波束形成是阵列信号处理中的一个重要研究方向，广泛应用于地震学、声呐、雷达、无线通信和医学成像等领域。波束形成通过对阵列上各通道数据进行复数加权求和达到提取期望信号并抑制干扰和噪声的目的。根据加权向量的计算是否依赖于接收数据，波束形成器可以分为两类：静态波束形成器和自适应波束形成器。作为一种常用的自适应波束形成器，Capon波束形成器可以通过自适应选择加权向量来最小化阵列输出功率，并保证期望信号不失真。与静态波束形成器相比，虽然Capon波束形成器有更高的分辨率和更好的干扰抑制能力，但是当期望信号导向矢量存在误差时，Capon波束形成器会将期望信号视为干扰并进行抑制，从而导致性能急剧下降。近年来，为了提高自适应波束形成器的稳健性，发展了许多稳健的波束形成方法。本文针对不同的信号形式和应用场景对稳健的自适应波束形成方法进行了深入研究，主要创新点和贡献包括： 1.针对基于样本协方差矩阵求逆波束形成器在期望信号导向矢量存在误差时出现的信号“自消”问题，提出了一种基于干扰加噪声协方差矩阵(Interference-Plus-Noise Covariance Matrix，IPNCM)重构的稳健波束形成算法。该算法的流程为先重构IPNCM，再估计期望信号的导向矢量，最后计算加权向量。在IPNCM重构中，首先通过Capon波束形成器对干扰区域的干扰信号来波方向进行粗估计，由此计算干扰信号的名义导向矢量；其次，对样本协方差矩阵进行特征值分解，求出干扰子空间；接着，基于名义导向矢量和干扰子空间，通过自适应迭代稳健Capon波束形成方法估计各干扰信号的真实导向矢量；最后，根据定义式重构IPNCM。在期望信号导向矢量估计过程中，本文根据不同的应用场景提出了三种方法；一种是通过求解二次约束二次规化问题估计期望信号的失配矢量，另外两种是分别通过协方差矩阵特征值分解方法和Oracle Approximating Shrinkage (OAS)估计器方法直接估计期望信号导向矢量。最后，利用估计的期望信号导向矢量和重构的IPN㎝，确定波束形成器的加权向量。该波束形成器不仅对期望信号和干扰信号的导向矢量误差具有稳健性，计算复杂度也较低。 2.对于非圆的期望信号和干扰信号，针对如何利用信号非圆特性来提局波束形成器的输出信干噪比问题，提出了稳健宽线性波束形成算法。它利用非圆信号共辆分量在希尔伯特空间能正交分解成同相分量和正交分量，且同相分量与信号本身完全相干这一性质来扩展协方差矩阵和期望信号导向矢量的维数，从而提高波束形成器的输出信干噪比。首先，推导了计算非圆系数空间谱的新方法，并结合Capon空间谱来重构扩展的干扰加噪声协方差矩阵(Augmented Interference-Plus-Noise Covariance Matrix，A-IPNCM)；然后，分别用迭代二次约束二次规划方法和Rao-Blackwell Ledoit-Wolf估计器方法估计期望信号的扩展导向矢量；最后，利用估计的期望信号扩展导向矢量和重构的A-IPNCM，计算宽线性波束形成器的加权向量。该算法在高信噪比的条件下也能保持良好的性能，同时它对期望信号大的来波方向估计误差稳健。 3.针对一般的多输入多输出(Multiple-Input Multiple-Output，MIMO)雷达波束形成方法不能灵活的控制波束宽度和面对快速移动目标时性能下降的问题，提出了基于不确定集的稳健MIMO雷达波束形成方法。由于现有基于幅度响应约束的MIMO波束形成算法未考虑阵列导向矢量误差，致使其性能在阵列通道存在校正误差时会下降；而所提算法在信号模型中考虑了阵列导向矢量误差，因此它对阵列校正误差稳健。由于最后所形成的为一个非凸问题，因此需先用一阶泰勒展开将非凸项线性化，然后通过半定规划技术求出最优加权向量(包括发射端和接收端的加权向量)。另外，为了进一步降低优化问题的维数(也即减小算法计算量)，提出了将原高维-非凸问题转化成两个低维-半定规划问题的降维算法。 4.针对传统自适应波束形成方法在干扰方向扰动时性能下降的问题，提出了基于零陷展宽的稳健波束形成算法。首先，对由干扰方向扰动引起传统自适应波束形成算法性能下降的问题进行了分析；然后，提出了通过构造投影矩阵来实现宽零陷的方法，也即先根据零陷区域的先验信息构建协方差矩阵，然后将该协方差矩阵进行特征值分解来构建投影矩阵，最后将阵列接收数据投影到投影矩阵实现零陷展宽。 关键词：稳健波束形成，非圆信号，导向矢量误差，协方差矩阵误差，协方差矩阵重构

 As a fundamental technique in array signal processing, adaptive beamforming has been widely used in radar, sonar, wireless communications, and medical-imaging. The beamforming methods are of two kinds: data-independent and data-dependent/adaptive. The standard Capon beamformer, as one of the well-known adaptive beamformers, adap-tively selects the weight vector to minimize the array output power, subject to the linear constraint that the signal-of-interest (SOI) does not suffer from any distortion. The Capon beamformer has better resolution and much better interference rejection capability than the data-independent beamformer. However, when the steering vector of the desired sig-nal is imprecise, the Capon beamformer may suppress the SOI as an interference, which results in significantly underestimated SOI power and dramatically reduced array output signal-to-interference-plus-noise ratio (SINR). In the last three decades, robust adaptive beamforming algorithms have been developed to improve the robustness of the Capon beamformer. In this paper, for different application scenarios and form of signal (in-cluding circular signal and non-circular signal), we propose some corresponding robust adaptive beamforming algorithms. The main innovative points and contributions of this dissertation are summarized as follows. 1.The performance of the sample covariance matrix inversion (SMI) based beam-former is very sensitive to the signal-of-interest's (SOI's) steering vector (SV) mismatch and covariance matrix mismatch, especially when the desired signal is present in the train-ing data. To account this problem, we have proposed a novel interference-plus-noise co-variance matrix reconstruction (IPNCM) based robust adaptive beamforming algorithm. Different from the previous IPNCM reconstruction by utilising the Capon spectral estima-tor integrated over an angular sector, we estimate each interference's SV first, and then reconstruct the IPNCM according to its definition. It means that the proposed method avoids the integration process and has a much lower complexity. To be specific, there are three main steps in estimating the SV of each interference. First, the presumed SV of the interference is determined through the Capon spatial spectrum estimator. Second, we construct the interference subspace by calculating the correlation coefficient between the interference's presumed SV and the sample covariance matrix (SCM) eigenvectors or by using the information theoretic criteria approach. Third, based on the interference's presumed SV and subspace, the iterative robust Capon beamformer (RCB) method is adopted to estimate the actual SV of interference. Moreover, for different application scenarios, three new methods are developed to estimate the SOI's SV. One approach is to estimate the mismatch vector of the desired signal by solving a quadratically con-strained quadratic progarmming (QCQP) problem. Moreover, for the other two methods, the SOI's SV is directly calculated by utilising the techniques of the covariance ma-trix eigendecomposition (ED) and the oracle approximating shrinkage (OAS). Finally, based on the reconstructed IPNCM and the estimated SV of the SOI, three new IPNCM reconstruction-based beamformer's weighting vectors are calculated. Importantly, the proposed beamformers have much lower complexities than the beamforming algorithms, and they are robust against a variety of SV mismatches of both the SOI and interference. 2.For non-circular signals, in order to further improve the beamformer's output SINR by exploing the second-order noncircularity of interferences and the SOI, we pro-pose two new augmented interference-plus-noise covariance matrix reconstruction (A-IPNCM) based widely linear beamforming algorithms. One is based on the techniques of the iterative adaptive approach (IAA) and the iterative robust Capon beamformer with adaptive uncertainty level (AU-IRCB). Firstly, different from the conventional IAA algorithm, we determine the positions of interferences first and then adopt the IAA algorithm to obtain the spatial spectrum. Secondly, the A-IPNCM is reconstructed based on the ac-quired spatial spectrum. Thirdly, for noncircular signals, a modified AU-IRCB algorithm is developed to estimate the extended SV of the desired signal. The main advantage of the proposed method is that it can suppress the coherent interferences. For the second algorithm, Different from the A-IPNCM reconstruction in the first method, we adopt a new method to calculate the spatial spectrum of the non-circularity coefficient, and then reconstruct the A-IPNCM by using the Capon spatial spectrum. Meanwhile, three meth-ods are developed to estimate the extended steering vector (ESV) of the desired signal for different application scenarios. One is simultaneously correct the SOI's SV and estimate the SOI's non-circularity coefficient by the proposed iterative quadratically constrained quadratic programming (IQCQP) procedure. For the other two methods, based on the cross correlation between the observation vector and the WL beamformer's output, the SOI's ESV is directly estimated by the modified Rao-Blackwell Ledoit-Wolf (RBLW) es-timator and oracle approximating shrinkage (OAS) estimator, respectively. Importantly, the proposed algorithms are robust against large look direction mismatch of the desired signal. 3.For the conventional MIMO radar beamformers, they cannot form a flap-top pat-tern and may not be able to provide sufficient robustness against large look direction mismatch. To account this problem, we propose a new robust beamforming algorithm for multiple-input multiple-output (MIMO) radar with MRC (magnitude response con-straints). Unlike the existing methods, steering vectors (SVs) mismatches are taken into account in the proposed MRC, which results in a more complicated non-convex problem. To cope with this problem, the non-convex term is linearized first based on the technique of first-order Taylor series expansion. Then, the optimal weight vector is obtained by us-ing the method of semidefinite programming (SDP). Moreover, in order to further reduce the computational complexity, we propose a dimension-reduced algorithm to convert the original non-convex problem into two low dimension SDP problems, and achieve the fi-nal solution by using the bi-iterative method. The proposed beamformer can precisely control the main beam in the presence of SVs uncertainties, and simulations are provided to demonstrate its superiority. 4.Traditional adaptive beamformers are vulnerable to severely degraded in the pres-ence of interference nonstationarity and array steering vector (ASV) mismatch, which often occurred in the situation of the antenna platform motion or propagation channel variability. To solve these problems, we propose two robust adaptive beamforming algo-rithms, which can broaden interference nulls. For the first method, we introduce the l₁ norm constraint to produce a broad trough at the direction of interference and adopts an idea of worst case performance optimization to robustly against the array steering vec-tor mismatch. For the other one, a new projection matrix with null broadening ability is constructed and then projects the array received data onto the projection matrix. Both the proposed methods are jointly against the interference motion and array steering vector mismatch. Keywords: robust adaptive beamforming, non-circular signal, steering vector error, co-variance matrix error, convariance matrix reconstruction