CN104408278A

CN104408278A - A method for forming steady beam based on interfering noise covariance matrix estimation

Info

Publication number: CN104408278A
Application number: CN201410525604.8A
Authority: CN
Inventors: 徐定杰; 刘向锋; 韩浩; 桑静; 周阳; 兰晓明; 迟晓彤; 张金丽; 李伟东
Original assignee: Harbin Engineering University
Current assignee: Harbin Engineering University
Priority date: 2014-10-09
Filing date: 2014-10-09
Publication date: 2015-03-11

Abstract

The present invention relates to the field of self-adaption beam forming during array signal processing, in particular, relates to a method for forming a steady beam based on an interfering noise covariance matrix estimation. The present invention includes using an antenna array to receive a distant field narrowband incident signal, using a limited snapshot number to estimate the covariance matrix for receiving data, then performing characteristic decomposition on the covariance matrix for receiving data, wherein prior information of the number of an incident signal source can be obtained via a method of estimating the number of the signal source; optimally obtaining a more accurate desired signal steering vector at a projection of a noise subspace according to an estimated desired signal steering vector, and performing estimation obtaining of the interfering noise covariance matrix according to interference signal steering vector prior information and an estimated noise power so as to perform beam forming. The present invention first performs the interfering noise covariance matrix estimation to get rid of the component of the desired signal in the training data, which can avoid the generation of signal cancellation.

Description

A Robust Beamforming Method Based on Interference Noise Covariance Matrix Estimation

技术领域technical field

本发明涉及阵列信号处理中自适应波束形成领域，具体涉及一种基于干扰噪声协方差矩阵估计的稳健波束形成方法。The invention relates to the field of adaptive beamforming in array signal processing, in particular to a robust beamforming method based on interference noise covariance matrix estimation.

背景技术Background technique

上世纪六七十年代以来，研究人员开始将一维信号处理逐渐延伸到多维信号处理领域，开辟了阵列信号处理这一新的重要研究领域。阵列信号处理是将几个或者几十个传感器依照一定的组合方式在空间不同位置排成传感器阵列，利用它对空间信号进行接收处理，提取出有用信号的信号特征，分析信号中包含的信息。与单个传感器接收信号的一维信号处理相比，传感器阵列具有灵活的波束控制、较高的处理增益、极强的干扰抑制和较高的空间分辨力等优点。因而最近几十年阵列信号得到飞速的发展，目前阵列信号处理已经成为信号处理领域极为重要的一个分支，广泛应用于雷达、声纳、通信、地震勘测、机电测量、射电天文以及医学诊断等多种国民经济和军事应用领域。Since the 1960s and 1970s, researchers began to gradually extend one-dimensional signal processing to the field of multi-dimensional signal processing, opening up a new important research field of array signal processing. Array signal processing is to arrange several or dozens of sensors into a sensor array at different positions in space according to a certain combination method, use it to receive and process spatial signals, extract signal features of useful signals, and analyze the information contained in the signals. Compared with the one-dimensional signal processing of the signal received by a single sensor, the sensor array has the advantages of flexible beam steering, high processing gain, strong interference suppression and high spatial resolution. Therefore, array signals have developed rapidly in recent decades. At present, array signal processing has become an extremely important branch in the field of signal processing, and is widely used in radar, sonar, communication, seismic survey, electromechanical measurement, radio astronomy, and medical diagnosis. A variety of national economy and military applications.

Capon(Minimum Variance Distortionless Respons，MVDR)波束形成算法使得期望信号无失真通过，同时对于噪声和干扰具有较好抑制作用的自适应阵列信号处理技术。在实际应用中，常常采用阵列接收信号协方差求逆的方法来构造MVDR，此方法在接收信号不包含期望信号时性能较好。然而在实际应用中，期望信号往往包含在阵列接收信号中，同时传播过程中波形变化失真、阵元位置误差、信号波达角(Direction of Arrive)估计误差、阵元不一致性等误差将导致期望信号导向矢量出现误差。Capon波束形成算法对于导向矢量误差非常敏感，此时期望信号将被当成干扰进行抑制，产生期望信号相消，造成性能的急剧下降。因此稳健的波束形成方法是学者的研究热点之一。The Capon (Minimum Variance Distortionless Respons, MVDR) beamforming algorithm enables the desired signal to pass through without distortion, and is an adaptive array signal processing technology that has a good suppression effect on noise and interference. In practical applications, the method of inverting the covariance of the array received signal is often used to construct the MVDR. This method has better performance when the received signal does not contain the desired signal. However, in practical applications, the desired signal is often included in the received signal of the array. At the same time, errors such as waveform distortion, array element position error, signal direction of arrival (Direction of Arrive) estimation error, and array element inconsistency will lead to the expected Error in signal steering vector. The Capon beamforming algorithm is very sensitive to the steering vector error. At this time, the desired signal will be suppressed as interference, resulting in the cancellation of the desired signal, resulting in a sharp decline in performance. Therefore, the robust beamforming method is one of the research hotspots of scholars.

发明内容Contents of the invention

本发明的目的在于提供一种避免信号相消，提供更稳健波束的一种基于干扰噪声协方差矩阵估计的稳健波束形成方法。The purpose of the present invention is to provide a robust beamforming method based on interference noise covariance matrix estimation which avoids signal cancellation and provides more robust beams.

本发明的目的是这样实现的：The purpose of the present invention is achieved like this:

(1)利用天线阵列接收远场窄带入射信号，取有限快拍数进行对接收数据协方差矩阵进行估计,然后对接收数据协方差矩阵进行特征分解，依据入射信号源数目的先验信息获取噪声子空间U_n及估计噪声功率入射信号源数目的先验信息可以由信号源数目估计方法获得，传感器阵列是由N个阵元组成的理想均匀等距线阵，远场空间目标期望信号和P个干扰信号，信号与干扰、干扰与干扰之间互不相关，各通道噪声为互相独立的零均值高斯白噪声，与信号、干扰均不相关，阵列模型，N×1维的阵列接收信号x(t)为：(1) Use the antenna array to receive far-field narrow-band incident signals, take a limited number of snapshots to estimate the covariance matrix of the received data, and then perform eigendecomposition on the covariance matrix of the received data, and obtain noise based on the prior information of the number of incident signal sources Subspace U _n and estimated noise power The prior information of the number of incident signal sources can be obtained by the method of estimating the number of signal sources. The sensor array is an ideal uniform equidistant linear array composed of N array elements, the desired signal of the far-field space target and P interference signals. The signal and interference, Interference and interference are not correlated with each other. The noise of each channel is independent zero-mean Gaussian white noise, which is uncorrelated with signal and interference. The array model, N×1-dimensional array received signal x(t) is:

$\begin{matrix} x x ((t t)) = = {Σ Σ}_{m m = = 00}^{P P} a a (({θ θ}_{m m})) {s the s}_{m m} ((t t)) + + n no ((t t)) \\ = = a a (({θ θ}_{00})) {s the s}_{00} ((t t)) + + {A A}_{I I} {S S}_{I I} ((t t)) + + n no ((t t)) \end{matrix};;$

θ_m,m＝1,2,…,P为干扰信号波达角方向，θ₀为期望信号波达角方向,a(θ_m),m＝0,1,2,…,P表示期望信号、干扰信号的导向矢量，a(θ₀)为期望信号导向矢量,s₀(t)为期望信号复包络,A_I＝[a(θ₁),a(θ₂),…,a(θ_P)]为干扰信号导向矢量组成的阵列流型,S_I(t)＝[s₁(t),s₂(t),…,s_P(t)]^T为干扰信号复包络，n(t)＝[n₁(t),n₂(t),…,n_N(t)]^T是高斯白噪声。(·)^T表示转置运算，阵列接收信号的协方差矩阵R为：θ _m ,m=1,2,...,P is the direction of the angle of arrival of the interference signal, θ ₀ is the direction of the angle of arrival of the desired signal, a(θ _m ),m=0,1,2,...,P represents the direction of the desired signal , the steering vector of the interference signal, a(θ ₀ ) is the steering vector of the desired signal, s ₀ (t) is the complex envelope of the desired signal, A _I =[a(θ ₁ ),a(θ ₂ ),…,a( θ _P )] is the array flow pattern composed of the steering vector of the interference signal, S _I (t)=[s ₁ (t),s ₂ (t),…,s _P (t)] ^T is the complex envelope of the interference signal, n(t)=[n ₁ (t), n ₂ (t), . . . , n _N (t)] ^T is Gaussian white noise. (·) ^T represents the transpose operation, and the covariance matrix R of the array received signal is:

$\begin{matrix} R R = = {R R}_{s the s} + + {R R}_{i i + + n no} = = {σ σ}_{00}^{22} a a (({θ θ}_{00})) {a a}^{H h} (({θ θ}_{00})) + + \\ {Σ Σ}_{k k = = 11}^{P P} {σ σ}_{k k}^{22} a a (({θ θ}_{k k})) {a a}^{H h} (({θ θ}_{k k})) + + {σ σ}_{n no}^{22} I I \end{matrix};;$

R_s和R_i+n分别为期望信号协方差矩阵和干扰噪声协方差矩阵，分别表示期望信号、P个干扰信号和空间白噪声信号的功率，I表示单位矩阵，(·)^H表示复共轭转置运算，通过有限的快拍数据估算接收信号数据协方差矩阵：R _s and R _i+n are the desired signal covariance matrix and interference noise covariance matrix respectively, Represent the power of the desired signal, P interference signals and spatial white noise signal respectively, I represents the identity matrix, (·) ^H represents the complex conjugate transpose operation, and the covariance matrix of the received signal data is estimated by the limited snapshot data:

$\overset{^^}{R R} = = \frac{11}{L L} {Σ Σ}_{k k = = 11}^{L L} {x x}_{k k} ((t t)) {x x}_{k k}^{H h} ((t t));;$

L表示快拍数，x_k(t)表示第k个快拍；L represents the number of snapshots, x _k (t) represents the kth snapshot;

信号源数目P+1<N，对进行特征分解，依据入射信号源数目可知：The number of signal sources P+1<N, for Carry out eigendecomposition, according to the number of incident signal sources:

$\overset{^^}{R R} = = {Σ Σ}_{i i = = 11}^{N N} {λ λ}_{i i} {u u}_{i i} {u u}_{i i}^{H h} = = {U u}_{s the s} {λ λ}_{s the s} {U u}_{s the s}^{H h} + + {U u}_{n no} {λ λ}_{n no} {U u}_{n no}^{H h};;$

其中是N个特征值，u_i,i＝1,2,…,N是其对应的特征向量，λ_s＝diag{λ₁,λ₂,…,λ_P+1}和λ_n＝diag{λ_P+2,λ_P+3,…,λ_N}分别表示较大特征值、较小特征值组成对角矩阵，U_s和U_n则分别表示信号干扰子空间和噪声子空间；in are N eigenvalues, u _i , i=1,2,…, N are their corresponding eigenvectors, λ _s =diag{λ ₁ ,λ ₂ ,…,λ _P+1 } and λ _n =diag{λ _P+2 ,λ _P+3 ,…,λ _N } respectively represent the larger eigenvalues and smaller eigenvalues to form a diagonal matrix, U _s and U _n represent the signal interference subspace and noise subspace respectively;

可以由接收信号协方差矩阵特征分解对应的小特征值取均值估计获得，即 It can be obtained by taking the mean value estimation of the small eigenvalues corresponding to the eigendecomposition of the covariance matrix of the received signal, namely

${σ σ}_{n no}^{22} = = {\overset{^^}{σ σ}}_{n no}^{22} = = \frac{11}{N N - - P P - - 11} {Σ Σ}_{i i = = P P + + 22}^{N N} {λ λ}_{i i};;$

(2)将期望信号导向矢量误差约束于球形不确定集中，依据估计的期望信号导向矢量在噪声子空间U_n的投影最优获取更为准确的期望信号导向矢量真实期望信号导向矢量与U_s展成同一子空间，由于U_s与U_n正交，则期望信号导向矢量与噪声子空间正交：(2) Constrain the error of the desired signal steering vector to a spherical uncertainty set, according to the estimated desired signal steering vector Optimal projection of the noise subspace U _n to obtain a more accurate steering vector of the desired signal The true desired signal steering vector and U _s expand into the same subspace, since U _s is orthogonal to U _n , the desired signal steering vector is orthogonal to the noise subspace:

${u u}_{i i}^{H h} a a (({θ θ}_{00})) = = 00,, i i = = P P + + 22,, P P + + 33,, . . . . . .,, N N,,$

${| | | | {U u}_{n no}^{H h} a a (({θ θ}_{00})) | | | |}_{22}^{22} = = {a a}^{H h} (({θ θ}_{00})) {U u}_{n no} {U u}_{n no}^{H h} a a (({θ θ}_{00})) = = 00,,$

期望信号导向矢量a(θ₀)具有估计误差，估计的期望信号导向矢量在噪声子空间中留有余量：The desired signal steering vector a(θ ₀ ) has an estimation error, the estimated desired signal steering vector Leave a margin in the noise subspace:

${| | | | {U u}_{n no}^{H h} \overset{^^}{a a} (({θ θ}_{00})) | | | |}_{22}^{22} &GreaterEqual; &Greater Equal; {| | | | {U u}_{n no}^{H h} a a (({θ θ}_{00})) | | | |}_{22}^{22} = = 00,,$

当与a(θ₀)相等时等号成立when The equality sign is established when it is equal to a(θ ₀ )

$\underset{a a}{min min} {| | | | {U u}_{n no}^{H h} a a | | | |}_{22}^{22} = = {| | | | {U u}_{n no}^{H h} a a (({θ θ}_{00})) | | | |}_{22}^{22} = = 00,,$

将期望信号导向矢量误差约束于球形不确定集中，可得基于球形不确定集的稳健波束：Constraining the steering vector error of the desired signal to the spherical uncertainty set, a robust beam based on the spherical uncertainty set can be obtained:

$\underset{a a}{min min} {| | | | {U u}_{n no}^{H h} a a | | | |}_{22}^{22} s the s . . t t . . {| | | | a a - - \overset{^^}{a a} (({θ θ}_{00})) | | | |}_{22}^{22} \leq \leq ϵ ϵ;;$

ε是球形不确定集的边界，进行求解得到最优的导向矢量 ε is the boundary of the spherical uncertain set, and the optimal steering vector is obtained by solving

(3)依据干扰信号导向矢量先验信息及估计的噪声功率进行干扰噪声协方差矩阵估计得到干扰信号导向矢量先验信息由谱估计方法及阵列模型获得，(3) According to the prior information of the interference signal steering vector and the estimated noise power Estimate the interference noise covariance matrix to get The prior information of the steering vector of the interference signal is obtained by the spectrum estimation method and the array model,

Capon波束形成器的功率谱为：The power spectrum of the Capon beamformer is:

$p p = = \frac{11}{{a a}^{H h} ((θ θ)) {R R}^{- - 11} a a ((θ θ))};;$

噪声为独立的高斯白噪声，干扰信号导向矢量先验信息已知，则干扰噪声协方差矩阵为：The noise is independent Gaussian white noise, and the prior information of the steering vector of the interference signal is known, then the interference noise covariance matrix for:

${\overset{^^}{R R}}_{i i + + n no} = = {Σ Σ}_{k k = = 11}^{P P} \frac{a a (({θ θ}_{k k})) {a a}^{H h} (({θ θ}_{k k}))}{{a a}^{H h} (({θ θ}_{k k})) {R R}^{- - 11} a a (({θ θ}_{k k}))} + + {\overset{^^}{σ σ}}_{n no}^{22} I I;;$

(4)计算最优权矢量w_opt，进行波束形成，(4) Calculate the optimal weight vector w _opt to perform beamforming,

最优权矢量：Best weight vector:

${w w}_{opt opt} = = \frac{{\overset{^^}{R R}}_{i i + + n no}^{- - 11} \overset{&OverBar; &OverBar;}{a a} (({θ θ}_{00}))}{{\overset{&OverBar; &OverBar;}{a a}}^{H h} (({θ θ}_{00})) {\overset{^^}{R R}}_{i i + + n no}^{- - 11} \overset{&OverBar; &OverBar;}{a a} (({θ θ}_{00}))};;$

则天线阵列输出即波束形成为：Then the antenna array output, i.e. beamforming, is:

$y the y = = {w w}_{opt opt}^{H h} x x ((t t)) . .$

本发明的有益效果在于：The beneficial effects of the present invention are:

(1)本发明首先进行了干扰噪声协方差矩阵估计，去除了训练数据中的期望信号成分，能够避免产生信号相消。(1) The present invention first estimates the interference noise covariance matrix, removes the expected signal components in the training data, and can avoid signal cancellation.

(2)本发明基于期望信号导向矢量在噪声子空间投影最优获取更为准确的导向矢量，因此对于期望信号导向矢量失配具有很强的稳健性，且阵列方向图能够指向正确的期望信号来向。(2) The present invention is based on the optimal projection of the desired signal steering vector in the noise subspace to obtain a more accurate steering vector, so it has strong robustness to the mismatch of the desired signal steering vector, and the array pattern can point to the correct desired signal where to go.

(3)本发明具有较高的阵列输出信干噪比，且在较高输入信噪比时阵列输出性能下降不明显。(3) The present invention has a relatively high array output signal-to-interference-noise ratio, and the performance degradation of the array output is not obvious when the input signal-to-noise ratio is relatively high.

附图说明Description of drawings

图1均匀线阵模型；Figure 1 uniform linear array model;

图2本发明算法流程图；Fig. 2 algorithm flowchart of the present invention;

图3本发明算法效果图。Fig. 3 is the effect diagram of the algorithm of the present invention.

具体实施方式Detailed ways

下面结合附图对本发明做进一步描述。The present invention will be further described below in conjunction with the accompanying drawings.

为了避免信号相消，本发明提出了一种基于干扰噪声协方差矩阵估计的稳健自适应波束形成方法。该方法针对入射信号为远场窄带互相独立信号，噪声为高斯白噪声的情况，需要知道入射信号源数目与入射信号的导向矢量等先验信息，具体的步骤如下：In order to avoid signal cancellation, the present invention proposes a robust adaptive beamforming method based on interference noise covariance matrix estimation. For the case where the incident signal is a far-field narrow-band independent signal and the noise is Gaussian white noise, the method needs to know prior information such as the number of incident signal sources and the steering vector of the incident signal. The specific steps are as follows:

步骤1：利用天线阵列接收远场窄带入射信号，取有限快拍数进行对接收数据协方差矩阵进行估计,然后对接收数据协方差矩阵进行特征分解，依据入射信号源数目的先验信息获取噪声子空间U_n及估计噪声功率入射信号源数目的先验信息可以由信号源数目估计方法获得。Step 1: Use the antenna array to receive the far-field narrow-band incident signal, take a limited number of snapshots to estimate the covariance matrix of the received data, and then perform eigendecomposition on the covariance matrix of the received data, and obtain the noise based on the prior information of the number of incident signal sources Subspace U _n and estimated noise power The prior information of the number of incident signal sources can be obtained by the method of estimating the number of signal sources.

步骤2：将期望信号导向矢量误差约束于球形不确定集中，依据估计的期望信号导向矢量在噪声子空间U_n的投影最优获取更为准确的期望信号导向矢量 Step 2: Constrain the desired signal steering vector error to a spherical uncertainty set, according to the estimated desired signal steering vector Optimal projection of the noise subspace U _n to obtain a more accurate steering vector of the desired signal

步骤3：依据干扰信号导向矢量先验信息及估计的噪声功率进行干扰噪声协方差矩阵估计得到干扰信号导向矢量先验信息可以由谱估计方法及阵列模型获得。Step 3: According to the prior information of the interference signal steering vector and the estimated noise power Estimate the interference noise covariance matrix to get The prior information of the interference signal steering vector can be obtained by spectrum estimation method and array model.

步骤4：按照MVDR波束形成方法计算最优权矢量w_opt，然后进行波束形成。Step 4: Calculate the optimal weight vector w _opt according to the MVDR beamforming method, and then perform beamforming.

本发明描述的方法是一种基于干扰噪声协方差矩阵估计的稳健波束形成方法，与常规波束形成方法相比，对于期望信号导向矢量失配具有稳健性，且能够避免信号相消现象的产生。The method described in the invention is a robust beamforming method based on interference noise covariance matrix estimation. Compared with the conventional beamforming method, it is robust to the mismatch of the steering vector of the desired signal and can avoid the generation of signal cancellation.

具体步骤如下：Specific steps are as follows:

考虑传感器阵列是由N个阵元组成的理想均匀等距线阵，远场空间存在一个目标期望信号和P个干扰信号，信号与干扰、干扰与干扰之间互不相关。各通道噪声为互相独立的零均值高斯白噪声，与信号、干扰均不相关。阵列模型由图1所示。N×1维的阵列接收信号x(t)可以表示为：Considering that the sensor array is an ideal uniform equidistant linear array composed of N array elements, there is a target desired signal and P interference signals in the far-field space, and there is no correlation between signal and interference, interference and interference. The noise of each channel is independent zero-mean Gaussian white noise, which is not related to signal and interference. The array model is shown in Figure 1. The N×1-dimensional array received signal x(t) can be expressed as:

$\begin{matrix} x x ((t t)) = = {Σ Σ}_{m m = = 00}^{P P} a a (({θ θ}_{m m})) {s the s}_{m m} ((t t)) + + n no ((t t)) \\ = = a a (({θ θ}_{00})) {s the s}_{00} ((t t)) + + {A A}_{I I} {S S}_{I I} ((t t)) + + n no ((t t)) \end{matrix} - - - - - - ((11))$

式中：θ_m,m＝1,2,…,P为干扰信号波达角方向，θ₀为期望信号波达角方向,a(θ_m),m＝0,1,2,…,P表示期望信号、干扰信号的导向矢量，a(θ₀)为期望信号导向矢量,s₀(t)为期望信号复包In the formula: θ _m ,m=1,2,...,P is the direction of the angle of arrival of the interference signal, θ ₀ is the direction of the angle of arrival of the desired signal, a(θ _m ),m=0,1,2,...,P Indicates the steering vector of the desired signal and the interference signal, a(θ ₀ ) is the steering vector of the desired signal, s ₀ (t) is the complex packet of the desired signal

络,A_I＝[a(θ₁),a(θ₂),…,a(θ_P)]为干扰信号导向矢量组成的阵列流型,S_I(t)＝[s₁(t),s₂(t),…,s_P(t)]^T为干扰信号复包络，n(t)＝[n₁(t),n₂(t),…,n_N(t)]^T是高斯白噪声。(·)^T表示转置运算。那么阵列接收信号的协方差矩阵R为：network, A _I = [a(θ ₁ ), a(θ ₂ ),…, a(θ _P )] is the array flow pattern composed of interference signal steering vectors, S _I (t) = [s ₁ (t), s ₂ (t),…,s _P (t)] ^T is the complex envelope of the interference signal, n(t)=[n ₁ (t),n ₂ (t),…,n _N (t)] ^T is Gaussian white noise. (·) ^T represents the transpose operation. Then the covariance matrix R of the array received signal is:

$\begin{matrix} R R = = {R R}_{s the s} + + {R R}_{i i + + n no} = = {σ σ}_{00}^{22} a a (({θ θ}_{00})) {a a}^{H h} (({θ θ}_{00})) + + \\ {Σ Σ}_{k k = = 11}^{P P} {σ σ}_{k k}^{22} a a (({θ θ}_{k k})) {a a}^{H h} (({θ θ}_{k k})) + + {σ σ}_{n no}^{22} I I \end{matrix} - - - - - - ((22))$

式中：R_s和R_i+n分别为期望信号协方差矩阵和干扰噪声协方差矩阵。分别表示期望信号、P个干扰信号和空间白噪声信号的功率。I表示单位矩阵，(·)^H表示复共轭转置运算。在实际应用中，常常通过有限的快拍数据估算接收信号数据协方差矩阵，即：In the formula: R _s and R _i+n are the desired signal covariance matrix and interference noise covariance matrix respectively. Denote the power of the desired signal, the P interference signals and the spatial white noise signal, respectively. I represents the identity matrix, and (·) ^H represents the complex conjugate transpose operation. In practical applications, the covariance matrix of received signal data is often estimated through limited snapshot data, namely:

$\overset{^^}{R R} = = \frac{11}{L L} {Σ Σ}_{k k = = 11}^{L L} {x x}_{k k} ((t t)) {x x}_{k k}^{H h} ((t t)) - - - - - - ((33))$

式中：L表示快拍数，x_k(t)表示第k个快拍。In the formula: L represents the number of snapshots, and x _k (t) represents the kth snapshot.

假设信号源数目P+1<N，对进行特征分解，依据入射信号源数目可知：Assuming that the number of signal sources P+1<N, for Carry out eigendecomposition, according to the number of incident signal sources:

$\overset{^^}{R R} = = {Σ Σ}_{i i = = 11}^{N N} {λ λ}_{i i} {u u}_{i i} {u u}_{i i}^{H h} = = {U u}_{s the s} {λ λ}_{s the s} {U u}_{s the s}^{H h} + + {U u}_{n no} {λ λ}_{n no} {U u}_{n no}^{H h} - - - - - - ((44))$

其中是N个特征值，u_i,i＝1,2,…,N是其对应的特征向量。λ_s＝diag{λ₁,λ₂,…,λ_P+1}和λ_n＝diag{λ_P+2,λ_P+3,…,λ_N}分别表示较大特征值、较小特征值组成对角矩in are N eigenvalues, u _i , i=1, 2, . . . , N are their corresponding eigenvectors. λ _s =diag{λ ₁ ,λ ₂ ,…,λ _P+1 } and λ _n =diag{λ _P+2 ,λ _P+3 ,…,λ _N } represent larger eigenvalues and smaller eigenvalues respectively make up the diagonal moment

阵。U_s和U_n则分别表示信号干扰子空间和噪声子空间。array. U _s and U _n represent the signal interference subspace and the noise subspace respectively.

${σ σ}_{n no}^{22} = = {\overset{^^}{σ σ}}_{n no}^{22} = = \frac{11}{N N - - P P - - 11} {Σ Σ}_{i i = = P P + + 22}^{N N} {λ λ}_{i i} - - - - - - ((55))$

由子空间理论可知，真实期望信号导向矢量与U_s展成同一子空间，又由于U_s与U_n正交，则期望信号导向矢量与噪声子空间正交。即：According to the subspace theory, the true desired signal steering vector and U _s expand into the same subspace, and because U _s is orthogonal to U _n , the desired signal steering vector is orthogonal to the noise subspace. Right now:

${u u}_{i i}^{H h} a a (({θ θ}_{00})) = = 00,, i i = = P P + + 22,, P P + + 33,, . . . . . .,, N N - - - - - - ((66))$

由此可知：From this we can see:

${| | | | {U u}_{n no}^{H h} a a (({θ θ}_{00})) | | | |}_{22}^{22} = = {a a}^{H h} (({θ θ}_{00})) {U u}_{n no} {U u}_{n no}^{H h} a a (({θ θ}_{00})) = = 00 - - - - - - ((77))$

在实际应用中，真实的期望信号导向矢量a(θ₀)常常具有估计误差，因此估计的期望信号导向矢量在噪声子空间中留有余量，因此有下面的不等式成立：In practical applications, the real desired signal steering vector a(θ ₀ ) often has an estimation error, so the estimated desired signal steering vector There is a margin in the noise subspace, so the following inequalities hold:

${| | | | {U u}_{n no}^{H h} \overset{^^}{a a} (({θ θ}_{00})) | | | |}_{22}^{22} &GreaterEqual; &Greater Equal; {| | | | {U u}_{n no}^{H h} a a (({θ θ}_{00})) | | | |}_{22}^{22} = = 00 - - - - - - ((88))$

显然，当与a(θ₀)相等时等号成立。即Obviously, when The equality sign is established when it is equal to a(θ ₀ ). Right now

$\underset{a a}{min min} {| | | | {U u}_{n no}^{H h} a a | | | |}_{22}^{22} = = {| | | | {U u}_{n no}^{H h} a a (({θ θ}_{00})) | | | |}_{22}^{22} = = 00 - - - - - - ((99))$

将期望信号导向矢量误差约束于球形不确定集中，由此可得基于球形不确定集的稳健波束形成算法如下：Constraining the steering vector error of the desired signal to the spherical uncertain set, the robust beamforming algorithm based on the spherical uncertain set can be obtained as follows:

$\underset{a a}{min min} {| | | | {U u}_{n no}^{H h} a a | | | |}_{22}^{22} s the s . . t t . . {| | | | a a - - \overset{^^}{a a} (({θ θ}_{00})) | | | |}_{22}^{22} \leq \leq ϵ ϵ - - - - - - ((1010))$

ε是球形不确定集的边界，上式是二阶凸优化问题，可以利用CVX工具包进行求解得到最优的导向矢量 ε is the boundary of a spherical uncertain set, and the above formula is a second-order convex optimization problem, which can be solved by using the CVX toolkit to obtain the optimal steering vector

Capon波束形成器的功率谱可由下式表示：The power spectrum of the Capon beamformer can be expressed by the following equation:

$p p = = \frac{11}{{a a}^{H h} ((θ θ)) {R R}^{- - 11} a a ((θ θ))} - - - - - - ((1111))$

由于干扰信号数目在空域中常常是有限的，噪声假定为独立的高斯白噪声，干扰信号导向矢量先验信息已知，则干扰噪声协方差矩阵可以表示为：Since the number of interference signals is usually limited in the space domain, the noise is assumed to be independent Gaussian white noise, and the prior information of the steering vector of the interference signal is known, then the interference noise covariance matrix It can be expressed as:

${\overset{^^}{R R}}_{i i + + n no} = = {Σ Σ}_{k k = = 11}^{P P} \frac{a a (({θ θ}_{k k})) {a a}^{H h} (({θ θ}_{k k}))}{{a a}^{H h} (({θ θ}_{k k})) {R R}^{- - 11} a a (({θ θ}_{k k}))} + + {\overset{^^}{σ σ}}_{n no}^{22} I I - - - - - - ((1212))$

步骤4：按照MVDR波束形成方法计算最优权矢量w_opt,并进行波束形成。Step 4: Calculate the optimal weight vector w _opt according to the MVDR beamforming method, and perform beamforming.

最优权矢量可由下式求得：The optimal weight vector can be obtained by the following formula:

${w w}_{opt opt} = = \frac{{\overset{^^}{R R}}_{i i + + n no}^{- - 11} \overset{&OverBar; &OverBar;}{a a} (({θ θ}_{00}))}{{\overset{&OverBar; &OverBar;}{a a}}^{H h} (({θ θ}_{00})) {\overset{^^}{R R}}_{i i + + n no}^{- - 11} \overset{&OverBar; &OverBar;}{a a} (({θ θ}_{00}))} - - - - - - ((1313))$

则阵列输出即波束形成为：The array output, i.e. the beamform, is then:

$y the y = = {w w}_{opt opt}^{H h} x x ((t t)) - - - - - - ((1414)) . .$

Claims

1., based on a robust ada-ptive beamformer method for interference noise covariance matrix, it is characterized in that, comprise the following steps:

(1) arrowband, antenna array receiver far field incoming signal is utilized, get limited fast umber of beats to carry out estimating reception data covariance matrix, then carry out feature decomposition to reception data covariance matrix, the prior imformation according to incident signal source number obtains noise subspace U _nand estimating noise power the prior imformation of incident signal source number can be obtained by source number estimation method, the desired homogeneous uniform line-array that sensor array is made up of N number of array element, far field space target wanted signal and P undesired signal, signal and interference, uncorrelated mutually between interference and interference, each channel noise is mutual independently zero mean Gaussian white noise, with signal, disturb all uncorrelated, Array Model, N × 1 tie up array received signal x (t) be:

\begin{matrix} x (t) = Σ_{m = 0}^{P} a (θ_{m}) s_{m} (t) + n (t) \\ = a (θ_{0}) s_{0} (t) + A_{I} S_{I} (t) + n (t); \end{matrix}

θ _m, m=1,2 ..., P is that undesired signal ripple reaches angular direction, θ ₀for expecting that signal wave reaches angular direction, a (θ _m), m=0,1,2 ..., P represents the steering vector of wanted signal, undesired signal, a (θ ₀) for expecting signal guide vector, s ₀t () is for expecting complex envelope, A _i=[a (θ ₁), a (θ ₂) ..., a (θ _p)] for undesired signal steering vector composition array manifold, S _i(t)=[s ₁(t), s ₂(t) ..., s _p(t)] ^tfor undesired signal complex envelope, n (t)=[n ₁(t), n ₂(t) ..., n _n(t)] ^tit is white Gaussian noise.() ^trepresent transpose operation, the covariance matrix R of array received signal is:

\begin{matrix} R = R_{s} + R_{i + n} = σ_{0}^{2} a (θ_{0}) a^{H} (θ_{0}) + \\ Σ_{k = 1}^{P} σ_{k}^{2} a (θ_{k}) a^{H} (θ_{k}) + σ_{n}^{2} I; \end{matrix}

R _sand R _i+nbe respectively wanted signal covariance matrix and interference noise covariance matrix, represent the power of wanted signal, a P undesired signal and space white noise signal respectively, I representation unit matrix, () ^hrepresent complex-conjugate transpose computing, the snap data estimation Received signal strength data covariance matrix by limited:

\hat{R} = \frac{1}{L} Σ_{k = 1}^{L} x_{k} (t) x_{k}^{H} (t);

L represents fast umber of beats, x _kt () represents a kth snap;

Number of sources P+1<N is right carry out feature decomposition, known according to incident signal source number:

\hat{R} = Σ_{i = 1}^{N} λ_{i} u_{i} u_{i}^{H} = U_{s} λ_{s} U_{s}^{H} + U_{n} λ_{n} U_{n}^{H};

Wherein

λ_{1} &GreaterEqual; λ_{2} &GreaterEqual; \cdot \cdot \cdot &GreaterEqual; λ_{P} &GreaterEqual; λ_{P + 1} &GreaterEqual; λ_{P + 2} = \cdot \cdot \cdot = λ_{N} = σ_{n}^{2}

N number of eigenwert, u _i, i=1,2 ..., N is its characteristic of correspondence vector, λ _s=diag{ λ ₁, λ ₂..., λ _p+1and λ _n=diag{ λ _p+2, λ _p+3..., λ _nrepresent larger eigenwert, less eigenvalue cluster diagonally matrix respectively, U _sand U _nthen represent signal disturbing subspace and noise subspace respectively;

estimation of Mean can be got obtain by the little eigenwert that Received signal strength covariance matrix feature decomposition is corresponding, namely

σ_{n}^{2} = {\hat{σ}}_{n}^{2} = \frac{1}{N - P - 1} Σ_{i = P + 2}^{N} λ_{i};

(2) by wanted signal steering vector error constraints in spherical uncertain concentrate, according to estimate wanted signal steering vector at noise subspace U _nprojection optimum obtain wanted signal steering vector more accurately true wanted signal steering vector and U _sthe same subspace of generate, due to U _swith U _northogonal, then wanted signal steering vector is orthogonal with noise subspace:

\begin{matrix} u_{i}^{H} a (θ_{0}) = 0 & i = P + 2, P + 3, \cdot \cdot \cdot, N, \end{matrix}

{| | U_{n}^{H} a (θ_{0}) | |}_{2}^{2} = a^{H} (θ_{0}) U_{n} U_{n}^{H} a (θ_{0}) = 0,

Wanted signal steering vector a (θ ₀) there is evaluated error, the wanted signal steering vector of estimation surplus is left in noise subspace:

{| | U_{n}^{H} \hat{a} (θ_{0}) | |}_{2}^{2} &GreaterEqual; {| | U_{n}^{H} a (θ_{0}) | |}_{2}^{2} = 0,

When with a (θ ₀) equal time equal sign set up

\min_{a} {| | U_{n}^{H} a | |}_{2}^{2} = {| | U_{n}^{H} a (θ_{0}) | |}_{2}^{2} = 0,

Wanted signal steering vector error constraints uncertainly to be concentrated in spherical, can based on the sane wave beam of spherical uncertain collection:

\begin{matrix} \min_{a} {| | U_{n}^{H} a | |}_{2}^{2} & s . t . & {| | a - \hat{a} (θ_{0}) | |}_{2}^{2} \end{matrix}, \leq ϵ;

ε is the border of spherical uncertain collection, carries out solving obtaining optimum steering vector

(3) noise power of foundation undesired signal steering vector prior imformation and estimation carry out interference noise covariance matrix to obtain undesired signal steering vector prior imformation is obtained by Power estimation method and Array Model,

The power spectrum of Capon Beam-former is:

p = \frac{1}{a^{H} (θ) R^{- 1} a (θ)};

Noise is independently white Gaussian noise, and undesired signal steering vector prior imformation is known, then interference noise covariance matrix for:

{\hat{R}}_{i + n} = Σ_{k = 1}^{P} \frac{a (θ_{k}) a^{H} (θ_{k})}{a^{H} (θ_{k}) R^{- 1} a (θ_{k})} + {\hat{R}}_{n}^{2} I;

(4) optimum weight vector w is calculated _opt, carry out Wave beam forming,

Optimum weight vector:

w_{opt} = \frac{{\hat{R}}_{i + n}^{- 1} \overset{&OverBar;}{a} (θ_{0})}{{\overset{&OverBar;}{a}}^{H} (θ_{0}) {\hat{R}}_{i + n}^{- 1} \overset{&OverBar;}{a} (θ_{0})};

Then aerial array output and Wave beam forming are:

y = w_{opt}^{H} x (t) .