DOA estimation method for nested array structure

Abstract

The invention discloses a DOA estimation method for a nested array structure, and the method comprises the steps: receiving data through a nested array, and calculating a covariance matrix of a received signal; vectorizing the covariance matrix of the received signal, and sorting and deleting a redundant part to obtain a virtual array received signal; extracting a continuous part of a virtual array receiving signal to obtain a receiving signal of a continuous virtual array; obtaining a received signal covariance matrix of the continuous virtual array through a spatial smoothing method; and carrying out eigenvalue decomposition on the covariance matrix to obtain a noise subspace, and constructing a rooting MUSIC formula to obtain a root and a corresponding DOA estimation result. According to the method, higher estimation precision can be realized, a spectrum peak search process is avoided, and the calculation complexity is relatively low.

Description

Technical Field

[0001] The present invention relates to the technical field of array signal processing, and in particular to a DOA estimation method for a nested array structure. Background Art

[0002] Array signal processing is an important branch of signal processing. It is widely used in various fields such as communication, sonar, radar, biomedicine, etc. Direction of Arrival (DOA) estimation is an important direction of array signal processing. It is a technology that estimates the location of the signal source through the signal received by the sensor array. The traditional antenna layout is limited by half a wavelength, that is, the spacing between array elements must be less than half a wavelength. Therefore, when the number of antennas is fixed, the aperture of the antenna is limited. In addition, the number of targets that can be identified by the traditional direction of arrival estimation algorithm is limited by the number of antenna elements in the physical array, that is, the degree of freedom. When the number of targets exceeds the number of antenna elements, many algorithms will fail.

[0003] Due to the sparse distribution of elements in the nested array structure, a very long continuous virtual array can be obtained after virtualization operation, which has a large degree of freedom, thus greatly improving the DOA estimation accuracy. Although the DOA estimation methods proposed for the virtual array of the nested array, such as SS-MUSIC, have high estimation accuracy, they have the problem of great complexity.

[0004] The invention with publication number CN114325568A discloses a method for estimating DOA of non-circular signals of nested arrays based on BNC in an impulse noise environment. A bounded nonlinear function is used to suppress outliers in the received signal, a BNC matrix is ​​constructed, vectorization processing is performed, and the received signal information of a virtual uniform linear array with an array element spacing of half a wavelength is obtained by rearranging and removing redundancy. A dimensionality reduction MUSIC method is used. However, since the invention cannot avoid the spectrum peak search process, it can only reduce the computational complexity to a certain extent. Summary of the invention

[0005] The purpose of the present invention is to propose a DOA estimation method for a nested array structure. After the virtualization operation, a root-finding MUSIC algorithm is used, and the DOA estimation result can be directly obtained through a closed-form solution, avoiding the spectrum peak search process. Therefore, the present invention can ensure a high DOA estimation accuracy while greatly reducing the calculation complexity when the total number of antennas is the same, and is easy to be applied in practice.

[0006] In order to achieve the above technical objectives, the technical solution adopted by the present invention is:

[0007] A DOA estimation method for a nested array structure, the DOA estimation method comprising the following steps:

[0008] S1, using nested arrays to receive data and calculate the covariance matrix of the received signal;

[0009] S2, vectorizing the covariance matrix of the received signal, sorting it and deleting the redundant parts to obtain a virtual array received signal;

[0010] S3, extracting a continuous part of the virtual array receiving signal to obtain a continuous virtual array receiving signal;

[0011] S4, obtaining the covariance matrix of the received signal of the continuous virtual array by a spatial smoothing method;

[0012] S5, performing eigenvalue decomposition on the covariance matrix to obtain the noise subspace and constructing the root-finding MUSIC formula to obtain the root and the corresponding DOA estimation result.

[0013] Step S1 further comprises the following steps:

[0014] Construct a nested array, the array element of the nested array is represented as d 1 =λ / 2,d 2 =(M 1 +1)λ / 2; where λ represents the wavelength of the incident signal; when the total number of array elements M is an even number, M 1 =M 2 =M / 2, when M is an odd number, M 1 =(M-1) / 2,M 2 =(M+1) / 2;

[0015] Assume that K far-field narrowband incident angles are θ k The irrelevant signal is incident on the nested array, and the array receives data represented as:

[0016]

[0017] Where k = 1, 2, ..., K, represents the direction matrix; represents the direction vector of the kth signal, D m represents the position of the mth array element; s(t)=[s 1 (t),s 2 (t),…,s K (t)] T represents the source vector; represents the kth received signal within L snapshots; n(t) represents the mean value of 0 and the variance of σ 2 Gaussian white noise vector; t∈[1,2,…L] represents the sampling time, and L represents the number of snapshots.

[0018] The covariance matrix of the received signal is expressed as:

[0019]

[0020] In the formula, is the power of the kth source; R s is the signal covariance matrix and satisfies diagonal non-singularity;

[0021] Considering a finite number of snapshots, the covariance matrix is ​​expressed as:

[0022]

[0023] Wherein, L represents the number of snapshots.

[0024] Step S2 further comprises the following steps:

[0025] The covariance matrix R xx Perform vectorized operations to obtain the matrix z:

[0026]

[0027] in, represents the direction matrix of the virtual array;

[0028]

[0029] Sort the vectorized matrix z to remove redundancy and get vector z 1 :

[0030]

[0031] In the formula, A 1 Yes A * ⊙A deletes duplicate rows and sorts them (M 2 +2M-2) / 2×K-dimensional new direction matrix, Indicates that M 2 / 4+M / 2 elements are 1, and all other elements are 0. 1 The data vector is received as a virtual array of a differential common array.

[0032] Step S4 further comprises the following steps:

[0033] The virtual uniform linear array is divided into (N+1) / 2 sub-arrays, where N = (M 2 +2M-2) / 2; each sub-array contains (N+1) / 2 array elements, and the array element position of the i-th sub-array is:

[0034] D ui ={(-i+1+n)d 1 ,n=0,1,…,(N-1) / 2};

[0035] Then the data vector of the i-th sub-matrix is:

[0036]

[0037] Among them, A 1i is the matrix A 1 The new array consists of rows (N+1) / 2-i+1 to N+1-i; is a column vector whose elements are all 0 except the i-th element which is 1;

[0038] The following relationship is obtained based on the spatial smoothing technique:

[0039]

[0040] Among them, A 11 Yes A 1 The first subarray of

[0041] Then the covariance matrix after spatial smoothing is:

[0042]

[0043] Step S5 further comprises the following steps:

[0044] Perform eigenvalue decomposition on R to obtain two parts: signal subspace and noise subspace:

[0045] ss

[0046]

[0047] in is K large eigenvalues ​​λ k The diagonal matrix composed of k = 1, 2, ..., K; is a diagonal matrix composed of the remaining (MK) small eigenvalues. According to the order of the eigenvalues, the eigenvectors corresponding to the K larger eigenvalues ​​constitute the matrix signal subspace E S , the eigenvectors corresponding to the remaining smaller eigenvalues ​​constitute the matrix noise subspace E N ;

[0048] The root-finding MUSIC polynomial is constructed as:

[0049]

[0050] where p(z)=[1,z,…,z (N-1) / 2 ]; Take the K roots with the largest magnitude within the unit circle The phase of gives the direction of arrival estimate:

[0051]

[0052] Compared with the prior art, the present invention has the following beneficial effects:

[0053] First, the DOA estimation method for a nested array structure of the present invention has a higher degree of freedom compared to a traditional uniform linear array; under the condition of the same number of array elements, more signal sources can be estimated with significantly higher estimation accuracy.

[0054] Secondly, compared with the spatial smoothing MUSIC algorithm under the nested array, the DOA estimation method for the nested array structure of the present invention avoids the spectrum peak search process while ensuring almost the same estimation performance, and has significantly lower complexity. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] Figure 1 is a flow chart of a DOA estimation method for a nested array structure of the present invention;

[0056] Figure 2 Schematic diagram of the nested array structure used in the present invention;

[0057] Figure 3 This is a comparison chart of the computational complexity in the present invention;

[0058] Figure 4 Schematic diagram of comparison of DOA estimation errors between the method of the present invention and the traditional DOA estimation method under different signal-to-noise ratios;

[0059] Figure 5 Schematic diagram of the comparison of DOA estimation errors between the method of the present invention and the traditional DOA estimation method under different snapshot numbers. DETAILED DESCRIPTION

[0060] The embodiments of the present invention are further described in detail below in conjunction with the accompanying drawings.

[0061] Symbolic representation: In this paper, bold uppercase letters, bold lowercase letters, and italic letters, such as A, a, and a, represent matrices, vectors, and scalars, respectively. p and [A] p,q denote the pth element of vector a and the element of pth row and qth column of matrix A respectively, (·) T , (·) H and(·) -1 denote the transpose, conjugate transpose, and inverse operations of a matrix, respectively. E{·} denotes the mathematical expectation. The letters with triangular superscripts represents the estimated value of R.

[0062] The present invention provides a DOA estimation method for a nested array structure, comprising the following steps:

[0063] S1, using nested arrays to receive data and calculate the covariance matrix of the received signal;

[0064] S2, vectorizing the covariance matrix of the received signal, sorting it and deleting the redundant parts to obtain a virtual array received signal;

[0065] S3, extracting a continuous part of the virtual array receiving signal to obtain a continuous virtual array receiving signal;

[0066] S4, obtaining the covariance matrix of the received signal of the continuous virtual array by a spatial smoothing method;

[0067] S5, performing eigenvalue decomposition on the covariance matrix to obtain the noise subspace and constructing the root-finding MUSIC formula to obtain the root and the corresponding DOA estimation result.

[0068] See also Figure 1 , the DOA estimation method specifically includes the following steps:

[0069] Step 1: Sample the nested array received signal and calculate the covariance matrix;

[0070] The elements of the nested array in step 1 can be expressed as d 1 =λ / 2,d 2 =(M 1 +1)λ / 2, where λ represents the wavelength of the incident signal. The optimal structure is when the degree of freedom of the nested linear array is the largest, that is, when the total number of array elements M is an even number, M 1 =M 2 =M / 2, when M is an odd number, M 1 =(M-1) / 2,M 2 =(M+1) / 2.

[0071] Assume that there are K far-field narrowband incident angles θ k The incoherent signals of (k=1,2,…,K) are incident on the nested array, and the array receiving data can be expressed as

[0072]

[0073] in, represents the direction matrix; s(t)=[s 1 (t),s 2 (t),…,s K (t)] T represents the source vector; n(t) represents the mean value is 0 and the variance is σ 2 Gaussian white noise vector; the direction matrix can be expressed as

[0074]

[0075] The covariance matrix of the received signal can be expressed as

[0076]

[0077] in is the power of the kth source; R s is the signal covariance matrix and satisfies diagonal non-singularity.

[0078] Considering a finite number of snapshots, the covariance matrix can be expressed as

[0079]

[0080] Wherein, L represents the number of snapshots.

[0081] Step 2: vectorize the covariance matrix, sort it and delete the redundant parts to obtain the virtual array receiving signal;

[0082] The covariance matrix R xx Perform vectorized operations to obtain

[0083]

[0084] in, represents the direction matrix of the virtual array; The vectorized covariance matrix z can be regarded as a received data vector of a virtual array. At this time, the direction matrix of the virtual array becomes A * ⊙A, but its array element positions have duplicates, which need to be processed.

[0085] Sort the vectorized matrix z to remove redundancy and obtain a new vector:

[0086]

[0087] At this time, A 1 Yes A * ⊙A deletes duplicate rows and sorts them (M 2 +2M-2) / 2×K-dimensional new direction matrix, the array element position distribution is (-M 2 / 4-M / 2+1)d 1 to (M 2 / 4+M / 2-1)d 1 The total number of elements in the virtual array is N = (M 2 +2M-2) / 2, Indicates that M 2 / 4+M / 2 elements are 1, and all other elements are 0. Based on the above, we can know that the direction matrix A of the virtual array 1 for

[0088]

[0089] So, the matrix z 1 A virtual array that can be viewed as a differential common array receives a data vector.

[0090] Step 3: extracting the continuous part of the virtual array receiving signal to obtain the receiving signal of the continuous virtual array;

[0091] Since the difference array obtained after virtualization of the nested array is a hole-free array, the z obtained in step 2 1 That is the received signal of the continuous virtual array.

[0092] Step 4: Obtain the received signal covariance matrix of the continuous virtual array by a spatial smoothing method;

[0093] The virtual uniform linear array is divided into (N+1) / 2 sub-arrays, where N = (M 2 +2M-2) / 2. Each subarray contains (N+1) / 2 array elements, and the array element position of the i-th subarray is

[0094] D ui ={(-i+1+n)d 1 ,n=0,1,…,(N-1) / 2}

[0095] Then the data vector of the i-th sub-matrix is

[0096]

[0097] Among them, A 1i is the matrix A 1 The new array consists of rows (N+1) / 2-i+1 to N+1-i; is a column vector in which all elements are 0 except the i-th element which is 1. Based on the spatial smoothing technique, the following relationship is obtained

[0098]

[0099] Among them, A 11 Yes A 1 The first subarray of

[0100] Then the covariance matrix after spatial smoothing is

[0101]

[0102] Step 5: Perform eigenvalue decomposition on the covariance matrix to obtain the noise subspace and construct the root-finding MUSIC formula to obtain the root and the corresponding DOA estimation result.

[0103] Rss By performing eigenvalue decomposition, we can obtain two parts: signal subspace and noise subspace, namely

[0104]

[0105] According to the order of eigenvalues, the eigenvectors corresponding to the K larger eigenvalues ​​constitute the matrix signal subspace E. S , the eigenvectors corresponding to the remaining smaller eigenvalues ​​constitute the matrix noise subspace E N .

[0106] The root-finding MUSIC polynomial is constructed as

[0107]

[0108] where p(z)=[1,z,…,z (N-1) / 2 ]. Take the K roots with the largest magnitude within the unit circle The phase of gives the direction of arrival estimate, namely

[0109]

[0110] Figure 3 It is a comparison chart of the computational complexity of the method described in the invention. Figure 3 It can be seen that compared with the traditional spatial smoothing MUSIC algorithm, the method of the present invention has very low computational complexity and is convenient for practical application.

[0111] The performance estimation standard of the present invention is the root mean square error (RMSE), which is defined as:

[0112]

[0113] in, It represents the estimated result of the kth source position in the qth trial, Q represents the number of Monte Carlo simulations, and the number of Monte Carlo simulations in this section is 500.

[0114] Figure 4 This is a comparison of the DOA estimation error between the method of the present invention and the traditional DOA estimation method under different signal-to-noise ratios. The source angle θ = [10°, 20°, 30°], the number of snapshots L = 500. Figure 5 It can be seen that, under the same signal-to-noise ratio condition, the present invention achieves higher estimation accuracy than the traditional DOA estimation algorithm.

[0115] Figure 5 This is a comparison of the DOA estimation error between the method of the present invention and the traditional DOA estimation method under different snapshot numbers. Where the source angle θ = [10°, 20°, 30°], signal-to-noise ratio SNR = 0dB. Figure 5 It can be seen that the present invention achieves higher estimation accuracy under the condition of the same number of snapshots.

[0116] The present invention calculates the covariance matrix according to the received signal; performs vectorization processing on the covariance matrix; sorts the vector and deletes the redundancy to obtain the received signal of the virtual array; extracts the continuous part of the received signal of the virtual array to obtain the received signal of the continuous virtual array element; obtains the covariance matrix of the virtual array by a spatial smoothing method; performs eigenvalue decomposition on the covariance matrix to obtain the noise subspace; constructs a root-finding MUSIC formula to obtain the root, and obtains the corresponding DOA estimation result. Compared with the existing algorithm, the method of the present invention has a DOA estimation accuracy similar to that of the nested array spatial smoothing MUSIC method, and has a higher estimation accuracy than the linear uniform array correlation algorithm. In addition, since the closed-form solution of DOA is obtained by the root-finding method, the spectrum peak search process is avoided, so the method of the present invention has a lower computational complexity while ensuring the DOA estimation performance.

[0117] Those skilled in the art will appreciate that the embodiments of the present application can be provided as methods, systems, or computer program products. Therefore, the present application can adopt the form of complete hardware embodiments, complete software embodiments, or embodiments in combination with software and hardware. Moreover, the present application can adopt the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) that contain computer-usable program code. The scheme in the embodiments of the present application can be implemented in various computer languages, for example, object-oriented programming language Java and literal scripting language JavaScript, etc.

[0118] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and / or box in the flowchart and / or block diagram, as well as the combination of the processes and / or boxes in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0119] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0120] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process in the computer or other programmable device. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0121] Although the preferred embodiments of the present application have been described, those skilled in the art may make other changes and modifications to these embodiments once they have learned the basic creative concept. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments and all changes and modifications falling within the scope of the present application.

[0122] Obviously, those skilled in the art can make various changes and modifications to the present application without departing from the spirit and scope of the present application. Thus, if these modifications and variations of the present application fall within the scope of the claims of the present application and their equivalents, the present application is also intended to include these modifications and variations.

Claims

1. A DOA estimation method for a nested array structure, characterized in that: The DOA estimation method comprises the following steps: S1, using nested arrays to receive data and calculate the covariance matrix of the received signal; S2, vectorizing the covariance matrix of the received signal, sorting it and deleting the redundant parts to obtain a virtual array received signal; S3, extracting a continuous part of the virtual array receiving signal to obtain a continuous virtual array receiving signal; S4, obtaining the covariance matrix of the received signal of the continuous virtual array by a spatial smoothing method; S5, performing eigenvalue decomposition on the covariance matrix to obtain the noise subspace and constructing the root-finding MUSIC formula to obtain the root and the corresponding DOA estimation result.

2. The DOA estimation method for a nested array structure according to claim 1, characterized in that: Step S1 further comprises the following steps: Construct a nested array, the array element of the nested array is represented as d1=λ / 2, d2=(M1+1)λ / 2, where λ represents the wavelength of the incident signal; when the total number of array elements M is an even number, M1=M2=M / 2, and when M is an odd number, M1=(M-1) / 2, M2=(M+1) / 2; Assume that K far-field narrowband incident angles are θ k The irrelevant signal is incident on the nested array, and the array receives data represented as: Where k = 1, 2, ..., K, represents the direction matrix; represents the direction vector of the kth signal, D m represents the position of the mth array element; s(t) = [s1(t), s2(t), …, s K (t)] T represents the source vector; represents the kth received signal within L snapshots; n(t) represents the mean value of 0 and the variance of σ 2 Gaussian white noise vector; t∈[1,2,…L] represents the sampling time, L represents the number of snapshots; The covariance matrix of the received signal is expressed as: In the formula, is the power of the kth source; R s is the signal covariance matrix and satisfies diagonal non-singularity; Considering a finite number of snapshots, the covariance matrix is ​​expressed as: Wherein, L represents the number of snapshots.

3. The DOA estimation method for a nested array structure according to claim 1, characterized in that: Step S2 further comprises the following steps: The covariance matrix R xx Perform vectorized operations to obtain the matrix z: in, represents the direction matrix of the virtual array; Sort the vectorized matrix z to remove redundancy and obtain vector z1: Where A1 is A * ⊙A deletes duplicate rows and sorts them (M 2 +2M-2) / 2×K-dimensional new direction matrix, Indicates that M 2 / 4+M / 2 elements are 1, and all other elements are 0. The vector z1 is used as a virtual array of the differential common array to receive the data vector.

4. The DOA estimation method for a nested array structure according to claim 1, characterized in that: Step S4 further comprises the following steps: The virtual uniform linear array is divided into (N+1) / 2 sub-arrays, where N = (M 2 +2M-2) / 2; each sub-array contains (N+1) / 2 array elements, and the array element position of the i-th sub-array is: D ui ={(-i+1+n)d1,n=0,1,…,(N-1) / 2}; Then the data vector of the i-th sub-matrix is: Among them, A 1i is a new array consisting of the (N+1) / 2-i+1 to N+1-i rows of matrix A1; is a column vector whose elements are all 0 except the i-th element which is 1; The following relationship is obtained based on the spatial smoothing technique: Among them, A 11 is the first subarray of A1, Then the covariance matrix after spatial smoothing is:

5. The DOA estimation method for a nested array structure according to claim 1, characterized in that: Step S5 further comprises the following steps: R ss Perform eigenvalue decomposition to obtain two parts: signal subspace and noise subspace: in is K large eigenvalues ​​λ k The diagonal matrix composed of k = 1, 2, ..., K; is a diagonal matrix composed of the remaining (MK) small eigenvalues; according to the order of the eigenvalues, the eigenvectors corresponding to the K larger eigenvalues ​​constitute the matrix signal subspace E S , the eigenvectors corresponding to the remaining smaller eigenvalues ​​constitute the matrix noise subspace E N ; The root-finding MUSIC polynomial is constructed as: where p(z)=[1,z,…,z (N-1) / 2 ]; Take the K roots with the largest magnitude within the unit circle The phase of gives the direction of arrival estimate:

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