CN100399730C - Blind estimating method for error of array antenna channel - Google Patents

Abstract

The present invention provides a blind estimating method for the error of an array antenna channel. The present invention adopts a narrow-band signal source for correcting to obtain two groups of data before moving the signal source and after moving the signal source by moving the signal source and altering the azimuthal angle of the signal source. Afterwards, an MUSIC algorithm is adopted to roughly estimate the azimuthal angle before and after moving the signal source and to define an objective function of which the extremum value is worked out for obtaining an accurate azimuthal angle before and after moving the signal source, and in this way, the amplitude error and the phase error of each array antenna channel can be obtained. The adoption of the method of the present invention can accurately estimate the amplitude error and the phase error of the array antenna channel under the condition of not measuring the azimuthal angle of the radio-frequency signal source for correcting.

Description

A kind of blind estimating method of array antenna channel error

Technical field:

The invention belongs to communication technical field, it is particularly related to the estimation technique of array antenna channel error.

Background technology:

The growth of multimedia mobile communication business has improved the requirement to the communication system data transmission rate, for this reason, needs to solve some mis-behave problems that cause owing to reasons such as multipath fading, common-channel interference.(SDMA) can effectively address this problem to division multiple access technology, and the core of SDMA technology is an array antenna, and the error of array antenna can have a strong impact on the performance of SDMA technology, also has identical problem in field of radar.

Based on the high-resolution DOA algorithm for estimating of characteristic value decomposition,, have a wide range of applications in fields such as radar, sonar, mobile communication as the MUSIC algorithm.Theory analysis and evidence, this class algorithm is under desirable array bar spare, and performance is fine, but this class algorithm is all very sensitive to noise disturbance and systematic error, and the performance of noise disturbance and this class algorithm of systematic error meeting severe exacerbation descends its resolution.When noise disturbance mainly showed little number of samples, low signal-to-noise ratio, there was a thresholding in this class algorithm, and when signal to noise ratio was lower than this thresholding, the resolution capability of algorithm sharply descended.Noise disturbance can reduce its influence with the increasing number of samples usually.Systematic error can make a big impact to the performance of algorithm equally.Strengthen the systematic error that number of samples can not reduce array.Propose a lot of algorithms at present and addressed this problem, can see in the literature, mainly contained three class bearing calibrations at present.The first kind is to place a signal source (to see document: Matrix-constructioncalibration method for antenna arrays in the far field of array antenna to be corrected, Hung, E.K.L.Aerospace and ElectronicSystems, IEEE Transactions on, Volume:36 Issue:3, July 2000, Page (s): 819-828, " the matrix correction method of array antenna "), its azimuth is known, uses the signal of this signal source emission that array antenna is proofreaied and correct.This class methods superior performance, but it is very big to implement difficulty in actual environment.Second class methods need two RF signal sources, its azimuth can be unknown, (see document: Array antenna errorscalibration using signal sources in unknown directions, Jia Yongkang but the differential seat angle between the two must be known; Bao Zheng; Wu Huan; Radar, 1996.Proceedings.CIE International Conference of, 8-10 Oct.1996, Page (s): 503-506 " the error in array antenna bearing calibration of the unknown signaling angle of arrival ").The shortcoming of this method also is that the enforcement difficulty is big.The 3rd class be correction signal with power splitter be separated into M road homophase, etc. the signal of amplitude, directly inject each array element passage, analyze the output signal of array, then the channel error of correction array antenna.These class methods can effectively solve the channel transfer error problem, but have improved the hardware complexity of system, and will do change on the hardware to system.

The MUSIC algorithm: the core concept of MUSIC algorithm is exactly that the covariance matrix of array output signal is made feature decomposition, feature space be divided into signal subspace and noise subspace.Signal subspace and noise subspace quadrature define MUSIC spectrum, search speed spectrum peak, the angle of spectrum peak correspondence be the direction of arrival of incoming signal [see document: open the prominent personage, protect polished, " Array Signal Processing ", 2000.12].

Summary of the invention:

The invention provides a kind of blind estimating method of array antenna channel error, adopt method of the present invention accurately to estimate the channel amplitude sum of errors phase error of array antenna not needing measurement update with under azimuthal situation of radio-frequency signal source.

For convenience of description, at first define:

Term definition:

Far field condition: generally be meant 10 times of wavelength that the distance between signal source and the array antenna transmits greater than signal source.

Direction of arrival (DOA): the angle between the line between the reference array element of signal source and array antenna and the normal of array antenna.

The blind estimating method of a kind of array antenna channel error of the present invention is characterized in that adopting following step:

Step 1 (signalization source):

And array antenna between distance satisfy under the situation of far field condition, place a narrow band signal source s (t), the direction of arrival of incoming signal (signal source emission signal) is θ ₁, as shown in Figure 1.The start signal source is in the data of the individual snap of the output collection N (N＞400) of array antenna, shutdown signal source then.The k that collects fast beat of data is:

x _1k＝[x _1k(1)…x _1k(M)] ^H (1)

X in the formula _1k(i) in N the snap that obtains before the expression displaced signal sources in k snap, i the data that array element is exported.() ^HExpression Hermitian transposition.

Step 2 (displaced signal sources):

Displaced signal sources s (t) is placed on the position that another one satisfies far field condition, and this moment, the azimuth of signal source was θ ₂(θ ₁≠ θ ₂).Start signal source once more is in the data that the output of array antenna is gathered the individual snap of N (N＞400), shutdown signal source.The k that collects fast beat of data is:

x _2k＝[x _2k(1)…x _2k(M)] ^H (2)

X in the formula _2k(i) in N the snap that obtains after the expression displaced signal sources in k snap, i the data that array element is exported;

Step 3 (data are synthetic):

Data according to twice collection before and after moving obtain two covariance matrix R ₁And R ₂

$R_1=\frac{1}{N}\underset{k=1}{\overset{N}{\mathrm{\Σ}}}{x}_{1k}{x}_{1k}^H---\left(3\right)$

$R_2=\frac{1}{N}\underset{k=1}{\overset{N}{\mathrm{\Σ}}}{x}_{2k}{x}_{2k}^H---\left(4\right)$

Step 4 (asking intermediate variable):

To R ₁And R ₂Make feature decomposition respectively, can obtain the characteristic vector u of two big characteristic values of correspondence _M1And u _M2, these two characteristic vectors are obtained two intermediate variables with its first element do normalization,

$\frac{u_{m1}}{u_{m1}\left(1\right)}=u_{s1}---\left(5\right)$

$\frac{u_{m2}}{u_{m2}\left(1\right)}=u_{s2}---\left(6\right)$

Step 5 (estimation azimuth):

Adopt MUSIC algorithm estimated signal source to move the azimuth of front and back, just can obtain With

Step 6 (DOA estimation domain):

Define two independent variable territories, with

With

Being the center, is that radius is expanded to both sides with δ (desirable 0.3 degree of reference value), obtains two DOA estimated value intervals

With

Step 7 (the estimation flow process of array antenna channel error)

At first, the phase error of k the passage of data rough estimate array antenna that obtains before moving according to signal source:

${\widehat{\mathrm{\φ}}}_{1k}\left({\widehat{\mathrm{\θ}}}_1\right)=\∠\left(u_{s1}\left(k\right)\right)+\frac{2\mathrm{\π}(k-1)d}{\mathrm{\λ}}\sin \left({\widehat{\mathrm{\θ}}}_1\right)---\left(7\right)$

In the formula (7), the angle of＜() operator representation calculated complex, d is the spacing of adjacent array element, λ is the wavelength of incoming signal.

The phase error of k the passage of data rough estimate array antenna that obtains after moving according to signal source:

${\widehat{\mathrm{\φ}}}_{2k}\left({\widehat{\mathrm{\θ}}}_2\right)=\∠\left(u_{s2}\left(k\right)\right)+\frac{2\mathrm{\π}(k-1)d}{\mathrm{\λ}}\sin \left({\widehat{\mathrm{\θ}}}_2\right)---\left(8\right)$

Then, introduce a parameter:

$\mathrm{\ξ}\left(l\right)=\underset{k=1}{\overset{M}{\mathrm{\Σ}}}{|{\widehat{\mathrm{\φ}}}_{1k}\left({\mathrm{\ψ}}_1\left(l\right)\right)-{\widehat{\mathrm{\φ}}}_{2k}\left({\mathrm{\ψ}}_2\left(l\right)\right)|}^2---\left(9\right)$

At last, determine the true incidence angle of signal source:

A with

With

Be starting point, $\begin{array}{c}{\mathrm{\ψ}}_1\left(0\right)={\widehat{\mathrm{\θ}}}_1-\mathrm{\δ}\\ {\mathrm{\ψ}}_2\left(0\right)={\widehat{\mathrm{\θ}}}_2-\mathrm{\δ}\end{array},$ Calculate according to formula (7) and (8)

With And then according to formula (9) calculating ξ (0); Get suitable step-length ε (reference value gets 0.01).Make l=0.

b?l＝l+1， $\begin{array}{c}{\mathrm{\ψ}}_1\left(l\right)={\mathrm{\ψ}}_1\left(0\right)+\mathrm{l\ϵ}\\ {\mathrm{\ψ}}_2\left(l\right)={\mathrm{\ψ}}_2\left(0\right)+\mathrm{l\ϵ}\end{array},$ Calculate ξ (l);

If c $\begin{array}{c}{\mathrm{\ψ}}_1\left(l\right)\≠{\widehat{\mathrm{\θ}}}_1+\mathrm{\δ}\\ {\mathrm{\ψ}}_2\left(l\right)\≠{\widehat{\mathrm{\θ}}}_2+\mathrm{\δ}\end{array},$ Then change b;

D seeks the minimum of ξ.If minimum does not exist, then suitably increase δ (reference value is got δ=δ+0.5), return a;

The angle value ψ of the minimum correspondence of e ξ ₁(l) and ψ ₂(l) be exactly real azimuth angle theta before and after signal source moves ₁, θ ₂

Step 8 (range error of computing array antenna channels and phase error)

The u that obtains according to step 4 _S1, the range error of k passage of computing array antenna is estimated

For:

${\widehat{\mathrm{\ρ}}}_k=\left|u_{s1}\left(k\right)\right|-1---\left(10\right)$

In the formula (10), u _S1(k) expression vector u _S1In k element

The u that obtains according to step 4 again _S1The θ that obtains with step 7 ₁, k channel phases estimation error of computing array antenna

For:

${\widehat{\mathrm{\φ}}}_k=\∠\left(u_{s1}\left(k\right)\right)+\frac{2\mathrm{\π}(k-1)d}{\mathrm{\λ}}\sin {\mathrm{\θ}}_1---\left(11\right)$

Through after the above-mentioned steps, just can accurately estimate the channel amplitude error of array antenna

And phase error

Operation principle of the present invention is:

Covariance matrix to the equidistant linear array antenna output signal of M unit carries out feature decomposition, with dominant eigenvalue characteristic of correspondence vector u _m, serve as that reference obtains do normalization with first element,

$\frac{u_m}{u_m\left(1\right)}=u_z---\left(12\right)$

The direction vector of array antenna is a (θ),

$a\left(\mathrm{\&theta;}\right)={\left[\begin{array}{cccc}1& e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="C20031011107600121.png,C20031011107600122.png"\; state="\{\{state\}\}">j</figure-callout>}\frac{2\mathrm{\&pi;d}}{\mathrm{\&lambda;}}\sin \mathrm{\&theta;}}& ...& e^{-j(M-1)\frac{2\mathrm{\&pi;d}}{\mathrm{\&lambda;}}\sin \mathrm{\&theta;}}\end{array}\right]}^T---\left(13\right)$

In the formula (13), θ is the angle of arrival of incoming signal, and d is the spacing of adjacent array element, and λ is the wavelength of incoming signal.

When there was channel amplitude sum of errors phase error in array antenna, the direction vector of incoming signal was:

$a^{\&prime;}\left(\mathrm{\&theta;}\right)=\mathrm{\&Lambda;a}\left(\mathrm{\&theta;}\right)$

$=\mathrm{\&Lambda;}{\left[\begin{array}{cccc}1& e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="C20031011107600121.png,C20031011107600122.png"\; state="\{\{state\}\}">j</figure-callout>}\frac{2\mathrm{\&pi;d}}{\mathrm{\&lambda;}}\sin \mathrm{\&theta;}}& ...& e^{-j(M-1)\frac{2\mathrm{\&pi;d}}{\mathrm{\&lambda;}}\sin \mathrm{\&theta;}}\end{array}\right]}^T---\left(14\right)$

$=\left[\begin{array}{ccccc}{\mathrm{\&rho;}}_1{e}^{j{\mathrm{\&phi;}}_1}& & & & \\ & .& & & \\ & & .& & \\ & & & .& \\ & & & & {\mathrm{\&rho;}}_M{e}^{j{\mathrm{\&phi;}}_M}\end{array}\right]{\left[\begin{array}{cccc}1& e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="C20031011107600121.png,C20031011107600122.png"\; state="\{\{state\}\}">j</figure-callout>}\frac{2\mathrm{\&pi;d}}{\mathrm{\&lambda;}}\sin \mathrm{\&theta;}}& ...& e^{-j(M-1)\frac{2\mathrm{\&pi;d}}{\mathrm{\&lambda;}}\sin \mathrm{\&theta;}}\end{array}\right]}^T$

ρ in the formula _KdThe amplitude gain of representing k passage, φ _kThe phase error of representing k passage.Can prove:

u _s＝a′(θ) (15)

Then have

$u_s\left(k\right)={\mathrm{\&rho;}}_k{e}^{j{\mathrm{\&phi;}}_k}{e}^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="C20031011107600121.png,C20031011107600122.png"\; state="\{\{state\}\}">j</figure-callout>}\frac{2\mathrm{\&pi;}(k-1)d}{\mathrm{\&lambda;}}\sin \mathrm{\&theta;}}$

Following formula is got phase information, then being estimated as of the phase error of k passage of array antenna:

${\widehat{\mathrm{\&phi;}}}_k\left(\mathrm{\&theta;}\right)=\&angle;\left(u_s\left(k\right)\right)+\frac{2\mathrm{\&pi;}(k-1)d}{\mathrm{\&lambda;}}\sin \left(\mathrm{\&theta;}\right)---\left(17\right)$

To the following formula delivery, being estimated as of the range error of k passage of array antenna then:

${\widehat{\mathrm{\&rho;}}}_k=\left|u_s\left(k\right)\right|-1---\left(18\right)$

In sum, the present invention use the narrow band signal source by adopting a correction, and mobile displaced signal sources changes the azimuth of signal source, before move in the picked up signal source and respectively one group of data after moving.And then adopt MUSIC algorithm rough estimate signal source to move the azimuth of front and back, define a target function, by asking the extreme value of target function, the accurate azimuth of front and back is moved in the picked up signal source, just can obtain the range error and the phase error of each passage of array antenna.

In the channel error alignment technique of array antenna, a correction radio-frequency signal source is set in the place of the condition that satisfies the far field, and correction accuracy is relevant with the certainty of measurement of the direction of arrival of radio-frequency signal source with correction.This algorithm can accurately be estimated the channel amplitude sum of errors phase error of array antenna not needing measurement update with under azimuthal situation of radio-frequency signal source.

Description of drawings:

Fig. 1 be among the present invention signal source schematic diagram is set

Wherein, s (t) represents testing source, θ ₁The expression signal source just incides the direction of arrival of the signal of array antenna, in the array antenna shown in the figure with respect to the azimuth of array antenna, 1 represents first array element, and m represents m array element, and m (1≤m≤M), M represents M array element, and M is a natural number.

Fig. 2 is the schematic diagram that is provided with after signal source moves among the present invention

Wherein, s (t) represents testing source, θ ₂The expression signal source just incides the direction of arrival of the signal of array antenna with respect to the azimuth of array antenna.In the array antenna shown in the figure, 1 represents first array element, m (1≤m≤M) represent the array element, M to represent M array element.M is a natural number.

Fig. 3 is the actual error table of array antenna passage

Wherein, K represents the channel position of array antenna, ρ _kThe physical channel range error of k passage of expression array antenna, φ _kThe physical channel phase error of k passage of expression array antenna.

Fig. 4 is the array antenna channel error result who adopts this algorithm to estimate

Wherein, K represents the channel position of array antenna, ρ _kThe range error of k the passage of array antenna that expression employing method of the present invention obtains is estimated φ _kThe phase error estimation and phase error of k the passage of array antenna that expression employing method of the present invention obtains.

Embodiment:

The blind estimation of 8 element array antenna channels errors:

We adopt equidistantly line array of 8 (M=8) unit, and array element distance is a half-wavelength.In the placed around of aerial array a signal source, and the distance between the array satisfies far field condition, the signal to noise ratio of signal is 20dB.Azimuth before and after signal source moves is respectively :-10 °, 20 °, the fast umber of beats of image data is 400, Fig. 3 is the actual margin sum of errors phase error of each passage of array antenna, utilizes method of the present invention to estimate, just can obtain amplitude gain sum of errors phase error shown in Figure 4.

Data shown in comparison diagram 3 and Fig. 4 adopt method of the present invention can effectively estimate the channel error of array antenna as can be seen.

Claims (1)

1. the blind estimating method of an array antenna channel error, the feature of this method are the steps below adopting:

Step 1: signalization source

And array antenna between distance satisfy under the situation of far field condition, place a narrow band signal source s (t), the direction of arrival of incoming signal is θ ₁The start signal source is in the data that the output of array antenna is gathered N snap, N 〉=400; The shutdown signal source; The k that collects fast beat of data is:

x _1k＝[x _1k(1)…x _1k(M)] ^H (1)

X in the formula _1k(i) in 400 snaps that obtain before the expression displaced signal sources in k snap, i the data that array element is exported, () ^HExpression Hermitian transposition;

Step 2: change source location

Signal source s (t) is placed on the position that another one satisfies far field condition, and the azimuth of establishing signal source is θ ₂And θ ₁≠ θ ₂, start signal source once more is in the data that the output of array antenna is gathered N snap, N＞400; The shutdown signal source; The k that collects fast beat of data is:

x _2k＝[x _2k(1)…x _2k(M)] ^H (2)

X in the formula _2k(i) expression changes in N the snap that obtains after the source location in k the snap i the data that array element is exported;

Step 3: data are synthetic

Data according to twice collection obtain two covariance matrix R ₁And R ₂,

$R_1=\frac{1}{N}\underset{k=1}{\overset{N}{\mathrm{\&Sigma;}}}{x}_{1k}{x}_{1k}^H---\left(3\right)$

$R_2=\frac{1}{N}\underset{k=1}{\overset{N}{\mathrm{\&Sigma;}}}{x}_{2k}{x}_{2k}^H---\left(4\right)$

Step 4: ask intermediate variable

To R ₁And R ₂Make feature decomposition respectively, can obtain the characteristic vector u of two big characteristic values of correspondence _M1And u _M2, these two characteristic vectors are obtained two intermediate variables with separately first element do normalization,

$\frac{u_{m1}}{u_{m1}\left(1\right)}=u_{s1}---\left(5\right)$

$\frac{u_{m2}}{u_{m2}\left(1\right)}=u_{s2}---\left(6\right)$

Step 5: estimate the azimuth

Adopt MUSIC algorithm estimated signal source to move the azimuth of front and back, just can obtain

With

Step 6:DOA estimation domain

Define two independent variable territories, with

With

Being the center, is that radius is expanded to both sides with δ, and desirable 0.3 degree of δ reference value obtains two DOA estimated value intervals

With

Step 7: the estimation flow process of array antenna channel error

At first, the phase error of k the passage of data rough estimate array antenna that obtains before moving according to signal source:

${\widehat{\mathrm{\&phi;}}}_{1k}\left({\widehat{\mathrm{\&theta;}}}_1\right)=\&angle;\left(u_{s1}\left(k\right)\right)+\frac{2\mathrm{\&pi;}(k-1)d}{\mathrm{\&lambda;}}\sin \left({\widehat{\mathrm{\&theta;}}}_1\right)---\left(7\right)$

In the formula (7), the angle of ∠ () operator representation calculated complex, d is the spacing of adjacent array element, λ is the wavelength of incoming signal; The phase error of k the passage of data rough estimate array antenna that obtains after moving according to signal source:

${\widehat{\mathrm{\&phi;}}}_{2k}\left({\widehat{\mathrm{\&theta;}}}_2\right)=\&angle;\left(u_{s2}\left(k\right)\right)+\frac{2\mathrm{\&pi;}(k-1)d}{\mathrm{\&lambda;}}\sin \left({\widehat{\mathrm{\&theta;}}}_2\right)---\left(8\right)$

Then, introduce a parameter:

$\mathrm{\&xi;}\left(l\right)=\underset{k=1}{\overset{M}{\mathrm{\&Sigma;}}}{|{\widehat{\mathrm{\&phi;}}}_{1k}\left({\mathrm{\&psi;}}_1\left(l\right)\right)-{\widehat{\mathrm{\&phi;}}}_{2k}\left({\mathrm{\&psi;}}_2\left(l\right)\right)|}^2---\left(9\right)$

At last, determine the true incidence angle of signal source:

A) with

With Be starting point, $\begin{array}{c}{\mathrm{\&psi;}}_1\left(0\right)={\widehat{\mathrm{\&theta;}}}_1-\mathrm{\&delta;}\\ {\mathrm{\&psi;}}_2\left(0\right)={\widehat{\mathrm{\&theta;}}}_2-\mathrm{\&delta;}\end{array},$ Calculate according to formula (7) and (8)

With

And then according to formula (9) calculating ξ (0); ε is a step-length, and the ε reference value can get 0.01, makes l=0;

b)l＝l+1， $\begin{array}{c}{\mathrm{\&psi;}}_1\left(l\right)={\mathrm{\&psi;}}_1\left(0\right)+\mathrm{l\&epsiv;}\\ {\mathrm{\&psi;}}_2\left(l\right)={\mathrm{\&psi;}}_2\left(0\right)+\mathrm{l\&epsiv;}\end{array},$ Calculate ξ (l);

C) if $\begin{array}{c}{\mathrm{\&psi;}}_1\left(l\right)\&NotEqual;{\widehat{\mathrm{\&theta;}}}_1+\mathrm{\&delta;}\\ {\mathrm{\&psi;}}_2\left(l\right)\&NotEqual;{\widehat{\mathrm{\&theta;}}}_2+\mathrm{\&delta;}\end{array},$ Then change b);

D) minimum of searching ξ if minimum does not exist, then suitably increases δ, and reference value is got δ=δ+0.5, returns a);

E) the angle value ψ of the minimum correspondence of ξ ₁(l) and ψ ₂(1) is exactly real azimuth angle theta before and after signal source moves ₁, θ ₂

Step 8: the range error of computing array antenna channels and phase error

The u that obtains according to step 4 _S1, the range error of k passage of computing array antenna is estimated

For:

${\widehat{\mathrm{\&rho;}}}_k=\left|u_{s1}\left(k\right)\right|-1---\left(10\right)$

In the formula (10), u _S1(k) expression vector u _S1In k element

The u that obtains according to step 4 again _S1The θ that obtains with step 7 ₁, k channel phases estimation error of computing array antenna

For:

${\widehat{\mathrm{\&phi;}}}_k=\&angle;\left(u_{s1}\left(k\right)\right)+\frac{2\mathrm{\&pi;}(k-1)d}{\mathrm{\&lambda;}}\sin {\mathrm{\&theta;}}_1---\left(11\right)$

Through after the above-mentioned steps, just can accurately estimate the channel amplitude error of array antenna

And phase error

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