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 PDF

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CN114755627A
CN114755627A CN202210413128.5A CN202210413128A CN114755627A CN 114755627 A CN114755627 A CN 114755627A CN 202210413128 A CN202210413128 A CN 202210413128A CN 114755627 A CN114755627 A CN 114755627A
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张婷
张敏
梁婧瑶
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Zhejiang University ZJU
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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

Compressed sensing and minimization processing combined co-prime area array two-dimensional DOA estimation method
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
Figure BDA0003604095920000021
The received data model of the sub-area array i is established as follows:
Figure BDA0003604095920000031
wherein,
Figure BDA0003604095920000032
is an x-axis array flow pattern matrix of the sub-area array i,
Figure BDA0003604095920000033
is a vector of the response of the array,
Figure BDA0003604095920000034
a y-axis array flow pattern matrix of sub-area array i, an array response vector
Figure BDA0003604095920000035
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,
Figure BDA0003604095920000036
respectively representing the azimuth and elevation angle, theta, of the kth signalk∈(-π，π)，
Figure BDA0003604095920000037
Represents the incident signal, K is the number of far-field narrow-band signals,
Figure BDA0003604095920000038
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
Figure BDA0003604095920000039
Figure BDA00036040959200000310
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 array
Figure BDA00036040959200000311
Received 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
Figure BDA0003604095920000041
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.
Figure BDA0003604095920000042
Wherein
Figure BDA0003604095920000043
And
Figure BDA0003604095920000044
respectively 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 as
Figure BDA0003604095920000061
Establishing a receiving data model of the sub-area array i:
Figure BDA0003604095920000062
wherein,
Figure BDA0003604095920000063
is an x-axis array flow pattern matrix of the sub-area array i,
Figure BDA0003604095920000064
in order to be the array response vector,
Figure BDA0003604095920000065
a y-axis array flow pattern matrix of the sub-area array i, an array response vector
Figure BDA0003604095920000066
The 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,
Figure BDA0003604095920000067
respectively representing the azimuth and elevation angle, theta, of the k-th signalk∈(-π，π)，
Figure BDA0003604095920000068
Which is representative of the incident signal, is,
Figure BDA0003604095920000069
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, satisfies
Figure BDA00036040959200000610
And Qi＞K；Φ1、Φ2The elements in (1) are randomly generated and meet the condition of line orthogonality; using compressed sensing kernel to be
Figure BDA00036040959200000611
Received 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 use
Figure BDA0003604095920000071
The 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
Figure BDA0003604095920000072
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;
Figure BDA0003604095920000073
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
Figure BDA0003604095920000074
Wherein,
Figure BDA0003604095920000075
q corresponding to the profile signal of the sub-area array iiA guide vector of x 1-dimension,
Figure BDA0003604095920000076
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
Figure BDA0003604095920000077
The process is traversed by the distance theta and,
Figure BDA0003604095920000078
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:
true DOA estimation angle
Figure BDA0003604095920000081
And the fuzzy angle of the sub-array i
Figure BDA0003604095920000082
Have the following relationship
Figure BDA0003604095920000083
Figure BDA0003604095920000084
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 same
Figure BDA0003604095920000085
According 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 2
Figure BDA0003604095920000086
And
Figure BDA0003604095920000087
For the sub-array 1, there are, according to the equations (7) and (8)
Figure BDA0003604095920000088
Figure BDA0003604095920000089
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
Figure BDA00036040959200000810
Figure BDA00036040959200000811
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
Figure BDA0003604095920000091
Figure BDA0003604095920000092
Due to M1And M2Relatively prime, to satisfy the above formula1，x＝β2，x＝0，β1，y＝β2，yIs equal to 0, i.e
Figure BDA0003604095920000093
Figure BDA0003604095920000094
To obtain
Figure BDA0003604095920000095
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 is
Figure BDA0003604095920000101
The computation complexity of the two-dimensional MUSIC method used by the co-prime area array contour signal is as follows thanks to the compressed sensing
Figure BDA0003604095920000102
Wherein 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 as
Figure FDA00036040959100000110
Establishing the receiving number of the sub-area array iAccording to the model, the method comprises the following steps:
Figure FDA0003604095910000011
wherein,
Figure FDA0003604095910000012
is an x-axis array flow pattern matrix of the sub-area array i,
Figure FDA0003604095910000013
in order to be the array response vector,
Figure FDA0003604095910000014
a y-axis array flow pattern matrix of the sub-area array i, an array response vector
Figure FDA0003604095910000015
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,
Figure FDA0003604095910000016
respectively representing the azimuth and elevation angle, theta, of the kth signalk∈(-π,π)，
Figure FDA0003604095910000017
Figure FDA0003604095910000018
Represents the incident signal, K is the number of far-field narrow-band signals,
Figure FDA0003604095910000019
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
Figure FDA0003604095910000026
Figure FDA0003604095910000027
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 array
Figure FDA0003604095910000028
Received 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
Figure FDA0003604095910000021
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;
Figure FDA0003604095910000022
wherein
Figure FDA0003604095910000023
And
Figure FDA0003604095910000024
and respectively obtaining two-dimensional spatial spectrum estimation results of the sub-area array 1 and the sub-area array 2.
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:
Figure FDA0003604095910000025
wherein,
Figure FDA0003604095910000031
q corresponding to the profile signal of the sub-area array iiA guide vector of x 1-dimension,
Figure FDA0003604095910000032
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
Figure FDA0003604095910000033
The process is traversed by the distance theta and,
Figure FDA0003604095910000034
obtaining two-dimensional MUSIC spatial spectrum P of each sub-area array2D-planararrayi。
CN202210413128.5A 2022-04-19 2022-04-19 Compressed sensing and minimization processing combined co-prime area array two-dimensional DOA estimation method Pending CN114755627A (en)

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