CN101325807B - Method for estimating signal wave direction - Google Patents

Abstract

The invention provides a signal DOA estimation method. The method supposes that an unknown noise covariance matrix has a symmetrical Toeplitz matrix character; according to the difference conception of the traditional covariance matrix, an imaginary number j is introduced so that the newly constructed covariance matrix changes into a central Hermitian matrix, thereby, the character decomposition can obtain the same DOA as the incident signal numbers. The method greatly reduces the number of the antenna array element required by estimating the signal wave arrival direction, and a wave crest is only formed in the wave arrival direction of the real signal. The method can reduce cost greatly in the practical application.

Description

Method for estimating signal wave direction

Technical field

The present invention relates to a kind of network positions technology, it is background with the cognitive radio technology, utilize smart antenna, the direction of arrival of antenna receiving signal is estimated, thereby can provide technical basis for security service, commerce services, network management and the information service relevant with the position.

Background technology

Along with the continuous development of mobile communication technology, location technology obtains general application in the mobile communications network in recent years.Location technology can be applied to security service, commerce services, network management and the information service relevant with the position.For example: positioning service can be used for the personnel rescue under the situations such as earthquake, battlefield, also can be used for the fields such as communication navigation, target following in city.

According to the demand of different location services to positioning accuracy, the embodiment of navigation system is divided into based on terminal, Network Based, and both such as mix at three kinds of different schemes.Navigation system based on portable terminal (as mobile phone) claims the travelling carriage freedom positioning system again, is representative with GPS assist location etc.What the GPS location utilized is satellite-signal, and locating effect is bad under conditions such as indoor, basement, tunnel, subway.And based on network wireless location system utilizes existing mobile communication network, in the signal of network terminal test travelling carriage generation and the various parameters of estimating signal, as direction of arrival parameter, the time of advent and time difference parameter, the target location is estimated according to these parameters.The enforcement of these class methods is expensive less, instant effect, is the main flow of localization method in the mobile communications network.

Wherein the method that positions according to the direction of arrival of signal is utilized the Energy distribution of signal on all directions of space, to the space different come to signal differentiate.The traditional classical method of estimated signal direction of arrival comprises methods such as multiple signal classification and invariable rotary subspace.Signal in the space when arriving antenna with different time delays, produces correlation because mulitpath is propagated between signal, cause the effectively direction of arrival of estimated signal of said method.Traditional space covariance difference method is from direction of arrival that at first can only estimated signal, to the development that can estimate coherent signal, all there are two significant drawbacks, the one, the requirement bay is counted the twice that M must count q greater than incoming signal, be M＞2q, the 2nd, all form the spectrum peak at ± θ place, wherein θ is that the true ripple of signal reaches the angle.Because top two shortcomings cause the cost increase in actual applications of traditional method.

Summary of the invention

Technical problem: the purpose of this invention is to provide a kind of method for estimating signal wave direction, this method is the correlation between ring off signal effectively, thereby can accurately estimate to arrive the direction of arrival of aerial signal, and can under limited antenna sensor number, estimate more signal number.

Technical scheme: the present invention is intended to utilize a kind of new space covariance difference method, and the direction of arrival of estimated signal when signal coherence, is removed because factor affecting such as multipath cause the correlation of signal.The present invention utilizes imaginary number j that traditional method performance is improved, here $j=\sqrt{-1},$ Advantage of the present invention is mainly reflected in three aspects: the one, and array number M and incoming signal are counted q and are satisfied M＞q, and the 2nd, only reach θ place, angle and form the spectrum peak at signal wave, the 3rd, can eliminate noise effect, with the Bo Dajiao of Search Space Smoothing binding energy estimation coherent signal.

The present invention can solve the direction of arrival estimation problem of signal under the Colored Noise,, combines with Search Space Smoothing and can remove this correlation because factor affecting such as multipath produce when being concerned with when signal, and therefore this invention also can be estimated the direction of arrival of coherent signal.

Method for estimating signal wave direction of the present invention utilizes the space covariance difference method, the direction of arrival of estimated signal, when signal coherence, remove because factor affecting such as multipath cause the correlation of signal, be embodied in three aspects: the one, array number M and incoming signal are counted q and are satisfied M＞q, the 2nd, only reach θ place, angle and form the spectrum peak at signal wave, the 3rd, can eliminate noise effect, with the Bo Dajiao of Search Space Smoothing binding energy estimation coherent signal;

The concrete steps of this method are:

1.) receive data vector X (t), according to formula according to aerial array $R_X=\frac{1}{N}\underset{n=1}{\overset{N}{\mathrm{\Σ}}}X\left(n\right)X^H\left(n\right)$ Construction data covariance matrix R _X, wherein N is a data snap length, n is the discrete time point, () ^HExpression conjugate transpose, X (n) are n reception data constantly,

2.) when signal is irrelevant,, get covariance difference matrix Δ R for eliminating the influence of background noise _XFor $\mathrm{\Δ}{R}_X=j\·(R_X-J{R}_X^{*}J);$ When signal coherence, for forward direction space smoothing covariance matrix R ^f, construct new covariance difference matrix $\mathrm{\Δ}{R}_X^f=j\·(R^f-J{\left(R^f\right)}^{*}J),$ Wherein $j=\sqrt{-1},$ J is a transposed matrix, () ^*The expression conjugate operation, Δ R _X ^fBe called R ^fThe covariance difference matrix,

3.) to covariance difference matrix Δ R _XCarry out feature decomposition, wherein M characteristic vector u ₁, u ₂, L, u _MConstitute matrix U=[u ₁, u ₂, L, u _M], with M eigenvalue ₁, λ ₂, L, λ _MBe diagonal entry, all the other elements are zero formation diagonal matrix sigma=diag (λ ₁, λ ₂, L, λ _M), diag () expression is a diagonal line value with the element in the round parentheses, other element is zero diagonal matrix,

4.) with the characteristic value of covariance difference matrix according to descending, q big characteristic value u ₁, u ₂, L, u _qPairing characteristic vector constitutes the signal vector matrix U of signal subspace _s=[u ₁, u ₂, L, u _q]; And M-q little characteristic value u _Q+1, u _Q+2, L, u _MThe characteristic of correspondence vector then constitutes noise subspace, i.e. the noise vector matrix U _N=[u _Q+1, u _Q+2, L, u _M],

5.) the noise vector matrix U _NAnd the steering vector a (θ) of signal=[1, e ^{-j2 π d (sin θ)/λ}, L, e ^{-j2 π d (M-1) (sin θ)/λ}] ^TSubstitution $P\left(\mathrm{\θ}\right)=\frac{1}{a^H\left(\mathrm{\θ}\right)U_N{U}_N^{H}a\left(\mathrm{\θ}\right)},$ Here, M is an array number, λ is a carrier wavelength, d is the array element interval, P (θ) is called power spectrum, when θ from 0 to 180 degree is got different values, obtains different power spectral value, q the maximum that equates with signal number wherein must be arranged, and the pairing abscissa of this q maximum point is exactly that the ripple of all q signal reaches angle.

Beneficial effect: the present invention proposes a kind of covariance difference method, this method can be estimated the direction of arrival of signal under the Colored Noise, suppose that promptly unknown coloured noise covariance matrix has the Toeplitz matrix characteristic of symmetry, according to this characteristic, by constructing the difference of two covariance matrixes, signal wave is reached the angle estimation effect thereby eliminate coloured noise.Introduce imaginary number j and make this method, can significantly reduce the bay number, and only form crest at the true direction of arrival θ of signal place with respect to traditional method.This invention can reduce cost in actual applications greatly.

Description of drawings

Fig. 1 provides even linear array received signal model;

Fig. 2 provides the invention process flow chart.

Embodiment

For unknown Colored Noise, we suppose that noise covariance matrix has the Toeplitz matrix properties of symmetry.Aerial array is a uniform straight line array, and each array element all is omnidirectional antenna, and array number is M, and array element is spaced apart d.Suppose that far field, q arrowband incoherent signal is respectively from direction θ _i, i=1, L, q incides antenna array.Then can be expressed as at moment t array received data vector:

X(t)＝AS(t)+n(t)

X (t)=[x wherein ₁(t), L, x _M(t)] ^TFor receiving data vector, A=[a (θ ₁), L, a (θ _q)] be M * q dimension direction matrix, a (θ)=[1, e ^{-j2 π d (sin θ)/λ}, L, e ^{-j2 π d (M-1) (sin θ)/λ}] ^TBe the steering vector corresponding to incidence angle θ, λ is a signal wavelength, S (t)=[s ₁(t), L, s _q(t)] ^TBe q * 1 dimensional signal vector, n (t)=[n ₁(t), L n _M(t)] ^TBe M * 1 dimension noise vector, () ^TThe computing of expression transposition.Here suppose that signal and array element noise statistics are independent.

Suppose x _i(t) be the zero-mean random process, structure array covariance matrix is:

R _X＝E{X(t)X ^H(t)}＝AR _SA ^H+Q

Wherein go up label " H " representing matrix conjugate transpose, R _S=E{S (t) S ^H(t) } be q * q dimensional signal covariance matrix, Q is that M * M ties up noise covariance matrix.According to above-mentioned assumed condition as can be known, matrix R _SFull rank, and matrix Q has symmetry Toeplitz character.

For sake of convenience, introduce following three theorems:

Theorem 1: Matrix C is called central Hermitian matrix, if C satisfies following condition:

C=JC ^*J, wherein J is a permutation matrix, is defined as:

$J=\left[\begin{array}{ccccc}0& 0& L& 0& 1\\ 0& 0& \mathrm{<figure-callout\; id="1"\; label="L"\; filenames="S2008100226553E00011.png"\; state="\{\{state\}\}">L</figure-callout>}& 1& 0\\ & & L& & \\ 0& 1& L& 0& 0\\ 1& 0& L& 0& 0\end{array}\right]$

Theorem 2: if C is symmetry Toeplitz matrix, C so ^H, C ^TWith JCJ also be the symmetry Toeplitz matrix.

Theorem 3: if n * n rank Matrix C is central Hermitian matrix, then its respective element satisfies:

$c_{\mathrm{ij}}=c_{n-j+1,n-i+1}^{*}$

Owing to the existence of noise, feasible estimation to the signal direction of arrival is had a strong impact in the communication environment.Existing covariance difference method utilizes the structure priori of noise covariance matrix Q, adopts a kind of reasonable manner transform array covariance matrix R _X, in this conversion, noise section is constant, and signal section obtains changing.Poor by the covariance matrix before and after the conversion, remove The noise, thereby obtain new covariance matrix.When tradition covariance difference method is removed noise, but brought two big shortcomings, the one, array number M and number of signals q must satisfy: M＞2q, the 2nd, ± the θ place forms the spectrum peak of symmetry.These two shortcomings cause conventional method to run into very big trouble in actual applications, use cost and heighten.We propose new covariance difference method for this reason.

In order to eliminate The noise, the method below traditional covariance calculus of finite differences has been constructed:

ΔR _X＝R _X-JR _XJ

The covariance matrix of this method construct is negative antisymmetric matrix, and these matrix characteristics are the always positive and negative paired appearance of characteristic value, and the result causes above-mentioned shortcoming, and in order to solve top shortcoming, we have invented following new method, make new covariance difference matrix be:

$\mathrm{\&Delta;}{R}_X=j\&CenterDot;(R_X-J{R}_X^{*}J)$

Here $j=\sqrt{-1},$ The introducing of j makes Δ R _XBecome central Hermitian matrix, make the not positive and negative appearance of classical inverse symmetrical matrix characteristic value for another example of covariance matrix of neotectonics, so this method estimated signals power spectrum has only q spectrum peak, promptly only at real signal incident direction θ _iThe place forms the spectrum peak.Simultaneously, new method requires array number M and number of signals q to satisfy M＞q to get final product.Can get after the simplification:

$\mathrm{\&Delta;}{R}_X=j\&CenterDot;({\mathrm{AR}}_S{A}^H-J{A}^{*}{R}_S^{*}{A}^{T}J)$

Top method only is fit to signal not height correlation or incoherent situation, when signal was concerned with owing to factors such as multipaths, conventional method lost efficacy, and we utilize the thought of forward direction Search Space Smoothing and this method to combine, produce the direction of arrival estimation problem that is fit under the coherent condition, even also

$\mathrm{\&Delta;}{R}_X^f=j\&CenterDot;(R^f-J{\left(R^f\right)}^{*}J)$

R wherein ^fBe forward direction mean space smoothed covariance matrix.Substitution and reduced equation get:

$\mathrm{\&Delta;}{R}_X^f=j\&CenterDot;(A{R}_s^f{A}^H-J{A}^{*}{\left(R_s^f\right)}^{*}{A}^{T}J)$

From top two kinds of new methods as can be seen, noise section is eliminated from the covariance of neotectonics fully through after the difference, thereby can eliminate noise to signal direction of arrival estimation effect.

At last to the structure new covariance matrix Δ R _XOr Δ R _X ^f, carry out characteristic value decomposition, can get q nonzero eigenvalue and M-q zero eigenvalue, wherein open into noise subspace corresponding to the characteristic vector of M-q zero eigenvalue, be constructed as follows power spectrum spectrum estimation formulas:

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

U wherein _n=[u ₁, L, u _M-q], u ₁, L, u _M-qCharacteristic vector for noise subspace.

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 _X

2.), when signal is irrelevant, construct new covariance difference matrix for eliminating The noise $\mathrm{\&Delta;}{R}_X=j\&CenterDot;(A{R}_S{A}^H-J{A}^{*}{R}_S^{*}{A}^{T}J);$ When signal coherence, structure covariance difference matrix $\mathrm{\&Delta;}{R}_X^f=j\&CenterDot;(A{R}_s^f{A}^H-J{A}^{*}{\left(R_s^f\right)}^{*}{A}^{T}J).$

3.) to Δ R _XCarry out feature decomposition,

4.) determine signal subspace U _SWith noise subspace U _N,

5.) according to noise subspace U _N, obtain power spectrum $P\left(\mathrm{\&theta;}\right)=\frac{1}{a^H\left(\mathrm{\&theta;}\right)U_N{U}_N^{H}a\left(\mathrm{\&theta;}\right)}$

6.) when θ from 0 to 180 degree is got different values, obtain different power spectral value, the abscissa of q maximum point correspondence is exactly the incident direction of q signal.

Claims (1)

1. method for estimating signal wave direction, it is characterized in that this method utilizes the space covariance difference method, the direction of arrival of estimated signal, when signal coherence, remove because the signal correlation that the multipath factor affecting causes is embodied in three aspects: the one, array number M and incoming signal are counted q and are satisfied M＞q, and the 2nd, only reach θ place, angle and form the spectrum peak at signal wave, the 3rd, can eliminate noise effect, with the Bo Dajiao of Search Space Smoothing binding energy estimation coherent signal;

The concrete steps of this method are:

1.) receive data vector X (t), according to formula according to aerial array

Construction data covariance matrix R _X, wherein N is a data snap length, and n is the discrete time point, and H represents conjugate transpose, and X (n) is n reception data constantly,

2.) when signal is irrelevant,, get covariance difference matrix Δ R for eliminating the influence of background noise _XFor

When signal coherence, for forward direction space smoothing covariance matrix R ^f, construct new covariance difference matrix

Wherein

J is a permutation matrix, () ^*The expression conjugate operation,

Be called R ^fThe covariance difference matrix,

3.) to covariance difference matrix Δ R _XCarry out feature decomposition, wherein M characteristic vector u ₁, u ₂..., u _MConstitute matrix U=[u ₁, u ₂..., u _M], with M eigenvalue ₁, λ ₂..., λ _MBe diagonal entry, all the other elements are zero formation diagonal matrix sigma=diag (λ ₁, λ ₂..., λ _M), diag () expression is a diagonal line value with the element in the round parentheses, other element is zero diagonal matrix,

4.) with the characteristic value of covariance difference matrix according to descending, q big characteristic value u ₁, u ₂..., u _qPairing characteristic vector constitutes the signal vector matrix U of signal subspace _S=[u ₁, u ₂..., u _q]; And M-q little characteristic value u _Q+1, u _Q+2..., u _MThe characteristic of correspondence vector then constitutes noise subspace, i.e. the noise vector matrix U _N=[u _Q+1, u _Q+2..., u _M],

5.) the noise vector matrix U _NAnd the steering vector of signal

A (θ)=[1, e ^{-j2 π d (sin θ)/λ}..., e ^{-j2 π d (M-1) (sin θ)/λ}] ^TSubstitution

Here, M is an array number, and λ is a carrier wavelength, and d is the array element interval, () ^TThe computing of expression transposition, P (θ) is called power spectrum, when θ from 0 to 180 degree is got different values, obtains different power spectral value, q the maximum that equates with signal number wherein must be arranged, and the pairing abscissa of this q maximum point is exactly that the ripple of all q signal reaches angle.

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