CN114236471A - Robust adaptive beam forming method under relevant interference source - Google Patents

Robust adaptive beam forming method under relevant interference source Download PDF

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CN114236471A
CN114236471A CN202111557249.9A CN202111557249A CN114236471A CN 114236471 A CN114236471 A CN 114236471A CN 202111557249 A CN202111557249 A CN 202111557249A CN 114236471 A CN114236471 A CN 114236471A
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叶中付
杨会超
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University of Science and Technology of China USTC
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Abstract

The invention discloses a method for forming a steady self-adaptive wave beam under a relevant interference source, which comprises the following steps: decomposing the characteristics of the sampling covariance matrix, and dividing the characteristic vector into a signal subspace and a noise subspace; estimating the noise power according to the characteristic value; estimating an initial angle of an expected signal and interference by utilizing subspace orthogonality, obtaining a nominal steering vector corresponding to the initial angle according to a known array shape, and projecting to a noise subspace to obtain an error vector of the nominal steering vector; updating and estimating a guide vector according to the subspace orthogonality to obtain a guide vector of the expected signal and the interference; reconstructing an interference-plus-noise covariance matrix according to the estimated expected signal and interference guide vector and the expected signal and interference part of the sampling covariance matrix; and performing beam forming on the array receiving data based on the estimated expected signal guide vector and the reconstructed interference and noise covariance matrix.

Description

Robust adaptive beam forming method under relevant interference source
Technical Field
The invention relates to the field of beam forming research in the field of array signal processing, in particular to a robust adaptive beam forming method under a relevant interference source.
Background
Although the conventional beamforming method can improve the robustness of the beamformer to a certain extent, when a desired signal appears in the covariance matrix, the beamformer suppresses the desired signal as interference, and a self-cancellation phenomenon occurs, which causes performance degradation of the beamformer. Although the performance of a beam former can be improved to a certain extent based on a covariance matrix reconstruction algorithm at present, the estimation of a desired signal steering vector is usually performed by solving a convex optimization problem, and the problems of high complexity, more redundant components in a reconstructed covariance matrix and the like exist. In addition, most of the current algorithms based on covariance matrix reconstruction adopt uncorrelated interference sources as assumed conditions, and more of the algorithms in practice are correlated interference sources, and the performance of the algorithms is improved to a limited extent under the condition of the correlated interference sources. In view of this, it is necessary to research a new beamforming algorithm in the scenario of the relevant interference source to improve the performance of the beamformer in practical applications.
Disclosure of Invention
The invention aims to provide a method for forming a robust adaptive beam under a relevant interference source, which further improves the performance of a beam forming device under the condition of actual array errors and the existence of the relevant interference source by estimating a steering vector of a desired signal and the relevant interference source and an interference power matrix.
The purpose of the invention is realized by the following technical scheme: a method of robust adaptive beamforming under correlated interferers, comprising:
step 1, carrying out characteristic decomposition on a sampling covariance matrix of array received data, wherein a characteristic vector corresponding to an expected signal and an interference characteristic value is called a signal subspace, and a characteristic vector corresponding to a residual characteristic value is called a noise subspace; obtaining an estimated value of noise power according to the characteristic value corresponding to the noise subspace;
step 2, obtaining a spectrum value of a full space according to the orthogonality of the signal subspace and the noise subspace in the step 1, obtaining an initial angle of an expected signal and interference by performing spectrum peak search on the spectrum value, and obtaining a nominal guide vector corresponding to the initial angle according to a known array shape; projecting the nominal guide vectors of the expected signals and the interference to the noise subspace in the step 1 to obtain error vectors of the expected signals and the interference guide vectors;
step 3, updating and estimating the guide vectors of the expected signals and the interference according to a subspace orthogonality principle by using the nominal guide vectors and the error vectors of the expected signals and the interference in the step 2 to obtain estimated values of the expected signals and the interference guide vectors;
step 4, reconstructing the interference and noise covariance matrix according to the noise power estimation value in the step 1, the estimation values of the expected signal and the interference guide vector in the step 3 and the expected signal and the interference part in the sampling covariance matrix of the array receiving data to obtain a reconstructed interference and noise covariance matrix;
and 5, forming a beam for the array receiving data based on the expected signal guide vector estimated in the step 3 and the interference and noise covariance matrix reconstructed in the step 4.
Further, performing characteristic decomposition on a sampling covariance matrix of array received data, wherein a characteristic vector corresponding to an eigenvalue of a desired signal and an interference is called a signal subspace, and a characteristic vector corresponding to a residual eigenvalue is called a noise subspace; obtaining an estimation value of noise power according to the feature value corresponding to the noise subspace includes:
the method provided by the invention is suitable for any array type, for convenience of description, taking an M-element uniform linear array as an example, the array element spacing is d, receiving L far-field narrow-band signal sources, including an expected signal and L-1 related interference sources, wherein the expected signal and the related interference sources are not related to each other, and then the received data of the array at the time k can be represented as:
Figure BDA0003419360900000021
wherein s is0(k) Represents the waveform of the desired signal at time k, a0A steering vector representing the desired signal,
Figure BDA0003419360900000022
l1, 2, …, L-1 represents the waveform of the L-th coherent interferer at time k, alGuide vector, x, representing the l-th relevant interferern(k) Representing the noise received by the array at time k. The mean values of the desired signal, interference and noise are assumed to be zero.
Further, the relevant interference sources can be expressed as:
sc＝Γsuc
wherein the content of the first and second substances,
Figure BDA0003419360900000023
representing the relevant interferer vector received by the array,
Figure BDA0003419360900000024
representing uncorrelated interferer vectors and Γ representing correlated interferer coefficient matrices. When Γ is a diagonal matrix, correlated interferers degrade into uncorrelated interferers. T denotes a transposition operation of a matrix or a vector. Ideally, the covariance matrix of the array received data can be expressed as:
Figure BDA0003419360900000031
wherein the content of the first and second substances,
Figure BDA0003419360900000032
representing the power of the desired signal, A ═ a0,Ai]＝[a0,a1,…,aL-1]A matrix of steering vectors representing the desired signal and the interference, Ai＝[a1,a2,…,aL-1]A matrix of steering vectors representing the sources of interference,
Figure BDA0003419360900000033
a power matrix representing uncorrelated interferers, diag { } represents a diagonal matrix,
Figure BDA0003419360900000034
1,2, …, L-1 denotes the power of the first uncorrelated interferer, Γ ΣucΓHA power matrix representing the associated interference source,
Figure BDA0003419360900000035
denotes the noise power, I denotes an identity matrix, and H denotes the conjugate transpose operation of a matrix or a vector.
In the step 1, performing characteristic decomposition on a sampling covariance matrix of array received data, wherein a characteristic vector corresponding to an eigenvalue of an expected signal and an interference is called a signal subspace, and a characteristic vector corresponding to a residual eigenvalue is called a noise subspace; obtaining an estimated value of noise power according to a feature value corresponding to a noise subspace, wherein the specific requirements comprise:
the sampling covariance matrix of the array received data is:
Figure BDA0003419360900000036
where x (K) represents the data received by the array at time K, K represents the fast beat number, and H represents the conjugate transpose operation of the matrix or vector.
And performing characteristic decomposition on the sampling covariance matrix to obtain:
Figure BDA0003419360900000037
wherein, M represents the number of array elements,
Figure BDA0003419360900000038
representing the eigenvalues in descending order,
Figure BDA0003419360900000039
and the feature vector corresponding to the feature value.
Figure BDA00034193609000000310
A matrix of the feature vectors is represented,
Figure BDA00034193609000000311
representing a diagonal matrix composed of eigenvalues;
Figure BDA00034193609000000312
and representing the eigenvector matrix corresponding to the first L eigenvalues, and called signal subspace,
Figure BDA00034193609000000313
a diagonal matrix composed of the first L eigenvalues is represented, and L represents the number of expected signals and interference;
Figure BDA00034193609000000314
the eigenvector matrix corresponding to the remaining M-L eigenvalues, and referred to as the noise subspace,
Figure BDA00034193609000000315
representing a diagonal matrix of the remaining M-L eigenvalues. According to the nature of feature decomposition, the power of noise is corresponding to the remaining M-L feature values, and then the estimated value of the noise power is represented as:
Figure BDA0003419360900000041
the step 2 comprises the following steps:
(21) according to the orthogonality of the signal subspace and the noise subspace in the step 1, obtaining a spectrum value of a total space as follows:
Figure BDA0003419360900000042
wherein the content of the first and second substances,
Figure BDA0003419360900000043
the nominal steering vector for the angle theta is represented and theta represents the full space. The initial angles of the expected signal and the interference obtained by performing the spectral peak search on the spectral values are respectively
Figure BDA0003419360900000044
And
Figure BDA0003419360900000045
obtaining a nominal steering vector corresponding to the initial angle based on the known array shape as
Figure BDA0003419360900000046
(22) Projecting the nominal guide vector of the desired signal and the interference to the noise subspace in the step 1 to obtain the error vector of the desired signal and the interference guide vector, wherein the error vector is as follows:
Figure BDA0003419360900000047
wherein | | | purple hair2Representing matrices or vectors2And (4) norm.
The obtaining of the estimated values of the desired signal and the interference steering vector by updating and estimating the desired signal and the interference steering vector according to the subspace orthogonality principle by using the nominal steering vector and the error vector of the desired signal and the interference in the step 2 comprises:
from the orthogonality of the signal subspace and the noise subspace, it can be seen that the more the guide vector is close to the true guide vector, the more orthogonal the guide vector is to the noise subspace, the larger its corresponding spectral value, i.e. the smaller the denominator in the spectral value. Based on this principle, the result of the steering vector estimation can be found as:
Figure BDA0003419360900000048
wherein the content of the first and second substances,
Figure BDA0003419360900000049
birepresents the interval [ -b, b]Where the ith value is spaced by η, b represents the upper bound of the search interval,
Figure BDA00034193609000000410
representing the total number of searches.
Reconstructing the interference-plus-noise covariance matrix according to the noise power estimation value in the step 1, the estimation values of the desired signal and the interference guide vector in the step 3, and the desired signal and the interference part in the sampling covariance matrix of the array received data, and obtaining the reconstructed interference-plus-noise covariance matrix includes:
for an ideal covariance matrix of the array received data, it can be expressed as:
Figure BDA0003419360900000051
the characteristic decomposition is carried out on the obtained product to obtain:
Figure BDA0003419360900000052
wherein, γmRepresenting the eigenvalues, u, in descending ordermAnd the feature vector corresponding to the feature value. U ═ US UN]＝[u1,u2,…,uM]Representing a feature vector matrix, Λ ═ diag { γ }1,γ2,…,γMDenotes a diagonal matrix composed of eigenvalues, US＝[u1,u2,…,uL]Representing the eigenvector matrix corresponding to the first L eigenvalues and called the signal subspace, ΛS＝diag{γ1,γ2,…,γLDenotes a diagonal matrix of the first L eigenvalues, UN＝[uL+1,uL+2,…,uM]The eigenvector matrix corresponding to the remaining M-L eigenvalues is called the noise subspace, ΛN＝diag{γL+1,γL+2,…,γMDenotes a diagonal matrix of the remaining M-L eigenvalues. Then it can be found that:
Figure BDA0003419360900000053
namely:
Figure BDA0003419360900000054
wherein the content of the first and second substances,
Figure BDA0003419360900000055
representing the pseudo-inverse of matrix a.
Noise power obtained from the estimation
Figure BDA0003419360900000056
Steering vector matrix
Figure BDA0003419360900000057
And the covariance matrix of the samples of the array received data may be used to derive a power matrix of the desired signal and interference as:
Figure BDA0003419360900000058
the reconstructed interference plus noise covariance matrix can then be expressed as:
Figure BDA0003419360900000059
the beamforming the array received data based on the desired signal steering vector estimated in step 3 and the interference-plus-noise covariance matrix reconstructed in step 4 includes:
based on the reconstructed interference-plus-noise covariance matrix and the estimated steering vector of the desired signal, the weight vector of the beamformer is represented as:
Figure BDA0003419360900000061
wherein the content of the first and second substances,
Figure BDA0003419360900000062
representing the estimated desired signal steering vector.
Beamforming the data received by the array according to the weight vector:
y(k)＝wHx(k)
where y (k) denotes the output signal of the beamformer. Thereby achieving enhancement of the desired signal and suppression of interference and noise.
Compared with the prior art, the invention has the advantages that:
(1) the method provided by the invention obtains the initial angle of the expected signal and the interference through spectrum peak search on the basis of the orthogonality of the signal subspace and the noise subspace, and has better angle resolution capability compared with the Capon power spectrum in the traditional beam, namely, more accurate initial values of the expected signal and the interference angle can be obtained.
(2) The method takes the projection of the nominal guide vector in the noise subspace as an error vector and the orthogonality of the subspace as an estimation criterion to carry out the guide vector estimation, avoids the solution of the convex optimization problem about the guide vector estimation in the traditional beam forming, reduces the calculation complexity and is more beneficial to the realization in practice.
(3) The invention realizes the estimation of the interference power matrix by sampling the expected signal and the interference part of the covariance matrix and the estimated guide vector matrix, and improves the performance of the invention under the condition of relevant interference sources. Since the uncorrelated interference sources are special cases of correlated interference sources, the method of the present invention is also applicable to adaptive beamforming of uncorrelated interference sources, i.e. the present invention can simultaneously handle beamforming problems of correlated interference sources and uncorrelated interference sources.
The invention is different from the prior art in that: the processing objects are different, the invention deals with the situation of relevant interference sources, while the prior art deals with non-relevant interference sources; the treatment method is different: the invention constructs the error vector of the guide vector on the basis of the subspace orthogonality, and estimates the guide vector by taking the maximum orthogonality of the noise subspace as a criterion, thereby reducing the calculation complexity of the method; the estimation of the relevant interference source power matrix is realized by sampling the expected signal and the interference component in the covariance matrix, and the interference plus noise covariance matrix is reconstructed, so that the method is more suitable for processing practical problems.
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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 these drawings without creative efforts.
FIG. 1 is a flow chart of a robust adaptive beamforming method under a coherent interferer in accordance with the present invention;
fig. 2 is a schematic diagram of a linear array signal receiving model provided in an embodiment of the present invention;
fig. 3 is a graph of performance provided by an embodiment of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention are clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments of the present invention without making any creative effort, shall fall within the protection scope of the present invention.
As shown in fig. 1, the robust adaptive beamforming method under the relevant interference source provided in the embodiment of the present invention mainly includes the following steps:
step 1, carrying out characteristic decomposition on a sampling covariance matrix of array received data, wherein a characteristic vector corresponding to an expected signal and an interference characteristic value is called a signal subspace, and a characteristic vector corresponding to a residual characteristic value is called a noise subspace; obtaining an estimated value of noise power according to the characteristic value corresponding to the noise subspace;
step 2, obtaining a spectrum value of a full space according to the orthogonality of the signal subspace and the noise subspace in the step 1, obtaining an initial angle of an expected signal and interference by performing spectrum peak search on the spectrum value, and obtaining a nominal guide vector corresponding to the initial angle according to a known array shape; projecting the nominal guide vectors of the expected signals and the interference to the noise subspace in the step 1 to obtain error vectors of the expected signals and the interference guide vectors;
step 3, updating and estimating the guide vectors of the expected signals and the interference according to a subspace orthogonality principle by using the nominal guide vectors and the error vectors of the expected signals and the interference in the step 2 to obtain estimated values of the expected signals and the interference guide vectors;
step 4, reconstructing the interference and noise covariance matrix according to the noise power estimation value in the step 1, the estimation values of the expected signal and the interference guide vector in the step 3 and the expected signal and the interference part in the sampling covariance matrix of the array receiving data to obtain a reconstructed interference and noise covariance matrix;
and 5, forming a beam for the array receiving data based on the expected signal guide vector estimated in the step 3 and the interference and noise covariance matrix reconstructed in the step 4.
As shown in fig. 2, the M-element uniform linear array has an array element spacing of d, receives L far-field narrowband signal sources, and includes a desired signal and L-1 correlated interference sources, where the desired signal and the correlated interference sources are uncorrelated with each other, and then the received data of the array at time k may be represented as:
Figure BDA0003419360900000081
wherein s is0(k) Represents the waveform of the desired signal at time k, a0A steering vector representing the desired signal,
Figure BDA0003419360900000082
l1, 2, …, L-1 represents the waveform of the L-th coherent interferer at time k, alGuide vector, x, representing the l-th relevant interferern(k) Representing the noise received by the array at time k. The mean values of the desired signal, interference and noise are assumed to be zero.
Further, the relevant interference sources can be expressed as:
sc＝Γsuc
wherein the content of the first and second substances,
Figure BDA0003419360900000083
representing the relevant interferer vector received by the array,
Figure BDA0003419360900000084
representing uncorrelated interferer vectors and Γ representing correlated interferer coefficient matrices. When Γ is a diagonal matrix, correlated interferers degrade into uncorrelated interferers. T denotes a transposition operation of a matrix or a vector. Ideally, the covariance matrix of the array received data can be expressed as:
Figure BDA0003419360900000085
wherein the content of the first and second substances,
Figure BDA0003419360900000086
representing the power of the desired signal, A ═ a0,Ai]＝[a0,a1,…,aL-1]A matrix of steering vectors representing the desired signal and the interference, Ai＝[a1,a2,…,aL-1]A matrix of steering vectors representing the sources of interference,
Figure BDA0003419360900000087
a power matrix representing uncorrelated interferers, diag { } represents a diagonal matrix,
Figure BDA0003419360900000088
1,2, …, L-1 denotes the power of the first uncorrelated interferer, Γ ΣucΓHA power matrix representing the associated interference source,
Figure BDA0003419360900000089
denotes the noise power, I denotes an identity matrix, and H denotes the conjugate transpose operation of a matrix or a vector.
Performing characteristic decomposition on a sampling covariance matrix of array received data, wherein a characteristic vector corresponding to an eigenvalue of an expected signal and an interference is called a signal subspace, and a characteristic vector corresponding to a residual eigenvalue is called a noise subspace; obtaining an estimation value of noise power according to a characteristic value corresponding to a noise subspace, comprising:
the sampling covariance matrix of the array received data is:
Figure BDA00034193609000000810
where x (K) represents the data received by the array at time K, K represents the fast beat number, and H represents the conjugate transpose operation of the matrix or vector.
And performing characteristic decomposition on the sampling covariance matrix to obtain:
Figure BDA0003419360900000091
wherein, M represents the number of array elements,
Figure BDA0003419360900000092
representing the eigenvalues in descending order,
Figure BDA0003419360900000093
and the feature vector corresponding to the feature value.
Figure BDA0003419360900000094
A matrix of the feature vectors is represented,
Figure BDA0003419360900000095
representing a diagonal matrix composed of eigenvalues;
Figure BDA0003419360900000096
and representing the eigenvector matrix corresponding to the first L eigenvalues, and called signal subspace,
Figure BDA0003419360900000097
a diagonal matrix composed of the first L eigenvalues is represented, and L represents the number of expected signals and interference;
Figure BDA0003419360900000098
the eigenvector matrix corresponding to the remaining M-L eigenvalues, and referred to as the noise subspace,
Figure BDA0003419360900000099
representing a diagonal matrix of the remaining M-L eigenvalues. According to the nature of feature decomposition, the power of noise is corresponding to the remaining M-L feature values, and then the estimated value of the noise power is represented as:
Figure BDA00034193609000000910
the step 2 comprises the following steps:
(21) according to the orthogonality of the signal subspace and the noise subspace in the step 1, obtaining a spectrum value of a total space as follows:
Figure BDA00034193609000000911
wherein the content of the first and second substances,
Figure BDA00034193609000000912
the nominal steering vector for the angle theta is represented and theta represents the full space. The initial angles of the expected signal and the interference obtained by performing the spectral peak search on the spectral values are respectively
Figure BDA00034193609000000913
And
Figure BDA00034193609000000914
obtaining a nominal steering vector corresponding to the initial angle based on the known array shape as
Figure BDA00034193609000000915
(22) Projecting the nominal guide vector of the desired signal and the interference to the noise subspace in the step 1 to obtain the error vector of the desired signal and the interference guide vector, wherein the error vector is as follows:
Figure BDA00034193609000000916
wherein | | | purple hair2Representing matrices or vectors2And (4) norm.
The obtaining of the estimated values of the desired signal and the interference steering vector by updating and estimating the desired signal and the interference steering vector according to the subspace orthogonality principle by using the nominal steering vector and the error vector of the desired signal and the interference in the step 2 comprises:
from the orthogonality of the signal subspace and the noise subspace, it can be seen that the more the guide vector is close to the true guide vector, the more orthogonal the guide vector is to the noise subspace, the larger its corresponding spectral value, i.e. the smaller the denominator in the spectral value. Based on this principle, the result of the steering vector estimation can be found as:
Figure BDA0003419360900000101
wherein the content of the first and second substances,
Figure BDA0003419360900000102
birepresents the interval [ -b, b]Where the ith value is spaced by η, b represents the upper bound of the search interval,
Figure BDA0003419360900000103
representing the total number of searches.
Reconstructing the interference-plus-noise covariance matrix according to the noise power estimation value in the step 1, the estimation values of the desired signal and the interference guide vector in the step 3, and the desired signal and the interference part in the sampling covariance matrix of the array received data, and obtaining the reconstructed interference-plus-noise covariance matrix includes:
for an ideal covariance matrix of the array received data, it can be expressed as:
Figure BDA0003419360900000104
the characteristic decomposition is carried out on the obtained product to obtain:
Figure BDA0003419360900000105
wherein, γmRepresenting the eigenvalues, u, in descending ordermAnd the feature vector corresponding to the feature value. U ═ US UN]＝[u1,u2,…,uM]Representing a feature vector matrix, Λ ═ diag { γ }1,γ2,…,γMDenotes a diagonal matrix composed of eigenvalues, US＝[u1,u2,…,uL]Representing the eigenvector matrix corresponding to the first L eigenvalues and called the signal subspace, ΛS＝diag{γ1,γ2,…,γLDenotes a diagonal matrix of the first L eigenvalues, UN＝[uL+1,uL+2,…,uM]The eigenvector matrix corresponding to the remaining M-L eigenvalues is called the noise subspace, ΛN＝diag{γL+1,γL+2,…,γMDenotes a diagonal matrix of the remaining M-L eigenvalues. Then it can be found that:
Figure BDA0003419360900000111
namely:
Figure BDA0003419360900000112
wherein the content of the first and second substances,
Figure BDA0003419360900000113
representing the pseudo-inverse of matrix a.
Noise power obtained from the estimation
Figure BDA0003419360900000114
Guide deviceVector matrix
Figure BDA0003419360900000115
And the covariance matrix of the samples of the array received data may be used to derive a power matrix of the desired signal and interference as:
Figure BDA0003419360900000116
the reconstructed interference plus noise covariance matrix can then be expressed as:
Figure BDA0003419360900000117
the beamforming the array received data based on the desired signal steering vector estimated in step 3 and the interference-plus-noise covariance matrix reconstructed in step 4 includes:
based on the reconstructed interference-plus-noise covariance matrix and the estimated steering vector of the desired signal, the weight vector of the beamformer is represented as:
Figure BDA0003419360900000118
wherein the content of the first and second substances,
Figure BDA0003419360900000119
representing the estimated desired signal steering vector.
Beamforming the data received by the array according to the weight vector:
y(k)＝wHx(k)
where y (k) denotes the output signal of the beamformer. Thereby achieving enhancement of the desired signal and suppression of interference and noise.
The performance curves of different methods with Signal-to-Noise Ratio (SNR) under 200 monte carlo experiments are given in fig. 3, where the direction of arrival error is subject to a uniform distribution over [ -4 °,4 ° ] under the condition of a dry-to-Noise Ratio of 20 dB. It can be seen from the figure that under the condition of relevant interference sources, the method provided by the invention can obtain obvious performance improvement, and the performance of the beam former close to the theoretical optimal performance is obtained, thus illustrating the effectiveness of the method provided by the invention. In addition, the method does not relate to the solution of any convex optimization problem, so that the calculation complexity is relatively low, and the method is more favorable for application in practice. The method of the invention is also applicable to adaptive beamforming of uncorrelated interference sources.
As shown in fig. 2, other array types may be used for the schematic diagram of the linear array signal receiving model provided in the embodiment of the present invention; the array consists of M omnidirectional microphones, wherein the rightmost side is a reference array element, the mth array element, M is 1,2, … and M-1, and the distance from the reference array element is dm. When a far-field narrow-band signal from an angle theta is incident on the array, the distance to the m-th array element is dmsin θ, will produce a certain time difference, reflected as a phase difference, to obtain the nominal steering vector according to the estimated angle and the array shape.
As shown in fig. 3, for the uniform linear array with M-10 array elements provided by the embodiment of the present invention, the array element spacing is half wavelength, and the desired signal comes from θ0At-5 °, the relevant interference source comes from θ1-40 ° and θ230 °, the matrix of correlation coefficients is Γ ═ g1,g2,g3]Wherein the correlation coefficient vectors are respectively g1＝[ejπ/3,0.5ejπ,0.5ejπ/9]T,g2＝[0.8ejπ/6,0.9ej6π/5,0.8ejπ/2]TAnd g3＝[0.6ejπ/4,0.4ejπ/5,0.1ej6π/5]TAnd there is an angle estimation error of 3 °. In the method of the invention, b is 0.01, eta is 10-3. The method of the invention is a deployed, and the comparison methods are respectively as follows: theoretical Optimal beam former (Optimal), covariance matrix reconstruction method (INCM-MEPS) based on maximum entropy spectrum, covariance matrix reconstruction algorithm (INCM-SPSS) based on spatial power spectrum sampling, robust adaptive beam forming method (INCM-subspace) based on subspace, and robust adaptive beam forming method (IN) based on projectionCM-projection), covariance matrix reconstruction method based on simple power estimation (INCM-SIPE), diagonal loading algorithm (LSMI) and worst-case performance optimization algorithm (WCB). Obey to-4 deg. and 4 deg. in the direction of arrival]The performance curve of different methods with Signal-to-Noise Ratio (SNR) in 200 Monte Carlo experiments.
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 (6)

1. A method for robust adaptive beamforming under correlated interference sources, comprising:
step 1, carrying out characteristic decomposition on a sampling covariance matrix of array received data, wherein a characteristic vector corresponding to an expected signal and an interference characteristic value is called a signal subspace, and a characteristic vector corresponding to a residual characteristic value is called a noise subspace; obtaining an estimated value of noise power according to the characteristic value corresponding to the noise subspace;
step 2, obtaining a spectrum value of a full space according to the orthogonality of the signal subspace and the noise subspace in the step 1, obtaining an initial angle of an expected signal and interference by performing spectrum peak search on the spectrum value, and obtaining a nominal guide vector corresponding to the initial angle according to a known array shape; projecting the nominal guide vectors of the expected signals and the interference to the noise subspace in the step 1 to obtain error vectors of the expected signals and the interference guide vectors;
step 3, updating and estimating the guide vectors of the expected signals and the interference according to a subspace orthogonality principle by using the nominal guide vectors and the error vectors of the expected signals and the interference in the step 2 to obtain estimated values of the expected signals and the interference guide vectors;
step 4, reconstructing an interference and noise covariance matrix according to the noise power estimation value in the step 1, the estimation values of the expected signal and the interference guide vector in the step 3 and the expected signal and the interference part in the sampling covariance matrix of the array receiving data to obtain a reconstructed interference and noise covariance matrix;
and 5, forming a beam for the array receiving data based on the expected signal guide vector estimated in the step 3 and the interference and noise covariance matrix reconstructed in the step 4.
2. The method of claim 1, wherein the method comprises: the step 1 is specifically realized as follows:
the sampling covariance matrix of the array received data is:
Figure FDA0003419360890000011
wherein x (K) represents data received by the array at time K, K represents fast beat number, and H represents conjugate transpose operation of matrix or vector;
and performing characteristic decomposition on the sampling covariance matrix to obtain:
Figure FDA0003419360890000012
wherein, M represents the number of array elements,
Figure FDA0003419360890000013
representing the eigenvalues in descending order,
Figure FDA0003419360890000014
a characteristic vector corresponding to the characteristic value;
Figure FDA0003419360890000021
a matrix of the feature vectors is represented,
Figure FDA0003419360890000022
representing a diagonal matrix composed of eigenvalues;
Figure FDA0003419360890000023
and representing the eigenvector matrix corresponding to the first L eigenvalues, and called signal subspace,
Figure FDA0003419360890000024
a diagonal matrix composed of the first L eigenvalues is represented, and L represents the number of expected signals and interference;
Figure FDA0003419360890000025
the eigenvector matrix corresponding to the remaining M-L eigenvalues, and referred to as the noise subspace,
Figure FDA0003419360890000026
and representing a diagonal matrix formed by the residual M-L eigenvalues, wherein according to the characteristic of the eigen decomposition, the residual M-L eigenvalues correspond to the power of the noise, and the estimated value of the noise power is represented as:
Figure FDA0003419360890000027
3. the method according to claim 1, wherein the step 2 comprises:
(21) according to the orthogonality of the signal subspace and the noise subspace in the step 1, obtaining a spectrum value of a total space as follows:
Figure FDA0003419360890000028
wherein the content of the first and second substances,
Figure FDA0003419360890000029
the nominal steering vector for the angle theta is represented and theta represents the full space. The initial angles of the expected signal and the interference obtained by performing the spectral peak search on the spectral values are respectively
Figure FDA00034193608900000210
And
Figure FDA00034193608900000211
obtaining a nominal steering vector corresponding to the initial angle based on the known array shape as
Figure FDA00034193608900000212
(22) Projecting the nominal guide vector of the desired signal and the interference to the noise subspace in the step 1 to obtain the error vector of the desired signal and the interference guide vector, wherein the error vector is as follows:
Figure FDA00034193608900000213
wherein | | | purple hair2Representing matrices or vectors
Figure FDA00034193608900000216
And (4) norm.
4. The method according to claim 1, wherein the estimated values of the desired signal and the interference steering vector in step 3 are:
Figure FDA00034193608900000214
wherein the content of the first and second substances,
Figure FDA00034193608900000215
birepresents the search interval [ -b, b [ -b]Where the ith value is spaced by η, b represents the upper bound of the search interval,
Figure FDA0003419360890000031
representing the total number of searches.
5. The method according to claim 1, wherein the interference-plus-noise covariance matrix reconstructed in step 4 is:
Figure FDA0003419360890000032
wherein the content of the first and second substances,
Figure FDA0003419360890000033
representing the estimated interference steering vector matrix,
Figure FDA0003419360890000034
and a power matrix representing the estimated interference, and I represents an identity diagonal matrix.
6. The method according to claim 1, wherein the beamforming in step 5 is performed on array received data based on the desired signal steering vector estimated in step 3 and the interference-plus-noise covariance matrix reconstructed in step 4, and comprises:
based on the reconstructed interference-plus-noise covariance matrix and the estimated steering vector of the desired signal, the weight vector of the beamformer is represented as:
Figure FDA0003419360890000035
wherein the content of the first and second substances,
Figure FDA0003419360890000036
representing the estimated desired signal steering vector;
beamforming the data received by the array according to the weight vector:
y(k)＝wHx(k)
where y (k) represents the output signal of the beamformer, achieving enhancement of the desired signal and suppression of interference and noise.
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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN114726385A (en) * 2022-04-21 2022-07-08 电子科技大学 Space domain anti-interference method of satellite navigation receiver based on power estimation

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN114726385A (en) * 2022-04-21 2022-07-08 电子科技大学 Space domain anti-interference method of satellite navigation receiver based on power estimation
CN114726385B (en) * 2022-04-21 2023-02-24 电子科技大学 Power estimation-based airspace anti-interference method for satellite navigation receiver

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