CN114647931A - Robust beam forming method based on desired signal elimination and spatial spectrum estimation - Google Patents

Robust beam forming method based on desired signal elimination and spatial spectrum estimation Download PDF

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CN114647931A
CN114647931A CN202210201803.8A CN202210201803A CN114647931A CN 114647931 A CN114647931 A CN 114647931A CN 202210201803 A CN202210201803 A CN 202210201803A CN 114647931 A CN114647931 A CN 114647931A
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曹菲
吕岩
许剑锋
冯晓伟
秦建强
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Rocket Force University of Engineering of PLA
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Abstract

The invention provides a robust beam forming method based on desired signal elimination and spatial spectrum estimation, which comprises the following steps: firstly, estimating DOA of a signal by using a MUSIC high-resolution spatial spectrum estimation algorithm. Then, the integral matrix of the area where the SOI is located is subjected to characteristic decomposition, and the SEM is constructed by utilizing the characteristic vectors corresponding to a plurality of larger characteristic values. The sampled covariance matrix is then projected onto the SEM to eliminate the effects of SOI and estimate the power of the interfering signal, thereby constructing INCM. The steering vectors of the SOI are optimized by solving a quadratic constraint quadratic programming problem. And finally, calculating the optimal weight vector of the array by using the reconstructed INCM and the estimated SOI guiding vector. The method has better robustness to errors such as the DOA error of the expected signal, the array element position disturbance error, the incoherent local scattering and the like, and has better comprehensive performance compared with a plurality of conventional typical robust beam forming methods.

Description

Robust beam forming method based on desired signal elimination and spatial spectrum estimation
Technical Field
The invention belongs to the technical field of array signal processing, relates to robust beam forming, and particularly relates to a robust beam forming method based on expected signal elimination and spatial spectrum estimation.
Background
Directional array antennas that form a beam pattern according to some optimal criterion are called smart antennas and are also considered adaptive array antennas. Smart antennas essentially mean that the computer can control the performance of the antenna, which greatly improves the performance of the array system. The adaptive array processing technique can adjust the weighting vector of the array antenna in real time according to the signal environment. It uses an adaptive algorithm to obtain a certain gain in the direction of a desired Signal (SOI) and suppress the interference signal in its direction, which is generally called adaptive beamforming.
However, adaptive beamforming algorithms are very sensitive to signal source errors and sensor errors, such as signal direction errors, sensor position perturbations, amplitude and phase errors, etc. Especially when SOI components are present in the data snapshot, the performance of the beamformer may be severely degraded. Therefore, there is a need to improve the robustness of beamforming in adaptive array processing.
A number of robust beamforming algorithms based on interference plus noise covariance matrix (INCM) reconstruction have been proposed so far, which can effectively remove SOI components in a sampling covariance matrix and output a signal to interference plus noise ratio (SINR) better under a high SNR condition.
The literature GU Y and LESHEM A. robust Adaptive Beamforming Based on Interference Covariance Matrix Reconstruction and engineering Vector Estimation [ J ]. IEEE Transactions on Signal Processing,2012,60(7):3881 and 3885. the INCM-line algorithm was proposed, which first reconstructs the INCM by combining the Capon spectral Estimation and the integral of the SOI angular sector separation region. The steering vectors of the SOI are then modified by solving a quadratic constraint quadratic programming problem.
The work in the literature ZHANG Z, LIU W, LENG W et al, interference plus Noise Covariance Matrix Reconstruction visual space Power Spectrum Sampling for Robust Beamforming [ J ]. IEEE Signal Processing Letters,2015,23(1): 121-.
The document ZHU X Y, YE Z F, XU X et al, covariane Matrix Reconstruction non Interference and Interference Powers Estimation for Robust Beamforming [ J ] IEEE Access,2019,7: 53262-. Although the performance of the algorithm is better than that of other algorithms, the algorithm has a large number of integration, matrix multiplication and matrix inversion operations, and the running time is increased.
The literature ZHENG Z, ZHENG Y, WANG W Q et al.covariant Matrix Reconstruction with Interference Vector and Power Estimation for Robust Adaptive Beamforming [ J ] IEEE Transactions on Vector Technology,2018,67(9):8495 and 8503 ] proposes the INCM-ISV algorithm, initially estimates the Interference signal Steering Vector by using a Capon Power spectrum, then corrects the Steering Vector by using an uncertainty set method, and reconstructs the INCM in a theoretical form. However, both of these methods neglect the resolution of Capon spectral estimates, which will not be effectively distinguishable when the interference signal angles are close, which will result in reconstruction errors.
Disclosure of Invention
Aiming at the defects in the prior art, the invention aims to provide a robust beam forming method based on desired signal elimination and spatial spectrum estimation, and aims to solve the technical problem of performance degradation of a beam former caused by errors of an array signal model and insufficient Capon spectrum estimation resolution.
In order to solve the technical problems, the invention adopts the following technical scheme:
a robust beamforming method based on desired signal cancellation and spatial spectrum estimation, the method comprising the steps of:
step 1, a uniform linear array composed of M isotropic array elements receives 1 desired signal and L interference signals from a far field, and a sampling covariance matrix obtained when K snapshots are received can be represented as:
Figure BDA0003529636490000031
in the formula:
Figure BDA0003529636490000032
representing a sampling covariance matrix;
x (k) represents the data received by the array at instant k;
(·)Hrepresenting a Hermitian transpose operation;
k represents the kth sampling fast beat number;
k represents the sampling fast beat number;
step 2, sampling covariance matrix
Figure BDA0003529636490000033
Decomposing the eigenvalue, determining the eigenvectors corresponding to M-L-1 smaller eigenvalues to form a noise subspace G according to the known number of the information sourcesNEstimating the DOA of the signal using the MUSIC algorithm;
Figure BDA0003529636490000034
in the formula:
Figure BDA0003529636490000035
a spatial spectrum representing the signal, the spectral peak positions representing the estimated DOA;
m represents the number of isotropic array elements;
l represents the number of interfering signals;
θ represents a scan angle;
GNrepresenting a noise subspace;
Figure BDA0003529636490000041
representing a steering vector determined from the scan angle θ and the known array structure;
Figure BDA0003529636490000042
can be expressed as
Figure BDA0003529636490000043
Figure BDA0003529636490000044
λ represents the incident signal wavelength;
d represents the array element spacing;
(·)Trepresenting a transpose operation;
step 3, calculating an expected signal angle region thetasIntegral of
Figure BDA0003529636490000045
Eigenvalue decomposition
Figure BDA0003529636490000046
Constructing an SEM;
Figure BDA0003529636490000047
U＝I-VVH
in the formula:
s represents the number of discrete sampling points;
s represents the s-th discrete sample point;
Figure BDA0003529636490000048
representing the angular region of the desired signal thetasIntegral of (1);
Θsrepresenting a desired signal angle region;
θsrepresents the scanning angle of the s discrete sampling point;
Figure BDA0003529636490000049
represents an angle thetasA steering vector of (a);
u represents SEM;
v is composed of
Figure BDA00035296364900000410
The feature vector corresponding to the larger feature value;
i represents an identity matrix;
step 4, estimating an interference signal covariance matrix by using the SEM, thereby eliminating the influence of the SOI;
Figure BDA0003529636490000051
in the formula:
Figure BDA0003529636490000052
representing an estimated interference signal covariance matrix;
Figure BDA0003529636490000053
is obtained from step 2
Figure BDA0003529636490000054
A minimum eigenvalue representing the estimated noise power;
(·)-1representing a matrix inversion operation;
step 5, estimating the power of the interference signal by using the estimated covariance matrix of the interference signal and the interference signal DOA obtained by the MUSIC algorithm;
Figure BDA0003529636490000055
Figure BDA0003529636490000056
reconstructed INCM can be:
Figure BDA0003529636490000057
in the formula:
Figure BDA0003529636490000058
a vector matrix is guided for interference;
Figure BDA0003529636490000059
an estimate representing the lth interference signal DOA;
Figure BDA00035296364900000510
indicating angle
Figure BDA00035296364900000511
A steering vector of (a);
diag {. is } represents the diagonal element operation of the matrix;
Figure BDA00035296364900000512
the diagonal elements of (a) represent the estimated interference signal power;
m represents the number of isotropic array elements;
l represents the number of interfering signals;
Figure BDA00035296364900000513
to representReconstructed INCM;
irepresenting an interference signature;
nrepresenting a noise signature;
step 6, solving a quadratic constraint quadratic programming problem to optimize an SOI (silicon on insulator) guide vector;
Figure BDA0003529636490000061
Figure BDA0003529636490000062
Figure BDA0003529636490000063
Figure BDA0003529636490000064
in the formula:
e⊥an error between a true steering vector and an estimated steering vector representing the SOI;
s.t. represents a constraint;
||·||2is Euclidean norm;
θ0DOA representing SOI;
Figure BDA0003529636490000065
denotes theta0A steering vector of (a);
Figure BDA0003529636490000066
representing the optimized SOI guide vector;
step 7, calculating an array optimal weight vector w by using the reconstructed INCM and the optimized SOI guide vector;
Figure BDA0003529636490000067
compared with the prior art, the invention has the following technical effects:
the method has better robustness to errors such as DOA (direction of arrival) errors of expected signals, array element position disturbance errors, incoherent local scattering and the like, and has better comprehensive performance compared with a plurality of conventional typical robust beam forming methods.
The method can reconstruct the interference-plus-noise covariance matrix more accurately and estimate the real expected signal guide vector, and different types of errors necessarily exist in the array in actual engineering application.
Drawings
FIG. 1 is a flow chart of an implementation of the present invention.
FIG. 2 is a graph showing the variation trend of output SINR with input SNR under DOA error conditions;
FIG. 3 is a diagram of the variation trend of output SINR with input SNR under the condition of array element position disturbance;
FIG. 4 is a graph showing the variation trend of output SINR with input SNR under the condition of incoherent local scattering;
fig. 5 is a graph showing the variation trend of SINR with fast beat numbers (snapshots) under the incoherent local scattering condition.
The present invention will be explained in further detail with reference to examples.
Detailed Description
The present invention provides a robust beamforming method based on desired signal cancellation and spatial spectrum estimation, as shown in fig. 1, the method includes:
first, a direction of arrival (DOA) of a Signal is estimated by using a Multiple Signal Classification (MUSIC) high-resolution spatial spectrum estimation algorithm.
Then, an integral matrix of the area where the SOI is located is subjected to characteristic decomposition, and an expected Signal Elimination Matrix (SEM) is constructed by utilizing eigenvectors corresponding to a plurality of larger eigenvalues.
The sampled covariance matrix is then projected onto the SEM to eliminate the effects of SOI and estimate the power of the interfering signal, thereby constructing INCM. The steering vectors of the SOI are optimized by solving a quadratic constraint quadratic programming problem.
And finally, calculating the optimal weight vector of the array by using the reconstructed INCM and the estimated SOI guiding vector.
It should be noted that all algorithms and methods of the present invention, unless otherwise specified, all employ those known in the art.
In the present invention, it is to be noted that:
MUSIC refers to multiple signal classification.
DOA refers to the direction of arrival.
SOI refers to the desired signal.
SEM refers to the desired signal cancellation matrix.
INCM refers to the interference plus noise covariance matrix.
SNR refers to the signal-to-noise ratio.
SINR refers to signal to interference plus noise ratio.
Hermitian transpose refers to a Hermitian transpose.
Euclidean norm refers to the Euclidean norm.
The INCM-linear method refers to a linear covariance matrix reconstruction method.
The INCM-ISV method refers to an interference-oriented vector estimation covariance matrix reconstruction method.
The INCM-SPSS method refers to a spatial power spectrum sampling covariance matrix reconstruction method.
The EIG method refers to a feature subspace method.
The INCM-RNE method refers to a residual noise cancellation covariance matrix reconstruction method.
The present invention is not limited to the following embodiments, and all equivalent changes based on the technical solutions of the present invention fall within the protection scope of the present invention.
Example (b):
the present embodiment provides a robust beamforming method based on desired signal cancellation and spatial spectrum estimation, which includes the following steps:
step 1, a uniform linear array composed of M isotropic array elements receives 1 desired signal and L interference signals from a far field, and a sampling covariance matrix obtained when K snapshots are received can be represented as:
Figure BDA0003529636490000091
in the formula:
Figure BDA0003529636490000092
representing a sampling covariance matrix;
x (k) represents the data received by the array at instant k;
(·)Hrepresenting a Hermitian transpose operation;
k represents the kth sampling fast beat number;
k represents the sampling fast beat number;
step 2, sampling covariance matrix
Figure BDA0003529636490000093
Decomposing the eigenvalue, determining the eigenvector corresponding to M-L-1 smaller eigenvalues to form a noise subspace G according to the known information source numberNEstimating the DOA of the signal using the MUSIC algorithm;
Figure BDA0003529636490000094
in the formula:
Figure BDA0003529636490000095
a spatial spectrum representing the signal, the spectral peak positions representing the estimated DOA;
m represents the number of isotropic array elements;
l represents the number of interference signals;
θ represents a scan angle;
GNrepresenting a noise subspace;
Figure BDA0003529636490000096
representing a steering vector determined from the scan angle θ and the known array structure;
Figure BDA0003529636490000097
can be expressed as
Figure BDA0003529636490000098
Figure BDA0003529636490000099
λ represents the incident signal wavelength;
d represents the array element spacing;
(·)Trepresenting a transpose operation;
step 3, calculating the angular region theta of the expected signalsIntegral of
Figure BDA0003529636490000101
Eigenvalue decomposition
Figure BDA0003529636490000102
Constructing an SEM;
Figure BDA0003529636490000103
U＝I-VVH
in the formula:
s represents the number of discrete sampling points;
s represents the s-th discrete sample point;
Figure BDA0003529636490000104
representing the angular region of the desired signal thetasIntegral of (2);
Θsrepresenting a desired signal angle region;
θsrepresents the scanning angle of the s discrete sampling point;
Figure BDA0003529636490000105
represents an angle thetasA steering vector of (a);
u represents SEM;
v is composed of
Figure BDA0003529636490000106
The feature vector corresponding to the larger feature value;
i represents an identity matrix;
step 4, estimating an interference signal covariance matrix by using the SEM, thereby eliminating the influence of the SOI;
Figure BDA0003529636490000107
in the formula:
Figure BDA0003529636490000108
representing an estimated interference signal covariance matrix;
Figure BDA0003529636490000109
is obtained from step 2
Figure BDA00035296364900001010
A minimum eigenvalue representing the estimated noise power;
(·)-1representing a matrix inversion operation;
step 5, estimating the power of the interference signal by using the estimated covariance matrix of the interference signal and the interference signal DOA obtained by the MUSIC algorithm;
Figure BDA0003529636490000111
Figure BDA0003529636490000112
reconstructed INCM can be:
Figure BDA0003529636490000113
in the formula:
Figure BDA0003529636490000114
a vector matrix is guided for interference;
Figure BDA0003529636490000115
an estimate representing the lth interference signal DOA;
Figure BDA0003529636490000116
indicating angle
Figure BDA0003529636490000117
The guide vector of (2);
diag {. is } represents the diagonal element operation of the matrix;
Figure BDA0003529636490000118
the diagonal elements of (a) represent the estimated interference signal power;
m represents the number of isotropic array elements;
l represents the number of interfering signals;
Figure BDA0003529636490000119
representing reconstructed INCM;
irepresenting an interference signature;
nrepresenting a noise signature;
step 6, solving a quadratic constraint quadratic programming problem to optimize an SOI (silicon on insulator) guide vector;
Figure BDA0003529636490000121
Figure BDA0003529636490000122
Figure BDA0003529636490000123
Figure BDA0003529636490000124
in the formula:
e⊥an error between a true steering vector and an estimated steering vector representing the SOI;
s.t. represents a constraint;
||·||2is Euclidean norm;
θ0DOA representing SOI;
Figure BDA0003529636490000125
denotes theta0A steering vector of (a);
Figure BDA0003529636490000126
representing the optimized SOI guide vector;
step 7, calculating an array optimal weight vector w by using the reconstructed INCM and the optimized SOI guide vector;
Figure BDA0003529636490000127
simulation example 1:
the simulation example provides a robust beam forming method based on the expected signal elimination and the spatial spectrum estimation based on the embodiment.
Simulation conditions are as follows:
the simulation is based on a uniform linear array with 10 array elements, the distance between the array elements is half wavelength of an incident signal, and the noise is additive Gaussian complex noise. 1 expected signal is positioned in the-5-degree direction, and the SOI interval is set to be thetas＝[-9°,-1°]The three interferers arrive at the array at 25dB power from-30 °, 24 ° and 28 °, respectively, and all results in the simulation experiment are the average of 100 monte carlo experiments.
To fully verify performance, the method of the present invention is compared to several typical methods available, such as: the INCM-linear method, the INCM-ISV method, the INCM-SPSS method, the EIG method and the INCM-RNE method were compared. The EIG method is implemented in LEE C and LEE J H. Eigenspace-based Adaptive Array beams with Robust Capabilities [ J ]. IEEE Transactions on Antennas and Propagation,1997,45(12):1711 and 1716.
Simulation content:
considering the effect of the desired signal DOA on the array, when the error between the DOA of all incident signals and the true DOA is randomly distributed in [ -4 °,4 ° ], and the sampling fast beat number K is 50.
Fig. 2 shows the output SINR versus SNR for all beamformers. When the SNR is high, the performance of the EIG is severely degraded. Because the INCM reconstructed by the method of the invention and the INCM-linear method contains all information of interference signals, the output SINR of two beam formers is higher than that of other methods, and the performance of the method of the invention is optimal.
Simulation example 2:
the simulation example provides a robust beam forming method based on the expected signal elimination and the spatial spectrum estimation based on the embodiment.
Simulation conditions are as follows:
the same as in simulation example 1.
Simulation content:
considering the influence of array element position disturbance errors on the array, the error of each array element is randomly distributed in the range of [ -0.02 lambda, 0.02 lambda ], and the sampling fast beat number K is 50.
Fig. 3 depicts the output SINR versus input SNR for all beamformers. It can be seen from the figure that the sensor position disturbance error has less influence on the present invention, and the SINR thereof is always at the highest position. In contrast, this error has a different degree of impact on other methods, where the performance degradation of INCM-linear is more severe.
Simulation example 3:
the simulation example provides a robust beam forming method based on the expected signal elimination and the spatial spectrum estimation based on the embodiment.
Simulation conditions are as follows:
the same as in simulation example 1.
Simulation content:
considering the effect of incoherent local scattering of the SOI on the array, the signal received by the array in this simulation is represented as:
Figure BDA0003529636490000141
in the formula:
xs(k) representing the SOI and scattered signals received by the array;
θ0DOA representing SOI;
θηrepresenting compliance with a Gaussian distribution N (θ)04 °) scattering angle;
a0(θ0) Denotes theta0A steering vector of (a);
aη(θη) Representing the scattering angle thetaηA steering vector of (a);
s0(k) represents SOI;
sη(k) represents a scattering signal, which is uniformly distributed in N (0, 1);
η represents the η -th scattering signal, η ═ 1,2,3, 4;
k represents the kth sampling fast beat number;
and sampling fast beat number K is 50.
It can be derived from fig. 4 that although the output SINR of the present invention is slightly lower than the INCM-linear method when the input SNR is greater than 20dB, under other SNR conditions the method of the present invention is better than the other methods and closer to the optimal SINR.
Simulation example 4:
the simulation example provides a robust beam forming method based on the expected signal elimination and the spatial spectrum estimation.
Simulation conditions are as follows:
the same as in simulation example 1.
Simulation content:
in accordance with the conditions of simulation example 3, the SNR was set to 10dB in the simulation in consideration of the influence of the snapshot number of the received data on the array output SINR.
As can be seen from fig. 5, when the number of snapshots is less than 20, the SINR output by the present invention has slight disturbance. However, as the number of snapshots increases, the present invention quickly reaches an optimum and the output SINR exceeds that of other beamformers.
In conclusion, the interference-plus-noise covariance matrix can be reconstructed more accurately and a real expected signal guide vector can be estimated, different types of errors necessarily exist in the array in actual engineering application, and the method has stronger beam forming robustness and higher engineering application value.

Claims (1)

1. A robust beamforming method based on desired signal cancellation and spatial spectrum estimation, the method comprising the steps of:
step 1, a uniform linear array composed of M isotropic array elements receives 1 desired signal and L interference signals from a far field, and a sampling covariance matrix obtained when K snapshots are received can be represented as:
Figure FDA0003529636480000011
in the formula:
Figure FDA0003529636480000012
representing a sampling covariance matrix;
x (k) represents the data received by the array at instant k;
(·)Hrepresenting a Hermitian transpose operation;
k represents the k-th sampling fast beat number;
k represents the sampling fast beat number;
step 2, sampling covariance matrix
Figure FDA0003529636480000013
Decomposing the eigenvalue, determining the eigenvectors corresponding to M-L-1 smaller eigenvalues to form a noise subspace G according to the known number of the information sourcesNEstimating the DOA of the signal using the MUSIC algorithm;
Figure FDA0003529636480000014
in the formula:
Figure FDA0003529636480000015
a spatial spectrum representing the signal, the spectral peak positions representing the estimated DOA;
m represents the number of isotropic array elements;
l represents the number of interfering signals;
θ represents a scan angle;
GNrepresenting a noise subspace;
Figure FDA0003529636480000021
representing the angle according to the scan theta and knownA steering vector determined by the array structure;
Figure FDA0003529636480000022
can be expressed as
Figure FDA0003529636480000023
Figure FDA0003529636480000024
λ represents the incident signal wavelength;
d represents the array element spacing;
(·)Trepresenting a transpose operation;
step 3, calculating an expected signal angle region thetasIntegral of
Figure FDA0003529636480000025
Eigenvalue decomposition
Figure FDA0003529636480000026
Constructing an SEM;
Figure FDA0003529636480000027
U＝I-VVH
in the formula:
s represents the number of discrete sampling points;
s represents the s-th discrete sample point;
Figure FDA0003529636480000028
representing the angular region of the desired signal thetasIntegral of (1);
Θsrepresenting a desired signal angle region;
θsrepresents the scan angle of the s-th discrete sample point;
Figure FDA0003529636480000029
represents an angle thetasA steering vector of (a);
u represents SEM;
v is composed of
Figure FDA00035296364800000210
The feature vector corresponding to the larger feature value;
i represents an identity matrix;
step 4, estimating an interference signal covariance matrix by using the SEM, thereby eliminating the influence of the SOI;
Figure FDA00035296364800000211
in the formula:
Figure FDA0003529636480000031
representing an estimated interference signal covariance matrix;
Figure FDA0003529636480000032
is obtained from step 2
Figure FDA0003529636480000033
A minimum eigenvalue representing the estimated noise power;
(·)-1representing a matrix inversion operation;
step 5, estimating the power of the interference signal by using the estimated covariance matrix of the interference signal and the interference signal DOA obtained by the MUSIC algorithm;
Figure FDA0003529636480000034
Figure FDA0003529636480000035
reconstructed INCM can be:
Figure FDA0003529636480000036
in the formula:
Figure FDA0003529636480000037
a vector matrix is guided for interference;
Figure FDA0003529636480000038
an estimate representing the lth interference signal DOA;
Figure FDA0003529636480000039
indicating an angle
Figure FDA00035296364800000310
A steering vector of (a);
diag {. is } represents the diagonal element operation of the matrix;
Figure FDA00035296364800000311
the diagonal elements of (a) represent the estimated interference signal power;
m represents the number of isotropic array elements;
l represents the number of interfering signals;
Figure FDA00035296364800000312
representing reconstructed INCM;
i represents an interference indicator;
n represents a noise signature;
step 6, solving a quadratic constraint quadratic programming problem to optimize an SOI (silicon on insulator) guide vector;
Figure FDA0003529636480000041
Figure FDA0003529636480000042
Figure FDA0003529636480000043
Figure FDA0003529636480000044
in the formula:
e⊥an error between a true steering vector and an estimated steering vector representing the SOI;
s.t. represents a constraint;
||·||2is Euclidean norm;
θ0DOA representing SOI;
Figure FDA0003529636480000045
denotes theta0The guide vector of (2);
Figure FDA0003529636480000046
representing the optimized SOI guide vector;
step 7, calculating an array optimal weight vector w by using the reconstructed INCM and the optimized SOI guide vector;
Figure FDA0003529636480000047
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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN114994595A (en) * 2022-08-03 2022-09-02 四川太赫兹通信有限公司 Direction-of-arrival acquisition method, terahertz phased array beam control method and system

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN114994595A (en) * 2022-08-03 2022-09-02 四川太赫兹通信有限公司 Direction-of-arrival acquisition method, terahertz phased array beam control method and system

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