A one-bit sampling DOA estimation method with array mutual coupling

Abstract

The present invention discloses a one-bit sampling DOA estimation method in the presence of array mutual coupling, which belongs to parameter estimation in the field of array signal processing. The present invention is as follows: a uniform linear array composed of M array elements is set, and one-bit sampling is performed on the measured value of each array element; the normalized original covariance matrix is ​​restored by using arcsine law; the guiding matrix structure of the normalized covariance matrix is ​​given by matrix transformation; a sparse vector is constructed by gridding the spatial domain; the influence of the normalized noise matrix on the eigenvalue decomposition is avoided by using the idea of ​​iteration, and an accurate noise subspace is obtained; a weighting matrix is ​​constructed to enhance the sparsity of the sparse vector; and finally a sparse recovery problem is proposed for DOA estimation. Therefore, the present invention greatly reduces the system cost, power consumption and data transmission and storage by using one-bit sampling data, and has the advantages of high estimation accuracy, high resolution, and accurate DOA estimation can be achieved without mutual coupling compensation.

Description

Technical Field

[0001] The invention belongs to parameter estimation in the field of array signal processing, and in particular relates to a one-bit sampling DOA estimation method with array mutual coupling. Background Art

[0002] DOA estimation has always been a key issue in the field of array signal processing and has broad application prospects in radar, sonar and communication systems.

[0003] In the past few decades, many DOA estimation methods have been proposed, such as subspace methods, compressed sensing and sparse recovery algorithms. These methods perform well in ideal situations (i.e., the array manifold is known). However, in specific projects, the unknown mutual coupling (MC) caused by the interaction between array elements will significantly affect the array reception data, causing the DOA estimation performance to degrade. In order to solve this problem, scholars at home and abroad have proposed some algorithms. In the paper "Liao B, Zhang ZG, Chan S C. DOA Estimation and Tracking of ULAs with Mutual Coupling [J]. IEEE Transactions on Aerospace & Electronic Systems, 2012, 48 (1): 891-905", the authors regard the direction-independent mutual coupling coefficient as the direction-dependent complex array gain, and use a subspace algorithm similar to MUSIC to realize the joint estimation of DOA and mutual coupling coefficient. The paper "Ateavc CS, Bahadrlar Y, Olak S A. DoA Estimation in the Presence of Mutual Coupling using Root-MUSIC Algorithm [C] / / 2021 8th International Conference on Electrical and Electronics Engineering (ICEEE). 2021" uses the root-MUSIC algorithm to effectively estimate the DOA and mutual coupling coefficient. In the paper "Hao L, Ping W. DOA estimation in an antenna array with mutual coupling based on ESPRIT [C] / / International Workshop on Microwave & Millimeter Wave Circuits & System Technology. IEEE, 2014", an ESPRIT-like algorithm is proposed to solve the DOA estimation problem under unknown mutual coupling coefficients.The paper "Dai J, Xu B, Nan H, et al. A Recursive RARE Algorithm for DOA Estimation With Unknown Mutual Coupling [J]. IEEE Antennas & Wireless Propagation Letters, 2014, 13: 1593-1596" studies a recursive rank reduction (RARE) algorithm. However, none of the above methods consider the sampling quantization of the received signal, which makes these algorithms unable to work well under limited quantization accuracy.

[0004] If we only consider the performance of the algorithm, high-resolution quantization must be the best choice. However, from the perspective of practical application, due to high hardware cost and high system power consumption, high-resolution quantization may be difficult to achieve in many complex systems. Therefore, one-bit sampling has attracted widespread attention in recent years, and many DOA estimation methods based on one-bit sampling have been proposed. The literature "Vleck J, Middleton D. The Spectrum of Clipped Noise [J]. Proceedings of the IEEE, 1966, 54 (1): 2-19" analyzes the impact of one-bit sampling on the correlation coefficient, and thus proposes the arcsine law. In the literature "Jacovitti G, Neri A. Estimation of the autocorrelation function of complex Gaussian stationary processes by amplitude clipped signals [J]. IEEE Transactions on Information Theory, 1994, 40 (1): 239-245", the authors applied this conclusion to DOA estimation and analyzed the impact of the number of quantization bits on the DOA estimation performance, paving the way for subsequent work. In the paper "Liu CL, Vaidyanathan P P. One-bit sparse array DOA estimation [C] / / ICASSP 2017-2017 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). IEEE, 2017", the method was extended to sparse arrays, using more virtual array elements to improve the DOA estimation performance. In addition, sparse Bayesian learning, joint sparse representation and other methods are also used in one-bit DOA estimation.

[0005] Although the problem of mutual coupling or one-bit sampling has been widely discussed in many literatures, the DOA estimation problem in the specific case where these two problems exist simultaneously has not been solved. Therefore, it is necessary to study how to perform robust DOA estimation under one-bit sampling. Summary of the invention

[0006] The purpose of the present invention is to propose a robust DOA estimation method based on one-bit sampling when there is mutual coupling effect between array elements, so as to avoid high hardware cost and high system power consumption caused by high-precision analog-to-digital converters. The method does not lose array aperture and does not require array calibration, and is relatively simple in actual operation.

[0007] The present invention provides a one-bit sampling DOA estimation method in the presence of array mutual coupling, the method comprising:

[0008] Step 1, setting an antenna array, wherein the antenna array is a uniform linear array composed of M array elements, wherein the array element spacing is d=λ / 2, λ represents the signal wavelength, and the number of received signals of the antenna array is defined as K, the unquantized observation data vector of the array is x(t), and the one-bit observation data vector of the array is y(t);

[0009] Step 2: Calculate the normalized covariance matrix:

[0010] (2a) Calculate the covariance matrix R of the observed data y(t) with N snapshots y ;

[0011] (2b) Calculate the normalized covariance matrix

[0012]

[0013] Among them, the matrix It is a diagonal matrix, and the values ​​of the middle M-2P+2 non-zero elements are the same, which is defined as γ. P represents the number of array element intervals that allow the mutual coupling effect to be ignored, that is, the mutual coupling effect between two array elements that are P array element intervals apart can be ignored. and Represent the real and imaginary parts of the complex number, j represents the imaginary unit, C represents the interconnected matrix, and A represents the array manifold matrix of K signals, represents the noise power, R s Represents the covariance matrix of the source.

[0014] Step 3: Matrix transformation processing:

[0015] (3a) Convert the product of the mutual coupling matrix and the steering vector into Ca(θ)=T(θ)α;

[0016] Where T(θ)=blkdiag{T1,T2,T3}, T1=diag{1,β(θ),...,β P-2 (θ)}, T2=[β P-1 (θ),...,β M-P (θ)] T ;

[0017] T3 = diag{β M-P+1 (θ),...,β M-1 (θ)}, β(θ)=e j2πdsinθλ , α=[μ1,...,μ P-1 ,τ(θ),α1,...,α P-1 ] T ;

[0018] (3b) According to the normalized matrix G -1 / 2 The structure and element size of the matrix T(θ) are converted into G -1 / 2 T(θ)=T(θ)D, and we get G -1 / 2 Ca(θ)=G -1 / 2 T(θ)α=T(θ)Dα, where D=diag[ρ1,ρ2,...,ρ P-1 ,γ,ν1,ν2,...,ν P-1 ] is a diagonal matrix of dimension 2P-1;

[0019] Step 4: Construct a sparse vector:

[0020] (4a) The normalized covariance matrix Column vectorization gives the equivalent received signal vector r:

[0021]

[0022] in, represents the power of the kth signal, vec(·) denotes column vectorization, and ⊙ denotes the Hadamard product.

[0023] (4b) The equivalent received signal vector r is transformed into:

[0024]

[0025] Where η=Dα, represents the Kronecker product;

[0026] (4c) The spatial angle is evenly divided into N grids, denoted as Where N>>K;

[0027] (4d) Re-express the equivalent received signal vector r as a sparse vector:

[0028]

[0029] in, is the dictionary matrix, Indicates that the sparsity is K(2P-1) 2 The block sparse column vector of ;

[0030] Step 5, obtain the accurate noise subspace:

[0031] (5a) Set the initial value of the number of iterations i (e.g., i=0), set the convergence threshold ε (e.g., ε=0.001), and initialize the matrix Q i , for example Q i =I M I M Represents the dimension as M×M identity matrix;

[0032] (5b) Eigenvalue decomposition, Get the signal subspace E is and the noise subspace E in and the corresponding eigenvalue matrix Λ is and Λ in ;

[0033] (5c) Update Q i+1 for in Represents a diagonal matrix consisting of the diagonal elements of the matrix in brackets, and updates i=i+1.

[0034] (5d) Repeat steps (5b) and (5c) until

[0035] Step 6, construct the weighted matrix:

[0036] (6a) According to the spatial grid angle Calculate separately Where E in is the noise subspace obtained in the last iteration of step 5, det(·) means finding the determinant;

[0037] (6b) Construct the weight matrix where w = max{w1,...,w N}.

[0038] Step 7, get the estimated DOA:

[0039] (7a) Block sparse vector based Constructing sparse vectors Among them, h o The nth element of express The lth element of

[0040] (7b) Use the equivalent received signal vector to construct the optimization problem:

[0041]

[0042] Where ξ is the regularization parameter, ||·||1 and ||·||2 represent the l1 and l2 norms respectively;

[0043] Solve the constructed optimization problem and obtain the sparse vector h o The angle corresponding to the largest K elements in is the estimated DOA.

[0044] The technical solution provided by the present invention brings at least the following beneficial effects:

[0045] In the present invention, one-bit sampling is used to reduce system cost and power consumption as well as data transmission storage; robust DOA estimation can be achieved without prior array calibration, which is relatively simple to implement; there is no loss of array aperture, and the angular resolution is high. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings required for use in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0047] Figure 1 The figure is a schematic diagram of the uniform linear array structure configuration targeted by the present invention.

[0048] Figure 2 Schematic diagram of the relationship between the root mean square error of DOA and SNR in the simulation experiment of the embodiment of the present invention.

[0049] Figure 3 Schematic diagram of the relationship between the root mean square error of DOA and the number of snapshots in the simulation experiment according to the embodiment of the present invention.

[0050] Figure 4 Schematic diagram of the relationship between DOA resolution probability and angular interval in a simulation experiment of an embodiment of the present invention. DETAILED DESCRIPTION

[0051] In order to make the objectives, technical solutions and advantages of the present invention more clear, the embodiments of the present invention will be further described in detail below with reference to the accompanying drawings.

[0052] The present invention is directed to a uniform linear array, wherein the number of array elements is M, the array element spacing is d=λ / 2, wherein λ is the signal wavelength, and the specific array structure is as follows: Figure 1 As shown. The specific algorithm is: first, a one-bit covariance matrix is ​​calculated using the one-bit observation vector of the array, and then the normalized covariance matrix is ​​restored according to the arcsine law. Then, in order to combat the unknown mutual coupling effect in the uniform linear array, the product of the mutual coupling matrix and the steering vector is reparameterized, and a matrix transformation is used to avoid the influence of the normalized matrix. Subsequently, a sparse vector is constructed through grid division. After that, the iterative step is used to solve the problem of inability to obtain an accurate noise subspace caused by the equivalent non-uniform noise matrix. Next, a weighting matrix is ​​constructed to enhance the sparsity of the sparse vector in the sparse recovery problem. Finally, a sparse recovery problem of a single measurement vector is constructed for DOA estimation.

[0053] The specific implementation steps include:

[0054] Step 1: Set up the antenna array:

[0055] Set up a Figure 1 The uniform linear array shown has a total of M = 11 array elements, and the array element spacing is d = λ / 2. Assume that a total of K narrowband stationary independent Gaussian signals are incident on the array, and the signal arrival directions are {θ1,θ2,…,θ K}, then the unquantized observation vector of the array at time t can be expressed as:

[0056]

[0057] Where s(t)=[s1(t),s2(t),...,s K (t)] T Represents the source signal waveform vector. Represents a noise vector whose elements follow a Gaussian distribution. The array manifold matrix representing K signals, θ K represents the arrival direction of the kth signal, where Represents the steering vector of the kth signal.

[0058] If the mutual coupling effect between array elements is considered, the above signal model will change. In particular, for uniform linear arrays, the mutual coupling matrix can be described as a complex symmetric band Toeplitz matrix. The greater the distance between array elements, the smaller the influence of the mutual coupling effect. When the distance between two array elements is far enough, it can be approximated to zero. If it is assumed that when any two array elements are When the array elements are separated by a gap, the mutual coupling effect between the two array elements can be ignored. Then, the mutual coupling matrix can be written as

[0059]

[0060] here And c1=1>|c2|>…>|c P |,c2~c P Represents the 2nd to Pth elements of the mutual coupling matrix C.

[0061] In this case, the signal model needs to be rewritten as:

[0062]

[0063] In order to reduce hardware cost and system power consumption, a one-bit ADC is used to quantize the received data, and the corresponding array output becomes:

[0064] y(t)=signe(x(t))=signe(CAs(t)+n(t)) (9)

[0065] in, represents a complex-valued quantization function, where sign(·) represents a sign function, and Represents the real and imaginary parts of a complex number respectively.

[0066] Step 2: Calculate the normalized covariance matrix:

[0067] First, the covariance matrix of x(t) can be written as

[0068]

[0069] Among them, E[] represents the mathematical expectation, R s represents the covariance matrix of the source, R s =E{s(t)s H (t)}, represents the noise power and I represents the identity matrix.

[0070] Then define the normalized covariance matrix for:

[0071]

[0072] where G is a diagonal matrix satisfying <g> m,m = <R x > m,m For ease of explanation, the spatial phase factor is defined as According to equation (10), the diagonal elements in G corresponding to the mth antenna (P-1<m<M-P+1) can be expressed as

[0073]

[0074] From formula (12), we can see that the values ​​of the diagonal elements from the P-1th to the M-P+1th of G are equal, which is denoted as γ here. Then G can be written as where ρ1,...,ρ P-1 and ν1,...,ν P-1 Represent the first P-1 and last P-1 diagonal elements of G respectively.

[0075] The covariance matrix R of the observed data y(t) y The calculation formula is:

[0076]

[0077] Where N is the number of snapshots. n ) represents the tth n Observation data of sampling points.

[0078] When the sources follow independent Gaussian distributions, the normalized covariance matrix and the one-bit covariance matrix R y The relationship between can be established by the arcsine law as

[0079]

[0080] in

[0081] Therefore, the normalized covariance matrix can be reconstructed using formula (14), expressed as

[0082]

[0083] in

[0084] Step 3: Matrix transformation:

[0085] To combat the unknown mutual coupling effect in uniform linear arrays, a classical transformation is used to convert the product of the mutual coupling matrix and the steering vector into

[0086] Ca(θ)=T(θ)α (16)

[0087] in

[0088]

[0089] is a matrix of dimension M×(2P-1), and

[0090] α=[μ1,...,μ P-1 ,τ(θ),α1,...,α P-1 ] T (18)

[0091] is a vector of length 2P-1, where

[0092] Based on the above transformation, we have G -1 / 2 Ca(θ)=G -1 / 2 T(θ)α. It is worth noting that multiplying a matrix by a diagonal matrix on the left is equivalent to multiplying each row of the matrix by the diagonal elements of the same row in the diagonal matrix, and multiplying a matrix by a diagonal matrix on the right is equivalent to multiplying each column of the matrix by the diagonal elements of the same column in the diagonal matrix. -1 / 2 The rows with the same value in the elements correspond to the middle M-P+2 rows of T(θ). Due to the special structure of T(θ), T(θ) can be transformed from a diagonal matrix multiplied on the right to another diagonal matrix multiplied on the left. Therefore,

[0093] G -1 / 2 Ca(θ)=G -1 / 2 T(θ)α=T(θ)Dα (19)

[0094] in

[0095] Step 4: Construct sparse vector:

[0096] First, the normalized covariance matrix Column vectorization to obtain the equivalent received signal vector;

[0097]

[0098] in is the source power vector,

[0099] Then, using the matrix transformation in formula (19), the above formula can be re-expressed as

[0100]

[0101] Where η=Dα,

[0102] So the matrix form r can be organized as:

[0103] r=Bh+i n (twenty two)

[0104] in

[0105] Then the spatial angle is discretized and divided into N grids in total: Where N>>K, r can be expressed as a sparse vector:

[0106]

[0107] in is an overcomplete dictionary matrix, Indicates that the sparsity is K(2P-1) 2 The column vector of each block is of dimension (2P-1) 2 .

[0108] Step 5: Obtain the accurate noise subspace:

[0109] In order to enhance the sparsity of sparse vectors, a weight matrix will be constructed, but the formula (11) It can be regarded as a non-uniform noise matrix, which will affect the result of eigenvalue decomposition and make it impossible to obtain an accurate subspace. To this end, through eigenvalue decomposition, the non-uniform noise matrix is ​​updated with a noise-free covariance matrix composed of K large eigenvalues ​​and K large eigenvectors until the iteration termination condition is met. The specific iteration steps are as follows:

[0110] (5a) First, initialize the iteration variables, set i = 0, Q0 = I M , ε=0.001.

[0111] (5b) Then Eigenvalue decomposition, Get the signal subspace and the noise subspace and the corresponding eigenvalue matrix and (E ks and E kn are matrices consisting of the eigenvectors corresponding to the K larger eigenvalues ​​and the MK smaller eigenvalues, respectively, ks and Λ kn is the diagonal matrix consisting of the corresponding eigenvalues).

[0112] (5c) Update Q i+1 for in It represents a diagonal matrix composed of the diagonal elements of the matrix in brackets, and sets i=i+1.

[0113] (5d) Repeat steps (5b) and (5c) until The E obtained in the last iteration in This is the exact noise subspace.

[0114] Step 6: Construct the weighting matrix:

[0115] Consider the normalized covariance matrix The noise-free part

[0116]

[0117] E obtained in the last iteration of step 5 in That is The noise subspace, then according to the subspace principle, for the true wave arrival direction θ k ,matrix It's strange.

[0118] Then according to the spatial grid angle Calculate separately det(·) means finding the determinant.

[0119] Finally, the weighted matrix is ​​constructed as where w = max{w1,...,w N }.

[0120] Step 7: Formulate the optimization problem:

[0121] Knowing that the source angle is a block sparse vector The positions of non-zero elements in are determined by The angles corresponding to the non-zero elements in the same block are also the same. Based on this feature, a sparse vector is constructed. The nth element of which is equal to The (n-1)(2P-1)th 2 +1 to nth (2P-1) 2 The l2 norm of the elements is express The lth element of .

[0122] Using the weighted matrix, the optimization problem is given

[0123]

[0124] Among them, large weight makes h o The corresponding elements in are more likely to be 0, and small weights make h o The corresponding elements in are retained, thereby enhancing h o The sparsity of .

[0125] Applying the LASSO model to the above optimization problem, we can get

[0126]

[0127] Where ξ is the regularization parameter, ||·||1 and ||·||2 represent the l1 and l2 norms respectively, and the sparse vector h o The angle corresponding to the largest K elements in is the estimated DOA.

[0128] In order to verify the performance of the algorithm, three simulation experiments are set up in this embodiment. In the simulation experiments, the method proposed in the present invention is compared with LASSO with mutual coupling, LASSO without mutual coupling, MUSIC with mutual coupling, MUSIC without mutual coupling and intermediate subarray algorithm. The first simulation experiment shows the relationship between the root mean square error of DOA estimation and the signal-to-noise ratio when the number of snapshots is 2000 for several algorithms. The second simulation experiment shows the relationship between the root mean square error of DOA estimation and the number of snapshots when the signal-to-noise ratio is 30dB for several algorithms. The third simulation experiment shows the relationship between the resolution probability of adjacent signal sources of the present invention and the intermediate subarray algorithm and the angular interval under the conditions of a signal-to-noise ratio of 30dB and a snapshot number of 2000. The experimental results are shown as follows: Figure 2 , 3 As shown in , the algorithm proposed in the figure refers to the one-bit sampling DOA estimation method with array mutual coupling provided by an embodiment of the present invention.

[0129] The number of random experiments in the three simulation experiments is 200. The uniform linear array used is the same, the number of array elements is 11, the array spacing is d=λ / 2, the mutual coupling parameters are set to P=3, c2=0.6864+0.4776i, c3=0.4864+0.3376i, and the regularization parameter is ξ=0.5. The number of incident signal sources in the first two experiments is K=2, and the arrival angles are θ1=10° and θ2=55° respectively. The third experiment also considers two signals, and the incident angles are θ1=10°-Δθ / 2 and θ2=10°+Δθ / 2 respectively, where Δθ is the angle interval. The present invention can use one-bit sampling data for DOA estimation when there is a mutual coupling effect between array elements, which greatly reduces the energy consumption of the system and the burden of data transmission and storage, and utilizes the entire array aperture, with higher DOA estimation performance and angular resolution.

[0130] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention.

[0131] The above are only some embodiments of the present invention. For those skilled in the art, several modifications and improvements can be made without departing from the creative concept of the present invention, which all belong to the protection scope of the present invention.< / g>

Claims

1. A one-bit sampling DOA estimation method with array mutual coupling, characterized in that: The following steps are involved: Step 1, setting an antenna array, wherein the antenna array is a uniform linear array composed of M array elements, wherein the array element spacing is d=λ / 2, λ represents the signal wavelength, and the number of received signals of the antenna array is defined as K, the unquantized observation data vector of the array is x(t), and the one-bit observation data vector of the array is y(t); Step 2: Calculate the normalized covariance matrix: (2a) Calculate the covariance matrix R of the observed data y(t) with N snapshots y ; (2b) Calculate the normalized covariance matrix Among them, the matrix is a diagonal matrix with the same value of the middle M-2P+2 non-zero elements, defined as γ, P represents the number of array element intervals that allow the mutual coupling effect to be ignored, C represents the mutual coupling matrix, and A represents the array manifold matrix of K signals, represents the noise power, R s represents the covariance matrix of the source; Step 3: Matrix transformation processing: (3a) Convert the product of the mutual coupling matrix and the steering vector into Ca(θ)=T(θ)α; Where T(θ) = blkdiag{T1,T2,T3}; T1=diag{1,β(θ),...,β P-2 (i)}; T2=[β P-1 (i),...,b M-P (i)] T ; T3=diag{β M-P+1 (i),...,b M-1 (θ)}, β(θ)=e j2πdsinθ / λ ; α=[μ1,...,μ l ,...,m P-1 ,τ(θ),α1,...,α l ,…,a P-1 ] T ; c k represents the kth element of the mutual coupling matrix C; (3b) According to the normalized matrix G -1 / 2 The structure and element size of the matrix T(θ) are converted into G -1 / 2 T(θ)=T(θ)D, and we get G -1 / 2 Ca(θ)=G -1 / 2 T(θ)α=T(θ)Dα, where D=diag[ρ1,ρ2,…,ρ P-1 ,γ,ν1,ν2,…,ν P-1 ] is a diagonal matrix of dimension 2P-1; Step 4: Construct a sparse vector: (4a) The normalized covariance matrix Column vectorization gives the equivalent received signal vector r: in, represents the power of the kth signal, vec(·) means column vectorization; (4b) The equivalent received signal vector r is transformed into: Where, η = Dα, (4c) The spatial angle is evenly divided into N grids, denoted as Where N>>K; (4d) Re-express the equivalent received signal vector r as a sparse vector: in, is the dictionary matrix, Indicates that the sparsity is K(2P-1) 2 The block sparse column vector of ; Step 5, obtain the accurate noise subspace: (5a) Set the initial value of the number of iterations i, set the convergence threshold ε, and initialize the matrix Q i ; (5b) Eigenvalue decomposition, Get the signal subspace E is And its eigenvalue matrix Λ is , the noise subspace E in And its eigenvalue matrix Λ in ; (5c) Update Q i+1 for in represents a diagonal matrix consisting of the diagonal elements of the matrix in brackets, and updates i=i+1; (5d) Repeat steps (5b) and (5c) until Step 6, construct the weighted matrix: (6a) According to the spatial grid angle Calculate separately Where E in is the noise subspace obtained in the last iteration of step 5, det(·) means finding the determinant; (6b) Construct the weighted matrix where w = max{w1,...,w N }; Step 7, get the estimated DOA: (7a) Block sparse vector based Constructing sparse vectors Among them, h o The nth element of express The lth element of (7b) Use the equivalent received signal vector to construct the optimization problem: Where ξ is the regularization parameter, ||·||1 and ||·||2 represent the l1 and l2 norms respectively; Solve the constructed optimization problem and obtain the sparse vector h o The angle corresponding to the largest K elements in is the estimated DOA.

2. The method according to claim 1, characterized in that In step 5 (5a), initialize Q i =I M , I M Represents an M×M identity matrix.

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