CN105354171A - Improved eigenvector projection subspace estimation adaptive beam forming method - Google Patents

Abstract

The invention relates to an improved eigenvector projection subspace estimation adaptive beam forming method. The method comprises: an array antenna performing sampling on an input signal; constructing a KR signal covariance vector by Khatri-Rao; estimating a guide vector with an eigenvector projection subspace method; and obtaining an output signal of the array antenna. Compared with a conventional beam former, convergence can be obtained in a relatively small snapshot; relatively high convergence precision is achieved; and the technology can be suitable for systems with relatively high real-time requirements.

Description

A kind of projection subspace estimation adaptive beam synthetic method improving eigenvector

Technical field

The present invention relates to a kind of projection subspace estimation adaptive beam synthetic method improving eigenvector.

Background technology

Array Signal Processing, as the new things risen, has been widely used in the various fields such as radar, sonar, navigation, communication.The synthesis of array antenna adaptive beam is as the importance of Array Signal Processing, there is stronger interference rejection capability, and effectively can improve output signal Signal to Interference plus Noise Ratio (Signaltointerferenceplusnoiseratio, SINR), therefore there is higher actual application value.Wherein, minimum variance undistorted response (Minimumvariabledistortionlessresponse, MVDR) Beam synthesis method is a kind of classic algorithm.But in actual applications, limited sampling snap, makes sample covariance matrix there is comparatively big error.Sensor position uncertainties and the factor such as array element phase response is inconsistent, make steering vector prior imformation inaccurate.How to make algorithm there is error in input steering vector prior imformation, take soon in less sampling simultaneously and restrained, and make output signal have higher SINR, there is important engineer applied and be worth.

Numerous scholars propose many robustness algorithms in succession, wherein representative algorithm has diagonal angle to load (Diagonalloading, DL) [7] Beam synthesis algorithm, proper subspace (Eigenspaceprojection, ESB) Beam synthesis algorithm etc.Wide-angle mismatch robustness (RobustbeamformingagainstlargeDOAmismatch, RLM) the adaptive beam composition algorithm that document [10] proposes, by the orthogonal subspaces eigenvector linear expression of wanted signal steering vector.Subspace estimation (the Eigenvectorprojectionapproachforsubspaceestimation of the eigenvector projection that document [Modifiedprojectionapproachforrobustadaptivearraybeamform ing] proposes, EPS) adaptive beam composition algorithm, by estimating wanted signal subspace to the projection of hypothesis steering vector, suppose that steering vector is to wanted signal subspace projection to reduce error.Using subspace method to reduce estimation error of the covarianee matrix is also the common method promoting Beam synthesis algorithm performance.Document [DOAestimationofquasi-stationarysignalsviaKhatri-raosubsp ace] proposes a kind of Khatri-Rao (KR) incoming wave angle algorithm for estimating, by studying the secondary data structure of accurate stationary signal, make KR subspace can effective stress release treatment covariance matrix, increase array element aperture simultaneously.Document [Sparsecovariancefittingfordirectionofarrivalestimation] uses steering vector structure dictionary structure to carry out rarefaction representation array covariance matrix.But above algorithm, not when reducing sample covariance matrix evaluated error, effectively being revised the evaluated error of steering vector, being enable algorithm be restrained less taking soon, and make to output signal there is higher SINR.

For above deficiency, a kind of subspace estimation (Modifiedeigenvectorprojectionapproachforsubspaceestimati on, MEPS) adaptive beam synthetic method improving eigenvector projection is proposed herein.First the evaluated error that KR signal subspace reduces sample covariance matrix is constructed.Next utilizes revised covariance matrix characteristic vector to construct interference plus noise subspace, by the rectangular projection of hypothesis steering vector to be reduced the evaluated error of sample covariance matrix to interference plus noise subspace.

Summary of the invention

The object of the invention is to propose a kind of can in the less projection subspace estimation adaptive beam synthetic method taking the improvement eigenvector converging to degree of precision soon.

The object of the present invention is achieved like this:

Comprise the steps:

(1) array antenna is sampled to input signal:

Sampled data sampled data covariance matrix is expressed as:

$R=\frac{1}{K}\underset{i=1}{\overset{K}{\Σ}}{x}^{H}x$

Wherein, K is the fast umber of beats of sampling, and x is input signal;

(2) by Khatri-Rao long-pending structure KR signal covariance vector:

$d\left(\mathrm{\θ}\right)=a\left(\mathrm{\θ}\right)\⊗a\left(\mathrm{\θ}\right)$

Vec () is stacked into first row for respectively being arranged by matrix:

d(θ)＝vec(a(θ)a ^H(θ))

Wherein, a (θ) is input signal steering vector;

Both sides ask covariance vector to obtain:

$\begin{array}{c}vec(R-{\mathrm{\σ}}_{noise}^{2}I)=\underset{i=1}{\overset{N}{\Σ}}{\mathrm{\σ}}_i^{2}vec\left(a\right({\mathrm{\θ}}_i\left)a^H\right({\mathrm{\θ}}_i\left)\right)\\ =\underset{i=1}{\overset{N}{\Σ}}{\mathrm{\σ}}_i^{2}d\left({\mathrm{\θ}}_i\right)\end{array}$

for the linear combination of wanted signal and undesired signal covariance vector, structural matrix S:

$S=\underset{0}{\overset{\mathrm{\π}}{\∫}}d\left(\mathrm{\θ}\right)d^H\left(\mathrm{\θ}\right)d\mathrm{\θ}$

Signal covariance vector by the proper vector linear expression of matrix S, d (θ) subspace dimension equals the number of matrix S nonzero eigenvalue;

Nonzero eigenvalue characteristic of correspondence vector structural matrix Q by matrix S:

Q＝[e ₁,e ₂,...,e _K]

Wherein, for the nonzero eigenvalue characteristic of correspondence vector of matrix Q, the row of Q are mutually orthogonal, form the proper subspace of signal covariance vector;

$vec\left(R_1\right)=Q{\left(Q^{H}Q\right)}^{-1}{Q}^{H}vec\left(\hat{R}\right)$

Wherein, Q (Q ^hq) ^-1q ^hfor the projection matrix of signal covariance vector subspace; for sample covariance matrix, R ₁represent project to signal covariance vector subspace;

(3) eigenvector projection subspace method estimates steering vector:

If try to achieve interference and noise subspace projection matrix U _i+n, by eliminating the evaluated error expecting steering vector to Orthogonal subspace projection:

$\tilde{a}=(I-U_{i+n}{U}_{i+n}^H)\hat{a}$

Wherein, for expecting steering vector estimated value, for expecting steering vector modified value, the R obtained ₁carrying out Eigenvalues Decomposition is:

$R_1=\underset{i=1}{\overset{N}{\Σ}}{\mathrm{\λ}}_i{e}_i{e}_i^H$

Wherein, λ ₁> λ ₂> ... > λ _k+1=...=λ _n=σ ²for covariance matrix R ₁eigenwert, e _ifor eigenwert characteristic of correspondence vector;

Each eigenvector e _iall to steering vector projection, chooses projection characteristic of correspondence vectorial structure interference plus noise signals subspace U _i+n;

By the projection of eigenvector to steering vector carry out descending sort to obtain: p _[M]>=p _[M-1]>=...>=p _[1];

Use eigenvector structure interference plus noise subspace;

$(p_{\&lsqb;m\&rsqb;}+p_{\&lsqb;m-1\&rsqb;}\&GreaterEqual;...\&GreaterEqual;p_{\&lsqb;1\&rsqb;})/\underset{i=1}{\overset{M}{\&Sigma;}}\left(i\right)<\mathrm{\&rho;}$

Along with the increase of m, be desired value when first time more than m value during ρ, structure interference plus noise subspace:

U _i+n＝[e _[1],e _[2],…,e _[m-1]]

Then interference plus noise subspace projection matrix is:

$P_{i+n}=U_{i+n}{U}_{i+n}^H$

And then can expect that subspace projection matrix is:

P _s＝I-P _i+n

Eliminate the evaluated error of interference plus noise sub-space portion, improve the estimated accuracy of steering vector:

$\tilde{a}=P_s\hat{a}$

Improve Beam synthesis weight vector:

$w=\frac{R_1\tilde{a}}{{\tilde{a}}^H{R}_1^{-1}\tilde{a}}$

(4) array antenna output signal is obtained:

y＝w ^Hx

Wherein, y is output signal.

Beneficial effect of the present invention is:

The present invention's main advantage compared with traditional adaptive beam compositor is as follows:

One, the present invention compares traditional beam synthesizer and can be restrained less taking soon;

Two, technology of the present invention is compared traditional beam synthesizer and is had higher convergence precision;

Three, technology of the present invention goes for the higher system of requirement of real-time.

Why there is as above advantage, main cause is the sample covariance matrix that MEPS beam synthesizing method adopts degree of precision, hypothesis steering vector is projected to signal subspace simultaneously, reduce steering vector evaluated error, enable MEPS obtain higher SINR output signal less taking soon.

Accompanying drawing explanation

Fig. 1 is 5 array element uniform straight line arrays, the ascending arranged distribution figure of eigenwert of matrix S.

Fig. 2 is without MEPS, RLM, EPS and MVDR convergence of algorithm rate curve during expectation signal angle mismatch.

Fig. 3 is without MEPS, RLM, EPS and MVDR convergence of algorithm precision curve during expectation signal angle mismatch.

There is MEPS, RLM, EPS and MVDR convergence of algorithm rate curve when expecting signal angle mismatch in Fig. 4.

There is MEPS, RLM, EPS and MVDR convergence of algorithm precision curve when expecting signal angle mismatch in Fig. 5.

Embodiment

Below in conjunction with accompanying drawing, the present invention is described further.

Array antenna beam synthesizes, and namely applies many antennas and receives spacing wave.Application Array Signal Processing algorithm, pair array signal carries out filtering, and then is weighted summation, obtains the output signal of larger Signal to Interference plus Noise Ratio (SINR).Be weighted in rear beam pattern and be shown as main lobe aligning wanted signal, zero falls into aligning undesired signal.Because algorithm has stronger rejection ability to interference, therefore beam pattern should possess lower side lobe levels.How improving Beam synthesis algorithm in the little speed of convergence that takes soon obtains more stable SINR and exports, and is the key that adaptive beam composition algorithm obtains engineer applied.Propose MEPS adaptive beam composition algorithm herein, first this method constructs KR signal subspace to eliminate the evaluated error of covariance matrix at noise subspace.Next utilizes revised covariance matrix principal eigenvector to construct to expect signal subspace, suppose that steering vector projects to signal subspace, reduction steering vector evaluated error, enables MEPS obtain higher SINR output signal less taking soon.

Based on a kind of Khatri-Rao (KR) covariance matrix building method, construct signal covariance matrix KR subspace herein, eliminate the evaluated error of covariance matrix.Secondly, utilize revised covariance matrix principal eigenvector to construct and expect signal subspace, suppose that steering vector projects to signal subspace, reduction steering vector evaluated error, enable MEPS obtain higher SINR output signal less taking soon.

Step one, array antenna are sampled to input signal.

Sampled data sampled data covariance matrix is expressed as:

$\begin{array}{c}R=\frac{1}{K}\underset{i=1}{\overset{K}{\&Sigma;}}{x}^{H}x\\ =\underset{i=1}{\overset{N}{\&Sigma;}}{\mathrm{\&sigma;}}_i^{2}a\left({\mathrm{\&theta;}}_i\right)a^H\left({\mathrm{\&theta;}}_i\right)+{\mathrm{\&sigma;}}_{noise}^{2}I\end{array}---\left(1\right)$

Wherein, K is the fast umber of beats of sampling, and x is input signal.

Step 2, can to construct " KR signal covariance vector " by Khatri-Rao is long-pending:

$d\left(\mathrm{\&theta;}\right)=a\left(\mathrm{\&theta;}\right)\&CircleTimes;a\left(\mathrm{\&theta;}\right)---\left(2\right)$

Definition vec () is stacked into first row for respectively being arranged by matrix, and be called herein " covariance vector ", then formula (2) can be expressed as:

d(θ)＝vec(a(θ)a ^H(θ))(3)

Wherein, a (θ) is appropriate for input signal leads.

Covariance vector is asked to obtain to formula (1) both sides:

$\begin{array}{c}vec(R-{\mathrm{\&sigma;}}_{noise}^{2}I)=\underset{i=1}{\overset{N}{\&Sigma;}}{\mathrm{\&sigma;}}_i^{2}vec\left(a\right({\mathrm{\&theta;}}_i\left)a^H\right({\mathrm{\&theta;}}_i\left)\right)\\ =\underset{i=1}{\overset{N}{\&Sigma;}}{\mathrm{\&sigma;}}_i^{2}d\left({\mathrm{\&theta;}}_i\right)\end{array}---\left(4\right)$

It is known, for the linear combination of wanted signal and undesired signal covariance vector, therefore, if structure covariance vector subspace, one fixes in this subspace.Can prove, if Received signal strength is uncorrelated mutually, N × N Received signal strength covariance matrix is Toeplitz matrix, and can use 2N-1 n-dimensional subspace n Complete Characterization.Structural matrix S is such as formula shown in (5):

$S=\underset{0}{\overset{\mathrm{\&pi;}}{\&Integral;}}d\left(\mathrm{\&theta;}\right)d^H\left(\mathrm{\&theta;}\right)d\mathrm{\&theta;}---\left(5\right)$

Then signal covariance vector can by the principal eigenvector linear expression of matrix S.D (θ) subspace dimension equals the number of matrix S nonzero eigenvalue.

By the nonzero eigenvalue characteristic of correspondence vector structural matrix Q of matrix S, shown in (6):

Q＝[e ₁,e ₂,...,e _K](6)

Wherein, for the nonzero eigenvalue characteristic of correspondence vector of matrix Q.Therefore, the row of Q are mutually orthogonal, form the proper subspace of signal covariance vector.

Definition R ₁as follows:

$vec\left(R_1\right)=Q{\left(Q^{H}Q\right)}^{-1}{Q}^{H}vec\left(\hat{R}\right)---\left(7\right)$

Wherein, Q (Q ^hq) ^-1q ^hfor the projection matrix of signal covariance vector subspace; for sample covariance matrix, then R ₁represent project to signal covariance vector subspace.

Step 3, eigenvector projection subspace method estimates steering vector

Similar with covariance matrix error correction, if try to achieve interference and noise subspace projection matrix U _i+n, then by eliminating the evaluated error expecting steering vector to its Orthogonal subspace projection, that is:

$\tilde{a}=(I-U_{i+n}{U}_{i+n}^H)\hat{a}---\left(8\right)$

Wherein, for expecting steering vector estimated value, for expecting steering vector modified value.At the R that formula (7) can obtain by this ₁carrying out Eigenvalues Decomposition is:

$R_1=\underset{i=1}{\overset{N}{\&Sigma;}}{\mathrm{\&lambda;}}_i{e}_i{e}_i^H---\left(9\right)$

Wherein, λ ₁> λ ₂> ... > λ _k+1=...=λ _n=σ ²for covariance matrix R ₁eigenwert, e _ifor eigenwert characteristic of correspondence vector.

Due to hypothesis steering vector with true steering vector a (θ ₀) angle difference is little, therefore each eigenvector e _iall to hypothesis steering vector projection, chooses less projection characteristic of correspondence vector and can construct interference plus noise signals subspace U _i+n.

By the projection of eigenvector to hypothesis steering vector carry out descending sort to obtain:

Because larger projection characteristic of correspondence vector can construct expectation signal subspace, therefore less eigenvector can construct interference plus noise subspace.

$(p_{\&lsqb;m\&rsqb;}+p_{\&lsqb;m-1\&rsqb;}\&GreaterEqual;...\&GreaterEqual;p_{\&lsqb;1\&rsqb;})/\underset{i=1}{\overset{M}{\&Sigma;}}p\left(i\right)<\mathrm{\&rho;}---\left(10\right)$

Along with the increase of m, the m value when first time exceedes right formula is desired value, and structure interference plus noise subspace is:

U _i+n＝[e _[1],e _[2],…,e _[m-1]](11)

Then interference plus noise subspace projection matrix can be expressed as:

$P_{i+n}=U_{i+n}{U}_{i+n}^H---\left(12\right)$

And then can expect that subspace projection matrix is:

P _s＝I-P _i+n(13)

Similar covariance matrix error correction algorithms, suppose steering vector to wanted signal subspace projection can undistorted mapping steering vector in the part of signal subspace, eliminate the evaluated error of interference plus noise sub-space portion.Therefore the estimated accuracy of steering vector can be improved.Specific formula for calculation is as follows:

$\tilde{a}=P_s\hat{a}---\left(14\right)$

Improving Beam synthesis weight vector computing formula is:

$w=\frac{R_1\tilde{a}}{{\tilde{a}}^H{R}_1^{-1}\tilde{a}}---\left(15\right)$

Step 4, obtain array antenna output signal.

y＝w ^Hx(16)

Wherein, y is output signal.

Present embodiment effect:

Phase of the present invention and traditional beam synthesizing method have following advantage:

Propose the evaluated error that a kind of MEPS adaptive beam composition algorithm reduces sampling covariance matrix herein, revise the evaluated error of hypothesis steering vector simultaneously.First this algorithm constructs KR signal subspace to estimate array covariance matrix, ensures that algorithm can take convergence soon less; Secondly use the covariance matrix eigenvector estimated to construct interference plus noise subspace, and reduce evaluated error by steering vector is carried out projection to its orthogonal subspaces.This algorithm, can estimated signal subspace more exactly without the need to information source number, substantially increases the dirigibility of engineer applied.Simulation result shows, herein innovatory algorithm can be restrained less taking soon, and under SNR input in a big way, obtains higher SINR export, and can not produce obvious signal cancellation phenomenon when higher SNR input.

One, present embodiment is compared traditional algorithm and can be obtained sampled signal accurately less taking soon;

Two, the technology of present embodiment is compared traditional algorithm and effectively can be revised expectation signal guide vector error;

Three, the technology of present embodiment is compared traditional algorithm and can be converged to degree of precision less taking soon.

Verified by following l-G simulation test:

Fig. 2 is respectively the speed of convergence curve of MEPS, RLM, EPS and MVDR.Wherein input signal-to-noise ratio (Signaltonoiserate, SNR) is 20dB, and therefore array optimum exports SINR=30dB.In figure, K is the fast umber of beats of sampling.Under the accurate known case of steering vector, the estimated accuracy of covariance matrix directly affects convergence of algorithm speed.The output SINR of contrast four kinds of algorithms can draw the following conclusions with the relation of the fast umber of beats of sampling: MEPS can take convergence soon less, this shows that MEPS can effectively reduce the evaluated error of sample covariance matrix.RLM, EPS and MVDR due to little snap down-sampling covariance matrix error comparatively large, algorithm convergence speed is slower.

Fig. 3 is respectively MEPS, RLM, EPS and MVDR four kinds of convergence of algorithm precision curves.The output SINR of contrast three kinds of algorithms can find out with the variation relation of input SNR: along with the change of input SNR, and MEPS remains that higher SINR exports, but RLM, EPS and MVDR three kinds of algorithm performance instability.That is: during SNR < 0dB, EPS has higher SINR output, and SNR > 5dB output SINR declines rapidly; The output SINR that RLM and MVDR obtains is all lower.In fact, when inputting SNR and increasing, estimation error of the covarianee matrix increases the impact exporting SINR, and RLM, EPS and MVDR will produce serious signal cancellation, and therefore its output SINR is lower.MEPS algorithm due to structure KR signal covariance vector subspace, and reduces the evaluated error of covariance matrix by projection, therefore improve the estimated accuracy of covariance matrix, export SINR higher.

Fig. 4 is MEPS when expecting signal guide vector mismatch, RLM, EPS and ESB four kinds of algorithms export the change curve of SINR with fast umber of beats.Estimate that wanted signal angle is 6 °.As seen from Figure 4, when there is steering vector mismatch, MEPS algorithm is comparatively slack-off without speed of convergence during mismatch, but because its sample covariance matrix projects at covariance vector subspace, reduce error, compare other three kinds of algorithm MEPS algorithms and still there is speed of convergence faster, stronger robustness is shown to steering vector mismatch.And the covariance matrix of RLM, EPS and ESB algorithm exists comparatively big error, reduce algorithm the convergence speed; Cause steering vector evaluated error comparatively large compared with the covariance matrix of big error, impact exports SINR.

Fig. 5 be MEPS, RLM, EPS and ESB output SINR with input SNR change curve.Estimate that wanted signal angle is 6 °.Can find out, when input SNR changes, RLM, EPS and ESB algorithm can not keep higher SINR to export, and MEPS algorithm possesses higher SINR output all the time.In fact, the covariance matrix precision adopted due to MEPS algorithm is higher, therefore effectively can estimate and expect steering vector more accurately.And RLM, EPS and ESB algorithm covariance matrix covariance exists comparatively big error, be therefore unable to estimate out and expect steering vector more accurately, therefore export SINR unstable.And during input SNR increase, RLM, EPS and ESB algorithm there will be wanted signal and disappears mutually, therefore export SINR and decline very fast.

In sum, MEPS adaptive beam composition algorithm reduces the evaluated error of sample covariance matrix, revises the evaluated error of hypothesis steering vector simultaneously.This algorithm, can estimated signal subspace more exactly without the need to information source number, substantially increases the dirigibility of engineer applied.Herein innovatory algorithm can be restrained less taking soon, and under SNR input in a big way, obtains higher SINR export, and can not produce obvious signal cancellation phenomenon when higher SNR input.

Claims (1)

1. improve a projection subspace estimation adaptive beam synthetic method for eigenvector, it is characterized in that, comprise the steps:

(1) array antenna is sampled to input signal:

Sampled data sampled data covariance matrix is expressed as:

$R=\frac{1}{K}\underset{i=1}{\overset{K}{\&Sigma;}}{x}^{H}x$

Wherein, K is the fast umber of beats of sampling, and x is input signal;

(2) by Khatri-Rao long-pending structure KR signal covariance vector:

$d\left(\mathrm{\&theta;}\right)=a\left(\mathrm{\&theta;}\right)\&CircleTimes;a\left(\mathrm{\&theta;}\right)$

Vec () is stacked into first row for respectively being arranged by matrix:

d(θ)＝vec(a(θ)a ^H(θ))

Wherein, a (θ) is input signal steering vector;

Both sides ask covariance vector to obtain:

$\begin{array}{c}vec(R-{\mathrm{\&sigma;}}_{noise}^{2}I)=\underset{i=1}{\overset{N}{\&Sigma;}}{\mathrm{\&sigma;}}_i^{2}vec\left(a\right({\mathrm{\&theta;}}_i\left)a^H\right({\mathrm{\&theta;}}_i\left)\right)\\ =\underset{i=1}{\overset{N}{\&Sigma;}}{\mathrm{\&sigma;}}_i^{2}d\left({\mathrm{\&theta;}}_i\right)\end{array}$

for the linear combination of wanted signal and undesired signal covariance vector, structural matrix S:

$S=\underset{0}{\overset{\mathrm{\&pi;}}{\&Integral;}}d\left(\mathrm{\&theta;}\right)d^H\left(\mathrm{\&theta;}\right)d\mathrm{\&theta;}$

Signal covariance vector by the proper vector linear expression of matrix S, d (θ) subspace dimension equals the number of matrix S nonzero eigenvalue;

Nonzero eigenvalue characteristic of correspondence vector structural matrix Q by matrix S:

Q＝[e ₁,e ₂,...,e _K]

Wherein, for the nonzero eigenvalue characteristic of correspondence vector of matrix Q, the row of Q are mutually orthogonal, form the proper subspace of signal covariance vector;

$vec\left(R_1\right)=Q{\left(Q^{H}Q\right)}^{-1}{Q}^{H}vec\left(\hat{R}\right)$

Wherein, Q (Q ^hq) ^-1q ^hfor the projection matrix of signal covariance vector subspace; for sample covariance matrix, R ₁represent project to signal covariance vector subspace;

(3) eigenvector projection subspace method estimates steering vector:

If try to achieve interference and noise subspace projection matrix U _i+n, by eliminating the evaluated error expecting steering vector to Orthogonal subspace projection:

$\tilde{a}=(I-U_{i+n}{U}_{i+n}^H)\hat{a}$

Wherein, for expecting steering vector estimated value, for expecting steering vector modified value, the R obtained ₁carrying out Eigenvalues Decomposition is:

$R_1=\underset{i=1}{\overset{N}{\&Sigma;}}{\mathrm{\&lambda;}}_i{e}_i{e}_i^H$

Wherein, λ ₁> λ ₂> ... > λ _k+1=...=λ _n=σ ²for covariance matrix R ₁eigenwert, e _ifor eigenwert characteristic of correspondence vector;

Each eigenvector e _iall to steering vector projection, chooses projection characteristic of correspondence vectorial structure interference plus noise signals subspace U _i+n;

By the projection of eigenvector to steering vector carry out descending sort to obtain: p _[M]>=p _[M-1]>=...>=p _[1];

Use eigenvector structure interference plus noise subspace;

$(p_{\&lsqb;m\&rsqb;}+p_{\&lsqb;m-1\&rsqb;}\&GreaterEqual;...\&GreaterEqual;p_{\&lsqb;1\&rsqb;})/\underset{i=1}{\overset{M}{\&Sigma;}}p\left(i\right)<\mathrm{\&rho;}$

Along with the increase of m, be desired value when first time more than m value during ρ, structure interference plus noise subspace:

U _i+n＝[e _[1],e _[2],…,e _[m-1]]

Then interference plus noise subspace projection matrix is:

$P_{i+n}=U_{i+n}{U}_{i+n}^H$

And then can expect that subspace projection matrix is:

P _s＝I-P _i+n

Eliminate the evaluated error of interference plus noise sub-space portion, improve the estimated accuracy of steering vector:

$\tilde{a}=P_s\hat{a}$

Improve Beam synthesis weight vector:

$w=\frac{R_1\tilde{a}}{{\tilde{a}}^H{R}_1^{-1}\tilde{a}}$

(4) array antenna output signal is obtained

y＝w ^Hx

Wherein, y is output signal.