CN103944624A - Sound beam forming method based on iterative algorithm - Google Patents

Abstract

The invention relates to the technology of sound and self-adaptive beam forming processing. A sound beam forming method based on the iterative algorithm is provided for solving the mismatching problem of array guiding vectors on the background of highly desired signals in the prior art. The sound beam forming method comprises the first step of working out the weight of the PI algorithm through a PI spectrum, the second step of reconstructing an interference noise covariance matrix out of the possible empty domain range of the desired signals according to the PI spectrum and the PI algorithm, and the last step of calculating the optimal weight of a beam forming device according to the reconstructed interference noise covariance matrix and repeatedly executing the PI algorithm, and the optimal weight vector of the beam forming device is updated. The interference noise covariance matrix is reconstructed based on the LMS iteration power inversion algorithm, and accordingly the matrix inverse operation in the traditional algorithm is directly avoided.

Description

Based on the sane Beamforming Method of iterative algorithm

Technical field

The present invention relates to robust adaptive beamforming treatment technology, particularly the sane Beamforming Method based on iterative algorithm

Background technology

One of topmost research contents of Array Signal Processing is exactly beam-forming technology, can be divided into common beam-forming technology and adaptive beam formation technology with this.Utilize beam-forming technology, can strengthen useful signal and suppress to disturb simultaneously.The weight coefficient of common beam-forming technology is fixed, and anti-interference is poor.And adaptive beam formation is equivalent to one dimension nanofiltration wave process, can be along with the signal environment changing regulates weight coefficient automatically, make wave beam main lobe aim at desired signal direction to strengthen useful signal, zero falls into aligning interference radiating way to suppress interference, it is maximum that thereby the output signal interference-to-noise ratio SINR that makes array reaches, the performance that can effectively improve system, is therefore widely used.

Adaptive beam former can be adjusted weight coefficient automatically along with the signal environment changing, make wave beam main lobe aim at desired signal direction of arrival, interference radiating way forms zero and falls into, and strengthens to reach the object that useful signal suppresses interference, makes to export Signal to Interference plus Noise Ratio and reaches maximum.But owing to inevitably there being various errors, as array element response error, channel frequence response error, element position agitation error, mutual coupling etc., and adaptive beam forms technology to comparatively sensitivity of these factors, especially utilize signal to add the adaptive approach of interference and noise covariance matrix, in the time that signal to noise ratio is larger, although it is little to disturb dead-center position to change, in desired signal direction, also may form zero and fall into, cause exporting Signal to Interference plus Noise Ratio degradation.Therefore sane beam-forming technology becomes major issue theoretical and that engineering circles is concerned about.

In recent ten years, sane wave beam forms theory and has obtained development at full speed, emerge the algorithm of large quantities of function admirables, the sane beamforming algorithm that these algorithms have diagonal angle to load, based on the sane beamforming algorithm of feature space, and a lot of scholars are incorporated into protruding optimum theory and method in sane beamforming algorithm, set up wave beam formation model under mismatch model, the optimum Beamforming Method of having derived under various mismatch models.1969, J.Capon has proposed famous Capon wave beam and has formed, and meeting in the undistorted situation of signal, minimizes power output that is:, conventionally real covariance matrix the unknown, the consistent valuation amount sample covariance matrix of conventional real covariance matrix replaces.In the time that the array steering vector of useful signal accurately obtains, Capon wave beam forms has good resolution and interference rejection capability, but in the time that the array steering vector of useful signal can not accurately obtain, the decline that the performance that Capon wave beam forms can be serious.In order to overcome array steering vector error, can adopt multi-point constraint, derivative constraints or integral constraint, carry out broadening adaptive beam main lobe by additional constraint, reduce the sensitiveness to desired signal error in pointing, thereby improve robustness, but shortcoming is the degree of freedom that system has been wasted in extra constraint, reduces the ability that system interference suppresses, and the mismatch of other types has not been had to good robustness.

But said method all can not solve the problem of steering vector mismatch under strong desired signal background: in the time containing desired signal in training sequence, when signal to noise ratio is larger and desired signal direction of arrival be inaccurate when known, in actual desired signal direction, can form zero and fall into, make to export SINR degradation.Therefore, the robust adaptive beamforming technology under strong desired signal background, becomes a new problem.In the time that the power of desired signal is brought up to a certain degree and when desired signal arrival bearing has error, the performance of existing Adaptive Anti-jamming nulling algorithm all can decline, even complete failure.

Summary of the invention

Technical problem to be solved by this invention, be exactly in prior art, the problem of array steering vector mismatch under strong desired signal background, a kind of sane Beamforming Method based on iterative algorithm is proposed, be inverted (Power Inversion by LMS iterative power, hereinafter to be referred as PI) algorithm, reconstruct interference noise covariance matrix, thus directly avoid the method for the matrix inversion operation in traditional algorithm.

The present invention solve the technical problem, and the technical scheme of employing is, based on the sane Beamforming Method of iterative algorithm, to comprise following step:

Step 1, use PI spectrum calculate the weights of PI algorithm;

Step 2, the weights reconstruct interference noise covariance matrix outside desired signal may spatial domain scope that utilizes PI spectrum and PI algorithm;

Step 3, utilize the interference noise covariance matrix of reconstruct, the optimum weights of calculating beamforming device, then repetitive cycling PI algorithm, thus upgrade the optimal weight vector of Beam-former.

Concrete, in described step 1, utilize LMS algorithm to carry out the weights of iterative computation PI algorithm, the weights of described PI algorithm, count w _pI;

w _PI=[w ₁,w ₂,…,w _M] ^T；

Wherein, M is array number, and T is for carrying out transposition calculating, w _mbe the PI algorithm weights of M array element.

Concrete, described step 2, comprises following step:

Step 21, calculate desired signal according to PI algorithm, go out the weight vector of PI algorithm according to desired signal iteration;

Step 22, according to the weight vector of PI algorithm, calculate PI spectrum estimated value;

Step 23, PI is composed to estimated value in the spatial domain of removing beyond the possible direction of desired signal, carry out integration, and then reconstruct interference noise covariance matrix.

Further, in described step 21, order: signal frequency vector, count a ₀:

a ₀=[1,0,…,0] ^T；

Order: n moment array signal vector, count x (n):

x(n)=[x ₁(n),x ₂(n),x ₃(n),…,x _M(n)] ^T；

By the weight vector constraints of PI algorithm, w ^ha ₀=1, the weights of the weight vector first via of known PI algorithm are always 1 and remain unchanged, i.e. w ₁=1;

Order: auxiliary weight vector, count w ' _pI(n):

w′ _PI(n)=[-w ₂,-w ₃,…,-w _M] ^T；

Order: auxiliary signal vector, count x ' (n):

x′(n)=[x ₂(n),x ₃(n),…,x _M(n)] ^T；

Output signal, count y (n):

$\begin{array}{c}y\left(n\right)=w_{\mathrm{PI}}^H\left(n\right)x\left(n\right)\\ =w_1{x}_1\left(n\right)-w_{\mathrm{PI}}^{\′H}\left(n\right)x^{\′}\left(n\right)\\ =x_1\left(n\right)-w_{\mathrm{PI}}^{\′H}\left(n\right)x^{\′}\left(n\right)\end{array};$

Wherein, the H transposition computing that represents to invert;

Regard first via signal as desired signal according to PI algorithm, described desired signal, counts d (n):

d(n)=x ₁(n)；

According to LMS iterative algorithm, can obtain following recursion public affairs:

$\left\{\begin{array}{c}{w}_{\mathrm{PI}}^{\′}(n+1)=w_{\mathrm{PI}}^{\′}\left(n\right)+{\mathrm{\μ}}_{\mathrm{PI}}{x}^{\′}\left(n\right)e^{*}\left(n\right)\\ \hat{d}(n+1)=w_{\mathrm{PI}}^{\′H}(n+1)x^{\′}(n+1)\\ e(n+1)=d(n+1)-\hat{d}(n+1)\end{array}\right.;$

Wherein, μ _pIfor PI spectrum step factor, e (n) is filter evaluated error, μ _pIx ' is e (n) ^*(n) represent it is the correction to auxiliary weight vector of n moment, for the desired signal estimated value in n+1 moment;

Obtain auxiliary weight vector w ' according to above-mentioned formula _pI(n), after value, just can obtain the PI algorithm weight vector w needing _pI(n).

Further, in described step 22, calculate PI algorithm weight vector w _pI(n), can be used for calculating required PI spectrum estimated value, be designated as

${\hat{P}}_{\mathrm{PI}}(n,\mathrm{\θ})=\frac{1}{d^H\left(\mathrm{\θ}\right)w_{\mathrm{PI}}\left(n\right)w_{\mathrm{PI}}^H\left(n\right)d\left(\mathrm{\θ}\right)};$

Wherein, θ is expressed as scanning angle, desired signal when d (θ) is θ for angle.

Further, in described step 23, use PI Estimation of Spatial Spectrum value, it is being removed to the possible direction of desired signal spatial domain in addition inside carry out integration, and then the interference noise covariance matrix R of reconstruct _in(n);

Order: the interference noise covariance matrix value of the reconstruct of moment n is ?

$\begin{array}{c}{\tilde{R}}_{\mathrm{in}}\left(n\right)=\underset{\stackrel{\‾}{\mathrm{\Θ}}}{\∫}{\hat{P}}_{\mathrm{PI}}(n,\mathrm{\θ})d\left(\mathrm{\θ}\right)d^H\left(\mathrm{\θ}\right)\mathrm{d\θ}\\ =\underset{\stackrel{\‾}{\mathrm{\Θ}}}{\∫}\frac{d\left(\mathrm{\θ}\right)d^H\left(\mathrm{\θ}\right)}{d^H\left(\mathrm{\θ}\right)w_{\mathrm{PI}}\left(n\right)w_{\mathrm{PI}}^H\left(n\right)d\left(\mathrm{\θ}\right)}\mathrm{d\θ}\end{array};$

Wherein, Θ be comprised desired signal the likely set of angle, the integral operation of carrying out according to scanning angle θ.

Concrete, described step 3 comprises following step:

Step 31, according to the undistorted response criteria of minimum power, set up optimization problem;

Step 32, calculate the weights of Beam-former according to optimization problem;

Step 33, draw the iterative formula of Beam-former optimal weight vector according to the renewal of Beam-former weights.

Further, described step 31, according to the undistorted response criteria of minimum power, the Beam-former weight vector in substitution n moment, counts w (n), and optimization problem is expressed as:

min?w(n) ^HR _in(n)w(n)

；

s.t.w(n) ^Ha(θ ₁)=1

Wherein, min represents to minimize, and s.t. represents extremum conditions, a (θ ₁) to be expressed as angle be θ ₁time signal frequency vector, and meet the constraints of weight vector.

Further, in described step 32, use Lagrange cost function, be designated as J ₁(w (n)):

J ₁(w(n))=w(n) ^HR _in(n)w(n)+λ(n)(w(n) ^Ha(θ ₁)-1)；

Wherein, λ (n) is Lagrange multiplier;

The method that Beam-former weight vector is adopted to gradient direction search, now Beam-former weight vector w (n) can be expressed as optimal weight vector w by optimal condition extreme value ₀(n), the iteration expression formula of Beam-former optimal weight vector is as follows:

$w_0(n+1)=w_0\left(n\right)-{\mathrm{\μ}}_w\▿J_1\left(w\left(n\right)\right);$

Wherein, μ _wfor step parameter, (w (n)) is Lagrange cost function J ₁the gradient of (w (n));

, gradient (w (n)) can be by the iteration expression formula of above formula to w (n) differentiate, and by the interference noise covariance matrix R of reconstruct _in(n) estimated value substitution:

${\▿J}_1\left(n\right)=2{\tilde{R}}_{\mathrm{in}}\left(n\right)w_0\left(n\right)+\mathrm{\λ}\left(n\right)a\left({\mathrm{\θ}}_1\right);$

Above formula is brought in Beam-former optimal weight vector iteration expression formula:

$w_0(n+1)=w_0\left(n\right)-{\mathrm{\μ}}_w(2{\tilde{R}}_{\mathrm{in}}\left(n\right)w_0\left(n\right)+\mathrm{\λ}\left(n\right)a\left({\mathrm{\θ}}_1\right));$

Due to, λ (n) can be updated in each iteration, because require at desired signal direction θ in MPDR algorithm ₁gain is 1, that is:

$w_0^H(n+1)a\left({\mathrm{\θ}}_1\right)=1;$

Above formula is brought in the iteration expression formula of Beam-former weight vector, can be upgraded the iterative formula of λ (n):

$\mathrm{\λ}\left(n\right)=\frac{1}{{\mathrm{\μ}}_w{a}^H\left({\mathrm{\θ}}_1\right)a\left({\mathrm{\θ}}_1\right)}(a^H\left({\mathrm{\θ}}_1\right)w_0\left(n\right)-1-2{\mathrm{\μ}}_w{a}^H\left({\mathrm{\θ}}_1\right){\tilde{R}}_{\mathrm{in}}\left(n\right)w_0\left(n\right));$

Finally, just can utilize the interference noise covariance matrix value of the n moment reconstruct having obtained carry out iterative computation and go out the optimal weight vector of Beam-former, concrete recurrence formula is as follows:

$\left\{\begin{array}{c}\mathrm{\λ}\left(n\right)=\frac{1}{{\mathrm{\μ}}_w{a}^H\left({\mathrm{\θ}}_1\right)a\left({\mathrm{\θ}}_1\right)}(a^H\left({\mathrm{\θ}}_1\right)w_0\left(n\right)-1-2{\mathrm{\μ}}_w{a}^H\left({\mathrm{\θ}}_1\right){\tilde{R}}_{\mathrm{in}}\left(n\right)w_0\left(n\right))\\ w_0(n+1)=w_0\left(n\right)-{\mathrm{\μ}}_w(2{\tilde{R}}_{\mathrm{in}}\left(n\right)w_0\left(n\right)+\mathrm{\λ}\left(n\right)a\left({\mathrm{\θ}}_1\right))\end{array}\right.;$

Now, by two step iterative process, just can save matrix inversion operation, directly obtain the optimal weight vector of Beam-former.

The invention has the beneficial effects as follows, by using PI(PI, Power Inversion) estimated value of spectrum replaces Capon spatial spectrum, and the weight w of PI algorithm _pIcan solve by LMS iterative algorithm, so just reduce inversion operation one time.At finding the inverse matrix time, adopt based on matrix lMS algorithm replace direct inversion operation to solve the weights of Beam-former, so avoided RAB-Rec(to rebuild the sane beamforming algorithm of interference noise covariance matrix completely) in inversion operation, the algorithm based on data block is improved for the iterative algorithm based on data simultaneously.

Embodiment

Describe technical scheme of the present invention in detail below in conjunction with embodiment:

The present invention is directed in prior art, under strong desired signal background, the problem of array steering vector mismatch, proposes a kind of sane Beamforming Method based on iterative algorithm, first, uses PI spectrum to calculate the weights of PI algorithm; Secondly, utilize weights reconstruct interference noise covariance matrix outside the scope of desired signal possibility spatial domain of PI spectrum and PI algorithm; Finally, utilize the interference noise covariance matrix of reconstruct, the optimum weights of calculating beamforming device, then repetitive cycling PI algorithm, thus upgrade the optimal weight vector of Beam-former.By replacing Capon spatial spectrum by the estimated value of PI spectrum, and the weight w of PI algorithm _pIcan solve by LMS iterative algorithm, so just reduce inversion operation one time.At finding the inverse matrix time, adopt based on matrix lMS algorithm replace direct inversion operation to solve the weights of Beam-former, so just avoided the inversion operation in RAB-Rec completely, the algorithm based on data block is improved for the iterative algorithm based on data simultaneously.

Embodiment

The sane Beamforming Method based on iterative algorithm of this example, first, uses PI spectrum to calculate the weights of PI algorithm; Secondly, utilize PI spectrum and PI algorithm to obtain weights reconstruct interference noise covariance matrix outside the scope of desired signal possibility spatial domain; Finally, utilize the interference noise covariance matrix of the reconstruct of having tried to achieve, the optimum weights of calculating beamforming device, then repetitive cycling PI algorithm, thus upgrade the optimal weight vector of Beam-former.

Concrete, the weights of calculating PI algorithm, as described below:

First utilize LMS algorithm to carry out the weights of iterative computation PI algorithm, described PI algorithm obtains weights, counts w _pI;

w _PI=[w ₁,w ₂,…,w _M] ^T

Wherein, M is array number, and T is for carrying out transposition calculating, w _mbe the PI algorithm weights of M array element.

Then, calculate desired signal according to PI algorithm, according to desired signal, iteration goes out the weight vector of PI algorithm;

Wherein, because PI algorithm does not need desired signal direction, just simply order:

Signal frequency vector, counts a ₀,

a ₀=[1,0,…,0] ^T；

Order: n moment array signal vector, count x (n),

x(n)=[x ₁(n),x ₂(n),x ₃(n),…,x _M(n)] ^T；

By the weight vector constraints of PI algorithm, w ^ha ₀=1, the weights of the weight vector first via of known PI algorithm are always 1 and remain unchanged, i.e. w ₁=1;

Order: auxiliary weight vector, count w ' _pI(n):

w′ _PI(n)=[-w ₂,-w ₃,…,-w _M] ^T；

Order: auxiliary signal vector, count x ' (n):

x′(n)=[x ₂(n),x ₃(n),…,x _M(n)] ^T；

Output signal, count y (n):

$\begin{array}{c}y\left(n\right)=w_{\mathrm{PI}}^H\left(n\right)x\left(n\right)\\ =w_1{x}_1\left(n\right)-w_{\mathrm{PI}}^{\′H}\left(n\right)x^{\′}\left(n\right)\\ =x_1\left(n\right)-w_{\mathrm{PI}}^{\′H}\left(n\right)x^{\′}\left(n\right)\end{array};$

Wherein, the H transposition computing that represents to invert;

Regard first via signal as desired signal according to PI algorithm, described desired signal, counts d (n):

d(n)=x ₁(n)；

According to LMS iterative algorithm, and then can obtain following recurrence formula:

$\left\{\begin{array}{c}{w}_{\mathrm{PI}}^{\′}(n+1)=w_{\mathrm{PI}}^{\′}\left(n\right)+{\mathrm{\μ}}_{\mathrm{PI}}{x}^{\′}\left(n\right)e^{*}\left(n\right)\\ \hat{d}(n+1)=w_{\mathrm{PI}}^{\′H}(n+1)x^{\′}(n+1)\\ e(n+1)=d(n+1)-\hat{d}(n+1)\end{array}\right.;$

Wherein, μ _pIfor PI spectrum step factor, e (n) is filter evaluated error, μ _pIx ' is e (n) ^*(n) represent it is the correction to auxiliary weight vector of n moment, for the desired signal estimated value in n+1 moment;

Obtain auxiliary weight vector w ' according to above-mentioned formula _pI(n), after value, just can obtain the PI algorithm weight vector w needing _pI(n).

In the time utilizing LMS algorithm to ask PI algorithm weights, only be that with the difference of general LMS algorithm PI algorithm regards the signal of the array first via as desired signal, other solution procedurees and LMS algorithm are as good as, therefore for the convergence of the LMS iteration of PI algorithm, can be directly with reference to the constringent conclusion of LMS algorithm weight vector, as step factor μ _pImeet:

$0<{\mathrm{\&mu;}}_{\mathrm{PI}}<\frac{2}{{\mathrm{\&lambda;}}_{\max }}$

Wherein, λ _maxto receive signal correlation matrix eigenvalue of maximum, now the average of weight vector levels off to optimal weight vector $\underset{n\&RightArrow;\&infin;}{\mathrm{limE}}\left\{w_{\mathrm{PI}}\left(n\right)\right\}=w_{\mathrm{PI}\_\mathrm{opt}}.$

Concrete, utilize the reconstruct of PI spectrum not containing the interference noise covariance matrix of desired signal components, as described below:

According to the weight vector of PI algorithm, calculate PI spectrum estimated value.

Concrete, above-mentioned calculate PI algorithm weight vector w _pI(n), can be used for calculating required PI spectrum estimated value, be designated as

${\hat{P}}_{\mathrm{PI}}(n,\mathrm{\&theta;})=\frac{1}{d^H\left(\mathrm{\&theta;}\right)w_{\mathrm{PI}}\left(n\right)w_{\mathrm{PI}}^H\left(n\right)d\left(\mathrm{\&theta;}\right)};$

Wherein, θ is expressed as scanning angle, desired signal when d (θ) is θ for angle.

Re-use PI Estimation of Spatial Spectrum value, it is being removed to the possible direction of desired signal spatial domain in addition inside carry out integration, and then the interference noise covariance matrix R of reconstruct _in(n);

Order: the interference noise covariance matrix value of the reconstruct of moment n is ?

$\begin{array}{c}{\tilde{R}}_{\mathrm{in}}\left(n\right)=\underset{\stackrel{\&OverBar;}{\mathrm{\&Theta;}}}{\&Integral;}{\hat{P}}_{\mathrm{PI}}(n,\mathrm{\&theta;})d\left(\mathrm{\&theta;}\right)d^H\left(\mathrm{\&theta;}\right)\mathrm{d\&theta;}\\ =\underset{\stackrel{\&OverBar;}{\mathrm{\&Theta;}}}{\&Integral;}\frac{d\left(\mathrm{\&theta;}\right)d^H\left(\mathrm{\&theta;}\right)}{d^H\left(\mathrm{\&theta;}\right)w_{\mathrm{PI}}\left(n\right)w_{\mathrm{PI}}^H\left(n\right)d\left(\mathrm{\&theta;}\right)}\mathrm{d\&theta;}\end{array};$

Wherein, Θ be comprised desired signal the likely set of angle, the integral operation of carrying out according to scanning angle θ.

Concrete, the interference noise covariance matrix of the reconstruct that utilization has been tried to achieve, the optimum weights of calculating beamforming device, then repetitive cycling PI algorithm, thus the optimal weight vector of renewal Beam-former is as described below:

Obtain the interference noise covariance matrix in n moment after, adopt a kind of based on matrix the LMS algorithm upgrading replaces direct matrix in verse to solve the weight vector of Beam-former.

According to the undistorted response of minimum power (MPDR, Minimum Power Distortionless Response) criterion, optimization problem is expressed as

min?w(n) ^HR _in(n)w(n)

；

s.t.w(n) ^Ha(θ ₁)=1

Wherein, min represents to minimize, and s.t. represents extremum conditions, a (θ ₁) to be expressed as angle be θ ₁time signal frequency vector, and meet the constraints of weight vector.

Re-use Lagrange cost function, be designated as J ₁(w (n)):

J ₁(w(n))=w(n) ^HR _in(n)w(n)+λ(n)(w(n) ^Ha(θ ₁)-1)；

Wherein, λ (n) is Lagrange multiplier;

The method that Beam-former weight vector is adopted to gradient direction search, now Beam-former weight vector w (n) can be expressed as optimal weight vector w by optimal condition extreme value ₀(n), the iteration expression formula of Beam-former optimal weight vector is as follows

$w_0(n+1)=w_0\left(n\right)-{\mathrm{\&mu;}}_w\&dtri;J_1\left(w\left(n\right)\right);$

Wherein, μ _wfor step parameter, (w (n)) is Lagrange cost function J ₁the gradient of (w (n));

, gradient (w (n)) can be by the iteration expression formula of above formula to w (n) differentiate, and by the interference noise covariance matrix R of reconstruct _in(n) estimated value substitution:

${\&dtri;J}_1\left(n\right)=2{\tilde{R}}_{\mathrm{in}}\left(n\right)w_0\left(n\right)+\mathrm{\&lambda;}\left(n\right)a\left({\mathrm{\&theta;}}_1\right);$

Above formula is brought in Beam-former optimal weight vector iteration expression formula:

$w_0(n+1)=w_0\left(n\right)-{\mathrm{\&mu;}}_w(2{\tilde{R}}_{\mathrm{in}}\left(n\right)w_0\left(n\right)+\mathrm{\&lambda;}\left(n\right)a\left({\mathrm{\&theta;}}_1\right));$

Due to, λ (n) can be updated in each iteration, because require at desired signal direction θ in MPDR algorithm ₁gain is 1, that is:

$w_0^H(n+1)a\left({\mathrm{\&theta;}}_1\right)=1;$

Above formula is brought in the iteration expression formula of Beam-former weight vector, can be upgraded the iterative formula of λ (n):

$\mathrm{\&lambda;}\left(n\right)=\frac{1}{{\mathrm{\&mu;}}_w{a}^H\left({\mathrm{\&theta;}}_1\right)a\left({\mathrm{\&theta;}}_1\right)}(a^H\left({\mathrm{\&theta;}}_1\right)w_0\left(n\right)-1-2{\mathrm{\&mu;}}_w{a}^H\left({\mathrm{\&theta;}}_1\right){\tilde{R}}_{\mathrm{in}}\left(n\right)w_0\left(n\right));$

Finally, just can utilize the interference noise covariance matrix value of the n moment reconstruct having obtained carry out iterative computation and go out the optimal weight vector of Beam-former, concrete recurrence formula is as follows:

$\left\{\begin{array}{c}\mathrm{\&lambda;}\left(n\right)=\frac{1}{{\mathrm{\&mu;}}_w{a}^H\left({\mathrm{\&theta;}}_1\right)a\left({\mathrm{\&theta;}}_1\right)}(a^H\left({\mathrm{\&theta;}}_1\right)w_0\left(n\right)-1-2{\mathrm{\&mu;}}_w{a}^H\left({\mathrm{\&theta;}}_1\right){\tilde{R}}_{\mathrm{in}}\left(n\right)w_0\left(n\right))\\ w_0(n+1)=w_0\left(n\right)-{\mathrm{\&mu;}}_w(2{\tilde{R}}_{\mathrm{in}}\left(n\right)w_0\left(n\right)+\mathrm{\&lambda;}\left(n\right)a\left({\mathrm{\&theta;}}_1\right))\end{array}\right.;$

Now, by two step iterative process, just can save matrix inversion operation, directly obtain the optimal weight vector of Beam-former.

Concrete, based on the LMS convergence problem of upgrading, as described below:

First, define vectorial e _w(n) be w ₀and w (n) _0optpoor:

e _w(n)=w ₀(n)-w _0opt；

The iteration expression formula both sides of weight vector are deducted to w simultaneously _0opt,

$\begin{array}{c}{e}_w(n+1)=e_w\left(n\right)-{\mathrm{\&mu;}}_w(2{\tilde{R}}_{\mathrm{in}}\left(n\right)w_0\left(n\right)+\mathrm{\&lambda;}\left(n\right)a\left({\mathrm{\&theta;}}_1\right))\\ =e_w\left(n\right)-{\mathrm{\&mu;}}_w(2{\tilde{R}}_{\mathrm{in}}\left(n\right)(e_w\left(n\right)+w_{0\mathrm{opt}})+\mathrm{\&lambda;}\left(n\right)a\left({\mathrm{\&theta;}}_1\right))\\ =[I-2{\mathrm{\&mu;}}_w{\tilde{R}}_{\mathrm{in}}\left(n\right)]e_w\left(n\right)-2{\mathrm{\&mu;}}_w{\tilde{R}}_{\mathrm{in}}\left(n\right)w_{0\mathrm{opt}}-{\mathrm{\&mu;}}_w\mathrm{\&lambda;}\left(n\right)a\left({\mathrm{\&theta;}}_1\right)\end{array};$

For optimum weight w _0opt, must meet that to make the gradient of cost function be zero,

$\&dtri;J_1\left(n\right)=2{\tilde{R}}_{\mathrm{in}}\left(n\right)w_{0\mathrm{opt}}+{\mathrm{\&lambda;}}_{\mathrm{opt}}a\left({\mathrm{\&theta;}}_1\right)=0;$

That is:

$w_{0\mathrm{opt}}=-\frac{{\mathrm{\&lambda;}}_{\mathrm{opt}}}{2}{\tilde{R}}_{\mathrm{in}}^{-1}\left(n\right)a\left({\mathrm{\&theta;}}_1\right);$

Bring above formula into error e _w(n), in, can obtain

$e_w(n+1)=[I-2{\mathrm{\&mu;}}_w{\tilde{R}}_{\mathrm{in}}\left(n\right)]e_w\left(n\right)-{\mathrm{\&mu;}}_w[\mathrm{\&lambda;}\left(n\right)-{\mathrm{\&lambda;}}_{\mathrm{opt}}]a\left({\mathrm{\&theta;}}_1\right);$

In above formula, there is uncertain factor and λ (n).And at w _pI(n) after convergence, also be tending towards a fixed matrix, be denoted as in the time that iteration is tending towards stable state, λ (n) is close to λ _opt, approximate λ (n) the ≈ λ that gets _optbe λ (n)-λ _opt> > 0, as n → ∞ time error e _w(n) have:

$\begin{array}{c}{e}_w(n+1)=[I-2{\mathrm{\&mu;}}_w{\tilde{R}}_{\mathrm{in}}\left(n\right)]{=e}_w\left(n\right)-{\mathrm{\&mu;}}_w[\mathrm{\&lambda;}\left(n\right)-{\mathrm{\&lambda;}}_{\mathrm{opt}}]a\left({\mathrm{\&theta;}}_1\right)\\ \&ap;[I-2{\mathrm{\&mu;}}_w{\tilde{R}}_{\mathrm{in}}]e_w\left(n\right)\end{array};$

Therefore, step factor μ _wspan have:

$0<{\mathrm{\&mu;}}_w<\frac{1}{{\widehat{\mathrm{\&lambda;}}}_{\max }};$

Wherein, for matrix eigenvalue of maximum, now the average of weight vector levels off to optimal weight vector $\underset{n\&RightArrow;\&infin;}{\mathrm{limE}}\left\{w_0\left(n\right)\right\}=w_{0\mathrm{opt}},$ Algorithm can be restrained.

The process of summing up iterative algorithm is as follows:

When step 1:n=0, initialization w _pI(0)=[1,0 ..., 0] ^tbe w ' _pI(0)=0, and w ₀(0)=0, chooses step factor μ _pIand μ _wvalue;

Step 2: get n=0,1,2 ... time:

I. calculate PI algorithm weights:

1) upgrade w ' _pI(n+1)=w ' _pI(n)+μ _pIx ' is e (n) ^*(n);

2) estimate $\hat{d}(n+1)=w_{\mathrm{PI}}^{\&prime;H}(n+1)x^{\&prime;}(n+1);$

3) estimate $e(n+1)=d(n+1)-\hat{d}(n+1);$

II. approach integration method by the method for the cumulative summation of formula, calculate the restructuring matrix in n moment

III. utilize the interference noise covariance matrix upgrading, the weight vector by LMS algorithm calculating beamforming device:

1) upgrade $\mathrm{\&lambda;}\left(n\right)=\frac{1}{{\mathrm{\&mu;}}_w{a}^H\left({\mathrm{\&theta;}}_1\right)a\left({\mathrm{\&theta;}}_1\right)}(a^H\left({\mathrm{\&theta;}}_1\right)w_0\left(n\right)-1-2{\mathrm{\&mu;}}_w{a}^H\left({\mathrm{\&theta;}}_1\right){\tilde{R}}_{\mathrm{in}}\left(n\right)w_0\left(n\right));$

2) calculate $w_0(n+1)=w_0\left(n\right)-{\mathrm{\&mu;}}_w(2{\tilde{R}}_{\mathrm{in}}\left(n\right)w_0\left(n\right)+\mathrm{\&lambda;}\left(n\right)a\left({\mathrm{\&theta;}}_1\right));$

In sum, the present invention is by replacing Capon spatial spectrum by the estimated value of PI spectrum, and the weight w of PI algorithm _pIcan solve by LMS iterative algorithm, so just reduce inversion operation one time.At finding the inverse matrix time, adopt based on matrix lMS algorithm replace direct inversion operation to solve the weights of Beam-former, so just avoided the inversion operation in RAB-Rec algorithm completely, the algorithm based on data block is improved for the iterative algorithm based on data simultaneously.

Claims (9)

1. the sane Beamforming Method based on iterative algorithm, is characterized in that, comprises following step:

Step 1, use PI spectrum calculate the weights of PI algorithm;

Step 2, the weights reconstruct interference noise covariance matrix outside desired signal may spatial domain scope that utilizes PI spectrum and PI algorithm;

Step 3, utilize the interference noise covariance matrix of reconstruct, the optimum weights of calculating beamforming device, then repetitive cycling PI algorithm, thus upgrade the optimal weight vector of Beam-former.

2. the sane Beamforming Method based on iterative algorithm according to claim 1, is characterized in that, in described step 1, utilizes LMS algorithm to carry out the weights of iterative computation PI algorithm, and the weights of described PI algorithm, count w _pI;

w _PI=[w ₁,w ₂,…,w _M] ^T；

Wherein, M is array number, and T is for carrying out transposition calculating, w _mbe the PI algorithm weights of M array element.

3. the sane Beamforming Method based on iterative algorithm according to claim 1, is characterized in that described step 2 comprises following step:

Step 21, calculate desired signal according to PI algorithm, go out the weight vector of PI algorithm according to desired signal iteration;

Step 22, according to the weight vector of PI algorithm, calculate PI spectrum estimated value;

Step 23, PI is composed to estimated value in the spatial domain of removing beyond the possible direction of desired signal, carry out integration, and then reconstruct interference noise covariance matrix.

4. the sane Beamforming Method based on iterative algorithm according to claim 3, is characterized in that, in described step 21, and order: signal frequency vector, count a ₀:

a ₀=[1,0,…,0] ^T；

Order: n moment array signal vector, count x (n):

x(n)=[x ₁(n),x ₂(n),x ₃(n),…,x _M(n)] ^T；

By the weight vector constraints of PI algorithm, w ^ha ₀=1, the weights of the weight vector first via of known PI algorithm are always 1 and remain unchanged, i.e. w ₁=1;

Order: auxiliary weight vector, count w ' _pI(n):

w′ _PI(n)=[-w ₂,-w ₃,…,-w _M] ^T；

Order: auxiliary signal vector, count x ' (n):

x′(n)=[x ₂(n),x ₃(n),…,x _M(n)] ^T；

Output signal, count y (n):

$\begin{array}{c}y\left(n\right)=w_{\mathrm{PI}}^H\left(n\right)x\left(n\right)\\ =w_1{x}_1\left(n\right)-w_{\mathrm{PI}}^{\&prime;H}\left(n\right)x^{\&prime;}\left(n\right)\\ =x_1\left(n\right)-w_{\mathrm{PI}}^{\&prime;H}\left(n\right)x^{\&prime;}\left(n\right)\end{array};$

Wherein, the H transposition computing that represents to invert;

Regard first via signal as desired signal according to PI algorithm, described desired signal, counts d (n):

d(n)=x ₁(n)；

According to LMS iterative algorithm, can obtain following recursion public affairs:

$\left\{\begin{array}{c}{w}_{\mathrm{PI}}^{\&prime;}(n+1)=w_{\mathrm{PI}}^{\&prime;}\left(n\right)+{\mathrm{\&mu;}}_{\mathrm{PI}}{x}^{\&prime;}\left(n\right)e^{*}\left(n\right)\\ \hat{d}(n+1)=w_{\mathrm{PI}}^{\&prime;H}(n+1)x^{\&prime;}(n+1)\\ e(n+1)=d(n+1)-\hat{d}(n+1)\end{array}\right.;$

Wherein, μ _pIfor PI spectrum step factor, e (n) is filter evaluated error, μ _pIx ' is e (n) ^*(n) represent it is the correction to auxiliary weight vector of n moment, for the desired signal estimated value in n+1 moment;

Obtain auxiliary weight vector w ' according to above-mentioned formula _pI(n), after value, just can obtain the PI algorithm weight vector w needing _pI(n).

5. the sane Beamforming Method based on iterative algorithm according to claim 3, is characterized in that, in described step 22, calculate PI algorithm weight vector w _pI(n), can be used for calculating required PI spectrum estimated value, be designated as

${\hat{P}}_{\mathrm{PI}}(n,\mathrm{\&theta;})=\frac{1}{d^H\left(\mathrm{\&theta;}\right)w_{\mathrm{PI}}\left(n\right)w_{\mathrm{PI}}^H\left(n\right)d\left(\mathrm{\&theta;}\right)};$

Wherein, θ is expressed as scanning angle, desired signal when d (θ) is θ for angle.

6. the sane Beamforming Method based on iterative algorithm according to claim 3, is characterized in that, in described step 23, uses PI Estimation of Spatial Spectrum value, and it is being removed to the possible direction of desired signal spatial domain in addition inside carry out integration, and then the interference noise covariance matrix R of reconstruct _in(n);

Order: the interference noise covariance matrix value of the reconstruct of moment n is ?

$\begin{array}{c}{\tilde{R}}_{\mathrm{in}}\left(n\right)=\underset{\stackrel{\&OverBar;}{\mathrm{\&Theta;}}}{\&Integral;}{\hat{P}}_{\mathrm{PI}}(n,\mathrm{\&theta;})d\left(\mathrm{\&theta;}\right)d^H\left(\mathrm{\&theta;}\right)\mathrm{d\&theta;}\\ =\underset{\stackrel{\&OverBar;}{\mathrm{\&Theta;}}}{\&Integral;}\frac{d\left(\mathrm{\&theta;}\right)d^H\left(\mathrm{\&theta;}\right)}{d^H\left(\mathrm{\&theta;}\right)w_{\mathrm{PI}}\left(n\right)w_{\mathrm{PI}}^H\left(n\right)d\left(\mathrm{\&theta;}\right)}\mathrm{d\&theta;}\end{array};$

Wherein, Θ be comprised desired signal the likely set of angle, the integral operation of carrying out according to scanning angle θ.

7. the sane Beamforming Method based on iterative algorithm according to claim 1, is characterized in that, described step 3 comprises following step:

Step 31, according to the undistorted response criteria of minimum power, set up optimization problem;

Step 32, calculate the weights of Beam-former according to optimization problem;

Step 33, draw the iterative formula of Beam-former optimal weight vector according to the renewal of Beam-former weights.

8. the sane Beamforming Method based on iterative algorithm according to claim 7, is characterized in that described step 31, according to the undistorted response criteria of minimum power, the Beam-former weight vector in substitution n moment, counts w (n), and optimization problem is expressed as:

min?w(n) ^HR _in(n)w(n)

；

s.t.w(n) ^Ha(θ ₁)=1

Wherein, min represents to minimize, and s.t. represents extremum conditions, a (θ ₁) to be expressed as angle be θ ₁time signal frequency vector, and meet the constraints of weight vector.

9. the sane Beamforming Method based on iterative algorithm according to claim 7, is characterized in that, in described step 32, uses Lagrange cost function, is designated as J ₁(w (n)):

J ₁(w(n))=w(n) ^HR _in(n)w(n)+λ(n)(w(n) ^Ha(θ ₁)-1)；

Wherein, λ (n) is Lagrange multiplier;

The method that Beam-former weight vector is adopted to gradient direction search, now Beam-former weight vector w (n) can be expressed as optimal weight vector w by optimal condition extreme value ₀(n), the iteration expression formula of Beam-former optimal weight vector is as follows:

$w_0(n+1)=w_0\left(n\right)-{\mathrm{\&mu;}}_w\&dtri;J_1\left(w\left(n\right)\right);$

Wherein, μ _wfor step parameter, (w (n)) is Lagrange cost function J ₁the gradient of (w (n));

, gradient (w (n)) can be by the iteration expression formula of above formula to w (n) differentiate, and by the interference noise covariance matrix R of reconstruct _in(n) estimated value substitution:

${\&dtri;J}_1\left(n\right)=2{\tilde{R}}_{\mathrm{in}}\left(n\right)w_0\left(n\right)+\mathrm{\&lambda;}\left(n\right)a\left({\mathrm{\&theta;}}_1\right);$

Above formula is brought in Beam-former optimal weight vector iteration expression formula:

$w_0(n+1)=w_0\left(n\right)-{\mathrm{\&mu;}}_w(2{\tilde{R}}_{\mathrm{in}}\left(n\right)w_0\left(n\right)+\mathrm{\&lambda;}\left(n\right)a\left({\mathrm{\&theta;}}_1\right));$

Due to, λ (n) can be updated in each iteration, because require at desired signal direction θ in MPDR algorithm ₁gain is 1, that is:

$w_0^H(n+1)a\left({\mathrm{\&theta;}}_1\right)=1;$

Above formula is brought in the iteration expression formula of Beam-former weight vector, can be upgraded the iterative formula of λ (n):

$\mathrm{\&lambda;}\left(n\right)=\frac{1}{{\mathrm{\&mu;}}_w{a}^H\left({\mathrm{\&theta;}}_1\right)a\left({\mathrm{\&theta;}}_1\right)}(a^H\left({\mathrm{\&theta;}}_1\right)w_0\left(n\right)-1-2{\mathrm{\&mu;}}_w{a}^H\left({\mathrm{\&theta;}}_1\right){\tilde{R}}_{\mathrm{in}}\left(n\right)w_0\left(n\right));$

Finally, just can utilize the interference noise covariance matrix value of the n moment reconstruct having obtained carry out iterative computation and go out the optimal weight vector of Beam-former, concrete recurrence formula is as follows:

$\left\{\begin{array}{c}\mathrm{\&lambda;}\left(n\right)=\frac{1}{{\mathrm{\&mu;}}_w{a}^H\left({\mathrm{\&theta;}}_1\right)a\left({\mathrm{\&theta;}}_1\right)}(a^H\left({\mathrm{\&theta;}}_1\right)w_0\left(n\right)-1-2{\mathrm{\&mu;}}_w{a}^H\left({\mathrm{\&theta;}}_1\right){\tilde{R}}_{\mathrm{in}}\left(n\right)w_0\left(n\right))\\ w_0(n+1)=w_0\left(n\right)-{\mathrm{\&mu;}}_w(2{\tilde{R}}_{\mathrm{in}}\left(n\right)w_0\left(n\right)+\mathrm{\&lambda;}\left(n\right)a\left({\mathrm{\&theta;}}_1\right))\end{array}\right.;$

Now, by two step iterative process, just can save matrix inversion operation, directly obtain the optimal weight vector of Beam-former.