CN114487990A - Two-dimensional DOA estimation method, device, equipment and medium based on parallel nested array - Google Patents

Two-dimensional DOA estimation method, device, equipment and medium based on parallel nested array Download PDF

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CN114487990A
CN114487990A CN202210028687.4A CN202210028687A CN114487990A CN 114487990 A CN114487990 A CN 114487990A CN 202210028687 A CN202210028687 A CN 202210028687A CN 114487990 A CN114487990 A CN 114487990A
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孙丰刚
兰鹏
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Shandong Agricultural University
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Abstract

The application discloses a two-dimensional DOA estimation method, a device, equipment and a medium based on a parallel nested array, wherein the method comprises the following steps: calculating a received signal of each subarray in the three parallel nested arrays; calculating a covariance matrix of each subarray according to the received signals of each subarray, and expanding the covariance matrix to obtain a virtual covariance matrix; calculating a cross covariance matrix between the sub-arrays according to the received signals of each sub-array, and expanding the cross covariance matrix to obtain a virtual cross covariance matrix; constructing a DOA estimation matrix according to the virtual covariance matrix and the virtual cross covariance matrix; and decomposing the eigenvalue of the DOA estimation matrix, and calculating an included angle between the incident signal and the X axis and an included angle between the incident signal and the Y axis according to the decomposed eigenvalue. According to the DOA estimation method provided by the application, the two-dimensional angle equalization estimation is realized with lower complexity, and the estimation precision is greatly improved.

Description

Two-dimensional DOA estimation method, device, equipment and medium based on parallel nested array
Technical Field
The invention relates to the technical field of communication signal processing, in particular to a two-dimensional DOA estimation method, a device, equipment and a medium based on a parallel nested array.
Background
Direction of Arrival (DOA) estimation is a technique for acquiring a signal incidence Direction by using array received signals, is an important research subject in the field of array signal processing, and is widely applied to the fields of radar, sonar, wireless communication, and the like. In order to realize two-dimensional DOA estimation, the planar array structure is most widely applied, such as an area array, a parallel array and the like. Most of the traditional planar arrays are uniform array structures and are composed of a plurality of linear sub-arrays which are uniformly spaced, and the spacing of array elements of the traditional planar arrays is generally not more than half wavelength of a signal so as to avoid phase ambiguity. Therefore, the conventional uniform array usually faces the problems of low degree of freedom, poor resolution, etc. caused by the limited physical aperture of the array.
Disclosure of Invention
The embodiment of the application provides a two-dimensional DOA estimation method, a device, equipment and a medium based on a parallel nested array. The following presents a simplified summary in order to provide a basic understanding of some aspects of the disclosed embodiments. This summary is not an extensive overview and is intended to neither identify key/critical elements nor delineate the scope of such embodiments. Its sole purpose is to present some concepts in a simplified form as a prelude to the more detailed description that is presented later.
In a first aspect, an embodiment of the present application provides a two-dimensional DOA estimation method based on a parallel nested array, including:
calculating a received signal of each subarray in the three parallel nested arrays;
calculating a covariance matrix of each subarray according to the received signals of each subarray, and expanding the covariance matrix to obtain a virtual covariance matrix;
calculating a cross covariance matrix between the sub-arrays according to the received signals of each sub-array, and expanding the cross covariance matrix to obtain a virtual cross covariance matrix;
constructing a DOA estimation matrix according to the virtual covariance matrix and the virtual cross covariance matrix;
and decomposing the eigenvalue of the DOA estimation matrix, and calculating an included angle between the incident signal and the X axis and an included angle between the incident signal and the Y axis according to the decomposed eigenvalue.
In an alternative embodiment, calculating the received signal for each of the three parallel nested arrays comprises:
the received signal for each sub-array is calculated according to the following formula:
yi(t)＝Ais(t)+ni(t),i＝1,2,3
wherein, Yi(t) represents the received signal of the ith sub-array, and S (t) represents the transmitted signal vectorAmount, ni(t) additive white Gaussian noise in the ith sub-array that is uncorrelated with the signal S (t),
Ai＝[ai(α1,β1),ai(α2,β2),…,ai(αK,βK)]an M × K dimensional direction matrix representing the ith sub-matrix and satisfying A2＝A1Φ12，A3＝A1Φ13Wherein
Figure BDA0003465528400000021
Figure BDA0003465528400000022
Response vector a1(αk,βk) Is a direction matrix A1The k-th column in (1) can be expressed as
Figure BDA0003465528400000023
In an optional embodiment, calculating a covariance matrix of each subarray according to the received signals of each subarray, and expanding the covariance matrix to obtain a virtual covariance matrix includes:
the covariance matrix for each sub-array is calculated according to the following formula:
Figure BDA0003465528400000024
the covariance matrix is expanded to obtain a virtual covariance matrix as follows:
Figure BDA0003465528400000025
wherein, the diagonal matrix Λ ═ diag (p)1,p2,…,pK)，
Figure BDA0003465528400000026
Is composed of
Figure BDA0003465528400000027
A dimension direction matrix.
In an optional embodiment, calculating a cross-covariance matrix between the sub-arrays according to the received signals of each sub-array, and expanding the cross-covariance matrix to obtain a virtual cross-covariance matrix, includes:
calculating a cross-covariance matrix between the sub-arrays according to the following formula:
Figure BDA0003465528400000031
the cross covariance matrix is expanded to obtain a virtual cross covariance matrix as follows:
Figure BDA0003465528400000032
wherein phi11＝IK，
Figure BDA0003465528400000033
Is composed of
Figure BDA0003465528400000034
A dimension direction matrix.
In an optional embodiment, constructing the DOA estimation matrix from the virtual covariance matrix and the virtual cross covariance matrix comprises:
constructing a DOA estimation matrix according to the following formula:
Figure BDA0003465528400000035
wherein,
Figure BDA0003465528400000036
a virtual covariance matrix is represented and,
Figure BDA0003465528400000037
representing a virtual cross-covariance matrix, (-)HRepresenting a conjugate transpose.
In an optional embodiment, performing eigenvalue decomposition on the DOA estimation matrix, and calculating an angle between the incident signal and the X-axis according to the decomposed eigenvalues, includes:
calculating the fuzzy phase of the included angle according to the following formula and the decomposed characteristic value:
Figure BDA0003465528400000038
Figure BDA0003465528400000039
two sets of estimates of the angle are calculated according to the following formula and the ambiguous phase of the angle:
Figure BDA00034655284000000310
Figure BDA00034655284000000311
determining the angle between the incident signal and the X-axis from the same of the two sets of estimates of the angle, where γ12,k、γ13,kRepresenting the characteristic value of the decomposition, u1、u2The angle (-) represents taking the phase as an integer varying with k.
In an alternative embodiment, performing eigenvalue decomposition on the DOA estimation matrix, and calculating an angle between the incident signal and the Y-axis according to the decomposed eigenvalues, includes:
calculating the included angle between the incident signal and the Y axis according to the following formula and the decomposed characteristic value:
Figure BDA0003465528400000041
wherein λ iskRepresenting the eigenvalues of the decomposition, and angle (·) representing the phase.
In a second aspect, an embodiment of the present application provides a two-dimensional DOA estimation apparatus based on parallel nested arrays, including:
the receiving signal calculating module is used for calculating the receiving signal of each sub-array in the three parallel nested arrays;
the covariance matrix expansion module is used for calculating a covariance matrix of each subarray according to the received signals of each subarray and expanding the covariance matrix to obtain a virtual covariance matrix;
the cross covariance matrix expansion module is used for calculating a cross covariance matrix between the sub-arrays according to the received signals of each sub-array and expanding the cross covariance matrix to obtain a virtual cross covariance matrix;
the DOA estimation matrix construction module is used for constructing a DOA estimation matrix according to the virtual covariance matrix and the virtual cross covariance matrix;
and the two-dimensional estimation module is used for decomposing the eigenvalue of the DOA estimation matrix and calculating the included angle between the incident signal and the X axis and the included angle between the incident signal and the Y axis according to the decomposed eigenvalue.
In a third aspect, an embodiment of the present application provides a two-dimensional DOA estimation apparatus based on a parallel nested array, including a processor and a memory storing program instructions, where the processor is configured to execute the two-dimensional DOA estimation method based on the parallel nested array provided in the foregoing embodiment when executing the program instructions.
In a fourth aspect, the present application provides a computer-readable medium, on which computer-readable instructions are stored, where the computer-readable instructions are executed by a processor to implement a two-dimensional DOA estimation method based on parallel nested arrays, provided by the foregoing embodiments.
The technical scheme provided by the embodiment of the application can have the following beneficial effects:
the embodiment of the application provides a two-dimensional DOA estimation method based on a three-parallel nested array, aiming at the problems of insufficient utilization of array receiving information, unbalanced two-dimensional angle estimation and the like in the traditional method, the method fully excavates covariance and cross covariance matrix information of each sub-array to reconstruct a DOA estimation matrix; furthermore, aperture expansion in two directions is realized through virtual array expansion and parallel subarray sparse arrangement in two directions, and balanced estimation of a two-dimensional angle is realized. The two-dimensional angle equalization estimation is realized with lower complexity, and the estimation precision is greatly improved.
It is to be understood that both the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive of the invention, as claimed.
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The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments consistent with the invention and together with the description, serve to explain the principles of the invention.
FIG. 1 is a schematic diagram illustrating a two-dimensional DOA estimation method based on parallel nested arrays in accordance with an exemplary embodiment;
FIG. 2 is a schematic diagram illustrating a two-dimensional DOA estimation method based on parallel nested arrays, according to an exemplary embodiment;
FIG. 3 is a schematic diagram of a three parallel nested array configuration shown in accordance with an exemplary embodiment;
FIG. 4 is a graphical illustration of a relationship between root mean square error and signal-to-noise ratio for various angles, according to an exemplary embodiment;
FIG. 5 is a graphical illustration of an overall root mean square error versus signal-to-noise ratio in accordance with an exemplary embodiment;
FIG. 6 is a graphical illustration of a relationship between root mean square error and snapshot count for various angles, according to an exemplary embodiment;
FIG. 7 is a graphical illustration of an overall root mean square error versus snapshot count, in accordance with an exemplary embodiment;
FIG. 8 is a schematic diagram illustrating a two-dimensional DOA estimation apparatus based on parallel nested arrays in accordance with an exemplary embodiment;
FIG. 9 is a schematic diagram illustrating a two-dimensional DOA estimation device based on parallel nested arrays in accordance with an exemplary embodiment;
FIG. 10 is a schematic diagram illustrating a computer storage medium in accordance with an exemplary embodiment.
Detailed Description
The following description and the drawings sufficiently illustrate specific embodiments of the invention to enable those skilled in the art to practice them.
It should be understood that the described embodiments are only some embodiments of the invention, and not all embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
When the following description refers to the accompanying drawings, like numbers in different drawings represent the same or similar elements unless otherwise indicated. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with the present invention. Rather, they are merely examples of systems and methods consistent with certain aspects of the invention, as detailed in the appended claims.
Generally, planar arrays are mostly uniform array structures, and are composed of several uniformly spaced linear sub-arrays, whose array element spacing should generally be no greater than half the wavelength of the signal to avoid phase ambiguity. Therefore, the conventional uniform array usually faces the problems of low degree of freedom, poor resolution, etc. caused by the limited physical aperture of the array.
Based on the above, the embodiment of the application provides an improved two-dimensional DOA estimation algorithm based on a three-parallel nested array. By sparse and co-prime arrangement and virtual array construction of three parallel nested linear arrays, the array aperture is improved, and the balanced estimation of a two-dimensional angle is realized. And further, the array received signal information is fully utilized, a new DOA estimation matrix is constructed based on the covariance matrix and the cross covariance matrix information of each sub-matrix, and finally the paired DOA estimation value is obtained by decomposing the eigenvalue of the expansion matrix. Compared with the prior art, the method can be used for fully mining the covariance matrix and the cross covariance matrix information of each subarray, improving the estimation freedom degree and precision, expanding the array aperture from two directions and realizing two-dimensional angle equalization estimation.
The two-dimensional DOA estimation method based on parallel nested arrays provided by the embodiments of the present application will be described in detail below with reference to the accompanying drawings. Referring to fig. 1, the method specifically includes the following steps.
S101 calculates a received signal for each sub-array in the three parallel nested arrays.
In an embodiment of the present application, the array model adopted is a parallel nested array structure, as shown in fig. 3, the array model includes three identical and mutually parallel nested arrays, which are respectively called as a sub-array 1, a sub-array 2, and a sub-array 3, the sub-array 1 is arranged along the Y-axis with the origin as the starting point, and the sub-array 2 and the sub-array 3 are respectively translated d along the X-axis12And d13A distance. Each nested subarray comprises M real physical array elements, and each subarray is formed by cascading two uniform linear arrays with different array element intervals. As shown in FIG. 3, the array has an array element spacing of d and an array element number of M1Array element spacing of (M)1+1) d array with M array elements2＝M-M1. Where d λ 2 is the basic array element spacing and λ is the incident signal wavelength.
For subarray 1, the array element position may be represented as (0, z)id) Wherein z isiBelong to
Figure BDA0003465528400000061
The array element positions of subarrays 2 and 3 may be respectively represented as (d)12,zid) And (d)13,zid)。
Suppose there are K far-field narrowband signals from different directions
Figure BDA0003465528400000071
Incident on the array, wherein αkAnd betakRespectively representing the angle of the signal incidence direction with the Y-axis and the X-axis. The received signal for each sub-array is calculated according to the following formula:
yi(t)＝Ais(t)+ni(t),i＝1,2,3
wherein Y isi(t) denotes a received signal of the ith sub-array, S (t) denotes a transmitted signal vector, ni(t) additive white Gaussian noise in the ith sub-array, uncorrelated with the signal S (t), with a mean of 0 and a variance of
Figure BDA0003465528400000072
Ai＝[ai(α1,β1),ai(α2,β2),…,ai(αK,βK)]An M × K dimensional direction matrix representing the ith sub-matrix and satisfying A2＝A1Φ12，A3＝A1Φ13Wherein
Figure BDA0003465528400000073
Figure BDA0003465528400000074
Response vector a1(αk,βk) Is a direction matrix A1The k-th column in (1) can be expressed as
Figure BDA0003465528400000075
S102, a covariance matrix of each subarray is calculated according to the received signals of each subarray, and the covariance matrix is expanded to obtain a virtual covariance matrix.
Specifically, the covariance matrix of each sub-array is calculated according to the following formula:
Figure BDA0003465528400000076
wherein, the diagonal matrix Λ ═ diag (p)1,p2,…,pK) Representing the covariance matrix of the received signal. When i is 2,3, Ai＝A1Φ1iThus, therefore, it is
Figure BDA0003465528400000077
For diagonal matrix phi1iAnd a, in respect of a and a,
formula phi1iΛ＝ΛΦ1iIs established, therefore there is
Figure BDA0003465528400000078
That is:
Figure BDA0003465528400000079
r is to beiAfter vectorization, the following results are obtained:
Figure BDA00034655284000000710
wherein,
Figure BDA00034655284000000711
p＝[p1,p2,…,pK]T. According to the nested nature of the arrays, B1In which 2M is included2(M1+1) -1 consecutive element. Removing repeated elements in the material and arranging the repeated elements in sequence to obtain:
Figure BDA00034655284000000712
wherein,
Figure BDA0003465528400000081
the expression dimension is (2M)2(M1A direction matrix of +1) -1) × K; e is one (2M)2(M1+1) -1) x 1-dimensional column vector, divided by the Mth2(M1+1) elements are other than 1, the remaining elements being 0.
By means of a counter-vector
Figure BDA0003465528400000082
The Toeplitz matrix reconstruction is carried out, and the obtained virtual covariance matrix is as follows:
Figure BDA0003465528400000083
wherein,
Figure BDA0003465528400000084
is composed of
Figure BDA0003465528400000085
Dimension direction matrix whose k-th column can be expressed as
Figure BDA0003465528400000086
S103, calculating a cross covariance matrix among the sub-arrays according to the received signals of each sub-array, and expanding the cross covariance matrix to obtain a virtual cross covariance matrix.
Specifically, the cross covariance matrix between sub-array i and sub-array j (i ≠ j) can be the following through the received signals of each sub-array:
Figure BDA0003465528400000087
wherein phi11＝IK，
Figure BDA0003465528400000088
Since the noise between the sub-arrays is uncorrelated, the cross-covariance matrix CijNot containing noise term, pair CijVectorizing to obtain:
cij＝vec(Cij)＝B1Θijp
removing repeated items c in the sequenceijAnd arranging the continuous items according to the sequence to obtain:
Figure BDA0003465528400000089
for vector
Figure BDA00034655284000000810
Constructing a Toeplitz matrix to obtain a virtual cross covariance matrix as follows:
Figure BDA00034655284000000811
wherein,
Figure BDA0003465528400000091
is composed of
Figure BDA0003465528400000092
Dimension direction matrix whose k-th column can be expressed as
Figure BDA0003465528400000093
S104, a DOA estimation matrix is constructed according to the virtual covariance matrix and the virtual cross covariance matrix.
Specifically, the virtual covariance matrix and the virtual cross covariance matrix of each sub-array are used to construct a DOA estimation matrix, which can be used for subsequent DOA estimation.
In an alternative embodiment, the DOA estimation matrix is constructed according to the following formula:
Figure BDA0003465528400000094
wherein,
Figure BDA0003465528400000095
a virtual covariance matrix is represented and,
Figure BDA0003465528400000096
representing a virtual cross-covariance matrix, (-)HRepresenting a conjugate transpose.
S105, eigenvalue decomposition is carried out on the DOA estimation matrix, and an included angle between the incident signal and the X axis and an included angle between the incident signal and the Y axis are calculated according to the decomposed eigenvalues.
In one possible implementation, the matrix is estimated for the DOA
Figure BDA0003465528400000097
The eigenvalue decomposition is carried out to obtain:
Figure BDA0003465528400000098
wherein, EsAnd EnRespectively represent
Figure BDA0003465528400000099
The signal subspace feature vector of the dimension, and
Figure BDA00034655284000000910
dimensional noisy subspace eigenvectors, diagonal matrix sigmasSum-sigmanRespectively containing eigenvalues corresponding to the signal subspace and the noise subspace. The spatial spectrum search function is constructed as:
Figure BDA00034655284000000911
in an alternative embodiment of the method of the present invention,
Figure BDA00034655284000000912
and for the array response vector corresponding to the parallel expanded virtual array, two-dimensional spectral peak searching is carried out on the formula to obtain the estimated values of the two-dimensional angles alpha and beta. However, the method is high in complexity and low in solving efficiency.
In an alternative embodiment, the angle between the incident signal and the X-axis and the angle between the incident signal and the Y-axis are solved according to the following manner. Due to EsThe signal subspace is characterized, so that a K matrix T exists which satisfies:
Figure BDA0003465528400000101
wherein, the matrix Es1，Es2And Es3All dimensions of (A) are
Figure BDA0003465528400000102
And satisfies the relationship:
Figure BDA0003465528400000103
by using Es1，Es2And Es3Respectively construct a matrix R12And R13Comprises the following steps:
Figure BDA0003465528400000104
Figure BDA0003465528400000105
it is known that R12And R13Respectively has a characteristic value of phi12And phi13Diagonal element of and12and phi13Including the angle information beta between the incident signal and the X-axis. Note that phi12And phi13And is spaced from the subarray by d12And d13And (4) correlating. In the following, R will be combined12And R13According to d12And d13The angle beta is estimated. Let R be12And R13The K eigenvalues obtained in the step (c) are respectively { gamma12,kK is 1,2, …, K and y13,k,k＝1,2,…,K}。
In a traditional double parallel array structure, the interval between two arrays usually needs to satisfy a constraint condition that the interval is not more than half wavelength of a signal so as to avoid phase ambiguity, which results in insufficient estimation accuracy of the angle beta. Increasing the array aperture by increasing the adjacent subarray spacing will help improve the estimation accuracy. While the phase ambiguity problem caused by large spacing can be solved by the co-prime property. Let us assume d12＝N1λ/2,d13＝N2λ/2, where N1And N2Are relatively prime integers. From the eigenvalues γ due to the larger adjacent subarray spacing12,k and gamma13,kThe fuzzy phases related to the included angle beta can be respectively recovered as follows:
Figure BDA0003465528400000106
Figure BDA0003465528400000107
according to the subarray interval relationship, two groups of estimation values of the included angle are calculated:
Figure BDA0003465528400000108
Figure BDA0003465528400000109
wherein, γ12,k、γ13,kRepresenting the characteristic value of the decomposition, u1、u2For integers varying with k, angle (-) means taking phase and guarantees
Figure BDA0003465528400000111
In the interval [ -1,1 [)]Within.
Two sets of estimated values are obtained separately
Figure BDA0003465528400000112
Based on the co-prime property, the angle information beta without ambiguitykCan be obtained from the common part of two sets of estimates, except for the true angle βkIn addition, some other ambiguous phases are included. Therefore, the two formulas calculate different estimated values, but the two estimated values contain the real angle βkTherefore, the two sets of estimation values can be combined to find a common part, and the finally estimated included angle can be determined.
In practice, due to the influence of noise, there are usually no completely coincident elements, so the mean of the nearest two elements can be found as the solution between the k incident signals and the X-axisAngle of (b) ofk。
In an alternative embodiment, performing eigenvalue decomposition on the DOA estimation matrix, and calculating an angle between the incident signal and the Y-axis according to the decomposed eigenvalues, includes:
by performing eigenvalue decomposition on the DOA estimation matrix, the matrix formed by corresponding eigenvalue vectors is the estimated value, and then:
Figure BDA0003465528400000113
wherein,
Figure BDA0003465528400000114
is composed of
Figure BDA0003465528400000115
According to the rotation invariant property, the matrix can be changed
Figure BDA0003465528400000116
Decomposed into two matrices
Figure BDA0003465528400000117
And
Figure BDA0003465528400000118
matrix of
Figure BDA0003465528400000119
Is taken from
Figure BDA00034655284000001110
Line 1 to
Figure BDA00034655284000001111
Line, first
Figure BDA00034655284000001112
Go to
Figure BDA00034655284000001113
Line, and
Figure BDA00034655284000001114
go to
Figure BDA00034655284000001115
A row; matrix array
Figure BDA00034655284000001116
Is taken from
Figure BDA00034655284000001117
Line 2 to
Figure BDA00034655284000001118
Line, line 1
Figure BDA00034655284000001119
Go to
Figure BDA00034655284000001120
Line, and
Figure BDA00034655284000001121
go to
Figure BDA00034655284000001122
And (6) rows. Matrix array
Figure BDA00034655284000001123
And
Figure BDA00034655284000001124
satisfies the following conditions:
Figure BDA00034655284000001125
wherein,
Figure BDA00034655284000001126
then there are:
Figure BDA00034655284000001127
obtaining a eigenvalue λ by solving ΨkCorresponding to the angle between the incident k signals and the Y axis
Figure BDA00034655284000001129
Estimated as:
Figure BDA00034655284000001128
wherein λ iskRepresenting the eigenvalues of the decomposition, and angle (·) representing the phase. In this way, the estimated included angle alpha with the Y axis can be obtainedk。
In the embodiment of the present application, (.)T，(·)*，(·)H，(·)-1And (·)+Respectively representing matrix transposition, conjugation, conjugate transposition, inversion and pseudo-inversion; e [. C]Expressing the expectation; diag (v) denotes a diagonal matrix composed of v as diagonal elements; vec (·) represents matrix vectorization; angle (·) denotes taking phase; and indicates a Khatri-Rao product.
By the two-dimensional DOA estimation method, the calculation complexity can be reduced, and the calculation efficiency can be improved.
In order to facilitate understanding of the two-dimensional DOA estimation method based on parallel nested arrays provided in the embodiments of the present application, the following description is made with reference to fig. 2. As shown in fig. 2, the method includes the following steps.
Firstly, acquiring a received signal based on a three-parallel nested array structure, and realizing the construction of an array received signal; further, the virtual expansion of the array is realized by utilizing the difference relation of the nested arrays, and a virtual covariance matrix and a virtual cross covariance are obtained; constructing a DOA estimation matrix based on the virtual covariance matrix and the virtual cross covariance matrix among the sub-matrices; finally, based on the position and phase relation between the sub-arrays, the design of the dimension reduction method is realized, and the included angle between the incident signal and the X axis and the included angle between the incident signal and the Y axis are obtained.
In one embodiment, fig. 4 shows the variation of the root mean square error performance of each angle of the method and the double parallel nested array method when the snapshot number is 200 as the signal-to-noise ratio increases. Figure 5 is the overall rms error performance variation under the same conditions. It can be seen that the estimation performance of the angle beta is obviously improved on the premise that the estimation performance of the angle alpha is slightly reduced by the method. And the performance of the whole root mean square error is obviously improved.
FIG. 6 shows the variation of the RMS error performance of each angle of the method of the present application and the dual parallel nested array method with increasing fast beats and a SNR of 0 dB. Figure 7 is the overall rms error performance variation under the same conditions. Similarly, the estimation performance of the angle beta is obviously improved on the premise that the estimation performance of the angle alpha is slightly reduced by the method. And the performance of the whole root mean square error is obviously improved.
The experimental results show that the method fully excavates the virtual array aperture expansion advantage and the subarray co-prime layout advantage of the three parallel nested arrays, so that the array aperture expansion in two directions is brought; the DOA estimation expansion matrix is reconstructed by further combining the covariance matrix and the cross covariance matrix information of each subarray, the two-dimensional angle equalization estimation can be realized, the two-dimensional angle equalization estimation is realized with low complexity, and the estimation precision can be improved.
An embodiment of the present application further provides a two-dimensional DOA estimation apparatus based on a parallel nested array, where the apparatus is configured to execute the two-dimensional DOA estimation method based on a parallel nested array according to the foregoing embodiment, and as shown in fig. 8, the apparatus includes:
a received signal calculation module 801, configured to calculate a received signal of each sub-array in the three parallel nested arrays;
a covariance matrix expansion module 802, configured to calculate a covariance matrix of each subarray according to the received signal of each subarray, and expand the covariance matrix to obtain a virtual covariance matrix;
a cross covariance matrix extension module 803, configured to calculate a cross covariance matrix between the sub-arrays according to the received signals of each sub-array, and extend the cross covariance matrix to obtain a virtual cross covariance matrix;
a DOA estimation matrix construction module 804, configured to construct a DOA estimation matrix according to the virtual covariance matrix and the virtual cross covariance matrix;
and a two-dimensional estimation module 805 configured to perform eigenvalue decomposition on the DOA estimation matrix, and calculate an included angle between the incident signal and the X axis and an included angle between the incident signal and the Y axis according to the decomposed eigenvalues.
It should be noted that, when the two-dimensional DOA estimation apparatus based on the parallel nested array provided in the foregoing embodiment executes the two-dimensional DOA estimation method based on the parallel nested array, only the division of the functional modules is illustrated, and in practical applications, the function distribution may be completed by different functional modules according to needs, that is, the internal structure of the device is divided into different functional modules, so as to complete all or part of the functions described above. In addition, the two-dimensional DOA estimation device based on the parallel nested array and the two-dimensional DOA estimation method based on the parallel nested array provided by the above embodiment belong to the same concept, and the embodiment of the implementation process is described in detail in the method embodiment, which is not described herein again.
The embodiment of the present application further provides an electronic device corresponding to the two-dimensional DOA estimation method based on the parallel nested array provided in the foregoing embodiment, so as to execute the two-dimensional DOA estimation method based on the parallel nested array.
Referring to fig. 9, a schematic diagram of an electronic device provided in some embodiments of the present application is shown. As shown in fig. 9, the electronic apparatus includes: the processor 900, the memory 901, the bus 902 and the communication interface 903, wherein the processor 900, the communication interface 903 and the memory 901 are connected through the bus 902; the memory 901 stores a computer program that can be executed on the processor 900, and when the processor 900 executes the computer program, the two-dimensional DOA estimation method based on parallel nested arrays provided by any of the foregoing embodiments of the present application is executed.
The Memory 901 may include a high-speed Random Access Memory (RAM) and may further include a non-volatile Memory (non-volatile Memory), such as at least one disk Memory. The communication connection between the network element of the system and at least one other network element is implemented through at least one communication interface 903 (which may be wired or wireless), and the internet, a wide area network, a local network, a metropolitan area network, and the like may be used.
Bus 902 can be an ISA bus, PCI bus, EISA bus, or the like. The bus may be divided into an address bus, a data bus, a control bus, etc. The memory 901 is used for storing a program, and the processor 900 executes the program after receiving an execution instruction, and the two-dimensional DOA estimation method based on a parallel nested array disclosed in any embodiment of the present application may be applied to the processor 900, or implemented by the processor 900.
The processor 900 may be an integrated circuit chip having signal processing capabilities. In implementation, the steps of the above method may be performed by integrated logic circuits of hardware or instructions in the form of software in the processor 900. The Processor 900 may be a general-purpose Processor, and includes a Central Processing Unit (CPU), a Network Processor (NP), and the like; but may also be a Digital Signal Processor (DSP), an Application Specific Integrated Circuit (ASIC), an off-the-shelf programmable gate array (FPGA) or other programmable logic device, discrete gate or transistor logic, discrete hardware components. The various methods, steps, and logic blocks disclosed in the embodiments of the present application may be implemented or performed. A general purpose processor may be a microprocessor or the processor may be any conventional processor or the like. The steps of the method disclosed in connection with the embodiments of the present application may be directly implemented by a hardware decoding processor, or implemented by a combination of hardware and software modules in the decoding processor. The software module may be located in ram, flash memory, rom, prom, or eprom, registers, etc. storage media as is well known in the art. The storage medium is located in the memory 901, and the processor 900 reads the information in the memory 901, and completes the steps of the above method in combination with the hardware thereof.
The electronic device provided by the embodiment of the application and the two-dimensional DOA estimation method based on the parallel nested array provided by the embodiment of the application have the same inventive concept and have the same beneficial effects as the method adopted, operated or realized by the electronic device.
Referring to fig. 10, the computer readable storage medium is an optical disc 1000, and a computer program (i.e., a program product) is stored thereon, and when being executed by a processor, the computer program executes the two-dimensional DOA estimation method based on the parallel nested array provided in any of the foregoing embodiments.
It should be noted that examples of the computer-readable storage medium may also include, but are not limited to, phase change memory (PRAM), Static Random Access Memory (SRAM), Dynamic Random Access Memory (DRAM), other types of Random Access Memory (RAM), Read Only Memory (ROM), Electrically Erasable Programmable Read Only Memory (EEPROM), flash memory, or other optical and magnetic storage media, which are not described in detail herein.
The computer-readable storage medium provided by the above-mentioned embodiment of the present application and the two-dimensional DOA estimation method based on parallel nested arrays provided by the embodiment of the present application have the same advantages as the method adopted, run or implemented by the application program stored in the computer-readable storage medium.
All possible combinations of the technical features in the above embodiments may not be described for the sake of brevity, but should be considered as being within the scope of the present disclosure as long as there is no contradiction between the combinations of the technical features.
The above examples only show some embodiments of the present invention, and the description thereof is more specific and detailed, but not construed as limiting the scope of the present invention. It should be noted that, for a person skilled in the art, several variations and modifications can be made without departing from the inventive concept, which falls within the scope of the present invention. Therefore, the protection scope of the present patent should be subject to the appended claims.

Claims (10)

1. A two-dimensional DOA estimation method based on a parallel nested array is characterized by comprising the following steps:
calculating a received signal of each subarray in the three parallel nested arrays;
calculating a covariance matrix of each subarray according to the received signals of each subarray, and expanding the covariance matrix to obtain a virtual covariance matrix;
calculating a cross covariance matrix between the sub-arrays according to the received signals of each sub-array, and expanding the cross covariance matrix to obtain a virtual cross covariance matrix;
constructing a DOA estimation matrix according to the virtual covariance matrix and the virtual cross covariance matrix;
and decomposing the eigenvalue of the DOA estimation matrix, and calculating an included angle between the incident signal and the X axis and an included angle between the incident signal and the Y axis according to the decomposed eigenvalue.
2. The method of claim 1, wherein computing the received signal for each of the three parallel nested arrays comprises:
the received signal for each sub-array is calculated according to the following formula:
yi(t)＝Ais(t)+ni(t),i＝1,2,3
wherein, Yi(t) denotes a received signal of the ith sub-array, S (t) denotes a transmitted signal vector, ni(t) additive white Gaussian noise in the ith sub-array that is uncorrelated with the signal S (t), Ai＝[ai(α1,β1),ai(α2,β2),…,ai(αK,βK)]An M × K dimensional direction matrix representing the ith sub-matrix and satisfying A2＝A1Φ12，A3＝A1Φ13Wherein
Figure FDA0003465528390000011
Figure FDA0003465528390000012
Response vector a1(αk,βk) Is a direction matrix A1The k-th column in (1) can be expressed as
Figure FDA0003465528390000013
3. The method of claim 1, wherein computing a covariance matrix for each subarray based on received signals for each subarray and expanding the covariance matrix to obtain a virtual covariance matrix comprises:
the covariance matrix for each sub-array is calculated according to the following formula:
Figure FDA0003465528390000021
expanding the covariance matrix to obtain a virtual covariance matrix as follows:
Figure FDA0003465528390000022
wherein, the diagonal matrix Λ ═ diag (p)1,p2,…,pK)，
Figure FDA0003465528390000023
Figure FDA0003465528390000024
Is composed of
Figure FDA0003465528390000025
A dimension direction matrix.
4. The method of claim 1, wherein computing a cross-covariance matrix between subarrays from the received signals of each subarray and expanding the cross-covariance matrix to obtain a virtual cross-covariance matrix comprises:
calculating a cross-covariance matrix between the sub-arrays according to the following formula:
Figure FDA0003465528390000026
expanding the cross covariance matrix to obtain a virtual cross covariance matrix as follows:
Figure FDA0003465528390000027
wherein phi11＝IK，
Figure FDA0003465528390000028
Figure FDA0003465528390000029
Is composed of
Figure FDA00034655283900000210
A dimension direction matrix.
5. The method of claim 1, wherein constructing a DOA estimation matrix from the virtual covariance matrix and a virtual cross covariance matrix comprises:
constructing the DOA estimation matrix according to the following formula:
Figure FDA0003465528390000031
wherein,
Figure FDA0003465528390000032
a virtual covariance matrix is represented and,
Figure FDA0003465528390000033
representing a virtual cross-covariance matrix, (-)HRepresenting a conjugate transpose.
6. The method of claim 1, wherein performing eigenvalue decomposition on the DOA estimation matrix and calculating an angle between an incident signal and an X-axis from the decomposed eigenvalues comprises:
calculating the fuzzy phase of the included angle according to the following formula and the decomposed characteristic value:
Figure FDA0003465528390000034
Figure FDA0003465528390000035
two sets of estimates of the angle are calculated according to the following formula and the ambiguous phase of the angle:
Figure FDA0003465528390000036
Figure FDA0003465528390000037
determining the angle between the incident signal and the X-axis from the same of the two sets of estimates of the angle, where γ12,k、γ13,kRepresenting the characteristic value of the decomposition, u1、u2The angle (-) represents taking the phase as an integer varying with k.
7. The method of claim 1, wherein performing eigenvalue decomposition on the DOA estimation matrix and calculating an angle between an incident signal and a Y-axis from the decomposed eigenvalues comprises:
calculating the included angle between the incident signal and the Y axis according to the following formula and the decomposed characteristic value:
Figure FDA0003465528390000038
wherein λ iskRepresenting the eigenvalues of the decomposition, and angle (·) representing the phase.
8. A two-dimensional DOA estimation apparatus based on parallel nested arrays, comprising:
the receiving signal calculating module is used for calculating the receiving signal of each sub-array in the three parallel nested arrays;
the covariance matrix expansion module is used for calculating a covariance matrix of each subarray according to the received signals of each subarray and expanding the covariance matrix to obtain a virtual covariance matrix;
the cross covariance matrix expansion module is used for calculating a cross covariance matrix between the sub-arrays according to the received signals of each sub-array and expanding the cross covariance matrix to obtain a virtual cross covariance matrix;
the DOA estimation matrix construction module is used for constructing a DOA estimation matrix according to the virtual covariance matrix and the virtual cross covariance matrix;
and the two-dimensional estimation module is used for decomposing the eigenvalue of the DOA estimation matrix and calculating an included angle between the incident signal and the X axis and an included angle between the incident signal and the Y axis according to the decomposed eigenvalue.
9. A two-dimensional DOA estimation device based on parallel nested arrays, characterized by comprising a processor and a memory storing program instructions, the processor being configured to perform the two-dimensional DOA estimation method based on parallel nested arrays according to any one of claims 1 to 7 when executing the program instructions.
10. A computer readable medium having computer readable instructions stored thereon which are executed by a processor to implement a parallel nested array based two dimensional DOA estimation method as claimed in any one of claims 1 to 7.
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* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN117192471A (en) * 2023-09-06 2023-12-08 无锡芯光互连技术研究院有限公司 HLS-based two-dimensional DOA estimation method, device and storage medium

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