Robust Adaptive Beamforming Under Quadratic Constraint with Recursive Method Implementation

When adaptive arrays are applied to practical problems, the performances of the conventional adaptive beamforming algorithms are known to degrade substantially in the presence of even slight mismatches between the actual and presumed array responses to the desired signal. Similar types of performance degradation can occur because of data nonstationarity and small training sample size, when the signal steering vector is known exactly. In this paper, to account for mismatches, we propose robust adaptive beamforming algorithm for implementing a quadratic inequality constraint with recursive method updating, which is based on explicit modeling of uncertainties in the desired signal array response and data covariance matrix. We show that the proposed algorithm belongs to the class of diagonal loading approaches, but diagonal loading terms can be precisely calculated based on the given level of uncertainties in the signal array response and data covariance matrix. The variable diagonal loading term is added at each recursive step, which leads to a simpler closed-form algorithm. Our proposed robust recursive algorithm improves the overall robustness against the signal steering vector mismatches and small training sample size, enhances the array system performance under random perturbations in sensor parameters and makes the mean output array SINR consistently close to the optimal one. Moreover, the proposed robust adaptive beamforming can be efficiently computed at a low complexity cost compared with the conventional adaptive beamforming algorithms. Computer simulation results demonstrate excellent performance of our proposed algorithm as compared with the existing adaptive beamforming algorithms.     

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.     

超高斯加载的稳健自适应波束形成及性能分析

该文提出了一种超高斯加载的稳健自适应波束形成方法,解决由于导向矢量和样本方差矩阵失配误差所导致的波束形成器性能下降的问题,利用p-范数来对两种误差不确定性进行总体修正,克服了2-范数不能同时兼顾两者实现最优修正的缺点。采用遗传算法求得最优范数p,验证了在不同实验设置下,当使用最优范数时,都比2-范数约束具有更好的性能。超高斯加载方法把复杂的不确定性建模问题转化为范数p的寻优问题,从而获得比对角加载方法更优异的性能。     

Efficient implementation of robust adaptive beamforming based on worst-case performance optimisation

Traditional adaptive beamforming methods undergo serious performance degradation when a mismatch between the presumed and the actual array responses to the desired source occurs. Such a mismatch can be caused by desired look direction errors, distortion of antenna shape, scattering due to multipath, signal fading as well as other errors. This mismatch entails robust design of the adaptive beamforming methods. Here, the robust minimum variance distortionless response (MVDR) beamforming based on worst-case (WC) performance optimisation is efficiently implemented using a novel ad hoc adaptive technique. A new efficient implementation of the robust MVDR beamformer with a single WC constraint is developed. Additionally, the WC optimisation formulation is generalised to include multiple WC constraints which engender a robust linearly constrained minimum variance (LCMV) beamformer with multiple-beam WC (MBWC) constraints. Moreover, the developed LCMV beamformer with MBWC constraints is converted to a system of nonlinear equations and is efficiently solved using a Newton-like method. The first proposed implementation requires low computational complexity compared with the existing techniques. Furthermore, the weight vectors of the two developed adaptive beamformers are iteratively updated using iterative gradient minimisation algorithms which eliminate the estimation of the sample matrix inversion. Several scenarios including angle-of-incidence mismatch and multipath scattering with small and large angular spreads are simulated to study the robustness of the developed algorithms.     

Widely linear generalized sidelobe canceling beamforming with variable diagonal loading

We propose a robust widely linear (WL) beamformer for noncircular (NC) signals in the presence of angle of arrival (AOA) errors or array random perturbations. In our beamformer, the block conjugate structure of covariance matrix is exploited to avoid updating the full weight vector, which reduces the computational loads. We add a variable diagonal loading term in the weight vector to improve the robustness of the WL beamformer. Moreover, the orthogonality constraint of block matrix is not required to calculate the amount of diagonal loading. Computer-simulation results show that the proposed WL beamforming provides improved performance over the conventional linear beamformers for NC signals in the presence of AOA errors and array random perturbations.     

Non-sensitive adaptive beamforming against mutual coupling

The standard Capon beamformer (SCB) is known to suffer from severe performance degradation when there is a mismatch between the presumed signal steering vector and the actual one. There may be several reasons leading to this result such as mutual coupling between array elements. The problem of adaptive beamforming in the presence of mutual coupling is studied based on a uniform linear array (ULA). By setting a group of auxiliary elements on each side of the ULA, the authors prove that the proposed method can inherently compensate the effect caused by the mutual coupling and greatly decrease the sensitivity of the SCB against mutual coupling. This technique can also be applied to most of the existing robust beamforming methods to further improve their performances. Theoretical analysis and simulation results demonstrate the robustness and effectiveness of this technique.     

基于改进互耦系数估计算法的自适应波束形成

阵列信号在实际应用中,常常会面临噪声的干扰,低信噪比(signal noise ratio, SNR)时波束形成器性能会急剧下降.针对该问题,提出一种基于改进互耦系数估计的抗互耦算法的自适应波束形成,即研究信号在不同输入SNR以及不同干扰波达方向(direction of arrival,DOA)估计误差下的互耦系数估计误差;并通过误差分析修正原算法不同SNR下参与估计信号的数目.改进算法改进了导向矢量和期望信号,提高了低SNR下互耦系数估计的准确度,对比分析验证了其在低SNR情况下有更强的抗干扰能力,对互耦现象有着更好的稳健性.     

频率不变约束的角加载稳健宽带波束形成算法

应用角加载技术能够提高波束形成算法稳健性,但是角加载量确定却是一个难解决问题。文中提出了一种基于频率不变约束的可变角加载最优稳健波束形成算法(Frequency Invariance Constraints-Variable Diagonal Loading,FIC-VDL)。该算法基于宽带波束形成的时域模型,根据多频点约束下导向矢量的不确定范围,利用频率不变约束因子将多频点变为参考频点约束来求解最优角加载量,并推导出真实的导向矢量。该方法能够改善宽带波束形成器在期望方向的频率不变特性,同时降低系统计算复杂度。计算机仿真结果验证了所提算法的稳健性。     

A Bayesian approach to robust adaptive beamforming

An adaptive beamformer that is robust to uncertainty in source direction-of-arrival (DOA) is derived using a Bayesian approach. The DOA is assumed to be a discrete random variable with a known a priori probability density function (PDF) that reflects the level of uncertainty in the source DOA. The resulting beamformer is a weighted sum of minimum variance distortionless response (MVDR) beamformers pointed at a set of candidate DOAs, where the relative contribution of each MVDR beamformer is determined from the a posteriori PDF of the DOA conditioned on previously observed data. A simple approximation to the a posteriori PDF results in a straightforward implementation. Performance of the approximate Bayesian beamformer is compared with linearly constrained minimum variance (LCMV) beamformers and data-driven approaches that attempt to estimate signal characteristics or the steering vector from the data     

Doubly constrained robust Capon beamformer

The standard Capon beamformer (SCB) is known to have better resolution and much better interference rejection capability than the standard data-independent beamformer when the array steering vector is accurately known. However, the major problem of the SCB is that it lacks robustness in the presence of array steering vector errors. In this paper, we will first provide a complete analysis of a norm constrained Capon beamforming (NCCB) approach, which uses a norm constraint on the weight vector to improve the robustness against array steering vector errors and noise. Our analysis of NCCB is thorough and sheds more light on the choice of the norm constraint than what was commonly known. We also provide a natural extension of the SCB, which has been obtained via covariance matrix fitting, to the case of uncertain steering vectors by enforcing a double constraint on the array steering vector, viz. a constant norm constraint and a spherical uncertainty set constraint, which we refer to as the doubly constrained robust Capon beamformer (DCRCB). NCCB and DCRCB can both be efficiently computed at a comparable cost with that of the SCB. Performance comparisons of NCCB, DCRCB, and several other adaptive beamformers via a number of numerical examples are also presented.     

A recursive least squares implementation for LCMP beamforming underquadratic constraint

Quadratic constraints on the weight vector of an adaptive linearly constrained minimum power (LCMP) beamformer can improve robustness to pointing errors and to random perturbations in sensor parameters. We propose a technique for implementing a quadratic inequality constraint with recursive least squares (RLS) updating. A variable diagonal loading term is added at each step, where the amount of loading has a closed-form solution. Simulations under different scenarios demonstrate that this algorithm has better interference suppression than both the RLS beamformer with no quadratic constraint and the RLS beamformer using the scaled projection technique, as well as faster convergence than LMS beamformers     

基于改进不确定集的稳健波束形成算法

基于不确定集约束的稳健MVDR波束形成算法在一定程度上依赖于期望信号导向矢量误差的先验知识,且当导向矢量失配较严重时干扰抑制性能也有所下降。为此,提出了一种基于投影变换的改进算法。该方法将约束方向矢量向信号干扰子空间投影,并作为新的约束方向矢量,从而等效于减小了期望信号导向矢量误差。这样,误差不确定参数只需设置为一较小的实数即可在任意导向矢量失配时获得最优的输出性能。计算机仿真结果证明了所提波束形成器具有较强的稳健性能。     

Robust Adaptive Microphone Array with Mainlobe and Response Ripple Control

Many existing adaptive beamformers possess robustness against arbitrary array steering vector (ASV) mismatches within presumed uncertainty set. However, when the array facing a large steering direction error, their performance degrade significantly since the uncertainty in steering direction generally gives rise to an outstanding mismatch in ASV. In the applications of microphone array, large steering direction error is often unavoidable because of the motion of target speaker. Meanwhile, in addition to conventional adaptive beamformers, microphone array also requests a controlled frequency response to target signal. In this paper, we propose a new adaptive microphone array implemented in frequency domain with controlled mainlobe and frequency response. A compact ASV uncertainty set explicitly modelling steering direction error and the other arbitrary ASV errors is exploited to derive beamformer with robust constraints on array magnitude response. Numerical results show that the proposed microphone array not only produces large controlled robust response region and robust frequency response, but also achieves high performance in SINR enhancement.     

基于投影对消处理技术的稳健自适应波束形成

针对传统自适应波束形成算法中目标波达方向(Direction of Arrival,DOA)估计不准确引起的波束形成性能下降问题,提出了一种采用投影对消矩阵的稳健自适应波束形成算法.首先,寻找与估计波达方向有最大相关性的特征矢量作为目标信号特征矢量,然后构建对消矩阵消除协方差矩阵中的信号分量,最后通过增加零点约束实现干扰抑制.与传统对角加载类稳健波束形成算法相比,所提算法不受对角加载因子的影响,且在信干噪比较大时仍然具有良好的抗干扰性能.仿真对比实验验证了所提算法的有效性.     

抑制快速运动强干扰的稳健自适应波束形成方法

针对存在快速运动强干扰时自适应波束形成性能的严重降低,提出了一种稳健的自适应波束形成方法。该方法使用零陷展宽技术修改采样协方差矩阵,使其自动地在干扰方位形成展宽的零陷以抑制运动强干扰,同时采用对角加载技术,以增强此方法对系统误差的稳健性,加载量通过约束扫描向量的误差来确定。仿真结果表明该方法能有效地提高当存在快速运动的强干扰时自适应波束形成的性能。     

Analysis of Effects of System Mismatches on the Performance of Adaptive Generalized Sidelobe Canceller and Compensation Methods

The effect of system mismatches on an adaptive linear constrained generalized sidelobe canceller(LC-GSC) is discussed in this paper.Based on the array gain index,two classic system mismatches,the direction of arrival(DOA) mismatch and the mismatches arising from array disturbance,are studied,respectively.To obtain the effective methods for compensating for the system mismatches,we analyze the performance of the improved LC-GSC with the diagonal loading and additional constraints(such as the directional constraints and derivative constraints).The computer simulations show that the techniques of diagonal loading and additional constraints can effectively compensate for the system mismatches.The loss of array gains can be controlled within 3 dB in the presence of 20% of array disturbances or DOA mismatch when the signal-to-noise ratio is less than 10 dB.The analysis illustrates that the proposed compensation methods are valid and feasible.     

Eigenspace-based adaptive array beamforming with robustcapabilities

This paper deals with adaptive array beamforming based on eigenspace-based (ESB) techniques with robust capabilities. It has been shown that ESB adaptive beamformers demonstrate the advantages of fast convergence speed and less sensitivity to steering angle error over conventional beamformers. In conjunction with a signal subspace construction method, we present an efficient technique to achieve the advantages of ESB adaptive beamforming with less computing cost and more robust capabilities over existing ESB techniques. Several computer simulation examples are provided for illustrating the effectiveness of the proposed technique     

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.     

Side-lobe constrained beamforming undervirtual expansion of L-shaped array

To reduce the side-lobe level of L-shaped expansion array and improve the output signal to interference and noise ratio (SINR), the algorithm of side-lobe constraint based on minimum variance distortionless response ( MVDR- SC) is proposed. Firstly, the approach of mixing diagonal loading and Mailloux-Zatman (DLMZ) is used to taper the covariance matrix of the expansion array. Then, the second order cone programming ( SOCP) obtained by constructing a new matrix is used to control the beam side-lobe. Finally, the new adaptive weight numbers are constructed by adjusting the proportion between DLMZ and SOCP. Simulation results show that the MVDR-SC algorithm can effectively reduce the side-lobe of beamforming under the L-shaped expansion array and obtain a larger output SINR. At the same time, it has good robustness to the mutual coupling error.     

Self-Calibration-Based Robust Near-Field Adaptive Beamforming for Microphone Arrays

Near-field beamforming using a microphone array has found many applications, such as sound acquisition in small rooms. However, robust near-field adaptive beamforming (NABF) against focal point errors has not been studied much in the literature until recently. In this brief, a robust near-field adaptive beamformer is proposed. The proposed method is developed by combining a new formulation of the point-constrained NABF and a self-calibration technique, in the presence of focal point uncertainties. The proposed method suffers from no loss in the degrees of freedom for interference rejection. Compared with conventional calibration-based adaptive beamformers, the proposed method has the advantage of not needing a noise-free calibration signal. Simulation results demonstrate that the performance of the proposed method is superior to that of the existing methods