改进的稳健Capon 波束形成算法性能分析

常规Capon 波束形成算法能够使波束在期望信号方向形成高增益,在干扰方向形成零陷,针对该算法在期望信号导向矢量失配的情况下,出现性能下降的问题,研究了期望信号导向矢量在不确定集约束下的求解。通过分析稳健Capon波束形成算法的特点,推导出了期望信号导向矢量在球形不确定集约束下的权矢量近似闭式解,并采用图像法,找到给定条件下的最优约束参数。在指向误差和相位误差存在情况下,对算法进行了仿真分析,仿真结果验证了算法在误差存在情况下的稳健性。     

基于不确定集的稳健Capon波束形成算法性能分析

该文针对常规Capon波束形成易受期望信号导向矢量失配影响,研究了基于导向矢量误差不确定集的稳健Capon自适应波束形成算法。推导出期望信号导向矢量属于球形不确定集时的自适应权矢量近似闭式解,并由此进行性能评估,得到目标功率估计和输出信号干扰噪声比的近似表达式,从而明确了各种因素对性能的影响关系。计算机仿真结果证明了该文分析的合理性。     

零陷优化的稳健波束形成算法

传统的自适应波束形成算法在干扰方向出现扰动且期望信号导向矢量失配时,不仅无法持续有效地抑制干扰,而且会在期望信号方向产生零陷致使期望信号相消,算法性能严重下降。针对该问题,本文提出了一种零陷优化的稳健波束形成算法。该算法首先通过干扰导向矢量的左右旋转来展宽零陷,接着将采样数据向干扰子空间投影,并对干扰分量进行加权处理以增强采样数据中的干扰强度,加深干扰零陷,最后采用导向矢量不确定集约束算法保证期望信号的接收增益。计算机仿真结果表明:该算法能够有效展宽干扰零陷,并能够保证期望信号增益,具有较好的稳健性。      

一种稳健的稀疏Capon波束形成算法

常规Capon波束形成算法具有相对较高的旁瓣增益,且在期望信号导向矢量存在失配时,阵列输出性能下降甚至失效。为解决这一问题,引入了稀疏约束Capon波束形成算法,该算法降低了旁瓣,对期望信号来向不确定具有一定稳健性,但在幅相误差、期望信号指向偏差等多种误差同时存在的情况下其性能下降。本文在稀疏约束Capon波束形成算法基础上,给出了一种稳健的稀疏Capon波束形成算法。该算法主要是在最差性能最优化的情况下,在稀疏Capon上增加了一个导向矢量存在偏差的约束条件。通过计算机仿真,验证了新算法在多种误差环境下的有效性与优越性。     

基于最坏情况性能优化的稳健自适应宽带波束形成

针对期望信号导向矢量失配会导致自适应波束形成算法的性能急剧下降这一问题,提出了一种新的基于最坏情况性能优化的稳健自适应宽带波束形成方法。该方法通过将实际期望信号的导向矢量约束于不确定集合中,来提高算法的稳健性;同时增加阵列空间响应偏差的二次型约束,可避免引起信号有较大失真。计算机仿真结果表明:该方法不仅能够抑制导向矢量偏差所带来的影响,有效控制波束主瓣区域内信号的畸变和旁瓣区域电平,还改善了阵列输出的信干噪比,使其更接近最优值。     

基于空时二维协方差矩阵修正的波束形成算法

在实际应用环境中,信源和阵列传感器等存在误差,假设期望信号的导向矢量与真实信源导向矢量的失配会导致阵列波束形成器把期望信号当作干扰来加以抑制。针对信号匹配误差导致自适应波束形成性能下降的问题,提出了一种基于空时二维协方差矩阵修正的波束形成算法,利用空时结构对宽带幅相误差校正的特性,对空时二维协方差矩阵进行重构,并对修正协方差矩阵进行特征值分解,分离出信号加干扰子空间,将失配导向矢量投影可使期望信号与噪声子空间严格正交,最后求解算法最优权值。算法有效改善了波束形成的输出信噪比,计算机仿真验证了理论分析的正确性和算法的稳健性。     

基于稳健Capon波束形成技术的矢量相关测向方法

为了弥补阵列天线导向矢量失配对测向性能的影响,提出基于稳健Capon波束形成技术的矢量相关测向方法。与直接使用相位差的常规相关干涉测向技术不同,该方法首先利用稳健Capon波束形成技术估计目标信号的真实导向矢量;然后通过导向矢量的相关拟合确定目标信号方向。通过仿真分析,得出了以测向为衡量标准时不确定集约束参数的选择原则。仿真结果表明该方法能够弥补阵列流型失配的影响、准确测量目标信号方向。     

基于导向矢量估计的鲁棒波束形成

针对标准Capon波束形成器中真实导向矢量与期望导向矢量存在误差时,其性能会急剧下降的问题,提出了基于加权空间平滑与导向矢量估计相结合的鲁棒波束形成算法。该算法利用加权空间平滑方法,对子阵进行特殊的划分,根据子阵间自相关矩阵与互相关矩阵权重差异,采用嵌套的方式获得加权矩阵,继而得到更加精确的协方差矩阵,接着,使用不确定范围约束期望导向矢量来获得真实导向矢量。仿真结果表明,和传统的自适应波束形成算法相比较,本文算法在面对协方差矩阵中含有期望信号以及角度失配问题时,鲁棒性得到明显提升。     

一种空域-极化域联合稳健自适应波束形成算法

为有效提高阵列对来波方向误差和极化参数误差的鲁棒性,提出一种空域-极化域联合稳健自适应波束形成算法,首先在每个干扰信号来波方向-极化角区间上重构干扰噪声协方差矩阵,然后在期望信号来波方向-极化角区间上估计其导向矢量,设计空域-极化域联合稳健波束加权。通过仿真实验可发现,所提算法对由来波方向角度误差和极化参数误差所引起的导向矢量失配具有很好的鲁棒性。     

一种稳健恒定束宽宽波束形成算法

传统宽带波束形成算法在导向矢量失配时输出性能下降,为解决该问题,文章提出一种稳健恒定束宽波束形成算法。该算法首先构造与快拍数相关的对角加载函数;其次,基于空域积分思想,结合入射信号的方向误差范围估计期望信号的实际入射方向,并结合构造的对角加载系数生成优化波束加权系数;最后,联合优化后的波束权值与FIR滤波器系数完成宽带波束响应的全局优化设计。经仿真实验验证,相比于传统分布设计法的时域宽带波束形成,文中方法可以得到较理想的恒定宽带主瓣响应和较低的旁瓣电平,同时在期望信号导向矢量失配情况下,仍有较好的输出信干噪比。     

一种联合修正的稳健Capon波束形成算法

指出了水平定向天线阵波束形成的主要难点,没有固定相位中心和受交叉极化来波的影响。阵列受随机性误差使得导向矢量存在较大失配,从而导致传统Capon算法性能下降甚至失效。在阵列误差模型下,给出了基于协方差矩阵与导向矢量联合修正的稳健Capon波束形成算法。该算法首先基于收缩得到一个增强的协方差矩阵,然后通过最大化Capon输出功率实现对导向矢量的修正,同时增加二次型约束防止修正的导向矢量接近于干扰导向矢量上。该算法可转化为二次约束二阶规划问题,并通过凸优化进行求解。仿真结果表明,该算法对天线阵模型中误差矩阵具有一定的稳健性,且较其他稳健算法具有较好的性能。     

Robust adaptive beamforming using worst-case performance optimization: a solution to the signal mismatch problem

Adaptive beamforming methods are known to degrade if some of underlying assumptions on the environment, sources, or sensor array become violated. In particular, if the desired signal is present in training snapshots, the adaptive array performance may be quite sensitive even to slight mismatches between the presumed and actual signal steering vectors (spatial signatures). Such mismatches can occur as a result of environmental nonstationarities, look direction errors, imperfect array calibration, distorted antenna shape, as well as distortions caused by medium inhomogeneities, near-far mismatch, source spreading, and local scattering. The similar type of performance degradation can occur when the signal steering vector is known exactly but the training sample size is small. In this paper, we develop a new approach to robust adaptive beamforming in the presence of an arbitrary unknown signal steering vector mismatch. Our approach is based on the optimization of worst-case performance. It turns out that the natural formulation of this adaptive beamforming problem involves minimization of a quadratic function subject to infinitely many nonconvex quadratic constraints. We show that this (originally intractable) problem can be reformulated in a convex form as the so-called second-order cone (SOC) program and solved efficiently (in polynomial time) using the well-established interior point method. It is also shown that the proposed technique can be interpreted in terms of diagonal loading where the optimal value of the diagonal loading factor is computed based on the known level of uncertainty of the signal steering vector. Computer simulations with several frequently encountered types of signal steering vector mismatches show better performance of our robust beamformer as compared with existing adaptive beamforming algorithms.     

Further Study on Robust Adaptive Beamforming With Optimum Diagonal Loading

Significant effort has gone into designing robust adaptive beamforming algorithms to improve robustness against uncertainties in array manifold. These uncertainties may be caused by uncertainty in direction-of-arrival (DOA), imperfect array calibration, near-far effect, mutual coupling, and other mismatch and modeling errors. A diagonal loading technique is obligatory to fulfil the uncertainty constraint where the diagonal loading level is amended to satisfy the constrained value. The major drawback of diagonal loading techniques is that it is not clear how to get the optimum value of diagonal loading level based on the recognized level of uncertainty constraint. In this paper, an alternative realization of the robust adaptive linearly constrained minimum variance beamforming with ellipsoidal uncertainty constraint on the steering vector is developed. The diagonal loading technique is integrated into the adaptive update schemes by means of optimum variable loading technique which provides loading-on-demand mechanism rather than fixed, continuous or ad hoc loading. We additionally enrich the proposed robust adaptive beamformers by imposing a cooperative quadratic constraint on the weight vector norm to overcome noise enhancement at low SNR. Several numerical simulations with DOA mismatch, moving jamming, and mutual coupling are carried out to explore the performance of the proposed schemes and compare their performance with other traditional and robust beamformers     

基于稳健最小二乘的鲁棒波束形成

为解决Capon波束形成器在存在导向矢量失配时的性能急剧下降问题,提出了一种结合广义旁瓣对消器和稳健最小二乘的鲁棒波束形成算法.该算法利用广义旁瓣对消器原理将Capon波束形成器转化为最小二乘问题,然后在数据协方差矩阵误差的范数约束下将其转化为二阶锥规划问题,并利用高效内点法得到最优解.所提出的算法经推导证明属于对角加载类.仿真分析表明,该算法在导向矢量失配和快拍不足时仍具有较好的性能.     

基于指向最小误差的宽带稳健波束形成方法

宽带自适应波束形成方法较常规延时求和波束形成方法具备更好的空间分辨能力和干扰抑制能力,但在实际应用中由于阵列误差和指向误差影响导致性能下降。文中在宽带指向最小误差(STMV)方法和窄带稳健Capon(RCB)方法基础上,提出了一种基于椭圆不确定集的宽带稳健波束形成方法。通过仿真验证分析了算法在强副瓣干扰和指向误差条件下弱目标检测能力;在幅频响应误差影响条件下的保持弱信号功率输出能力;并验证算法对快拍数要求低于STMV 方法。     

Robust Recursive Beamforming in the Presence of Impulsive Noise and Steering Vector Mismatch

This paper proposes a new method for robust beamforming in the presence of impulsive noise as well as steering vector mismatch. In our proposed method, the idea of M-estimation is firstly incorporated into the traditional orthonormal PAST (OPAST) algorithm for subspace tracking to combat the hostile effect of impulsive noise. Taking advantage of the subspace principle, we show that the steering vector mismatch can be recursively and robustly estimated in closed form. Then, by making use of the estimated steering vector, the problem of robust beamforming in the presence of impulsive noise is formulated. The solution of this problem is analytically derived and the resultant robust beamformer is shown to have a similar form to the Capon beamformer, whereas the array covariance matrix and the steering vector are robustly estimated. Different from conventional methods, the impulsive noise and the steering vector mismatch are simultaneously handled by extending the traditional OPAST algorithm, and hence the proposed method has low complexity and it is feasible to nonstationary scenarios with moving sources. Simulation results demonstrate the validity and superiority of the proposed method over conventional methods in impulsive noise environment with steering vector mismatch.     

Quadratically Constrained Beamforming Robust Against Direction-of-Arrival Mismatch

It is well known that the performance of the minimum variance distortionless response (MVDR) beamformer is very sensitive to steering vector mismatch. Such mismatches can occur as a result of direction-of-arrival (DOA) errors, local scattering, near-far spatial signature mismatch, waveform distortion, source spreading, imperfectly calibrated arrays and distorted antenna shape. In this paper, an adaptive beamformer that is robust against the DOA mismatch is proposed. This method imposes two quadratic constraints such that the magnitude responses of two steering vectors exceed unity. Then, a diagonal loading method is used to force the magnitude responses at the arrival angles between these two steering vectors to exceed unity. Therefore, this method can always force the gains at a desired range of angles to exceed a constant level while suppressing the interferences and noise. A closed-form solution to the proposed minimization problem is introduced, and the diagonal loading factor can be computed systematically by a proposed algorithm. Numerical examples show that this method has excellent signal-to-interference-plus-noise ratio performance and a complexity comparable to the standard MVDR beamformer.