CN111337872A - Generalized DOA matrix method for coherent information source direction finding - Google Patents

Generalized DOA matrix method for coherent information source direction finding Download PDF

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CN111337872A
CN111337872A CN202010107568.9A CN202010107568A CN111337872A CN 111337872 A CN111337872 A CN 111337872A CN 202010107568 A CN202010107568 A CN 202010107568A CN 111337872 A CN111337872 A CN 111337872A
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CN111337872B (en
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戴祥瑞
张小飞
叶长波
朱倍佐
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Nanjing University of Aeronautics and Astronautics
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Abstract

The invention discloses a generalized DOA matrix method for coherent information source direction finding, which fully utilizes autocorrelation information and cross-correlation information of received data of a double parallel array, divides the double parallel array into a plurality of sub-arrays which are overlapped in a smooth mode, combines the autocorrelation information and the cross-correlation information of each sub-array, deduces respective autocorrelation matrix and cross-correlation matrix, and then performs averaging operation to obtain each correlation matrix which can replace the correlation matrix in the original sense. The invention fully utilizes the autocorrelation matrix and the cross-correlation matrix of the received data of the double parallel arrays, thereby having better DOA estimation performance, and adopts a space smoothing mode, thereby being capable of well realizing decoherence and effectively estimating the DOA of the signal; the method does not need space spectrum search, has lower algorithm complexity, and can realize automatic pairing of the obtained DOA estimation angle.

Description

Generalized DOA matrix method for coherent information source direction finding
Technical Field
The invention belongs to the field of array signal processing, and particularly relates to a generalized DOA matrix method for coherent signal source direction finding.
Background
Since the signal receiving array can receive coherent signals in different directions, the coherent signals can cause rank loss of the signal source covariance matrix, and therefore the signal feature vectors are scattered to a noise subspace. The important content of the coherent signal DOA estimation is to consider what method is used for restoring the rank of the signal covariance matrix to be equal to the number of signal sources by starting from solving the rank deficiency of the matrix. Spatial smoothing techniques are efficient methods for dealing with coherent or strongly correlated signals. The basic idea is to divide an equidistant linear array into a plurality of overlapping sub-arrays. If the array manifolds of the sub-arrays are the same (the assumption is applicable to the equidistant linear arrays), the covariance matrixes of the sub-arrays can be added and then averagely replace the covariance matrixes in the original sense, so that the decoherence is realized.
The generalized DOA matrix method provided by the invention keeps the advantages that the traditional DOA matrix method can completely avoid polynomial search and the calculation amount is small, and simultaneously, the autocorrelation information and the cross-correlation information of the received signals of each subarray of the two arrays are completely utilized, so that a generalized DOA matrix is constructed, and the two-dimensional DOA angle estimation performance is improved.
Disclosure of Invention
The purpose of the invention is as follows: the invention provides a generalized DOA matrix method for coherent source direction finding, which aims to solve the problem of two-dimensional DOA estimation of coherent signals under a double parallel array and has higher estimation performance.
The technical scheme is as follows: the invention relates to a generalized DOA matrix method for coherent information source direction finding, which comprises the following steps:
(1) constructing a double parallel array composed of two uniform linear arrays on a two-dimensional space, wherein the double parallel array is respectively called an array 1 and an array 2, and dividing the two double parallel arrays into N overlapped sub-arrays in a sliding mode;
(2) a generalized DOA matrix is constructed by completely utilizing and averaging the autocorrelation matrix and the cross-correlation matrix of the received signals of each subarray;
(3) and decomposing the characteristics of the generalized DOA matrix to obtain the DOA angle of the information source signal.
Further, the step (1) is realized as follows:
each array has 2M sensors, the distance between two adjacent sensors along X direction and the distance between two sub-arrays are d, and there are K coherent narrow-band same-carrier signals s in spacek(t)(1≤kK) is incident on the array, the signal wavelength is lambda, and the angle between the signal and the x-axis is αkβ from the y-axiskEach subarray has M +1 array elements; the output of the nth forward sub-array of array 1 is:
Figure BDA0002388911830000021
wherein ,nx(t) is noise, xn(t) is the output of the nth array element of array 1, AM+1Direction matrix for (M +1) × K dimensions:
Figure BDA0002388911830000022
d is a rotation matrix among the sub-arrays:
Figure BDA0002388911830000023
the output of the nth sub-array of array 2 is:
Figure BDA0002388911830000024
wherein ,ny(t) is noise, yn(t) is the output of the nth array element of array 2, D1Is a rotation matrix between arrays 1 and 2:
Figure BDA0002388911830000025
further, the generalized DOA matrix in step (2) is:
Figure BDA0002388911830000026
wherein ,
Figure BDA0002388911830000027
Figure BDA0002388911830000028
an autocorrelation matrix which is a subarray 1, wherein RS＝E[s(t)sH(t)]Is a signal covariance matrix, and I is an identity matrix;
Figure BDA0002388911830000029
an autocorrelation matrix which is subarray 2;
Figure BDA0002388911830000031
a cross-correlation matrix for subarrays 1 and 2;
Figure BDA0002388911830000032
a cross-correlation matrix for subarrays 2 and 1;
Figure BDA0002388911830000034
wherein ,σ2Is the noise variance.
Further, the step (3) is realized as follows:
R′AE＝AED1
wherein ,
Figure BDA0002388911830000035
definition uk＝cosαk and vk＝cosβkAnd performing characteristic decomposition on the DOA matrix R', and obtaining the following characteristic values according to the characteristic values:
Figure BDA0002388911830000036
according to AEDefinition of (A) by classifying it asM+1And
Figure BDA0002388911830000037
two parts, after feature decomposition, the estimation of the two parts is respectively
Figure BDA0002388911830000038
And
Figure BDA0002388911830000039
least squares fit to be Bc ═ T, where c1＝[c01,uk]TAnd has:
Figure BDA00023889118300000310
Figure BDA00023889118300000311
wherein ,
Figure BDA00023889118300000312
is cos αk1Can then be derived
Figure BDA00023889118300000313
Estimation of (2):
Figure BDA0002388911830000041
in the same way, we can get from
Figure BDA0002388911830000042
To obtain
Figure BDA0002388911830000043
Thus DOA angle αkEstimation of (2):
Figure BDA0002388911830000044
has the advantages that: compared with the prior art, the invention has the beneficial effects that: 1. compared with the traditional DOA matrix method, the method provided by the invention completely utilizes the self-correlation information and the cross-correlation information of the array receiving signals; 2. compared with the traditional DOA matrix method, the method provided by the invention has better DOA estimation performance; 3. the method has lower complexity.
Drawings
FIG. 1 is a topological diagram of an array structure of the present invention;
FIG. 2 is a simulated scatter plot of the method of the present invention;
FIG. 3 is a graph comparing the angular RMSE performance of the method of the present invention and a spatially smoothed DOA matrix method under different SNR conditions;
FIG. 4 is a graph comparing the angle RMSE performance of the method of the present invention and a spatially smoothed DOA matrix method under different snapshot conditions;
FIG. 5 is a graph comparing the RMSE performance of the method of the present invention at different subarray numbers under different SNR conditions;
FIG. 6 is a graph of the comparison of the RMSE performance of the method of the present invention at different source numbers under different SNR conditions.
Detailed Description
The present invention is described in further detail below with reference to the attached drawing figures.
The symbols represent: used in the invention (·)TRepresentation matrix transposition, (.)HRepresenting the conjugate transpose of the matrix (.)*Representing the conjugate of the matrix, the capital letter X representing the matrix, the lower case letter X (-) representing the vector, IMAn identity matrix denoted as M × M,
Figure BDA0002388911830000045
representing the Hadamard product, diag (v) representing a diagonal matrix of elements in v, E [ ·]Indicating the expectation of the matrix, and angle (·) indicates the phase angle operation.
1. A double parallel array composed of two uniform linear arrays is constructed in a two-dimensional space, the double parallel array is respectively called an array 1 and an array 2, and the two double parallel arrays are divided into N overlapped sub-arrays in a sliding mode.
Each array having 2M sensors, two adjacent sensorsThe pitch in the X direction and the two sub-arrays are d. It is assumed that there are K coherent narrow-band co-carrier signals s in spacek(t) (K is more than or equal to 1 and less than or equal to K) is incident to the array, the wavelength of the signal is lambda, and the included angle between the signal and the x axis is αkβ from the y-axisk. As shown in fig. 1, the two arrays are divided in a sliding manner into N overlapping sub-arrays, each sub-array having M +1 array elements. The output of the nth forward sub-array defining array 1 is
Figure BDA0002388911830000051
wherein ,nx(t) is noise, xn(t) is the output of the nth array element of array 1, AM+1Direction matrix for (M +1) × K dimensions:
Figure BDA0002388911830000052
d is a rotation matrix between each subarray
Figure BDA0002388911830000053
Similarly, the output of the nth sub-array of array 2 is:
Figure BDA0002388911830000054
wherein ,ny(t) is noise, yn(t) is the output of the nth array element of array 2, D1Is a rotation matrix between arrays 1 and 2
Figure BDA0002388911830000055
2. A generalized DOA matrix is constructed by completely utilizing and averaging the autocorrelation matrix and the cross-correlation matrix of the received signals of each subarray; and decomposing the characteristics of the generalized DOA matrix to further obtain the DOA angle of the information source signal.
The autocorrelation matrix of the nth forward sub-array of array 1 is:
Figure BDA0002388911830000056
wherein ,RS＝E[s(t)sH(t)]Is a signal covariance matrix and I is an identity matrix. .
The cross-correlation matrix of the nth forward sub-array of array 2 and the nth forward sub-array of array 1 is:
Figure BDA0002388911830000061
similarly, the autocorrelation matrix of the nth forward sub-array of array 2 is:
Figure BDA0002388911830000062
the cross-correlation matrix of the nth forward sub-array of array 1 and the nth forward sub-array of array 2 is:
Figure BDA0002388911830000063
the forward spatially smoothed autocorrelation matrix defining array 1 is:
Figure BDA0002388911830000064
the spatially smoothed cross-correlation matrix defining array 2 and array 1 is:
Figure BDA0002388911830000065
similarly, the forward spatially smoothed autocorrelation matrix for array 2 is:
Figure BDA0002388911830000066
the spatially smoothed cross-correlation matrices for array 1 and array 2 are:
Figure BDA0002388911830000067
to RxxPerforming eigenvalue decomposition (EVD) to let ε1,…,εKIs a matrix RxxUnder the assumption of white noise, the noise variance σ can be obtained by averaging the M-K small eigenvalues2Is estimated. Then, by removing the influence of noise, it is possible to obtain:
Figure BDA0002388911830000068
the same can be obtained:
Figure BDA0002388911830000071
defining:
Figure BDA0002388911830000072
Figure BDA0002388911830000073
defining:
Figure BDA0002388911830000074
thus, it is possible to provide
Figure BDA0002388911830000075
Figure BDA0002388911830000076
According to the idea of the DOA matrix method, the following generalized DOA matrix can be defined:
Figure BDA0002388911830000077
wherein ,
Figure BDA0002388911830000078
if A isM+1 and RSFull rank, D1Without the same diagonal elements, the K non-zero eigenvalues of the DOA matrix R' are equal to D1K diagonal elements, and the eigenvectors corresponding to these values are equal to the corresponding signal direction vectors, i.e.
R′AE＝AED1
Definition uk＝cosαk and vk＝cosβk(K1, 2, …, K), the DOA matrix R' is subjected to eigen decomposition to obtain the matrix aM+1 and D1. According to D1Can obtain vkIs estimated value of
Figure BDA0002388911830000079
Further obtaining DOA angle βkEstimation of (2):
Figure BDA00023889118300000710
according to AEBy definition of (A), we classify it asM+1And
Figure BDA00023889118300000711
two parts, after feature decomposition, the estimation of the two parts is respectively
Figure BDA0002388911830000081
And
Figure BDA0002388911830000082
estimate out
Figure BDA0002388911830000083
And
Figure BDA0002388911830000084
then is provided with
Figure BDA0002388911830000085
A certain column ofkAnd carrying out DOA angle estimation on the direction matrix by utilizing the Vandermonde characteristics of the direction matrix. First opposite direction vector akNormalizing to make the first term 1. Taking angle (a)k) Estimating the phase difference between the arrays, and finally estimating the DOA angle by using a least square method. Because a isk＝[1,exp(j2πdcosαk/λ),…,exp(j2πMdcosαk/λ)]TThus can obtain
T＝angle(ak)
＝[0,2πdcosαk/λ,2Mπdcosαk/λ]T
Least squares fit to be Bc ═ T, where c1＝[c01,uk]TAnd has:
Figure BDA0002388911830000086
obtaining:
Figure BDA0002388911830000087
wherein ,
Figure BDA0002388911830000088
is cos αk1Can then be derived
Figure BDA0002388911830000089
Estimation of (2):
Figure BDA00023889118300000810
in the same way, we can get from
Figure BDA00023889118300000811
To obtain
Figure BDA00023889118300000812
Thus DOA angle αkEstimation of (2):
Figure BDA00023889118300000813
complexity analysis is carried out on the DOA angle estimation method, and the complexity of the obtained autocorrelation and cross-correlation matrix is O {4LM2L represents the number of received signal fast beats; computing
Figure BDA00023889118300000814
Has a complexity of O {5M }3}; computing
Figure BDA00023889118300000815
Has a complexity of O {4M }3}; the complexity of characteristic decomposition of R' is O {8M3}. The total complexity of the calculation algorithm is O {4LM2+17M3}。
The method of the invention completely utilizes the autocorrelation information and the cross-correlation information of the array received data to construct a generalized DOA matrix, and the traditional DOA matrix method does not completely utilize the autocorrelation information and the cross-correlation information of the array received data, so that the method of the invention has higher DOA angle estimation performance than the traditional DOA matrix method.
And (3) simulation results:
three narrow-band signals in the far field of space are assumed (α)1,β1)＝(50°,55°)，(α2,β2) Equal to (60 °,65 °) and (α)3,β3) Incident on the array of figure 1 at (70, 75) the signals are uncorrelated with each other. The DOA estimation performance is evaluated by 1000 Monte Carlo simulations, and the Root Mean Square Error (RMSE) expression is defined as follows
Figure BDA0002388911830000091
wherein
Figure BDA0002388911830000092
And
Figure BDA0002388911830000093
representing the parameter estimation results of the kth source at the nth Monte Carlo simulation αk and βkRepresenting the true value of the parameter for the kth source.
Fig. 2 shows a scatter distribution diagram of a generalized DOA matrix method of a dual parallel array, where simulation parameters are set to be the array element numbers 2M of the array 1 and the array 2 in the dual parallel array as 20, each array is divided into a sub-array number N as 10 smoothly, each sub-array element number is M +1 as 11, a snapshot number L as 500 and an SNR as 20dB smoothly. The two-dimensional DOA of the source is evident from the figure.
Fig. 3 shows the angle estimation performance of the dual parallel matrix conventional DOA matrix algorithm and the generalized DOA matrix algorithm as a function of the signal-to-noise ratio (SNR) under the same conditions and a comparison graph with the CRB performance. It can be seen that the generalized DOA matrix method has higher angle estimation performance.
Fig. 4 shows a performance graph of angle estimation performance of a dual-parallel-matrix conventional DOA matrix algorithm and a generalized DOA matrix algorithm with a snapshot under the same SNR, where the SNR is set to 20 dB. Therefore, the angle estimation performance of the generalized DOA matrix method is obviously superior to that of the traditional DOA matrix method along with the increase of the fast beat number.
Fig. 5 shows a graph of the angle estimation performance of the generalized DOA matrix method as the signal-to-noise ratio (SNR) varies when the number of sub-array elements varies under the same conditions. It can be seen that the angle estimation performance of the generalized DOA matrix method is obviously reduced with the increase of the number of the array elements of the subarray.
Fig. 6 shows a graph of the angle estimation performance of the generalized DOA matrix method as a function of the signal-to-noise ratio (SNR) under the same conditions, when the source number varies. It can be seen that as the number of sources increases, the angle estimation performance of the generalized DOA matrix method is obviously reduced.
The above embodiments are only for illustrating the technical idea of the present invention, and the protection scope of the present invention is not limited thereby, and any modifications made on the basis of the technical scheme according to the technical idea of the present invention fall within the protection scope of the present invention.

Claims (4)

1. A generalized DOA matrix method for coherent source direction finding, comprising the steps of:
(1) constructing a double parallel array composed of two uniform linear arrays on a two-dimensional space, wherein the double parallel array is respectively called an array 1 and an array 2, and dividing the two double parallel arrays into N overlapped sub-arrays in a sliding mode;
(2) a generalized DOA matrix is constructed by completely utilizing and averaging the autocorrelation matrix and the cross-correlation matrix of the received signals of each subarray;
(3) and decomposing the characteristics of the generalized DOA matrix to obtain the DOA angle of the information source signal.
2. A generalized DOA matrix method for coherent source direction finding according to claim 1, wherein said step (1) is implemented as follows:
each array has 2M sensors, the distance between two adjacent sensors along X direction and the distance between two sub-arrays are d, and there are K coherent narrow-band same-carrier signals s in spacek(t) (K is more than or equal to 1 and less than or equal to K) is incident to the array, the wavelength of the signal is lambda, and the included angle between the signal and the x axis is αkβ from the y-axiskEach subarray has M +1 array elements; the output of the nth forward sub-array of array 1 is:
Figure FDA0002388911820000011
wherein ,nx(t) is noise, xn(t) is the output of the nth array element of array 1, AM+1Direction matrix for (M +1) × K dimensions:
Figure FDA0002388911820000012
d is a rotation matrix among the sub-arrays:
Figure FDA0002388911820000013
the output of the nth sub-array of array 2 is:
Figure FDA0002388911820000014
wherein ,ny(t) is noise, yn(t) is the output of the nth array element of array 2, D1Is a rotation matrix between arrays 1 and 2:
Figure FDA0002388911820000015
3. the method of claim 1, wherein the generalized DOA matrix in step (2) is:
Figure FDA0002388911820000021
wherein ,
Figure FDA0002388911820000022
Figure FDA0002388911820000023
an autocorrelation matrix which is a subarray 1, wherein RS＝E[s(t)sH(t)]Is a signal covariance matrix, and I is an identity matrix;
Figure FDA0002388911820000024
an autocorrelation matrix which is subarray 2;
Figure FDA0002388911820000025
a cross-correlation matrix for subarrays 1 and 2;
Figure FDA0002388911820000026
a cross-correlation matrix for subarrays 2 and 1;
Figure FDA0002388911820000027
Figure FDA0002388911820000028
wherein ,σ2Is the noise variance.
4. A generalized DOA matrix method for coherent source direction finding according to claim 1, wherein said step (3) is implemented as follows:
R′AE＝AED1
wherein ,
Figure FDA0002388911820000029
definition uk＝cosαk and vk＝cosβkAnd performing characteristic decomposition on the DOA matrix R', and obtaining the following characteristic values according to the characteristic values:
Figure FDA0002388911820000031
according to AEDefinition of (A) by classifying it asM+1And
Figure FDA0002388911820000032
two parts, after feature decomposition, the estimation of the two parts is respectively
Figure FDA0002388911820000033
And
Figure FDA0002388911820000034
least squares fit to be Bc ═ T, where c1＝[c01,uk]TAnd has:
Figure FDA0002388911820000035
Figure FDA0002388911820000036
wherein ,
Figure FDA0002388911820000037
is cos αk1Can then be derived
Figure FDA0002388911820000038
Estimation of (2):
Figure FDA0002388911820000039
in the same way, we can get from
Figure FDA00023889118200000310
To obtain
Figure FDA00023889118200000311
Thus DOA angle αkEstimation of (2):
Figure FDA00023889118200000312
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