A coherent signal DOA estimation method based on coprime array

Abstract

The present invention discloses a coherent signal DOA estimation method based on a coprime array. First, the covariance matrix of the coprime array is calculated, and eigendecomposition is performed on it to find the eigenvector corresponding to the maximum eigenvalue. The eigenvector is then decomposed into two parts according to the number of array elements of the coprime array, and the elements of the two parts are rearranged to obtain two Hankel matrices H1 and H2. Next, singular value decomposition is performed on H1 and H2 to obtain the noise subspaces of H1 and H2. Finally, based on the noise subspaces of H1 and H2, the spatial spectra of H1 and H2 are plotted using the MUSIC method. The same spectral peaks in the spatial spectra of H1 and H2 are found, and the DOA values ​​corresponding to the spectral peaks in the spatial spectra of H1 and H2 are recorded and averaged to obtain the final DOA estimate. The method of the present invention does not require vectorization of the received signal of the sparse array, can fully utilize the coprime characteristics of the array, and obtain the angle estimate of the coherent signal, thus filling the gap in coherent signal arrival angle estimation for coprime arrays.

Description

Technical Field

[0001] The present invention relates to the field of coherent signal DOA estimation, and in particular to a coprime array-based coherent signal DOA estimation method. Background Art

[0002] Using coprime arrays for angle estimation of far-field signals has attracted considerable attention. This is because, compared to traditional uniform linear arrays, coprime arrays have an element spacing greater than half a wavelength, making them less susceptible to inter-element coupling. Furthermore, with the same number of elements, coprime arrays have a larger aperture due to the larger element spacing. However, current research on coprime array-based angle-of-arrival estimation relies primarily on incoherent incident signals. However, in practice, coherent signals are ubiquitous, significantly limiting the practical application of coprime arrays. Therefore, the problem of how to use coprime arrays to estimate the angle of arrival of coherent signals urgently needs to be addressed. Summary of the Invention

[0003] The technical problem to be solved by the present invention is to provide a coherent signal DOA estimation method based on a coprime array in order to address the defects involved in the background technology.

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

[0005] A coherent signal DOA estimation method based on a coprime array comprises the following steps:

[0006] Step 1), for coprime arrays Find the covariance matrix R of coprime arrays xx ;

[0007] Step 2), perform eigendecomposition on the covariance matrix;

[0008] Step 3), after eigendecomposition, find the eigenvector e1 corresponding to the maximum eigenvalue;

[0009] Step 4) Decompose e1 into two parts, g1 and g2, according to the number of elements of the coprime arrays.

[0010] Step 5), rearrange the elements in g1 and g2 to obtain two Hankel matrices, denoted as H1 and H2;

[0011] Step 6), perform singular value decomposition on H1 and H2 respectively to obtain the noise subspace of H1 and H2;

[0012] Step 7) Based on the noise subspace of H1 and H2, the MUSIC method is applied to draw the spatial spectrum of H1 and H2, find the same spectral peak in the spatial spectrum of H1 and H2, record the DOA value corresponding to the spectral peak in the spatial spectrum of H1 and H2, and average them to obtain the final DOA estimate.

[0013] As a further optimization scheme of the coherent signal DOA estimation method based on a coprime array of the present invention, in step 1), the coprime array

[0014] Among them, M and N are two mutually prime integers, d is the unit spacing of the array elements, which is set to half the wavelength of the incident signal. and Coprime matrices Two subarrays of ;

[0015] Coprime array output vector

[0016] in, is the direction matrix, a(θ k )=[a1(θ k ) T ,a2(θ k ) T ] T is the steering vector, n(t)=[n1(t) T ,n2(t) T ] T is the noise vector; A1 and A2 correspond to the sub-matrix Subarray The steering matrix, A1=[a1(θ1),a1(θ2),...,a1(θ K )](k∈[1,2,...,K]), is the steering vector of A1; A2=[a2(θ1),a2(θ2),...,a2(θ K )](k∈[1,2,...,K]), is the steering vector of A2; s(t)=[s1(t),s2(t),...,s K (t)] T is the signal vector, n(t), n1(t), n2(t) are zero-mean Gaussian white noise vectors, and C is the mutual coupling matrix; is the mutual coupling coefficient, |c1|=0.4, c0=1>|c1|>|c2|>...>|c4|>0;

[0017] The covariance matrix of coprime arrays is

[0018] Among them, R 11 、R 22 Sub-arrays Subarray The autocorrelation covariance matrix, R 12 、R 21 Sub-arrays Correlation subarray Subarray Correlation subarray The cross-correlation covariance matrix of .

[0019] As a further optimization scheme of the coherent signal DOA estimation method based on a coprime array of the present invention, the covariance matrix is ​​decomposed according to the following formula in step 2):

[0020]

[0021] Among them, U s 、U n are the signal subspace and the noise subspace respectively, D s 、D n are the eigenvalue matrices corresponding to the signal subspace and the noise subspace respectively.

[0022] As a further optimization scheme of the coherent signal DOA estimation method based on coprime arrays of the present invention, the eigenvector corresponding to the maximum eigenvalue in step 3) is Among them, α(k) is the linear combination factor.

[0023] As a further optimization solution of the coherent signal DOA estimation method based on a coprime array of the present invention, in step 4), g1=e1(1:M), g2=e1(M+1:M+N).

[0024] As a further optimization solution of the coherent signal DOA estimation method based on a coprime array of the present invention, in step 5):

[0025]

[0026]

[0027] in To round up.

[0028] Compared with the prior art, the present invention adopts the above technical solution and has the following technical effects:

[0029] The present invention can use a coprime array to perform angle estimation of a coherent signal, making up for the deficiency of a coprime array in coherent signal angle estimation, and can effectively and accurately obtain the incident angle of a coherent signal. The method of the present invention can cleverly circumvent the problem of fuzzy angle estimation of sub-arrays of a coprime array, and by rearranging the elements in the maximum eigenvector, two rank-recovered Hankel matrices are obtained, and then the coprime characteristics are used to search for the positions where overlapping spectral peaks appear, thereby obtaining the angle estimation value of the coherent signal. Compared with the traditional uniform linear array for coherent signal estimation, the method of the present invention has higher coherent signal angle estimation accuracy and can more reliably perform target positioning. Compared with the incoherent angle estimation of a coprime array, the method of the present invention can effectively estimate the target angle in a multipath (coherent) scenario, and has greater application value. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] Figure 1 It is a schematic diagram of the process of the present invention;

[0031] Figure 2 is the MUSIC spectrum of the present invention;

[0032] Figure 3 Schematic diagram of the angle estimation performance of the present invention under different signal-to-noise ratios;

[0033] Figure 4 Schematic diagram of the angle estimation performance of the present invention when it changes with snapshots. DETAILED DESCRIPTION

[0034] The technical solution of the present invention is further described in detail below with reference to the accompanying drawings:

[0035] 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 convey the scope of the invention to those skilled in the art. In the accompanying drawings, components are enlarged for clarity.

[0036] like Figure 1 As shown, the present invention discloses a coherent signal DOA estimation method based on a coprime array, which is specifically as follows:

[0037] Step 1), for coprime arrays Find the covariance matrix R of coprime arrays xx ;

[0038] Coprime arrays

[0039] Among them, M and N are two mutually prime integers, d is the unit spacing of the array elements, which is set to half the wavelength of the incident signal. and Coprime matrices Two subarrays of ;

[0040] Coprime array output vector

[0041] in, is the direction matrix, a(θ k )=[a1(θ k ) T ,a2(θ k ) T ] T is the steering vector, n(t)=[n1(t) T ,n2(t) T ] T is the noise vector; A1 and A2 are the sub-arrays corresponding to Subarray The steering matrix, A1=[a1(θ1),a1(θ2),...,a1(θ K )](k∈[1,2,...,K]), is the steering vector of A1; A2=[a2(θ1),a2(θ2),...,a2(θ K )](k∈[1,2,...,K]), is the steering vector of A2; s(t)=[s1(t),s2(t),...,s K (t)] T is the signal vector, n(t), n1(t), n2(t) are zero-mean Gaussian white noise vectors, and C is the mutual coupling matrix; c l =c1e -j(l-1)π / 8 / l(l∈[2,4]) is the mutual coupling coefficient, |c1|=0.4, c0=1>|c1|>|c2|>...>|c4|>0;

[0042] The covariance matrix of coprime arrays is

[0043] Among them, R 11 、R 22 Sub-arrays Subarray The autocorrelation covariance matrix, R 12 、R 21 Sub-arrays Correlation subarray Subarray Correlation subarray The cross-correlation covariance matrix of .

[0044] Step 2), perform eigendecomposition on the covariance matrix;

[0045]

[0046] Among them, U s 、U n are the signal subspace and the noise subspace respectively, D s 、D n are the eigenvalue matrices corresponding to the signal subspace and the noise subspace respectively.

[0047] Step 3), after eigendecomposition, find the eigenvector corresponding to the maximum eigenvalue Among them, α(k) is the linear combination factor.

[0048] Step 4) Decompose e1 into two parts according to the number of elements of the coprime array, namely g1 and g2, where g1 = e1(1:M) and g2 = e1(M+1:M+N).

[0049] Step 5) Rearrange the elements in g1 and g2 to obtain two Hankel matrices, denoted as H1 and H2:

[0050]

[0051]

[0052] in To round up.

[0053] Step 6), perform singular value decomposition on H1 and H2 respectively to obtain the noise subspace of H1 and H2.

[0054] Step 7) Based on the noise subspace of H1 and H2, the MUSIC method is applied to draw the spatial spectrum of H1 and H2, find the same spectral peak in the spatial spectrum of H1 and H2, record the DOA value corresponding to the spectral peak in the spatial spectrum of H1 and H2, and average them to obtain the final DOA estimate.

[0055] In order to verify the correctness and advancement of the method of this embodiment, a simulation experiment was conducted on the method, assuming that the initial array element positions of the coprime array are The coprime integers selected are M=5, N=8, 0.5 is the unit spacing of the array elements, and there are K=2 coherent signals incident on the array from angles of 10° and 40°, such as Figure 2 As shown in Figure 2, it can be seen that the two spectra overlap at 10° and 40°, and the overlap position corresponds to the incident angle of the coherent signal. Figure 3 As shown in , compared with the uniform linear array and spatial smoothing methods, when the signal-to-noise ratio is greater than 0 dB, this method can greatly improve the DOA estimation accuracy. At the same time, the greater the signal-to-noise ratio, the higher the estimation accuracy. Figure 4 As shown in Figure 3, this method can effectively improve the DOA estimation accuracy when the number of snapshots is greater than 200. At the same time, the larger the number of snapshots, the higher the estimation accuracy.

[0056] In summary, the present invention proposes a coherent signal DOA estimation method based on a coprime array. The method of the present invention can cleverly circumvent the problem of ambiguity in the angle estimation of the coprime array subarrays. By rearranging the elements in the maximum eigenvector, two rank-recovered Hankel matrices are obtained. Then, the coprime characteristics are used to search for the positions where the overlapping spectral peaks appear, thereby obtaining the angle estimation value of the coherent signal. Compared with the traditional uniform linear array for coherent signal estimation, the method of the present invention has higher coherent signal angle estimation accuracy and can more reliably locate the target. Compared with the incoherent angle estimation of the coprime array, the method of the present invention can effectively estimate the target angle in a multipath (coherent) scenario and has greater application value.

[0057] 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 commonly 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 their meanings in the context of the prior art and, unless defined as such, will not be interpreted in an idealized or overly formal sense.

[0058] 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 coherent signal DOA estimation method based on a coprime array, characterized in that: The following steps are involved: Step 1), for coprime arrays Find the covariance matrix R of coprime arrays xx ; Step 2), perform eigendecomposition on the covariance matrix; Step 3), after eigendecomposition, find the eigenvector e1 corresponding to the maximum eigenvalue; Step 4) Decompose e1 into two parts, g1 and g2, according to the number of elements of the coprime arrays. Step 5), rearrange the elements in g1 and g2 to obtain two Hankel matrices, denoted as H1 and H2; Step 6), perform singular value decomposition on H1 and H2 respectively to obtain the noise subspace of H1 and H2; Step 7) Based on the noise subspace of H1 and H2, the MUSIC method is applied to draw the spatial spectrum of H1 and H2, find the same spectral peak in the spatial spectrum of H1 and H2, record the DOA value corresponding to the spectral peak in the spatial spectrum of H1 and H2, and average them to obtain the final DOA estimate.

2. The coherent signal DOA estimation method based on a coprime array according to claim 1, characterized in that: In the step 1), the mutually prime arrays Among them, M and N are two mutually prime integers, d is the unit spacing of the array elements, which is set to half the wavelength of the incident signal. and Coprime matrices Two subarrays of ; Coprime array output vector in, is the direction matrix, a(θ k )=[a1(θ k ) T ,a2(θ k ) T ] T is the steering vector, n(t)=[n1(t) T ,n2(t) T ] T is the noise vector; A1 and A2 correspond to the sub-matrix Subarray The steering matrix, A1=[a1(θ1),a1(θ2),...,a1(θ K )](k∈[1,2,...,K]), is the steering vector of A1; A2=[a2(θ1),a2(θ2),...,a2(θ K )](k∈[1,2,...,K]), is the steering vector of A2; s(t)=[s1(t),s2(t),...,s K (t)] T is the signal vector, n(t), n1(t), n2(t) are zero-mean Gaussian white noise vectors, and C is the mutual coupling matrix; c l =c1e -j(l-1)π / 8 / l(l∈[2,4]) is the mutual coupling coefficient, |c1|=0.4, c0=1>|c1|>|c2|>...>|c4>|0; The covariance matrix of coprime arrays is Among them, R 11 、R 22 Sub-arrays Subarray The autocorrelation covariance matrix, R 12 、R 21 Sub-arrays Correlation subarray Subarray Correlation subarray The cross-correlation covariance matrix of .

3. The coherent signal DOA estimation method based on a coprime array according to claim 2, characterized in that: In the step 2), the covariance matrix is ​​decomposed according to the following formula: Among them, U s 、U n are the signal subspace and the noise subspace respectively, D s 、D n are the eigenvalue matrices corresponding to the signal subspace and the noise subspace respectively.

4. The coherent signal DOA estimation method based on a coprime array according to claim 3, characterized in that: The eigenvector corresponding to the maximum eigenvalue in step 3) Among them, α(k) is the linear combination factor.

5. The coherent signal DOA estimation method based on a coprime array according to claim 4, characterized in that: In the step 4), g1 = e1 (1:M), g2 = e1 (M+1:M+N).

6. The coherent signal DOA estimation method based on a coprime array according to claim 5, characterized in that: In the step 5): in To round up.

Images