CN105354171B - A kind of projection subspace estimation adaptive beam synthetic method for improving characteristic vector - Google Patents
A kind of projection subspace estimation adaptive beam synthetic method for improving characteristic vector Download PDFInfo
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Abstract
The present invention relates to a kind of projection subspace estimation adaptive beam synthetic method for improving characteristic vector.The present invention includes：Array antenna samples to input signal；Construction KR signal covariance vectors are accumulated by Khatri Rao；Characteristic vector projection subspace method estimation steering vector；Obtain array antenna output signal.The present invention can be restrained compared to traditional beam synthesizer in smaller take soon；The technology of the present invention has higher convergence precision compared to traditional beam synthesizer；The technology of the present invention goes for the higher system of requirement of real-time.
Description
Technical field
The present invention relates to a kind of projection subspace estimation adaptive beam synthetic method for improving characteristic vector.
Background technology
Array signal processing is widely used to numerous necks such as radar, sonar, navigation, communication as the things newly risen
Domain.Array antenna adaptive beam synthesizes the importance as array signal processing, has stronger interference rejection capability, and
And output signal Signal to Interference plus Noise Ratio (Signal to interference plus noise ratio, SINR) can be effectively improved,
Therefore there is higher actual application value.Wherein, undistorted response (the Minimum variable of minimum variance
Distortionless response, MVDR) Beam synthesis method is a kind of classic algorithm.However, in actual applications, it is limited
Sampling snap so that larger error be present in sample covariance matrix.Sensor position uncertainties and array element phase response are inconsistent etc.
Factor, make steering vector prior information inaccurate.Algorithm how is set error to be present in input steering vector prior information, while
Less sampling is taken soon to be restrained, and output signal is had higher SINR, has important engineering application value.
Numerous scholars propose many robustness algorithms in succession, wherein representative algorithm has diagonal loading
(Diagonal loading, DL) [7] Beam synthesis algorithm, proper subspace (Eigenspace projection, ESB) ripple
Beam composition algorithm etc..Wide-angle mismatch robustness (the Robust beamforming against large that document [10] proposes
DOA mismatch, RLM) adaptive beam composition algorithm, it would be desirable to signal guide vector orthogonal subspaces characteristic vector line
Property represent.Document [Modified projection approach for robust adaptive array
Beamforming] propose characteristic vector projection subspace estimation (Eigenvector projection approach
For subspace estimation, EPS) adaptive beam composition algorithm, by estimating the phase to steering vector projection is assumed
Hope signal subspace, it is assumed that steering vector reduces error to desired signal subspace projection.Reduce with subspace method
Estimation error of the covarianee matrix is also the common method for lifting Beam synthesis algorithm performance.Document [DOA estimation of
Quasi-stationary signals via Khatri-rao subspace] propose that a kind of Khatri-Rao (KR) carrys out wave angle
Algorithm for estimating is spent, by studying the secondary data structure of quasi- stationary signal, KR subspaces is effectively eliminated noise covariance
Matrix, while increase array element aperture.Document [Sparse covariance fitting for direction of arrival
Estimation] with steering vector construction dictionary structure carry out rarefaction representation array covariance matrix.But algorithm above does not exist
When reducing sample covariance matrix evaluated error, the evaluated error of steering vector is effectively corrected, enables algorithm in smaller snap
Under restrained, and cause output signal there is higher SINR.
The deficiency for more than, set forth herein a kind of subspace estimation (Modified for improving characteristic vector projection
Eigenvector projection approach for subspace estimation, MEPS) adaptive beam synthesis side
Method.KR signal subspaces are constructed first to reduce the evaluated error of sample covariance matrix.Secondly revised covariance is utilized
Matrix characteristic vector construction interference plus noise subspace, by it will be assumed steering vector rectangular projection to interference plus noise subspace
To reduce the evaluated error of sample covariance matrix.
The content of the invention
It is an object of the invention to propose a kind of to converge to the improvement characteristic vector of degree of precision in less take soon
Projection subspace estimation adaptive beam synthetic method.
The object of the present invention is achieved like this：
Comprise the following steps：
(1) array antenna samples to input signal：
Sampled data is expressed as with sampled data covariance matrix：
Wherein, for K to sample fast umber of beats, x is input signal；
(2) construction KR signal covariance vectors are accumulated by Khatri-Rao：
Vec () is stacked into first row for matrix is respectively arranged：
D (θ)=vec (a (θ) aH(θ))
Wherein, a (θ) is input signal steering vector；
Covariance vector is asked to obtain in both sides：
For the linear combination of desired signal and interference signal covariance vector, structural matrix S：
Signal covariance vectorBy matrix S characteristic vector linear expression, d (θ) subspace dimension etc.
In the number of matrix S nonzero eigenvalues；
The characteristic vector structural matrix Q as corresponding to matrix S nonzero eigenvalue：
Q=[e1,e2,...,eK]
Wherein,For characteristic vector corresponding to matrix Q nonzero eigenvalue, Q row are mutually orthogonal, form signal association
The proper subspace of Variance Vector；
Wherein, Q (QHQ)-1QHFor the projection matrix of signal covariance vector subspace；For sample covariance matrix, R1Table
ShowProjected to signal covariance vector subspace；
(3) characteristic vector projection subspace method estimation steering vector：
If try to achieve interference and noise subspace projection matrix Ui+n, by being led to Orthogonal subspace projection to eliminate expectation
To the evaluated error of vector：
Wherein,It is expected steering vector estimate,It is expected steering vector correction value, obtained R1Carry out characteristic value point
Xie Wei：
Wherein, λ1＞ λ2＞ ... ＞ λK+1=...=λN=σ2For covariance matrix R1Characteristic value, eiIt is corresponding to be characterized value
Characteristic vector；
Each characteristic vector eiTo steering vectorProjection, choose characteristic vector construction interference plus noise corresponding to projection
Signal subspace Ui+n；
By projection of the characteristic vector to steering vectorDescending is carried out to arrange：p[M]≥
p[M-1]≥…≥p[1]；
Use characteristic vector construction interference plus noise subspace；
With m increase, m values when for the first time more than ρ are desired value, construct interference plus noise subspace：
Ui+n=[e[1],e[2],…,e[m-1]]
Then interference plus noise subspace projection matrix is：
And then it can must it is expected that subspace projection matrix is：
Ps=I-Pi+n
The evaluated error of interference plus noise sub-space portion is eliminated, improves the estimated accuracy of steering vector：
Improve Beam synthesis weight vector：
(4) array antenna output signal is obtained：
Y=wHx
Wherein, y is output signal.
The beneficial effects of the present invention are：
The main advantage of the invention compared with traditional adaptive beam synthesizer is as follows：
First, the present invention can be restrained compared to traditional beam synthesizer in smaller take soon；
2nd, technology of the invention has higher convergence precision compared to traditional beam synthesizer；
3rd, technology of the invention goes for the higher system of requirement of real-time.
Why there is as above advantage, main cause is the sampling covariance that MEPS beam synthesizing methods use degree of precision
Matrix, while it will be assumed that steering vector projects to signal subspace, reduce steering vector evaluated error, enable MEPS smaller
Take to obtain higher SINR output signals soon.
Brief description of the drawings
Fig. 1 is 5 array element uniform straight line arrays, the matrix S ascending arranged distribution figure of characteristic value.
MEPS, RLM, EPS and MVDR convergence of algorithm rate curve when Fig. 2 is without expectation signal angle mismatch.
MEPS, RLM, EPS and MVDR convergence of algorithm precision curve when Fig. 3 is without expectation signal angle mismatch.
Fig. 4 is MEPS, RLM, EPS and MVDR convergence of algorithm rate curve when desired signal angle mismatching be present.
Fig. 5 is MEPS, RLM, EPS and MVDR convergence of algorithm precision curve when desired signal angle mismatching be present.
Embodiment
The present invention is described further below in conjunction with the accompanying drawings.
Array antenna beam synthesizes, i.e., spacing wave is received using more antennas.Calculated using array signal processing
Method, array signal is filtered, and then is weighted summation, obtain larger Signal to Interference plus Noise Ratio (SINR) output signal.Carry out
Main lobe alignment desired signal, null alignment interference signal are shown as after weighting in beam pattern.Because algorithm has stronger to interference
Rejection ability, therefore beam pattern should possess relatively low side lobe levels.How Beam synthesis algorithm is improved in the small receipts taken soon
The SINR outputs held back speed and relatively stablized, are the keys that adaptive beam composition algorithm obtains engineer applied.Carry herein
Go out MEPS adaptive beam composition algorithms, the method constructs KR signal subspaces to eliminate covariance matrix in noise subspace first
Evaluated error.Secondly signal subspace it is expected using revised covariance matrix principal eigenvector construction, it is assumed that be oriented to arrow
Measure and projected to signal subspace, reduce steering vector evaluated error, enable MEPS it is smaller take to obtain higher SINR soon it is defeated
Go out signal.
Based on a kind of Khatri-Rao (KR) covariance matrix building method, it is empty that signal covariance matrix KR is constructed herein
Between, to eliminate the evaluated error of covariance matrix.Secondly, constructed using revised covariance matrix principal eigenvector and it is expected letter
Work song space, it is assumed that steering vector projects to signal subspace, reduces steering vector evaluated error, enables MEPS smaller fast
Take to obtain higher SINR output signals.
Step 1: array antenna samples to input signal.
Sampled data is expressed as with sampled data covariance matrix：
Wherein, for K to sample fast umber of beats, x is input signal.
Step 2: it can be constructed " KR signal covariances vector " by Khatri-Rao products：
Define vec () and be stacked into first row for matrix is respectively arranged, be called " covariance vector " herein, then formula (2) can
It is expressed as：
D (θ)=vec (a (θ) aH(θ)) (3)
Wherein, a (θ) is that input signal is oriented in right amount.
Covariance vector is asked to obtain on formula (1) both sides：
Understand,For the linear combination of desired signal and interference signal covariance vector, therefore, if structure
Covariance vector subspace is made,One is scheduled in the subspace.It can prove, if the mutual not phase of reception signal
Close, N × N reception signals covariance matrix is Toeplitz matrixes, and can be characterized completely with 2N-1 n-dimensional subspace ns.Structural matrix
Shown in S such as formulas (5)：
Then signal covariance vectorCan be by matrix S principal eigenvector linear expression.D (θ) are empty
Between dimension be equal to matrix S nonzero eigenvalues number.
The characteristic vector structural matrix Q as corresponding to matrix S nonzero eigenvalue, as shown in formula (6)：
Q=[e1,e2,...,eK] (6)
Wherein,For characteristic vector corresponding to matrix Q nonzero eigenvalue.Therefore, Q row are mutually orthogonal, form letter
The proper subspace of number covariance vector.
Define R1It is as follows：
Wherein, Q (QHQ)-1QHFor the projection matrix of signal covariance vector subspace；For sample covariance matrix, then R1
RepresentProjected to signal covariance vector subspace.
Step 3: characteristic vector projection subspace method estimation steering vector
It is similar with covariance matrix error correction, if trying to achieve interference and noise subspace projection matrix Ui+n, then can pass through
The evaluated error of expectation steering vector is eliminated to its Orthogonal subspace projection, i.e.,：
Wherein,It is expected steering vector estimate,It is expected steering vector correction value.Formula (7) can be obtained herein
R1Carrying out Eigenvalues Decomposition is：
Wherein, λ1＞ λ2＞ ... ＞ λK+1=...=λN=σ2For covariance matrix R1Characteristic value, eiIt is corresponding to be characterized value
Characteristic vector.
As it is assumed that steering vectorWith true steering vector a (θ0) angle difference is little, therefore each characteristic vector ei
To hypothesis steering vectorProjection, characteristic vector corresponding to the smaller projection of selection can construct interference plus noise signals subspace
Ui+n。
By projection of the characteristic vector to hypothesis steering vectorDescending is carried out to arrange：p[M]
≥p[M-1]≥…≥p[1]。
Because characteristic vector corresponding to larger projection can construct expectation signal subspace, therefore less characteristic vector
Interference plus noise subspace can be constructed.
With m increase, the m values when first time exceeding right formula are desired value, and construction interference plus noise subspace is：
Ui+n=[e[1],e[2],…,e[m-1]] (11)
Then interference plus noise subspace projection matrix is represented by：
And then it can must it is expected that subspace projection matrix is：
Ps=I-Pi+n (13)
Similar covariance matrix error correction algorithms, it is assumed that steering vector can be with undistorted to desired signal subspace projection
Mapping steering vector in the part of signal subspace, eliminate the evaluated error of interference plus noise sub-space portion.Therefore can be with
Improve the estimated accuracy of steering vector.Specific formula for calculation is as follows：
Improving Beam synthesis weight vector calculation formula is：
Step 4: obtain array antenna output signal.
Y=wHx (16)
Wherein, y is output signal.
Present embodiment effect：
It is of the invention mutually to have following advantage with traditional beam synthesizing method：
The evaluated error of sampling covariance matrix is reduced set forth herein a kind of MEPS adaptive beam composition algorithm, simultaneously
The evaluated error of steering vector is assumed in amendment.The algorithm constructs KR signal subspaces to estimate array covariance matrix first, protects
Card algorithm can take convergence soon in less；Secondly interference plus noise is constructed with the covariance matrix characteristic vector of estimation
Subspace, and projected by being directed to vector to its orthogonal subspaces to reduce evaluated error.The algorithm is without having believed
Source number, you can accurately estimate signal subspace, substantially increase the flexibility of engineer applied.Simulation result shows, this
Literary innovatory algorithm can be restrained in less take soon, and higher SINR outputs are obtained under the inputs of SNR in a big way,
Obvious signal cancellation phenomenon will not be produced during higher SNR inputs.
First, present embodiment can take to obtain accurate sampled signal soon compared to traditional algorithm smaller；
2nd, the technology of present embodiment can be corrected effectively compared to traditional algorithm it is expected signal guide vector error；
3rd, the technology of present embodiment can converge to degree of precision compared to traditional algorithm in smaller take soon.
Verified by following l-G simulation test：
Fig. 2 is respectively MEPS, RLM, EPS and MVDR convergence rate curve.Wherein input signal-to-noise ratio (Signal to
Noise rate, SNR) it is 20dB, therefore the optimal output SINR=30dB of array.K is the fast umber of beats of sampling in figure.In steering vector
In the case of accurately known, the estimated accuracy of covariance matrix directly affects convergence of algorithm speed.Four kinds of algorithms of contrast it is defeated
Going out SINR can draw the following conclusions with sampling the relation of fast umber of beats：MEPS can take convergence soon less, it is possible thereby to see
The evaluated error of sample covariance matrix can be effectively reduced by going out MEPS.RLM, EPS and MVDR are due to small snap down-sampling association side
Poor matrix error is larger, and algorithmic statement speed is slower.
Fig. 3 is respectively tetra- kinds of convergence of algorithm precision curves of MEPS, RLM, EPS and MVDR.Contrast the output of three kinds of algorithms
SINR can be seen that with input SNR variation relation：With input SNR change, MEPS remains higher SINR outputs,
But tri- kinds of algorithm performances of RLM, EPS and MVDR are unstable.I.e.：There is EPS higher SINR to export during SNR ＜ 0dB, and SNR ＞
5dB outputs SINR declines rapidly；The output SINR that RLM and MVDR is obtained is relatively low.In fact, when inputting SNR increases, association side
Poor Matrix Estimation error increases the influence for exporting SINR, and RLM, EPS and MVDR will produce serious signal cancellation, therefore its
It is relatively low to export SINR.MEPS algorithms reduce covariance square due to constructing KR signal covariance vector subspaces by projection
The evaluated error of battle array, therefore the estimated accuracy of covariance matrix is improved, output SINR is higher.
Tetra- kinds of algorithms of MEPS, RLM, EPS and ESB export SINR with fast umber of beats when Fig. 4 is it is expected signal guide vector mismatch
Change curve.It is 6 ° to estimate desired signal angle.As seen from Figure 4, when steering vector mismatch be present, MEPS algorithms compared with
Convergence rate is slack-off during without mismatch, but because its sample covariance matrix is projected in covariance vector subspace, reduces
Error, still there is faster convergence rate compared to other three kinds of algorithm MEPS algorithms, steering vector mismatch is shown stronger
Robustness.And the covariance matrix of RLM, EPS and ESB algorithm has larger error, algorithm the convergence speed is reduced；Larger error
Covariance matrix causes steering vector evaluated error larger, influences to export SINR.
Fig. 5 is MEPS, RLM, EPS and ESB output SINR with input SNR change curve.Estimate desired signal angle
For 6 °.As can be seen that when input SNR changes, the SINR that RLM, EPS and ESB algorithm can not keep higher is exported, and MEPS
Algorithm possesses higher SINR outputs all the time.In fact, because the covariance matrix precision that MEPS algorithms use is higher, because
This can effectively estimate accurate expectation steering vector.And RLM, EPS and ESB algorithm covariance matrix covariance exist compared with
Big error, therefore accurate expectation steering vector is unable to estimate out, therefore it is unstable to export SINR.And during input SNR increases,
Desired signal cancellation occurs in RLM, EPS and ESB algorithm, therefore exports SINR and decline comparatively fast.
In summary, MEPS adaptive beam composition algorithm reduces the evaluated error of sample covariance matrix, repaiies simultaneously
The positive evaluated error for assuming steering vector.The algorithm is without information source number, you can accurately estimates signal subspace, greatly
The big flexibility for improving engineer applied.This paper innovatory algorithms can be restrained in less take soon, and in SNR in a big way
Input is lower to obtain higher SINR outputs, and obvious signal cancellation phenomenon will not be produced when higher SNR is inputted.
Claims (1)
1. a kind of projection subspace estimation adaptive beam synthetic method for improving characteristic vector, it is characterised in that including as follows
Step：
(1) array antenna samples to input signal：
Sampled data is expressed as with sampled data covariance matrix：
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(2) construction KR signal covariance vectors are accumulated by Khatri-Rao：
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Wherein, a (θ) is input signal steering vector；
Covariance vector is asked to obtain in both sides：
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The proper subspace of amount；
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Improve Beam synthesis weight vector：
<mrow>
<mi>w</mi>
<mo>=</mo>
<mfrac>
<mrow>
<msub>
<mi>R</mi>
<mn>1</mn>
</msub>
<mover>
<mi>a</mi>
<mo>~</mo>
</mover>
</mrow>
<mrow>
<msup>
<mover>
<mi>a</mi>
<mo>~</mo>
</mover>
<mi>H</mi>
</msup>
<msubsup>
<mi>R</mi>
<mn>1</mn>
<mrow>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msubsup>
<mover>
<mi>a</mi>
<mo>~</mo>
</mover>
</mrow>
</mfrac>
</mrow>
(4) array antenna output signal is obtained
Y=wHx
Wherein, y is output signal.
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