A method for complex scene DOA estimation based on matrix reconstruction

Abstract

The application belongs to the technical field of signal processing. The application provides a complex scene DOA estimation method based on matrix reconstruction. The method comprises the following steps: obtaining 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 characteristic vector corresponding to a signal subspace; extracting a maximum signal characteristic vector corresponding to a maximum eigenvalue of the signal characteristic vector, and performing element rearrangement on the maximum signal characteristic vector to obtain a reconstruction matrix; and performing DOA estimation based on the reconstruction matrix and in combination with a Root-MUSIC algorithm based on polynomial reconstruction to obtain a DOA estimation value. The correction matrix in the embodiment of the disclosure is a square matrix, and the DOA estimation under a complex scene can be realized only by performing eigenvalue decomposition. Moreover, the success probability is high, the signal-to-noise ratio threshold is low, and the estimation performance is good.

Description

TECHNICAL FIELD

[0001] The embodiment of the present disclosure relates to the technical field of signal processing, in particular to a complex scene DOA estimation method based on matrix reconstruction. BACKGROUND

[0002] In a complex electromagnetic environment, radar targets, multipath effects, coherent decoys and other independent radiation sources coexist, and when the signals are strongly correlated or completely coherent, the subspace entanglement phenomenon occurs. The traditional subspace-based algorithm has a sharp decline in performance or even fails in the presence of coherent or highly correlated signals. The spatial smoothing-based algorithm and the matrix reconstruction-based algorithm can effectively estimate coherent signals. Although the performance of the matrix reconstruction-based algorithm is better than that of the spatial smoothing-based algorithm, the modified covariance matrix is a long rectangle, which needs to be singular value decomposed. The maximum likelihood method has good de-coherent effect, but the implementation process is complex, multi-dimensional search is required, and the initial value has a great influence on the DOA direction finding. Although the sparse reconstruction algorithm based on the theory of compressed sensing or the concept of spatial sparsity is not sensitive to the coherent signal environment, the extremely large amount of calculation of the algorithm hinders the process of engineering practicalization.

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

[0004] It should be noted that this section aims 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 merely because it is included in this section. SUMMARY

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

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

[0007] Obtaining a received signal, and obtaining a signal covariance matrix of the received signal according to the received signal;

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

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

[0010] Based on the reconstruction matrix, DOA estimation is performed using the Root-MUSIC algorithm based on polynomial reconstruction to obtain the DOA estimate.

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

[0012] The received signal is acquired using a receiving array of a uniform linear array with N array elements and d array element spacing;

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

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

[0015]

[0016] Where s0(t) is the composite envelope of the desired signal, a(θ0) is the steering vector of the desired signal, and s l (t) represents 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 The composite envelope s of the l-th desired signal multipath l g is the fading factor relative to the composite envelope s0(t) of the desired signal. v For the composite envelope of incoherent interference signals, a(θ) v ) is the steering vector of the incoherent interference signal, and N(t) is the noise;

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

[0018]

[0019] Where E{} denotes the mathematical expectation operation, H is the transpose conjugate, σ0 is the desired signal-noise power, and σ l For the multipath coherent signal noise power, σ v R represents the power of incoherent interference noise. N Here is the noise covariance matrix;

[0020] Using the covariance matrix of 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.

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

[0024] Based on the signal covariance matrix, solve the eigenvalues λ, λ = λ1, λ2, … λ i , … λ N ;

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

[0026] Sort all the first eigenvectors in descending order to obtain a first eigenvector group u1, u2, … u N ;

[0027] Use the first Q eigenvectors in u1, u2, … u N to construct the signal eigenvector U corresponding to the signal subspace S = [u1, u2, … u Q ].

[0028] Further, the expression for solving the eigenvalues is:

[0029]

[0030] Wherein, I is the unit matrix, and det represents the determinant of the matrix. The eigenvalues λ1, λ2, … λ N of the covariance matrix R x are solved;

[0031] The expression for solving the eigenvectors is:

[0032]

[0033] Wherein, λ i is the ith eigenvalue.

[0034] Further, in the step of extracting the maximum signal eigenvector corresponding to the maximum eigenvalue of the signal eigenvector and rearranging the elements of the maximum signal eigenvector to obtain a reconstruction matrix, comprising:

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

[0036] Rearrange the elements of u maxThe elements of the matrix Y are rearranged, the number of sub-matrices is set to p, p < N, and the number of elements in each sub-matrix is n, to obtain a modified matrix Y f ;

[0037] The modified matrix Y f is autocorrelated to obtain an autocorrelation matrix Y ff , Y ff = [Y f1 , Y f2 , …, Y fp ], and all elements of the autocorrelation matrix Y ff are averaged to obtain the reconstruction matrix Y out .

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

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

[0040] wherein 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 modified matrix Y f is:

[0042]

[0043] The expression of the autocorrelation matrix is:

[0044] Y ff = [Y f1 , Y f2 , …, Y fp ]

[0045] wherein Y f1 is the first element in the autocorrelation matrix, Y f2 is the second element in the autocorrelation matrix, and Y fp is the pth element in the autocorrelation matrix.

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

[0047] Y out = (Y f1 + … + Y fp ) / p

[0048] Wherein, p is the number of subarrays.

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

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

[0051] Sort all the second eigenvectors in descending order to obtain a second eigenvector group;

[0052] Use the last N-Q second eigenvectors in the second eigenvector group to form an eigenvector matrix U N corresponding to a signal subspace, where U Q+1 = [u Q+2 , u N , …, u 2 ];

[0053] Perform segmentation and reorganization on a noise subspace , and combine the eigenvector matrix to obtain the DOA estimation value.

[0054] Further, define a polynomial:

[0055]

[0056] Wherein, z = exp(jw), j M-1 = -1, w is a spatial frequency, and p(z) = [1, z, …, z T ] m , p(z) is a 2(M-1) order polynomial, and there are (M-1) pairs of roots.

[0057] Take the phases of K roots with the largest amplitude in the unit circle to give a DOA estimation value, that is:

[0058]

[0059] Wherein, θ m is the DOA estimation value, is the phase of the K roots with the largest amplitude in the unit circle

[0060] The technical scheme provided by the embodiments of the present disclosure can include the following beneficial effects:

[0061] In the embodiments of the present disclosure, by using the 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 eigenvector corresponding to the signal subspace; the maximum signal eigenvector corresponding to the maximum eigenvalue of the signal eigenvector is extracted, and the maximum signal eigenvector is subjected to element rearrangement to obtain a reconstruction matrix; based on the reconstruction matrix, the Root-MUSIC algorithm based on polynomial reconstruction is combined to perform DOA estimation to obtain a DOA estimation value. On the other hand, the correction matrix in the method is a square matrix, and only eigenvalue decomposition is needed to realize DOA estimation in a complex scene. The success probability is high, the signal-to-noise ratio threshold is low, and the estimation performance is good. BRIEF DESCRIPTION OF DRAWINGS

[0062] The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments consistent with the present disclosure and serve to explain the principles of the present disclosure. It is readily apparent to one of ordinary skill in the art that the accompanying drawings shown below are only some embodiments of the present disclosure, and other drawings can be obtained according to the drawings without creative labor.

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

[0064] Figure 2 A comparison diagram of the success probability 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 of the root mean square error of the method of the present application and the existing subspace algorithm with respect to the change of the signal-to-noise ratio in an exemplary embodiment of the present disclosure is shown;

[0066] Figure 4 A comparison diagram of the estimation deviation of the method of the present application and the existing subspace algorithm with respect to the change of the signal-to-noise ratio in an exemplary embodiment of the present disclosure is shown;

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

[0068] Example implementations will now be described more fully with reference to the accompanying drawings. Example implementations can be implemented in any

[0069] In addition, the accompanying drawings are included to provide a thorough understanding of the example implementations. The description and drawings are not intended to limit the example implementations in any way. Instead, the description and drawings are provided to illustrate example implementations so that a person skilled in the art can better understand to make and use one or more example implementations.

[0070] In the present example implementation, a complex scene DOA estimation method based on matrix reconstruction is provided. Referring to FIG. 1, the complex scene DOA estimation method based on matrix reconstruction can include steps S101-S104. Figure 1

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

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

[0073] Step S103: Extract a maximum signal eigenvector corresponding to a maximum eigenvalue of the signal eigenvector, and perform element rearrangement on the maximum signal eigenvector to obtain a reconstruction matrix;

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

[0075] Through the above complex scene DOA estimation method based on matrix reconstruction, on the one hand, a received signal is obtained, and a 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 a signal eigenvector corresponding to a signal subspace; a maximum signal eigenvector corresponding to a maximum eigenvalue of the signal eigenvector is extracted, and element rearrangement is performed on the maximum signal eigenvector to obtain a reconstruction matrix; based on the reconstruction matrix, a Root-MUSIC algorithm based on polynomial reconstruction is combined to perform DOA estimation to obtain a DOA estimation value. On the other hand, the correction matrix in the method is a square matrix, and only eigenvalue decomposition is required to realize DOA estimation in a complex scene. The success probability is high, the signal-to-noise ratio threshold is low, and the estimation performance is good. ​

[0076] The following will refer to Figures 1 to 5 The various steps of the above-mentioned complex scene DOA estimation method based on matrix reconstruction in the present example embodiment will be described in more detail.

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

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

[0079]

[0080] where s0(t) is the complex envelope of the desired signal, a(θ0) is the steering vector of the desired signal, s l (t) is the complex 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 fading factor of the complex envelope s l (t) of the lth desired signal multipath relative to the complex envelope s0(t) of the desired signal, g v is the complex envelope of the non-coherent interference signal, a(θ v ) is the steering vector of the non-coherent interference signal, and N(t) is the noise.

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

[0082]

[0083] In practical applications, the covariance matrix R x of K times the number of snapshots is generally used instead of the covariance matrix R , i.e.:

[0084]

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

[0086] In step S102, the signal eigenvector is obtained by performing eigenvalue decomposition on the received signal covariance matrix, i.e.:

[0087] First, the eigenvalue λ is solved, and the following characteristic polynomial needs to be solved:

[0088]

[0089] where I is the identity matrix, det denotes the determinant of a matrix, and the covariance matrix R is obtained by solving the above equation x N .

[0090] For each eigenvalue λ i , the corresponding eigenvector u i is found by solving the following linear equation:

[0091]

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

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

[0094] The N eigenvectors corresponding to the signal subspace are obtained from step S102, and the signal eigenvector u max corresponding to the largest eigenvalue of the signal subspace is extracted and can be represented 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-matrices is set to p, p < N, and the number of elements in each sub-matrix is n (to ensure that the number of selected elements n is greater than the number of sources), to obtain the modified matrix Y f , which can be represented as:

[0097]

[0098] The autocorrelation matrix of the modified matrix Y f is calculated to obtain Y ff , Y ff = [Y f1 , Y f2 , …, Y fp ], and the average of all elements of Y ff is calculated to obtain the reconstruction matrix Y out : ​

[0099] Y out =(Y f1 +…+Y fp ) / p

[0100] In step S104, coherent source DOA estimation

[0101] For the reconstruction matrix Y out Perform eigenvalue decomposition to obtain the second eigenvector u. j Sort all the second eigenvectors in descending order to obtain the second eigenvector group; use the last NQ second eigenvectors in the second eigenvector group to construct 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 recombination are performed, and the DOA estimate is obtained by combining the feature vector matrix.

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

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

[0104] Root-MUSIC requires defining a polynomial first, namely:

[0105] Define a 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 polynomial of degree 2(M-1) and has (M-1) pairs of roots;

[0108] Take the K roots with the largest amplitude inside the unit circle. The phase gives the DOA estimate, that is:

[0109]

[0110] Where, θ mfor the DOA estimation value, for the K roots with the largest amplitude (closest to the unit circle) in the unit circle

[0111] In one specific embodiment, the method of the present application is further verified by the following experiment.

[0112] Experimental software platform: MTALAB-R2017a

[0113] Experimental hardware platform: computer

[0114] Experimental steps:

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

[0116] 1. Set the number of snapshots to 1024, snr = [-15, 20], and perform 300 times of Monte Carlo simulation. The success probability of the present application when the error is less than 0.2 is as shown in Figure 3 From the figure, it can be seen that the success rate of each algorithm increases with the increase of signal-to-noise ratio. The effect of the method of the present application and the matrix reconstruction type algorithm is better than that of the spatial smoothing type algorithm, and the success rate is greater than 60%, and 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 times of Monte Carlo simulation. The root mean square error of the method of the present application and the existing subspace algorithm changes with the signal-to-noise ratio as shown in Figure 4

[0118] 3. Set the number of snapshots to 1024, snr = [-15, 20], and perform 300 times of Monte Carlo simulation. The estimation bias of the method of the present application and the existing subspace algorithm changes with the signal-to-noise ratio as shown in Figure 5

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

[0120] ​​​By the 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 eigenvector corresponding to the signal subspace; the maximum signal eigenvector corresponding to the maximum eigenvalue of the signal eigenvector is extracted, and the maximum signal eigenvector is subjected to element rearrangement to obtain a reconstruction matrix; based on the reconstruction matrix, the Root-MUSIC algorithm based on polynomial reconstruction is combined to perform DOA estimation to obtain a DOA estimation value. On the other hand, the correction matrix in the method is a square matrix, and only eigenvalue decomposition is needed to realize DOA estimation in a complex scene. The success probability is high, the signal-to-noise ratio threshold is low, and the estimation performance is good.

[0121] It should be understood that the terms "center", "longitudinal", "transverse", "length", "width", "thickness", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", "clockwise", "counterclockwise" and the like in the above description indicate the orientation or positional relationship based on the orientation or positional relationship shown in the 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 devices or elements referred to must have a particular orientation, be constructed and operated in a particular orientation, and therefore cannot be understood as a limitation on the embodiments of the present disclosure.

[0122] In addition, the terms "first", "second" are only for descriptive purposes and cannot be understood as indicating or implying relative importance or implicitly indicating the number of the technical features indicated. Therefore, the features defined with "first", "second" can explicitly or implicitly include one or more of the features. In the description of the embodiments of the present disclosure, the meaning of "a plurality of" is two or more, unless otherwise explicitly specified and limited.

[0123] In the embodiments of the present disclosure, unless otherwise explicitly specified and limited, the terms "mounting", "connection", "connecting", "fixing" and the like should be understood in a broad sense, for example, can be fixed connection, can also be detachable connection, or integral; can be mechanical connection, can also be electrical connection; can be directly connected, can also be indirectly connected through an intermediate medium, can be the internal communication of two elements or the interaction relationship between two elements. For those skilled in the art, the specific meaning of the above terms in the present disclosure can be understood according to the specific circumstances.

[0124] In the embodiments of the present disclosure, unless specifically defined and limited otherwise, "on" or "under" of a first feature to a second feature can include that the first and second features are in direct contact, or that the first and second features are not in direct contact but are in contact through another feature between them. Moreover, "on", "above" and "over" of a first feature to a second feature include that the first feature is directly above and obliquely above the second feature, or only indicates that the first feature is higher than the second feature in horizontal height. "Under", "below" and "underneath" of a first feature to a second feature include that the first feature is directly below and obliquely below the second feature, or only indicates that the first feature is lower than the second feature in horizontal height.

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

[0126] Other embodiments of the present disclosure will be apparent to those skilled in the art upon consideration of the specification and practice of the applications disclosed. The present application is intended to cover any variations, uses or adaptive changes of the present disclosure following the general principles of the present disclosure and including known or customary practices in the art not disclosed in the present disclosure. The specification and examples are only considered as exemplary, and the true scope and spirit of the present disclosure are indicated by the appended claims.

Claims

1. A method for complex scene DOA estimation based on matrix reconstruction, characterized in that, The method comprises: 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 a signal subspace; extracting a maximum signal eigenvector corresponding to a maximum eigenvalue of the signal eigenvector, and performing element rearrangement on the maximum signal eigenvector to obtain a reconstruction matrix; performing DOA estimation based on the reconstruction matrix and in combination with a Root-MUSIC algorithm based on polynomial reconstruction to obtain a DOA estimation value; wherein the step of extracting the maximum signal eigenvector corresponding to the maximum eigenvalue of the signal eigenvector and performing element rearrangement on the maximum signal eigenvector to obtain the reconstruction matrix comprises: a signal feature vector corresponding to a maximum eigenvalue of the extracted signal feature vector ; Reorder the elements of , set the number of subarrays to , , and the number of elements in each subarray to , to obtain the modified matrix ; to the correction matrix autocorrelation matrix , , to the autocorrelation matrix all elements of the autocorrelation matrix ; signal feature vector The expression is: wherein, is a first element in the signal feature vector, is a second element in the signal feature vector, is an Nth element in the signal feature vector; correction matrix The expression for the correction matrix the expression of the autocorrelation matrix is: wherein is a first element in the autocorrelation matrix, is a second element in the autocorrelation matrix, is a pth element in the autocorrelation matrix; reconstruction matrix The expression for the reconstruction matrix is: wherein p is the number of subarrays; the step of performing DOA estimation based on the reconstruction matrix and in combination with the Root-MUSIC algorithm based on polynomial reconstruction to obtain the DOA estimation value comprises: reconstructing the matrix performing an eigenvalue decomposition to obtain a second eigenvector ; sorting all the second eigenvectors in descending order to obtain a second eigenvector group; The signal subspace corresponding to the second feature vector matrix is constituted by using the last second feature vector in the second feature vector group ;​ Noise subspace The DOA estimation value is obtained by performing segmentation and recombination combined with the feature vector matrix. defining a polynomial: wherein , , w is a spatial frequency, , is a polynomial of degree two, with roots; The phase of the root with the largest amplitude in the unit circle gives the DOA estimate, i.e. ​ wherein, is the DOA estimate, is the root with the largest magnitude within the unit circle roots , is the signal wavelength, is the inter-element spacing.

2. The method of claim 1, wherein, the step of acquiring the received signal and obtaining the signal covariance matrix of the received signal according to the received signal comprises: acquiring the received signal by using a receiving array with an element number N and an element spacing d; solving the received signal by using a covariance matrix equation of the array receiving signal to obtain the signal covariance matrix of the received signal.

3. The method of claim 2, wherein, the expression of the received signal is: in, The composite envelope of the desired signal. The steering vector of the desired signal. For the composite envelope of the desired signal multipath, The steering vector for the desired signal multipath. The number of multipaths. , For the first The composite envelope of a desired signal multipath Composite envelope relative to the desired signal The decay factor, The composite envelope of incoherent interference signals. The steering vector for incoherent interference signals. For noise, The number of incoherent interferences; the expression of the signal covariance matrix is: where E{} denotes the mathematical expectation operation, H is the transpose conjugate, is the desired signal noise power, is the multipath coherent signal noise power, is the non-coherent interference noise power, is the noise covariance matrix; Utilizing Covariance matrix at next snapshot number Substitute signal covariance matrix , we obtain: wherein is the received data vector for the th snapshot number.

4. The method of claim 3, wherein, the step of performing eigenvalue decomposition on the signal covariance matrix to obtain the signal eigenvector corresponding to the signal subspace comprises: Solving eigenvalues based on signal covariance matrix , ; For each eigenvalue , obtain its corresponding first eigenvector ; Sort all the first feature vectors in descending order to obtain a first feature vector group ; wherein, N is the number of first feature vectors; Utilizing the first feature vector in the first feature vector vector corresponding to the signal subspace .

5. The method of claim 4, wherein, the expression of solving the eigenvalue is: wherein is the identity matrix, denotes the determinant of a matrix, the eigenvalues of the covariance matrix are solved ; the expression of solving the eigenvector is: wherein, is the ith eigenvalue.

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