CN101592721A - Method for estimating angle of arrival of coherent signal based on eigenvalue reconstruction - Google Patents

Abstract

Method for estimating angle of arrival of coherent signal based on eigenvalue reconstruction utilizes the big eigenwert characteristic of correspondence vector of signal covariance matrix to re-construct new covariance matrix, by new covariance matrix being carried out characteristic value decomposition, the direction of arrival of estimated signal; When signal coherence, remove because factor affecting such as multipath cause the correlativity of signal, make the order of new signal covariance matrix be restored, under same bay number, can estimate simultaneously the arrival direction of more coherent signal, the present invention has two big advantages compared to traditional method: 1. arrival direction that can the estimation space coherent signal, 2. estimate the same number of signal angle of arrival, the present invention only needs bay still less, therefore greatly reduces operating cost.

Description

Method for estimating angle of arrival of coherent signal based on eigenvalue reconstruction

Technical field

The present invention relates to incoming signal arrival direction angle, a kind of space estimation technique, it is an actual application background with fields such as radio communication, radar, sonars, utilize Array Signal Processing, obtain the arrival angle (direction) of the incoming signal that aerial array receives, and suppress to disturb and noise.

Background technology

In recent years, along with the fast development of microelectric technique, Digital Signal Processing, parallel processing technique, the theory and the practical application of Array Signal Processing are also developed rapidly.As important of Array Signal Processing field development, signal angle of arrival estimation technique obtains general application in numerous military affairs such as radar, communication, sonar, earthquake, exploration, radio astronomy, electronic countermeasure, target monitoring and tracking and national economy field, has brought many facilities for people's life.

Signal angle of arrival estimation technique utilizes the energy distribution of signal on all directions of space, to the space different come to signal differentiate.The conventional subspace class methods at estimated signal arrival direction angle comprise with the multiple signal classification to be the noise subspace class of representative and to be the methods such as signal subspace class of representative with the invariable rotary subspace.These methods all have a common hypothesis, and promptly the signal on all directions of space is uncorrelated or irrelevant.In the practical communication environment, because multiple scattering, signal no longer occurs with single signal content, but comprises various multipath components.These multipath components have caused producing the coherence between signal from different directions, when arriving receiving antenna with different time delays, make signal subspace and noise subspace interpenetrate, and cause the effectively arrival direction angle of estimated signal of said method.

The technology of handling relevant or angle of arrival of coherent signal problem at present mainly comprises methods such as space smoothing class, matrix reconstruct class, subspace fitting class.These methods or only utilize the information of signal subspace, or only utilize the information of noise subspace.We then combine signal subspace and noise subspace, utilize more, more accurate statistical information estimates coherent signal arrival direction angle, to solve the problem that exists in the middle of the reality.

Summary of the invention

Technical matters: the purpose of this invention is to provide a kind of method for estimating angle of arrival of coherent signal based on eigenvalue reconstruction, this method utilizes the method for eigenvalue reconstruction to estimate the coherent signal arrival direction, the effective coherence between ring off signal, thereby can accurately estimate the direction of arrival of the coherent signal that received by antenna array signals, this method can be estimated more signal number under limited bay number.

Technical scheme: direction of arrival of signal angle estimation technique is a subject matter in Array Signal Processing field, the aerial array that it utilizes a plurality of bays to form at the space diverse location, multiple parameter to signal of interest is accurately estimated, the angle of arrival comprising signal is estimated, thereby can correctly judge the direction of signal source, Array Signal Processing all has very wide application prospect in various fields such as radar, communication, sonars.The present invention is intended to utilize big eigenwert, the proper vector of the original covariance matrix that aerial array receives that original covariance matrix is reconstructed, and the coherence between ring off signal also effectively estimates the arrival direction of coherent signal.The present invention can remove because the signal coherency that factor affecting such as multiple scattering, multipath arrival cause effectively calculates the incident direction angle that coherent signal arrives aerial array.The arrival direction general using multiple signal classification method of traditional method estimation space signal.In the practical communication environment, because multiple scattering, signal no longer occurs with single signal content, but comprises various multipath components.These multipath components have caused producing between signal the coherence from different directions, when arriving receiving antenna with different time delays.At this moment, the order of the covariance matrix of the received signal of array antenna produces loss, has caused the multiple signal classification method to lose efficacy.Be the coherence of ring off signal, a Search Space Smoothing is handled this problem before and after selecting usually.But front and back item Search Space Smoothing also exists very big defective, that is: it need divide into groups antenna array technically, the spacing wave decreased number that each antenna submatrix after the grouping can be estimated, and the packet count of antenna array can not be less than the spacing wave number.Therefore in actual applications, but this method can reduce the estimated signal number, increases operating cost.For remedying this defective, we have proposed to re-construct the method that covariance matrix is estimated angle of arrival of coherent signal with proper vector.Compared to traditional method, the present invention has two big advantages: arrival direction that 1, can the estimation space coherent signal; 2, can estimate the angle of arrival (maximum number of signals of estimation are lacked than array number) of more signal; Therefore, under the condition of the signal number of estimating as much, the present invention only needs bay number still less, thereby greatly reduces operating cost.

This method utilizes the pairing proper vector of big eigenwert of original covariance matrix to re-construct new covariance matrix, by new covariance matrix is carried out characteristic value decomposition, estimates the direction of arrival of coherent signal; This method is repaired the problem of the order loss of the signal covariance matrix that causes owing to signal coherence effectively, removes the coherence who causes signal owing to factors such as multipaths, can estimate the arrival direction of more coherent signal under same bay number.

The concrete steps of this method are:

1.) receive data vector X (n), according to estimator by aerial array ${\hat{R}}_X=\frac{1}{N}\underset{n=1}{\overset{N}{\mathrm{\Σ}}}X\left(n\right)X^H\left(n\right)$ Computational data covariance matrix R _XEstimated value

Wherein N is the fast umber of beats of data, and " H " is the computing of Matrix Conjugate transposition, and n represents constantly.

2. right Carry out characteristic value decomposition, obtain ${\hat{R}}_X={\mathrm{<figure-callout\; id="1"\; label="U"\; filenames="A2009100327570009H1.png"\; state="\{\{state\}\}">U</figure-callout>}}_1{\mathrm{\&Sigma;}}_1{U_1}^H,$ U ₁=[u ₁..., u _M] represent by proper vector u ₁..., u _MConstitute matrix, ∑ ₁=diag (λ ₁..., λ _M) represent with eigenvalue ₁..., λ _MDiagonal matrix for diagonal entry.

3.) with eigenwert with descending sort, q is big, and eigenwert characteristic of correspondence vector constitutes signal subspace

Promptly ${\hat{U}}_S=[{\mathrm{<figure-callout\; id="1"\; label="u"\; filenames="A2009100327570009H1.png"\; state="\{\{state\}\}">u</figure-callout>}}_1,...,u_q],$ u ₁..., u _qQ big eigenwert characteristic of correspondence vector of expression, wherein, u ₁=e ₁=[e ₁(1) e ₁(2) ... e ₁(M)] ^T..., u _q=e _q=[e _q(1) e _q(2) ... e _q(M)] ^T

4.) get

5.) re-constructing covariance matrix obtains

6. right

Carry out feature decomposition, obtain

=U ∑ U ^H, U=[u wherein ₁..., u _M] represent by proper vector u ₁..., u _MConstitute matrix, ∑=diag (λ ₁..., λ _M) represent with eigenvalue ₁..., λ _MBe the diagonal matrix of diagonal entry,

7.) with eigenwert with descending sort, q is big, and eigenwert characteristic of correspondence vector constitutes signal subspace, promptly ${\hat{U}}_S=[{\mathrm{<figure-callout\; id="1"\; label="u"\; filenames="A2009100327570009H1.png"\; state="\{\{state\}\}">u</figure-callout>}}_1,...,u_q],$ u ₁..., u _qQ big eigenwert characteristic of correspondence vector of expression, and M-q little eigenwert characteristic of correspondence vector constitutes noise subspace, promptly ${\hat{U}}_N=[u_{q+1},...,u_M],$ u _Q+1..., u _MM-q little eigenwert characteristic of correspondence vector of expression,

8.) according to noise subspace

Structure spectrum estimation formulas: $P\left(\mathrm{\&omega;}\right)=\frac{1}{a^H\left(\mathrm{\&omega;}\right){\hat{U}}_N{\hat{U}}_N^{H}a\left(\mathrm{\&omega;}\right)},$ Wherein P (ω) is a power spectral value, and a (ω) is a steering vector,

9.) according to spectrum estimation formulas result of calculation, the angle of maximum point correspondence is exactly signal incident direction θ _i, i=1 ..., the estimated value of q.

The invention that we propose mainly is to utilize the uniform straight line array row, and wherein each array element all is omnidirectional antenna, and establishing array element number is M, and the distance between the array element is d.Suppose that q arrowband far field point source signal is respectively from direction θ _i, i=1 ..., q incides antenna array.Then accepting data vector at moment t array can be expressed as:

X(t)＝AS(t)+n(t)

X (t)=[x wherein ₁(t) ..., x _M(t)] ^TM * 1 dimensional vector that the data that M bay receives when being illustrated in t are formed, x _i(t) (i=1 ..., M) i array element of expression is in the observation data of moment t, and subscript T represents vector or matrix transpose computing, A=[a (ω ₁) ..., a (ω _q)] be M * q dimension direction matrix, $a\left({\mathrm{\&omega;}}_i\right)={[1,e^{-j{\mathrm{\&omega;}}_i},...,e^{-j(M-1){\mathrm{\&omega;}}_i}]}^T$ For corresponding to phase differential ω _iSteering vector, ω _i=2 π dsin (θ _i)/λ represents two phase differential between adjacent array element, θ _iBe the signal incident angle, λ is a signal wavelength, S (t)=[s ₁(t) ..., s _q(t)] ^TBe q signal s ₁(t) ..., s _q(t) q of Zu Chenging * 1 dimensional signal vector, n (t)=[n ₁(t) ..., n _M(t)] ^TBe noise n on each bay ₁(t) ..., n _M(t) M of Zu Chenging * 1 dimensional vector.Here suppose that signal and array element noise statistics are independent, separate between each array element noise, and hypothesis array element noise is an additive white Gaussian noise.

Suppose x _i(t) be the zero-mean stationary stochastic process, according to the t data configuration array covariance matrix R that receives of antenna constantly _XFor:

R _X＝E{X(t)X ^H(t)}＝AR _SA ^H+σ ²I

Wherein E{} represents the ensemble average computing, H representing matrix conjugate transpose, R _S=E{S (t) S ^H(t) } be q * q dimensional signal covariance matrix, σ ²I is that M * M ties up noise covariance matrix, σ ²Be noise variance, I is a unit matrix.When practical application, the covariance of signal is calculated with following formula:

${\hat{R}}_X=\frac{1}{L}\underset{t=1}{\overset{L}{\mathrm{\&Sigma;}}}X\left(t\right)X{\left(t\right)}^H$

Wherein

Expression R _XEstimated value, L represents the snap data length.

When space incoming signal process mulitpath is propagated the arrival antenna array, produce between the signal that antenna receives and be correlated with, therefore cause R _SOrder loss, the multiple signal classification method lost efficacy.

(the individual arrowband of q≤M-1) far-field signal incides on the aerial array that M array element forms, and then the direction rank of matrix is q, and the order of signal covariance matrix is K (K≤q), suppose noise covariance matrix R as q _NBe non-singular matrix, then signal characteristic vector and direction guiding vector satisfy following relational expression:

$R_N{e}_k\left(\mathrm{\&omega;}\right)=\underset{n=1}{\overset{q}{\mathrm{\&Sigma;}}}{\mathrm{\&alpha;}}_k\left(n\right)a\left({\mathrm{\&theta;}}_n\right)$

E wherein _k(ω) expression is corresponding to eigenvalue _k, the signal characteristic vector of 1≤k≤K, α _k(n) be the linear combination factor.When the array element noise was desirable white noise, the noise covariance matrix abbreviation was:

R _N＝σ ²I

Therefore have

$e_k\left(\mathrm{\&omega;}\right)=\underset{n=1}{\overset{q}{\mathrm{\&Sigma;}}}{\mathrm{\&alpha;}}_k\left(n\right)a\left({\mathrm{\&theta;}}_n\right)$

When all incoming signals are relevant fully, have only an eigenvalue of maximum characteristic of correspondence vector in the signal subspace:

$e=\underset{n=1}{\overset{q}{\mathrm{\&Sigma;}}}\mathrm{\&alpha;}\left(n\right)a\left({\mathrm{\&theta;}}_n\right)$

Wherein α (n) (n=1 ..., q) corresponding to the linear combination coefficient of eigenvalue of maximum.As previously mentioned, eigenvalue of maximum characteristic of correspondence vector e can be expressed as form:

e＝[e(1)e(2)…e(M)] ^T

Wherein e (i) (i=1 ..., M) corresponding concrete element value among the expression e. and by being expressed as more again:

$e={(\underset{n=1}{\overset{q}{\mathrm{\&Sigma;}}}\mathrm{\&alpha;}\left(n\right),\underset{n=1}{\overset{q}{\mathrm{\&Sigma;}}}\mathrm{\&alpha;}\left(n\right)e^{-j{\mathrm{\&omega;}}_n},...,\underset{n=1}{\overset{q}{\mathrm{\&Sigma;}}}\mathrm{\&alpha;}\left(n\right)e^{-j(M-1){\mathrm{\&omega;}}_n})}^T$

For the coherence who causes owing to factors such as multipaths between ring off signal, we re-construct covariance matrix at big eigenwert characteristic of correspondence vector

Then to the structure new covariance matrix

Carry out characteristic value decomposition, can get q signal characteristic vector and M-q noise feature vector, wherein the M-q noise feature vector is opened into noise subspace U _n, and be constructed as follows the spectrum estimation formulas:

$P\left(\mathrm{\&omega;}\right)=\frac{1}{a^H\left(\mathrm{\&omega;}\right)U_n{U}_n^{H}a\left(\mathrm{\&omega;}\right)}$

Wherein P (ω) is corresponding power spectral value, U _n=[u ₁..., u _M-q], u ₁..., u _M-qThe proper vector corresponding to the noise characteristic value into noise subspace is opened in expression.At last according to spectrum estimation formulas signal calculated incident direction θ _i, i=1 ..., the estimated value of q.

Beneficial effect: the present invention proposes a kind ofly to re-construct the method for covariance matrix based on big eigenwert characteristic of correspondence vector, this method can fine ring off signal between because the coherence that factors such as multipath cause, therefore can estimate the arrival direction of coherent signal.Compare with classic method, under same array number, the present invention can estimate the arrival direction of more incoming signals, and therefore, this invention can reduce hardware cost in actual applications greatly.

Description of drawings

Fig. 1 provides even linear array received signal model,

Fig. 2 provides the process flow diagram based on the method for estimating angle of arrival of coherent signal of eigenvalue reconstruction,

Fig. 3 provides coherent signal and design sketch from the independent signal of 60 degree of estimating two from-20 degree, 40 degree of the present invention.

Embodiment

The present invention is intended to utilize a kind of method based on big eigenvalue reconstruction, the arrival direction of estimated signal.When signal coherence, the present invention can remove because the correlativity of the signal that factor affecting such as multipath cause effectively estimates the incident direction angle that spacing wave arrives antenna.The arrival direction general using multiple signal classification method of traditional method estimation space signal.When spacing wave took place to be correlated with owing to the influence of reality factors such as travel path or be relevant, the multiple signal classification method lost efficacy.At this moment, a Search Space Smoothing is handled this problem before and after general the selection.But also there is great defective in front and back item Search Space Smoothing: it need divide into groups antenna array technically, the spacing wave decreased number that each antenna array after the grouping can be estimated, and also the antenna array packet count can not be less than the spacing wave number.Therefore this method can reduce the estimated signal number in actual applications, increases operating cost.In order to address this problem, we propose the signal angle of arrival method of estimation based on eigenvalue of maximum reconstruct.The present invention has two big advantages compared to traditional method: arrival direction that 1, can the estimation space coherent signal, and 2, estimate the same number of signal angle of arrival, the present invention only needs bay still less, therefore greatly reduces operating cost.

The present invention is further described below in conjunction with accompanying drawing.

1.) receive data vector X (t) and obtain data covariance matrix R according to aerial array _XEstimated value

2.) to covariance matrix

Carry out characteristic value decomposition, right

Carry out characteristic value decomposition, obtain ${\hat{R}}_X={\mathrm{<figure-callout\; id="1"\; label="U"\; filenames="A2009100327570009H1.png"\; state="\{\{state\}\}">U</figure-callout>}}_1{\mathrm{\&Sigma;}}_1{U_1}^H,$ U ₁=[u ₁..., u _M] represent by proper vector u ₁..., u _MConstitute matrix, ∑ ₁=diag (λ ₁..., λ _M) represent with eigenvalue ₁..., λ _MDiagonal matrix for diagonal entry.

3.) with eigenwert with descending sort, q is big, and eigenwert characteristic of correspondence vector constitutes signal subspace Promptly ${\hat{U}}_S=[{\mathrm{<figure-callout\; id="1"\; label="u"\; filenames="A2009100327570009H1.png"\; state="\{\{state\}\}">u</figure-callout>}}_1,...,u_q],$ u ₁..., u _qQ big eigenwert characteristic of correspondence vector of expression, wherein, u ₁=e ₁=[e ₁(1) e ₁(2) ... e ₁(M)] ^T..., u _q=e _q=[e _q(1) e _q(2) ... e _q(M)] ^T

4.) get

5.) re-constructing covariance matrix obtains

6.) to the neotectonics covariance matrix

Carry out characteristic value decomposition, obtain the matrix U that noise feature vector is opened _n=[u ₁..., u _M-q], u ₁..., u _M-qBe the noise subspace proper vector.

7.) according to the noise feature vector matrix U _n=[u ₁..., u _M-q], structure spectrum estimation formulas: $P\left(\mathrm{\&omega;}\right)=\frac{1}{a^H\left(\mathrm{\&omega;}\right)U_n{U}_n^{H}a\left(\mathrm{\&omega;}\right)},$ Wherein P (ω) is a power spectral value, and a (ω) is the steering vector corresponding to phase differential ω.

8.) according to spectrum estimation formulas result of calculation, the angle of maximum point correspondence is exactly signal incident direction θ _i, i=1 ..., the estimated value of q.

Claims (1)

1. coherent signal Wave arrival direction estimating method, it is characterized in that this method utilizes the big eigenwert characteristic of correspondence vector of signal covariance matrix to re-construct new covariance matrix, by new covariance matrix being carried out characteristic value decomposition, the direction of arrival of estimated signal; When signal coherence, remove because factor affecting such as multipath cause the correlativity of signal, make the order of new signal covariance matrix be restored, under same bay number, can estimate the arrival direction of more coherent signal simultaneously,

The concrete steps of this method are:

1.) receive data vector X (n), according to estimator by aerial array $\hat{R}x=\frac{1}{N}\underset{n=1}{\overset{N}{\mathrm{\&Sigma;}}}X\left(n\right)X^H\left(n\right)$ Computational data covariance matrix R _xEstimated value

Wherein N is the fast umber of beats of data, and " H " is the computing of Matrix Conjugate transposition, and n represents constantly;

2.) to covariance matrix

Carry out characteristic value decomposition, right

Carry out characteristic value decomposition, obtain $\hat{R}x=U_1{\mathrm{\&Sigma;}}_1{U_1}^H,$ U ₁=[u ₁..., u _M] represent by proper vector u ₁..., u _MConstitute matrix, ∑ ₁=diag (λ ₁..., λ _M) represent with eigenvalue ₁..., λ _MDiagonal matrix for diagonal entry;

3.) with eigenwert with descending sort, q is big, and eigenwert characteristic of correspondence vector constitutes signal subspace Promptly ${\hat{U}}_S=[u_1,...,u_q],$ u ₁..., u _qQ big eigenwert characteristic of correspondence vector of expression, wherein, u ₁=e ₁=[e ₁(1) e ₁(2) ... e ₁(M)] ^T..., u _q=e _q=[e _q(1) e _q(2) ... e _q(M)] ^T

4.) get

5.) re-constructing covariance matrix obtains

6. right

Carry out feature decomposition, obtain

=U ∑ U ^H, U=[u wherein ₁..., u _M] represent by proper vector u ₁..., u _MConstitute matrix, ∑=diag (λ ₁..., λ _M) represent with eigenvalue ₁..., λ _MBe the diagonal matrix of diagonal entry,

7.) with eigenwert with descending sort, q is big, and eigenwert characteristic of correspondence vector constitutes signal subspace, promptly

${\hat{U}}_S=[u_1,...,u_q],$ u ₁..., u _qQ big eigenwert characteristic of correspondence vector of expression, and M-q little eigenwert characteristic of correspondence vector constitutes noise subspace, promptly ${\hat{U}}_N=[u_{q+1},...,u_M],$ u _Q+1..., u _MM-q little eigenwert characteristic of correspondence vector of expression,

8.) according to noise subspace

Structure spectrum estimation formulas: $P\left(\mathrm{\&omega;}\right)=\frac{1}{a^H\left(\mathrm{\&omega;}\right){\hat{U}}_N{\hat{U}}_N^{H}a\left(\mathrm{\&omega;}\right)},$ Wherein P (ω) is a power spectral value, and a (ω) is a steering vector,

9.) according to spectrum estimation formulas result of calculation, the angle of maximum point correspondence is exactly signal incident direction θ _i, i=1 ..., the estimated value of q.

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