CN104931937A - Submatrix-level orthogonal projection (OP) wave beam forming method based on covariance matrix normalization - Google Patents
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Abstract
Description
技术领域 technical field
本发明涉及阵列信号处理技术领域,具体涉及一种基于协方差矩阵归一化的子阵级正交投影波束形成方法。 The invention relates to the technical field of array signal processing, in particular to a subarray-level orthogonal projection beamforming method based on covariance matrix normalization.
背景技术 Background technique
阵列信号处理是信号处理领域的一个重要分支,它在雷达、声纳、通信、导航、地震监测、语音信号处理以及生物医学工程等得到了广泛的应用。自适应波束形成是阵列信号处理中的一项重要研究内容,其实质就是通过对各阵元自适应加权,进行空域滤波,从而达到增强期望信号、抑制干扰信号和减弱噪声信号的目的。最小方差无失真响应(MVDR)是一种比较常用的算法,它通过在期望信号方向约束阵列增益为1,且使阵列输出功率最小,从而达到抑制干扰的目的。协方差矩阵求逆(SMI)算法是实现MVDR算法的一种常用的方法,但在较低快拍时,此算法的输出SINR(信干噪比)和自适应方向图的收敛速度较慢。 Array signal processing is an important branch in the field of signal processing, and it has been widely used in radar, sonar, communication, navigation, earthquake monitoring, speech signal processing, and biomedical engineering. Adaptive beamforming is an important research content in array signal processing. Its essence is to perform spatial filtering by adaptively weighting each array element, so as to achieve the purpose of enhancing desired signal, suppressing interference signal and weakening noise signal. Minimum Variance Distortionless Response (MVDR) is a commonly used algorithm, which suppresses interference by constraining the array gain to be 1 in the desired signal direction and minimizing the array output power. The covariance matrix inversion (SMI) algorithm is a commonly used method to realize the MVDR algorithm, but the output SINR (signal-to-interference-noise ratio) of this algorithm and the convergence speed of the adaptive pattern are slow at low snapshots.
在实际应用中,综合考虑硬件条件和环境因素,计算自适应权值采用的采样快拍数较少。为了在低快拍情况下,解决SMI算法带来的问题,正交投影(OP)算法得到了广泛的应用,其实质是将静态权矢量投影到干扰子空间的正交补空间(即噪声子空间)上,进而得到自适应权矢量。此算法中,小特征值对应的特征向量并没有参与自适应权矢量的计算,所以在低快拍条件下,此算法可使输出SINR和自适应方向图快速收敛到最优值。但是当OP算法应用到子阵级时,子阵的不均匀划分会造成各子阵噪声输出功率不相等,进而会影响MDL准则估计的准确性,从而导致估计的干扰子空间不准确,造成自适应方向图主瓣变形 且旁瓣升高,输出SINR严重下降。 In practical applications, considering hardware conditions and environmental factors, the number of sampling snapshots used to calculate adaptive weights is relatively small. In order to solve the problems caused by the SMI algorithm in the case of low snapshots, the Orthogonal Projection (OP) algorithm has been widely used. Its essence is to project the static weight vector to the orthogonal complement space of the interference subspace (ie, the noise subspace Space), and then get the adaptive weight vector. In this algorithm, the eigenvector corresponding to the small eigenvalue does not participate in the calculation of the adaptive weight vector, so under the condition of low snapshot, this algorithm can make the output SINR and the adaptive direction map converge to the optimal value quickly. However, when the OP algorithm is applied to the sub-array level, the uneven division of the sub-arrays will cause the noise output power of each sub-array to be unequal, which will affect the accuracy of the MDL criterion estimation, resulting in inaccurate estimated interference subspace, resulting in The main lobe of the adaptive pattern is deformed and the side lobe is increased, and the output SINR is severely reduced.
发明内容 Contents of the invention
有鉴于此,本发明提供了一种基于协方差矩阵归一化的子阵级正交投影波束形成方法,能够有效地抑制干扰,并能使自适应方向图的主瓣保形和旁瓣降低,且能获得较高的输出SINR和较快的收敛速度。 In view of this, the present invention provides a subarray-level orthogonal projection beamforming method based on covariance matrix normalization, which can effectively suppress interference and reduce the shape of the main lobe and side lobe of the adaptive pattern , and can obtain higher output SINR and faster convergence speed.
本发明的基于协方差矩阵归一化的子阵级正交投影波束形成方法,包括如下步骤: The subarray-level orthogonal projection beamforming method based on covariance matrix normalization of the present invention comprises the following steps:
步骤1,对子阵级接收信号进行归一化处理,计算归一化后的干扰加噪声协方差矩阵Rsub_norm:其中,Rin_sub为子阵级的协方差矩阵;TL为归一化矩阵:其中,L为子阵个数,
步骤2,利用MDL准则估计干扰子空间: Step 2, use the MDL criterion to estimate the interference subspace:
步骤2.1,对归一化后的干扰加噪声协方差矩阵Rsub_norm进行特征值分解,获得特征值及其对应的特征向量,并将特征值进行由大到小的排列; Step 2.1, perform eigenvalue decomposition on the normalized interference-plus-noise covariance matrix R sub_norm , obtain the eigenvalues and their corresponding eigenvectors, and arrange the eigenvalues from large to small;
步骤2.2,利用MDL准则估计出干扰信号源的个数为P,则步骤2.1中特征矢量的前P个列向量组成干扰子空间; Step 2.2, using the MDL criterion to estimate the number of interference signal sources as P, then the first P column vectors of the feature vector in step 2.1 form the interference subspace;
步骤3,利用步骤2估计出的干扰子空间,采用正交投影自适应波束形成方法,求解出自适应权矢量; Step 3, using the interference subspace estimated in step 2, using the orthogonal projection adaptive beamforming method to solve the adaptive weight vector;
步骤4,利用步骤3获得的自适应权矢量,对接收的回波数据进行加权处理,获得自适应波束。 In step 4, the adaptive weight vector obtained in step 3 is used to perform weighting processing on the received echo data to obtain an adaptive beam.
有益效果: Beneficial effect:
本发明解决了在子阵划分不均匀且较低采样快拍的情况下,传统的子阵级正交投影算法估计的干扰子空间不准确,造成干扰不能被有效抑制,以及自适应方向图的主瓣变形、旁瓣升高的问题,能够有效地完成子阵级自适应波束形成,在干扰方向自适应的形成零陷,且在有效抑制干扰的同时使得自适应方向图的主瓣保形和旁瓣降低,本发明在自适应波束形成处理之后有较高的输出信干噪比,且输出信干噪比有较快的收敛速度。 The present invention solves the problem of inaccurate interference subspace estimated by the traditional subarray-level orthogonal projection algorithm in the case of uneven division of subarrays and low sampling snapshots, resulting in interference that cannot be effectively suppressed, and the problem of adaptive pattern The problem of main lobe deformation and side lobe elevation can effectively complete subarray-level adaptive beamforming, adaptively form nulls in the interference direction, and keep the main lobe shape of the adaptive pattern while effectively suppressing interference and sidelobe reduction, the present invention has a higher output SINR after adaptive beamforming processing, and the output SINR has a faster convergence speed.
附图说明 Description of drawings
图1为本发明流程图。 Fig. 1 is the flow chart of the present invention.
图2为本发明方法和改进前方法自适应方向图对比图(快拍数为2倍子阵个数时)。 Fig. 2 is a comparison diagram of the adaptive direction diagram between the method of the present invention and the method before improvement (when the number of snapshots is twice the number of sub-arrays).
图3为本发明方法和改进前方法自适应方向图对比图(快拍数为10倍子阵个数时)。 Fig. 3 is a comparison diagram of the adaptive direction diagram between the method of the present invention and the method before improvement (when the number of snapshots is 10 times the number of sub-arrays).
图4为本发明方法与改进前方法输出SINR随快拍数变化曲线对比图。 Fig. 4 is a graph comparing the output SINR curve with the number of snapshots between the method of the present invention and the method before improvement.
图5为本发明方法与改进前方法输出SINR随波束指向变化曲线对比图。 Fig. 5 is a graph comparing the output SINR curves with beam pointing changes between the method of the present invention and the method before improvement.
具体实施方式 Detailed ways
下面结合附图并举实施例,对本发明进行详细描述。 The present invention will be described in detail below with reference to the accompanying drawings and examples.
本发明提供了一种基于协方差矩阵归一化的子阵级正交投影波束形成方 法,首先对子阵级接收信号进行归一化处理,并计算出相应的归一化采样协方差矩阵;然后利用MDL准则估计出干扰信号源个数,进而得到干扰子空间;最后将静态权矢量投影到干扰子空间的正交补空间而得到自适应权矢量。在子阵划分不均匀且较低采样快拍的情况下,本发明能够有效地抑制干扰,并能使自适应方向图的主瓣保形和旁瓣降低,且能获得较高的输出SINR和较快的收敛速度。本发明的流程如图1所示,具体步骤如下: The present invention provides a subarray-level orthogonal projection beamforming method based on covariance matrix normalization. First, the subarray-level received signals are normalized, and the corresponding normalized sampling covariance matrix is calculated. ; Then use the MDL criterion to estimate the number of interference signal sources, and then obtain the interference subspace; finally, project the static weight vector to the orthogonal complement space of the interference subspace to obtain the adaptive weight vector. In the case of uneven division of sub-arrays and low sampling snapshots, the present invention can effectively suppress interference, reduce the shape of the main lobe and side lobes of the adaptive pattern, and obtain higher output SINR and Faster convergence speed. Flow process of the present invention is as shown in Figure 1, and concrete steps are as follows:
步骤一、构造归一化的子阵级协方差矩阵 Step 1. Construct a normalized subarray-level covariance matrix
①信号模型的建立 ①Establishment of signal model
假设一个窄带线阵,共N个阵元,阵元为各向同性,P个干扰信号,干扰信号均为远场窄带信号,假设各阵元噪声是相互独立、功率相等的空时白噪声并且干扰信号和噪声互不相关。则阵列接收到的信号模型可表示为 Assume a narrowband linear array with a total of N array elements, the array elements are isotropic, and P interference signals, all of which are far-field narrowband signals, assuming that the noise of each array element is a space-time white noise with independent power and equal power and The interfering signal and the noise are not correlated with each other. Then the signal model received by the array can be expressed as
Xin(t)=AS(t)+N(t) (1) X in (t) = AS (t) + N (t) (1)
式中,A=[a(θ1),a(θ2),…a(θP)]为阵列流型矩阵,a(θi)(i=1,2,…P)为干扰信号的导向矢量,设第n个阵元与参考点的间距为dn(n=0,1,2,…,N-1),通常以第0个阵元为参考点,此时d0=0,λ为波长,则θi(i=1,2,…P)为干扰信号的入射角度,[·]T为矩阵转置,S(t)=[S1(t),S2(t),…Sp(t)]T,Si(t)(i=1,2,…P)为第i个干扰信号的复包络,N(t)=[n1(t),n2(t),…,nN(t)]为背景白噪声。 In the formula, A=[a(θ 1 ), a(θ 2 ),…a(θ P )] is the array flow pattern matrix, a(θ i )(i=1,2,…P) is the interference signal Steering vector, set the distance between the nth array element and the reference point as d n (n=0,1,2,…,N-1), usually take the 0th array element as the reference point, at this time d 0 =0 , λ is the wavelength, then θ i (i=1,2,...P) is the incident angle of the interference signal, [·] T is the matrix transpose, S(t)=[S 1 (t),S 2 (t),...S p ( t)] T , S i (t) (i=1,2,…P) is the complex envelope of the i-th interference signal, N(t)=[n 1 (t),n 2 (t),… ,n N (t)] is background white noise.
从而得到阵列协方差矩阵为 Thus, the array covariance matrix is obtained as
Rin=E{Xin(t)Xin H(t)} (2) R in =E{X in (t)X in H (t)} (2)
式中,E{·}表示数学期望,(·)H表示复共轭转置。 In the formula, E{·} represents the mathematical expectation, and (·) H represents the complex conjugate transpose.
实际应用中,根据最大似然估计准则,由有限快拍数据Xin(ti)来估计阵列协方差矩阵,得 In practical applications, according to the maximum likelihood estimation criterion, the array covariance matrix is estimated from the finite snapshot data X in (t i ), and we get
式中,Xin(ti)为i(i=1,2,…,K)时刻阵列的采样值,K为采样快拍数。 In the formula, X in (t i ) is the sampling value of the array at time i (i=1,2,...,K), and K is the number of sampling snapshots.
在子阵级处理时,将阵列划分为L个子阵,且(L≥P+1),可以是非重叠子阵或重叠子阵,子阵转换矩阵可表示为 When processing at the sub-array level, the array is divided into L sub-arrays, and (L≥P+1), can be non-overlapping sub-arrays or overlapping sub-arrays, and the sub-array conversion matrix can be expressed as
T=φ0WT0 (4) T=φ 0 WT 0 (4)
其中表示移相器的作用,设波束指向与期望信号方向相同;W=diag(wn)n=0,1,…,N-1,其中wn为第n个阵元的加权系数,用于抑制方向图的旁瓣电平;T0为N×L的子阵形成矩阵,在其第l(l=0,1,…,L-1)列的所有元素中,只有与第l个子阵的阵元序号相对应的元素值为1,其余均为0(在非重叠子阵的情况下,T0的列向量相互正交)。 in Indicates the role of the phase shifter, assuming that the beam is directed in the same direction as the desired signal; W=diag(w n ) n=0,1,…,N-1 , where w n is the weighting coefficient of the nth array element, used for Suppress the side lobe level of the pattern; T 0 is a matrix of N×L sub-arrays, and among all the elements in the lth (l=0,1,...,L-1) column, only the lth sub-array The value of the element corresponding to the array element number of is 1, and the rest are all 0 (in the case of non-overlapping sub-arrays, the column vectors of T 0 are mutually orthogonal).
则子阵级上接收的采样快拍信号为 Then the sampling snapshot signal received at the sub-array level is
Xin_sub(t)=THXin(t) (5) X in_sub (t) = T H X in (t) (5)
则子阵级的协方差矩阵为 Then the covariance matrix of the subarray level is
②协方差矩阵的归一化 ②Normalization of the covariance matrix
首先对各子阵输出进行归一化,归一化通过矩阵TL完成 First, the output of each sub-array is normalized, and the normalization is completed by the matrix T L
其中 in
U=N0+N1+…+Nl-1-J0-J1-…-Jl-1+1 U=N 0 +N 1 +...+N l-1 -J 0 -J 1 -...-J l-1 +1
Q=N0+N1+…+Nl-J0-J1-…-Jl-1 Q=N 0 +N 1 +...+N l -J 0 -J 1 -...-J l-1
Ni为第i(0≤i≤L-1)个子阵包含的阵元数,Ji为第i(0≤i≤L-2)个子阵的和第i+1个子阵的重叠阵元数。 N i is the number of array elements contained in the i-th (0≤i≤L-1) sub-array, and J i is the overlapping array elements of the i-th (0≤i≤L-2) sub-array and the i+1-th sub-array number.
归一化后的干扰加噪声协方差矩阵为 The normalized interference plus noise covariance matrix is
通过归一化处理,使得每个子阵的噪声功率一致,从而使得MDL准则能够适用。 Through normalization, the noise power of each sub-array is consistent, so that the MDL criterion can be applied.
步骤二、估计干扰子空间 Step 2. Estimate the interference subspace
对归一化的协方差矩阵Rsub_norm进行特征值分解 Eigenvalue decomposition of the normalized covariance matrix R sub_norm
式中,λi(i=1,2,…,L)为协方差矩阵Rsub_norm的特征值,为与特征值λi对应的特征向量,λi由大到小排列 In the formula, λ i (i=1,2,...,L) is the eigenvalue of the covariance matrix R sub_norm , is the eigenvector corresponding to the eigenvalue λ i , and λ i is arranged from large to small
利用MDL准则估计出干扰信号源的个数,进而估计出干扰子空间。 The MDL criterion is used to estimate the number of interference signal sources, and then the interference subspace is estimated.
MDL准则的函数为 The function of the MDL criterion is
其中 in
由MDL准则可知,当d的数值变化时,当式(11)取最小值时对应的d的值即为干扰信号源的个数P,选取特征矢量的前P个列向量组成干扰子空 间Us,即由数学知识可知矢量与矢量a(θ1),a(θ2),…,a(θp)张成同一个矢量空间,即: According to the MDL criterion, when the value of d changes, the value of d corresponding to the minimum value of formula (11) is the number P of interference signal sources, and the feature vector is selected The first P column vectors form the interference subspace U s , namely It can be known from mathematical knowledge that the vector and vector a(θ 1 ), a(θ 2 ),…,a(θ p ) form the same vector space, namely:
其中,span{·}表示矢量张成的空间,即为干扰子空间的估计。 Among them, span{ } represents the space formed by the vector, is the estimate of the interference subspace.
步骤三、求解改进算法的自适应权矢量 Step 3: Solve the adaptive weight vector of the improved algorithm
利用步骤二估计出的干扰子空间,采用正交投影自适应波束形成方法,求解出改进算法的自适应权矢量。 Using the interference subspace estimated in step 2, the adaptive weight vector of the improved algorithm is solved by using the orthogonal projection adaptive beamforming method.
采用传统正交投算法的思想,将静态权矢量wq_sub向步骤二中估计出的干扰子空间Us的正交补空间投影,得到改进算法的自适应权矢量为 Using the idea of the traditional orthogonal projection algorithm, the static weight vector w q_sub is projected to the orthogonal complement space of the interference subspace U s estimated in step 2, and the adaptive weight vector of the improved algorithm is obtained as
式中,I为L×L维单位矩阵,η为一常数,wq_sub为静态权矢量,且各元素均为1的L维列向量,的作用是使天线主波束方向的增益保持不变。 In the formula, I is an L×L-dimensional unit matrix, η is a constant, w q_sub is a static weight vector, and each element is an L-dimensional column vector of 1, The effect of is to keep the gain in the main beam direction of the antenna unchanged.
步骤四,对接收到的回波进行自适应波束形成 Step 4: Perform adaptive beamforming on the received echoes
在得到自适应权矢量之后,可对接收的回波数据进行加权处理: After getting the adaptive weight vector, the received echo data can be weighted:
Y=WHX(t) (13) Y =WHX(t) (13)
式中,X(t)为接收的回波信号,从而有效地去除了干扰和减弱噪声,且增强期望信号。 In the formula, X(t) is the received echo signal, which effectively removes the interference and weakens the noise, and enhances the desired signal.
自此,就完成了一种基于协方差矩阵归一化的子阵级正交投影子自适应波束形成方法对回波数据的处理。 Since then, a sub-array-level orthogonal projection sub-adaptive beamforming method based on covariance matrix normalization has been completed to process the echo data.
为了验证本发明提出的一种基于协方差矩阵归一化的子阵级正交投影自适 应波束形成方法,进行自适应波束方向图及输出信干噪比(SINR)的仿真,仿真采用窄带均匀线阵,仿真参数如表1所示。改进前算法是子阵级的采样快拍信号直接采用正交投影(OP)算法计算自适应权矢量。 In order to verify a subarray-level orthogonal projection adaptive beamforming method based on covariance matrix normalization proposed by the present invention, carry out the simulation of adaptive beam pattern and output signal-to-interference-noise ratio (SINR), and the simulation adopts narrowband Uniform linear array, the simulation parameters are shown in Table 1. Before the improvement, the algorithm uses the orthogonal projection (OP) algorithm to calculate the adaptive weight vector directly from the sub-array-level sampling snapshot signal.
表1 仿真参数设置 Table 1 Simulation parameter settings
图2和图3是本发明改进算法与改进前算法的自适应波束方向图的比较(仿真1次),采样快拍数分别为20和100,波束指向角度均为0°,可以看出,改进前算法得到的自适应波束方向图主瓣变形且旁瓣电平严重升高;改进后算法得到的自适应波束方向图主瓣保形且旁瓣电平较低,接近于静态波束方向图,性能较改进前大大地提高。 Fig. 2 and Fig. 3 are the comparison (simulation 1 time) of the self-adaptive beam pattern of the improved algorithm of the present invention and the improved algorithm, and the number of sampling snapshots is respectively 20 and 100, and the beam pointing angle is 0°, as can be seen, The main lobe of the adaptive beam pattern obtained by the improved algorithm is deformed and the side lobe level is seriously increased; the main lobe of the adaptive beam pattern obtained by the improved algorithm is conformal and the side lobe level is low, which is close to the static beam pattern , the performance is greatly improved than before.
图4是在不同采样快拍条件下,期望信号角度为0°,输入信噪比为0dB,其它仿真条件同图2,本发明改进算法以及改进前算法的输出信干噪比(SINR)的比较。由仿真结果可知,改进后算法的输出SINR较高,且收敛很快;而改进前算法的输出SINR较低,收敛较慢,且随着快拍数的增加,输出SINR有所下降,因为采样快拍数越高,估计的干扰子空间的精确度降低,干扰不能被有效 抑制,导致输出的SINR会严重下降。 Fig. 4 is under different sampling snapshot conditions, the expected signal angle is 0 °, the input signal-to-noise ratio is 0dB, other simulation conditions are the same as Fig. 2, the improved algorithm of the present invention and the output signal-to-interference-noise ratio (SINR) of the improved algorithm Compare. It can be seen from the simulation results that the output SINR of the improved algorithm is higher and the convergence is fast; while the output SINR of the improved algorithm is lower and the convergence is slower, and as the number of snapshots increases, the output SINR decreases, because the sampling The higher the number of snapshots, the lower the accuracy of the estimated interference subspace, and the interference cannot be effectively suppressed, resulting in a severe drop in the output SINR.
图5是在不同波束指向角度时,本发明改进算法以及改进前算法的输出信干噪比(SINR)的比较,输入信噪比为0dB,其它仿真条件同图2,可以看出改进后算法能有效地抑制干扰,且输出的SINR较高。 Figure 5 is a comparison of the improved algorithm of the present invention and the output signal-to-interference-noise ratio (SINR) of the improved algorithm at different beam pointing angles, the input signal-to-noise ratio is 0dB, and other simulation conditions are the same as in Figure 2, and it can be seen that the improved algorithm Can effectively suppress interference, and the output SINR is high.
从图2~图5可以得到,本发明改进算法能够增强期望信号,具有良好的抗干扰性能,是一种稳健的子阵级自适应波束形成算法。 It can be seen from FIG. 2 to FIG. 5 that the improved algorithm of the present invention can enhance the desired signal, has good anti-interference performance, and is a robust subarray-level adaptive beamforming algorithm.
综上所述,以上仅为本发明的较佳实施例而已,并非用于限定本发明的保护范围。凡在本发明的精神和原则之内,所作的任何修改、等同替换、改进等,均应包含在本发明的保护范围之内。 To sum up, the above are only preferred embodiments of the present invention, and are not intended to limit the protection scope of the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention shall be included within the protection scope of the present invention.
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