CN102118187A - Wave number calculating device and coherent signal number estimation method based on L array - Google Patents

Abstract

The invention discloses a wave number calculating device and a coherent signal number estimation method based on an L array. The L array consists of two uniform linear arrays which are perpendicular to each other. The method comprises the following steps: utilizing geometrical features and transfer invariance of the array to de-cohere signals; finding cross-correlation between array element data of the uniform linear arrays; obtaining a reconstructed matrix through a cross-correlation matrix; and carrying out QR decomposition on cartesian product of the reconstructed matrix. The number of ranks of upper trapezoidal factors on QR is equal to that of signal sources. Since the cross-correlation between the data of the two arrays is found, the influence of noise is reduced to the lowest level. With the method, the fuzzy cone problem which can not be solved in the linear arrays is solved, that is, the number of signals can be identified from now on when the two incidence angles of signals are equal.

Description

A kind of wave number calculation element reaches the coherent signal number estimation method based on the L battle array

Technical field:

The number that the present invention relates to radio wave under the relevant situation is estimated and tracking.Concrete the present invention relates to a kind of based on the L battle array and utilize the self adaptation wave number of the QR decomposition method of matrix to estimate and tracking, the number of the far field narrowband radio ripple that is used to estimate and follow the tracks of that L type array received arrives.

Background technology:

In recent years, the research and development for the mobile communication system of using adaptive array antenna is subjected to extensive concern.Typical array antenna comprises a plurality of antenna a period of time, and these antenna a period of time is arranged on different locus, so that the profile in these antenna a period of time has particular geometric shapes.The number of the radio wave (hereinafter, from the signal processing angle, radio wave being called signal) that arrives array antenna is estimated it substantially the most also is unusual one of important techniques.

In the various technical methods (as: MUSIC) of Array Signal Processing, if the unknown of signal number, they are with ineffective so.As seen the signal number is accurately estimated it is a problem the most basic.

Want the number of estimated signal, a kind of method is a threshold method, and it is a number of determining signal by the size of the characteristic value of judging the covariance of observing vector.The method that Bartlet and Lawley propose just is based on a series of hypothesis testings, in each check, likelihood ratio and thresholding is compared, and the hypothesis testing that surpasses thresholding for the first time will be accepted.The problem of this kind method maximum is exactly the subjectivity that thresholding is set.

Another kind also is that present most popular method is the information theory criterion, that is, AIC and MDL method, their formula is represented that by characteristic value the signal number equals to make the value of AIC and MDL criterion minimum.The information theory criterion is exactly the thresholding that need not subjective judgement with respect to the great advantage of threshold method.Although the method is because its calculating simply and is extensively paid close attention to, when signal correction or when relevant, performance has very big decline.Adopt space smoothing AIC and MDL criterion can solve signal correction or relevant problem to a certain extent, yet their performance is very sensitive to the accuracy of estimating characteristic value, simultaneously they can not solve circular cone fuzzy problem in the linear array (that is, when two signal incidence angles are identical can't identification signal number).These methods need EVD or SVD in addition, and very big amount of calculation is arranged, and for online execution great difficulty are arranged.

The inventor has proposed a kind of method of the non-parametric estmation signal number based on the L battle array.The L battle array is made up of two mutually perpendicular even linear arrays.Utilize the geometrical property and the transfer consistency of array on average signal to be separated relevant by submatrix.Array element data to two even linear arrays are asked cross-correlation, obtain a reorganization matrix from cross-correlation matrix, and to the carrying out QR from product and decompose of reorganization matrix, the R matrix that obtains after QR is decomposed carries out simple row operation and can obtain the signal number.Owing to be the cross-correlation of asking two array datas, so that the influence of noise is lowered to is minimum.This method not only can solve the circular cone fuzzy problem, has also reduced amount of calculation, has high actual application value.

Summary of the invention:

The object of the invention is based on the number estimation of signal and the tracking of L type array, and this method is by to the carrying out QR from product matrix and decompose of the cross-correlation matrix that obtains, and then the R matrix that obtains is carried out simply row and handles the estimated value that obtains the signal number.The maximum characteristics of this method are that to need not the characteristic value decomposition amount of calculation little.

A kind of wave number calculation element is used to utilize array antenna to estimate the number of radio wave, and this array antenna has L type structure, is arranged on the different position, space with identical distance along straight line, and this device comprises:

Instantaneous correlation calculations device is used at each sampling time, calculates the instantaneous correlation between the data that the data that received by an antenna a period of time and another antenna a period of time received;

Instantaneous correlation matrix calculation device is used for calculating instantaneous correlation matrix according to described instantaneous correlation;

The estimated value calculation element, the R matrix after being used for going out QR and decomposing according to described instantaneous correlation matrix calculation carries out the estimated value that corresponding computing obtains wave number to the R matrix then.

Based on the wave number method of estimation of the described wave number calculation element of claim 1, be used to utilize array antenna to estimate the number of radio wave, wherein this array antenna is made up of two orthogonal even linear arrays, may further comprise the steps:

Step S1: the submatrix size is set; If orthogonal two even linear arrays of L battle array are formed by M array element, then the submatrix size can be set

Here The maximum integer that is not more than (M+1)/2 is got in expression;

Step S2:, use wave number to estimate to upgrade instantaneous correlation between the array data that N snapshot during the K at interval calculate antenna a period of time at sampling time K;

Step S3:, form instantaneous correlation matrix according to this instantaneous correlation at sampling time K; Wherein sampling rate is 1/T _S

Step S4: from this instantaneous correlation matrix, extract corresponding forward direction and back to the instantaneous correlation matrix of son according to the submatrix size that is provided with;

Step S5: forward direction and back the reorganization to the instantaneous correlation matrix of son that S4 is obtained become a new instantaneous correlation matrix;

Step S6: carrying out QR from product and decompose to the new instantaneous correlation matrix among the S5;

Step S7: the R matrix that obtains after at last QR being decomposed carries out row operation and can obtain the signal number.

A kind of new wave number method of estimation based on L type array that need not characteristic value decomposition has been proposed here.Wherein L type array is made up of two orthogonal even linear arrays.This method may further comprise the steps: suitable submatrix size is set; Calculate instantaneous cross covariance matrix according to instantaneous sampling value; From this cross covariance matrix, extract corresponding forward direction and back according to the submatrix size that is provided with to sub-cross covariance matrix; Forward direction that obtains and back the reorganization to sub-cross covariance matrix are become a new associating cross-correlation matrix; Carrying out QR from product and decompose the new associating cross-correlation matrix that obtains; The R matrix that obtains is carried out the estimated value that suitable row operation can obtain the signal number.

In order to realize above purpose, according to the present invention, a kind of wave number calculation element is provided, be used to utilize array antenna to estimate the number of radio wave, this array antenna has L type structure, is arranged on the different position, space with identical distance along straight line, and this device comprises: instantaneous correlation calculations device, be used at each sampling time, calculate the instantaneous correlation between the data that the data that received by an antenna a period of time and another antenna a period of time received; Instantaneous correlation matrix calculation device is used for calculating instantaneous correlation matrix according to described instantaneous correlation; The estimated value calculation element, the R matrix after being used for going out QR and decomposing according to described instantaneous correlation matrix calculation carries out the estimated value that corresponding computing obtains wave number to the R matrix then.

Read following explanation in conjunction with the drawings, above and other purpose of the present invention, feature and advantage will become clear, and accompanying drawing shows the preferred embodiments of the present invention in the mode of example.

Description of drawings:

Fig. 1 is the structure of expression L type array.

Fig. 2 is the outline flowchart of expression according to the embodiment of the invention.

Fig. 3 shows wave number and upgrades at interval and the relation between the sampling interval.

Fig. 4 shows the structure in the array antenna and the source of transmission.

Embodiment:

Following summary description is estimated and tracking according to the radio wave number of the embodiment of the invention.

Estimate and the especially suitable following situation of tracking according to the radio wave number of the embodiment of the invention: online arrival wave number is estimated and the arrival wave number of time to time change is followed the tracks of.

Each even linear array all comprises M isotropic antenna a period of time (as Fig. 1) in two even linear arrays of the supposition formation L type array antenna of current description.The present invention is applicable to forward direction subarray, back to subarray and forward direction and back to subarray.

In addition, the present invention is applicable to comprising incoherent signal, and coherent signal (relevant fully) is in the estimation and the tracking of interior incoming signal number.

Fig. 1 is the structure of expression L type array.

L type array is made up of two orthogonal even linear arrays.Every even linear array is pressed equidistant arrangement by M antenna a period of time at the space diverse location.As shown in Figure 1, the even linear array of horizontal positioned is designated as the x axle, and the even linear array of placing perpendicular to the x axle is designated as the z axle.Pitching angle theta _kAnd azimuth

As shown in Figure 1.

Suppose to have far field, p arrowband coherent signal { s _k(n) } with carrier frequency f ₀Incide on the L battle array.Then the signal that receives on x axle and z axle is respectively:

z(n)＝A _zs(n)+w _z(n) (1)；

x(n)＝A _xs(n)+w _x(n) (2)；

Z (n)=[z wherein ₀(n), z ₁(n) ... z _M-1(n)] ^T, x (n)=[x ₁(n), x ₂(n) ... x _M(n)] ^T,

$w_z\left(n\right)={[w_{z_0}\left(n\right),w_{z_1}\left(n\right),...w_{z_{M-1}}\left(n\right)]}^T,w_x\left(n\right)={[w_{x_1}\left(n\right),w_{x_2}\left(n\right),...w_{x_M}\left(n\right)]}^T,$

s(n)＝[s ₁(n)，s ₂(n)，…s _p(n)] ^T，A _z＝[a(θ ₁)，a(θ ₂)，…a(θ _p)]，

$a\left({\mathrm{\&theta;}}_k\right)={[1,e^{-j{\mathrm{\&omega;}}_0{\mathrm{\&tau;}}_z\left({\mathrm{\&theta;}}_k\right)},...,e^{-j(M-1){\mathrm{\&omega;}}_0{\mathrm{\&tau;}}_z\left({\mathrm{\&theta;}}_k\right)}]}^T,a({\mathrm{\&theta;}}_k,{\stackrel{\&OverBar;}{\mathrm{\&phi;}}}_k)={[e^{-j{\mathrm{\&omega;}}_0{\mathrm{\&tau;}}_x({\mathrm{\&theta;}}_k,{\stackrel{\&OverBar;}{\mathrm{\&phi;}}}_k)},e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000037501000000012.png"\; state="\{\{state\}\}">j</figure-callout>}2{\mathrm{\&omega;}}_0{\mathrm{\&tau;}}_x({\mathrm{\&theta;}}_k,{\stackrel{\&OverBar;}{\mathrm{\&phi;}}}_k)}...,e^{-\mathrm{jM}{\mathrm{\&omega;}}_0{\mathrm{\&tau;}}_x({\mathrm{\&theta;}}_k,{\stackrel{\&OverBar;}{\mathrm{\&phi;}}}_k)}]}^T,$

ω ₀＝2πf ₀，τ _z(θ _k)＝(d/c)cosθ _k，

Wherein c is a propagation velocity of electromagnetic wave....(3)

Coherent signal can be expressed as s in the present invention _k(n)=β _ks ₁(n) ... (4)

Here β _kBe multiple attenuation coefficient and β _k≠ 0, β ₁=1.

Signal s ₁(n) be a time white complex gaussian noise with zero-mean and

Additional noise ω _x(n) and ω _z(n) be have zero-mean, covariance is σ ²The space-time white complex gaussian noise.

Fig. 2 is the outline flowchart of expression according to the embodiment of the invention.

Fig. 3 shows wave number and upgrades at interval and the relation between the sampling interval.

Suppose and sampling interval T _sCompare, wave number is slower over time, and the renewal interval T can be expressed as T=NT _s, wherein N is the quantity of the snapshot during the period T.Suppose also that in addition the relation between sampling time K and the direction updated time n can be expressed as K=nN, nN+1 ..., (n+1) N-1.

Step according to the wave number method of estimation of embodiment shown in Figure 2 is as described below.At first, the submatrix size is set; If orthogonal two even linear arrays of L battle array are formed by M array element, then the submatrix size can be set Here The maximum integer that is not more than (M+1)/2 is got in expression; (step S1).

At sampling time K, use wave number to estimate to upgrade instantaneous correlation (step S2) between the array data that N snapshot during the interval T calculate antenna a period of time.

(wherein sampling rate is 1/T at sampling time K _S), form instantaneous correlation matrix (step S3) according to this instantaneous correlation.

Then, from this instantaneous correlation matrix, extract corresponding forward direction and back according to the submatrix size that is provided with to the instantaneous correlation matrix of son (step S4).

Forward direction and back the reorganization to the instantaneous correlation matrix of son that S4 is obtained become a new instantaneous correlation matrix (step S5).

Afterwards, carrying out QR from product and decompose (step S6) the new instantaneous correlation matrix among the S5.

At last, the R matrix that obtains after the QR decomposition is carried out suitable row operation and can obtain signal number (step S7).

By above-mentioned wave number method of estimation, can estimate and follow the tracks of the number of coherent signal accurately, and operand is proper according to this embodiment.

Below describe present embodiment in detail.

Fig. 4 shows the structure in the array antenna and the source of transmission.

Direct wave 6 is 10 direct radio waves that arrive the array antenna 8 of base station from the transmission source.Reflected wave 7 is going out arrival base station, reflection back through the object such as building B L1 and BL2.Although Fig. 4 only shows two reflected waves 7, this specification hypothesis is launched the ripple of p altogether that comprises direct wave 6 and reflected wave 7 from transmission source 10.Between this direct wave 6 and the transmitted wave 7 in the relation of specific sampling time K as shown in Equation (4).

The cross covariance matrix that we can obtain array according to formula 1～4 is:

$R_{\mathrm{XZ}}=E\left\{x\left(n\right)z^H\left(n\right)\right\}=A_x{R}_S{A}_z^H---\left(5\right);$

R wherein _s=E{s (n) s ^H(n) }=r _sβ β ^H, β=[β here ₁, β ₂... β _p] ^T

Covariance matrix in the formula 5 obtains by instantaneous cross covariance Matrix Estimation.That is:

${\hat{R}}_{\mathrm{xz}}=\frac{1}{N}\underset{n=1}{\overset{N}{\mathrm{\&Sigma;}}}x\left(n\right)z^H\left(n\right)---\left(6\right);$

Suitable submatrix size is set on the x axle.The submatrix size is set in the present invention

Here

The integer that is not more than x is got in expression.The x axle is divided into L forward direction and back to the stack subarray.L forward direction subarray comprise (l, l+1 ..., l+m-1) array element, l back to subarray comprise the (M-l+1, M-l ... L-l+1) array element, l=1 wherein, 2 ... L, L=M-m+1.

Then l forward direction is respectively with the data that the back receives to subarray on the x axle:

$x_l\left(n\right)={[x_l\left(n\right),x_{l+1}\left(n\right),...x_{l+m-1}\left(n\right)]}^T={\tilde{A}}_x{D}_x^{l-1}s\left(n\right)+{\mathrm{\&omega;}}_{\mathrm{xl}}\left(n\right)---\left(7\right);$

${\stackrel{\&OverBar;}{x}}_l\left(n\right)={[x_{M-l+1}\left(n\right),x_{M-l}\left(n\right),...x_{L-l+1}\left(n\right)]}^H={\tilde{A}}_x{D}_x^{-(M-l)}{s}^{*}\left(n\right)+{\stackrel{\&OverBar;}{\mathrm{\&omega;}}}_{\mathrm{xl}}\left(n\right)---\left(8\right);$

Here ω _Xl(n)=[ω _Xl(n), ω _Xl+1(n) ... ω _Xl+m-1(n)] ^T,

${\stackrel{\&OverBar;}{\mathrm{\&omega;}}}_{\mathrm{xl}}\left(n\right)={[{\mathrm{\&omega;}}_{M-l+1}\left(n\right),{\mathrm{\&omega;}}_{M-l}\left(n\right),...{\mathrm{\&omega;}}_{L-l+1}\left(n\right)]}^H,$

And here

Be by the A in the formula 5 _xCapable form of preceding m.

Our the cross covariance matrix that can obtain on the x axle l forward direction subarray and z axle is now:

${\mathrm{\&Phi;}}_{\mathrm{xl}}=E\left\{x_l\left(n\right)z^H\left(n\right)\right\}=r_s{\tilde{A}}_x{D}_x^{l-1}\mathrm{\&beta;}{\mathrm{\&beta;}}^H{A}_z^H---\left(9\right);$

Then can obtain the cross covariance matrix of a LM * m through top computing

${\mathrm{\&Phi;}}_x={[{\mathrm{\&phi;}}_{x1},{\mathrm{\&phi;}}_{x2},...,{\mathrm{\&phi;}}_{\mathrm{xL}}]}^H=r_s\left[\begin{array}{c}{A}_z\mathrm{\&beta;}{\mathrm{\&beta;}}^H{\tilde{A}}_x^H\\ A_z\mathrm{\&beta;}{\mathrm{\&beta;}}^H{D}_x^{-1}{\tilde{A}}_x^H\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ A_z\mathrm{\&beta;}{\mathrm{\&beta;}}^H{D}_x^{-(L-1)}{\tilde{A}}_x^H\end{array}\right]=r_s{C}_z{\stackrel{\&OverBar;}{A}}_x{B}^{*}{D}_x{\tilde{A}}_x^H---\left(10\right);$

Wherein

B=diag (β ₁, β ₂..., β _p).Symbol

Expression Kronecker is long-pending.

In like manner, we can obtain on the x axle l back and to the cross covariance matrix of subarray and z axle are:

${\stackrel{\&OverBar;}{\mathrm{\&Phi;}}}_{\mathrm{xl}}=E\left\{{\stackrel{\&OverBar;}{x}}_l\left(n\right)z^T\left(n\right)\right\}=r_s{\tilde{A}}_x{D}_x^{-(M-l+2)}{\mathrm{\&beta;}}^{*}{\mathrm{\&beta;}}^T{A}_z^T---\left(11\right);$

${\stackrel{\&OverBar;}{\mathrm{\&Phi;}}}_x={[{\stackrel{\&OverBar;}{\mathrm{\&Phi;}}}_{x1},{\stackrel{\&OverBar;}{\mathrm{\&Phi;}}}_{x2},...,{\stackrel{\&OverBar;}{\mathrm{\&Phi;}}}_{\mathrm{xL}}]}^H=r_s\left[\begin{array}{c}{A}_z^{*}{\mathrm{\&beta;}}^{*}{\mathrm{\&beta;}}^T{D}_x^{M-1}{\tilde{A}}_x^H\\ A_z^{*}{\mathrm{\&beta;}}^{*}{\mathrm{\&beta;}}^T{D}_x^{M-2}{\tilde{A}}_x^H\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ A_z^{*}{\mathrm{\&beta;}}^{*}{\mathrm{\&beta;}}^T{D}_x^{M-L}{\tilde{A}}_x^H\end{array}\right]=r_s{C}_z^{*}{\stackrel{\&OverBar;}{A}}_{x}B{D}_x^{M+2}{\tilde{A}}_x^H---\left(12\right);$

Wherein

Here the Ф in the formula 9 _xWith in the formula 11

Can pass through in the formula 6

Obtain.Ф _XlBe by

L, l+1 ..., (l=1,2 of the capable formation of l+m-1 ..., L).

To we have finished step S4 herein.

The Ф that obtains among the step S4 _xWith

The carrying out combination again cross covariance matrix Ф that obtains a 2LM * m be shown below:

$\mathrm{\&Phi;}=\left[\begin{array}{c}{\mathrm{\&Phi;}}_x\\ {\stackrel{\&OverBar;}{\mathrm{\&Phi;}}}_x\end{array}\right]=r_{s}F{\mathrm{BD}}_x{\tilde{A}}_x^H---\left(13\right);$

Wherein

The cross covariance matrix φ involution that obtains is above obtained

$\mathrm{\&Psi;}={\mathrm{\&Phi;}}^H\mathrm{\&Phi;}=r_s^2{\tilde{A}}_x{D}_x^{-1}{B}^H{F}^H{\mathrm{FBD}}_x{\tilde{A}}_x^H$

Finish step S5 herein, obtained instantaneous correlation matrix ψ.

The instantaneous correlation matrix ψ that obtains is above carried out QR decompose, as follows:

$\mathrm{\&Psi;}=\mathrm{QR}=q\left[\begin{array}{c}{R}_{11},R_{12}\\ 0_{(m-p)\&times;m}\end{array}\right]---\left(14\right);$

R among the matrix R that obtains after the decomposition ₁₁And R ₁₂Be a matrix that p is capable, m is capable altogether for the R matrix.(completing steps S6)

We use following method the characteristic of the R matrix that obtains after decomposing according to QR:

It is as follows to introduce an auxiliary quantity ζ (i)

$\mathrm{\&zeta;}\left(i\right)=\underset{k=i}{\overset{m}{\mathrm{\&Sigma;}}}\left|r_{\mathrm{ik}}\right|+\mathrm{\&epsiv;},i=\mathrm{1,2,3}...,m---\left(15\right);$

Wherein ε is for often being worth (as 10 arbitrarily ^-10) to avoid occurring 0/0 situation.

Defining a ratio ξ (i) then is

$\mathrm{\&xi;}\left(i\right)=\frac{\mathrm{\&zeta;}\left(i\right)}{\mathrm{\&zeta;}(i+1)},i=\mathrm{1,2,3}...,m-1---\left(16\right);$

We can obtain the estimated value of wave number at last

$\hat{p}=\underset{i}{\arg \max }\mathrm{\&xi;}\left(i\right)---\left(17\right);$

Great advantage of the present invention is to carry out QR and decomposes and to have reduced amount of calculation and be convenient to practical application.Aforementioned content only is an explanation of the principles of the present invention.In addition, owing to those skilled in the art will readily appreciate that numerous modifications and variations, so be not intended to the present invention is defined as shown and illustrated definite structure and application, therefore can think that modification that all are suitable and equivalent all fall within claims and the scope of the present invention that equivalent limited thereof.

Above content is to further describing that the present invention did in conjunction with concrete preferred implementation; can not assert that the specific embodiment of the present invention only limits to this; for the general technical staff of the technical field of the invention; without departing from the inventive concept of the premise; can also make some simple deduction or replace, all should be considered as belonging to the present invention and determine scope of patent protection by claims of being submitted to.

Claims (2)

1. a wave number calculation element is used to utilize array antenna to estimate the number of radio wave, and this array antenna has L type structure, is arranged on the different position, space with identical distance along straight line, it is characterized in that this device comprises:

Instantaneous correlation calculations device is used at each sampling time, calculates the instantaneous correlation between the data that the data that received by an antenna a period of time and another antenna a period of time received;

Instantaneous correlation matrix calculation device is used for calculating instantaneous correlation matrix according to described instantaneous correlation;

The estimated value calculation element, the R matrix after being used for going out QR and decomposing according to described instantaneous correlation matrix calculation carries out the estimated value that corresponding computing obtains wave number to the R matrix then.

2. based on the wave number method of estimation of the described wave number calculation element of claim 1, be used to utilize array antenna to estimate the number of radio wave, wherein this array antenna is made up of two orthogonal even linear arrays, it is characterized in that, may further comprise the steps:

Step S1: the submatrix size is set; If orthogonal two even linear arrays of L battle array are formed by M array element, then the submatrix size can be set

Here

The maximum integer that is not more than (M+1)/2 is got in expression;

Step S2:, use wave number to estimate to upgrade instantaneous correlation between the array data that N snapshot during the K at interval calculate antenna a period of time at sampling time K;

Step S3:, form instantaneous correlation matrix according to this instantaneous correlation at sampling time K; Wherein sampling rate is 1/T _S

Step S4: from this instantaneous correlation matrix, extract corresponding forward direction and back to the instantaneous correlation matrix of son according to the submatrix size that is provided with;

Step S5: forward direction and back the reorganization to the instantaneous correlation matrix of son that S4 is obtained become a new instantaneous correlation matrix;

Step S6: carrying out QR from product and decompose to the new instantaneous correlation matrix among the S5;

Step S7: the R matrix that obtains after at last QR being decomposed carries out row operation and can obtain the signal number.

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