CN101149429B - Array mutual coupling calibration and source direction estimation method suitable for uniform circular array - Google Patents

Abstract

This invention relates to an array cross coupling proofreading and information source direction measuring method for homogeneous round array. This method uses array information disposing technique to estimate round array cross coupling error and information source AOA at the same time. Approaches are as follows: First collects data from each channel and saves it to the system memory. Then the data needs to be adaptive equalizing disposed. Next range the disposed data to a covariance matrix and disassemble it according to their character. After this can get noise subspace consisted of small characterized vector. By using subspace construction expense function, the azimuth angle and cross coupling errors can be figured out. Finally through the complexor from cross coupling error to homogeneous round array, finish the proofreading. This invention can universally apply to cross coupling proofreading and information source direction measuring in radar and communicating field. It is worth to wildly apply.

Description

Be applicable to the array mutual coupling calibration and the source direction estimation method of uniform circular array

Technical field

The invention belongs to radar, communication technical field, relate to a kind of Estimation of Spatial Spectrum signal processing method in this field, specifically, the present invention relates to a kind of method that is applicable to array mutual coupling calibration and source direction estimation in the uniform circular array antenna multichannel Radar Signal Processing system.

Background technology

Estimation of Spatial Spectrum is widely used in fields such as radar, sonar, communication, seismic prospecting, is a kind of gordian technique that improves the parameter estimation performance.But when there was error in space array, the performance of Estimation of Spatial Spectrum can seriously descend, even can't use, so array error is a key factor that influences the Estimation of Spatial Spectrum performance.Compare with other array error, the mutual coupling effect between array element and the electromagnetic property of array are closely related, because its complicacy, it is proofreaied and correct with compensation and does not find simple and effective solution always.It is by electromagnetic measurement or method of moment electromagnetism to be carried out in mutual coupling to calculate that early stage mutual coupling is calculated, yet the array element mutual coupling often changes with the variation of environment and electromagnetic parameter, its measured value or computational accuracy often can not satisfy actual needs, and when mutual coupling being compensated, tend to make azimuthal estimated performance to worsen more with mutual coupling measured value that has error or calculated value.

After the nineties, people are by carrying out modeling to array mutual coupling, and it is a parameter estimation problem that array mutual coupling calibration is gradated.The array correcting method of parameter class can be divided into active correction class and self-correcting class usually.Compare with the method for directly array mutual coupling being measured, it is high a lot of that the precision that parameter class method of estimation is proofreaied and correct is wanted, but its operand is quite big.

Uniform circular array is a kind of center symmetric array, compares with even linear array, and it has the characteristic of many excellences, as the simultaneously position angle and the angle of pitch of estimated signal, no matter in any direction and the position angle can cover 360 °,, all have approximately uniform estimated accuracy and resolving power etc.China 3G (Third Generation) Moblie TD-SCDMA smart antenna (Smart Antenna) has just adopted 8 array element uniform circular arrays, and direction of arrival estimation and the mutual coupling automatic correcting method therefore studied under the uniform circular array mutual coupling condition have important practical significance.

Summary of the invention

In order to proofread and correct the array mutual coupling error of uniform circular array better, the purpose of this invention is to provide a kind of simple and convenient, operand is few, can take into account the array mutual coupling calibration that is applicable to uniform circular array that mutual coupling calibration and information source angle estimate and the method for source direction estimation simultaneously.

For achieving the above object, the present invention is by the following technical solutions: a kind of array mutual coupling calibration and source direction estimation method that is applicable to uniform circular array, it utilizes array signal process technique simultaneously array mutual coupling error and information source incident direction to be estimated that it may further comprise the steps:

(1), gather the data that each passage receives, and be stored in the Installed System Memory;

(2), data that each passage is received make adaptive equalization and handle, and its objective is the array amplitude phase error of proofreading and correct with orientation-independent;

(3), the data after will handling through adaptive equalization generate the array covariance matrix, and covariance matrix are carried out feature decomposition, obtain the noise subspace E that is made up of little proper vector _N

(4), utilize cost function of subspace principles of construction:

$Q\left(\mathrm{\θ}\right)=T^H\left[a\left(\mathrm{\θ}\right)\right]E_N{E}_N^{H}T\left[a\left(\mathrm{\θ}\right)\right]$

(5), utilize the cost function of above-mentioned structure to carry out the calculating of azimuthal estimation and mutual coupling error, realize the array mutual coupling calibration and the source direction estimation of uniform circular array;

Wherein, utilize following formula to carry out azimuthal estimation:

$f_1\left(\mathrm{\θ}\right)=\frac{1}{\det \left\{\tilde{Q}\left(\mathrm{\θ}\right)\right\}}$ Or $f_2\left(\mathrm{\θ}\right)=\frac{1}{{\mathrm{\λ}}_{\min }\left\{\tilde{Q}\left(\mathrm{\θ}\right)\right\}}$

Utilize following formula to find the solution array element mutual coupling error:

$c=e_{\min }\left\{\tilde{Q}\left(\mathrm{\θ}\right)\right\}$ Or $c=\frac{{\tilde{Q}}^{+}\left(\mathrm{\θ}\right)w}{w^T{\tilde{Q}}^{+}\left(\mathrm{\θ}\right)w}$

Wherein, λ _Min{ g} represents to ask the minimal eigenvalue of matrix, e _MinG} represents to ask matrix minimal eigenvalue characteristic of correspondence vector, and w=[1,0 ..., 0] ^T, Be matrix

Generalized inverse matrix;

(6), utilize the mutual coupling error that obtains that the array steering vector of uniform circular array is proofreaied and correct;

Updating formula is:

a(θ，c)＝Ca(θ)＝T[a(θ)]c。

Described (4) step: utilize subspace principles of construction cost function $Q\left(\mathrm{\θ}\right)=T^H\left[a\left(\mathrm{\θ}\right)\right]E_N{E}_N^{H}T\left[a\left(\mathrm{\θ}\right)\right]$ Further may further comprise the steps:

(a), utilize the banded cycle characteristics and the symmetry Toeplitz of uniform circular array mutual coupling matrix, the mutual coupling error matrix of uniform circular array is expressed as N * N three banded circular matrixes;

If C represents the mutual coupling error matrix of uniform circular array, as if the mutual coupling effect of only considering between three adjacent array elements of the left and right sides, i.e. mutual coupling degree of freedom q=3, then the circulation vector of circular matrix C can be expressed as:

$\hat{c}=[c_0,c_1,c_2,0,\·\·\·,0,c_2,c_1],$ And 0＜| c ₂|＜| c ₁|＜c ₀=1 (1)

Correspondingly, N * N three banded circular matrix C can be expressed as:

$C=\mathrm{toeplitz}(\hat{c},\hat{c})=\mathrm{toeplitz}\left\{\right[c_0,c_1,c_2,0,\·\·\·,0,c_2,c_1],[c_0,c_1,c_2,0,\·\·\·0,c_2,c_1\left]\right\}---\left(2\right)$

Wherein,

Expression is by vector

The symmetry Toeplitz matrix that forms;

(b), obtain actual steering vector under the mutual coupling error condition;

Mutual coupling has changed desirable array steering vector, and this moment, the actual steering vector of array was

a(θ，c)＝Ca(θ)＝T[a(θ)]c (3)

Wherein, c=[c ₀, c ₁..., c _Q-1] ^T, N * q rank matrix T [a (θ)] can be expressed as:

T＝T ₁+T ₂+T ₃+T ₄ (4)

${\left[T_1\right]}_{i,j}=\left\{\begin{array}{cc}{a}_{i+j-1}& i+j\≤N+1\\ 0& \mathrm{otherwise}\end{array}\right.---\left(5\right)$

${\left[T_2\right]}_{i,j}=\left\{\begin{array}{cc}{a}_{i-j+1}& i\≥j\≥2\\ 0& \mathrm{otherwise}\end{array}\right.---\left(6\right)$

${\left[T_3\right]}_{i,j}=\left\{\begin{array}{cc}{a}_{N+1+i-j}& i<j\&le;p\\ 0& \mathrm{otherwise}\end{array}\right.---\left(7\right)$

${\left[T_4\right]}_{i,j}=\left\{\begin{array}{cc}{a}_{i+j-N-1}& 2\&le;j\&le;p,i+j\&GreaterEqual;N+2\\ 0& \mathrm{otherwise}\end{array}\right.---\left(8\right)$

Wherein, when array number N is even number, p=N/2; When N is odd number, p=(N+1)/2;

(c), utilize cost function of subspace principles of construction.

Have by the subspace principle:

$a^H(\mathrm{\&theta;},c)E_N{E}_N^{H}a(\mathrm{\&theta;},c)=0---\left(9\right)$

With formula (3) substitution formula (9), the cost function that can be constructed as follows:

$c^H{T}^H\left[a\left(\mathrm{\&theta;}\right)\right]E_N{E}_N^{H}T\left[a\left(\mathrm{\&theta;}\right)\right]c=c^{H}Q\left(\mathrm{\&theta;}\right)c=0---\left(10\right)$

In the formula, E _NBe noise subspace, q * q rank matrix Q (θ) are defined as

$Q\left(\mathrm{\&theta;}\right)=T^H\left[a\left(\mathrm{\&theta;}\right)\right]E_N{E}_N^{H}T\left[a\left(\mathrm{\&theta;}\right)\right]---\left(11\right)$

By formula (11) as can be seen, Q (θ) is independent of mutual coupling parameter vector c.

Described (3) step: the formula that the data after will handling through adaptive equalization generate the array covariance matrix is:

$R=\frac{1}{L}\underset{i=1}{\overset{L}{\mathrm{\&Sigma;}}}{V}_i{V_i}^H$

In the formula, vector sample Vi (i=1,2 ..., L) represent the reception data vector of each array element synchronization.

Described (3) step: utilize little proper vector to form noise subspace E _NMethod be:

Array covariance matrix R is carried out feature decomposition to be got:

$R=\underset{i=1}{\overset{M}{\mathrm{\&Sigma;}}}{\mathrm{\&lambda;}}_i{e}_i{e_i}^H+\underset{i=M+1}{\overset{N}{\mathrm{\&Sigma;}}}{\mathrm{\&lambda;}}_i{e}_i{e_i}^H$

Wherein, λ _i, e _iBe respectively eigenwert and the characteristic of correspondence vector thereof of matrix R.Can find that the eigenwert of R has following distribution:

λ ₁≥λ ₂≥L≥λ _M≥λ _M+1＝λ _M+2＝L＝λ _N

The matrix E that constitutes by little proper vector _N=[e _M+1, e _M+2..., e _N] linear subspaces that generated are called noise subspace.

Because the present invention adopts above technical scheme, so the present invention has not only solved the problem that direct array flow pattern mutual coupling calibration needs a large amount of manpowers, equipment, and has solved the big problem of parameter operand.The present invention has that steady key is strong, and Project Realization is simple and convenient, can take into account advantages such as mutual coupling calibration and angle estimation simultaneously.

Description of drawings

Fig. 1 is the graph of a relation of uniform circular array, information source and incident angle in the specific embodiment of the invention;

Fig. 2 realizes the process flowchart of uniform circular array array mutual coupling calibration and source direction estimation for the present invention.

Embodiment

The present invention utilizes array signal process technique simultaneously array mutual coupling error and information source incident angle to be estimated its principle:

(1) utilizes the banded cycle characteristics and the symmetry Toeplitz of uniform circular array mutual coupling matrix, the mutual coupling error matrix of uniform circular array is expressed as N * N three banded circular matrixes.

If C represents the mutual coupling error matrix of uniform circular array, by the characteristic of uniform circular array as can be known, can carry out modeling with one three banded circular matrix, it is expressed as N * N three banded circular matrixes.If only consider the mutual coupling effect between three adjacent array elements of the left and right sides, i.e. mutual coupling degree of freedom q=3, then the circulation vector of circular matrix C can be expressed as:

$\hat{c}=[c_0,c_1,c_2,0,\&CenterDot;\&CenterDot;\&CenterDot;,0,c_2,c_1],$ And 0＜| c ₂|＜| c ₁|＜c ₀=1 (1)

Correspondingly, N * N three banded circular matrix C can be expressed as:

$C=\mathrm{toeplitz}(\hat{c},\hat{c})=\mathrm{toeplitz}\left\{\right[c_0,c_1,c_2,0,\&CenterDot;\&CenterDot;\&CenterDot;,0,c_2,c_1],[c_0,c_1,c_2,0,\&CenterDot;\&CenterDot;\&CenterDot;0,c_2,c_1\left]\right\}---\left(2\right)$

Wherein,

Expression is by vector

The symmetry Toeplitz matrix that forms.

(2) obtain actual steering vector under the mutual coupling error condition.

Mutual coupling has changed desirable array steering vector, and this moment, the actual steering vector of array was

a(θ，c)＝Ca(θ)＝T[a(θ)]c (3)

Wherein, c=[c ₀, c ₁..., c _Q-1] ^T, N * q rank matrix T [a (θ)] can be expressed as:

T＝T ₁+T ₂+T ₃+T ₄ (4)

${\left[T_1\right]}_{i,j}=\left\{\begin{array}{cc}{a}_{i+j-1}& i+j\&le;N+1\\ 0& \mathrm{otherwise}\end{array}\right.---\left(5\right)$

${\left[T_2\right]}_{i,j}=\left\{\begin{array}{cc}{a}_{i-j+1}& i\&GreaterEqual;j\&GreaterEqual;2\\ 0& \mathrm{otherwise}\end{array}\right.---\left(6\right)$

${\left[T_3\right]}_{i,j}=\left\{\begin{array}{cc}{a}_{N+1+i-j}& i<j\&le;p\\ 0& \mathrm{otherwise}\end{array}\right.---\left(7\right)$

${\left[T_4\right]}_{i,j}=\left\{\begin{array}{cc}{a}_{i+j-N-1}& 2\&le;j\&le;p,i+j\&GreaterEqual;N+2\\ 0& \mathrm{otherwise}\end{array}\right.---\left(8\right)$

Wherein, when array number N is even number, p=N/2; When N is odd number, p=(N+1)/2.

(3) utilize cost function of subspace principles of construction.

Have by the subspace principle:

$a^H(\mathrm{\&theta;},c)E_N{E}_N^{H}a(\mathrm{\&theta;},c)=0---\left(9\right)$

With formula (3) substitution formula (9), the cost function that can be constructed as follows:

$c^H{T}^H\left[a\left(\mathrm{\&theta;}\right)\right]E_N{E}_N^{H}T\left[a\left(\mathrm{\&theta;}\right)\right]c=c^{H}Q\left(\mathrm{\&theta;}\right)c=0---\left(10\right)$

In the formula, E _NBe noise subspace, q * q rank matrix Q (θ) are defined as

$Q\left(\mathrm{\&theta;}\right)=T^H\left[a\left(\mathrm{\&theta;}\right)\right]E_N{E}_N^{H}T\left[a\left(\mathrm{\&theta;}\right)\right]---\left(11\right)$

By formula (11) as can be seen, Q (θ) is independent of mutual coupling parameter vector c.Because the The mutual coupling coefficient vector is not 0 entirely, i.e. c ≠ 0, so have only when matrix Q (θ) contraction (for singular matrix), formula (11) could be set up.When q≤N-M, Q (θ) is q * q non-singular matrix usually, has only the win the confidence true bearing { θ in source as θ _i} _I=1 ^MThe time, matrix Q (θ) contraction becomes singular matrix.

Above-mentioned procedure declaration the banded cycle characteristics and the symmetry Toeplitz of uniform circular array mutual coupling matrix help us that " decoupling " carried out in information source orientation and array element mutual coupling, thereby realize both estimations of uniting, Here it is principle of the present invention place.

(4) utilize the cost function of above-mentioned structure to carry out the calculating of azimuthal estimation and mutual coupling error.Wherein, utilize following formula to carry out DOA estimation:

$f_1\left(\mathrm{\&theta;}\right)=\frac{1}{\det \left\{\tilde{Q}\left(\mathrm{\&theta;}\right)\right\}}$ Or $f_2\left(\mathrm{\&theta;}\right)=\frac{1}{{\mathrm{\&lambda;}}_{\min }\left\{\tilde{Q}\left(\mathrm{\&theta;}\right)\right\}}---\left(12\right)$

Utilize following formula to find the solution sensor position uncertainties:

$c=e_{\min }\left\{\tilde{Q}\left(\mathrm{\&theta;}\right)\right\}$ Or $c=\frac{{\tilde{Q}}^{+}\left(\mathrm{\&theta;}\right)w}{w^T{\tilde{Q}}^{+}\left(\mathrm{\&theta;}\right)w}---\left(13\right)$

Wherein, λ _Min{ g} represents to ask the minimal eigenvalue of matrix, e _MinG} represents to ask matrix minimal eigenvalue characteristic of correspondence vector, and w=[1,0 ..., 0] ^T,

Be matrix

Generalized inverse matrix.

Below in conjunction with accompanying drawing array mutual coupling calibration and the source direction estimation method that the present invention realizes uniform circular array is described in further detail.

Fig. 1 is the graph of a relation of uniform circular array, information source and incident angle in the specific embodiment of the invention.This embodiment is the uniform circular array of 8 array elements, and circle battle array radius is 0.6 times a incident wavelength; Relation between uniform circular array, information source and the incident angle as shown in the figure.

Fig. 2 realizes the process flowchart of uniform circular array array mutual coupling calibration and source direction estimation for the present invention.As shown in the figure, the present invention realizes the method for uniform circular array array mutual coupling calibration and source direction estimation, may further comprise the steps:

1, gathers the data that each passage receives, and be stored in the Installed System Memory.

In data acquisition, it should be noted that: the fast umber of beats L of each receiving cable is conditional, and is excessive if L gets, follow-up DOA is estimated it is favourable, but this will cause the distance range of sampled data too big; If it is too small that L gets, the statistical property that then receives data is easily affected by noise, and this will cause follow-up DOA estimated performance seriously to descend.For the performance loss that causes by not satisfying condition is limited in the 3dB, require L to get and be no less than 2～3 times degree of freedom in system.

2, the data that each passage is received are done the adaptive equalization processing.

This mainly is for the array amplitude phase error of proofreading and correct each passage and orientation-independent and the inconsistent problem of frequency band.What adopt here is conventional adaptive equalization technique---i.e. 32 grades FIR wave filter.

3, will generate the array covariance matrix through the data after the adaptive equalization processing, and covariance matrix will be carried out feature decomposition, obtain the noise subspace E that forms by little proper vector _N

The formula that generates the array covariance matrix is as follows:

$R=\frac{1}{L}\underset{i=1}{\overset{L}{\mathrm{\&Sigma;}}}{V}_i{V_i}^H$

In the formula, vector sample V _i(i=1,2 ..., L) represent the reception data vector of each array element synchronization.And covariance matrix carried out feature decomposition, obtain the noise subspace E that forms by little proper vector _N

Array covariance matrix R is carried out feature decomposition to be got:

$R=\underset{i=1}{\overset{M}{\mathrm{\&Sigma;}}}{\mathrm{\&lambda;}}_i{e}_i{e_i}^H+\underset{i=M+1}{\overset{N}{\mathrm{\&Sigma;}}}{\mathrm{\&lambda;}}_i{e}_i{e_i}^H$

Wherein, λ _i, e _iBe respectively eigenwert and the characteristic of correspondence vector thereof of matrix R.Can find that the eigenwert of R has following distribution:

λ ₁≥λ ₂≥L≥λ _M≥λ _M+1＝λ _M+2＝L＝λ _N

The matrix E that constitutes by little proper vector _N=[e _M+1, e _M+2, L, e _N] linear subspaces that generated are called noise subspace.

4, utilize cost function of subspace principles of construction:

$Q\left(\mathrm{\&theta;}\right)=T^H\left[a\left(\mathrm{\&theta;}\right)\right]E_N{E}_N^{H}T\left[a\left(\mathrm{\&theta;}\right)\right]$

In the formula, T[a (θ)] see formula (4)-(8) with the relation of true array steering vector a (θ).

5, utilize the cost function of above-mentioned structure to carry out the calculating of azimuthal estimation and mutual coupling error, realize the array mutual coupling calibration and the source direction estimation of uniform circular array.

Wherein, utilize following formula to carry out azimuthal estimation: $f_1\left(\mathrm{\&theta;}\right)=\frac{1}{\det \left\{\tilde{Q}\left(\mathrm{\&theta;}\right)\right\}}$ Or $f_2\left(\mathrm{\&theta;}\right)=\frac{1}{{\mathrm{\&lambda;}}_{\min }\left\{\tilde{Q}\left(\mathrm{\&theta;}\right)\right\}}$

Utilize following formula to find the solution array element mutual coupling error: $c=e_{\min }\left\{\tilde{Q}\left(\mathrm{\&theta;}\right)\right\}$ Or $c=\frac{{\tilde{Q}}^{+}\left(\mathrm{\&theta;}\right)w}{w^T{\tilde{Q}}^{+}\left(\mathrm{\&theta;}\right)w}$

Wherein, λ _Min{ g} represents to ask the minimal eigenvalue of matrix, e _MinG} represents to ask matrix minimal eigenvalue characteristic of correspondence vector, and w=[1,0 ..., 0] ^T, Be matrix

Generalized inverse matrix.

6, utilize the mutual coupling error that obtains that the array steering vector of uniform circular array is proofreaied and correct.

Utilize following formula to proofread and correct:

a(θ，c)＝Ca(θ)＝T[a(θ)]c

Purpose of the present invention can also reach by following technical measures:

(1) mutual coupling is carried out electromagnetic measurement or by method of moment electromagnetism calculating carried out in mutual coupling.

(2) by being set in the space, the accurate known auxiliary information source in orientation comes the array mutual coupling parameter is carried out the off-line estimation.This type of active correction algorithm has the little advantage of operand, but this class algorithm has higher accuracy requirement to the orientation of auxiliary information source, and because the time-varying characteristics of systematic parameter and signal, and the multipath effect of spacing wave, this type of correcting algorithm is difficult to satisfy actual needs.

The present invention compared with prior art has the following advantages:

(1) the present invention takes into full account the practical application environment that spatial spectrum is estimated, both avoid whole arrays to carry out a large amount of man power and materials that array manifold is measured, avoided again the macrooperation amount of parameter class error algorithm, so equipment required for the present invention is simple, with low cost, upgrading is convenient.

(2) the present invention can realize the array mutual coupling and azimuthally unite estimation, and it is littler to unite the amount of calculation of estimation, and the engineering implementation complexity is low, and realizability is strong.

(3) DOA of algorithm estimate and the mutual coupling self-correcting based on equal nicely rounded battle array data models, China is had important practical significance based on the smart antenna wireless location technology of TD-SCDMA standard.

Claims (4)

1. an array mutual coupling calibration and source direction estimation method that is applicable to uniform circular array, it is characterized in that: this method utilizes array signal process technique simultaneously array mutual coupling error and information source incident direction to be estimated that it may further comprise the steps:

(1), gather the data that each passage receives, and be stored in the Installed System Memory;

(2), data that each passage is received make adaptive equalization and handle, and its objective is the array amplitude phase error of proofreading and correct with orientation-independent;

(3), the data after will handling through adaptive equalization generate the array covariance matrix, and covariance matrix are carried out feature decomposition, obtain the noise subspace E that is made up of little proper vector _N

(4), utilize cost function of subspace principles of construction:

$Q\left(\mathrm{\&theta;}\right)=T^H\left[a\left(\mathrm{\&theta;}\right)\right]E_N{E}_N^{H}T\left[a\left(\mathrm{\&theta;}\right)\right]$

(5), utilize the cost function of above-mentioned structure to carry out the calculating of azimuthal estimation and mutual coupling error, realize the array mutual coupling calibration and the source direction estimation of uniform circular array;

Wherein, utilize following formula to carry out azimuthal estimation:

$f_1\left(\mathrm{\&theta;}\right)=\frac{1}{\det \left\{\tilde{Q}\left(\mathrm{\&theta;}\right)\right\}}$ Or $f_2\left(\mathrm{\&theta;}\right)=\frac{1}{{\mathrm{\&lambda;}}_{\min }\left\{\tilde{Q}\left(\mathrm{\&theta;}\right)\right\}}$

Utilize following formula to find the solution array element mutual coupling error:

$c=e_{\min }\left\{\tilde{Q}\left(\mathrm{\&theta;}\right)\right\}$ Or $c=\frac{{\tilde{Q}}^{+}\left(\mathrm{\&theta;}\right)w}{w^T{\tilde{Q}}^{+}\left(\mathrm{\&theta;}\right)w}$

Wherein, λ _Min{ g} represents to ask the minimal eigenvalue of matrix, e _MinG} represents to ask matrix minimal eigenvalue characteristic of correspondence vector, and w=[1,0 ..., 0] ^T,

Be matrix Generalized inverse matrix;

(6), utilize the mutual coupling error that obtains that the array steering vector of uniform circular array is proofreaied and correct;

Updating formula is:

a(θ，c)＝Ca(θ)＝T[a(θ)]c。

2. array mutual coupling calibration and the source direction estimation method that is applicable to uniform circular array according to claim 1 is characterized in that: described (4) step: utilize subspace principles of construction cost function $Q\left(\mathrm{\&theta;}\right)=T^H\left[a\left(\mathrm{\&theta;}\right)\right]E_N{E}_N^{H}T\left[a\left(\mathrm{\&theta;}\right)\right]$ Further may further comprise the steps:

(a), utilize the banded cycle characteristics and the symmetry Toeplitz of uniform circular array mutual coupling matrix, the mutual coupling error matrix of uniform circular array is expressed as N * N three banded circular matrixes;

If C represents the mutual coupling error matrix of uniform circular array, as if the mutual coupling effect of only considering between three adjacent array elements of the left and right sides, i.e. mutual coupling degree of freedom q=3, then the circulation vector of circular matrix C can be expressed as:

$\hat{c}=[c_0,c_1,c_2,0,\&CenterDot;\&CenterDot;\&CenterDot;,0,c_2,c_1],$ And 0＜| c ₂|＜| c ₁|＜c ₀=1 (1)

Correspondingly, N * N three banded circular matrix C can be expressed as:

$C=\mathrm{toeplitz}(\hat{c},\hat{c})=\mathrm{toeplitz}\left\{\right[c_0,c_1,c_2,0,\&CenterDot;\&CenterDot;\&CenterDot;,0,c_2,c_1],[c_0,c_1,c_2,0,\&CenterDot;\&CenterDot;\&CenterDot;,0,c_2,c_1\left]\right\}---\left(2\right)$

Wherein,

Expression is by vector

The symmetry Toeplitz matrix that forms;

(b), obtain actual steering vector under the mutual coupling error condition;

Mutual coupling has changed desirable array steering vector, and this moment, the actual steering vector of array was

a(θ，c)＝Ca(θ)＝T[a(θ)]c (3)

Wherein, c=[c ₀, c ₁..., c _Q-1] ^T, N * q rank matrix T [a (θ)] can be expressed as:

T＝T ₁+T ₂+T ₃+T ₄ (4)

${\left[T_1\right]}_{i,j}=\left\{\begin{array}{cc}{a}_{i+j-1}& i+j\&le;N+1\\ 0& \mathrm{otherwise}\end{array}\right.---\left(5\right)$

${\left[T_2\right]}_{i,j}=\left\{\begin{array}{cc}{a}_{i-j+1}& i\&GreaterEqual;j\&GreaterEqual;2\\ 0& \mathrm{otherwise}\end{array}\right.---\left(6\right)$

${\left[T_3\right]}_{i,j}=\left\{\begin{array}{cc}{a}_{N+1+i-j}& i<j\&le;p\\ 0& \mathrm{otherwise}\end{array}\right.---\left(7\right)$

${\left[T_4\right]}_{i,j}=\left\{\begin{array}{cc}{a}_{i+j-N-1}& 2\&le;j\&le;p,i+j\&GreaterEqual;N+2\\ 0& \mathrm{otherwise}\end{array}\right.---\left(8\right)$

Wherein, when array number N is even number, p=N/2; When N is odd number, p=(N+1)/2;

(c), utilize cost function of subspace principles of construction.

Have by the subspace principle:

$a^H(\mathrm{\&theta;},c)E_N{E}_N^{H}a(\mathrm{\&theta;},c)=0---\left(9\right)$

With formula (3) substitution formula (9), the cost function that can be constructed as follows:

$c^H{T}^H\left[a\left(\mathrm{\&theta;}\right)\right]E_N{E}_N^{H}T\left[a\left(\mathrm{\&theta;}\right)\right]c=c^{H}Q\left(\mathrm{\&theta;}\right)c=0---\left(10\right)$

In the formula, E _NBe noise subspace, q * q rank matrix Q (θ) are defined as

$Q\left(\mathrm{\&theta;}\right)=T^H\left[a\left(\mathrm{\&theta;}\right)\right]E_N{E}_N^{H}T\left[a\left(\mathrm{\&theta;}\right)\right]---\left(11\right)$

By formula (11) as can be seen, Q (θ) is independent of mutual coupling parameter vector c.

3. array mutual coupling calibration and the source direction estimation method that is applicable to uniform circular array according to claim 2 is characterized in that: described (3) step: the formula that the data after will handling through adaptive equalization generate the array covariance matrix is:

$R=\frac{1}{L}\underset{i=1}{\overset{L}{\mathrm{\&Sigma;}}}{V}_i{V}_i^H$

In the formula, vector sample Vi (i=1,2 ..., L) represent the reception data vector of each array element synchronization.

4. array mutual coupling calibration and the source direction estimation method that is applicable to uniform circular array according to claim 3 is characterized in that: described (3) step: utilize little proper vector to form noise subspace E _NMethod be:

Array covariance matrix R is carried out feature decomposition to be got:

$R=\underset{i=1}{\overset{M}{\mathrm{\&Sigma;}}}{\mathrm{\&lambda;}}_i{e}_i{e}_i^H+\underset{i=M+1}{\overset{N}{\mathrm{\&Sigma;}}}{\mathrm{\&lambda;}}_i{e}_i{e}_i^H$

Wherein, λ _i, e _iBe respectively eigenwert and the characteristic of correspondence vector thereof of matrix R.Can find that the eigenwert of R has following distribution:

λ ₁≥λ ₂≥L≥λ _M≥λ _M+1＝λ _M+2＝L＝λ _N

The matrix E that constitutes by little proper vector _N=[e _M+1, e _M+2..., e _N] linear subspaces that generated are called noise subspace.

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