q first feature vectors in the signal subspace constitute the signal feature vector U corresponding to the signal S =[u1,u2,…u Q ].

[0028] Furthermore, the expression for solving the eigenvalue is:

[0029]

[0030] Among them, I is the identity matrix, det represents the determinant of the matrix, and the covariance matrix R is obtained by solving x The eigenvalues ​​λ1,λ2,…λ N ;

[0031] The expression for solving the characteristic vector is:

[0032]

[0033] Among them, λ i is the ith eigenvalue.

[0034] Further, the step of extracting the maximum signal feature vector corresponding to the maximum eigenvalue of the signal feature vector and rearranging elements of the maximum signal feature vector to obtain a reconstructed matrix includes:

[0035] Extract the signal feature vector u corresponding to the maximum eigenvalue of the signal feature vector max ;

[0036] To u maxRearrange the elements, set the number of sub-arrays as p, where p < N, and the number of elements in each sub-array as n, to obtain the corrected matrix Y f ;

[0037] For the corrected matrix Y f Obtain the autocorrelation matrix by taking the autocorrelation of the matrix to get the autocorrelation matrix Y ff , Y ff = [Y f1 , Y f2 , …, Y fp . For all elements of the autocorrelation matrix Y ff , calculate the average value respectively to obtain the reconstructed matrix Y out .

[0038] Furthermore, the expression of the signal feature vector u max is:

[0039] u max = [u max,1 , u max,2 , … u max,N

[0040] where u max,1 is the first element in the signal feature vector, u max,2 is the second element in the signal feature vector, and u max,N is the Nth element in the signal feature vector;

[0041] The expression of the corrected matrix Y f is:

[0042]

[0043] The expression of the autocorrelation matrix is:

[0044] Y ff = [Y f1 , Y f2 , …, Y fp

[0045] where Y f1 is the first element in the autocorrelation matrix, Y f2 is the second element in the signal feature vector, and Y fp is the pth element in the autocorrelation matrix;

[0046] The expression of the reconstructed matrix Y out is:

[0047] Y out = (Y f1 + … + Y fp ) / p

[0048] ​​Among them, p is the number of sub-arrays.

[0049] Further, based on the reconstruction matrix, the step of performing DOA estimation in combination with the Root-MUSIC algorithm based on polynomial reconstruction to obtain the DOA estimation value includes:

[0050] The reconstruction matrix Y out Perform eigenvalue decomposition to obtain the second eigenvector u j ;

[0051] Sort all the second feature vectors from large to small to obtain a second feature vector group;

[0052] The eigenvector matrix U corresponding to the signal subspace is constructed by using the last NQ second eigenvectors in the second eigenvector group. N =[u Q+1 ,u Q+2 ,…u N ];

[0053] For the noise subspace The DOA estimation value is obtained by performing segmentation and reorganization and combining the feature vector matrix.

[0054] Furthermore, we define the polynomial:

[0055]

[0056] Where z = exp(jw), j 2 = -1, w is the spatial frequency, p(z) = [1, z,…, z M-1 ] T , p(z) is a 2(M-1)th degree polynomial with (M-1) pairs of roots;

[0057] Take the K roots with the largest magnitude within the unit circle The phase of gives the DOA estimate, namely:

[0058]

[0059] Among them, θ m is the estimated value of DOA, are the K roots with the largest magnitude in the unit circle

[0060] The technical solution provided by the embodiments of the present disclosure may have the following beneficial effects:

[0061] In the embodiments of the present disclosure, through the above-mentioned complex scene DOA estimation method based on matrix reconstruction, on the one hand, the received signal is obtained, and the signal covariance matrix of the received signal is obtained according to the received signal; the signal covariance matrix is ​​subjected to eigenvalue decomposition to obtain the signal feature vector corresponding to the signal subspace; the maximum signal feature vector corresponding to the maximum eigenvalue of the signal feature vector is extracted, and the elements of the maximum signal feature vector are rearranged to obtain a reconstruction matrix; based on the reconstruction matrix, the DOA estimation is performed in combination with the Root-MUSIC algorithm based on polynomial reconstruction to obtain the DOA estimation value. On the other hand, the correction matrix in this method is a square matrix, and only eigenvalue decomposition is required to realize DOA estimation in complex scenes. And the success probability is high, there is a low signal-to-noise ratio threshold, and it has good estimation performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0062] The accompanying drawings herein are incorporated into the specification and constitute a part of the specification, illustrate embodiments consistent with the present disclosure, and together with the specification are used to explain the principles of the present disclosure. Obviously, the accompanying drawings described below are only some embodiments of the present disclosure, and for ordinary technicians in this field, other accompanying drawings can be obtained based on these accompanying drawings without creative work.

[0063] Figure 1 A step diagram showing a complex scene DOA estimation method based on matrix reconstruction in an exemplary embodiment of the present disclosure;

[0064] Figure 2 A comparison diagram of the success probabilities of the method of the present application and the existing subspace algorithm in an exemplary embodiment of the present disclosure is shown;

[0065] Figure 3 A comparison diagram showing the change of the root mean square error of the method of the present application and the existing subspace algorithm with the signal-to-noise ratio in an exemplary embodiment of the present disclosure is shown;

[0066] Figure 4 A comparison diagram showing the estimated deviation of the method of the present application and the existing subspace algorithm as the signal-to-noise ratio changes in an exemplary embodiment of the present disclosure;

[0067] Figure 5 A comparison chart showing how the root mean square error of the method of the present application and the existing subspace algorithm varies with the number of snapshots in an exemplary embodiment of the present disclosure is shown. DETAILED DESCRIPTION

[0068] Example embodiments will now be described more fully with reference to the accompanying drawings. However, example embodiments can be implemented in a variety of forms and should not be construed as limited to the examples set forth herein; rather, these embodiments are provided so that the disclosure will be more comprehensive and complete and to fully convey the concepts of the example embodiments to those skilled in the art. The described features, structures, or characteristics may be combined in any suitable manner in one or more embodiments.

[0069] In addition, the accompanying drawings are only schematic illustrations of the embodiments of the present disclosure and are not necessarily drawn to scale. The same reference numerals in the figures represent the same or similar parts, and their repeated descriptions will be omitted. Some of the block diagrams shown in the accompanying drawings are functional entities and do not necessarily correspond to physically or logically independent entities.

[0070] This example embodiment provides a complex scene DOA estimation method based on matrix reconstruction. Figure 1 As shown in , the complex scene DOA estimation method based on matrix reconstruction may include: steps S101 to S104.

[0071] Step S101: acquiring a received signal, and obtaining a signal covariance matrix of the received signal according to the received signal;

[0072] Step S102: performing eigenvalue decomposition on the signal covariance matrix to obtain a signal eigenvector corresponding to the signal subspace;

[0073] Step S103: extracting the maximum signal characteristic vector corresponding to the maximum eigenvalue of the signal characteristic vector, and rearranging the elements of the maximum signal characteristic vector to obtain a reconstructed matrix;

[0074] Step S104: Based on the reconstruction matrix, a Root-MUSIC algorithm based on polynomial reconstruction is used to perform DOA estimation to obtain a DOA estimation value.

[0075] Through the above-mentioned complex scene DOA estimation method based on matrix reconstruction, on the one hand, the received signal is obtained, and the signal covariance matrix of the received signal is obtained according to the received signal; the signal covariance matrix is ​​decomposed by eigenvalue to obtain the signal feature vector corresponding to the signal subspace; the maximum signal feature vector corresponding to the maximum eigenvalue of the signal feature vector is extracted, and the elements of the maximum signal feature vector are rearranged to obtain the reconstruction matrix; based on the reconstruction matrix, the Root-MUSIC algorithm based on polynomial reconstruction is combined to perform DOA estimation to obtain the DOA estimation value. On the other hand, the correction matrix in this method is a square matrix, and only eigenvalue decomposition is required to realize DOA estimation in complex scenes. And the success probability is high, there is a low signal-to-noise ratio threshold, and it has good estimation performance.

[0076] Next, we will refer to Figures 1 to 5 Each step of the complex scene DOA estimation method based on matrix reconstruction in this example implementation is described in more detail.

[0077] In step S101, the covariance matrix of the array received data is solved

[0078] The present application adopts a uniform linear array with N array elements and an array element spacing of d=λ / 2 as a receiving array. The received signal includes a desired signal, multipath interference of the desired signal, and incoherent interference. The received signal can be expressed as:

[0079]

[0080] Where s0(t) is the complex envelope of the desired signal, a(θ0) is the steering vector of the desired signal, and s l (t) is the composite envelope of the desired signal multipath, a(θ l ),l=1,2,…,L is the steering vector of the desired signal multipath, s l (t) = β l s0(t),β l is the composite envelope s of the lth desired signal multipath l (t) is the attenuation factor of the complex envelope s0(t) of the desired signal, g v is the composite envelope of the incoherent interference signal, a(θ v ) is the steering vector of the incoherent interference signal, and N(t) is the noise.

[0081] The covariance matrix R of the array received signal x It can be expressed as:

[0082]

[0083] In practical applications, the covariance matrix under K snapshots is generally used Instead of the covariance matrix R x ,Right now:

[0084]

[0085] Wherein, X(k) is the received data vector of the kth snapshot number.

[0086] In step S102, the received signal covariance matrix is ​​subjected to eigenvalue decomposition to obtain a signal eigenvector, namely:

[0087] First, to solve the eigenvalue λ, you need to solve the following characteristic polynomial:

[0088]

[0089] where I is the identity matrix and det represents the determinant of the matrix. Solving the above equation gives the covariance matrix R x with eigenvalues λ1, λ2, …, λ N .

[0090] For each eigenvalue λ i , the following linear equation needs to be solved to find the eigenvector u corresponding to each eigenvalue i :

[0091]

[0092] The corresponding eigenvectors arranged in ascending order are u1, u2, …, u N ; the first Q largest eigenvalues and the last N - Q smallest eigenvalues respectively form the eigenvector matrix U corresponding to the signal subspace S = [u1, u2, …, u Q and the eigenvector matrix U corresponding to the noise subspace N = [u Q+1 , u Q+2 , …, u N .

[0093] In step S103, matrix reconstruction is performed based on the signal eigenvectors

[0094] From step S102, the N eigenvectors corresponding to the signal subspace are obtained, and the signal eigenvector u corresponding to the largest eigenvalue of the signal subspace is extracted max , which can be expressed as:

[0095] u max = [u max,1 , u max,2 , …, u max,N

[0096] The elements of u max are rearranged, the number of sub - arrays is set to p, p < N, and the number of elements in each sub - array is n (ensuring that the number of selected elements n is greater than the number of signal sources), resulting in the modified matrix Y f , which can be expressed as:

[0097]

[0098] The autocorrelation matrix of the modified matrix Y f is obtained to get Y ff , Y ff = [Y f1 , Y f2 , …, Y fp , and the average value of all elements of Y ff is obtained respectively to get the reconstructed matrix Y out : ​

[0099] Y out =(Y f1 +…+Y fp ) / p

[0100] In step S104, the coherent source DOA is estimated

[0101] Reconstruct the matrix Y out Perform eigenvalue decomposition to obtain the second eigenvector u j ; Sort all the second eigenvectors from large to small to obtain a second eigenvector group; Use the last NQ second eigenvectors in the second eigenvector group to form the eigenvector matrix U corresponding to the signal subspace N =[u Q+1 ,u Q+2 ,…u N ]; for the noise subspace The segmentation and reorganization are combined based on the eigenvector matrix to obtain the DOA estimation value.

[0102] Using the reconstruction matrix Y out The DOA estimation of coherent sources is realized by combining the Root-MUSIC algorithm based on polynomial reconstruction.

[0103] The correction matrix Y obtained in step S103 out Perform eigenvalue decomposition, the decomposition method is the same as the method in step S102, and obtain the eigenvector matrix U corresponding to the noise subspace N =[u Q+1 ,u Q+2 ,…u N ].

[0104] Root-MUSIC needs to define a polynomial first, namely:

[0105] Define the polynomial:

[0106]

[0107] Where z = exp(jw), j 2 = -1, w is the spatial frequency, p(z) = [1, z,…, z M-1 ] T , p(z) is a 2(M-1)th degree polynomial with (M-1) pairs of roots;

[0108] Take the K roots with the largest magnitude within the unit circle The phase of gives the DOA estimate, namely:

[0109]

[0110] Among them, θ mis the estimated value of DOA, are the K roots with the largest magnitude (closest to the unit circle) within the unit circle

[0111] In a specific embodiment, the method of the present application is further verified through the following experiments.

[0112] Experimental software platform: MTALAB-R2017a

[0113] Experimental hardware platform: computer

[0114] Experimental steps:

[0115] A uniform linear array with 8 elements is set as the receiving array. The element spacing is half a wavelength. The array receiving signal contains the desired signal with an angle of 5°, coherent interference with an incident angle of -10°, incoherent interference with an incident angle of 20°, and independently distributed Gaussian white noise signals. The uniform linear array signal model is as follows: Figure 2 The method of the present application is compared and analyzed with the existing spatial smoothing algorithms (FSS, BSS, FBSS) and matrix reconstruction algorithms (MD, ESVD).

[0116] 1. Set the number of snapshots to 1024, snr = [-15, 20], and perform 300 Monte Carlo simulations. If the error is less than 0.2, the success probability of this application is as follows: Figure 3 As shown in the figure, it can be seen that the success rate of each algorithm increases with the increase of the signal-to-noise ratio. The method of the present application and the matrix reconstruction algorithm are better than the spatial smoothing algorithm, with a success rate of more than 60%. Moreover, the success probability of the method of the present application tends to 1 when the signal-to-noise ratio is greater than 8.

[0117] 2. Set the number of snapshots to 1024, snr = [-15, 20], and perform 300 Monte Carlo simulations. The root mean square error of the method of the present application and the existing subspace algorithm varies with the signal-to-noise ratio as follows: Figure 4 shown.

[0118] 3. Set the number of snapshots to 1024, snr = [-15, 20], and perform 300 Monte Carlo simulations. The estimated deviation of the method of the present application and the existing subspace algorithm varies with the signal-to-noise ratio as follows: Figure 5 shown.

[0119] 4. Set snr=0, the number of snapshots is 128:128:1024, and perform 300 Monte Carlo simulations. The root mean square error of each algorithm changes with the signal-to-noise ratio as follows: Figure 5 shown.

[0120] Through the above-mentioned complex scene DOA estimation method based on matrix reconstruction, on the one hand, the received signal is obtained, and the signal covariance matrix of the received signal is obtained according to the received signal; the signal covariance matrix is ​​decomposed by eigenvalue to obtain the signal feature vector corresponding to the signal subspace; the maximum signal feature vector corresponding to the maximum eigenvalue of the signal feature vector is extracted, and the elements of the maximum signal feature vector are rearranged to obtain the reconstruction matrix; based on the reconstruction matrix, the Root-MUSIC algorithm based on polynomial reconstruction is combined to perform DOA estimation to obtain the DOA estimation value. On the other hand, the correction matrix in this method is a square matrix, and only eigenvalue decomposition is required to realize DOA estimation in complex scenes. And the success probability is high, there is a low signal-to-noise ratio threshold, and it has good estimation performance.

[0121] It should be understood that the terms "center", "longitudinal", "lateral", "length", "width", "thickness", "up", "down", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inside", "outside", "clockwise", "counterclockwise" and the like in the above description indicate orientations or positional relationships based on the orientations or positional relationships shown in the accompanying drawings, and are only for the convenience of describing the embodiments of the present disclosure and simplifying the description, and do not indicate or imply that the referred device or element must have a specific orientation, be constructed and operated in a specific orientation, and therefore should not be understood as a limitation on the embodiments of the present disclosure.

[0122] In addition, the terms "first" and "second" are used for descriptive purposes only and should not be understood as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of the features. In the description of the embodiments of the present disclosure, the meaning of "multiple" is two or more, unless otherwise clearly and specifically defined.

[0123] In the embodiments of the present disclosure, unless otherwise clearly specified and limited, the terms "installed", "connected", "connected", "fixed" and the like should be understood in a broad sense, for example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be a direct connection or an indirect connection through an intermediate medium, it can be the internal connection of two elements or the interaction relationship between two elements. For ordinary technicians in this field, the specific meanings of the above terms in the present disclosure can be understood according to specific circumstances.

[0124] In the embodiments of the present disclosure, unless otherwise clearly specified and limited, a first feature being "above" or "below" a second feature may include the first and second features being in direct contact, or may include the first and second features not being in direct contact but being in contact through another feature between them. Moreover, a first feature being "above", "above" and "above" a second feature includes the first feature being directly above and obliquely above the second feature, or simply indicates that the first feature is higher in level than the second feature. A first feature being "below", "below" and "below" a second feature includes the first feature being directly below and obliquely below the second feature, or simply indicates that the first feature is lower in level than the second feature.

[0125] In the description of this specification, the description with reference to the terms "one embodiment", "some embodiments", "example", "specific example" or "some examples" etc. means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present disclosure. In this specification, the schematic representations of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described may be combined in any one or more embodiments or examples in a suitable manner. In addition, those skilled in the art may combine and combine the different embodiments or examples described in this specification.

[0126] Those skilled in the art will readily appreciate other embodiments of the present disclosure after considering the specification and practicing the invention disclosed herein. This application is intended to cover any modification, use or adaptation of the present disclosure, which follows the general principles of the present disclosure and includes common knowledge or customary techniques in the art that are not disclosed in the present disclosure. The specification and examples are intended to be exemplary only, and the true scope and spirit of the present disclosure are indicated by the appended claims.

Claims

1. A complex scene DOA estimation method based on matrix reconstruction, characterized in that: The method includes: Acquire a received signal, and obtain a signal covariance matrix of the received signal based on the received signal; Performing eigenvalue decomposition on the signal covariance matrix to obtain a signal eigenvector corresponding to the signal subspace; Extracting a maximum signal feature vector corresponding to a maximum eigenvalue of the signal feature vector, and rearranging elements of the maximum signal feature vector to obtain a reconstruction matrix; Based on the reconstruction matrix, the DOA estimation is performed in combination with the Root-MUSIC algorithm based on polynomial reconstruction to obtain a DOA estimation value.

2. The complex scene DOA estimation method based on matrix reconstruction according to claim 1 is characterized in that: The step of acquiring a received signal and obtaining a signal covariance matrix of the received signal based on the received signal includes: Acquire the received signal using a uniform linear array receiving array having N array elements and d array element spacing; The received signal is solved using a covariance matrix equation of the array received signal to obtain the signal covariance matrix of the received signal.

3. The complex scene DOA estimation method based on matrix reconstruction according to claim 2 is characterized in that: The expression of the received signal is: Where s0(t) is the complex envelope of the desired signal, a(θ0) is the steering vector of the desired signal, and s l (t) is the composite envelope of the desired signal multipath, a(θ l ),l=1,2,…,L is the steering vector of the desired signal multipath, s l (t) = β l s0(t),β l is the composite envelope s of the lth desired signal multipath l (t) is the attenuation factor of the complex envelope s0(t) of the desired signal, g v is the composite envelope of the incoherent interference signal, a(θ v ) is the steering vector of the incoherent interference signal, and N(t) is the noise; The expression of the signal covariance matrix is: Where E{} represents the mathematical expectation operation, H is the transposed conjugate, σ0 is the expected signal noise power, σ l is the multipath coherent signal noise power, σ v is the incoherent interference noise power, R N is the noise covariance matrix; Using the covariance matrix under K snapshots Instead of the signal covariance matrix R x ,get: Wherein, X(k) is the received data vector of the kth snapshot number.

4. The complex scene DOA estimation method based on matrix reconstruction according to claim 3 is characterized in that: The step of performing eigenvalue decomposition on the signal covariance matrix to obtain a signal eigenvector corresponding to the signal subspace includes: Based on the signal covariance matrix, solve the eigenvalue λ, λ = λ1, ... λ i ,…λ N ; For each eigenvalue λ i , and obtain its corresponding first eigenvector u i ; Sort all the first feature vectors from large to small to obtain a first feature vector group u1, u2, ... u N ; Using u1,u2,…u N The first Q first feature vectors in the signal subspace constitute the signal feature vector U corresponding to the signal S =[u1,u2,…u Q ].

5. The complex scene DOA estimation method based on matrix reconstruction according to claim 4 is characterized in that: The expression for solving the eigenvalue is: Among them, I is the identity matrix, det represents the determinant of the matrix, and the covariance matrix R is obtained by solving x The eigenvalues ​​λ1,λ2,…λ N ; The expression for solving the characteristic vector is: Among them, λ i is the i-th eigenvalue.

6. The complex scene DOA estimation method based on matrix reconstruction according to claim 5 is characterized in that: The step of extracting the maximum signal feature vector corresponding to the maximum eigenvalue of the signal feature vector and rearranging elements of the maximum signal feature vector to obtain a reconstructed matrix includes: Extract the signal feature vector u corresponding to the maximum eigenvalue of the signal feature vector max ; For u max rearrange the elements, set the number of sub-arrays as p, where p < N, and the number of elements in each sub-array as n, to obtain the corrected matrix Y f ; Correction matrix Y f Obtain the autocorrelation matrix to obtain the autocorrelation matrix Y ff , Y ff =[Y f1 ,Y f2 ,…,Y fp ], for the autocorrelation matrix Y ff The reconstruction matrix Y is obtained by taking the average value of all elements of out .

7. The complex scene DOA estimation method based on matrix reconstruction according to claim 6, characterized in that: The signal characteristic vector u max The expression is: in max =[in max,1 ,in max,2 ,…in max,N ] Among them, u max,1 is the first element in the signal feature vector, u max,2 is the second element in the signal feature vector, u max,N is the Nth element in the signal feature vector; The correction matrix Y f The expression is: The expression of the autocorrelation matrix is: AND ff =[And f1 ,AND f2 ,…,AND fp ] Among them, Y f1 is the first element in the autocorrelation matrix, Y f2 is the second element in the signal feature vector, Y fp is the pth element in the autocorrelation matrix; The reconstruction matrix Y out The expression is: AND out (And f1 +…+And fp ) / p Among them, p is the number of sub-arrays.

8. The complex scene DOA estimation method based on matrix reconstruction according to claim 7, characterized in that: The step of performing DOA estimation based on the reconstruction matrix and the Root-MUSIC algorithm based on polynomial reconstruction to obtain the DOA estimation value includes: The reconstruction matrix Y out Perform eigenvalue decomposition to obtain the second eigenvector u j ; Sort all the second feature vectors from large to small to obtain a second feature vector group; The eigenvector matrix U corresponding to the signal subspace is constructed by using the last NQ second eigenvectors in the second eigenvector group. N =[u Q+1 ,u Q+2 ,…u N ]; For the noise subspace The DOA estimation value is obtained by performing segmentation and reorganization and combining the feature vector matrix.

9. The complex scene DOA estimation method based on matrix reconstruction according to claim 8, characterized in that: Define the polynomial: Where z = exp(jw), j 2 = -1, w is the spatial frequency, p(z) = [1, z,…, z M-1 ] T , p(z) is a 2(M-1)th degree polynomial with (M-1) pairs of roots; Take the K roots with the largest magnitude within the unit circle The phase of gives the DOA estimate, namely: Among them, θ m is the estimated value of DOA, are the K roots with the largest magnitude in the unit circle

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