CN114755627A - Compressed sensing and minimization processing combined co-prime area array two-dimensional DOA estimation method - Google Patents
Compressed sensing and minimization processing combined co-prime area array two-dimensional DOA estimation method Download PDFInfo
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Abstract
A coprime area array two-dimensional DOA estimation method based on combination of compressed sensing and minimization processing comprises the steps of decomposing a coprime area array into two sparse sub-area arrays, and establishing a data model of each sub-area array; then introducing compressed sensing, and constructing a compressed sensing kernel to respectively perform compressed projection on the sub-area array received data to obtain a contour signal of the sub-area array after dimension reduction; then processing the outline signal of the sub-area array by using a DOA estimation algorithm to obtain two-dimensional space spectrum estimation of the sub-area array; and finally, combining two sub-area array two-dimensional DOA estimation results by using a minimum processing method, eliminating angle ambiguity and obtaining a co-prime area array two-dimensional DOA estimation result. The invention introduces compressed sensing in the traditional co-prime area array two-dimensional DOA estimation method, reduces data dimension, reduces data storage space and operand, and simultaneously combines a minimum processing method to eliminate angle ambiguity without comparing the spectral peaks of the subarrays in sequence, thereby further simplifying calculation.
Description
Technical Field
The invention belongs to the technical field of array signal processing, and particularly relates to a co-prime area array two-dimensional DOA estimation method.
Background
Direction-of-Arrival (DOA), also known as spatial spectrum estimation, is an important branch of the array signal field, and has a wide engineering application in the fields of radar, sonar, wireless communication, and the like. Two-dimensional DOA estimation utilizes a sensor array to estimate the pitch and azimuth of a target signal. Array structures commonly used in two-dimensional DOA estimation are uniform area arrays, uniform L-arrays, co-prime area arrays, and the like. Compared with a uniform array, the co-prime array with the sparse structure uses fewer array elements, has larger array aperture and higher resolution.
The traditional co-prime area array two-dimensional DOA estimation method is based on the thought of sub-array decomposition to process, and respectively and directly uses the DOA estimation algorithm for data received by the sub-area array. One method is to perform spatial spectrum estimation from a one-dimensional angle by using a Signal Parameter estimation algorithm (ESPRIT) and a Root-finding Multiple Signal classification algorithm (Root-Multiple Signal classification) based on a rotation invariant technology, independently obtain an azimuth angle and an estimation value of a pitch angle, and then perform angle pairing on the pitch angle and the azimuth angle. One is to perform an angle space search using a two-dimensional Multiple Signal classification (MUSIC) algorithm. After the two are matched, all the spectral peaks are compared in sequence to find a common spectral peak, so that the angle ambiguity is eliminated. The traditional method has high data redundancy degree, occupies unnecessary data storage space, and has higher computational complexity and system complexity. The computational complexity and the system complexity are important consideration factors of the DOA estimation problem in practical application, the lower system complexity can reduce the hardware cost, and the lower computational complexity is important for ensuring the real-time performance of the system.
Disclosure of Invention
In order to solve the problem that the traditional co-prime area array two-dimensional DOA estimation method is high in computation complexity and system complexity, the invention provides a co-prime area array two-dimensional DOA estimation method based on combination of compressed sensing and minimization processing.
According to the invention, compressed sensing is introduced after the co-prime area array receiving data is obtained, so that the data storage space and the calculation complexity are greatly reduced; after the space spectrum estimation of the sub-area array is obtained, the angle blurring is eliminated by utilizing minimization processing, and the calculation complexity is further reduced.
The invention relates to a co-prime area array two-dimensional DOA estimation method based on combination of compressed sensing and minimization processing, which comprises the following steps:
s1, establishing a data model of the sub-area array;
according to the relatively prime planar array structure, the relatively prime planar array is decomposed into two array elements M1×M1And M2×M2The array elements of the sub-area array 1 in the x-axis direction and the y-axis direction are respectively M1With an array element spacing of d1=M2d, the array element numbers of the sub-area array 2 in the x-axis direction and the y-axis direction are respectively M2With an array element spacing of d2=M1d,M1And M2Satisfying the relation of reciprocity, d is lambda/2, and lambda is the wavelength of the incident signal. The two sub-area arrays are only overlapped at the origin, so the total array element number of the co-prime area array can be expressed as The received data model of the sub-area array i is established as follows:
wherein,is an x-axis array flow pattern matrix of the sub-area array i,is a vector of the response of the array,a y-axis array flow pattern matrix of sub-area array i, an array response vectorThe array element number of the sub-area array i is Mi×Mi,diThe distance between the array elements is the length of the array elements,respectively representing the azimuth and elevation angle, theta, of the kth signalk∈(-π,π),Represents the incident signal, K is the number of far-field narrow-band signals,denotes the kronecker product, Dm(. is) a diagonal matrix constructed from m rows of the matrix, nim(t) is additive white Gaussian noise of the array elements of the sub-area array i on the m-th sub-array.
S2, introducing compressed sensing, and respectively performing dimensionality reduction on the sub-area array received data;
introducing compressed sensing to process received signals and constructing two random compressed sensing cores phi1、Φ2,Φ1Is a Q1×M1Dimension matrix, phi2Is a Q2×M2A dimension matrix; wherein QiIs a compression factor, satisfies And Qi>K;Φ1、Φ2The elements in (1) are randomly generated and meet the condition of line orthogonality; using compressed sensing kernel to respectively correspond to each sub-area arrayReceived signal x of dimensioni(t) carrying out dimensionality reduction treatment in a random projection mode to obtain each sub-area array QiX 1 dimensional contour signal yi(t):
yi(t)=Φixi(t) (2)
S3, performing two-dimensional DOA estimation of the sub-area array by using the contour signal;
selecting a DOA estimation algorithmProcessing the profile signal of the sub-area array by the method to obtain the two-dimensional space spectrum estimation result of each sub-area array
S4, combining the sub-area array two-dimensional DOA estimation results by using a minimum processing method to obtain a co-prime area array two-dimensional DOA estimation result;
and performing minimum operation on the space spectrums of the two sub-area arrays by a minimum processing method, wherein the position of the common spectrum peak is a two-dimensional DOA estimation result of a co-prime area array.
WhereinAndrespectively are two-dimensional space spectrum estimation results of the sub-area array 1 and the sub-area array 2.
The invention combines compressed sensing with a minimum processing method in co-prime area array two-dimensional DOA estimation. On one hand, the data received by each sub-area array is compressed and reduced in dimension, and the data storage space is greatly reduced; and the compressed contour signal is used for carrying out two-dimensional DOA estimation of the sub-area array, so that the data dimension is reduced, and the calculation complexity is reduced. On the other hand, the angle ambiguity is eliminated by using a minimum processing method, the complex operation of sequentially comparing all the spectrum peaks in the traditional method is avoided, and the calculation is further simplified.
Compared with the traditional co-prime area array two-dimensional DOA estimation method, the method has the characteristics that:
(1) the idea of compressed sensing is introduced. The calculation complexity of the traditional co-prime area array two-dimensional DOA estimation method is closely related to the data dimension, and if the data dimension is large, the calculation complexity is increased, and the required data storage space is increased. The compressed sensing theory can simplify redundant information by compressing and reducing the dimension of the signal, and realizes efficient signal processing under undersampling. The sub-area array received signals are compressed into contour signals through dimension reduction processing, core information contained in original received signals is reserved, DOA estimation is directly carried out through the contour signals, data dimensions are reduced, and capacity requirements and calculation amount of data storage are reduced.
(2) And a minimum processing method is adopted, so that the computational complexity is further reduced. The traditional co-prime area array two-dimensional DOA estimation method needs to compare the spectral peaks of the subarrays in sequence, so that the angle ambiguity is removed, and the process is relatively complex. The minimum processing method combines the space spectrum of the sub-area array by utilizing the co-prime characteristic, obtains the space spectrum of the whole co-prime area array by using minimum processing, and simply and conveniently realizes effective non-fuzzy estimation of the azimuth angle and the pitch angle.
Drawings
FIG. 1 is a general flow diagram of the method of the present invention.
FIG. 2 is a schematic diagram of an array structure of the present invention.
Fig. 3-4 show the comparison of the estimation results of the two-dimensional MUSIC algorithm selected according to the present invention and the conventional co-prime area-array two-dimensional MUSIC algorithm when the SNR is 20dB and the sampling fast-beat number L is 100. Wherein, fig. 3 is a spatial power spectrum estimation result diagram of the two-dimensional MUSIC algorithm selected in step S3 by the method of the present invention, and fig. 4 is a spatial power spectrum estimation result diagram of the co-prime area array directly using the two-dimensional MUSIC algorithm to process the received signal.
Detailed Description
The present invention will be described in detail below with reference to the drawings and examples.
Referring to fig. 1, the implementation steps of the co-prime area array two-dimensional DOA estimation method based on the combination of compressed sensing and minimization processing are as follows:
S1, establishing a data model of the sub-area array;
as shown in FIG. 2, assuming that K far-field narrow-band signals in the space enter the array in a plane wave mode, the co-prime area array is decomposed into two array elements with M elements1×M1And M2×M2The array elements of the sub-area array 1 in the x-axis direction and the y-axis direction are respectively M1With an array element spacing of d1=M2d,The array element numbers of the sub-area array 2 in the x-axis and y-axis directions are respectively M2With an array element spacing of d2=M1d,M1And M2Satisfying the relation of reciprocity, d is lambda/2, and lambda is the wavelength of the incident signal. The two sub-area arrays are only overlapped at the origin, so the total array element number of the co-prime area array can be expressed asEstablishing a receiving data model of the sub-area array i:
wherein,is an x-axis array flow pattern matrix of the sub-area array i,in order to be the array response vector,a y-axis array flow pattern matrix of the sub-area array i, an array response vectorThe array element number of the sub-area array i is Mi×Mi,diThe distance between the array elements is the same as the distance between the array elements,respectively representing the azimuth and elevation angle, theta, of the k-th signalk∈(-π,π),Which is representative of the incident signal, is,denotes the kronecker product, Dm(. is) a diagonal matrix constructed from m rows of the matrix, nim(t) isThe sub-area array i is additive white Gaussian noise of array elements on the m-th sub-array.
S2, introducing compressed sensing, and respectively performing dimensionality reduction on the sub-area array received data;
Constructing two compressed sensing kernels phi1、Φ2,Φ1Is a Q1×M1Dimension matrix, Φ2Is a Q2×M2Dimension matrix; wherein QiIs a compression factor, satisfiesAnd Qi>K;Φ1、Φ2The elements in (1) are randomly generated and meet the condition of line orthogonality; using compressed sensing kernel to beReceived signal x of wiener area array ii(t) compressing to Q in a random projection manneriX 1 dimensional contour signal yi(t) use of QiSubsequent processing and calculation of the x 1-dimensional contour signal, compared to direct useThe dimension receiving signal removes redundant information, and reduces the storage space and the calculation amount of data.
yi(t)=Φixi(t) (2)
S3, performing two-dimensional DOA estimation of the sub-area array by using the contour signal;
selecting a DOA estimation algorithm, and respectively calculating the two-dimensional DOA estimation result of each sub-area array to obtain
S4, combining the two-dimensional DOA estimation result of each sub-area array by using a minimum processing method to obtain a co-prime area array two-dimensional DOA estimation result;
the minimum processing method is used for carrying out minimum operation on the space spectrums of the two sub-area arrays, so that false peaks can be removed, angle ambiguity is eliminated, and a co-prime area array two-dimensional DOA estimation space spectrum is obtained;
preferably, in step S3, the two-dimensional MUSIC algorithm is selected to process the contour signal of the sub-area array, and the two-dimensional MUSIC spatial spectrum power function of the sub-area array i is
Wherein,q corresponding to the profile signal of the sub-area array iiA guide vector of x 1-dimension,is the covariance matrix R of the contour signal of the sub-area array iiyyNoise subspace and covariance matrix R obtained by performing eigenvalue decompositioniyyCalculated from the following equation
The process is traversed by the distance theta and,obtaining two-dimensional MUSIC spatial spectrum P of each sub-area array2D-planar arrayi。
Preferably, in step S4, because the sub-area array is sparsely arranged, and the array element spacing is greater than half a wavelength, the spatial spectrum of the sub-area array may generate false peaks, which may result in angular ambiguity. According to the co-prime theory of the planar array, the pseudo peak positions of the two-dimensional MUSIC spatial spectrums of the two sub-area arrays are not overlapped, and the position of the common spectrum peak is the two-dimensional DOA estimation result of the co-prime area array. The demonstration process is as follows:
Wherein beta isi,xAnd betai,yAre all integers. At least one angle between subarrays 1 and 2 has the same estimation result, i.e. the estimation result is the sameAccording to the characteristics of the co-prime array, when the DOA estimation is carried out by adopting the algorithm of the embodiment, the problem of angle ambiguity does not exist, and the following proves that beta isi,xAnd betai,yUniqueness of existence.
Suppose that there are two identical estimation results for subarray 1 and subarray 2And For the sub-array 1, there are, according to the equations (7) and (8)
Wherein beta is1,xAnd beta1,yAre all integers, and are takenThe value ranges are respectively (-M)2,M2) And (-M)2/2,M2/2). For the same reason, the subarray 2 has
Wherein beta is2,xAnd beta2,yAre all integers and have a value range of (-M)1,M1) And (-M)1/2,M1/2). The formula (9) to the formula (12) are arranged to obtain
Due to M1And M2Relatively prime, to satisfy the above formula1,x=β2,x=0,β1,y=β2,yIs equal to 0, i.e
The effect of the present invention will be further described with reference to the simulation example
Simulation example:
in the model shown in fig. 2, a two-dimensional MUSIC algorithm is selected for step S3, and the spatial power spectrum obtained by directly using the two-dimensional MUSIC algorithm on the co-prime area array received signal is compared with the method provided by the present invention.
Simulation conditions are as follows: selecting the co-prime factor parameter of the co-prime area array contour signal as M1=4,M25, compression factor Q1=Q 212, i.e. from the group comprising 42+52And (3) randomly extracting 24 array element data from a relatively prime area array with 1-40 array elements. The co-prime factor parameter of the co-prime area array receiving signal is also selected as M1=4,M2The total array element number is 40, 5. Constructed compressed sensing kernel phiiSatisfy the element obeys the random Gaussian distribution with independent and same distribution, the mean value is 0, the variance is 1/Mi 2. The azimuth angle and the pitch angle of 2 narrow-band incident signals with K are respectively (20 degrees, 10 degrees), (21.2 degrees, 11.2 degrees), the noise is white Gaussian noise, and the signal-to-noise ratio is 20 dB. The angular domain range of the spatial power spectrum is [ -90 DEG, 90 DEG ] ]The uniform sampling interval of the spatial domain grid points is set to 0.1 °.
In the case that the sampling fast beat number L is 100, fig. 3-4 respectively show the spatial power spectrum corresponding to the two-dimensional MUSIC algorithm selected by the method of the present invention and the two-dimensional MUSIC method directly used by the co-prime area array received signal. The invention can perform two-dimensional DOA estimation relatively more accurately.
And (3) complexity analysis: the computation complexity of the method of directly using two-dimensional MUSIC for the co-prime area array receiving signal isThe computation complexity of the two-dimensional MUSIC method used by the co-prime area array contour signal is as follows thanks to the compressed sensingWherein n isgIndicates the number of peak searches.
The invention provides a co-prime area array two-dimensional DOA estimation method based on combination of compressed sensing and minimization processing, which comprises the steps of firstly decomposing a co-prime area array into two sparse sub-area arrays, and establishing a data model of each sub-area array; then introducing compressed sensing, constructing a compressed sensing kernel to respectively perform compressed projection on the sub-area array received data, and obtaining a contour signal of the sub-area array after dimension reduction; then processing the outline signals of the sub-area arrays by using a DOA estimation algorithm to obtain two-dimensional space spectrum estimation of each sub-area array; and finally, combining the two-dimensional DOA estimation results of the sub-area arrays by using a minimum processing method, eliminating angle ambiguity and obtaining the two-dimensional DOA estimation results of the co-prime area arrays. The invention introduces compressed sensing in the traditional co-prime area array two-dimensional DOA estimation method, reduces data dimensionality, reduces data storage space and computation amount, and simultaneously combines a minimum processing method to eliminate angle ambiguity without sequentially comparing common spectral peaks of sub-arrays, thereby further simplifying calculation.
The embodiments described in this specification are merely illustrative of implementations of the inventive concept and the scope of the present invention should not be considered limited to the specific forms set forth in the embodiments but rather by the equivalents thereof as may occur to those skilled in the art upon consideration of the present inventive concept.
Claims (2)
1. A co-prime area array two-dimensional DOA estimation method based on combination of compressed sensing and minimization processing comprises the following steps:
s1, establishing a data model of the sub-area array;
according to the co-prime area array structure, the co-prime area array is decomposed into two array elements M1×M1And M2×M2The array elements of the sub-area array 1 in the x-axis direction and the y-axis direction are respectively M1With an array element spacing of d1=M2d, the array element numbers of the sub-area array 2 in the x-axis direction and the y-axis direction are respectively M2With an array element spacing of d2=M1d,M1And M2Satisfying the relation of reciprocity, d is lambda/2, and lambda is the wavelength of the incident signal; the two sub-area arrays are only overlapped at the origin, so the total array element number of the co-prime area array can be expressed asEstablishing the receiving number of the sub-area array iAccording to the model, the method comprises the following steps:
wherein,is an x-axis array flow pattern matrix of the sub-area array i,in order to be the array response vector,a y-axis array flow pattern matrix of the sub-area array i, an array response vector The array element number of the sub-area array i is Mi×Mi,diThe distance between the array elements is the length of the array elements,respectively representing the azimuth and elevation angle, theta, of the kth signalk∈(-π,π), Represents the incident signal, K is the number of far-field narrow-band signals,denotes the kronecker product, Dm(. is) a diagonal matrix constructed from m rows of the matrix, nim(t) additive white Gaussian noise of the array element of the sub-area array i on the mth sub-array;
s2, introducing compressed sensing, and respectively performing dimensionality reduction on the sub-area array received data;
introducing compressed sensing to process received signals and constructing two random compressed sensing cores phi1、Φ2,Φ1Is a Q1×M1Dimension matrix, phi2Is a Q2×M2A dimension matrix; wherein QiIs a compression factor, satisfies And Qi>K;Φ1、Φ2The elements in (1) are randomly generated and meet the condition of line orthogonality; using compressed sensing kernel to respectively correspond to each sub-area arrayReceived signal x of dimensioni(t) carrying out dimensionality reduction treatment in a random projection mode to obtain each sub-area array QiX 1 dimensional contour signal yi(t):
yi(t)=Φixi(t) (2)
S3, performing two-dimensional DOA estimation of the sub-area array by using the contour signal;
processing the outline signals of the sub-area arrays by using a DOA estimation algorithm to obtain a two-dimensional space spectrum estimation result of each sub-area array
S4, combining the two-dimensional DOA estimation results of the sub-area arrays by using a minimum processing method to obtain a co-prime area array two-dimensional DOA estimation result;
Performing minimum operation on the space spectrums of the two sub-area arrays by a minimum processing method, wherein the position of a common spectrum peak is a two-dimensional DOA estimation result of a co-prime area array;
2. The co-prime area array two-dimensional DOA estimation method based on the combination of compressed sensing and minimization processing according to claim 1, wherein the step S3 is specifically as follows:
and (3) processing the contour signal by selecting a two-dimensional MUSIC algorithm, wherein the two-dimensional MUSIC spatial spectrum power function corresponding to the contour signal of the sub-area array i is as follows:
wherein,q corresponding to the profile signal of the sub-area array iiA guide vector of x 1-dimension,is the covariance matrix R of the contour signal of the sub-area array iiyyNoise subspace and covariance matrix R obtained by performing eigenvalue decompositioniyyCalculated from the following equation
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