CN108872946A - The robust ada- ptive beamformer method of steering vector and covariance matrix Joint iteration - Google Patents
The robust ada- ptive beamformer method of steering vector and covariance matrix Joint iteration Download PDFInfo
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Abstract
The invention discloses the robust ada- ptive beamformer method of steering vector and covariance matrix Joint iteration, solve it is expected signal guide vector sum interference plus noise covariance matrix estimation problem in Adaptive beamformer technology.Realization process is：Sample covariance matrix is estimated using the radar return data of array acquisition；Initialize desired signal steering vector and interference plus noise covariance matrix；Establish convex optimization method estimation desired signal steering vector error；Steering vector and covariance matrix, alternating iteration are updated, until obtaining the optimal estimation of steering vector and covariance matrix；It calculates weight and realizes robust ada- ptive beamformer.The present invention is when direction of arrival and array calibration error exist simultaneously, improve desired signal steering vector restriction ability, desired signal estimation interference plus noise covariance matrix is accurately rejected from sample covariance matrix, it avoids desired signal from ' disappearing certainly ' phenomenon, can be used for that there are realize Adaptive beamformer under direction of arrival and array calibration error.
Description
Technical field
The invention belongs to array signal processing field, relate generally to it is expected signal guide vector sum in Adaptive beamformer
The steady wave beam of interference plus noise covariance matrix estimation problem, specifically a kind of steering vector and covariance matrix Joint iteration
Forming method, the Adaptive beamformer that can be used under array calibration error.
Background technique
Adaptive beamformer technology is widely used in Aeronautics and Astronautics, radar and communication system, by desired signal side
To gain, interference radiating way formation null is formed, output Signal to Interference plus Noise Ratio (Signal to Interference andNoise is improved
Ratio,SINR).But there are sensor position uncertainties, channel amplitude phase errors etc. in actual working environment, and expectation is caused to believe
There are deviations for the constraint of number steering vector.Theoretical research shows there is constraint deviation when desired signal guide vector, in low signal-to-noise ratio
In the case of (Signal to Noise Ratio, SNR), in fact it could happen that the problems such as main lobe deviates reduces output SINR；In high SNR
In the case of, if receiving data contains desired signal, or even it will appear signal and ' disappear certainly ' phenomenon, cause to export SINR and sharply deteriorate.
For the optimal power Solve problems of Adaptive beamformer under a variety of errors, typical solution has：Diagonal load
Class method, subspace class algorithm, constrained optimization class method, interference noise covariance matrix reconstruct class method etc., wherein：
Diagonal loading classes method：This method is by artificially injecting noise, in pair of sample data covariance matrix
A lesser amount is loaded in the element of angle, to reduce the disturbance journey of noise characteristic value in sample data covariance matrix
Degree, the corresponding influence for reducing noise feature vector weight vector in beam forming process, advantage are to improve algorithm to number of snapshots
Robustness slows down signal and ' disappears certainly ' phenomenon.But also there is beam pattern interference position null to shoal simultaneously, export under SINR
Drop, the uncontrollable disadvantage of loaded value.
Subspace class algorithm：This method utilizes signal interference under conditions of information source and noise are mutually indepedent mutually incoherent
The orthogonality of subspace and noise subspace, it would be desirable to which signal guide vector projects on signal interference subspace, to get rid of
Component of the abstention vector in noise subspace, weakens influence of the disturbance of noise subspace to beamforming algorithm performance.It should
Algorithm is uncertain to desired signal steering vector caused by any error to suffer from good robustness, but the algorithm is only applicable in
It in the environment of high SNR, and needs accurately to know signal interference subspace dimension, otherwise Beam-former performance can decrease notably.
Constrained optimization class method：This method is by convex optimization tool, generally to maximize output power or maximize defeated
Signal to Interference plus Noise Ratio is target out, by the uncertain collection that desired signal steering vector is constrained in experienced expectation signal guide vector
In or constrain it close to signal interference subspace to optimize desired signal steering vector.The algorithm is oriented in desired signal and swears
Good performance can be obtained in the case where the accurate constraint of amount, but once there is error, to the pact of desired signal steering vector
Shu Nengli decline, then algorithm can not finally optimize to obtain optimal solution, while the general computation complexity of constrained optimization class method is higher.
Interference noise covariance matrix reconstructs class method：This method utilize signal airspace sparsity, interference signal can
Energy region, which is utilized, is likely to occur domain integral in interference signal such as Capon power spectrum, PI spectrum, SPICE spectrum, estimates and is free of
The interference plus noise covariance matrix of desired signal improves Beam-former performance, then utilizes the interference noise association side of reconstruct
Poor matrix is combining some optimization methods to estimate desired signal steering vector, so that array obtains good output performance.But it should
Method needs to know accurate array configuration information, that is, only considered signal wave up to deflection error, do not consider sensor position uncertainties,
Amplitude-phase error etc., there are interference plus noise covariance matrix mismatches in actual working environment.
The above-mentioned diagonal loading classes method being mentioned to can improve the small performance taken fastly, but exist under strong desired signal
Desired signal ' disappears ' phenomenon certainly；Subspace class method can be improved the estimation performance of steering vector under strong desired signal, but
There are large errors under weak desired signal；Constrained optimization class method due to exist desired signal guide vector constraint deviation,
Cause performance boost limited；Interference noise covariance matrix reconstructs class method in array accurate calibration, can significantly mention
High adaptive beam former performance, but under array calibration error, lose interference rejection capability.
Summary of the invention
It is an object of the invention to overcome above-mentioned existing methods insufficient, it is undistorted to desired signal to propose a kind of realization
The robust ada- ptive beamformer method of steering vector and covariance matrix Joint iteration that output simultaneously sufficiently inhibits interference signal.
The present invention is the robust ada- ptive beamformer method of a kind of steering vector and covariance matrix Joint iteration, and feature exists
In, including have the following steps：
Step (1) receives echo data：Even linear array is X (t), uniform line in the radar return data that t moment receives
Battle array is arranged by M array element by half-wavelength, time in the reception data of even linear array containing a desired signal and J interference signal
Wave information；
Step (2) calculates covariance matrix：Calculate the covariance matrix for the radar return data that linear array collects
K is number of snapshots, ()HIndicate conjugate transposition；
Step (3) initializes desired signal steering vector and interference plus noise covariance matrix：Assuming that k is current iteration time
Number, the initial value of k are 0, and desired signal substantially angular interval is Θ, using sample covariance matrix combination Capon power spectrum in area
Between Θ reconstruct desired signal matrix Q, it is decomposed, the corresponding characteristic vector of its maximum eigenvalue is obtained, as the phase of initialization
Hope signal guide vectorUtilize the desired signal steering vector of initializationEstimate desired signal power, is assisted from sampling
Variance matrixDesired signal components are rejected, and load one to be initialized to avoid the small diagonal matrix δ I of rank defect
Interference plus noise covariance matrix
Step (4) estimates noise subspace matrix UNWith interference space matrix UJ：To sample covariance matrixDo feature
Value is decomposed, and characteristic value descending is arranged, and obtains the noise subspace of the corresponding characteristic vector of rear M-J-1 small characteristic value
UN；Then to the interference plus noise covariance matrix of estimationEigenvalues Decomposition is done, J big characteristic value is corresponding before obtaining
The interference space U of characteristic vectorJ；
Step (5) establishes convex optimization method, estimates desired signal steering vector error quadrature component e⊥：By maximizing the phase
It hopes output power signal, while utilizing the noise subspace U of estimationNWith interference space UJUpdated desired signal is constrained to lead
Convex optimization method is established closer to desired signal true directions compared with the desired signal steering vector before update to vector, estimates the phase
The error component e for hoping signal guide vector error e orthogonal with the desired signal steering vector just estimated⊥；
Step (6) updates expectation signal guide vector sum interference plus noise covariance matrix：The expectation letter that estimation is obtained
Number steering vector error quadrature component e⊥The desired signal steering vector not updated is compensated, is completed to desired signal steering vector
Update, desired signal power is then reevaluated, further according to updated desired signal steering vector and desired signal power
Estimate desired signal autocorrelation matrix, rejects updated desired signal autocorrelation matrix from sample covariance matrix, and load
One can complete the update to interference plus noise covariance matrix to avoid the small diagonal matrix δ I of rank defect；
Step (7) stopping criterion in iteration：If the desired signal power after iteration is greater than the desired signal power before iteration,
K=k+1 is enabled, iteration is continued, repeats step 4, step 5 and step 6, until iteration ends；If the desired signal function after iteration
Rate is less than or equal to the desired signal power before iteration, then iteration ends, executes step (8)；
Step (8) calculates the optimal power of Adaptive beamformer：Utilize desired signal guide vectorAnd interference plus noise
CovarianceOptimal estimation calculate the optimal power W of Adaptive beamformer, complete steering vector and covariance matrix joint
The robust ada- ptive beamformer of iteration.
The present invention just estimates desired signal steering vector and interference plus noise covariance matrix, and then estimation obtains noise
Space and interference space update expectation signal guide vector sum interference plus noise association side in conjunction with convex optimization method alternating iteration
Poor matrix gradually reduces the evaluated error to desired signal steering vector and interference plus noise covariance matrix, finally obtains the phase
The optimal estimation for hoping signal guide vector sum interference plus noise covariance matrix is calculated optimal adaptive beam row and swears at power
Amount completes Wave beam forming, realizes the undistorted output to desired signal and the abundant inhibition to interference signal.
Compared with prior art, the present invention having the following advantages that：
(1) the present invention is based on subspace theories, are contained in signal interference subspace using true desired signal steering vector
This characteristic, by estimating noise subspace matrix to sample covariance matrix Eigenvalues Decomposition, to interference-plus-noise covariance
Eigenvalue Decomposition estimates interference space matrix, so that the desired signal steering vector of restrained split-flow is empty to signal interference
Between close, while principle interference space, guarantee that the desired signal steering vector of estimation is close to true directions, improve to the phase
Hope the restriction ability of signal guide vector；
(2) present invention estimates desired signal autocorrelation matrix using the desired signal steering vector of estimation, then from association side
Poor matrix rejects desired signal components, estimates interference plus noise covariance matrix, improves and adds under array calibration error to interference
The estimated capacity of noise covariance matrix；
(3) present invention estimates desired signal steering vector and interference plus noise covariance matrix by Joint iteration, improves
The estimation performance of Adaptive beamformer weight under array calibration error significantly slows down signal and ' disappears certainly ' phenomenon.
Detailed description of the invention
Fig. 1 is general flow chart of the invention；
Fig. 2 is array received schematic diagram data of the invention；
Fig. 3 is that the present invention from three kinds of control methods exports Signal to Interference plus Noise Ratio and input signal-to-noise ratio relational graph under different errors,
Wherein Fig. 3 (a) is that the present invention and three kinds of control methods export Signal to Interference plus Noise Ratio and input signal-to-noise ratio relational graph under direction of arrival error,
Fig. 3 (b) is that the present invention exports Signal to Interference plus Noise Ratio with three kinds of control methods under direction of arrival error and sensor position uncertainties and input is believed
It makes an uproar than relational graph, Fig. 3 (c) is that of the invention export under direction of arrival error and amplitude-phase error with three kinds of control methods believes dry make an uproar
Than with input signal-to-noise ratio relational graph；
Fig. 4 is that the present invention from three kinds of control methods exports Signal to Interference plus Noise Ratio and number of snapshots relational graph under different errors, wherein
Fig. 4 (a) is that the present invention and three kinds of control methods export Signal to Interference plus Noise Ratio and number of snapshots relational graph under direction of arrival error, and Fig. 4 (b) is
The present invention and three kinds of control methods export Signal to Interference plus Noise Ratio and number of snapshots relational graph under direction of arrival error and sensor position uncertainties, scheme
4 (c) be that the present invention exports Signal to Interference plus Noise Ratio with three kinds of control methods under direction of arrival error and amplitude-phase error and number of snapshots are closed
System's figure.
Specific embodiment
In conjunction with the accompanying drawings and embodiments to the detailed description of the invention
Embodiment 1
Adaptive beamformer technology with a particular focus on to the undistorted output of desired signal, while guarantee to interference signal into
Row sufficiently inhibits, and this requires accurately estimating desired signal steering vector and interference plus noise covariance matrix, and existing son is empty
Between algorithm and constrained optimization method can not accurately estimate desired signal steering vector, loading classes algorithm and interference noise covariance square
Battle array can not accurately estimate interference plus noise covariance matrix, for this purpose, the present invention proposes a kind of steering vector by innovation research
With the robust ada- ptive beamformer method of covariance matrix Joint iteration, referring to Fig. 1, including have the following steps：
Step (1) receives echo data：Even linear array is X (t), uniform line in the radar return data that t moment receives
Battle array is arranged by M array element by half-wavelength, time in the reception data of even linear array containing a desired signal and J interference signal
Wave information is estimated that the power of desired signal and interference signal according to the information of desired signal and interference signal.
Step (2) calculates sample covariance matrix：The whole echo datas received using radar are calculated linear array and acquired
The covariance matrix of the radar return data arrived
K is number of snapshots, ()HIndicate conjugate transposition.
Step (3) initializes desired signal steering vector and interference plus noise covariance matrix：K is current iteration number, k
Initial value be 0, desired signal substantially angular interval is Θ, and desired signal substantially angular interval can use some low resolution
Angle estimating method obtains, and reconstructs desired signal square in substantially section Θ using sample covariance matrix combination Capon power spectrum
Battle array Q obtains the corresponding characteristic vector of its maximum eigenvalue to desired signal matrix Q feature decomposition, i.e. expectation signal guide vector
First estimationUtilize the desired signal steering vector just estimatedDesired signal power is estimated, then from sampling association side
Poor matrixDesired signal components are rejected, and loading one can be to avoid the small diagonal matrix δ I of rank defect, that is just estimated is dry
Disturb plus noise covariance matrix
Step (4) estimates noise subspace UNWith interference space UJ：To sample covariance matrixEigenvalues Decomposition is done,
And arrange characteristic value descending, obtain the noise subspace matrix U of the corresponding characteristic vector of rear M-J-1 small characteristic valueN；
Then to the interference plus noise covariance matrix of initializationEigenvalues Decomposition is done, J big characteristic value is corresponding before obtaining
The interference space matrix U of characteristic vectorJ；Specifically：
To sample covariance matrixEigenvalues Decomposition is done, is broken down into：
In formula, λi(i=1,2 ..., M) indicate sample covariance matrixCharacteristic value, it be arranged in decreasing order forui(i=1,2 ..., M) indicates corresponding characteristic vector,For white noise function
Rate；USJThe signal interference subspace of J+1 characteristic vector, U before indicatingNWhat M-J-1 characteristic vector was opened after expression makes an uproar
Phonon space；ΓSJ=diag { λ1,λ2,…,λJ+1And ΓN=diag { λJ+2,λJ+3,…,λMRespectively indicate corresponding characteristic value
Matrix；
To the interference plus noise covariance matrix of estimationEigenvalues Decomposition is done, is broken down into：
In formula, γi(i=1,2 ..., M) indicate the interference plus noise covariance matrix estimatedCharacteristic value, it
It is arranged in decreasing order as γ1≥…≥γJ≥γJ+1=...=γM, νi(i=1,2 ..., M) indicate corresponding characteristic vector；UJTable
The interference space of J characteristic value character pair vector, U ' before showingNThe orthogonal complement space for indicating interference space, by rear
M-J characteristic value character pair vector at；ΛJ=diag { γ1,γ2,…,γJAnd ΛN=diag { γJ+1,γJ+2,…,
γMRespectively indicate corresponding eigenvalue matrix.
Step (5) establishes convex optimization method, estimates desired signal steering vector error quadrature component e⊥：By minimizing the phase
It hopes the inverse of output power signal, while utilizing the noise subspace U of estimationNWith interference space UJConstrain updated expectation
Signal guide vectorCompared with the desired signal steering vector before updateCloser to desired signal true directions, complete
Foundation to convex optimization method solves convex optimization method and estimates to obtain desired signal steering vector error quadrature component e⊥。
Step (6) updates expectation signal guide vector sum interference plus noise covariance matrix：The expectation obtained using estimation
Signal guide vector error quadrature component e⊥Expectation signal guide vector is updated, i.e., the desired signal steering vector before iteration is mended
Repay the desired signal steering vector error quadrature component e that estimation obtains⊥；The phase is estimated using updated desired signal steering vector
It hopes signal power, estimates to obtain desired signal auto-correlation further according to updated desired signal steering vector and desired signal power
Matrix rejects updated desired signal autocorrelation matrix from sample covariance matrix, and loads one and avoid the small of rank defect
Diagonal matrix δ I completes the update to interference plus noise covariance matrix.
Step (7) stopping criterion in iteration：If the desired signal power after iteration is greater than the desired signal power before iteration,
K=k+1 is enabled, iteration is continued, is repeated step (4), step (5) and step (6), until iteration ends；If the expectation after iteration
Signal power is less than or equal to the desired signal power before iteration, then iteration ends, executes step (8), specifically：
Using the desired signal power before and after Capon spectra calculation iteration, if desired signal power is greater than after iteration
Desired signal power before iteration, i.e.,：
Then continue iteration, enable k=k+1, repeat step (4), step (5) and step (6), until iteration ends；If repeatedly
For rear desired signal power less than or equal to desired signal power before iteration, i.e.,：
Then iteration termination executes step (8).
Step (8) calculates the optimal power of Adaptive beamformer：The desired signal steering vector obtained using iteration endsAnd interference-plus-noise covarianceThe optimal power W of Adaptive beamformer is calculated, completes Adaptive beamformer, specifically
It is：
Then Wave beam forming is realized using the optimal power W of Adaptive beamformer, obtain array output data Y (t)=WHX
(t), the robust ada- ptive beamformer of steering vector and covariance matrix Joint iteration is completed.
The desired signal steering vector that the present invention is initialized using the method for sparse reconstruct, and then desired signal is divided
Amount rejects the interference plus noise covariance matrix initialized from sample covariance matrix；Then sample covariance matrix is utilized
Noise subspace and interference space are estimated respectively with interference plus noise covariance matrix；In conjunction with convex optimization method exact constraint
Desired signal steering vector, estimation obtains desired signal steering vector error quadrature component, and updates desired signal guide vector,
Again desired signal components are rejected again from sample covariance matrix, estimation obtains better interference plus noise covariance matrix,
Such alternating iteration, until obtaining the optimal estimation of desired signal steering vector and interference plus noise covariance matrix；Last benefit
Adaptive beamformer weight vector is calculated with the optimal estimation of desired signal steering vector and interference plus noise covariance matrix, it is real
Existing Wave beam forming.
Embodiment 2
The robust ada- ptive beamformer method of steering vector and covariance matrix Joint iteration is with embodiment 1, described in step 5
Convex optimization method is established, estimates desired signal steering vector error quadrature component e⊥It is to be realized by following formula：
Indicate the desired signal steering vector that kth time iteration does not update,Indicate sample covariance matrix, UNIt indicates
Estimate obtained noise subspace, UJIndicate that the interference space that estimation obtains, ε indicate a small relaxation factor (being greater than 0),
Objective function guarantees that updated desired signal power is greater than the desired signal function not updated by maximizing desired signal power
Rate, orthogonality of first constraint condition based on noise subspace Yu signal interference subspace, guarantees updated desired signal
Closer to signal interference subspace, Article 2 constraint condition guarantee updated desired signal will not close to interference space, the
Three constraint conditions, which ensure that, updates the desired signal steering vector of front and back there is no length is fuzzy, and add small relaxation because
Son can guarantee there is certain space when searching for desired signal error quadrature component, and Article 4 constraint condition then guarantees desired signal
Steering vector error quadrature component e⊥It is orthogonal with the desired signal steering vector not updated.
The present invention is based on subspace theory, the noise subspace estimated using Eigenvalues Decomposition sample covariance matrix
The interference space matrix that matrix and Eigenvalues Decomposition interference plus noise covariance matrix are estimated, constrains updated expectation
Signal guide vector is close to signal interference subspace, while far from interference space, to guarantee to add desired signal error
Desired signal steering vector after quadrature component is close to desired signal steering vector true directions, improves to desired signal
The restriction ability of steering vector, therefore can accurately estimate to obtain desired signal steering vector.
Embodiment 3
The robust ada- ptive beamformer method of steering vector and covariance matrix Joint iteration is with embodiment 1-2, described in step 3
Initialization desired signal steering vectorSpecifically assume that k is current iteration number, the initial value of k is 0, and desired signal is big
Cause angular interval is Θ, and the angle estimating method that desired signal substantially angular interval can use some low resolution obtains, benefit
Desired signal matrix Q is reconstructed in substantially section Θ with sample covariance matrix combination Capon power spectrum, to desired signal matrix Q
Feature decomposition obtains the corresponding characteristic vector of its maximum eigenvalue, that is, it is expected the first estimation of signal guide vectorInclude
Following steps：
3.1 (a) utilize Capon Power spectrum reconstruction desired signal matrix Q：
A (θ) is the airspace steering vector of the corresponding even linear array of angle, θ, and angle, θ is desired signal substantially angular interval Θ
In angle variables, it is practical to calculate, replace integral operation to reconstruct desired signal matrix Q using cumulative summation；
The desired signal matrix Q of reconstruct is carried out feature decomposition by 3.1 (b), is expressed as：
In formula, μi(i=1,2 ..., M) indicates the characteristic value of desired signal matrix Q, it is arranged in decreasing order as μ1> μ2> ...
> μM-2> ... > μM, qi(i=1,2 ..., M) indicates corresponding characteristic vector (M is array element sum, and i is serial number)；
3.1 (c) the desired signal steering vectors initialized
||·||2The L-2 norm of vector is sought in expression；
The present invention is based on signals in the sparsity of airspace range, utilizes Capon power in desired signal substantially angular interval
Spectrum reconstruct desired signal matrix, since substantially only one signal of angular interval, initialization desired signal steering vector are
The corresponding characteristic vector of the maximum eigenvalue of desired signal matrix, estimation obtain true near desired signal in substantially section
The desired signal steering vector in direction.
Embodiment 4
The robust ada- ptive beamformer method of steering vector and covariance matrix Joint iteration is with embodiment 1-3, described in step 3
Initialization interference plus noise covariance matrixFirst with the desired signal steering vector of initializationThe estimation phase
Signal power is hoped, then from sample covariance matrixDesired signal components are rejected, and loads a small diagonal matrix δ I and keeps away
Exempt from rank defect, completes initialization interference plus noise covariance matrixIt specifically includes and has the following steps：
3.2 (a) utilize the desired signal steering vector just estimatedEstimate desired signal power
And then obtain desired signal autocorrelation matrix
3.2 (b) from sample covariance matrixMiddle rejecting desired signal autocorrelation matrixAnd it loads one small
Diagonal matrix δ I avoids rank defect, the interference plus noise covariance matrix initializedFor：
The present invention estimates desired signal energy using the desired signal steering vector of initialization, then from sampling covariance square
Battle array rejects desired signal components and estimates to obtain the initial value of interference plus noise covariance matrix, it is ensured that the interference initialized adds
Noise covariance matrix still represents the real features of interference signal in the presence of array calibration error.
A more detailed example is given below, the present invention is further described：
Embodiment 5
The robust ada- ptive beamformer method of steering vector and covariance matrix Joint iteration with embodiment 1-4,
Referring to Fig.1, realize that step of the invention is described as follows：
Step 1 is acquired using the even linear array reception of the M array element compositions by half-wavelength arrangement in t moment referring to Fig. 2
Radar return data X (t).
Step 2 calculates sample covariance matrix, is implemented as follows：
The radar return data X (t) acquired using even linear array, is calculated sample covariance matrix
Above formula K is number of snapshots.
Step 3 initializes desired signal steering vector and interference plus noise covariance matrix, is implemented as follows：
(3a) desired signal substantially angular interval is known as Θ, is reconstructed and it is expected in the interval integral using Capon power spectrum
Signal matrix Q is as follows：
A (θ) is the airspace steering vector of the corresponding even linear array of angle, θ, and angle, θ is desired signal substantially angular interval Θ
In angle variables, it is practical when calculating, replace integral operation using cumulative summation, Eigenvalues Decomposition desired signal matrix Q is：
In formula, μi(i=1,2 ..., M) indicates the characteristic value of desired signal matrix Q, it is arranged in decreasing order as μ1> μ2> ...
> μM-2> ... > μM, qi(i=1,2 ..., M) indicates corresponding characteristic vector, it is assumed that k is that current iteration number (is initialized as
0) the desired signal steering vector, then initializedFor：
The desired signal steering vector that (3b) utilizes formula (4) to obtainEstimate that desired signal power isAnd then estimate desired signal autocorrelation matrix
Then desired signal components are rejected from sample covariance matrix, and loading one can be to avoid the small diagonal of rank defect
Matrix delta I, the interference plus noise covariance matrix initializedFor：
Step 4 estimates noise subspace and interference space, is implemented as follows：
The sample covariance matrix that (4a) obtains formula (1)Eigenvalues Decomposition is：
In formula, λi(i=1,2 ..., M) indicate sample covariance matrixCharacteristic value, it be arranged in decreasing order for For noise power, ui(i=1,2 ..., M) indicates corresponding characteristic vector,
USJThe signal interference subspace of J+1 characteristic value character pair vector, U before indicatingNM-J-1 characteristic value is corresponding after expression
The noise subspace of characteristic vector, ΓSJ=diag { λ1,λ2,…,λJ+1And ΓN=diag { λJ+2,λJ+3,…,λMRespectively
Indicate corresponding eigenvalue matrix；
The interference plus noise covariance matrix Eigenvalues Decomposition that estimation obtains is by (4b)：
In formula, γi(i=1,2 ..., M) indicate interference plus noise covariance matrixCharacteristic value, it is with descending
It is arranged as γ1≥…≥γJ≥γJ+1=...=γM, νi(i=1,2 ..., M) indicates corresponding characteristic vector, UJJ before indicating
The interference space of characteristic value character pair vector, U 'NThe orthogonal complement space for indicating interference space, it is special by latter M-J
Value indicative character pair vector is at ΛJ=diag { γ1,γ2,…,γJAnd ΛN=diag { γJ+1,γJ+2,…,γMRespectively
Indicate corresponding eigenvalue matrix.
Step 5 establishes convex optimization method, estimates desired signal steering vector error quadrature component e⊥, specific step is as follows：
To minimize the inverse of desired signal output powerFor objective function, simultaneously
The noise subspace U obtained using formula (7)NConstrain updated desired signal steering vectorCompared with the expectation before update
Signal guide vectorCloser to signal interference subspace, the interference space U obtained using formula (8)JIt constrains updated
Desired signal steering vectorCompared with the desired signal steering vector before updateFar from interference space, and ensure
It is long consistent to update front and back mould, establishes following convex optimization method, is solving convex optimization method estimation desired signal steering vector error just
Hand over component e⊥：
The present invention solves formula (9) using convex optimization tool, obtains desired signal steering vector error quadrature component e⊥, then
By desired signal steering vector error quadrature component e⊥Desired signal steering vector before compensating update.Due to formula
(9) constraint condition may insure that updated desired signal steering vector is interfered close to signal interference subspace and principle simultaneously
Subspace improves the restriction ability to desired signal steering vector, and it is hereby ensured that the desired signal steering vectors of update
Closer to desired signal steering vector true directions, and then improve the estimation performance to desired signal steering vector.
Step 6 updates expectation signal guide vector sum interference plus noise covariance matrix, and specific step is as follows：
(6a) utilizes the steering vector error component e of formula (9) estimation⊥, it is as follows to update expectation signal guide vector：
(6b) reevaluates desired signal power using the desired signal steering vector that formula (10) updateFurther estimation desired signal autocorrelation matrix is：
Desired signal components are rejected from sample covariance matrix, and loading one can be to avoid the small diagonal matrix δ of rank defect
I, updating interference plus noise covariance matrix is：
Step 7 is iterated termination judgement, and specific step is as follows：
Using the desired signal power before and after Capon spectra calculation iteration, if desired signal power is greater than after iteration
Desired signal power before iteration, i.e.,：
Then continue iteration, k=k+1 repeats step (4), step (5) and step (6), until iteration ends；
If the desired signal power after iteration is less than or equal to the desired signal power before iteration, i.e.,：
Then iteration ends execute step (8).
Step 8 calculates Adaptive beamformer weight, realizes Wave beam forming, specific step is as follows：
Utilize the optimal estimation value of desired signal guide vectorWith the optimal estimation value of interference-plus-noise covarianceCalculate the optimal power of Adaptive beamformer：
Adaptive weight vector W is used for Wave beam forming, obtains array output data Y (t)=WHX (t) realizes the present invention
Robust ada- ptive beamformer.
The present invention, which is utilized, just estimates there is desired signal guide vector using sparse reconstructing method, then from sampling covariance
Matrix rejects the initialization that desired signal components realize interference noise covariance matrix, obtains preferable initial value；It is then based on son
Space Theory exact constraint desired signal steering vector establishes convex optimization method, updates expectation signal guide vector sum interference and adds
Noise covariance matrix, alternating iteration, until obtaining the optimal of desired signal steering vector and interference plus noise covariance matrix
Estimation calculates adaptive power, in the presence of realizing direction of arrival error, sensor position uncertainties and amplitude-phase error, believes expectation
Number undistorted output sufficiently inhibits interference signal.
Effect of the invention can be further illustrated by following emulation：
Embodiment 6
The robust ada- ptive beamformer method of steering vector and covariance matrix Joint iteration with embodiment 1-5,
Experiment condition and simulation parameter
Experiment condition：Even linear array (array number M=8), array element spacing are 0.5 λ (λ=0.05), and information source number 3 includes
One desired signal, the true arrival bearing of desired signal is 10 °, priori arrival bearing is 8 °, two interference signals, interference signal
True arrival bearing is -20 °, 30 °, dry to make an uproar than being 30dB；Test carries out 200 Monte Carlo simulations every time；
Simulation parameter
Joint iteration estimation method (Joint Iterative EstimationAlgorithm, JIEA) of the invention is set
Setting desired signal substantially section is [3 °, 13 °], 0.1 ° is divided between summation, loading capacity δ is M- after sampling covariance eigenvalue decomposes
10 times of J-1 characteristic value arithmetic average, ε is set as 0.1.The prior art setting of comparison is as follows：Alterably diagonal loading algorithm
(Variable Diagonal Loading, VDL) sums section as [3 °, 13 °], and 0.1 ° is divided between summation；The constraint of RCB algorithm
Parameter is 0.3M；Interference noise covariance matrix restructing algorithm (Interference plus Noise Covariance
Matrix-Quadratic Constraint Quadratic Problem, IPNM-QCQP) summation section be [- 90 °, 3 °) ∪
(13 °, 90 °], 0.1 ° is divided between summation；
Experimental result, there is only target arrival bearing's errors, signal-to-noise ratio are incremented to 40dB from -30dB, number of snapshots are fixed
It is 100 times, output Signal to Interference plus Noise Ratio and input signal-to-noise ratio relationship such as Fig. 3 (a) are shown；
Fig. 3 (a) discovery is observed, when there is only desired signal arrival bearing's error, when input SNR is in -30dB to 0dB
Range, the present invention and other methods performance are almost the same, when input SNR is in 0dB to 35dB range, the present invention and IPNM-
QCQP method is obvious compared with other two methods performance advantages.
Embodiment 7
The robust ada- ptive beamformer method of steering vector and covariance matrix Joint iteration is imitated with embodiment 1-5, experiment condition
True parameter is with embodiment 6, while experiment condition further includes obeying (- 0.05 λ, 0.05 λ) equally distributed sensor position uncertainties；
Signal-to-noise ratio is incremented to by experimental result there are under target arrival bearing error and sensor position uncertainties from -30dB
40dB, number of snapshots are fixed as 100 times, and output Signal to Interference plus Noise Ratio and input signal-to-noise ratio relationship such as Fig. 3 (b) are shown；
Observe Fig. 3 (b) discovery, when existing simultaneously direction of arrival error and sensor position uncertainties, when input SNR is in-
30dB to 0dB range, in addition to IPNM-QCQP method performance declines to a great extent, the present invention and other two methods performances are almost the same,
When input SNR is in 0dB to 30dB, the present invention is with the obvious advantage compared with other three kinds of method performances, when signal-to-noise ratio is greater than 30dB, this hair
Bright performance is declined, but still better than other technologies, this is because there are larger for the desired signal steering vector of initialization
Error interferes plus noise covariance matrix inaccuracy, and there are error, nothings for the constraint condition for causing in convex optimization method
Method accurately estimates desired signal steering vector, and performance is caused to decline to a great extent.
Embodiment 8
The robust ada- ptive beamformer method of steering vector and covariance matrix Joint iteration is imitated with embodiment 1-5, experiment condition
True parameter is with embodiment 6, while experiment condition further includes amplitude-phase error, and range error is obeyed (- 5dB, 5dB) and is uniformly distributed
, phase error is obeyed (- 5 °, 5 °) and is uniformly distributed；
Experimental result exists simultaneously target arrival bearing error and amplitude-phase error, and signal-to-noise ratio is incremented to from -30dB
40dB, number of snapshots are fixed as 100 times, and output Signal to Interference plus Noise Ratio and input signal-to-noise ratio relationship such as Fig. 3 (c) are shown.
Fig. 3 (c) discovery is observed, when desired signal arrival bearing error and amplitude-phase error exist simultaneously, as input SNR
0dB range is arrived in -30dB, in addition to IPNM-QCQP method performance declines to a great extent, the present invention and other two methods performances are basic
Unanimously, when input SNR is in 0dB to 30dB, the present invention is with the obvious advantage compared with other three kinds of method performances, when signal-to-noise ratio is greater than
30dB, inventive can be declined, but still better than other technologies, this is because the desired signal steering vector of initialization
There are large errors, interfere plus noise covariance matrix inaccuracy, the constraint condition in convex optimization method is caused to be deposited
In error, it can not accurately estimate desired signal steering vector, performance is caused to decline to a great extent.
Embodiment 9
The robust ada- ptive beamformer method of steering vector and covariance matrix Joint iteration is imitated with embodiment 1-5, experiment condition
True parameter is the same as embodiment 6；
Experimental result, there is only target arrival bearing's errors, number of snapshots are incremented to 200 times from 10 times, signal-to-noise ratio is fixed
For 0dB, export shown in Signal to Interference plus Noise Ratio and number of snapshots relationship such as Fig. 4 (a).
Fig. 4 (a) discovery is observed when there are desired signal arrival bearing's error, IPNM-QCQP method is steady to number of snapshots
Strong property is best, but when number of snapshots of the present invention are 50 times restrains substantially, still better than other two methods, the property under fewer snapshots
Can also there be some superiority.
Embodiment 10
The robust ada- ptive beamformer method of steering vector and covariance matrix Joint iteration is imitated with embodiment 1-5, experiment condition
True parameter is with embodiment 6, while experiment condition further includes obeying (- 0.05 λ, 0.05 λ) equally distributed sensor position uncertainties；
Experimental result exists simultaneously target arrival bearing error and sensor position uncertainties, and number of snapshots are incremented to from 10 times
200 times, signal-to-noise ratio is fixed as 0dB, and output Signal to Interference plus Noise Ratio and number of snapshots relationship such as Fig. 4 (b) are shown.
Fig. 4 (b) discovery is observed when there are desired signal arrival bearing error and sensor position uncertainties, IPNM-QCQP methods
Best to number of snapshots robustness, but when number of snapshots of the present invention are 50 times, restrains substantially, is still better than other two methods,
Performance also has some superiority under fewer snapshots.
Embodiment 11
The robust ada- ptive beamformer method of steering vector and covariance matrix Joint iteration is imitated with embodiment 1-5, experiment condition
True parameter is with embodiment 6, while experiment condition further includes amplitude-phase error, and range error is obeyed (- 5dB, 5dB) and is uniformly distributed
, phase error is obeyed (- 5 °, 5 °) and is uniformly distributed；
Experimental result exists simultaneously target arrival bearing error and amplitude-phase error, and number of snapshots are incremented to from 10 times
200 times, signal-to-noise ratio is fixed as 0dB, and output Signal to Interference plus Noise Ratio and number of snapshots relationship such as Fig. 4 (c) are shown.
Fig. 4 (c) discovery is observed when there are desired signal arrival bearing error and amplitude-phase error, IPNM-QCQP methods
Best to number of snapshots robustness, but when number of snapshots of the present invention are 50 times, restrains substantially, is still better than other two methods,
Performance also has some superiority under fewer snapshots.
In brief, the robust ada- ptive beamformer method of steering vector and covariance matrix Joint iteration disclosed by the invention,
It mainly solves it is expected signal guide vector sum interference plus noise covariance matrix estimation problem in Adaptive beamformer technology.Its
Realization process is：Sample covariance matrix is estimated using the radar return data of array acquisition；Initialize desired signal guiding arrow
Amount and interference plus noise covariance matrix；Establish convex optimization method estimation desired signal steering vector error quadrature component；It updates
Desired signal steering vector and interference plus noise covariance matrix, alternating iteration, until obtaining desired signal steering vector and doing
Disturb the optimal estimation of plus noise covariance matrix；It calculates adaptive power and realizes robust ada- ptive beamformer.The present invention, which has, realizes that wave reaches
When angle error and array calibration error exist simultaneously, the restriction ability to desired signal steering vector is improved, is estimated more ideal
Desired signal steering vector, desired signal Composition Estimation interference-plus-noise covariance is accurately rejected from sample covariance matrix
Matrix, avoid the occurrence of desired signal ' disappear certainly ' phenomenon the advantages of, can be used for that there are real under direction of arrival error and array calibration error
Existing Adaptive beamformer.
Claims (4)
1. a kind of robust ada- ptive beamformer method of steering vector and covariance matrix Joint iteration, which is characterized in that including just like
Lower step：
Step (1) receives echo data：Even linear array is X (t) in the radar return data that t moment receives, and even linear array is by M
A array element is arranged by half-wavelength, the echo letter containing a desired signal and J interference signal in the reception data of even linear array
Breath；
Step (2) calculates covariance matrix：Calculate the covariance matrix for the radar return data that linear array collects
K is number of snapshots, ()HIndicate conjugate transposition；
Step (3) initializes desired signal steering vector and interference plus noise covariance matrix：Assuming that k is current iteration number,
Desired signal substantially angular interval is Θ, reconstructs expectation letter in section Θ using sample covariance matrix combination Capon power spectrum
Number matrix Q, decomposes it, obtains the corresponding characteristic vector of its maximum eigenvalue, that is, completes initialization desired signal steering vectorUtilize the desired signal steering vector of initializationIts power is estimated, then from sample covariance matrixThe rejecting phase
Hope signal component, and load one to complete initialization interference-plus-noise covariance square to avoid the small diagonal matrix δ I of rank defect
Battle array
Step (4) estimates noise subspace UNWith interference space UJ：To sample covariance matrixEigenvalues Decomposition is done, and will be special
The arrangement of value indicative descending obtains the noise subspace U of the corresponding characteristic vector of rear M-J-1 small characteristic valueN；Then to estimation
Interference plus noise covariance matrixDo Eigenvalues Decomposition, before obtaining the corresponding characteristic vector of the big characteristic value of J at
Interference space UJ；
Step (5) establishes convex optimization method, estimates desired signal steering vector error quadrature component e⊥：By maximizing expectation letter
Number output power, while utilizing the noise subspace U of estimationNWith interference space UJConstrain updated desired signal guiding arrow
Desired signal steering vector before amount relatively update establishes convex optimization method, estimation expectation letter closer to desired signal true directions
Number steering vector error e error component e orthogonal with the desired signal steering vector just estimated⊥；
Step (6) updates expectation signal guide vector sum interference plus noise covariance matrix：The desired signal that estimation obtains is led
To vector error quadrature component e⊥The desired signal steering vector not updated is compensated, is completed to desired signal steering vector more
Newly, desired signal power is then reevaluated, is estimated further according to updated desired signal steering vector and desired signal power
Desired signal autocorrelation matrix, and then updated desired signal autocorrelation matrix is rejected from sample covariance matrix, and load
One can complete the update to interference plus noise covariance matrix to avoid the small diagonal matrix δ I of rank defect；
Step (7) stopping criterion in iteration：If the desired signal power after iteration is greater than the desired signal power before iteration, k is enabled
=k+1 continues iteration, repeats step 4, step 5 and step 6, until iteration ends；If the desired signal power after iteration is small
In or equal to desired signal power before iteration, then iteration ends, execute step (8)；
Step (8) calculates the optimal power of Adaptive beamformer：Utilize desired signal guide vectorWith interference plus noise association side
DifferenceOptimal estimation calculate the optimal power W of Adaptive beamformer, complete steering vector and covariance matrix Joint iteration
Robust ada- ptive beamformer.
2. the robust ada- ptive beamformer method of steering vector according to claim 1 and covariance matrix Joint iteration, special
Sign is, convex optimization method estimation steering vector error quadrature component e is established described in step (5)⊥It is realized by following formula:
s.t.
Indicate the desired signal steering vector that kth time iterative estimate obtains,Indicate sample covariance matrix, UNExpression is estimated
Count obtained noise subspace, UJIndicate that the interference space that estimation obtains, ε represent relaxation factor (being greater than 0).
3. the robust ada- ptive beamformer method of steering vector according to claim 1 and covariance matrix Joint iteration, special
Sign is, initialization desired signal steering vector described in step (3)Assuming that k is that current iteration number (is initialized as
0), desired signal substantially angular interval is Θ, is reconstructed and it is expected in section Θ using sample covariance matrix combination Capon power spectrum
Signal matrix Q, decomposes it, obtains the corresponding characteristic vector of its maximum eigenvalue, that is, completes initialization desired signal guiding arrow
AmountIt specifically includes and has the following steps：
3.1 (a) utilize Capon Power spectrum reconstruction desired signal matrix Q：
A (θ) is the airspace steering vector of the corresponding even linear array of angle, θ, and angle, θ is in desired signal substantially angular interval Θ
Angle variables, it is practical to calculate, replace integral operation to reconstruct desired signal matrix Q using cumulative summation；
3.1 (b) carry out feature decomposition to the desired signal matrix Q of reconstruct, are expressed as：
In formula, μi(i=1,2 ..., M) indicates the characteristic value of desired signal matrix Q, it is arranged in decreasing order as μ1> μ2> ... >
μM-2> ... > μM, qi(i=1,2 ..., M) indicate corresponding characteristic vector；
3.1 (c) the desired signal steering vectors initializedFor：
||·||2The L-2 norm of vector is sought in expression, and the desired signal steering vector of the initialization is more accurately characterized in substantially area
The feature of interior desired signal.
4. the robust ada- ptive beamformer method of steering vector according to claim 1 and covariance matrix Joint iteration, special
Sign is, initialization interference plus noise covariance matrix described in step (3)It is led first with the desired signal of initialization
To vectorDesired signal power is estimated, then from sample covariance matrixDesired signal components are rejected, and load one
Initialization interference plus noise covariance matrix can be completed to avoid the small diagonal matrix δ I of rank defectSpecifically include just like
Lower step：
3.2 (a) utilize the desired signal steering vector just estimatedEstimate desired signal power
And then obtain desired signal autocorrelation matrix
3.2 (b) from sample covariance matrixMiddle rejecting desired signal autocorrelation matrixAnd load one can be to avoid
The small diagonal matrix δ I of rank defect, the interference plus noise covariance matrix initializedFor：
The interference plus noise covariance matrix of the initialization more accurately characterizes interference signal when there are array calibration error
Feature.
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| CN114048431A (en) * | 2021-09-29 | 2022-02-15 | 湖北工业大学 | Beam forming method based on covariance matrix reconstruction and ADMM |
| CN114048431B (en) * | 2021-09-29 | 2023-06-13 | 湖北工业大学 | Beam forming method based on covariance matrix reconstruction and ADMM |
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| CN114966640A (en) * | 2022-07-29 | 2022-08-30 | 宁波博海深衡科技有限公司 | Direction estimation method and system based on array background noise statistical covariance estimation |
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