CN116244561A - Linear array expansion method based on combined subarray covariance matrix - Google Patents
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Abstract
A linear array expansion method based on a combined subarray covariance matrix relates to the technical field of array signal processing, and aims at solving the problem that the azimuth estimation accuracy is low in the prior art. The method has better weak target detection capability and azimuth resolution on the basis of inhibiting grating lobes, and has higher azimuth estimation accuracy.
Description
Technical Field
The invention relates to the technical field of array signal processing, in particular to a linear array expansion method based on a combined subarray covariance matrix.
Background
Target detection and direction estimation are important branches in array signal processing, and are widely applied to the fields of sonar, radar, communication and the like. The beam forming method is one of the most classical target detection and azimuth estimation methods, and when the physical aperture of the array is small, the main lobe of the array beam is wide, the side lobe is high, and the practical application requirement is difficult to meet under the condition of low signal-to-noise ratio. The array expansion technology is an important approach for solving the problem, and the received signals of the virtual array elements are simulated by processing the received signals of the real array elements, so that the limitation of the physical aperture of the array is broken through, and the better azimuth resolution capability is obtained.
Aiming at the problem that the existing linear array expansion method has reduced weak target detection and azimuth estimation capability, an expansion method based on a parity subarray is provided, which divides the linear array into parity subarrays, utilizes subarray covariance matrix to reconstruct received data, and finally realizes target detection and azimuth estimation so as to improve the detection performance of weak targets. However, the array element spacing of the odd-even subarray is doubled compared with the original array, so that the half-wavelength relation between the processing frequency band and the array element spacing is not satisfied, grating lobes are easy to appear on the azimuth spectrum, the grating lobes of the strong target signals can cause serious interference to the detection of weak target signals incident from the grating lobe azimuth while the false alarm probability is increased, and the azimuth estimation accuracy is low.
Disclosure of Invention
The purpose of the invention is that: aiming at the problem of low azimuth estimation accuracy in the prior art, a linear array expansion method based on a combined subarray covariance matrix is provided.
The technical scheme adopted by the invention for solving the technical problems is as follows:
a linear array expansion method based on a combined subarray covariance matrix comprises the following steps:
step one: obtaining M real receiving array elements, wherein the array element spacing is uniform, the array element number M is an even number, the real receiving array elements are divided into odd array elements and even array elements, and then the odd array elements and the even array elements are utilized to respectively calculate the data cross covariance R of the odd array elements and the even array elements re Singular element autocovariance matrix R oo Even element autocovariance matrix R ee Expressed as:
wherein ,xi Representing the received signal vector for the i-th element,
representing a conjugate operation, i=1, 2, … M;
step two: m virtual receiving array elements are constructed, the original array is expanded into a 2M element uniform linear array, wherein 1 to M represent real array elements, M+1 to 2M represent virtual array elements, then the virtual array elements are divided into odd array elements and even array elements, and the parity array element data cross covariance R of the virtual array elements is obtained vi Expressed as:
step three: by Y C1 、Y C2 Respectively represent R re The matrix of the front M/2-1 column and the rear M/2-1 column is formed by Y C3 、Y C4 Respectively represent R vi A matrix of the first M/2-1 columns and the last M/2-1 columns, whereby the spread receive array signal is represented as
Step four: by Y A1 、Y A2 Respectively represent covariance matrix R oo The matrix of the front M/2-1 column and the rear M/2-1 column is formed by Y A3 、Y A4 Respectively represent covariance matrix R ee Taking the matrix formed by the conjugated front M/2-1 column and the conjugated rear M/2-1 column, the final extended array signal is expressed as:
step five: in Y C Adding Y to an extension signal A Expanding the signal to obtain an expanded signal Y AC That is to say, Y is adopted A2 And Y is equal to C1 ，Y C2 ，Y C3 ，Y C4 Constitute a new spread signal, spread signal Y AC Expressed as:
step six: acquiring an extension signal Y AC And beam forming is performed by using a minimum variance undistorted response beam forming method.
Further, the received signal vector x of the ith array element in the step one i Expressed as:
wherein ,sk Represents the kth narrowband signal vector, lambda k Represents the wavelength of the kth narrowband signal, n i Representing an additive white gaussian noise vector, θ, at the ith element k Represents the kth signal incident angle, K represents the incident source number, d represents the array element spacing, and j represents the imaginary part.
Further, the received signal vector of the virtual array element is expressed as:
wherein ,
indicating the phase difference between the received signals of the virtual array element and the real array element.
Further, the specific steps of the step six are as follows:
when the received signal is a wideband signal, performing Fourier transform on the wideband signal vector received by the ith array element to obtain frequency domain data x i (f) After which x is i (f) Evenly dividing the data into L narrow-band data, and acquiring an array received data vector X (f) of the first narrow-band l ) The array receives a data vector X (f l ) Expressed as:
X(f l )＝[x 1 (f l ),x 2 (f l ),···,x M (f l )] T
x (f) l ) After the first step to the fifth step, the obtained result is used for calculating a covariance matrix, namely R AC (f l ) According to R thereafter AC (f l ) And minimum variance undistorted response beamforming to obtain the target azimuth spectrum P (theta, f) of the narrow band l ) And obtaining the final total output P (theta) of the broadband MVDR beam forming according to the target azimuth spectrum of the narrow band.
Further, the target azimuth spectrum P (θ, f l ) Expressed as:
wherein ,[·]H Representing the conjugate transpose of the matrix, w l Corresponding to the spread signalThe weight of the array element.
Further, the weight w of the array element corresponding to the extension signal l Expressed as:
w l ＝[(a o ) T ，(a o b -1 ) T ，(a o b -2 ) T ，(a o b 2 ) T ，(a o ) T ] T
wherein b represents an intermediate parameter, a o Represents the steering vector, lambda of subarrays formed by odd array elements l Indicating the wavelength corresponding to the first narrowband signal.
Further, the odd array elements form a guide vector a of the subarray o Expressed as:
further, the total output P (θ) of the final wideband MVDR beamforming is expressed as:
further, M is 12.
Further, the array element distance d is 0.3m.
The beneficial effects of the invention are as follows:
the method solves the problem that the array element spacing does not meet the half-wavelength condition when only cross covariance is used for expanding signals, and effectively realizes array expansion and simultaneously suppresses grating lobes. The method has better weak target detection capability and azimuth resolution on the basis of inhibiting grating lobes, and has higher azimuth estimation accuracy.
Drawings
FIG. 1 is a graph of azimuthal spectrum contrast of the expansion algorithm of the present application;
fig. 2 is a graph of detection probability as a function of SNR;
fig. 3 is a graph of root mean square error as a function of SNR;
fig. 4 is a graph of azimuth resolution probability as a function of SNR;
fig. 5 is a graph of azimuth resolution probability as a function of angular interval.
Detailed Description
It should be noted in particular that, without conflict, the various embodiments disclosed herein may be combined with each other.
The first embodiment is as follows: referring to fig. 1, a specific description is given of a linear array expansion method based on a combined subarray covariance matrix according to the present embodiment, and the technical idea mainly includes 6 steps:
(1.1) obtaining array elements, dividing the array into odd array element subarrays and even array element subarrays, and calculating an even array element autocovariance matrix and a cross covariance matrix of an actual array element;
(1.2) constructing a parity array element cross covariance matrix of the virtual array element according to the mapping relation between the actual array element and the virtual array element;
(1.3) constructing a cross covariance extension signal according to rotation invariance of the linear array by using the cross covariance of the parity array elements of the actual array elements and the virtual array elements;
(1.4) constructing an autocovariance spread signal by using the odd-even array element autocovariance of the actual array element;
(1.5) combining the auto-covariance extension signal with the cross-covariance extension signal as final received data;
(1.6) mapping the azimuth spectrum of the spread signal using a minimum variance distortion free response (Minimum Variance Distortionless Response, MVDR) algorithm.
The core technical content of the method is that virtual subarray cross covariance data are built by utilizing array rotation invariance to realize array expansion, then subarray cross covariance and auto covariance are combined to reconstruct received data, the grating lobe problem caused by subarray spacing increase is avoided, and finally grating lobes are restrained while array expansion is effectively realized.
The main technical characteristics of the application include:
1. and calculating the covariance of the virtual parity array element data by utilizing the rotation invariance of the uniform linear array, and constructing an extension signal, thereby realizing array extension.
2. The auto-covariance extension signal is combined with the cross-covariance extension signal to solve the grating lobe problem when constructing an azimuth spectrum using only the cross-covariance extension signal.
The cross covariance and the auto covariance of the subarrays are combined to reconstruct the received data, so that the grating lobe problem caused by the increase of the subarray distance is avoided. Simulation experiments prove that the method can realize effective virtual expansion of the small-aperture array, and can realize the inhibition of grating lobes under the condition of not depending on additional prior information. By means of the method and the device, the accuracy of detection and azimuth estimation of the weak target can be effectively improved.
Calculating the parity array element covariance matrix of the actual array element
Setting M element uniform linear array, setting interval of array element as d, even number of array element M, making K (K < M) far-field narrow-band signals be incident on uniform linear array in the form of plane wave, making the signals uncorrelated, setting kth signal incident angle as theta k 。
Obtaining M real receiving array elements with uniform spacing
Let x i Received signal vector representing the i-th element:
wherein sk Lambda is the kth narrowband signal vector k Is the wavelength of the kth narrowband signal, n i Is the additive white gaussian noise vector on the ith element.
Dividing the real array elements into odd array elements and even array elements,
and respectively calculating parity array element data cross covariance R by using odd array elements and even array elements re Auto-covariance matrix of odd array elements and even array elements
Expressed as:
similarly, the odd and even element autocovariance matrices may be represented as R oo 、R ee ；
Calculating the parity array element covariance matrix R of the virtual array element vi
M virtual receiving array elements are constructed, and the original array is expanded into a 2M-element uniform linear array. Wherein 1 to M represent real array elements, m+1 to 2M represent constructed virtual array elements, and when the number of incident sources is k=1, for a virtual array element with a sequence number i, the received signal of the virtual array element with a sequence number i is 2m+1-i, multiplied by a corresponding phase difference, which is expressed as:
where θ is the angle of incidence of the signal and λ is the wavelength of the narrowband signal. For a system with fixed array element spacing and processing frequency, the phase difference between the received signals of the virtual array element and the real array element is only related to the array element serial number and the signal orientation, and is used herein
And (3) representing. The received signal for the virtual array element is expressed as:
the parity element data cross covariance of the virtual elements is expressed as:
wherein ,
representing a conjugate operation. Combining equations (2) and (5) shows that the virtual parity array element data cross covariance R vi Is true parity array element data cross covariance R re Is inverted and then conjugated.
Constructing cross covariance extension signals
By Y C1 、Y C2 Respectively represent covariance matrix R re Matrix of front M/2-1 columns and rear M/2-1 columns, Y C3 、Y C4 Representing covariance matrix R vi A matrix of the first M/2-1 columns and the last M/2-1 columns. The spread receive array signal is represented as
Such a spread signal constructed based on parity subarray cross covariance is referred to herein as a cross covariance spread signal Y C 。
Constructing an autocovariance spread signal
By Y A1 、Y A2 Representing covariance matrix R oo Matrix of front M/2-1 columns and rear M/2-1 columns, Y A3 、Y A4 Representing covariance matrix R ee And taking a matrix formed by the front M/2-1 column and the rear M/2-1 column after conjugation. The final spread array signal is expressed as:
such an extended signal constructed based on odd subarray autocovariance and even subarray autocovariance is referred to herein as an autocovariance extended signal Y A 。
Combining spread signals
In Y C Adding Y to an extension signal A Extension signal, in order to mitigate noise correlation between two kinds of extension signals, only at Y A Selecting one of the spread signals and Y C The method performance of the different combination modes is close to that of the combination of the spread signals.
For example, using Y A2 And Y is equal to C1 ，Y C2 ，Y C3 ，Y C4 A new spread signal is composed, expressed as:
drawing azimuth spectrum
When the received signal is a wideband signal, the wideband signal vector x received for the ith array element i Fourier transforming to obtain frequency domain data x i (f) Will x i (f) Evenly divided into L pieces of narrowband data, for the first narrowband, the array received data vector is expressed as:
then X (f) l ) The result obtained by the above steps is calculated covariance, namely R AC (f l )
The covariance matrix of the extended array receiving signals constructed by the method (9) is R AC (f l ) According to R AC (f l ) And minimum variance undistorted response (Minimum Variance Distortionless Response, MVDR) beamforming yields the narrowband target azimuth spectrum, expressed as:
w l ＝[(a o ) T ，(a o b -1 ) T ，(a o b -2 ) T ，(a o b 2 ) T ，(a o ) T ，] (11)
in the formula (14)
a o The steering vector of subarrays formed by odd array elements is expressed as
wherein λl Is the wavelength corresponding to the first narrowband signal.
And then according to the target azimuth spectrum of the narrow band, the final total output of the broadband MVDR beam forming is obtained as follows:
example:
a 12-element uniform linear array is adopted, and the array element spacing is 0.3m; the incident Signal is 2 kHz-3 kHz band-limited Noise, the incident azimuth is 60 degrees, the Signal-to-Noise Ratio (SNR) is set to be-10 dB, the Noise is isotropic zero-mean Gaussian Noise, and the signals are mutually independent from each other and from different array elements. The sampling rate of the sonar system is 8kHz, the noise frequency band is the same as the working frequency band, and the sonar system is uniformly divided into 20 narrow frequency bands for processing; the number of shots is 1024. After the array data is processed by unexpanded, even-odd subarray expansion and the application, the MVDR algorithm is used for carrying out azimuth estimation.
The azimuth spectrum is first analyzed as shown in fig. 1. It can be seen that the azimuth spectrum of the odd-even sub-array expansion algorithm has obvious grating lobes, and serious negative effects are caused on the correct detection of targets in the grating lobe range. Whereas in the azimuth spectrum of the present application grating lobes are almost completely suppressed. Compared with an unexpanded array, the spectrum peak of the method is obviously narrowed, and the side lobe is reduced by about 8 dB. Because of a certain noise correlation between the introduced auto-covariance extension signal and the cross-covariance extension signal, the sidelobe is about 4dB higher than the dipole array extension algorithm.
In terms of detection probability, as shown in fig. 2, the performance of the application is inferior to that of a parity subarray expansion algorithm due to the influence of noise correlation, but is superior to that of an unexpanded array;
in terms of azimuth estimation accuracy, as shown in fig. 3, the present application is superior to the parity-subarray expansion algorithm, approaching the error of an unexpanded array.
In terms of azimuth resolution probability, as shown in fig. 4 and 5, the present application has higher azimuth resolution than an unexpanded array, but is also weaker than the parity subarray expansion algorithm.
It should be noted that the detailed description is merely for explaining and describing the technical solution of the present invention, and the scope of protection of the claims should not be limited thereto. All changes which come within the meaning and range of equivalency of the claims and the specification are to be embraced within their scope.
Claims (10)
1. A linear array expansion method based on a combined subarray covariance matrix is characterized by comprising the following steps of:
step one: obtaining M real receiving array elements, wherein the array element spacing is uniform, the array element number M is an even number, the real receiving array elements are divided into odd array elements and even array elements, and then the odd array elements and the even array elements are utilized to respectively calculate the data cross covariance R of the odd array elements and the even array elements re Singular element autocovariance matrix R oo Even element autocovariance matrix R ee Expressed as:
wherein ,xi Representing the received signal vector for the i-th element,
representing a conjugate operation, i=1, 2, … M;
step two: m virtual receiving array elements are constructed, the original array is expanded into a 2M element uniform linear array, wherein 1 to M represent real array elements, M+1 to 2M represent virtual array elements, then the virtual array elements are divided into odd array elements and even array elements, and the parity array element data cross covariance R of the virtual array elements is obtained vi Expressed as:
step three: by Y C1 、Y C2 Respectively represent R re The matrix of the front M/2-1 column and the rear M/2-1 column is formed by Y C3 、Y C4 Respectively represent R vi A matrix of the first M/2-1 columns and the last M/2-1 columns, whereby the spread receive array signal is represented as
Step four: by Y A1 、Y A2 Respectively represent covariance matrix R oo The matrix of the front M/2-1 column and the rear M/2-1 column is formed by Y A3 、Y A4 Respectively represent covariance matrix R ee Taking the matrix formed by the conjugated front M/2-1 column and the conjugated rear M/2-1 column, the final extended array signal is expressed as:
step five: in Y C Adding Y to an extension signal A Expanding the signal to obtain an expanded signal Y AC That is to say, Y is adopted A2 And Y is equal to C1 ，Y C2 ，Y C3 ，Y C4 Constitute a new spread signal, spread signal Y AC Expressed as:
step six: acquiring an extension signal Y AC And beam forming is performed by using a minimum variance undistorted response beam forming method.
2. The linear array expansion method based on combined subarray covariance matrix according to claim 1, wherein said step one is characterized in that the received signal vector x of the ith array element i Expressed as:
wherein ,sk Represents the kth narrowband signal vector, lambda k Represents the wavelength of the kth narrowband signal, n i Representing an additive white gaussian noise vector, θ, at the ith element k Represents the kth signal incident angle, K represents the incident source number, d represents the array element spacing, and j represents the imaginary part.
3. The linear array expansion method based on combined subarray covariance matrix according to claim 2, wherein the received signal vector of the virtual array element is expressed as:
wherein ,
indicating the phase difference between the received signals of the virtual array element and the real array element.
4. The linear array expansion method based on the combined subarray covariance matrix according to claim 1, wherein the specific steps of the step six are as follows:
when the received signal is a wideband signal, performing Fourier transform on the wideband signal vector received by the ith array element to obtain frequency domain data x i (f) After which x is i (f) Evenly dividing the data into L narrow-band data, and acquiring an array received data vector X (f) of the first narrow-band l ) The array receives a data vector X (f l ) Expressed as:
X(f l )＝[x 1 (f l ),x 2 (f l ),···,x M (f l )] T
x (f) l ) After the first step to the fifth step, the obtained result is used for calculating a covariance matrix, namely R AC (f l ) According to R thereafter AC (f l ) And minimum variance undistorted response beamforming to obtain the target azimuth spectrum P (theta, f) of the narrow band l ) And obtaining the final total output P (theta) of the broadband MVDR beam forming according to the target azimuth spectrum of the narrow band.
5. The linear array expansion method based on combined subarray covariance matrix according to claim 4, wherein the target azimuth spectrum P (θ, f) l ) Expressed as:
wherein ,[·]H Representing the conjugate transpose of the matrix, w l The weight of the array element corresponding to the extension signal.
6. The linear array expansion method based on combined subarray covariance matrix according to claim 5, wherein the weight w of the array element corresponding to the expansion signal l Expressed as:
w l ＝[(a o ) T ，(a o b -1 ) T ，(a o b -2 ) T ，(a o b 2 ) T ，(a o ) T ] T
wherein b represents an intermediate parameter, a o Represents the steering vector, lambda of subarrays formed by odd array elements l Indicating the wavelength corresponding to the first narrowband signal.
7. The linear array expansion method based on combined subarray covariance matrix as claimed in claim 6, wherein said odd array elements constitute subarrays of steering vector a o Expressed as:
8. the linear array expansion method based on combined subarray covariance matrix according to claim 5, wherein the final wideband MVDR beamforming total output P (θ) is expressed as:
9. a linear array expansion method based on combined subarray covariance matrix according to claim 1, wherein M is 12.
10. The linear array expansion method based on combined subarray covariance matrix according to claim 1, wherein the array element distance d is 0.3m.
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| 梁国龙 等: "一种基于组合子阵协方差矩阵的阵列扩展方法", 兵工学报, pages 1 - 4 * |
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