CN111337872B - Generalized DOA matrix method for coherent source direction finding - Google Patents
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- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
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Abstract
The invention discloses a generalized DOA matrix method for coherent source direction finding, which fully utilizes the autocorrelation information and the cross-correlation information of received data of a double parallel array, divides the double parallel array into a plurality of overlapped subarrays in a smooth mode, combines the autocorrelation information and the cross-correlation information of each subarray to derive respective autocorrelation matrixes and cross-correlation matrixes, and then carries out averaging operation, wherein each obtained correlation matrix 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, so that the DOA estimation performance is better, and the decorrelation can be well realized by adopting a space smoothing mode, so that the DOA of the signal can be effectively estimated; the DOA estimation angle automatic pairing method does not need space spectrum searching, has lower algorithm complexity, and can realize automatic pairing of the DOA estimation angles.
Description
Technical Field
The invention belongs to the field of array signal processing, and particularly relates to a generalized DOA matrix method for coherent source direction finding.
Background
Since the signal receiving array receives coherent signals in different directions, the coherent signals may cause rank impairment of the source covariance matrix, so that signal eigenvectors diverge into noise subspaces. The important content of the coherent signal DOA estimation is to consider what approach to restore the rank of the signal covariance matrix to be equal to the number of signal sources, starting from solving the rank deficiency of the matrix. Spatial smoothing techniques are an effective way to cope with coherent or strongly correlated signals. The basic idea is to divide an equidistant linear array into several overlapping sub-arrays. If the array manifolds of the subarrays are the same (this assumption applies to equidistant linear arrays), the subarray covariance matrices can be added to replace the original covariance matrix on average, so that decoherence is realized.
The generalized DOA matrix method provided by the invention has the advantages that polynomial search can be completely avoided and the operand is smaller while the traditional DOA matrix method is maintained, and simultaneously, the self-correlation 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 invention aims to: 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 discloses a generalized DOA matrix method for coherent source direction finding, which comprises the following steps:
(1) Constructing a double parallel array formed by two uniform linear arrays on a two-dimensional space, namely an array 1 and an array 2 respectively, and dividing the two double parallel arrays into N overlapped subarrays in a sliding mode;
(2) A generalized DOA matrix is constructed by fully 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 implementation process of the step (1) is as follows:
each array has 2M sensors, the distance between two adjacent sensors along X direction and the distance between two subarrays are d, and K coherent narrow-band same-carrier signals s are arranged in space k (t) (K is not less than 1) incident on the array, the wavelength of the signal is lambda, and the included angle between the signal and the x-axis is alpha k An included angle with the y-axis is beta k Each subarray has M+1 array elements; the output of the nth forward subarray of array 1 is:
wherein ,nx (t) is noise, x n (t) is the input of the nth element of array 1Go out, A M+1 A direction matrix of (m+1) ×k dimensions:
d is the rotation matrix between each subarray:
the output of the nth subarray of array 2 is:
wherein ,ny (t) is noise, y n (t) is the output of the nth element of array 2, D 1 For the rotation matrix between arrays 1 and 2:
further, the generalized DOA matrix in the step (2) is:
wherein ,
is an autocorrelation matrix of subarray 1, where R S ＝E[s(t)s H (t)]The signal covariance matrix is represented by I, which is a unit matrix;
is the autocorrelation matrix of subarray 2;
cross-correlation matrices for subarrays 1 and 2;
cross-correlation matrices for sub-arrays 2 and 1;
wherein ,σ2 Is the noise variance.
Further, the implementation process of the step (3) is as follows:
R′A E ＝A E D 1
wherein ,
definition u k ＝cosα k and vk ＝cosβ k Performing feature decomposition on the DOA matrix R', and obtaining according to the feature value:
according to A E Is divided into A M+1 Andtwo parts, after feature decomposition, the two parts are estimated as +.> and />
The least squares fit is bc=t, where c 1 ＝[c 01 ,u k ] T And has:
wherein ,namely cos alpha k1 Is then able to obtain +.>Is estimated by (a):
similarly, we can select fromObtain->Thus DOA angle alpha k Is estimated by (a):
the beneficial effects are 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 fully utilizes the autocorrelation information and the cross-correlation information of the array received 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 topology 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 of angular RMSE performance versus the method of the invention and the spatially smoothed DOA matrix method for different signal-to-noise ratios;
FIG. 4 is a graph of the angular RMSE performance of the method of the invention and the spatially smoothed DOA matrix method under different snapshot conditions;
FIG. 5 is a graph of the angular RMSE performance of the method of the invention at different subarrays under different signal to noise ratios;
fig. 6 is a graph showing the performance of the RMSE of the method of the present invention at different signal-to-noise ratios at different source numbers.
Detailed Description
The invention is described in further detail below with reference to the accompanying drawings.
The symbols represent: used in the present invention (& gt) T Representing a matrix transpose (.) H Representing the conjugate transpose of the matrix, (. Cndot.) * Representing matrix conjugation, capital letter X representing matrix, lowercase letter X (·) representing vector, I M Represented as an M x M identity matrix,representing Hadamard product, diag (v) representing a diagonal matrix of elements in v, E [. Cndot.]Indicating the desire for the matrix, angle (·) indicates the phase angle operation.
1. A double parallel array formed by two uniform linear arrays is constructed in a two-dimensional space and is respectively called an array 1 and an array 2, and the two double parallel arrays are divided into N overlapped subarrays in a sliding mode.
Each array has 2M sensors, and the distance between two adjacent sensors along the X direction and the distance between two subarrays are d. Let K coherent narrowband co-carrier signals s in space k (t) (1. Ltoreq.k. Ltoreq.K) incident on the array, believedThe number wavelength is lambda, and the included angle between the signal and the x axis is alpha k An included angle with the y-axis is beta k . As shown in fig. 1, two arrays are divided into N overlapping subarrays in a sliding manner, each subarray having m+1 array elements. Defining the output of the nth forward subarray of array 1 as
wherein ,nx (t) is noise, x n (t) is the output of the nth element of array 1, A M+1 A direction matrix of (m+1) ×k dimensions:
d is the rotation matrix between subarrays
Similarly, the output of the nth sub-array of array 2 is:
wherein ,ny (t) is noise, y n (t) is the output of the nth element of array 2, D 1 For a rotation matrix between arrays 1 and 2
2. A generalized DOA matrix is constructed by fully 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 obtain the DOA angle of the information source signal.
The autocorrelation matrix of the nth forward subarray of array 1 is:
wherein ,RS ＝E[s(t)s H (t)]The signal covariance matrix is represented by I, and the identity matrix is represented by I. .
The cross correlation matrix of the nth forward subarray of array 2 and the nth forward subarray of array 1 is:
similarly, the autocorrelation matrix of the nth forward subarray of array 2 is:
the cross correlation matrix of the nth forward subarray of array 1 and the nth forward subarray of array 2 is:
the forward spatially smoothed autocorrelation matrix of array 1 is defined as:
the spatially smoothed cross-correlation matrix defining array 2 and array 1 is:
similarly, the forward spatially smoothed autocorrelation matrix of array 2 is:
the spatially smoothed cross-correlation matrices for array 1 and array 2 are:
for R xx Performing eigenvalue decomposition (EVD) to make ε 1 ,…,ε K For matrix R xx Under the assumption of white noise, the noise variance sigma can be obtained from the average of M-K small eigenvalues 2 Is a function of the estimate of (2). Then, by removing the influence of noise, it is possible to obtain:
the same principle can be obtained:
definition:
definition:
thus (2)
According to the idea of the DOA matrix method, the following generalized DOA matrix can be defined:
wherein ,
if A M+1 and RS Full rank, D 1 Without the same diagonal elements, the K non-zero eigenvalues of DOA matrix R' are equal to D 1 In K diagonal elements, and the eigenvectors corresponding to these values are equal to the corresponding signal direction vectors, i.e
R′A E ＝A E D 1
Definition u k ＝cosα k and vk ＝cosβ k (k=1, 2, …, K) and performing feature decomposition on the DOA matrix R' to obtain a matrix a M+1 and D1 . According to D 1 The characteristic value of (2) can be obtained as v k Estimate of (2)Thereby obtaining DOA angle beta k Is estimated by (a):
according to A E We divide it into A M+1 Andtwo parts, after feature decomposition, the two parts are estimated as +.> and />
Estimated out and />After that, let in->Is a in a certain column k And estimating DOA angle of the direction matrix by utilizing Vandermonde characteristics of the direction matrix. First, the direction vector a k Normalizing to make the first term 1. Taking angle (a) k ) The phase difference between the arrays is estimated, and finally the DOA angle is estimated by using a least squares method. Because a k ＝[1,exp(j2πdcosα k /λ),…,exp(j2πMdcosα k /λ)] T Therefore, it can obtain
T＝angle(a k )
＝[0,2πdcosα k /λ,2Mπdcosα k /λ] T
The least squares fit is bc=t, where c 1 ＝[c 01 ,u k ] T And has:
the method comprises the following steps:
wherein ,namely cos alpha k1 Is then able to obtain +.>Is estimated by (a):
similarly, we can select fromObtain->Thus DOA angle alpha k Is estimated by (a):
complexity analysis is carried out on the DOA angle estimation method, and the complexity of the obtained autocorrelation and cross-correlation matrix is O {4LM 2 Where L represents the number of received signal beats; calculation ofIs of the complexity of O {5M 3 -a }; calculate->Is of the complexity of O {4M 3 -a }; the complexity of the feature decomposition of R' is O {8M ] 3 }. The total complexity of the calculated algorithm is O {4LM 2 +17M 3 }。
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, while the traditional DOA matrix method does not completely utilize the autocorrelation information and the cross-correlation information of the array received data, so the method of the invention has higher DOA angle estimation performance than the traditional DOA matrix method.
Simulation results:
assume that three narrowband signals (α) are spatially far-field 1 ,β 1 )＝(50°,55°)，(α 2 ,β 2 )＝(60°,65 DEG) and (alpha) 3 ,β 3 ) Incident on the array shown in fig. 1, the signals are uncorrelated with each other = (70 °,75 °). 1000 Monte Carlo simulations were used herein to evaluate DOA estimation performance, defining the Root Mean Square Error (RMSE) expression as follows
wherein and />Representing the parameter estimation result, alpha, of the kth information source in the nth Monte Carlo simulation k and βk Representing 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 double parallel array, where simulation parameters are set to 2m=20 array elements of array 1 and array 2 in the double parallel array, each array is divided smoothly into n=10 subarrays, each subarray element number is m+1=11, snapshot number l=500 and snr=20 dB. The two-dimensional DOA of the source is apparent from the figure.
Fig. 3 shows the angular estimation performance of a conventional and generalized DOA matrix algorithm for a double parallel array under the same conditions as a function of signal-to-noise ratio (SNR) and a graph comparing the performance with CRB. 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 conventional DOA matrix algorithm and a generalized DOA matrix algorithm of a double parallel array with a snap-shot change under the same signal-to-noise ratio condition, where the signal-to-noise ratio is set to snr=20 dB. It can be seen that the angle estimation performance of the generalized DOA matrix method is significantly better than that of the conventional DOA matrix method as the snapshot count increases.
Fig. 5 shows a graph of the angular estimation performance of the generalized DOA matrix method as a function of signal-to-noise ratio (SNR) under the same conditions as the number of sub-array elements varies. 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 subarray array elements.
Fig. 6 shows a graph of the angular estimation performance of the generalized DOA matrix method as a function of signal-to-noise ratio (SNR) under the same conditions as the number of sources varies. It can be seen that the angle estimation performance of the generalized DOA matrix method is significantly reduced with the increase of the number of sources.
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 thereto, and any modification made on the basis of the technical scheme according to the technical idea of the present invention falls within the protection scope of the present invention.
Claims (2)
1. The generalized DOA matrix method for coherent source direction finding is characterized by comprising the following steps:
(1) Constructing a double parallel array formed by two uniform linear arrays on a two-dimensional space, namely an array 1 and an array 2 respectively, and dividing the two double parallel arrays into N overlapped subarrays in a sliding mode;
(2) A generalized DOA matrix is constructed by fully utilizing and averaging the autocorrelation matrix and the cross correlation matrix of the received signals of each subarray;
(3) Decomposing the characteristics of the generalized DOA matrix to obtain the DOA angle of the information source signal;
the implementation process of the step (1) is as follows:
each array has 2M sensors, the distance between two adjacent sensors along X direction and the distance between two subarrays are d, and K coherent narrow-band same-carrier signals s are arranged in space k (t) (K is not less than 1) incident on the array, the wavelength of the signal is lambda, and the included angle between the signal and the x-axis is alpha k An included angle with the y-axis is beta k Each subarray has M+1 array elements; the output of the nth forward subarray of array 1 is:
wherein ,nx (t) is noise, x n (t) the nth element of array 1Output, A M+1 A direction matrix of (m+1) ×k dimensions:
d is the rotation matrix between each subarray:
the output of the nth subarray of array 2 is:
wherein ,ny (t) is noise, y n (t) is the output of the nth element of array 2, D 1 For the rotation matrix between arrays 1 and 2:
the implementation process of the step (2) is as follows:
the autocorrelation matrix of the nth forward subarray of array 1 is:
wherein ,RS ＝E[s(t)s H (t)]The signal covariance matrix is represented by I, which is a unit matrix;
the cross correlation matrix of the nth forward subarray of array 2 and the nth forward subarray of array 1 is:
similarly, the autocorrelation matrix of the nth forward subarray of array 2 is:
the cross correlation matrix of the nth forward subarray of array 1 and the nth forward subarray of array 2 is:
the forward spatially smoothed autocorrelation matrix of array 1 is defined as:
the spatially smoothed cross-correlation matrix defining array 2 and array 1 is:
similarly, the forward spatially smoothed autocorrelation matrix of array 2 is:
the spatially smoothed cross-correlation matrices for array 1 and array 2 are:
for R xx Decomposing the characteristic value to make epsilon 1 ,…,ε K For matrix R xx Under the assumption of white noise, the noise variance sigma is obtained from the average of (M-K) small eigenvalues 2 Is determined by the estimation of (a);by removing the influence of noise, we get:
the same principle can be obtained:
wherein ,σ2 Is the noise variance;
definition:
definition:
thus:
the following generalized DOA matrix is defined:
wherein ,
2. the generalized DOA matrix method for coherent source direction finding of claim 1, wherein said step (3) is implemented as follows:
R′A E ＝A E D 1
wherein ,
definition u k ＝cosα k and vk ＝cosβ k Performing feature decomposition on the DOA matrix R', and obtaining according to the feature value:
according to A E Is divided into A M+1 Andtwo parts, after feature decomposition, the two parts are estimated as +.> and />
Least squares fit to Bc 1＝T wherein c1 ＝[c 01 ,u k ] T And has:
wherein ,namely cos alpha k1 Estimate of (2) then get->Is estimated by (a):
similarly, fromObtain->Thus DOA angle alpha k Is estimated by (a):
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