CN114047481A - Robust adaptive beam forming method based on subspace orthogonality - Google Patents

Robust adaptive beam forming method based on subspace orthogonality Download PDF

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CN114047481A
CN114047481A CN202111317676.XA CN202111317676A CN114047481A CN 114047481 A CN114047481 A CN 114047481A CN 202111317676 A CN202111317676 A CN 202111317676A CN 114047481 A CN114047481 A CN 114047481A
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叶中付
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University of Science and Technology of China USTC
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Abstract

The invention relates to a method for forming a steady self-adaptive wave beam based on subspace orthogonality, which comprises the steps of firstly estimating the direction of arrival of signals and interference, and generating initial values of all guide vectors; secondly, correcting the expected signal guide vector to estimate a more accurate expected signal guide vector; thirdly, correcting the interference guide vector to estimate a more accurate interference guide vector; fourthly, estimating the noise power by using the average value of the characteristic values corresponding to the noise subspace; fifthly, estimating each interference power together with the signal subspace and the eigenvalue matrix thereof; sixthly, reconstructing an interference and noise covariance matrix; and seventhly, calculating an optimal weight vector to form robust adaptive beam output for the array received data. The method can obtain more accurate interference and noise covariance matrix and the guide vector of the expected signal, the optimal weight vector is more accurate, and the robustness of the adaptive beam former is improved.

Description

Robust adaptive beam forming method based on subspace orthogonality
Technical Field
The invention relates to the field of beam forming research in the field of array signal processing, in particular to a method for improving the robustness of adaptive beam forming better by more accurately reconstructing an expected signal steering vector and an interference and noise covariance matrix under the non-ideal condition that various errors possibly exist.
Background
Among the conventional robust adaptive beamforming methods, the following methods are representative: a linear constrained minimum variance method, a diagonal loading method, a feature subspace method, and an indeterminate set method. However, considering the uncertainty of parameter selection and the constraint of inherent property of the method, the performance of these beamforming methods is significantly attenuated in the presence of array errors, and thus the ideal effect cannot be obtained.
In recent years, an adaptive beamforming method based on interference plus noise covariance matrix reconstruction is researched, and the method is more robust. The method mainly utilizes the Capon space power spectrum, and takes the integral of the Capon space power spectrum in an undesired signal angle area as an estimated value of an interference plus noise covariance matrix, thereby effectively removing the desired signal components. However, the reconstruction method only directly uses the Capon space power spectrum to integrate the angle variable in the angle region of the undesired signal, and finally, the reconstructed interference plus noise covariance matrix is not accurate enough, so that the method only has certain robustness on the arrival direction error, and when other types of steering vector errors exist, the performance of the method cannot be guaranteed. Subsequently, an interference plus noise covariance matrix reconstruction method for any type of array error is proposed. A robust adaptive beamforming method (ZL 201711417222.3) improves the reconstruction accuracy of an interference-plus-noise covariance matrix, and a multiple robust adaptive beamforming method (ZL 202010360284.0) further obtains a more accurate interference-plus-noise covariance matrix and a steering vector of a desired signal by introducing a plurality of robust technologies, thereby improving the robustness of an adaptive beamformer. However, most methods perform interference plus noise covariance matrix reconstruction based on the Capon space power spectrum, which is limited by Capon space power spectrum estimation methods, and a certain error still exists in the reconstruction process.
In view of the above analysis, it is necessary to research a new robust method to improve the robustness of the beamformer.
Disclosure of Invention
The technical problem of the invention is solved: the method overcomes the defects of the prior art, fully utilizes the orthogonality of the signal subspace and the noise subspace and the information contained in the corresponding characteristic value matrix, provides a steady self-adaptive beam forming method based on the subspace orthogonality, and greatly improves the robustness of the beam forming device to any type of array errors through more accurate reconstruction of an expected signal steering vector and an interference and noise covariance matrix.
The purpose of the invention is realized by the following technical scheme:
the invention relates to a method for forming a steady self-adaptive wave beam based on subspace orthogonality, which firstly preprocesses array received data and comprises the following steps: and estimating an array covariance matrix, and performing characteristic decomposition on the matrix to obtain a signal subspace and a noise subspace and characteristic value matrixes corresponding to the signal subspace and the noise subspace. The method comprises the following steps:
step 1, based on a noise subspace obtained by preprocessing, using a nominal steering vector in a multiple signal classification method, estimating the arrival direction of signals and interference, and generating initial values of the steering vectors;
step 2, correcting the expected signal guide vector by utilizing the orthogonal property of the signal subspace and the noise subspace, and estimating a more accurate expected signal guide vector;
step 3, correcting the interference guide vector by utilizing the orthogonal property of the signal subspace and the noise subspace, and estimating a more accurate interference guide vector;
step 4, estimating the noise power by using the average value of the characteristic values corresponding to the noise subspace;
step 5, estimating each interference power by using the estimated more accurate steering vector of each interference together with the signal subspace and the eigenvalue matrix thereof;
step 6, reconstructing a noise covariance matrix according to the estimated noise power, reconstructing an interference covariance matrix according to the estimated more accurate guide vectors and power of each interference, and reconstructing an interference-plus-noise covariance matrix;
and 7, calculating an optimal weight vector according to the reconstructed interference and noise covariance matrix and the more accurate expected signal guide vector, and forming stable self-adaptive beam output for array received data.
Further, the above robust adaptive beamforming method based on subspace orthogonality first preprocesses M-ary array received data, including: estimating the covariance matrix of the array
Figure BDA0003344131200000021
The characteristic decomposition is carried out on the matrix,
Figure BDA0003344131200000022
Esand ΛsRespectively, a diagonal matrix of signal (including interference) subspaces and their corresponding eigenvalues, EnAnd ΛnRespectively, a diagonal matrix of noise subspaces and their corresponding eigenvalues, EsAnd EnAre orthogonal. Subscripts s and n are symbols for distinguishing signals and noise, respectively, and superscript H is a conjugate transpose operator of the matrix.
The step 1 comprises the following steps:
step 11, generating a nominal guide vector with a corresponding direction angle theta according to the array structure
Figure BDA0003344131200000023
|| ||2Is a vector l2A norm operator;
step 12, noise subspace E obtained based on preprocessingnTo guide a vector
Figure BDA0003344131200000024
For the multiple signal classification Method (MUSIC), the MUSIC spatial spectrum is calculated as follows:
Figure BDA0003344131200000031
estimating the direction of arrival of the desired signal
Figure BDA0003344131200000032
Number of interferers L (M > L +1) and direction of arrival of all interferers
Figure BDA0003344131200000033
Generating initial value of guide vector of expected signal according to array structure
Figure BDA0003344131200000034
Initial value of each interference steering vector
Figure BDA0003344131200000035
The step 2 comprises the following steps:
step 21, giving a steering vector perpendicular to the desired signal
Figure BDA0003344131200000036
Micro neighborhoods on a plane, including a two-dimensional rectangular neighborhood, a square neighborhood, an elliptical neighborhood, a circular neighborhood, a cross neighborhood, a one-dimensional neighborhood,
Figure BDA0003344131200000037
is the center of the neighborhood, and discretizes the neighborhood into R points, the steering vector of the R-th point is
Figure BDA0003344131200000038
Figure BDA0003344131200000039
As a guide vector
Figure BDA00033441312000000310
An error vector introduced at the r-th point; the micro neighborhood means
Figure BDA00033441312000000311
Step 22, initial value of guide vector for expected signal
Figure BDA00033441312000000312
According to its steering vector
Figure BDA00033441312000000313
The MUSIC spatial spectrum is calculated as follows:
Figure BDA00033441312000000314
by the orthogonal nature of the signal subspace and the noise subspace, the number of R ions in a small neighborhoodScattered point internal search
Figure BDA00033441312000000315
Finally, the modified steering vector of the desired signal is obtained as:
Figure BDA00033441312000000316
if multiple maximum values appear, the vector is averaged and still recorded as
Figure BDA00033441312000000317
The step 3 comprises the following steps:
step 31, initial values of steering vectors perpendicular to each interference are given
Figure BDA00033441312000000318
Micro neighborhoods on a plane, including a two-dimensional rectangular neighborhood, a square neighborhood, an elliptical neighborhood, a circular neighborhood, a cross neighborhood, a one-dimensional neighborhood,
Figure BDA00033441312000000319
is the center of the neighborhood, and discretizes the neighborhood into R points, the steering vector of the R-th point is
Figure BDA00033441312000000320
Figure BDA0003344131200000041
As a guide vector
Figure BDA0003344131200000042
An error vector introduced at the r-th point; the micro neighborhood means
Figure BDA0003344131200000043
Step 32, steering vectors for each disturbance
Figure BDA0003344131200000044
According to its steering vector
Figure BDA0003344131200000045
The MUSIC spatial spectrum is calculated as follows:
Figure BDA0003344131200000046
by utilizing the orthogonal property of the signal subspace and the noise subspace, the method searches in R discrete points of a small neighborhood
Figure BDA0003344131200000047
Finally, the guiding vector of the corrected interference is obtained, and is:
Figure BDA0003344131200000048
if multiple maximum values appear, the vector is averaged and still recorded as
Figure BDA0003344131200000049
The step 4 comprises the following steps:
eigenvalue matrix Lambda corresponding with noise subspacenTaking the average value of the diagonal elements to estimate the noise power, namely:
Figure BDA00033441312000000410
wherein tr { } is the trace operator for the matrix.
The step 5 comprises the following steps:
step 51, deducting the noise-to-signal subspace eigenvalue matrix LambdasThe modified signal subspace eigenvalue matrix is:
Figure BDA00033441312000000411
wherein, IL+1Is an L +1 dimensional identity matrix;
step 52, using the estimated interference steering vectors
Figure BDA00033441312000000412
Signal subspace EsAnd its corrected eigenvalue matrix
Figure BDA00033441312000000413
Estimating the interference power according to the following formula:
Figure BDA00033441312000000414
of course, the eigenvalue matrix Λ may also be used directlysEstimating the interference power according to the following formula:
Figure BDA0003344131200000051
only with a slight decrease in accuracy.
The step 6 comprises the following steps:
step 61, estimating the noise power according to the estimated noise power
Figure BDA0003344131200000052
Reconstructing a noise covariance matrix:
Figure BDA0003344131200000053
wherein, IMIs an M-dimensional identity matrix;
step 62, steering vectors based on the estimated interference
Figure BDA0003344131200000054
And power
Figure BDA0003344131200000055
The interference covariance matrix is reconstructed as follows:
Figure BDA0003344131200000056
step 63, according to the reconstructed noise covariance matrix
Figure BDA0003344131200000057
Sum interference covariance matrix
Figure BDA0003344131200000058
The interference plus noise covariance matrix is reconstructed as follows:
Figure BDA0003344131200000059
the step 7 comprises the following steps:
step 71, reconstructing an interference plus noise covariance matrix
Figure BDA00033441312000000510
And more accurate desired signal steering vector
Figure BDA00033441312000000511
The optimal weight vector is calculated as follows:
Figure BDA00033441312000000512
step 72, weighting the k-th snapshot data x (k) received by the array with the optimal weight vector w to obtain the output signal y (k) w of the beam formerHx (k), robust adaptive beamforming is achieved.
Compared with the prior art, the invention has the advantages that: the technical scheme provided by the invention can be seen that the feature decomposition of the covariance matrix of the array received data is carried out to obtain the signal subspace and the noise subspace, the more accurate expected signal and interference guide vector are estimated by utilizing the orthogonal property of the signal subspace and the noise subspace, the more accurate noise power and interference power are estimated by utilizing the information contained in the signal subspace eigenvalue matrix and the noise subspace eigenvalue matrix, the more accurate interference and noise covariance matrix is reconstructed, the optimal weight vector is more accurate, and the optimal weight vector has better adaptability to any type of array errors, so that the robustness of the adaptive beam former can be obviously improved.
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In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings needed to be used in the description of the embodiments are briefly introduced below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings based on the drawings without creative efforts.
Fig. 1 is a flowchart of a robust adaptive beamforming method based on subspace orthogonality according to an embodiment of the present invention;
fig. 2 is a schematic diagram of an array signal receiving model according to an embodiment of the present invention.
Detailed Description
The embodiment of the invention decomposes the characteristics of the covariance matrix of the array received data to obtain a signal subspace and a noise subspace, estimates more accurate expected signals and interference guide vectors by utilizing the orthogonal properties of the signal subspace and the noise subspace, estimates more accurate noise power and interference power by utilizing the information contained in the signal subspace eigenvalue matrix and the noise subspace eigenvalue matrix, reconstructs a more accurate interference-plus-noise covariance matrix, obtains more accurate optimal weight vectors, and can further improve the robustness of the adaptive beam forming method under various array error conditions.
As shown in fig. 1, the method first preprocesses array received data, including: and estimating an array covariance matrix, and performing characteristic decomposition on the matrix to obtain a signal subspace and a noise subspace and characteristic value matrixes corresponding to the signal subspace and the noise subspace.
The method mainly comprises the following steps:
step 1, based on a noise subspace obtained by preprocessing, using a nominal steering vector in a multiple signal classification method, estimating the arrival direction of signals and interference, and generating initial values of the steering vectors;
step 2, correcting the expected signal guide vector by utilizing the orthogonal property of the signal subspace and the noise subspace, and estimating a more accurate expected signal guide vector;
step 3, correcting the interference guide vector by utilizing the orthogonal property of the signal subspace and the noise subspace, and estimating a more accurate interference guide vector;
step 4, estimating the noise power by using the average value of the characteristic values corresponding to the noise subspace;
step 5, estimating each interference power by using the estimated more accurate steering vector of each interference together with the signal subspace and the eigenvalue matrix thereof;
step 6, reconstructing a noise covariance matrix according to the estimated noise power, reconstructing an interference covariance matrix according to the estimated more accurate guide vectors and power of each interference, and reconstructing an interference-plus-noise covariance matrix;
and 7, calculating an optimal weight vector according to the reconstructed interference and noise covariance matrix and the more accurate expected signal guide vector, and forming stable self-adaptive beam output for array received data.
Compared with the existing interference and noise covariance matrix reconstruction type robust adaptive beam forming method, the scheme of the invention estimates more accurate expected signals and interference guide vectors by utilizing the orthogonal property of the signal subspace and the noise subspace after the characteristic decomposition of the covariance matrix of array received data is carried out to obtain the signal subspace and the noise subspace, estimates more accurate noise power and interference power by utilizing the information contained in the signal subspace characteristic value matrix and the noise subspace characteristic value matrix, reconstructs the more accurate interference and noise covariance matrix, and the optimal weight vector is more accurate, thereby being capable of better improving the robustness of the beam forming device to any type of array errors.
For ease of understanding, the Capon beamforming method is introduced first, then the preprocessing is introduced, and then the above seven steps are explained in detail.
The embodiment of the invention is suitable for any type of array form, including linear arrays, circular arrays, conformal arrays and the like, and the suitable directions of arrival include one-dimensional azimuth angles, one-dimensional pitch angles, two-dimensional azimuth angles and pitch angles. For the sake of computational convenience, only the linear array is discussed here, and the specific array signal model is as follows:
considering an array containing M-elements that receives a narrow-band far-field signal from space, the received data of the array at observation time k (referred to as the kth snapshot data received by the array) is represented as:
x(k)＝xs(k)+xi(k)+xn(k)；
wherein x iss(k)、xi(k) And xn(k) Respectively representing desired signals, interference and noise, and are statistically independent of each other; x is the number ofs(k)＝s(k)a0S (k) is the waveform of the desired signal, a0Is the true steering vector of the desired signal,
Figure BDA0003344131200000071
representing the interference vector, L being the number of interferences, sl(k) Is the waveform of the first disturbance, alFor the corresponding true interference steering vector,
Figure BDA0003344131200000072
xn(k) is additive independent and uniformly distributed white Gaussian noise, signal s (k), each interference sl(k) And noise xn(k) Are all zero mean. FIG. 2 shows a schematic diagram of a narrow-band far-field signal source in a linear array receiving space, where the arrival direction of a signal (or interference) source is theta and is approximately considered to be incident on each array element in the form of a plane wave, d1,d2,…,dM-1Is the distance between each array element and the reference array element.
For a specific direction signalTo perform enhancement, which is equivalent to increasing the directional gain, it is necessary to assign a specific weighting coefficient to each array element, and how to design the optimal weight w ═ w1,w2,…,wM]TIt is the main work of beamforming technology that the array system that can achieve this is often called a beamformer, which is essentially a spatial filter. The output of the beam former is the weighted summation of the received signals of each array element, namely:
y(k)＝wHx(k)；
for a beamformer with a given weight vector, in order to evaluate its beamforming performance, in addition to being visually demonstrated by the array pattern, the output signal-to-interference-and-noise ratio is often used as a quantitative measure of the overall performance of the beamformer, which is defined as follows:
Figure BDA0003344131200000073
wherein x isi+n(k)＝xi(k)+xn(k) In order to add a noise component to the interference,
Figure BDA0003344131200000081
is an interference plus noise covariance matrix.
Figure BDA0003344131200000082
Is the power of the desired signal.
In order to maximize the output signal-to-noise ratio, Capon et al propose to minimize the array output power while ensuring a certain response to the desired signal direction, forming the following optimization problem:
Figure BDA0003344131200000083
wherein R ═ E { x (k) xH(k) The covariance matrix of the data received by the array. Thus, the weight vector of the beamformer can be obtained as:
Figure BDA0003344131200000084
this is the Capon beamforming method, and the maximum output signal to interference and noise ratio can be achieved under ideal conditions. Substituting the obtained weight vector into an objective function of an optimization problem to obtain the output power of the array as follows:
Figure BDA0003344131200000085
this power, also known as Capon power, is the minimum power output by the array when the desired signal is received without distortion, and thus Capon power is considered an estimate of the desired signal power. When the steering vector is regarded as a variable, the output power expression is used for representing the signal power condition in each steering vector direction, namely the space power spectrum.
In practical situations, ideal signal statistical information is difficult to obtain, and is usually implemented by using an algorithm of sample matrix inversion, and the main idea is to use a sample covariance matrix
Figure BDA0003344131200000086
Instead of the ideal covariance matrix R, the weight vector is solved, which is defined as:
Figure BDA0003344131200000087
wherein K is the fast beat number of the array received data. Because finite snapshots introduce random errors to R and also consider that a true steering vector is difficult to obtain accurately, a steering vector obtained according to a known array structure needs to be used for calculation, and then a corresponding Capon spatial power spectrum can be represented as:
Figure BDA0003344131200000088
wherein the content of the first and second substances,
Figure BDA0003344131200000089
i.e. the nominal steering vector assumed according to the array structure and corresponding to a direction angle theta.
The Capon beamforming method can degrade significantly in performance in the presence of various errors in the array.
The purpose of the invention is: the method comprises the steps of estimating more accurate expected signals and interference guide vectors by utilizing the orthogonal property of a signal subspace and a noise subspace, estimating more accurate noise power and interference power by utilizing the information contained in a signal subspace characteristic value matrix and a noise subspace characteristic value matrix, estimating more accurate expected signal guide vectors and a noise-plus-interference covariance matrix, obtaining more accurate weight vectors, further improving the performance of the beam forming method and having robustness. The pretreatment is followed by seven steps as follows.
Pretreatment:
covariance matrix for receiving data estimation array using M-ary array
Figure BDA0003344131200000091
To pair
Figure BDA0003344131200000092
The characteristic decomposition is carried out, and the characteristic decomposition is carried out,
Figure BDA0003344131200000093
Esand ΛsRespectively, a diagonal matrix of signal (including interference) subspaces and their corresponding eigenvalues, EnAnd ΛnRespectively, a diagonal matrix of noise subspaces and their corresponding eigenvalues, EsAnd EnAre orthogonal. Wherein, K is the number of snapshots of the data received by the array, x (K) is the kth snapshot data received by the array, subscripts and n are respectively the symbols for distinguishing signals and noise, and superscript H is the conjugate transpose operator of the matrix.
Step 1:
step 11, generating a nominal guide vector with a corresponding direction angle theta according to the array structure
Figure BDA0003344131200000094
|| ||2Is a vector l2A norm operator;
step 12, noise subspace E obtained based on preprocessingnTo guide a vector
Figure BDA0003344131200000095
For the multiple signal classification Method (MUSIC), the MUSIC spatial spectrum is calculated as follows:
Figure BDA0003344131200000096
estimating the direction of arrival of the desired signal
Figure BDA0003344131200000097
Number of interferers L (M > L +1) and direction of arrival of all interferers
Figure BDA0003344131200000098
Generating initial value of guide vector of expected signal according to array structure
Figure BDA0003344131200000099
Initial value of each interference steering vector
Figure BDA00033441312000000910
Step 2:
step 21, giving a steering vector perpendicular to the desired signal
Figure BDA00033441312000000911
Micro neighborhoods on a plane, including a two-dimensional rectangular neighborhood, a square neighborhood, an elliptical neighborhood, a circular neighborhood, a cross neighborhood, a one-dimensional neighborhood,
Figure BDA00033441312000000912
is the center of the neighborhood, and discretizes the neighborhood into R points, the steering vector of the R-th point is
Figure BDA00033441312000000913
Figure BDA00033441312000000914
As a guide vector
Figure BDA00033441312000000915
An error vector introduced at the r-th point; the micro neighborhood means
Figure BDA00033441312000000916
Step 22, initial value of guide vector for expected signal
Figure BDA0003344131200000101
According to its steering vector
Figure BDA0003344131200000102
The MUSIC spatial spectrum is calculated as follows:
Figure BDA0003344131200000103
according to the orthogonal property of the signal subspace and the noise subspace, searching in R discrete points of a small neighborhood
Figure BDA0003344131200000104
Finally, the steering vector of the desired signal thus corrected is obtained as:
Figure BDA0003344131200000105
if multiple maximum values appear, the vector is averaged and still recorded as
Figure BDA0003344131200000106
And step 3:
step (ii) of31. Giving initial values of steering vectors perpendicular to each interference
Figure BDA0003344131200000107
Micro neighborhoods on a plane, including a two-dimensional rectangular neighborhood, a square neighborhood, an elliptical neighborhood, a circular neighborhood, a cross neighborhood, a one-dimensional neighborhood,
Figure BDA0003344131200000108
is the center of the neighborhood, and discretizes the neighborhood into R points, the steering vector of the R-th point is
Figure BDA0003344131200000109
Figure BDA00033441312000001010
As a guide vector
Figure BDA00033441312000001011
An error vector introduced at the r-th point; the micro neighborhood means
Figure BDA00033441312000001012
Step 32, steering vectors for each disturbance
Figure BDA00033441312000001013
According to its steering vector
Figure BDA00033441312000001014
The MUSIC spatial spectrum is calculated as follows:
Figure BDA00033441312000001015
by utilizing the orthogonal property of the signal subspace and the noise subspace, the method searches in R discrete points of a small neighborhood
Figure BDA00033441312000001018
Is the most important ofThe large value, the final steering vector of the corrected interference is:
Figure BDA00033441312000001016
if multiple maximum values appear, the vector is averaged and still recorded as
Figure BDA00033441312000001017
And 4, step 4:
eigenvalue matrix Lambda corresponding with noise subspacenTaking the average value of the diagonal elements to estimate the noise power, namely:
Figure BDA0003344131200000111
wherein tr { } is the trace operator for the matrix.
And 5:
step 51, deducting the noise-to-signal subspace eigenvalue matrix LambdasThe modified signal subspace eigenvalue matrix is:
Figure BDA0003344131200000112
wherein, IL+1Is an L +1 dimensional identity matrix;
step 52, using the estimated interference steering vectors
Figure BDA0003344131200000113
Signal subspace EsAnd its corrected eigenvalue matrix
Figure BDA0003344131200000114
Estimating the interference power according to the following formula:
Figure BDA0003344131200000115
of course, the eigenvalue matrix Λ may also be used directlysEstimating the interference power according to the following formula:
Figure BDA0003344131200000116
only with a slight decrease in accuracy.
Step 6:
step 61, estimating the noise power according to the estimated noise power
Figure BDA0003344131200000117
The noise covariance matrix is reconstructed as follows:
Figure BDA0003344131200000118
wherein, IMIs an M-dimensional identity matrix in an M-ary array;
step 62, steering vectors based on the estimated interference
Figure BDA0003344131200000119
And power
Figure BDA00033441312000001110
The interference covariance matrix is reconstructed as follows:
Figure BDA00033441312000001111
step 63, according to the reconstructed noise covariance matrix
Figure BDA00033441312000001112
Sum interference covariance matrix
Figure BDA00033441312000001113
The interference plus noise covariance matrix is reconstructed as follows:
Figure BDA00033441312000001114
and 7:
step 71, reconstructing an interference plus noise covariance matrix
Figure BDA0003344131200000121
And more accurate desired signal steering vector
Figure BDA0003344131200000122
The optimal weight vector is calculated as follows:
Figure BDA0003344131200000123
step 72, weighting the k-th snapshot data x (k) received by the array with the optimal weight vector w to obtain the output signal y (k) w of the beam formerHx (k), robust adaptive beamforming is achieved.
Through the above description of the embodiments, it is clear to those skilled in the art that the above embodiments can be implemented by software, and can also be implemented by software plus a necessary general hardware platform. With this understanding, the technical solutions of the embodiments can be embodied in the form of a software product, which can be stored in a non-volatile storage medium (which can be a CD-ROM, a usb disk, a removable hard disk, etc.), and includes several instructions for enabling a computer device (which can be a personal computer, a server, or a network device, etc.) to execute the methods according to the embodiments of the present invention.
The above description is only for the preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope of the present invention are included in the scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.

Claims (8)

1. A method for forming stable self-adaptive beam based on subspace orthogonality includes preprocessing M-element array received data to estimate covariance matrix of array
Figure FDA0003344131190000011
Performing characteristic decomposition on the matrix to obtain a signal subspace and a noise subspace and corresponding characteristic value matrixes thereof, wherein
Figure FDA0003344131190000012
EsAnd ΛsRespectively, a diagonal matrix of signal subspaces and their corresponding eigenvalues, EnAnd ΛnRespectively, a diagonal matrix of noise subspaces and their corresponding eigenvalues, EsAnd EnIs orthogonal, where subscripts s and n are the symbols that distinguish signal and noise, respectively, and superscript H is the conjugate transpose operator of the matrix, characterized in that: also comprises the following steps:
step 1, based on a noise subspace obtained by preprocessing, using a nominal guide vector in a multiple signal classification method, estimating the arrival directions of expected signals and interference, and generating an initial value of the guide vector of the expected signals and initial values of all interference guide vectors;
step 2, correcting the initial value of the expected signal guide vector in the step 1 by utilizing the orthogonal property of the signal subspace and the noise subspace, and estimating a more accurate expected signal guide vector;
step 3, correcting the initial values of the interference guide vectors in the step 1 by utilizing the orthogonal property of the signal subspace and the noise subspace, and estimating more accurate interference guide vectors;
step 4, estimating noise power by using the average value of the characteristic values corresponding to the noise subspace obtained by preprocessing;
step 5, estimating each interference power by using each estimated more accurate interference guide vector in the step 3 together with the signal subspace and the eigenvalue matrix thereof;
step 6, reconstructing a noise covariance matrix according to the noise power estimated in the step 4; reconstructing an interference covariance matrix according to each interference guide vector estimated in the step 3 and each interference power in the step 5; finally, according to the reconstructed noise covariance matrix and the interference covariance matrix, reconstructing an interference-plus-noise covariance matrix;
and 7, calculating an optimal weight vector according to the interference plus noise covariance matrix reconstructed in the step 6 and the more accurate expected signal guide vector reconstructed in the step 2, and forming stable self-adaptive beam output for array received data.
2. The robust adaptive beamforming method based on subspace orthogonality, according to claim 1, characterized in that: the step 1 comprises the following steps:
step 11, generating a nominal guide vector with a corresponding direction angle theta according to the array structure
Figure FDA0003344131190000013
Figure FDA0003344131190000014
|| ||2Is a vector l2A norm operator;
step 12, noise subspace E obtained based on preprocessingnTo guide the nominal vector
Figure FDA0003344131190000015
In the multi-signal classification method MUSIC, the MUSIC spatial spectrum is calculated according to the following formula:
Figure FDA0003344131190000021
estimating the direction of arrival of the desired signal
Figure FDA0003344131190000022
Number of interferers L and direction of arrival of all interferers
Figure FDA0003344131190000023
M is more than L + 1; generating initial value of guide vector of expected signal according to array structure
Figure FDA0003344131190000024
Initial value of each interference steering vector
Figure FDA0003344131190000025
3. The robust adaptive beamforming method based on subspace orthogonality, according to claim 2, characterized in that: the step 2 comprises the following steps:
step 21, initial values of steering vectors perpendicular to the expected signal are given
Figure FDA0003344131190000026
A small neighborhood on a plane, the neighborhood comprising a two-dimensional rectangular neighborhood, a square neighborhood, an elliptical neighborhood, a circular neighborhood, a cross neighborhood, or a one-dimensional neighborhood,
Figure FDA0003344131190000027
is the center of the neighborhood, and discretizes the neighborhood into R points, the steering vector of the R-th point is
Figure FDA0003344131190000028
Figure FDA0003344131190000029
Figure FDA00033441311900000210
Figure FDA00033441311900000211
As a guide vector
Figure FDA00033441311900000212
An error vector introduced at the r-th point; the micro neighborhood means
Figure FDA00033441311900000213
Step 22, initial value of guide vector for expected signal
Figure FDA00033441311900000214
According to its steering vector
Figure FDA00033441311900000215
The MUSIC spatial spectrum is calculated as follows:
Figure FDA00033441311900000216
according to the orthogonal property of the signal subspace and the noise subspace, searching in R discrete points of a small neighborhood
Figure FDA00033441311900000222
Finally, the modified steering vector of the desired signal is obtained as:
Figure FDA00033441311900000217
if multiple maximum values appear, the vector is averaged and still recorded as
Figure FDA00033441311900000218
Figure FDA00033441311900000219
4. A robust adaptive beamforming method based on subspace orthogonality, according to claim 3, characterized in that: the step 3 comprises the following steps:
step 31, initial values of steering vectors perpendicular to each interference are given
Figure FDA00033441311900000220
A small neighborhood of the light on the plane is,
Figure FDA00033441311900000221
is the center of the neighborhood, and discretizes the neighborhood into R points, the steering vector of the R-th point is
Figure FDA0003344131190000031
Figure FDA0003344131190000032
Figure FDA0003344131190000033
As a guide vector
Figure FDA0003344131190000034
An error vector introduced at the r-th point; the micro neighborhood means
Figure FDA0003344131190000035
Step 32, steering vectors for each disturbance
Figure FDA0003344131190000036
According to its steering vector
Figure FDA0003344131190000037
The MUSIC spatial spectrum is calculated as follows:
Figure FDA0003344131190000038
by utilizing the orthogonal property of the signal subspace and the noise subspace, the method searches in R discrete points of a small neighborhood
Figure FDA0003344131190000039
Finally, the guiding vector of the corrected interference is obtained, and is:
Figure FDA00033441311900000310
if multiple maximum values appear, the vector is averaged and still recorded as
Figure FDA00033441311900000311
Figure FDA00033441311900000312
5. A robust adaptive beamforming method based on subspace orthogonality, according to claim 4, characterized in that: the step 4 comprises the following steps:
eigenvalue matrix Lambda corresponding with noise subspacenTaking the average value of the diagonal elements to estimate the noise power, namely:
Figure FDA00033441311900000313
wherein tr { } is the trace operator for the matrix.
6. A robust adaptive beamforming method based on subspace orthogonality, according to claim 5, characterized in that: the step 5 comprises the following steps:
step 51, deducting the noise-to-signal subspace eigenvalue matrix LambdasThe modified signal subspace eigenvalue matrix is:
Figure FDA00033441311900000314
wherein, IL+1Is an L +1 dimensional identity matrix;
step 52, using the estimated interference steering vectors
Figure FDA00033441311900000315
Signal subspace EsAnd its corrected eigenvalue matrix
Figure FDA00033441311900000316
Estimating the interference power according to the following formula:
Figure FDA0003344131190000041
or directly using the eigenvalue matrix ΛsEstimating the interference power according to the following formula:
Figure FDA0003344131190000042
7. a robust adaptive beamforming method based on subspace orthogonality, according to claim 6, characterized in that: the step 6 comprises the following steps:
step 61, estimating the noise power according to the estimated noise power
Figure FDA0003344131190000043
Reconstructing a noise covariance matrix:
Figure FDA0003344131190000044
wherein, IMIs an M-dimensional identity matrix;
step 62, steering vectors based on the estimated interference
Figure FDA0003344131190000045
And power
Figure FDA0003344131190000046
The interference covariance matrix is reconstructed as follows:
Figure FDA0003344131190000047
step 63, according to the reconstructed noise covariance matrix
Figure FDA0003344131190000048
Sum interference covariance matrix
Figure FDA0003344131190000049
The interference plus noise covariance matrix is reconstructed as follows:
Figure FDA00033441311900000410
8. the robust adaptive beamforming method based on subspace orthogonality, according to claim 7, characterized in that: the step 8 comprises the following steps:
step 71, reconstructing an interference plus noise covariance matrix
Figure FDA00033441311900000411
And more accurate desired signal steering vector
Figure FDA00033441311900000412
The optimal weight vector is calculated as follows:
Figure FDA00033441311900000413
step 72, weighting the k-th snapshot data x (k) received by the array with the optimal weight vector w to obtain the output signal y (k) w of the beam formerHx (k), robust adaptive beamforming is achieved.
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CN114609581B (en) * 2022-03-07 2024-05-10 中国科学技术大学 Array super-resolution direction finding method for comparing maximum value of vector projection in scanning direction

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