Two-dimensional DOA estimation method for coprime arrays based on compressed sensing and minimization processing

Abstract

A two-dimensional DOA estimation method for coprime arrays based on a combination of compressed sensing and minimization processing first decomposes the coprime array into two sparse sub-arrays and establishes a data model for each sub-array. Compressed sensing is then introduced, and a compressed sensing kernel is constructed to compress and project the received data of the sub-arrays to obtain the contour signals of the sub-arrays after dimensionality reduction. The contour signals of the sub-arrays are then processed using a DOA estimation algorithm to obtain a two-dimensional spatial spectrum estimate of the sub-arrays. Finally, a minimum processing method is used to combine the two-dimensional DOA estimation results of the sub-arrays to eliminate angular ambiguity and obtain a two-dimensional DOA estimation result for the coprime arrays. The present invention introduces compressed sensing into the traditional two-dimensional DOA estimation method for coprime arrays, reducing data dimensionality, data storage space, and computational complexity. At the same time, the minimum processing method is combined to eliminate angular ambiguity, eliminating the need to sequentially compare the spectral peaks of the sub-arrays and further simplifying the calculation.

Description

Technical Field

[0001] The invention belongs to the technical field of array signal processing, and in particular relates to a two-dimensional DOA estimation method for a coprime array. Background Art

[0002] Direction-of-Arrival (DOA) estimation, also known as spatial spectrum estimation, is an important branch of array signal processing, with extensive engineering applications in radar, sonar, wireless communications, and other fields. Two-dimensional DOA estimation utilizes sensor arrays to estimate the elevation and azimuth of target signals. Commonly used array structures for two-dimensional DOA estimation include uniform planar arrays, uniform L-arrays, coprime L-arrays, and coprime planar arrays. Compared to uniform arrays, coprime arrays with sparse structures use fewer elements, have larger array apertures, and offer higher resolution.

[0003] Traditional two-dimensional DOA estimation methods for coprime arrays are based on the concept of subarray decomposition, directly applying DOA estimation algorithms to the data received by each subarray. One approach uses algorithms such as Estimating Signal Parameter via Rotational Invariance Techniques (ESPRIT) and Root-Multiple Signal Classification (Root-MUSIC) to estimate the spatial spectrum from a one-dimensional perspective, independently deriving azimuth and elevation angle estimates, and then pairing the elevation and azimuth angles. Another approach uses a two-dimensional Multiple Signal Classification (MUSIC) algorithm to search the angular space. Both methods require sequentially comparing all spectral peaks after pairing to identify common peaks and eliminate angular ambiguity. Traditional methods suffer from high data redundancy, occupy unnecessary data storage space, and have high computational and system complexity. Computational and system complexity are important considerations in practical DOA estimation. Lower system complexity reduces hardware costs, and lower computational complexity is crucial for ensuring real-time system performance. Summary of the Invention

[0004] In order to solve the problem of high computational complexity and system complexity of traditional coprime array two-dimensional DOA estimation methods, the present invention provides a coprime array two-dimensional DOA estimation method based on the combination of compressed sensing and minimization processing.

[0005] The present invention introduces compressed sensing after obtaining the received data of the coprime array, which greatly reduces the data storage space and computational complexity; after obtaining the spatial spectrum estimation of the sub-array, the minimization process is used to eliminate the angular ambiguity, further reducing the computational complexity.

[0006] The present invention provides a two-dimensional DOA estimation method for a coprime array based on a combination of compressed sensing and minimization processing, comprising the following steps:

[0007] S1. Establishing the data model of the sub-surface array;

[0008] According to the coprime array structure, the coprime array is decomposed into two uniform sparse arrays with M1×M1 and M2×M2 elements respectively. The number of elements in the x-axis and y-axis directions of sub-array 1 is M1, and the element spacing is d1=M2d. The number of elements in the x-axis and y-axis directions of sub-array 2 is M2, and the element spacing is d2=M1d. M1 and M2 satisfy the coprime relationship, d=λ / 2, and λ is the wavelength of the incident signal. The two sub-arrays overlap only at the origin, so the total number of elements in the coprime array can be expressed as The receiving data model of sub-array i is established as:

[0009]

[0010] in, is the x-axis array manifold matrix of sub-surface array i, is the array response vector, is the y-axis array flow matrix of sub-array i, and the array response vector The number of array elements of sub-surface array i is M i ×M i , d i is the array element spacing, denote the azimuth and elevation angles of the kth signal, θ k ∈(-π,π), represents the incident signal, K is the number of far-field narrowband signals, represents the Kronecker product, D m (·) is a diagonal matrix constructed from the m rows of the matrix, n im (t) is the additive Gaussian white noise of the array elements in the mth sub-array of sub-array i.

[0011] S2, introduce compressed sensing to perform dimensionality reduction processing on the sub-array received data;

[0012] Compressed sensing is introduced to process the received signal, and two random compressed sensing kernels Φ1 and Φ2 are constructed. Φ1 is a Q1×M1 dimensional matrix, and Φ2 is a Q2×M2 dimensional matrix. i is the compression coefficient, satisfying And Q i >K; the elements in Φ1 and Φ2 are randomly generated and meet the conditions of row orthogonality; the compressed sensing kernel is used to analyze each sub-array separately. The received signal x i (t) Perform dimensionality reduction processing by random projection to obtain each sub-array Q i ×1-dimensional contour signal y i (t):

[0013] y i (t)=Φ i x i (t) (2)

[0014] S3, using the contour signal to perform sub-array two-dimensional DOA estimation;

[0015] A DOA estimation algorithm is used to process the contour signal of the sub-array to obtain the two-dimensional spatial spectrum estimation result of each sub-array.

[0016] S4, using the minimum processing method to combine the two-dimensional DOA estimation results of the sub-arrays to obtain the two-dimensional DOA estimation results of the coprime arrays;

[0017] The minimum operation is performed on the spatial spectra of the two sub-arrays through the minimum processing method, and the position of the common spectrum peak is the two-dimensional DOA estimation result of the coprime array.

[0018]

[0019] in and These are the two-dimensional spatial spectrum estimation results of sub-array 1 and sub-array 2 respectively.

[0020] This invention combines compressed sensing with minimum processing for two-dimensional DOA estimation of coprime arrays. Firstly, the received data from each sub-array is compressed and reduced in dimensionality, significantly reducing data storage space. The compressed profile signals are then used to estimate the two-dimensional DOA of the sub-arrays, reducing data dimensionality and computational complexity. Secondly, the minimum processing method eliminates angular ambiguity, avoiding the complex sequential comparison of all spectral peaks required in traditional methods and further simplifying the calculation.

[0021] Compared with the traditional coprime array two-dimensional DOA estimation method, the characteristics of the present invention are:

[0022] (1) The idea of ​​compressed sensing was introduced. The computational complexity of the traditional coprime array two-dimensional DOA estimation method is closely related to the data dimension. The larger the data dimension, the higher the computational complexity and the more data storage space required. The compressed sensing theory can reduce redundant information and achieve efficient signal processing under undersampling by compressing the signal and reducing the dimensionality. The sub-array received signal is compressed into a contour signal through dimensionality reduction processing, retaining the core information contained in the original received signal. The contour signal is directly used for DOA estimation, reducing the data dimension, reducing the data storage capacity requirements and the amount of computation.

[0023] (2) The minimum value processing method is used to further reduce the computational complexity. The traditional coprime array 2D DOA estimation method requires sequentially comparing the spectrum peaks of the sub-arrays to remove the angle ambiguity, which is a relatively complex process. The minimum value processing method uses the coprime property, combines the spatial spectrum of the sub-arrays, and uses minimum processing to obtain the spatial spectrum of the entire coprime array, thus easily achieving effective and unambiguous estimation of the azimuth and elevation angles. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] Figure 1 It is an overall flow chart of the method of the present invention.

[0025] Figure 2 It is a schematic diagram of the array structure of the present invention.

[0026] Figure 3-Figure 4 The present invention shows the comparison of the estimation results of the two-dimensional MUSIC algorithm selected according to the present invention and the traditional coprime array two-dimensional MUSIC algorithm when SNR=20dB and the number of sampling snapshots L is 100. Figure 3 is a spatial power spectrum estimation result diagram of the method proposed in the present invention using the two-dimensional MUSIC algorithm in step S3, Figure 4 This is the result of spatial power spectrum estimation of the received signal directly processed by the coprime array using the two-dimensional MUSIC algorithm. DETAILED DESCRIPTION

[0027] The present invention is described in detail below with reference to the accompanying drawings and embodiments.

[0028] Reference Figure 1 The specific implementation steps of the two-dimensional DOA estimation method for coprime arrays based on the combination of compressed sensing and minimization processing are as follows:

[0029] S1. Establishing the data model of the sub-surface array;

[0030] like Figure 2As shown in Figure 1, assuming that there are K far-field narrowband signals incident on the array in the form of plane waves, the coprime array is decomposed into two uniform sparse arrays with M1×M1 and M2×M2 elements respectively. The number of elements in the x-axis and y-axis directions of sub-array 1 is M1, and the element spacing is d1=M2d. The number of elements in the x-axis and y-axis directions of sub-array 2 is M2, and the element spacing is d2=M1d. M1 and M2 satisfy the coprime relationship, d=λ / 2, where λ is the wavelength of the incident signal. The two sub-arrays overlap only at the origin, so the total number of elements in the coprime array can be expressed as Establish the receiving data model of sub-array i:

[0031]

[0032] in, is the x-axis array manifold matrix of sub-surface array i, is the array response vector, is the y-axis array flow matrix of sub-array i, and the array response vector The number of array elements of sub-surface array i is M i ×M i , d i is the array element spacing, denote the azimuth and elevation angles of the kth signal, θ k ∈(-π,π), represents the incident signal, represents the Kronecker product, D m (·) is a diagonal matrix constructed from the m rows of the matrix, n im (t) is the additive Gaussian white noise of the array elements in the mth sub-array of sub-array i.

[0033] S2, introduce compressed sensing to perform dimensionality reduction processing on the sub-array received data;

[0034] Construct two compressed sensing kernels Φ1 and Φ2, Φ1 is a Q1×M1 dimensional matrix, Φ2 is a Q2×M2 dimensional matrix; where Q i is the compression coefficient, satisfying And Q i >K; the elements in Φ1 and Φ2 are randomly generated and meet the conditions of row orthogonality; using the compressed sensing kernel The received signal x of the sub-array i i (t) is compressed into Q by random projection i ×1-dimensional contour signal y i (t), using Q i ×1-dimensional contour signal for subsequent processing and calculation, compared to directly using It can receive signals in multiple dimensions, remove redundant information, and reduce data storage space and computational complexity.

[0035] y i (t)=Φ i x i (t) (2)

[0036] S3, using the contour signal to perform sub-array two-dimensional DOA estimation;

[0037] Select a DOA estimation algorithm and calculate the two-dimensional DOA estimation results of each sub-array separately to obtain

[0038] S4, using the minimum processing method to combine the two-dimensional DOA estimation results of each sub-array to obtain the two-dimensional DOA estimation results of the coprime array;

[0039] By performing the minimum operation on the spatial spectra of the two sub-arrays through the minimum processing method, the pseudo peaks can be removed, the angle ambiguity can be eliminated, and the two-dimensional DOA estimation spatial spectrum of the coprime array can be obtained.

[0040]

[0041] Preferably, in step S3, a two-dimensional MUSIC algorithm is used to process the contour signal of the sub-array, and the two-dimensional MUSIC spatial spectrum power function of the sub-array i is:

[0042]

[0043] in, Q corresponding to the contour signal of sub-array i i ×1-dimensional steering vector, is the covariance matrix R of the contour signal of the sub-surface array i iyy The noise subspace obtained by eigenvalue decomposition, the covariance matrix R iyy Calculated by the following formula

[0044]

[0045] Traverse θ, Get the two-dimensional MUSIC spatial spectrum P of each sub-array 2D-planar arrayi .

[0046] Preferably, in step S4, because the sub-arrays are sparsely arranged and the element spacing is greater than half a wavelength, pseudo-peaks will appear in the spatial spectrum of the sub-arrays, resulting in angular ambiguity. According to the coprime theory of planar arrays, the pseudo-peak positions of the two-dimensional MUSIC spatial spectra of the two sub-arrays do not overlap, and the location of the common spectral peak is the two-dimensional DOA estimation result of the coprime arrays. The proof process is as follows:

[0047] True DOA estimation angle and the blur angle of sub-array i There are the following relations between

[0048]

[0049]

[0050] where β i，x and β i，y are all integers. There is at least one angle estimation result that is the same between sub-matrix 1 and sub-matrix 2, that is According to the characteristics of coprime arrays, when the algorithm of this embodiment is used to estimate DOA, there is no angle ambiguity problem. The following proves that β i，x and β i，y The uniqueness of existence.

[0051] Assume that there are two identical estimation results for sub-matrix 1 and sub-matrix 2 and For sub-array 1, according to formula (7) and formula (8), we have

[0052]

[0053]

[0054] where β 1，x and β 1，y are all integers, and their value ranges are (-M2, M2) and (-M2 / 2, M2 / 2) respectively. Similarly, for sub-matrix 2,

[0055]

[0056]

[0057] where β 2，x and β 2，y are all integers, and their value ranges are (-M1, M1) and (-M1 / 2, M1 / 2) respectively. Arranging formula (9)-formula (12) yields

[0058]

[0059]

[0060] Since M1 and M2 are mutually prime, to satisfy the above formula, β 1，x =β 2，x =0,β 1，y =β 2，y =0, that is

[0061]

[0062]

[0063] get

[0064] The effects of the present invention are further described below with reference to simulation examples.

[0065] Simulation example:

[0066] We pass Figure 2 In the model shown, a two-dimensional MUSIC algorithm is selected for step S3, and the spatial power spectrum obtained by the method proposed in the present invention and the two-dimensional MUSIC method is directly used to receive the signal of the coprime array to be compared.

[0067] Simulation conditions: The coprime factor parameters of the coprime array profile signal are selected as M1=4, M2=5, and the compression coefficient Q1=Q2=12, that is, from the 4 2 +5 2 24 array elements are randomly selected from the coprime array with -1=40 array elements. The coprime factor parameters of the coprime array receiving signal are also selected as M1=4, M2=5, and the total number of array elements is 40. The constructed compressed sensing kernel Φ i The elements are subject to an independent and identically distributed random Gaussian distribution with a mean of 0 and a variance of 1 / M. i 2 Assume that there are K = 2 narrowband incident signals with azimuth and elevation angles of (20°, 10°) and (21.2°, 11.2°), respectively, white Gaussian noise, and a signal-to-noise ratio of 20 dB. The angular domain of the spatial power spectrum is [-90°, 90°], and the spatial domain grid points are uniformly sampled at 0.1°.

[0068] When the number of sampling snapshots L = 100, Figure 3-Figure 4 The method proposed in the present invention uses a two-dimensional MUSIC algorithm and directly uses the spatial power spectrum corresponding to the two-dimensional MUSIC algorithm for receiving signals from a coprime array. The present invention can perform two-dimensional DOA estimation more accurately.

[0069] Complexity analysis: The computational complexity of the two-dimensional MUSIC method for receiving signals from a coprime array is Thanks to compressed sensing, the computational complexity of the two-dimensional MUSIC method for the coprime array profile signal is where n g Indicates the number of peak searches.

[0070] The present invention proposes a two-dimensional DOA estimation method for coprime arrays based on a combination of compressed sensing and minimization processing. First, the coprime array is decomposed into two sparse sub-arrays, and a data model for each sub-array is established. Then, compressed sensing is introduced, and a compressed sensing kernel is constructed to compress and project the received data of the sub-arrays to obtain the contour signals of the reduced sub-arrays. The contour signals of the sub-arrays are then processed using a DOA estimation algorithm to obtain a two-dimensional spatial spectrum estimate for each sub-array. Finally, a minimum processing method is used to combine the two-dimensional DOA estimation results of the sub-arrays to eliminate angular ambiguity and obtain the two-dimensional DOA estimation results of the coprime arrays. The present invention introduces compressed sensing into the traditional two-dimensional DOA estimation method for coprime arrays, reducing the data dimension, data storage space and computational complexity. At the same time, the minimum processing method is combined to eliminate angular ambiguity, eliminating the need to sequentially compare the common spectral peaks of the sub-arrays, further simplifying the calculation.

[0071] The contents described in the embodiments of this specification are merely an enumeration of the implementation forms of the inventive concept. The scope of protection of the present invention should not be regarded as limited to the specific forms described in the embodiments. The scope of protection of the present invention also extends to equivalent technical means that can be conceived by those skilled in the art based on the inventive concept.

Claims

1. A two-dimensional DOA estimation method for coprime arrays based on a combination of compressed sensing and minimization processing includes the following steps: S1. Establishing the data model of the sub-surface array; According to the coprime array structure, the coprime array is decomposed into two uniform sparse arrays with M1×M1 and M2×M2 elements respectively. The number of elements in the x-axis and y-axis directions of sub-array 1 is M1, and the element spacing is d1=M2d. The number of elements in the x-axis and y-axis directions of sub-array 2 is M2, and the element spacing is d2=M1d. M1 and M2 satisfy the coprime relationship, d=λ / 2, and λ is the wavelength of the incident signal. The two sub-arrays overlap only at the origin, so the total number of elements in the coprime array is expressed as The receiving data model of sub-array i is established as: in, is the x-axis array manifold matrix of sub-surface array i, is the array response vector, is the y-axis array flow matrix of sub-array i, and the array response vector The number of array elements of sub-surface array i is M i ×M i , i=1,2,d i is the array element spacing, denote the azimuth and elevation angles of the kth signal, θ k ∈(-π,π), represents the incident signal, K is the number of far-field narrowband signals, represents the Kronecker product, D m (·) is a diagonal matrix constructed from the m rows of the matrix, n im (t) is the additive white Gaussian noise of the array elements of the mth sub-array of the sub-array i, m = 1, 2, ..., M i ; S2, introduce compressed sensing to perform dimensionality reduction processing on the sub-array received data; Compressed sensing is introduced to process the received signal, and two random compressed sensing kernels Φ1 and Φ2 are constructed. Φ1 is a Q1×M1 dimensional matrix, and Φ2 is a Q2×M2 dimensional matrix. i is the compression coefficient, satisfying And Q i >K; the elements in Φ1 and Φ2 are randomly generated and meet the conditions of row orthogonality; the compressed sensing kernel is used to analyze each sub-array separately. The received signal x i (t) Perform dimensionality reduction processing by random projection to obtain each sub-array Q i ×1-dimensional contour signal y i (t): y i (t)=Φ i x i (t) (2) S3, using the contour signal to perform sub-array two-dimensional DOA estimation; A DOA estimation algorithm is used to process the contour signal of the sub-array to obtain the two-dimensional spatial spectrum estimation result of each sub-array. S4, using the minimum processing method to combine the two-dimensional DOA estimation results of the sub-arrays to obtain the two-dimensional DOA estimation results of the coprime arrays; The minimum operation is performed on the spatial spectra of the two sub-arrays by the minimum processing method, and the position of the common spectrum peak is the two-dimensional DOA estimation result of the coprime array; in and These are the two-dimensional spatial spectrum estimation results of sub-array 1 and sub-array 2 respectively.

2. The method for estimating two-dimensional DOA of a coprime array based on a combination of compressed sensing and minimization processing according to claim 1, characterized in that: Step S3 is specifically as follows: The two-dimensional MUSIC algorithm is used to process the contour signal. The two-dimensional MUSIC spatial spectrum power function corresponding to the contour signal of the sub-array i is: in, Q corresponding to the contour signal of sub-array i i ×1-dimensional steering vector, is the covariance matrix of the contour signal of the sub-surface array i The noise subspace obtained by eigenvalue decomposition, the covariance matrix Calculated by the following formula Traverse θ, Get the two-dimensional MUSIC spatial spectrum P of each sub-array 2D-planararrayi .

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