CN106093920A

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

Info

Publication number: CN106093920A
Application number: CN201610538089.6A
Authority: CN
Inventors: 邓正宏; 李学强; 黄杰; 黄一杰; 付明月; 马春苗
Original assignee: Northwestern Polytechnical University
Current assignee: Northwestern Polytechnical University
Priority date: 2016-07-09
Filing date: 2016-07-09
Publication date: 2016-11-09
Anticipated expiration: 2036-07-09
Also published as: CN106093920B

Abstract

The invention discloses an adaptive beamforming algorithm based on diagonal loading, which relates to the technical field of smart antennas. Firstly, the sampling covariance matrix of the sampling signal collected by the receiving element of the line array is obtained as the sample covariance matrix estimate. Then, the sampling covariance matrix is reconstructed by using the diagonal loading technique, so that it satisfies the matrix inversion lemma formula and avoids the matrix inversion operation. Finally, combined with the minimum mean square error (MSE) criterion, the optimal solution of the direction weight vector is obtained, and the reconstructed sampling covariance matrix is used to replace the iterative operation, which greatly reduces the convergence time of the algorithm. This algorithm not only effectively solves and optimizes the convergence time problem of the adaptive digital beamforming algorithm, but also verifies that the performance of the algorithm is relatively stable in high and low signal-to-noise ratio environments through simulation experiments, and can also eliminate the model error to a certain extent sensitive issues.

Description

An Adaptive Beamforming Algorithm Based on Diagonal Loading

技术领域technical field

本发明涉及智能天线技术领域，尤其涉及一种基于对角加载的自适应波束形成算法。The invention relates to the technical field of smart antennas, in particular to an adaptive beamforming algorithm based on diagonal loading.

背景技术Background technique

水下声成像技术主要用于水下目标探测与搜索，水底地貌绘制，海底沉船、救援、黑盒子打捞等众多军事和民用领域。已经在国防和民用领域取得广泛的应用。为了实现一定距离下水下目标的高清晰声成像目的，就必须研究复杂水声环境下的稳定成像技术，并且同时要满足一定的成像帧率和较远的作用距离。这就要求在研究水声成像的自适应波束形成算法时，不仅也需要考虑鲁棒性问题，也要尽量提高系统的输出信噪比，同时减小自适应波束形成算法的运算量。Underwater acoustic imaging technology is mainly used in many military and civilian fields such as underwater target detection and search, underwater landform mapping, submarine sunken ship, rescue, black box salvage, etc. It has been widely used in national defense and civilian fields. In order to achieve high-definition acoustic imaging of underwater targets at a certain distance, it is necessary to study stable imaging technology in complex underwater acoustic environments, and at the same time satisfy a certain imaging frame rate and a long range. This requires that when studying the adaptive beamforming algorithm of underwater acoustic imaging, not only the robustness problem must also be considered, but also the output signal-to-noise ratio of the system should be improved as much as possible, while reducing the computational load of the adaptive beamforming algorithm.

自适应波束形成技术通过调整权重向量来改变阵列的方向图，使波束主瓣对准期望信号，旁瓣和零陷对准干扰信号，从而提高输出的信干噪比，以实现某准则下的最佳接收。Adaptive beamforming technology changes the pattern of the array by adjusting the weight vector, so that the main lobe of the beam is aligned with the desired signal, and the side lobes and nulls are aligned with the interference signal, thereby improving the output signal-to-interference-noise ratio to achieve a certain criterion. Best received.

LMS自适应波束形成算法是一种结构简单、算法复杂度低、易于实现和稳定性高的波束形成方法。但一直因为其收敛速度较慢，在工程应用上受到一定程度的限制。为此，各学者相继以不同的调整策略：瞬时误差、权矢量的前向预测以及平滑梯度矢量等，提出变步长的LMS算法来平衡收敛速度和算法失调。虽然在平衡收敛速度和失调方面优于经典LMS算法，但应对突变能力较差。LMS adaptive beamforming algorithm is a beamforming method with simple structure, low algorithm complexity, easy implementation and high stability. However, because of its slow convergence speed, it has been limited to a certain extent in engineering applications. For this reason, various scholars successively use different adjustment strategies: instantaneous error, forward prediction of weight vector and smooth gradient vector, etc., and propose LMS algorithm with variable step size to balance the convergence speed and algorithm imbalance. Although it is better than the classic LMS algorithm in terms of balancing convergence speed and misalignment, it has poor ability to deal with sudden changes.

作为判断最佳接收的准则之一，均方误差(MSE)性能量度由威德鲁等人提出。并由Wiener、Hopf推导出最优的维纳解。经典LMS算法正是在MSE准则的基础上，运用最优化方法如：最速下降法、加速梯度算法等迭代运算出最优权向量的。As one of the criteria for judging the best reception, the mean square error (MSE) performance metric was proposed by Widrew et al. And the optimal Wiener solution is deduced by Wiener and Hopf. The classic LMS algorithm is based on the MSE criterion, using optimization methods such as steepest descent method, accelerated gradient algorithm, etc. to iteratively calculate the optimal weight vector.

基于以上所述，本文提出一种基于MSE准则和对角加载技术的鲁棒自适应波束形成算法。在该算法中，通过在采样协方差矩阵对角线上人工注入白噪声，即对角加载，重构采样协方差矩阵。然后运用矩阵求逆引理，避免矩阵求逆运算和迭代运算，而且将对角加载系数转化为LMS算法步长因子的函数。仿真结果表明此算法不仅能有效降低收敛时间，并在高、低信噪比环境下能都表现出较好的性能，有较好的鲁棒性。Based on the above, this paper proposes a robust adaptive beamforming algorithm based on MSE criterion and diagonal loading technique. In this algorithm, the sampling covariance matrix is reconstructed by artificially injecting white noise on the diagonal of the sampling covariance matrix, that is, diagonal loading. Then the matrix inversion lemma is used to avoid matrix inversion operation and iterative operation, and the diagonal loading coefficient is transformed into a function of the step factor of the LMS algorithm. The simulation results show that the algorithm can not only effectively reduce the convergence time, but also show better performance and better robustness in both high and low SNR environments.

发明内容Contents of the invention

为了改进现有自适应波束形成方法在收敛速度上偏慢的缺点，突破采样频率限制，获得更精准的权重方向向量，本发明的第一目的是在LMS算法和MVDR的基础上避免循环迭代和矩阵求逆运算，缩短算法收敛时间，使其能很好地在工程中得到应用。该方法可以在形成自适应波束中通过重构采样协方差矩阵，并在此基础上应用矩阵求逆引理，从而避免了求逆运算和迭代运算，具有较好的指向性能和干扰抑制能力。In order to improve the slow convergence speed of existing adaptive beamforming methods, break through the sampling frequency limit, and obtain more accurate weight direction vectors, the first purpose of the present invention is to avoid cyclic iteration and The matrix inversion operation shortens the convergence time of the algorithm, so that it can be well applied in engineering. This method can reconstruct the sampling covariance matrix in forming adaptive beam, and apply matrix inversion lemma on this basis, thus avoiding inversion operation and iterative operation, and has better pointing performance and interference suppression ability.

本发明的第二目的在于为减小各种误差导致的副瓣电平升高、主瓣便宜、波束畸变、SINR下降等问题，将对角加载技术引入自适应波束形成中，并给出了确定加载系数的公式。该方法实现简单，有利于减少波束形成过程中的偏差，提高波束形成的准确性和稳健性。The second purpose of the present invention is to introduce diagonal loading technology into adaptive beamforming in order to reduce the problems of sidelobe level rise, mainlobe cheapness, beam distortion, and SINR drop caused by various errors, and gives Formula for determining the loading factor. The method is simple to implement, is beneficial to reduce the deviation in the beamforming process, and improves the accuracy and robustness of the beamforming.

为实现上述目的，本发明提供一种基于对角加载的自适应波束形成算法，所述方法包含如下步骤：In order to achieve the above object, the present invention provides an adaptive beamforming algorithm based on diagonal loading, the method includes the following steps:

步骤1：考虑平面空间的等距均匀线阵，设阵元数为M,阵元间距为d，其中d＝λ/2(λ为阵列接收单元接收信号的波长)，假设有L个信源回波(M>L)，设波达方向为θ₁,θ₂,...,θ_L，以阵列的第一个阵元作为基准点，则在第k次快拍的采样点m处的采样值为：Step 1: Consider an equidistant uniform linear array in planar space, set the number of array elements as M, and the distance between array elements as d, where d=λ/2 (λ is the wavelength of the signal received by the array receiving unit), assuming that there are L sources Echo (M>L), let the direction of arrival be θ ₁ , θ ₂ ,..., θ _L , take the first element of the array as the reference point, then at the sampling point m of the k-th snapshot The sampling value of is:

${X x}_{m m} ((k k)) = = {Σ Σ}_{i i = = 11}^{L L} {s the s}_{i i} ((k k)) exp exp [[j j \frac{22 π π}{λ λ} ((m m - - 11)) d d {sinθ sinθ}_{i i}]] + + {n no}_{m m} ((k k)) - - - - - - ((11))$

式中n_m(k)表示第m个阵元上的噪声，s_i(k)表示各信源回波在基准点的基带信号。步骤2：各阵元在快拍k时刻接收到的信号分别为X₁(k),X₂(k),…,X_M(k),即：X(k)＝[X₁(k),X₂(k),...,X_M(k)]^T,此为阵列输入矢量。得到协方差矩阵估计值为式中K表示阵列天线的快拍数，X(k)表示阵列天线上第k次快拍接收到的信号(k＝1,2,...,K)，上标H表示矩阵共轭转置。In the formula, n _m (k) represents the noise on the mth array element, and s _i (k) represents the baseband signal of each source echo at the reference point. Step 2: The signals received by each array element at the moment of snapshot k are X ₁ (k), X ₂ (k), ..., X _M (k), that is: X(k)=[X ₁ (k) ,X ₂ (k),...,X _M (k)] ^T , this is the array input vector. The estimated value of the covariance matrix is In the formula, K represents the number of snapshots of the array antenna, X(k) represents the signal received by the kth snapshot on the array antenna (k=1,2,...,K), and the superscript H represents the matrix conjugate rotation place.

步骤3：在时域中，阵列输出为Step 3: In the time domain, the array output is

y(t)＝ω^TX(t) (2)y(t)= ^ωT X(t) (2)

参考信号d(t)与实际输出信号的误差为The error between the reference signal d(t) and the actual output signal is

ε(t)＝d(t)-y(t)＝d(t)-ω^TX(t) (3)ε(t)=d(t)-y(t)=d(t)-ω ^T X(t) (3)

对(3)式求平方可得Square the formula (3) to get

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

对上式两边取数学期望可得Taking the mathematical expectation on both sides of the above formula, we can get

$E E. {{{ϵ ϵ}^{22} ((t t))}} = = \overset{&OverBar; &OverBar;}{{d d}^{22} ((t t))} - - 22 {ω ω}^{T T} {R R}_{x x d d} + + {ω ω}^{T T} {R R}_{x x x x} ω ω - - - - - - ((55))$

式中表示对d(t)取数学期望，互相关矩阵R_xd为R_xd＝E{d(k)X^T(k)}，令则In the formula Represents the mathematical expectation of d(t), the cross-correlation matrix R _xd is R _xd =E{d(k)X ^T (k)}, let but

E{ε²(t)}＝S-2ω^TR_xd+ω^TR_xxω (6)E{ε ² (t)}＝S-2ω ^T R _xd +ω ^T R _xx ω (6)

适当选择权重向量ω可使E{ε²(t)}达到最小。可知式(6)是ω的二次函数，该函数的极值是一个最小值，由式(6)对权重向量求梯度并令其为零，求出使E{ε²(t)}最小的ω值，得到权重向量的最优值满足下式：Proper selection of the weight vector ω can minimize E{ε ² (t)}. It can be seen that formula (6) is a quadratic function of ω, and the extremum of the function is a minimum value. From formula (6), calculate the gradient of the weight vector and make it zero, and find the minimum E{ε ² (t)} The ω value of , the optimal value of the weight vector is obtained to satisfy the following formula:

${ω ω}_{o o p p t t} = = {R R}_{x x x x}^{- - 11} {R R}_{x x d d} - - - - - - ((77))$

步骤4：在波束形成算法方面，LMS算法作为常步长LMS算法，其权向量的迭代公式可表述为：Step 4: In terms of the beamforming algorithm, the LMS algorithm is a constant-step LMS algorithm, and the iterative formula of its weight vector can be expressed as:

$ω ω ((k k + + 11)) = = ω ω ((k k)) - - μ μ &dtri; &dtri; ((n no)) - - - - - - ((88))$

为了克服矩阵求逆等运算，LMS算法采用最陡下降法求解式(8)，得到LMS算法的迭代公式In order to overcome operations such as matrix inversion, the LMS algorithm uses the steepest descent method to solve equation (8), and the iterative formula of the LMS algorithm is obtained

ω(k+1)＝ω(k)+μX(k)e^*(k) (9)ω(k+1)=ω(k)+μX(k)e ^* (k) (9)

式中，μ为步长因子，可以控制自适应的速率。通过分析可知，μ步长因子的取值范围满足关系：可以证明当迭代次数无限增加时，权重向量的期望值可以收敛至维纳解。In the formula, μ is the step size factor, which can control the rate of self-adaptation. Through the analysis, it can be known that the value range of the μ step size factor satisfies the relationship: It can be proved that when the number of iterations increases infinitely, the expected value of the weight vector can converge to the Wiener solution.

步骤5：在增强自适应波束形成器的鲁棒性方面，对角加载技术被用于抑制方向图畸变。在本文所依据的信号模型基础上，实际计算采样协方差矩阵R_xx是由K次采样信号得到的估计值Step 5: In enhancing the robustness of the adaptive beamformer, the diagonal loading technique is used to suppress the pattern distortion. On the basis of the signal model based on this paper, the actual calculation of the sampling covariance matrix R _xx is the estimated value obtained from the K sampling signal

${\overset{^^}{R R}}_{x x x x} = = \frac{11}{K K} {Σ Σ}_{k k = = 11}^{K K} x x ((k k)) {x x}^{H h} ((k k)) - - - - - - ((1010))$

所代替，则instead of

${ω ω}_{o o p p t t} = = {\overset{^^}{R R}}_{x x x x}^{- - 11} {R R}_{x x d d} - - - - - - ((1111))$

将对角加载技术运用到LMS算法的权向量计算中，得到Applying the diagonal loading technique to the weight vector calculation of the LMS algorithm, we get

${\overset{~ ~}{R R}}_{x x x x} = = ((α α I I + + {\overset{^^}{R R}}_{x x x x})) - - - - - - ((1212))$

引理：令矩阵A∈C^n×n的逆矩阵存在，并且x，y是两个n×1维向量，使得(A+xy^H)可逆，则Lemma: Let the inverse matrix of matrix A∈C ^n×n exist, and x, y are two n×1-dimensional vectors, so that (A+xy ^H ) is invertible, then

${((A A + + {xy xy}^{H h}))}^{- - 11} = = {A A}^{- - 11} - - \frac{{A A}^{- - 11} {xy xy}^{H h} {A A}^{- - 11}}{11 + + {y the y}^{H h} {A A}^{- - 11} x x} - - - - - - ((1313))$

将其推广为矩阵之和求逆公式，即为：It can be extended to the matrix sum inversion formula, which is:

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

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

因为采样协方差是Hermitian矩阵，则由式(11)可以推导出Because of the sampling covariance is a Hermitian matrix, then it can be deduced from formula (11)

${\overset{^^}{R R}}_{x x x x} = = {UΛU UΛU}^{H h} = = {Σ Σ}_{i i = = 11}^{M m} {γ γ}_{i i} {u u}_{i i} {u u}_{i i}^{H h} - - - - - - ((1515))$

式中，U为特征向量矩阵，Λ＝diag(γ₁,γ₂,...,γ_M)，γ_i为的特征值。In the formula, U is the eigenvector matrix, Λ=diag(γ ₁ ,γ ₂ ,...,γ _M ), γ _i is eigenvalues of .

根据上述矩阵求逆公式可以推导出According to the above matrix inversion formula, it can be deduced that

$\begin{matrix} {[[α α I I + + X x ((k k)) {PX PX}^{H h} ((k k))]]}^{- - 11} = = \frac{I I}{α α} - - \frac{I I}{α α} I I X x ((k k)) {[[\frac{{X x}^{H h} ((k k)) I I X x ((k k))}{α α} + + {P P}^{- - 11}]]}^{- - 11} {X x}^{H h} ((k k)) \frac{I I}{α α} \\ = = \frac{I I}{α α} - - \frac{I I}{α α} I I X x ((k k)) {[[\frac{{P P}^{- - 11}}{α α} + + {P P}^{- - 11}]]}^{- - 11} {X x}^{H h} ((k k)) \frac{I I}{α α} \\ = = \frac{11}{α α} [[I I - - X x ((K K)) \frac{α α}{11 + + α α} P P X x ((k k)) \frac{I I}{α α}]] \\ = = \frac{11}{α α} [[I I - - \frac{X x ((K K)) {PX PX}^{H h} ((K K))}{11 + + α α}]] \end{matrix} - - - - - - ((1616))$

由式(10)可知是M个阵元的K次采样数据相关矩阵的均值。将转化为谱分解形式后(式(15))应用到上式的推导过程中，替代第k次采样数据相关矩阵X(k)PX^H(k)(P取单位矩阵)得到It can be seen from formula (10) is the mean value of the correlation matrix of K times sampling data of M array elements. Will After being transformed into spectral decomposition form (Equation (15)), it is applied to the derivation process of the above equation, replacing the k-th sampling data correlation matrix X(k)PX ^H (k) (P takes the identity matrix) to get

${(({\overset{^^}{R R}}_{x x x x} + + α α I I))}^{- - 11} = = \frac{11}{α α} [[I I - - \frac{{\overset{^^}{R R}}_{x x x x}}{11 + + α α}]] - - - - - - ((1717))$

然后将式(17)代入结果(12)中，则：Then substitute formula (17) into result (12), then:

${ω ω}_{o o p p t t} = = {(({\overset{^^}{R R}}_{x x x x} + + α α I I))}^{- - 11} {R R}_{x x d d} = = \frac{11}{α α} [[I I - - \frac{{\overset{^^}{R R}}_{x x x x}}{11 + + α α}]] {R R}_{x x d d} - - - - - - ((1818))$

式中α表示加载系数，定义：其中0<λ<1。因此，对角加载系数的确定可以由LMS算法中的步长因子μ和λ确定。In the formula, α represents the loading coefficient, defined as: where 0<λ<1. Therefore, the determination of the diagonal loading factor can be determined by the step factors μ and λ in the LMS algorithm.

最后，输出自适应波束为Finally, the output adaptive beam is

y(k)＝ω_opt ^TX(k) (19)y(k)=ω _opt ^T X(k) (19)

本发明的有益效果是：通过在采样协方差矩阵对角线上人工注入白噪声，即对角加载，重构采样协方差矩阵。然后运用矩阵求逆引理，推导出一种鲁棒的自适应波束形成算法。重构后的采样协方差矩阵满足矩阵求逆引理的条件，推导出的权向量公式避免了矩阵求逆和循环迭代，实现了快速收敛的目的。同时，重构的采样协方差矩阵引入了对角加载因子，使得该算法的具有一定的鲁棒性。通过实验的验证，该算法可以同时应用在低信噪比和高信噪比的各种复杂环境中，并且在收敛速度和输出信噪比上相对传统的MVDR和LMS算法有很大的提升，使其可以应用在水声成像的复杂环境中，从而保证了成像的稳定性和成像的帧率。The beneficial effects of the present invention are: the sampling covariance matrix is reconstructed by artificially injecting white noise on the diagonal of the sampling covariance matrix, that is, diagonal loading. Then, using the matrix inversion lemma, a robust adaptive beamforming algorithm is derived. The reconstructed sampling covariance matrix satisfies the condition of matrix inversion lemma, and the derived weight vector formula avoids matrix inversion and loop iteration, and achieves the purpose of fast convergence. At the same time, the reconstructed sampling covariance matrix introduces a diagonal loading factor, which makes the algorithm more robust. Through experimental verification, the algorithm can be applied in various complex environments with low SNR and high SNR at the same time, and has a great improvement in convergence speed and output SNR compared with traditional MVDR and LMS algorithms. It can be applied in the complex environment of underwater acoustic imaging, thus ensuring the stability of imaging and the frame rate of imaging.

附图说明Description of drawings

图1流程图。Figure 1 Flowchart.

图2低信噪比(-3dB)环境下各自适应波束指向图。Fig. 2 Direction diagrams of respective adaptive beams in a low signal-to-noise ratio (-3dB) environment.

图3高信噪比(30dB)环境下各自适应波束指向图Figure 3 Direction diagram of respective adaptive beams in a high SNR (30dB) environment

图4高信噪比(40dB)环境下各自适应波束指向图Figure 4 Direction diagram of respective adaptive beams in a high SNR (40dB) environment

图5低信噪比(-3dB)对角加载因子对波束形成的影响图Figure 5 Effect of low SNR (-3dB) diagonal loading factor on beamforming

图6高信噪比(40dB)对角加载因子对波束形成的影响图Figure 6 Effect of high SNR (40dB) diagonal loading factor on beamforming

具体实施方式detailed description

以下将结合附图，对本发明的优选实施例进行详细的描述；应当理解，优选实施例仅为了说明本发明，而不是为了限制本发明的保护范围。The preferred embodiments of the present invention will be described in detail below in conjunction with the accompanying drawings; it should be understood that the preferred embodiments are only for illustrating the present invention, rather than limiting the protection scope of the present invention.

图1是本发明算法的流程图，如图所示：本发明提供的一种基于对角加载的自适应波束形成方法，包括以下步骤：Fig. 1 is a flowchart of the algorithm of the present invention, as shown in the figure: a kind of adaptive beamforming method based on diagonal loading provided by the present invention comprises the following steps:

S1:均匀线阵各阵元对信号进行采样X(k)；S1: Each element of the uniform linear array samples the signal X(k);

S2:对采样信号求其采样协方差矩阵做为样本协方差矩阵的估计；S2: Find the sampling covariance matrix for the sampled signal As an estimate of the sample covariance matrix;

S3:利用对角加载技术对采样协方差矩阵进行重构 S3: Reconstruction of the sampling covariance matrix using the diagonal loading technique

S4:结合最小均方误差(MSE)准则，计算出方向权向量的最优解将S3中的替代并应用矩阵求逆公式进行推导，得到 S4: Combined with the minimum mean square error (MSE) criterion, calculate the optimal solution of the direction weight vector will be in S3 replace And apply the matrix inversion formula to deduce, get

S5：将得到的方向权值对采样信号数据进行加权求和，得到自适应波束信号y(k)＝ω_opt ^TX(k)。S5: Perform weighted summation of the obtained direction weights on the sampled signal data to obtain an adaptive beam signal y(k)=ω _opt ^T X(k).

具体实施步骤：Specific implementation steps:

步骤1：根据本算法依据的信号模型，第k次快拍的采样点m的采样值为：Step 1: According to the signal model based on this algorithm, the sampling value of the sampling point m of the kth snapshot is:

${X x}_{m m} ((k k)) = = {Σ Σ}_{i i = = 11}^{L L} {s the s}_{i i} ((k k)) exp exp [[j j \frac{22 π π}{λ λ} ((m m - - 11)) d d {sinθ sinθ}_{i i}]] + + {n no}_{m m} ((k k))$

各阵元在快拍k时刻接收到的信号分别为X₁(k),X₂(k),…,X_M(k),即：X(k)＝[X₁(k),X₂(k),...,X_M(k)]^T；The signals received by each array element at the moment of snapshot k are X ₁ (k), X ₂ (k), ..., X _M (k), namely: X(k)=[X ₁ (k), X ₂ (k),...,X _M (k)] ^T ;

步骤2：得到协方差矩阵估计值为Step 2: Get the estimated covariance matrix as

${\overset{^^}{R R}}_{x x x x} = = \frac{11}{K K} {Σ Σ}_{i i = = 11}^{K K} X x (({t t}_{i i})) {x x}^{H h} (({t t}_{i i}))$

做为样本协方差矩阵的估计；As an estimate of the sample covariance matrix;

步骤3：将对角加载技术运用到算法的权向量计算中，得到Step 3: Apply the diagonal loading technique to the weight vector calculation of the algorithm, and get

${\overset{~ ~}{R R}}_{x x x x} = = ((α α I I + + {\overset{^^}{R R}}_{x x x x}))$

是M个阵元的K次采样数据相关矩阵的均值，α为对角加载系数。 is the mean value of the correlation matrix of K sampling data of M array elements, and α is the diagonal loading coefficient.

步骤4：将转化为谱分解形式替代第k次采样数据相关矩阵X(k)PX^H(k)(P取单位矩阵)并应用到矩阵求逆公式的推导过程中，得到Step 4: Put Convert to Spectral Decomposition Form Substitute the correlation matrix X(k)PX ^H (k) of the kth sampling data (P takes the unit matrix) and apply it to the derivation process of the matrix inversion formula, and get

${(({\overset{^^}{R R}}_{x x x x} + + α α I I))}^{- - 11} = = \frac{11}{α α} [[I I - - \frac{{\overset{^^}{R R}}_{x x x x}}{11 + + α α}]]$

将式(17)代入结果(12)中，则：Substituting formula (17) into result (12), then:

${ω ω}_{o o p p t t} = = {(({\overset{^^}{R R}}_{x x x x} + + α α I I))}^{- - 11} {R R}_{x x d d} = = \frac{11}{α α} [[I I - - \frac{{\overset{^^}{R R}}_{x x x x}}{11 + + α α}]] {R R}_{x x d d}$

式中α表示加载系数，使其满足关系式：其中0<λ<1。In the formula, α represents the loading coefficient, so that it satisfies the relational expression: where 0<λ<1.

步骤5：将得到的方向权值对采样信号数据进行加权求和，得到自适应波束信号y(k)＝ω_opt ^TX(k)。Step 5: Perform weighted summation of the obtained direction weights on the sampled signal data to obtain an adaptive beam signal y(k)=ω _opt ^T X(k).

为了验证该算法的有效性，利用MATLAB仿真工具进行算法仿真。仿真实验采用由16个阵元组成的均匀线阵，阵元间隔为半个波长。假设期望信号和干扰的波达方向分别为0°和40°，并且期望信号和干扰互不相干。噪声均值为0，方差为1的加性高斯白噪声。在仿真实验中，将本文提出的算法DL-MSE与经典的LMS算法、MVDR算法进行对比分析。采样数均为500，LMS算法的迭代次数也为500。μ＝0.0005，λ＝0.5。In order to verify the validity of the algorithm, the algorithm simulation is carried out by using MATLAB simulation tool. The simulation experiment adopts a uniform linear array composed of 16 array elements, and the array element interval is half a wavelength. Assume that the directions of arrival of the desired signal and the interference are 0° and 40° respectively, and the desired signal and interference are independent of each other. Additive white Gaussian noise with a mean of 0 and a variance of 1. In the simulation experiment, the algorithm DL-MSE proposed in this paper is compared with the classic LMS algorithm and MVDR algorithm. The number of samples is 500, and the number of iterations of the LMS algorithm is also 500. μ=0.0005, λ=0.5.

实验1：在该实验中，验证各种算法在低信噪比环境下的指向性能，取SNR＝-3dB。结果如图2所示，在低信噪比的情况下，LMS算法性能严重失调，跟踪效果变得很差。而本文提出的算法DL-MSE和MVDR算法的效果比较接近，性能良好。在干扰方向上，DL-MSE算法稍差于MVDR算法。Experiment 1: In this experiment, verify the pointing performance of various algorithms in a low SNR environment, and take SNR=-3dB. The results are shown in Figure 2. In the case of low SNR, the performance of the LMS algorithm is seriously out of tune, and the tracking effect becomes poor. The algorithm DL-MSE proposed in this paper is similar to the MVDR algorithm and has good performance. In the interference direction, the DL-MSE algorithm is slightly worse than the MVDR algorithm.

实验2：在该实验中，验证各种算法在高信噪比环境下的指向性能，取SNR分别为30dB、40dB。结果如图3、图4所示，在高信噪比的情况下，MVDR算法性能严重失调，而本文提出的算法DL-MSE算法和LMS算法的性能比较稳定。在干扰抑制上，DL-MSE算法稍优于LMS算法，都能在干扰方向上形成零陷。随着SNR的升高，对比图3和图4可以发现DL-MSE算法和LMS算法都表现出较好的性能，能保持稳定的跟踪指向性能。对比Cox等提出的对角加载方法，本文提出的方法解决了在较高信噪比(SNR)条件下，采用对角加载方法的自适应波束形成器有较严重的性能衰落。Experiment 2: In this experiment, verify the directivity performance of various algorithms in the environment of high signal-to-noise ratio, and take the SNR as 30dB and 40dB respectively. The results are shown in Figure 3 and Figure 4. In the case of high SNR, the performance of the MVDR algorithm is seriously out of balance, while the performance of the DL-MSE algorithm and the LMS algorithm proposed in this paper are relatively stable. In terms of interference suppression, the DL-MSE algorithm is slightly better than the LMS algorithm, and can form nulls in the interference direction. As the SNR increases, comparing Figure 3 and Figure 4, it can be found that both the DL-MSE algorithm and the LMS algorithm show better performance and can maintain stable tracking performance. Compared with the diagonal loading method proposed by Cox et al., the method proposed in this paper solves the serious performance degradation of the adaptive beamformer using the diagonal loading method under the condition of high signal-to-noise ratio (SNR).

实验3：在本文提出设计的自适应波束形成算法中，作为对角加载的系数，α和LMS算法步长因子之间满足线性关系。当系数λ取不同值时，加载系数随之发生变化。图5、图6说明了在低信噪比(-3dB)和高信噪比(40dB)两种情况下λ取不同的值时，DL-MSE算法的性能变化。在低信噪比时，加载系数越大，算法对噪声的抑制效果越好，并在干扰方向上的形成较深的零陷。而在高信噪比的环境中，算法性能对加载系数的变化不敏感，但也同样能在干扰方向上形成较好的零陷。Experiment 3: In the adaptive beamforming algorithm proposed in this paper, as a diagonally loaded coefficient, α satisfies a linear relationship with the step factor of the LMS algorithm. When the coefficient λ takes different values, the loading coefficient changes accordingly. Figure 5 and Figure 6 illustrate the performance changes of the DL-MSE algorithm when λ takes different values in the two cases of low SNR (-3dB) and high SNR (40dB). At low SNR, the loading factor The larger the value, the better the algorithm's suppression effect on the noise, and the deeper the zero trap will be formed in the interference direction. In the environment with high signal-to-noise ratio, the performance of the algorithm is not sensitive to the change of the loading coefficient, but it can also form a better null in the interference direction.

在算法的收敛速度上，本文提出的算法由于避免了MVDR算法的矩阵求逆运算和LMS算法循环迭代更新权向量，所以在收敛速度上相对MVDR算法和LMS算法都有一定的优势，表1列出了在采样500次或者LMS迭代500次的情况下，自适应波束收敛情况。从表1对比可知，通过采样后进行协方差矩阵求逆运算得到权向量的MVDR和通过循环迭代的LMS算法在收敛速度上差距不大。而本文提出的DL-MSE算法在收敛速度上有很大的优势，说明本发明的算法可以被应用在实时性要求较高的场合中。In terms of the convergence speed of the algorithm, the algorithm proposed in this paper has certain advantages over the MVDR algorithm and the LMS algorithm in terms of convergence speed because it avoids the matrix inversion operation of the MVDR algorithm and the cyclic iteration of the LMS algorithm to update the weight vector, as shown in Table 1. In the case of 500 samples or 500 LMS iterations, the adaptive beam convergence is shown. From the comparison in Table 1, it can be seen that the MVDR of the weight vector obtained by inverting the covariance matrix after sampling and the LMS algorithm through loop iteration have little difference in convergence speed. However, the DL-MSE algorithm proposed in this paper has a great advantage in convergence speed, indicating that the algorithm of the present invention can be applied in occasions with high real-time requirements.

LMSLMS DL-MSEDL-MSE MVDRMVDR 低信噪比low signal to noise ratio 0.015625s0.015625s 0.005290s0.005290s 0.011544s0.011544s 高信噪比high signal to noise ratio 0.016108s0.016108s 0.005345s0.005345s 0.010175s 0.010175s

表1 各自适应波束权向量形成时间对比Table 1 Time comparison of adaptive beam weight vectors

最后说明的是，以上所述仅为本发明的较佳实例而已，并不用以限制本发明，凡在本发明的精神和原则之内所作的任何修改，等同替换和改进等，均应包含在本发明的保护范围之内。Finally, it is noted that the above descriptions are only preferred examples of the present invention, and are not intended to limit the present invention. Any modifications made within the spirit and principles of the present invention, equivalent replacements and improvements, etc., should be included in the within the protection scope of the present invention.

Claims

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}}_{x x} = (α I + {\hat{R}}_{x x})

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)。