CN112668155A - Steady beam forming method and system based on secondary reconstruction - Google Patents

Steady beam forming method and system based on secondary reconstruction Download PDF

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CN112668155A
CN112668155A CN202011468017.1A CN202011468017A CN112668155A CN 112668155 A CN112668155 A CN 112668155A CN 202011468017 A CN202011468017 A CN 202011468017A CN 112668155 A CN112668155 A CN 112668155A
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covariance matrix
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CN112668155B (en
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巩朋成
王兆彬
邓薇
潘懋舜
贺章擎
李婕
李利荣
刘聪
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Hubei University of Technology
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Abstract

The invention discloses a method and a system for forming a steady beam based on secondary reconstruction, wherein the method comprises the following steps: s1: constructing a first projection operator; s2: constructing an interference covariance matrix for the first time by using a first projection operator; s3: secondarily reconstructing an interference covariance matrix by utilizing Capon power spectral density integral; s4: reconstructing an interference plus noise covariance matrix; s5: constructing a second projection operator; s6: reconstructing an expected covariance matrix; s7: obtaining an optimal weight vector based on the optimal guide vector; s8: and carrying out weighted summation on the received signals by using the optimal weight vector to form a steady beam. The method carries out steady processing on the self-adaptive beam forming based on the interference covariance matrix of secondary reconstruction, greatly improves the anti-interference performance, the anti-steering vector angle mismatch performance and the interference suppression capacity under the conditions of different input SNR, different fast beat numbers and steering vector mismatch, and can reduce the generation of main lobe deviation and 'self-cancellation'.

Description

Steady beam forming method and system based on secondary reconstruction
Technical Field
The invention belongs to the technical field of array signal processing, and particularly relates to a method and a system for forming a steady beam based on secondary reconstruction.
Background
The adaptive beamforming technology is widely applied to aviation, aerospace, radar and communication systems, and improves the output Signal to interference and Noise Ratio (SINR) by forming gain and null in the target direction. However, in an actual working environment, array element position errors, channel amplitude phase errors and the like exist, so that target steering vector constraints have deviations. Theoretical research shows that when a target guide vector has constraint deviation, under the condition of low Signal-to-Noise Ratio (SNR), problems such as main lobe deviation and the like can occur, and the output SINR is reduced; in the case of high SNR, if the received data includes a target signal, a target "self-cancellation" phenomenon may occur, and the output SINR may be rapidly deteriorated. Therefore, it becomes important to robustly process the adaptive beamforming method.
The present covariance matrix reconstruction study mainly includes three aspects: 1) quickly eliminating the component of an expected signal in a signal covariance matrix by using an equivalent signal subspace theory, and designing an interference covariance matrix reconstructed for the first time; 2) integrating within an interference signal angle range by using a Capon power spectral density function, and designing an interference covariance matrix of secondary reconstruction; 3) and reconstructing an expected signal covariance matrix by using an equivalent signal subspace theory, and further estimating an optimal guide vector. Considering the error of the target steering vector, the calculation of the weight vector of the beam former by using the sampling covariance matrix containing the target is the root cause of the target self-cancellation phenomenon, so the invention improves the performance of the beam former by estimating the interference and noise covariance matrix without the target.
Disclosure of Invention
The invention aims to provide a method and a system for forming a stable beam based on secondary reconstruction aiming at the situation of target steering vector mismatch.
The idea of the invention is as follows:
and reconstructing a covariance matrix of interference components in the array receiving signals aiming at the problem of array mismatch in the self-adaptive beam forming method. Firstly, reconstruction is carried out by combining a projection operator and an equivalent signal subspace theory, and secondary reconstruction is carried out by combining Capon power spectrum integration. And then, reconstructing the covariance matrix of the expected component in the array signal by using the equivalent signal subspace theory again to obtain an estimated guide vector, and obtaining a weight vector by using the interference covariance matrix of the secondary reconstruction and the estimated guide vector, so that the weight vector is adaptive and the system has better robustness.
The technical scheme of the invention is as follows:
a robust beam forming method based on secondary reconstruction comprises the following steps:
s1: constructing a first projection operator P1＝Y1Y1 H，Y1＝[y1,y2,...,yL]The subspace formed by the guide vectors in the undesired direction is the same as the subspace formed by the guide vectors in the undesired direction, and the guide vectors in different directions are mutually orthogonal;
s2: first constructing an interference covariance matrix
Figure BDA0002835162500000021
Wherein K represents the total number of snapshots, Xi(k) Representing interference received by the kth snapshot arraySignal, Xn(k) Representing the noise signal received by the kth snapshot array;
s3: quadratic reconstruction of interference covariance matrix using Capon power spectral density integrals
Figure BDA0002835162500000022
Wherein, thetaiRepresenting an interference angle sector, a (theta) representing an array steering vector, and theta being an interference signal incident angle;
s4: reconstructing interference-plus-noise covariance matrix
Figure BDA0002835162500000023
Wherein I is an identity matrix;
Figure BDA0002835162500000024
to be composed of
Figure BDA0002835162500000025
Performing characteristic decomposition to obtain the minimum value of all characteristic values, and taking the minimum value as noise power;
s5: constructing a second projection operator
Figure BDA0002835162500000026
U1＝[u1,u2,…,uP]A subspace spanned by the alternative desired signal steering vectors;
s6: reconstructing an expected covariance matrix
Figure BDA0002835162500000027
Wherein, Xs(k) Desired signal, X, received for the kth snapshot arrayi(k) Interference signals received for the kth snapshot array, Xn(k) A noise signal received for the kth snapshot array; estimating an optimal steering vector from a reconstructed expected covariance matrix
Figure BDA0002835162500000028
S7: based on optimal steering vector
Figure BDA0002835162500000029
Obtaining the optimal weight vector
Figure BDA00028351625000000210
S8: and carrying out weighted summation on the received signals by using the optimal weight vector to form a steady beam.
Further, in step S1, the first projection operator P1The construction method specifically comprises the following steps:
to sampling covariance matrix
Figure BDA00028351625000000211
Performing characteristic decomposition to obtain a signal subspace USAnd noise subspace UN；
Since the signal steering vector is orthogonal to the noise subspace, AH·UNIs equal to 0, so
Figure BDA00028351625000000212
A represents a steering vector matrix, and A ═ a (θ)0),a(θ1),...,a(θP)]TA (theta) in the steering vector matrix0) Representing a desired signal steering vector, and the rest are interference signal steering vectors;
will USIs marked as US＝[u0,u1,...,uP]With span { a (θ)0),a(θ1),...，a(θP)}＝span{u0,u1,...,uP}；
Combining with the equivalent signal subspace theory, searching the angular sector where each signal is located by using the low-resolution power spectrum, and dividing the whole area theta into two complementary signal angular sectors thetaIAnd non-signal angle sectors
Figure BDA0002835162500000031
Let thetaSAnd ΘiRespectively, a desired signal angle sector and an interference angle sector, and thetaI＝Θs+Θi；
Defining a correlation matrix
Figure BDA0002835162500000032
And to QiCharacteristic decomposition to obtain Qi＝YΣYHΣ and Y are a diagonal matrix and a unitary matrix, respectively, Σ ═ diag [ γ [ [ γ ])1,γ2,...,γM]，Y＝[y1,y2,...,yM]；
Let Y1＝[y1,y2,...,yL]，Y1Middle column vector and a (theta)0) Are orthogonal and guarantee Y1Y1 HNot equal to I, order P1＝Y1Y1 HWherein L is selected as an empirical value.
Further, L is preferably 5.
Further, in step S6, an optimal guide vector is estimated
Figure BDA0002835162500000033
The method specifically comprises the following steps:
to pair
Figure BDA0002835162500000034
Performing feature decomposition to obtain maximum value U of feature vectormaxThen the optimal steering vector
Figure BDA0002835162500000035
M denotes the number of array elements.
A robust beamforming system based on quadratic reconstruction, comprising:
a first module for constructing a first projection operator P1＝Y1Y1 H，Y1＝[y1,y2,...,yL]The subspace formed by the guide vectors in the undesired direction is the same as the subspace formed by the guide vectors in the undesired direction, and the guide vectors in different directions are mutually orthogonal;
a second module for constructing an interference covariance matrix for a first time
Figure BDA0002835162500000036
Wherein K represents the total number of snapshots, Xi(k) Watch (A)Showing the interference signal, X, received by the kth snapshot arrayn(k) Representing the noise signal received by the kth snapshot array;
a third module for reconstructing an interference covariance matrix using Capon power spectral density integral quadratic
Figure BDA0002835162500000037
Wherein, thetaiRepresenting an interference angle sector, a (theta) representing an array steering vector, and theta being an interference signal incident angle;
a fourth module for reconstructing an interference plus noise covariance matrix
Figure BDA0002835162500000038
Wherein I is an identity matrix;
Figure BDA0002835162500000039
to be composed of
Figure BDA00028351625000000310
Performing characteristic decomposition to obtain the minimum value of all characteristic values, and taking the minimum value as noise power;
a fifth module for constructing a second projection operator
Figure BDA00028351625000000311
U1＝[u1,u2,…,uP]A subspace spanned by the alternative desired signal steering vectors;
a sixth module for reconstructing the expected covariance matrix
Figure BDA0002835162500000041
Wherein, Xs(k) Desired signal, X, received for the kth snapshot arrayi(k) Interference signals received for the kth snapshot array, Xn(k) A noise signal received for the kth snapshot array; estimating an optimal steering vector from a reconstructed expected covariance matrix
Figure BDA0002835162500000042
A seventh module for determining a best steering vector based on the optimal steering vector
Figure BDA0002835162500000043
Obtaining the optimal weight vector
Figure BDA0002835162500000044
And the eighth module is used for performing weighted summation on the received signals by using the optimal weight vector to form the robust beam.
The invention has the following advantages and beneficial effects:
the method carries out steady processing on the self-adaptive beam forming based on the interference covariance matrix of secondary reconstruction, greatly improves the anti-interference performance, the anti-steering vector angle mismatch performance and the interference suppression capacity under the conditions of different input SNR, different fast beat numbers and steering vector mismatch, and can reduce the generation of main lobe deviation and 'self-cancellation'.
Drawings
FIG. 1 is a flow chart of the method of the present invention;
FIG. 2 is a beam pattern of different methods under different SNR in simulation experiment, wherein the patterns (a) and (b) are the beam patterns with SNR of 20dB and 5dB, respectively;
fig. 3 is a relationship diagram of input SNR and output SINR of different methods in a simulation experiment, where diagrams (a) and (b) are a relationship diagram under the condition of presence of pilot vector mismatch and under the condition of absence of pilot vector mismatch, respectively;
fig. 4 is a diagram of the relationship between the output SINR of different methods and the snapshot number in a simulation experiment, where diagrams (a) and (b) are respectively a diagram of the relationship when the snapshot number is lower than 50 and the snapshot number is higher than 50;
FIG. 5 is a comparison graph of the mismatching of the angle of the steering resistant vector of different methods in the simulation experiment.
Detailed Description
The following detailed description is given of relevant theories upon which the invention is based and specific implementations such that advantages and features of the invention may be more readily understood by those skilled in the art, and the scope of the invention is more clearly and clearly defined.
The reference signs referred to herein are: (.)HRepresents a conjugate transpose operation, (.)TRepresenting a transpose operation, E {. is the desired operation.
(I) Signal model construction
The array receiving signal model is an equidistant linear array, the array element distance d (d is 0.5 lambda), and lambda is the signal wavelength, and the array receiving signal model is composed of M omnidirectional array elements. Considering that the distance between the narrow-band signal source and the receiving array is far, the included angle between the incident direction of each signal and each array element on the linear array is basically consistent. Assuming that P signals are incident on the array in the signal space, the set of signal incident angles is denoted as { θlWhere l denotes a signal number, θ, 0,1, 2, …, P }, where l denotes a signal numberlIs the angle of incidence of the l-th signal.
The k-th snapshot of the array then receives the signal:
X(k)＝As(k)+n(k) (1)
in formula (1):
x (k) represents a received signal vector of M × 1 dimensions;
a represents a steering vector matrix of M × (P +1) dimensions, and A ═ a (θ)0),a(θ1),...,a(θP)]TA (theta) in the steering vector matrix0) Representing a desired signal steering vector, and the rest are interference signal steering vectors;
s (k) denotes a signal source vector, s (k) s0(k),s1(k),…,sN(k)]T，si(k) Is the complex envelope of the ith signal, i is 0,1 … N, N is the total number of desired and interfering signals, and N is a positive integer;
n (k) represents complex white gaussian noise which is uncorrelated with the incident signal.
Then the covariance matrix R of the array received signal is expressed as follows:
Figure BDA0002835162500000051
in formula (2):
Rspresentation periodThe covariance matrix of the desired signal is then determined,
Figure BDA0002835162500000052
Ri+nrepresenting the interference-plus-noise covariance matrix,
Figure BDA0002835162500000053
i is an M-dimensional identity matrix;
a(θ0) Which represents the steering vector of the desired signal,
Figure BDA0002835162500000054
representing the power of the desired signal;
ala steering vector representing the l-th interfering signal,
Figure BDA0002835162500000055
represents the power of the i-th interfering signal,
Figure BDA0002835162500000056
sl(k) indicating the ith interference signal in the kth snapshot, wherein L is not equal to 0, and L indicates the number of the interference signals;
Figure BDA0002835162500000057
representing the power of white noise.
And performing weighted summation on signals received by each array element at the time t to obtain the output of the beam former, wherein a Capon optimal weight vector w is generally adopted:
Figure BDA0002835162500000058
in formula (3): r is a sampling covariance matrix of the array received signal, a (theta)0) Representing the desired signal steering vector.
However, in practice, the ideal covariance matrix R and the error-free desired signal steering vector a (θ)0) Are difficult to obtain, so when calculating the weight vector w, the sampling covariance is neededMatrix array
Figure BDA0002835162500000061
And a nominal desired signal steering vector
Figure BDA0002835162500000062
If the substitution is made, equation (3) is rewritten as follows:
Figure BDA0002835162500000063
in the formula (4), the reaction mixture is,
Figure BDA0002835162500000064
k is the number of sampled snapshots, x (K) represents the array received signal for the kth snapshot.
(II) equivalent signal subspace
Assuming that there is no noise in the space, the array received signal model shown in equation (1) can be rewritten as follows:
X(k)＝As(k) (5)
Figure BDA0002835162500000065
x (k) is a steering vector matrix a ═ a (θ)0),a(θ1),...，a(θP)]TThe linear combination of (1) and (k) belongs to the steering vector (a (θ) as known from the linear algebraic theory0),a(θ1),...，a(θP) ) a spanned subspace.
Namely:
Figure BDA0002835162500000066
in the formula (7), C is a complex field, span is an expansion space in linear algebra, and betajAre complex coefficients in a linear combination.
The set of linear representations of the steering vectors described above is referred to as the signal subspace.
In noisy environments, x (k) can be expressed as the sum of its own projections in the signal subspace and the noise subspace, known from subspace projection theory, i.e.:
X(k)＝PSAs(k)+PNAs(k) (8)
in formula (8):
PSrepresenting signal subspace projection operators, PNRepresents a noise subspace projection operator, and
Figure BDA0002835162500000067
PS+PN＝I。
by pairs
Figure BDA0002835162500000068
Feature decomposition to obtain USAnd UN，USAnd UNRespectively a signal subspace and a noise subspace.
Since the signal steering vector is orthogonal to the noise subspace, the projection of the signal in the noise subspace is zero. Namely has AH·U N0, the formula (8) has:
X(k)＝PSAs(k) (9)
Figure BDA0002835162500000071
will USIs marked as US＝[u0,u1,...,uP]Then, equation (10) becomes:
X(k)＝〈u0,As(k)>u0+<u1,As(k)>u1+...+<uP,As(k)>uP (11)
in the formula (11), the reaction mixture is,<·>representing the inner product of the vector, i.e. As (k) at u0、u1、……uPRandom projection of (a).
As can be seen from the above formula, X (k) can be represented by u0,u1,...,uPThe linear representation, namely:
Figure BDA0002835162500000072
from the formulas (7) and (12), span { a (θ) }0),a(θ1),...，a(θP)}＝span{u0,u1,...,uPThus they are uniform spaces.
Combining with the equivalent signal subspace theory, the low-resolution power spectrum search can be utilized to obtain the approximate azimuth angle sector where each signal is located, and the whole area theta is divided into two complementary signal angle sectors thetaIAnd non-signal angle sectors
Figure BDA0002835162500000073
Namely, it is
Figure BDA0002835162500000074
Figure BDA0002835162500000075
Let thetaSAnd ΘiRespectively, a desired signal angle sector and an interference angle sector, and thetaI＝Θs+Θi。
Defining a correlation matrix QiThe matrix is used to describe the dependence of the steering vector on angle:
Figure BDA0002835162500000076
in formula (13):
θ represents an incident angle; thetaiRepresents an interference angular sector, i.e. an angular sector containing an interfering signal; a (θ) represents the nominal array steering vector.
Can know QiIncluding spatial information of the interference region. Will QiCharacteristic decomposition to obtain Qi＝YΣYHWhere Σ and Y are a diagonal matrix and a unitary matrix, respectively, and Σ ═ diag [ γ [ [ γ ])1,γ2,...,γM]，Y＝[y1,y2,...,yM]. Known from the equivalent signal subspace theory, span { y }1,y2,...,yM}＝span{a(θ1),a(θ2),...，a(θP) Y is the same with the subspace spanned by the guide vectors in the undesired direction, and is orthogonal to the guide vectors in different directions, so that Y is1＝[y1,y2,...,yL]Is known to be Y1Column vector of (2) and a (θ)0) Is orthogonal to, let P1＝Y1Y1 HI.e. projection operator, can be used to reconstruct the covariance matrix of the interference signal, having:
Figure BDA0002835162500000078
Figure BDA0002835162500000079
thus, P can be utilized1Only the desired signal in the received signal is rejected and the interfering signal is retained. P in formula (14)1 Ha(θ0) Proximity to zero, depending on ai(theta) and subspace Y1Depending on the choice of L, L is generally chosen to ensure Y1Y1 HNot equal to I. The simulation experiment of the invention selects L-5 according to experience.
Removing desired signal components from snapshots of the received signal to arrive at a reconstructed array received signal
Figure BDA0002835162500000077
The purpose of (1) is as follows:
Figure BDA0002835162500000081
wherein, Xs(k) The desired signal received for the array.
First constructing an interference covariance matrix
Figure BDA0002835162500000082
Figure BDA0002835162500000083
In formulae (16) to (17):
k represents the sampling fast beat number, and the larger K is, the higher the output SINR is;
Xi(k) an interference signal received for the array;
Xn(k) is the noise signal received by the array.
Capon power spectrum P (θ) is expressed as:
Figure BDA0002835162500000084
because of the sampling covariance matrix
Figure BDA0002835162500000085
The desired signal is contained so there is an error in the covariance matrix reconstructed using the power spectrum. To reduce errors, the present invention utilizes an interference covariance matrix that rejects the desired signal
Figure BDA0002835162500000086
Instead of the covariance matrix of the power spectral density function, the interval of the interfering signal is integrated.
By utilizing Capon power spectral density integral, secondary reconstruction is more accurate interference covariance matrix
Figure BDA0002835162500000087
The following were used:
Figure BDA0002835162500000088
in formula (17): thetaiThe sector of the interference angle is represented,
Figure BDA0002835162500000089
representing integralsThe resulting interference covariance matrix, i.e., the quadratic reconstructed interference covariance matrix.
Constructing a reconstructed interference plus noise covariance matrix
Figure BDA00028351625000000810
Wherein the content of the first and second substances,
Figure BDA00028351625000000811
to be composed of
Figure BDA00028351625000000813
And the minimum value of all characteristic values obtained by characteristic decomposition is used as the noise power.
The angular sector theta in which the desired signal is located is takenS＝[θ0-Δθ,θ0+Δθ]，
Figure BDA00028351625000000814
Δ θ is the width of the interval containing the desired signal. Constructing a steering vector correlation matrix Q containing the desired signal using the interval and the array steering vectorSIt is clear that it contains a significant fraction of the desired signal components, and that the interval is assumed to be free of interfering components. Then the matrix Q isSThe definition is as follows:
Figure BDA0002835162500000091
in the formula (18), the reaction mixture,
Figure BDA0002835162500000092
representing the true desired signal, theta0Representing the desired signal. To facilitate the actual calculation, let Θ beSThe interval is divided into J sampling points, and a (theta) is calculated for each sampling pointj)aH(θj) J is 1, 2, …, J, and these values are added up to obtain the matrix QSAn approximation of (d).
Will QSPerforming characteristic decomposition to obtain QS＝UΣUHWherein U and Σ are respectively a unitary matrix and a diagonal matrixArray, U ═ U [ U ]1,u2,...,uM]，Σ＝diag[γ1,γ2,...,γM]. The diagonal element in sigma is QSAnd satisfies the characteristic value of gamma1≥γ2≥…≥γMIs more than or equal to 0. And the column vector in U is QSThe feature vectors of (a) are in one-to-one correspondence with diagonal elements in Σ.
Is provided with a U1＝[u1,u2,...,uP]P represents the number of incident signals, P is less than or equal to M, and the first P eigenvectors in U are selected to form U1. According to the equivalent signal subspace theory:
span{u1,u2,...,uP}＝span{a(θ1),a(θ2),...，a(θP)} (21)
let U1Instead of the subspace spanned by the desired steering vectors, a (θ)0) And a (theta)i) The orthogonality is satisfied, and the guide vector a (theta) is obviously interferedi) In subspace U1Is zero, a projection operator is constructed
Figure BDA0002835162500000093
U1＝[u1,u2,…,uP]Instead of the subspace spanned by the desired steering vector, the steering vector a is clearly disturbedi(theta) in subspace U1Is zero. Can utilize PSOnly the interference signals in the received signals are removed and the desired signals are retained.
Reconstructing an expected covariance matrix
Figure BDA0002835162500000094
Figure BDA0002835162500000095
Due to the fact that
Figure BDA0002835162500000096
The value is small, can be ignored,
Figure BDA0002835162500000097
i.e. the reconstructed desired signal covariance matrix.
Due to the fact that
Figure BDA0002835162500000098
Without interference components, the desired signal steering vector may be formed from
Figure BDA0002835162500000099
Is estimated for the feature vector of
Figure BDA00028351625000000910
Performing characteristic decomposition:
Figure BDA00028351625000000911
wherein U iss＝[us1,us2,…,usM]Each column is
Figure BDA00028351625000000912
Is the diagonal element in Σ of
Figure BDA00028351625000000913
And in descending order and with UsAre in one-to-one correspondence. Let Umax＝Us1Then the estimated desired signal steering vector a (θ) may be given by:
a(θ)＝Umax (23)
in general, the steering vector satisfies the following equation in practical applications:
a(θ)aH(θ)＝M (24)
then the estimated desired steering vector is:
Figure BDA0002835162500000101
according to the above solution thought, the following provides the specific steps of the robust beamforming method based on the quadratic reconstruction of the present invention:
s1: constructing projection operator P1＝Y1Y1 H，Y1＝[y1,y2,…,yL]The same subspace spanned by the guide vectors in the undesired directions, orthogonal to the guide vectors in different directions, is formed by P1The desired signal in the received signal is rejected and the interfering signal is retained.
S2: using projection operator P1And equation (16) first reconstructs the interference covariance matrix (see equation (17))
Figure BDA0002835162500000102
S3: using the interference covariance matrix reconstructed at step S2 and the Capon power spectrum (see equation (18)), the interference covariance matrix is reconstructed quadratic by integrating the Capon power spectral density (see equation (19)).
S4: constructing a reconstructed interference plus noise covariance matrix
Figure BDA0002835162500000103
Figure BDA0002835162500000104
To be composed of
Figure BDA0002835162500000105
And the minimum value of all characteristic values obtained by characteristic decomposition is used as the noise power.
S5: construction signal subspace projection operator
Figure BDA0002835162500000106
U1Instead of the subspace spanned by the desired steering vector, the steering vector a is clearly disturbedi(theta) in subspace U1Is zero, using PSThe interference signals in the received signal are removed and the desired signal is retained.
S6: deriving weights using signal subspace projection operatorsThe desired covariance matrix of the structure (see equation (22)); obtaining the optimal steering vector using equations (24) and (25)
Figure BDA0002835162500000107
(see formula (26)).
S7: based on optimal steering vector
Figure BDA0002835162500000108
Obtaining the optimal weight vector
Figure BDA0002835162500000109
S8: and carrying out weighted summation on the received signals by using the optimal weight vector to form a steady beam.
(III) simulation experiment
In order to examine the comprehensive performance of the method, the method (abbreviated as PROPOSE) is compared with the following prior methods to carry out simulation tests: diagonal loading (abbreviated as DL), eigen subspace-based beamforming (abbreviated as EIG), a steering vector correction method (abbreviated as RCBD), covariance matrix reconstruction (abbreviated as INCR) and optimal conditions (abbreviated as OPT). In the simulation experiment, an array receiving signal model is set as a linear array with the distance d between adjacent array elements being lambda/2, wherein lambda is the wavelength of a signal; the array element number M is 10. The noise vector is set to obey N (0, 1)2) A gaussian distribution of (a). The signals have no influence on each other, and the signals and the noise are independent. In addition, in order to reduce the test error, the experiment is repeated 100 times under the condition of ensuring that each experiment is independent, and the experimental result is the average value of the addition of the experimental values of 100 times.
Referring to fig. 2, there is shown a comparison of the beam patterns of the different methods at different SNRs (signal-to-noise ratios), from which the depth of the interference nulls can be seen. The simulation parameters are set as follows: desired signal angle of incidence θsThe input SNR is 5dB and 20dB respectively at 0 °, the sampling fast beat number K is 200, the incident angles of the two Interference signals are-40 ° and 50 °, and the Interference and Noise ratios INR (INR) are both 30 dB. Expected signal distribution interval ΘS＝[θs-5°,θs+5°]Air dryingThe distribution interval of the interference signal is theta1＝[θ1-5°,θ1+5°]，Θ2＝[θ2-5°,θ2+5°]。
Fig. 2(a) shows the beam pattern of each method when the input SNR is 20dB, and it can be seen that the main lobe beams of the present invention, the EIG method and the RCBD method can be directed to the real desired signal direction, but the present invention has high interference rejection capability close to that of the DL method. Since the EIG method and the RCBD method are algorithms based on signal subspaces, when a desired signal is strong, the interference suppression capability is weak. The main lobe beam pointing direction of the INCR method still has small error with the real direction, while the DL method can accurately form deep null at the interference position, but the main lobe pointing direction has large deviation with the real expected signal direction, which indicates that the expected signal is partially suppressed.
Fig. 2(b) shows the beam patterns of the respective methods when the input SNR is 5dB, and it can be seen from this that the beam shapes of the present invention and the INCR method and the DL method are basically unchanged, but the nulls of the EIG method and the RCBD method are deepened, which shows that the present invention and the INCR method and the DL method have strong interference rejection capability under the condition of low signal-to-noise ratio.
Fig. 3 is a diagram showing a relationship between an input SNR and an output SINR of each method in a simulation experiment, where (a) is a diagram showing a relationship when a pilot vector mismatch exists, and (b) is a diagram showing a relationship when a pilot vector mismatch does not exist.
Referring to fig. 3(a), the EIG, DL, RCBD methods do not rise any more in high SNR situations because the covariance matrix contains the desired components. Fig. 3(b)) shows that the output SINR of the RCBD method is lower than other methods under the condition that the input SNR is lower when the presence of steering vector mismatch is considered, because the desired signal steering vector estimation is not accurate enough. When the input SNR is higher, the output SINR of the invention and the INCR method is higher, and the method of the invention is even slightly higher than the INCR method, because the INCR constructed by the invention is more accurate, and the output SINR of the DL and EIG methods is obviously reduced.
Fig. 4 is a graph of the output SINR of each method in a simulation experiment as a function of the fast beat number, where graphs (a) and (b) respectively correspond to two cases, i.e., the fast beat number K is lower than 50 and the fast beat number K is higher than 50.
It can be seen from fig. 4(a) that when the snapshot number is lower than 50, and when only the angular mismatch exists and the snapshot number is lower, the output SINR of the present invention is higher than that of other methods, which indicates that the present invention can estimate an accurate steering vector, and the interference-plus-noise covariance matrix obtained through reconstruction is relatively ideal. As can be seen from fig. 4(b), when the number of snapshots is higher than 50, the output of the present invention is still higher than that of other methods, the covariance matrix of the DL method does not reject the desired signal, and the desired steering vector is mismatched, so the output performance is the lowest. While the EIG method can improve the expected steering vector mismatch, the improvement degree is limited. And the covariance matrix still contains the desired components, the output performance is only higher than the DL method.
FIG. 5 shows the mismatching of the steering vector angles in each method in the simulation experiment. As can be seen from fig. 5, the method of the present invention can better resist the angle mismatch with the RCBD method and the INCR method, but the present invention has a higher output SINR. When the mismatching angle is large, the output performance of the DL method, the SMI method and the EIG method is sharply reduced, and the mismatching performance of the guide vector angle is poor. The EIG method cannot handle large angle mismatch.
The above description is only an embodiment of the present invention, and not intended to limit the scope of the present invention, and all modifications of equivalent structures and equivalent processes performed by the present specification and drawings, or directly or indirectly applied to other related technical fields, are included in the scope of the present invention.

Claims (5)

1. A robust beam forming method based on secondary reconstruction is characterized by comprising the following steps:
s1: constructing a first projection operator P1＝Y1Y1 H，Y1＝[y1,y2,...,yL]The subspace formed by the guide vectors in the undesired direction is the same as the subspace formed by the guide vectors in the undesired direction, and the guide vectors in different directions are mutually orthogonal;
s2: first constructing an interference covariance matrix
Figure FDA0002835162490000011
Wherein K represents the total number of snapshots, Xi(k) Indicating the kth snapshot array receptionOf the interference signal Xn(k) Representing the noise signal received by the kth snapshot array;
s3: quadratic reconstruction of interference covariance matrix using Capon power spectral density integrals
Figure FDA0002835162490000012
Wherein, thetaiRepresenting an interference angle sector, a (theta) representing an array steering vector, and theta being an interference signal incident angle;
s4: reconstructing interference-plus-noise covariance matrix
Figure FDA0002835162490000013
Wherein I is an identity matrix;
Figure FDA0002835162490000014
to be composed of
Figure FDA0002835162490000015
Performing characteristic decomposition to obtain the minimum value of all characteristic values, and taking the minimum value as noise power;
s5: constructing a second projection operator
Figure FDA0002835162490000016
U1＝[u1,u2,…,uP]A subspace spanned by the alternative desired signal steering vectors;
s6: reconstructing an expected covariance matrix
Figure FDA0002835162490000017
Wherein, Xs(k) Desired signal, X, received for the kth snapshot arrayi(k) Interference signals received for the kth snapshot array, Xn(k) A noise signal received for the kth snapshot array; estimating an optimal steering vector from a reconstructed expected covariance matrix
Figure FDA0002835162490000018
S7: based on the mostOptimal guide vector
Figure FDA0002835162490000019
Obtaining the optimal weight vector
Figure FDA00028351624900000110
S8: and carrying out weighted summation on the received signals by using the optimal weight vector to form a steady beam.
2. A robust beamforming method based on quadratic reconstruction according to claim 1, characterized by:
in step S1, the first projection operator P1The construction method specifically comprises the following steps:
to sampling covariance matrix
Figure FDA00028351624900000111
Performing characteristic decomposition to obtain a signal subspace USAnd noise subspace UN；
Since the signal steering vector is orthogonal to the noise subspace, AH·UNIs equal to 0, so
Figure FDA00028351624900000112
A represents a steering vector matrix, and A ═ a (θ)0),a(θ1),...,a(θP)]TA (theta) in the steering vector matrix0) Representing a desired signal steering vector, and the rest are interference signal steering vectors;
will USIs marked as US＝[u0,u1,...,uP]With span { a (θ)0),a(θ1),...，a(θP)}＝span{u0,u1,...,uP}；
Combining with the equivalent signal subspace theory, searching the angular sector where each signal is located by using the low-resolution power spectrum, and dividing the whole area theta into two complementary signal angular sectors thetaIAnd non-signal angle sectors
Figure FDA0002835162490000021
Let thetaSAnd ΘiRespectively, a desired signal angle sector and an interference angle sector, and thetaI＝Θs+Θi；
Defining a correlation matrix
Figure FDA0002835162490000022
And to QiCharacteristic decomposition to obtain Qi＝YΣYHΣ and Y are a diagonal matrix and a unitary matrix, respectively, Σ ═ diag [ γ [ [ γ ])1,γ2,...,γM]，Y＝[y1,y2,...,yM]；
Let Y1＝[y1,y2,...,yL]，Y1Middle column vector and a (theta)0) Are orthogonal and guarantee Y1Y1 HNot equal to I, order P1＝Y1Y1 HWherein L is selected as an empirical value.
3. A robust beamforming method based on quadratic reconstruction according to claim 2, characterized by:
l is preferably 5.
4. A robust beamforming method based on quadratic reconstruction according to claim 1, characterized by:
in step S6, an optimal steering vector is estimated
Figure FDA0002835162490000023
The method specifically comprises the following steps:
to pair
Figure FDA0002835162490000024
Performing feature decomposition to obtain maximum value U of feature vectormaxThen the optimal steering vector
Figure FDA0002835162490000025
M denotes the number of array elements.
5. A robust beamforming system based on quadratic reconstruction, comprising:
a first module for constructing a first projection operator P1＝Y1Y1 H，Y1＝[y1,y2,...,yL]The subspace formed by the guide vectors in the undesired direction is the same as the subspace formed by the guide vectors in the undesired direction, and the guide vectors in different directions are mutually orthogonal;
a second module for constructing an interference covariance matrix for a first time
Figure FDA0002835162490000026
Wherein K represents the total number of snapshots, Xi(k) Representing the interference signal, X, received by the kth snapshot arrayn(k) Representing the noise signal received by the kth snapshot array;
a third module for reconstructing an interference covariance matrix using Capon power spectral density integral quadratic
Figure FDA0002835162490000027
Wherein, thetaiRepresenting an interference angle sector, a (theta) representing an array steering vector, and theta being an interference signal incident angle;
a fourth module for reconstructing an interference plus noise covariance matrix
Figure FDA0002835162490000028
Wherein I is an identity matrix;
Figure FDA0002835162490000029
to be composed of
Figure FDA00028351624900000210
Performing characteristic decomposition to obtain the minimum value of all characteristic values, and taking the minimum value as noise power;
a fifth module for constructing a second projection operator
Figure FDA00028351624900000211
U1＝[u1,u2,…,uP]A subspace spanned by the alternative desired signal steering vectors;
a sixth module for reconstructing the expected covariance matrix
Figure FDA0002835162490000031
Wherein, Xs(k) Desired signal, X, received for the kth snapshot arrayi(k) Interference signals received for the kth snapshot array, Xn(k) A noise signal received for the kth snapshot array; estimating an optimal steering vector from a reconstructed expected covariance matrix
Figure FDA0002835162490000032
A seventh module for determining a best steering vector based on the optimal steering vector
Figure FDA0002835162490000033
Obtaining the optimal weight vector
Figure FDA0002835162490000034
And the eighth module is used for performing weighted summation on the received signals by using the optimal weight vector to form the robust beam.
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