CN104931937A - Submatrix-level orthogonal projection (OP) wave beam forming method based on covariance matrix normalization - Google Patents

Abstract

The invention discloses a submatrix-level OP wave beam forming method based on covariance matrix normalization. The method can be used to effectively inhibit interference, make a main lobe of a self-adaptive directional diagram conformal, reduce side lobes the self-adaptive directional diagram and obtain higher output SINR and convergence speed. The method comprises that submatrix-level reception signals are normalized, and a corresponding normalized sampling covariance matrix is calculated; the amount of interference signal sources is estimated by utilizing the MDL criterion, and further an interference subspace is obtained; and finally, the static weight vector is projected to an orthogonal complement space of the interference subspace to obtain a self-adaptive weight vector.

Description

Based on covariance matrix normalized Subarray rectangular projection Beamforming Method

Technical field

The present invention relates to array signal process technique field, be specifically related to a kind of based on covariance matrix normalized Subarray rectangular projection Beamforming Method.

Background technology

Array Signal Processing is an important branch in signal transacting field, and it is widely used in radar, sonar, communication, navigation, seismic monitoring, Speech processing and biomedical engineering etc.Adaptive beamformer is an important research content in Array Signal Processing, and its essence is exactly by adaptive weighted to each array element, carries out airspace filter, thus reaches and strengthen wanted signal, suppress undesired signal and weaken the object of noise signal.Response that minimum variance is undistorted (MVDR) is a kind of relatively conventional algorithm, and it is by being 1 at wanted signal direction constrain array gain, and makes array output power minimum, thus reaches the object suppressing to disturb.Covariance matrix is inverted (SMI), and algorithm is a kind of conventional method realizing MVDR algorithm, but when lower snap, the output SINR (Signal to Interference plus Noise Ratio) of this algorithm and the speed of convergence of adaptive direction figure slower.

In actual applications, consider hardware condition and environmental factor, the fast umber of beats of sampling calculating adaptive weight employing is less.In order in low snap situation, solve the problem that SMI algorithm brings, rectangular projection (OP) algorithm is widely used, and its essence is and is projected to by static weight vector in the orthogonal complement space (i.e. noise subspace) of interference space, and then obtain self-adaptation weight vector.In this algorithm, little eigenwert characteristic of correspondence vector does not participate in the calculating of self-adaptation weight vector, so under low snap condition, this algorithm can make output SINR and adaptive direction figure rapidly converge to optimal value.But when OP algorithm application is to Subarray, the uneven division of submatrix can cause each submatrix noise output power unequal, and then the accuracy of MDL criterion estimation can be affected, thus cause the interference space of estimation inaccurate, cause adaptive direction figure main lobe to be out of shape and secondary lobe rising, export SINR degradation.

Summary of the invention

In view of this, the invention provides a kind of based on covariance matrix normalized Subarray rectangular projection Beamforming Method, effectively can suppress interference, and the main lobe conformal of adaptive direction figure and secondary lobe can be made to reduce, and higher output SINR and speed of convergence faster can be obtained.

Of the present invention based on covariance matrix normalized Subarray rectangular projection Beamforming Method, comprise the steps:

Step 1, is normalized Subarray Received signal strength, calculates the interference-plus-noise covariance matrix R after normalization _{sub_norm}: wherein, R _{in_sub}for the covariance matrix of Subarray; T _lfor normalization matrix: wherein, L is submatrix number, $c_l=\left\{\begin{array}{cc}{\left(\underset{i=1}{\overset{N_0}{\Σ}}{w}_i^2\right)}^{1/2}& l=0\\ {\left(\underset{i=U}{\overset{Q}{\Σ}}{w}_i^2\right)}^{1/2}& l\≥1\end{array}\right.,$ W _ibe the weighting coefficient of i-th array element, U=N ₀+ N ₁+ ... + N _l-1-J ₀-J ₁-...-J _l-1+ 1, Q=N ₀+ N ₁+ ... + N _l-J ₀-J ₁-...-J _l-1, N _ibe the array number that i-th (0≤i≤L-1) individual submatrix comprises, J _ibe i-th (0≤i≤L-2) individual submatrix with the overlapping array number of the i-th+1 submatrix; () ^hrepresent complex-conjugate transpose;

Step 2, utilizes MDL criterion to estimate interference space:

Step 2.1, to the interference-plus-noise covariance matrix R after normalization _{sub_norm}carry out Eigenvalues Decomposition, obtain eigenwert and characteristic of correspondence vector thereof, and eigenwert is carried out descending arrangement;

Step 2.2, utilizes MDL criterion to estimate the number of interference signal source for P, then in step 2.1, front P column vector of eigenvector forms interference space;

Step 3, utilizes the interference space that step 2 estimates, and adopts rectangular projection Adaptive beamformer method, solves self-adaptation weight vector;

Step 4, the self-adaptation weight vector utilizing step 3 to obtain, is weighted process to the echo data received, and obtains adaptive beam.

Beneficial effect:

The invention solves when the uneven and lower sampling snap of Subarray partition, the interference space that traditional Subarray orthogonal projection algorithm is estimated is inaccurate, interference is caused not to be effectively suppressed, and the main lobe distortion of adaptive direction figure, the problem that secondary lobe raises, can effectively complete Subarray Adaptive beamformer, fall in the adaptive formation zero of interference radiating way, and while effectively suppressing interference, make the main lobe conformal of adaptive direction figure and secondary lobe reduce, the present invention has higher output Signal to Interference plus Noise Ratio after Adaptive beamformer process, and output Signal to Interference plus Noise Ratio has speed of convergence faster.

Accompanying drawing explanation

Fig. 1 is process flow diagram of the present invention.

Fig. 2 is the inventive method and improves front method adaptive direction figure comparison diagram (when fast umber of beats is 2 times of submatrix numbers).

Fig. 3 is the inventive method and improves front method adaptive direction figure comparison diagram (when fast umber of beats is 10 times of submatrix numbers).

Fig. 4 is that the inventive method exports SINR with fast umber of beats change curve comparison diagram with the front method of improvement.

Fig. 5 is that the inventive method exports SINR with beam position change curve comparison diagram with the front method of improvement.

Embodiment

To develop simultaneously embodiment below in conjunction with accompanying drawing, describe the present invention.

The invention provides a kind of based on covariance matrix normalized Subarray rectangular projection Beamforming Method, first Subarray Received signal strength is normalized, and calculates corresponding normalization sample covariance matrix; Then utilize MDL criterion to estimate interference signal source number, and then obtain interference space; Finally static weight vector projected to the orthogonal complement space of interference space and obtain self-adaptation weight vector.When the uneven and lower sampling snap of Subarray partition, the present invention can suppress interference effectively, and the main lobe conformal of adaptive direction figure and secondary lobe can be made to reduce, and can obtain higher output SINR and speed of convergence faster.As shown in Figure 1, concrete steps are as follows for flow process of the present invention:

Step one, construct normalized Subarray covariance matrix

1. the foundation of signal model

Suppose an arrowband linear array, altogether N number of array element, array element is isotropy, P undesired signal, and undesired signal is far field narrow band signal, white noise when supposing that each array element noise is separate, power equal empty and undesired signal and noise are uncorrelated mutually.Then array received to signal model can be expressed as

X _in(t)＝AS(t)+N(t) (1)

In formula, A=[a (θ ₁), a (θ ₂) ... a (θ _p)] be array manifold matrix, a (θ _i) (i=1,2 ... P) be the steering vector of undesired signal, if the spacing of the n-th array element and reference point is d _n(n=0,1,2 ..., N-1), usually with the 0th array element for reference point, now d ₀=0, λ is wavelength, then θ _i(i=1,2 ... P) be the incident angle of undesired signal, [] ^tfor matrix transpose, S (t)=[S ₁(t), S ₂(t) ... S _p(t)] ^t, S _i(t) (i=1,2 ... P) be the complex envelope of i-th undesired signal, N (t)=[n ₁(t), n ₂(t) ..., n _n(t)] be background white noise.

Thus obtain array covariance matrix and be

R _in＝E{X _in(t)X _in ^H(t)} (2)

In formula, E{} represents mathematical expectation, () ^hrepresent complex-conjugate transpose.

In practical application, according to maximal possibility estimation criterion, by limited fast beat of data X _in(t _i) estimate array covariance matrix,

$R_{in}=\frac{1}{K}\underset{i=1}{\overset{K}{\Σ}}{X}_{in}\left(t_i\right){X_{in}}^H\left(t_i\right)---\left(3\right)$

In formula, X _in(t _i) for i (i=1,2 ..., K) and the sampled value of moment array, K is the fast umber of beats of sampling.

When Subarray process, be L submatrix by array partition, and (L >=P+1), can be non-overlapped submatrix or overlapping submatrix, submatrix transition matrix can be expressed as

T＝φ ₀WT ₀(4)

Wherein represent the effect of phase shifter, if beam position is identical with wanted signal direction; W=diag (w _n) _{n=0,1 ..., N-1}, wherein w _nbe the weighting coefficient of the n-th array element, for suppressing the sidelobe level of directional diagram; T ₀for N × L submatrix formed matrix, its l (l=0,1 ..., L-1) in all elements that arranges, only have the element value corresponding with the array element sequence number of l submatrix to be 1, all the other be 0 (when non-overlapped submatrix, T ₀column vector mutually orthogonal).

The sampling snap signal then Subarray received is

X _{in_sub}(t)＝T ^HX _in(t) (5)

Then the covariance matrix of Subarray is

$\begin{array}{c}{R}_{in\_sub}=\frac{1}{K}\underset{i=1}{\overset{K}{\Σ}}{X}_{in\_sub}\left(t_i\right)X_{in\_sub}^H\left(t_i\right)\\ =\frac{1}{K}\underset{i=1}{\overset{K}{\Σ}}{T}^H{X}_{in}\left(t_i\right)X_{in}^H\left(t_i\right)T=T^H{R}_{in}T\end{array}---\left(6\right)$

2. the normalization of covariance matrix

First export each submatrix and be normalized, matrix T is passed through in normalization _lcomplete

$T_L=diag{\left(c_l^{-1}\right)}_{l=0,1,2,\mathrm{...},L-1}---\left(7\right)$

Wherein

$c_l=\left\{\begin{array}{cc}{\left(\underset{i=1}{\overset{N_0}{\Σ}}{w}_i^2\right)}^{1/2}& l=0\\ {\left(\underset{i=U}{\overset{Q}{\Σ}}{w}_i^2\right)}^{1/2}& l\≥1\end{array}\right.$

U＝N ₀+N ₁+…+N _l-1-J ₀-J ₁-…-J _l-1+1

Q＝N ₀+N ₁+…+N _l-J ₀-J ₁-…-J _l-1

N _ibe the array number that i-th (0≤i≤L-1) individual submatrix comprises, J _ibe i-th (0≤i≤L-2) individual submatrix with the overlapping array number of the i-th+1 submatrix.

Interference-plus-noise covariance matrix after normalization is

$R_{sub\_norm}=T_L^H{R}_{in\_sub}{T}_L---\left(8\right)$

By normalized, make the noise power of each submatrix consistent, thus MDL criterion can be suitable for.

Step 2, estimation interference space

To normalized covariance matrix R _{sub_norm}carry out Eigenvalues Decomposition

$R_{sub\_norm}=\underset{i=1}{\overset{L}{\Σ}}{\mathrm{\λ}}_i{u}_i{u}_i^H---\left(9\right)$

In formula, λ _i(i=1,2 ..., L) and be covariance matrix R _{sub_norm}eigenwert, for with eigenvalue λ _icharacteristic of correspondence vector, λ _idescending arrangement

Utilize MDL criterion to estimate the number of interference signal source, and then estimate interference space.

The function of MDL criterion is

$MDL\left(d\right)=L_d\left(d\right)+\frac{1}{2}\[d(2L-d)+1\]\ln K---\left(10\right)$

Wherein

$L_d\left(d\right)=K(L-d)\ln \left\{\frac{\frac{1}{L-d}\underset{i=d+1}{\overset{L}{\Σ}}{\widehat{\mathrm{\λ}}}_i}{{\Π}_{i=d+1}^L{{\widehat{\mathrm{\λ}}}_i}^{\frac{1}{L-d}}}\right\}---\left(11\right)$

From MDL criterion, when the numerical value change of d, the value of the d corresponding when formula (11) gets minimum value is the number P of interference signal source, selected characteristic vector front P column vector composition interference space U _s, namely by the known vector of mathematical knowledge with vector a (θ ₁), a (θ ₂) ..., a (θ _p) open into same vector space, that is:

$span\{{\hat{u}}_1,{\hat{u}}_2,\mathrm{...},{\hat{u}}_P\}=span\{a\left({\mathrm{\θ}}_1\right),a\left({\mathrm{\θ}}_2\right),\mathrm{...},a\left({\mathrm{\θ}}_P\right)\}---\left(11\right)$

Wherein, span{} represents the space that vector is opened, be the estimation of interference space.

Step 3, solve the self-adaptation weight vector of innovatory algorithm

Utilize the interference space that step 2 estimates, adopt rectangular projection Adaptive beamformer method, solve the self-adaptation weight vector of innovatory algorithm.

Conventional orthogonal is adopted to throw the thought of algorithm, by static weight vector w _{q_sub}the interference space U estimated in step 2 _sthe orthogonal complement space projection, the self-adaptation weight vector of the algorithm that is improved is

$\begin{array}{c}W={\mathrm{\ηT}}_L(I-\underset{i=1}{\overset{P}{\Σ}}{\hat{u}}_i{\hat{u}}_i^H)T_L^{-1}{w}_{q\_sub}\\ ={\mathrm{\ηT}}_L(I-U_s{U}_S^H)T_L^{-1}{w}_{q\_sub}\end{array}---\left(12\right)$

In formula, I is that L × L ties up unit matrix, and η is a constant, w _{q_sub}for static weight vector, and each element is the L dimensional vector of 1, effect be that the gain in antenna main beam direction is remained unchanged.

Step 4, carries out Adaptive beamformer to the echo received

After obtaining self-adaptation weight vector, process can be weighted to the echo data received:

Y＝W ^HX(t) (13)

In formula, X (t) is the echoed signal received, thus effectively removes interference and weaken noise, and strengthens wanted signal.

Since then, just complete a kind of based on the sub-Adaptive beamformer method of covariance matrix normalized Subarray rectangular projection to the process of echo data.

In order to verify that one that the present invention proposes is based on covariance matrix normalized Subarray rectangular projection Adaptive beamformer method, carry out the emulation of adaptive beam directional diagram and output Signal to Interference plus Noise Ratio (SINR), emulation adopts arrowband even linear array, and simulation parameter is as shown in table 1.The front algorithm of improvement is that the sampling snap signal of Subarray directly adopts rectangular projection (OP) algorithm to calculate self-adaptation weight vector.

Table 1 simulation parameter is arranged

Fig. 2 and Fig. 3 be innovatory algorithm of the present invention with improve before the comparing (emulating 1 time) of adaptive beam directional diagram of algorithm, fast umber of beats of sampling is respectively 20 and 100, beam position angle is 0 °, can find out, the adaptive beam major lobe of directional diagram that before improving, algorithm obtains is out of shape and sidelobe level seriously raises; The adaptive beam major lobe of directional diagram conformal that obtains of algorithm after improving and sidelobe level is lower, close to static beam pattern, performance improves compared with before-improvement widely.

Fig. 4 is that wanted signal angle is 0 °, and input signal-to-noise ratio is 0dB, the same Fig. 2 of other simulated conditions under difference sampling snap condition, the comparison of the output Signal to Interference plus Noise Ratio (SINR) of innovatory algorithm of the present invention and the front algorithm of improvement.From simulation result, after improving, the output SINR of algorithm is higher, and convergence is very fast; And the output SINR of algorithm is lower before improving, convergence is comparatively slow, and along with the increase of fast umber of beats, export SINR to decline to some extent, because fast umber of beats of sampling is higher, the degree of accuracy of the interference space of estimation reduces, interference can not be effectively suppressed, and causes the SINR meeting degradation exported.

Fig. 5 is when different beams orientation angle, the comparison of the output Signal to Interference plus Noise Ratio (SINR) of innovatory algorithm of the present invention and the front algorithm of improvement, input signal-to-noise ratio is 0dB, the same Fig. 2 of other simulated conditions, can find out that after improving, algorithm can suppress interference effectively, and the SINR exported is higher.

Can obtain from Fig. 2 ~ Fig. 5, innovatory algorithm of the present invention can strengthen wanted signal, has good interference free performance, is a kind of sane Subarray adaptive beam-forming algorithm.

In sum, these are only preferred embodiment of the present invention, be not intended to limit protection scope of the present invention.Within the spirit and principles in the present invention all, any amendment done, equivalent replacement, improvement etc., all should be included within protection scope of the present invention.

Claims (1)

1., based on a covariance matrix normalized Subarray rectangular projection Beamforming Method, it is characterized in that, comprise the steps:

Step 1, is normalized Subarray Received signal strength, calculates the interference-plus-noise covariance matrix R after normalization _{sub_norm}: wherein, R _{in_sub}for the covariance matrix of Subarray; T _lfor normalization matrix: wherein, L is submatrix number, $c_l=\left\{\begin{array}{cc}{\left(\underset{i=1}{\overset{N_0}{\mathrm{\Σ}}}{w}_i^2\right)}^{1/2}& l=0\\ {\left(\underset{i=U}{\overset{Q}{\mathrm{\Σ}}}{w}_i^2\right)}^{1/2}& l\≥1\end{array}\right.,$ W _ibe the weighting coefficient of i-th array element, U=N ₀+ N ₁+ ... + N _l-1-J ₀-J ₁-...-J _l-1+ 1, Q=N ₀+ N ₁+ ... + N _l-J ₀-J ₁-...-J _l-1, N _ibe the array number that i-th (0≤i≤L-1) individual submatrix comprises, J _ibe i-th (0≤i≤L-2) individual submatrix with the overlapping array number of the i-th+1 submatrix; () ^hrepresent complex-conjugate transpose;

Step 2, utilizes MDL criterion to estimate interference space:

Step 2.1, to the interference-plus-noise covariance matrix R after normalization _{sub_norm}carry out Eigenvalues Decomposition, obtain eigenwert and characteristic of correspondence vector thereof, and eigenwert is carried out descending arrangement;

Step 2.2, utilizes MDL criterion to estimate the number of interference signal source for P, then in step 2.1, front P column vector of eigenvector forms interference space;

Step 3, utilizes the interference space that step 2 estimates, and adopts rectangular projection Adaptive beamformer method, solves self-adaptation weight vector;

Step 4, the self-adaptation weight vector utilizing step 3 to obtain, is weighted process to the echo data received, and obtains adaptive beam.