CN106093920A - A kind of adaptive beam-forming algorithm loaded based on diagonal angle - Google Patents

Abstract

The invention discloses a kind of adaptive beam-forming algorithm loaded based on diagonal angle, relate to intelligent antenna technology field, the sampled signal first collected linear array reception array element seeks its sample covariance matrix, as the estimation of sample covariance matrix.Then utilize diagonal angle loading technique that sample covariance matrix is reconstructed so that it is to meet matrix inversion lemma formula, it is to avoid to carry out matrix inversion operation.Last in conjunction with least mean-square error (MSE) criterion, obtain the optimum solution of direction weight vector, use the sample covariance matrix of reconstruct to instead of interative computation, algorithmic statement time is greatly reduced.This algorithm the most effectively solves and optimizes self-adaptive numerical integration algorithm convergence of algorithm matter of time, and it is the most more stable to demonstrate this algorithm performance under high low signal-to-noise ratio environment by emulation experiment, the tender subject to model error can also be eliminated to a certain extent simultaneously.

Description

A kind of adaptive beam-forming algorithm loaded based on diagonal angle

Technical field

The present invention relates to intelligent antenna technology field, particularly relate to a kind of Adaptive beamformer loaded based on diagonal angle and calculate Method.

Background technology

Underwater acoustic imaging is mainly used in Underwater Target Detection and search, and water-bed landforms are drawn, Watership Down, rescue, Numerous military and civilian fields such as flight data recorder salvaging.Obtain in national defence and civil area and be widely applied.In order to realize one The high-resolution acoustic imaging purpose of submarine target under set a distance, is necessary for studying the stable imaging technique under complicated Underwater Acoustic Environment, and And to meet certain imaging frame rate and operating distance farther out simultaneously.This just requires the adaptive beam at research acoustic imaging During formation algorithm, not only it is also required to consider robustness problem, also to improve the output signal-to-noise ratio of system as far as possible, reduce adaptive simultaneously Answer the operand of beamforming algorithm.

Adaptive beamformer technology changes the directional diagram of array by adjusting weight vectors, makes beam main lobe to meeting the deadline Hope that signal, secondary lobe and zero fall into alignment interference signal, thus improve the Signal to Interference plus Noise Ratio of output, to realize most preferably connecing under certain criterion Receive.

LMS adaptive beam-forming algorithm is a kind of simple in construction, algorithm complex is low, it is high with stability to be easily achieved Beamforming Method.But always because its convergence rate is relatively slow, engineer applied is somewhat limited.To this end, it is each Scholar is in succession with different adjustable strategies: instantaneous error, the forward prediction of weight vector and smooth gradient vector etc., proposes to become step Long LMS algorithm balances convergence rate and algorithm imbalance.Although being better than classical LMS in terms of balance convergence rate and imbalance to calculate Method, but reply sudden change ability is poor.

As one of criterion judging optimum reception, mean square error (MSE) performance metric is proposed by Shandong, Vad et al..And by Wiener, Hopf derive the wiener solution of optimum.Classical LMS algorithm, just on the basis of MSE criterion, uses optimization method As: the interative computation such as steepest descent method, Speed gradient algorithm goes out optimal weight vector.

Based on the above, set forth herein a kind of robust adaptive wave beam shape based on MSE criterion and diagonal angle loading technique Become algorithm.In the algorithm, by being artificially injected white noise on sample covariance matrix diagonal, i.e. diagonal angle loads, reconstruct Sample covariance matrix.Then use matrix inversion lemma, it is to avoid matrix inversion operation and interative computation, and diagonal angle is loaded Coefficient is converted into the function of LMS algorithm step factor.Simulation result shows that this algorithm can not only effectively reduce convergence time, and Can all show preferable performance under high and low signal to noise ratio environment, have preferable robustness.

Summary of the invention

The shortcoming the slowest in convergence rate in order to improve existing Adaptive beamformer method, breaks through sample frequency limit System, it is thus achieved that weight direction vector more accurately, the first object of the present invention is to avoid circulation on the basis of LMS algorithm and MVDR Iteration and matrix inversion operation, shorten the algorithmic statement time so that it is can be applied in engineering well.The method can be Formed by reconstructed sample covariance matrix in adaptive beam, and application matrix inversion lemma on this basis, thus avoid Inversion operation and interative computation, have preferable pointing capability and an interference rejection capability.

The second object of the present invention is that the minor level caused for reducing various errors raises, main lobe is cheap, wave beam is abnormal Degradation problem under change, SINR, introduces diagonal angle loading technique in Adaptive beamformer, and gives the public affairs determining loading coefficient Formula.The method realizes simple, advantageously reduces the deviation in beam forming process, improves the accuracy of Wave beam forming with sane Property.

For achieving the above object, the present invention provides a kind of adaptive beam-forming algorithm loaded based on diagonal angle, described side Method comprises the steps of:

Step 1: considering the equidistant even linear array of plane space, if array number is M, array element distance is d, wherein d=λ/2 (λ The wavelength of signal is received for array received unit), it is assumed that there is L information source echo (M > L), if direction of arrival is θ₁,θ₂,...,θ_L, Using first array element of array as datum mark, then the sampled value at the sampled point m of kth time snap is:

$X_m\left(k\right)=\underset{i=1}{\overset{L}{\Σ}}{s}_i\left(k\right)\exp \[j\frac{2\mathrm{\π}}{\mathrm{\λ}}(m-1)d{\mathrm{sin\θ}}_i\]+n_m\left(k\right)---\left(1\right)$

N in formula_mK () represents the noise in m-th array element, s_iK () represents each information source echo baseband signal at datum mark. Step 2: each array element snap k reception to signal be respectively X₁(k),X₂(k),…,X_M(k), that is: X (k)=[X₁(k), X₂(k),...,X_M(k)]^T, this is array input vector.Obtaining covariance matrix value isIn formula, K represents the fast umber of beats of array antenna, and X (k) represents that on array antenna, kth time snap connects The signal that receives (k=1,2 ..., K), subscript H representing matrix conjugate transpose.

Step 3: in the time domain, array is output as

Y (t)=ω^TX(t) (2)

Reference signal d (t) with the error of real output signal is

ε (t)=d (t)-y (t)=d (t)-ω^TX(t) (3)

Obtain (3) formula is squared

ε²(t)=d²(t)-2d(t)ω^TX(t)+ω^TX(t)X^T(t)ω (4)

Above formula both sides are taken mathematic expectaion can obtain

$E\left\{{\mathrm{\ϵ}}^2\left(t\right)\right\}=\stackrel{\‾}{d^2\left(t\right)}-2{\mathrm{\ω}}^T{R}_{xd}+{\mathrm{\ω}}^T{R}_{xx}\mathrm{\ω}---\left(5\right)$

In formulaRepresent and d (t) is taken mathematic expectaion, cross-correlation matrix R_xdFor R_xd=E{d (k) X^T(k) }, orderThen

E{ε²(t) }=S-2 ω^TR_xd+ω^TR_xxω (6)

Suitably select weight vectors ω can make E{ ε²(t) } minimize.Understand the quadratic function that formula (6) is ω, this function Extreme value be a minima, formula (6) weight vectors asked gradient and to make it is zero, obtain and make E{ ε²(t) } minimum ω Value, obtains the optimal value of weight vectors and meets following formula:

${\mathrm{\ω}}_{opt}=R_{xx}^{-1}{R}_{xd}---\left(7\right)$

Step 4: in terms of beamforming algorithm, LMS algorithm is as normal step size LMS algorithm, the iterative formula of its weight vector Can be expressed as:

$\mathrm{\ω}(k+1)=\mathrm{\ω}\left(k\right)-\mathrm{\μ}\▿\left(n\right)---\left(8\right)$

In order to overcome the computings such as matrix inversion, LMS algorithm uses steepest descent method to solve formula (8), obtains changing of LMS algorithm For formula

ω (k+1)=ω (k)+μ X (k) e^*(k) (9)

In formula, μ is step factor, can control adaptive speed.By analyzing, the value model of μ step factor Enclose and meet relation:May certify that, when iterations infinitely increases, the expected value of weight vectors can converge to Wiener solution.

Step 5: in terms of strengthening the robustness of adaptive beam former, diagonal angle loading technique is used for suppressing directional diagram Distortion.On the basis of the signal model of this paper institute foundation, Practical Calculation sample covariance matrix R_xxIt is to be obtained by K sampled signal Estimated value

${\hat{R}}_{xx}=\frac{1}{K}\underset{k=1}{\overset{K}{\Σ}}x\left(k\right)x^H\left(k\right)---\left(10\right)$

Replaced, then

${\mathrm{\ω}}_{opt}={\hat{R}}_{xx}^{-1}{R}_{xd}---\left(11\right)$

Apply to diagonal angle loading technique, in the weight vector calculating of LMS algorithm, obtain

${\tilde{R}}_{xx}=(\mathrm{\α}I+{\hat{R}}_{xx})---\left(12\right)$

Lemma: order matrix A ∈ C^n×nInverse matrix exist, and x, y be two n × 1 dimensional vectors so that (A+xy^H) can Inverse, then

${(A+{\mathrm{xy}}^H)}^{-1}=A^{-1}-\frac{A^{-1}{\mathrm{xy}}^H{A}^{-1}}{1+y^H{A}^{-1}x}---\left(13\right)$

It is extended to matrix sum Inversion Formula, is:

(A+UBV)^-1=A^-1-A^-1UB(B+BVA^-1UB)^-1BVA^-1

=A^-1-A^-1U(I+BVA^-1U)^-1BVA^-1 (14)

Because sampling covarianceIt is Hermitian matrix, then can be derived by formula (11)

${\hat{R}}_{xx}={\mathrm{U\ΛU}}^H=\underset{i=1}{\overset{M}{\Σ}}{\mathrm{\γ}}_i{u}_i{u_i}^H---\left(15\right)$

In formula, U is characterized vector matrix, Λ=diag (γ₁,γ₂,...,γ_M), γ_iForEigenvalue.

Can derive according to above-mentioned matrix inversion formula

$\begin{array}{c}{\[\mathrm{\α}I+X\left(k\right){\mathrm{PX}}^H\left(k\right)\]}^{-1}=\frac{I}{\mathrm{\α}}-\frac{I}{\mathrm{\α}}IX\left(k\right){\[\frac{X^H\left(k\right)IX\left(k\right)}{\mathrm{\α}}+P^{-1}\]}^{-1}{X}^H\left(k\right)\frac{I}{\mathrm{\α}}\\ =\frac{I}{\mathrm{\α}}-\frac{I}{\mathrm{\α}}IX\left(k\right){\[\frac{P^{-1}}{\mathrm{\α}}+P^{-1}\]}^{-1}{X}^H\left(k\right)\frac{I}{\mathrm{\α}}\\ =\frac{1}{\mathrm{\α}}\[I-X\left(K\right)\frac{\mathrm{\α}}{1+\mathrm{\α}}PX\left(k\right)\frac{I}{\mathrm{\α}}\]\\ =\frac{1}{\mathrm{\α}}\[I-\frac{X\left(K\right){\mathrm{PX}}^H\left(K\right)}{1+\mathrm{\α}}\]\end{array}---\left(16\right)$

From formula (10)It it is the average of K sampled data correlation matrix of M array element.WillIt is converted into spectral factorization After form, (formula (15)) are applied in the derivation of above formula, substitute kth time sampled data correlation matrix X (k) PX^HK () (P takes Unit matrix) obtain

${({\hat{R}}_{xx}+\mathrm{\α}I)}^{-1}=\frac{1}{\mathrm{\α}}\[I-\frac{{\hat{R}}_{xx}}{1+\mathrm{\α}}\]---\left(17\right)$

Then formula (17) is substituted in result (12), then:

${\mathrm{\ω}}_{opt}={({\hat{R}}_{xx}+\mathrm{\α}I)}^{-1}{R}_{xd}=\frac{1}{\mathrm{\α}}\[I-\frac{{\hat{R}}_{xx}}{1+\mathrm{\α}}\]R_{xd}---\left(18\right)$

In formula, α represents loading coefficient, definition:Wherein 0 < λ < 1.Therefore, the determination of diagonal angle loading coefficient is permissible Determined by step factor μ and λ in LMS algorithm.

Finally, output adaptive wave beam is

Y (k)=ω_opt ^TX(k) (19)

The invention has the beneficial effects as follows: by being artificially injected white noise on sample covariance matrix diagonal, i.e. diagonal angle Load, reconstructed sample covariance matrix.Then use matrix inversion lemma, derive the Adaptive beamformer of a kind of robust Algorithm.Sample covariance matrix after reconstruct meets the condition of matrix inversion lemma, and the weight vector formula derived avoids square Battle array is inverted and loop iteration, it is achieved that the purpose of Fast Convergent.Meanwhile, the sample covariance matrix of reconstruct introduces diagonal angle loading The factor so that this algorithm there is certain robustness.By the checking of experiment, this algorithm can be applied at low signal-to-noise ratio simultaneously Calculate with MVDR and LMS in the various complex environments of high s/n ratio and relatively conventional in convergence rate and output signal-to-noise ratio Method has greatly improved so that it is can apply in the complex environment of acoustic imaging, thus ensure that the stability of imaging and become The frame per second of picture.

Accompanying drawing explanation

Fig. 1 flow chart.

Each self adaptation beam position figure under Fig. 2 low signal-to-noise ratio (-3dB) environment.

Each self adaptation beam position figure under Fig. 3 high s/n ratio (30dB) environment

Each self adaptation beam position figure under Fig. 4 high s/n ratio (40dB) environment

Fig. 5 low signal-to-noise ratio (-3dB) diagonal angle load factor affects figure to Wave beam forming

Fig. 6 high s/n ratio (40dB) diagonal angle load factor affects figure to Wave beam forming

Detailed description of the invention

Below with reference to accompanying drawing, the preferred embodiments of the present invention are described in detail；Should be appreciated that preferred embodiment Only for the explanation present invention rather than in order to limit the scope of the invention.

Fig. 1 is the flow chart of inventive algorithm, as shown in the figure: a kind of self adaptation loaded based on diagonal angle that the present invention provides Beamforming Method, comprises the following steps:

The each array element of S1: even linear array carries out the X (k) that samples to signal；

S2: sampled signal is asked its sample covariance matrixAs sample covariance matrix Estimation；

S3: utilize diagonal angle loading technique that sample covariance matrix is reconstructed

S4: combine least mean-square error (MSE) criterion, calculate the optimal solution of direction weight vector By in S3SubstituteAnd application matrix Inversion Formula derives, obtain

S5: sampled signal data is weighted by the directional weighting obtained summation, obtains adaptive beam signal y (k) =ω_opt ^TX(k)。

It is embodied as step:

Step 1: according to the signal model of this algorithm foundation, the sampled value of the sampled point m of kth time snap is:

$X_m\left(k\right)=\underset{i=1}{\overset{L}{\&Sigma;}}{s}_i\left(k\right)\exp \&lsqb;j\frac{2\mathrm{\&pi;}}{\mathrm{\&lambda;}}(m-1)d{\mathrm{sin\&theta;}}_i\&rsqb;+n_m\left(k\right)$

Each array element snap k reception to signal be respectively X₁(k),X₂(k),…,X_M(k), that is: X (k)=[X₁ (k),X₂(k),...,X_M(k)]^T；

Step 2: obtaining covariance matrix value is

${\hat{R}}_{xx}=\frac{1}{K}\underset{i=1}{\overset{K}{\&Sigma;}}X\left(t_i\right)x^H\left(t_i\right)$

Estimation as sample covariance matrix；

Step 3: apply to diagonal angle loading technique, in the weight vector calculating of algorithm, obtain

${\tilde{R}}_{xx}=(\mathrm{\&alpha;}I+{\hat{R}}_{xx})$

Being the average of K sampled data correlation matrix of M array element, α is diagonal angle loading coefficient.

Step 4: willIt is converted into spectral factorization formSubstitute kth time sampled data to be correlated with Matrix X (k) PX^HK () (P takes unit matrix) is also applied to the derivation of matrix inversion formula, obtain

${({\hat{R}}_{xx}+\mathrm{\&alpha;}I)}^{-1}=\frac{1}{\mathrm{\&alpha;}}\&lsqb;I-\frac{{\hat{R}}_{xx}}{1+\mathrm{\&alpha;}}\&rsqb;$

Formula (17) is substituted in result (12), then:

${\mathrm{\&omega;}}_{opt}={({\hat{R}}_{xx}+\mathrm{\&alpha;}I)}^{-1}{R}_{xd}=\frac{1}{\mathrm{\&alpha;}}\&lsqb;I-\frac{{\hat{R}}_{xx}}{1+\mathrm{\&alpha;}}\&rsqb;R_{xd}$

In formula, α represents loading coefficient so that it is meet relational expression:Wherein 0 < λ < 1.

Step 5: sampled signal data is weighted by the directional weighting obtained summation, obtains adaptive beam signal y (k)=ω_opt ^TX(k)。

In order to verify the effectiveness of this algorithm, MATLAB emulation tool is utilized to carry out algorithm simulating.Emulation experiment use by The even linear array of 16 array element compositions, array element is spaced apart half wavelength.Assume that the direction of arrival of desired signal and interference is respectively 0 ° and 40 °, and desired signal is mutually incoherent with interference.Noise average is 0, and variance is the additive white Gaussian noise of 1.In emulation In experiment, algorithm DL-MSE in this paper is analyzed with classical LMS algorithm, MVDR algorithm.Hits is 500, the iterations of LMS algorithm is also 500.μ=0.0005, λ=0.5.

Experiment 1: in this experiment, verify various algorithm pointing capability under low signal-to-noise ratio environment, take SNR=-3dB. Result is as in figure 2 it is shown, in the case of low signal-to-noise ratio, LMS algorithm performance numerous imbalances, tracking effect becomes very poor.And herein The algorithm DL-MSE proposed and the effectiveness comparison of MVDR algorithm are close, functional.On interference radiating way, DL-MSE algorithm is slightly worse In MVDR algorithm.

Experiment 2: in this experiment, verify various algorithm pointing capability under high s/n ratio environment, takes SNR and is respectively 30dB、40dB.Result as shown in Figure 3, Figure 4, in the case of high s/n ratio, MVDR algorithm performance numerous imbalances, and carrying herein The algorithm DL-MSE algorithm gone out and the Performance comparision of LMS algorithm are stable.On AF panel, DL-MSE algorithm is slightly better than LMS and calculates Method, can be upwardly formed zero disturber and fall into.Along with the rising of SNR, comparison diagram 3 and Fig. 4 is it appeared that DL-MSE algorithm and LMS Algorithm all shows preferable performance, can keep stable tracking pointing capability.The diagonal angle loading method of the propositions such as contrast Cox, Method in this paper solves under the conditions of relatively high s/n ratio (SNR), uses the Adaptive beamformer of diagonal angle loading method Device has more serious performance degradations.

Experiment 3: in the adaptive beam-forming algorithm that set forth herein design, the coefficient loaded as diagonal angle, α and LMS Linear relationship is met between the algorithm step-size factor.When coefficient lambda takes different value, loading coefficient changes therewith.Fig. 5, Fig. 6 say Understand when in the case of low signal-to-noise ratio (-3dB) and high s/n ratio (40dB) two kinds, λ takes different values, the performance of DL-MSE algorithm Change.When low signal-to-noise ratio, loading coefficientThe biggest, algorithm is the best to the inhibition of noise, and on interference radiating way Formation deeper zero fall into.And in the environment of high s/n ratio, algorithm performance is insensitive to the change of loading coefficient, but too Preferable zero can be upwardly formed disturber to fall into.

In convergence of algorithm speed, algorithm in this paper due to avoid MVDR algorithm matrix inversion operation and LMS algorithm loop iteration updates weight vector, so have certain excellent in convergence rate relative to MVDR algorithm and LMS algorithm Gesture, table 1 lists in the case of sampling 500 times or LMS iteration 500 times, adaptive beam convergence situation.Contrast from table 1 Understand, obtain the MVDR of weight vector and by the LMS algorithm of loop iteration by carrying out covariance matrix inversion operation after sampling In convergence rate, gap is little.And DL-MSE algorithm in this paper has the biggest advantage in convergence rate, this is described Bright algorithm can be used in the occasion that requirement of real-time is higher.

	LMS	DL-MSE	MVDR
				Low signal-to-noise ratio	0.015625s	0.005290s	0.011544s
High s/n ratio	0.016108s	0.005345s	0.010175s

Table 1 each self adaptation beam weight vector forms time contrast

Finally illustrate, the foregoing is only the preferred embodiments of the present invention, not in order to limit the present invention, all Any amendment made within the spirit and principles in the present invention, equivalent and improvement etc., should be included in the protection of the present invention Within the scope of.

Claims (6)

1. the adaptive beam-forming algorithm loaded based on diagonal angle, it is characterised in that: comprise the following steps:

Signal is sampled by each array element of S1: even linear array；

S2: seek its sample covariance matrix, as the estimation of sample covariance matrix；

S3: utilize diagonal angle loading technique that sample covariance matrix is reconstructed；

S4: combine least mean-square error (MSE) criterion, calculate the optimal solution of direction weight vector；

S5: sampled signal data is weighted by the directional weighting obtained summation, obtains adaptive beam signal.

A kind of adaptive beam-forming algorithm loaded based on diagonal angle the most according to claim 1, its It is characterised by: in described step 1: when signal is sampled by each array element, basis signal modelWherein n_mK () represents the noise in m-th array element, s_i(k) Representing each information source echo baseband signal at datum mark, L represents information source number；The sampled value obtaining kth time snap is X₁(k),X₂ (k),…,X_M(k), that is: X (k)=[X₁(k),X₂(k),...,X_M(k)]^T, wherein M represents element number of array.

A kind of adaptive beam-forming algorithm loaded based on diagonal angle the most according to claim 1, it is characterised in that: described In step 2: be indicated the meansigma methods receiving vector second-order statistic, i.e. signal autocorrelation matrix, as covariance square Battle array estimated valueWherein K represents the fast umber of beats of array antenna, and X (k) represents kth time on array antenna Signal that snap receives (k=1,2 ..., K), subscript H representing matrix conjugate transpose.

A kind of adaptive beam-forming algorithm loaded based on diagonal angle the most according to claim 1, it is characterised in that: described In step 3: apply to diagonal angle loading technique, in the weight vector calculating of algorithm, obtain

${\tilde{R}}_{xx}=(\mathrm{\&alpha;}I+{\hat{R}}_{xx})$

In formulaBeing the average of K sampled data correlation matrix of M array element, α is diagonal angle loading coefficient.

A kind of adaptive beam-forming algorithm loaded based on diagonal angle the most according to claim 1, it is characterised in that: described In step 4: obtain the optimal solution of direction weight vector.Specifically include following steps:

S41: due to sampling covarianceFor Hermitian matrix, then can represent spectral factorization form:Wherein U is characterized vector matrix, Λ=diag (γ₁,γ₂,...,γ_M), γ_iForSpy Value indicative；

S42: by matrix inversion lemma by [α I+X (k) PX^H(k)]^-1Be converted toRepresent；

S43: by S41 stepReplace X (k) PX in S42 step^HK () (P takes unit matrix) obtainsWherein α represents loading coefficient；

S44: definition diagonal angle loading coefficientStep factor during wherein μ represents LMS algorithm, λ is constant, and span is 0<λ<1；

S45: divide equally error criterion according to MSE minimum, obtains direction weight vector optimal solution

A kind of adaptive beam-forming algorithm loaded based on diagonal angle the most according to claim 1, it is characterised in that: described In step 5: sampled signal data is weighted by the directional weighting obtained summation, obtain adaptive beam signal y (k)= ω_opt ^TX(k)。