CN111368256B - Single snapshot direction finding method based on uniform circular array - Google Patents

Single snapshot direction finding method based on uniform circular array Download PDF

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CN111368256B
CN111368256B CN202010209642.8A CN202010209642A CN111368256B CN 111368256 B CN111368256 B CN 111368256B CN 202010209642 A CN202010209642 A CN 202010209642A CN 111368256 B CN111368256 B CN 111368256B
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熊钊
彭晓燕
魏逸凡
李万春
魏平
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University of Electronic Science and Technology of China
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Abstract

The invention belongs to the technical field of electronic countermeasure, and particularly relates to a single snapshot direction finding method based on a uniform circular array. According to the invention, for the array receiving data of the uniform circular array, the data is converted into the receiving data of the virtual linear array through mode space conversion, so that the array flow pattern has a Vandemonde form. And then constructing a pseudo covariance matrix to enable the pseudo covariance matrix for subsequent processing to reach a full rank, so that subsequent eigen decomposition can correctly divide a signal subspace and a noise subspace. The method firstly converts the array flow pattern of the uniform circular array into a virtual linear array, then constructs a pseudo covariance matrix, and finally carries out the MUSIC algorithm. The method has the advantages that the method can use uniform circular arrays to carry out single snapshot direction finding, and is simple and good in effect.

Description

Single snapshot direction finding method based on uniform circular array
Technical Field
The invention belongs to the technical field of electronic countermeasure, and relates to a single snapshot direction finding method based on a uniform circular array.
Background
Angle of arrival (DOA) estimation is one of the main problems to be studied in array signal processing, and DOA estimation has wide application in the fields of radio communication, electronic reconnaissance and the like. And single snapshot DOA estimation, namely, only the data of a single snapshot is processed, so that the estimation of the direction of arrival of the input signal is realized. At present, with the continuous improvement of DOA estimation on the real-time requirement, the algorithm operation amount is reduced by reducing the sampling fast beat number, the system real-time is improved, and the DOA estimation method becomes a hot spot of research in the DOA estimation field in recent years.
Among the single-snapshot direction finding algorithms, the most widely applied is the study based on the pseudo covariance matrix and spatial smoothing. The array under a certain rule is divided into a plurality of sub-arrays by a space smoothing method, each sub-array has the same rule, and an array covariance matrix corresponding to each sub-array is obtained. The new covariance matrix is constructed by processing the data to replace the whole matrix which is not divided into sub-matrices. The other method is a pseudo covariance matrix method, which converts a covariance matrix into a pseudo covariance matrix by processing received data under the condition of single snapshot, thereby increasing useful information quantity, enabling the rank of the matrix to reach the signal source number, and further applying the classical direction finding algorithm to the condition of single snapshot with the limit of fast snapshot number. However, both methods can only process matrices in the form of vandermonde, and when using uniform circular arrays, single snapshot direction finding cannot be performed directly.
Disclosure of Invention
Aiming at the problems, the invention provides a uniform circular array single snapshot direction finding method based on a pseudo covariance matrix.
The technical scheme adopted by the invention is as follows:
and for the received single snapshot data, converting the array flow pattern of the circular array into a virtual linear array by using mode space conversion, wherein the processed data is equivalent to the array flow pattern of the virtual linear array multiplied by a signal. The array flow pattern now has the vandenonde form. And constructing a pseudo covariance matrix by taking the processed data. The matrix is subjected to eigenvalue decomposition, a guide vector of a signal subspace is orthogonal to a noise subspace under an ideal condition, the product is very small under an actual condition, a spectral peak search is carried out on an azimuth angle from 0 degree to 360 degrees, and an angle corresponding to a maximum value point is a signal incidence direction.
Consider a uniform circular array of discrete fourier transforms that receive data. Suppose N farField signal source (theta) 1 ,…,θ N ) Is incident on a uniform circular array of M array elements, the circular array elements are isotropic, and the received data matrix is x = As + n (1)
Where n is the noise matrix.
If each signal only receives a single snapshot, the snapshot data on the array element l is:
Figure BDA0002422378270000021
wherein the content of the first and second substances,
Figure BDA0002422378270000022
θ i is the azimuth angle, s, of the i-th signal incidence i Is the ith signal.
The steering vector of the circular array is
Figure BDA0002422378270000023
Spatial DFT of array snapshot data
Figure BDA0002422378270000024
Figure BDA0002422378270000025
In J, J k (. Beta.) denotes the K-th order Bessel function of the first kind, K being the element of K, -K +1, \ 8230A, K-1, K, the definition of the Bessel function being:
Figure BDA0002422378270000026
when the number of the array elements is uniform
Figure BDA0002422378270000027
When there is J kM-q (-β)0, so the above equation can be simplified to
Figure BDA0002422378270000031
Wherein the content of the first and second substances,
Figure BDA0002422378270000032
if u ordered q ＝v -q Then the above equation can be written in the form of a matrix as follows:
Figure BDA0002422378270000033
writing the above equation in matrix form:
Figure BDA0002422378270000034
namely:
Figure BDA0002422378270000035
Figure BDA0002422378270000036
the re-exploration space DFT itself has
Figure BDA0002422378270000037
The above formula is abbreviated as
u＝F H x (12)
Namely that
Figure BDA0002422378270000041
Is provided with
F H F＝MI (14)
F is an orthogonal matrix.
By
Figure BDA0002422378270000042
Figure BDA0002422378270000043
Obtaining a pre-processing matrix
Figure BDA0002422378270000044
Carrying out mode space transformation on single snapshot data x obtained by us from a uniform circular array through a matrix:
Figure BDA0002422378270000045
after transformation, the uniform circular array becomes a virtual linear array, and the number of array elements is M' =2K +1,
Figure BDA0002422378270000046
data from the K +1 th line to the 2K +1 th line of y, namely data from the K +1 st array element to the 2K +1 st array element of the virtual linear array, are
Figure BDA0002422378270000051
Wherein y is k Is the data on the k-th row of the matrix y, i.e. the k-th array element of the virtual line array.
Figure BDA0002422378270000052
n z Line K +1 to line 2K +1 of Tn. It can be seen that the component of the k-th array element of the steering vector corresponding to signal iComprises the following steps:
b k (θ i )＝exp(j(k-1)θ i ) (19)
constructing a pseudo covariance matrix with z as follows:
Figure BDA0002422378270000053
wherein z is k Is the kth data of matrix z. Is provided with
Figure BDA0002422378270000054
In the formula n k Is a noise matrix n z The kth element of (1).
R can be written as
R＝BDB H +N r (22)
Wherein the content of the first and second substances,
Figure BDA0002422378270000061
Figure BDA0002422378270000062
it is clear that the rank of D is the number of incident signals N, and that B is a Van der Monde matrix, so B and BDB H The rank of R is N, so that the rank of R is N, and the subsequent characteristic decomposition can separate N large characteristic values and M-N small characteristic values, namely, the signal subspace and the noise subspace can be decomposed correctly.
In order to further improve the algorithm performance, the conjugate information of the data output by the array is fully utilized, and the following matrix is constructed on the basis of the formula (22):
R'＝[R,QR * Q] (25)
in the formula, Q is an inverse-diagonal matrix, i.e., elements on the inverse-diagonal are all 1, and other elements are 0.
Originally, (K + 1) x (K + 1) -dimensional pseudo-covariance matrix is expanded to (K + 1) x 2 (K + 1) -dimensional pseudo-covariance matrix, the effect of increasing effective information is achieved, and the direction finding precision of the algorithm is further improved.
The new matrix in equation (25) that has been combined with the conjugate enhancement method is then second order accumulated:
Figure BDA0002422378270000063
for the pseudo covariance matrix R obtained above ISS Performing characteristic decomposition:
Figure BDA0002422378270000064
obtaining a signal subspace U S Sum noise subspace U N . Steering vector b of signal subspace after mode space conversion under ideal conditions H (theta) and noise subspace U N Orthogonal:
b H (θ)U N ＝0 (28)
and in practice b H (theta) and U N Are not completely orthogonal. The azimuth angle θ can be obtained from a 1 degree to 360 degree search by a minimum optimization search:
Figure BDA0002422378270000071
the spectral estimation formula is:
Figure BDA0002422378270000072
the method has the advantages that the method can use uniform circular arrays to carry out single snapshot direction finding, and is simple and good in effect.
Drawings
FIG. 1 is a model of a circular array received signal, the invention is based on pitch angle
Figure BDA0002422378270000073
In the case of 90 deg..
FIG. 2 is a flow chart of a uniform circular array single snap array direction-finding algorithm based on the ISS-MUISC method.
FIG. 3 is a plot of spectral estimation using the method of the present invention for direction finding.
Fig. 4 shows the positioning error for different signal-to-noise ratios.
Detailed Description
The present invention is described in detail below with reference to examples:
examples
In this embodiment, matlab is used to verify the single snapshot array direction finding algorithm scheme based on the uniform circular array, and for simplification, the following assumptions are made for the algorithm model:
1. all engineering errors are superposed into equivalent noise;
2. assuming the target is stationary;
step 1, 4 targets are set at azimuth angles (100 degrees, 150 degrees, 200 degrees and 250 degrees). The target is measured using a uniform circular array of 24 elements. The radius of the circular array r =1.5 λ. Assuming that the noise of the observation station follows Gaussian distribution with the mean value of zero;
step 2, obtaining received array signal data, wherein each array element only receives one snapshot;
step 3, calculating beta according to the radius-wavelength ratio of the circular array, thereby obtaining K;
step 4, constructing matrixes F and J according to K and the above formula (13) and formula (9), and obtaining a pretreatment matrix T according to formula (12);
step 5, preprocessing the received signal x, wherein y = Tx;
step 6, taking the K +1 th row to the 2K +1 th row of y to obtain a matrix z;
and 7, constructing a matrix R by the formula (20), and obtaining the matrix R by the formula (25) and the formula (26) ISS ；
Step 8, for R ISS Performing characteristic decomposition to obtain a signal subspace U S Sum noise subspace U N ；
And 9, according to the formula (30), performing minimum optimization search on the azimuth angle theta from 1 degree to 360 degrees to obtain an accurate positioning result of the target.
The ISS-MUSIC method-based uniform circular array single snapshot direction finding algorithm has the following effects:
as shown in fig. 3, a spectrum peak diagram of the target appearing in the observation area can be seen, and the position of the spectrum peak is the positioning result of the target. Fig. 4 shows the trend of the positioning error with the signal-to-noise ratio.

Claims (1)

1. A single snapshot direction finding method based on a uniform circular array is characterized by comprising the following steps:
s1, receiving data by adopting a uniform circular array, and N far-field signal sources (theta) 1 ,…,θ N ) The signal is incident on a uniform circular array of M array elements, the circular array elements are isotropic, and single snapshot data received by the array are
x＝As+n
Where A is the array pattern of the uniform circular array, and s is the signal vector composed of the N signals, i.e., s = [ s ] 1 ,s 2 ,…s N ] T And n is a noise data,
Figure FDA0002422378260000011
if each signal only receives a single snapshot, the snapshot data on the array element l is:
Figure FDA0002422378260000012
wherein the content of the first and second substances,
Figure FDA0002422378260000013
λ is the wavelength, r is the radius of the circular array, n l Is the i-th element, θ, of the noise data n i Is the azimuth angle, s, of the i-th signal incidence i Is the ith signal;
the steering vector of the circular array is
Figure FDA0002422378260000014
S2, performing mode space transformation on the received data matrix to construct a mode space transformation matrix
Figure FDA0002422378260000015
Wherein
Figure FDA0002422378260000016
Figure FDA0002422378260000021
In J, J k (. Beta.) represents K-order Bessel function of the first kind, K is the maximum phase mode number excited by the uniform circular array, K is the-K, -K +1, \ 8230and K-1, K and K
Figure FDA0002422378260000022
r is the radius of the circular array;
s3, preprocessing single snapshot data x obtained from the uniform circular array:
Figure FDA0002422378260000023
wherein
Figure FDA0002422378260000024
After the mode space is transformed, the array flow pattern of the virtual linear array is as follows:
Figure FDA0002422378260000025
after transformation, the uniform circular array becomes a virtual linear array, and the number of array elements is M' =2K +1,
Figure FDA0002422378260000026
s4, data from the K +1 th line to the 2K +1 th line of y, namely data from the K +1 st array element to the 2K +1 st array element of the virtual linear array, are
Figure FDA0002422378260000027
Wherein y is k Is the k-th row of the matrix y, namely the data on the k-th array element of the virtual line array,
Figure FDA0002422378260000031
b is an array flow pattern formed by K array elements to 2K +1 array elements of the virtual line array, n z Taking the line K +1 to the line 2K +1 for Tn, the component of the kth array element of the steering vector corresponding to the signal i is:
b k (θ i )＝exp(j(k-1)θ i )
s5, constructing a pseudo covariance matrix by using z as follows:
Figure FDA0002422378260000032
wherein z is k Is the kth data of matrix z:
Figure FDA0002422378260000033
in the formula n k Is a noise matrix n z The kth element of (1);
write R as
R＝BDB H +N r
Wherein the content of the first and second substances,
Figure FDA0002422378260000034
Figure FDA0002422378260000041
the rank of D is the number of incident signals N, and B is a Van der Monde matrix, so B and BDB H Are all N, thus the rank of R is N;
s6, constructing the following matrix on the basis of the matrix R:
R'＝[R,QR * Q]
in the formula, Q is an anti-diagonal matrix, namely elements on anti-diagonal lines are all 1, and other elements are 0;
and then carrying out second-order accumulation on the matrix R':
Figure FDA0002422378260000042
obtaining a pseudo covariance matrix R ISS ；
S7, carrying out pair on the obtained pseudo covariance matrix R ISS Performing characteristic decomposition:
Figure FDA0002422378260000043
obtaining a signal subspace U S Sum noise subspace U N ；
S8, searching from 1 degree to 360 degrees by the minimum optimization search to obtain an azimuth angle theta:
Figure FDA0002422378260000044
wherein B (theta) is a guide vector corresponding to the array flow pattern B, namely:
Figure FDA0002422378260000051
the spectral estimation formula is:
Figure FDA0002422378260000052
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