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.     

鲁棒约束恒模自适应波束形成算法

线性约束恒模算法能够有效克服恒模算法中存在的干扰捕获问题,但在信号方向向量存在偏差的情况下,其性能将会受到影响.针对上述问题,本文提出了鲁棒约束恒模自适应算法并对其性能进行了分析.该算法收敛速度快,抗扰动性强,对信号方向向量的偏差具有较强的鲁棒性,改善了系统的输出信干噪比.仿真实验表明,与线性约束恒模算法相比,鲁棒约束恒模算法具有很好的性能.     

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.     

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.     

The statistical performance of eigenspace-based adaptive arraybeamformers

We analyze the statistical performance of several eigenspace-based adaptive array beamformers, including conventional direct-form beamformers and generalized sidelobe canceler (GSC). It is shown that the convergence rate of eigenspace-based adaptive array beamforming depends on the number of array elements, the input signal-to-noise ratio (SNR), and the number of interferers when the desired signal is present during the weight adaptation. In contrast, the misadjustment of the array output power is a function of the number of interferers and is independent of the number of array elements when the desired signal is absent. Several simulation examples are also provided to confirm the theoretical results     

PSO Assisted DD-ESB Beamforming with Robust Capabilities

This paper deals with adaptive array beamforming based on the decision-directed eigenspace-based (DD-ESB) technique with robust capabilities. It has been shown that DD-ESB adaptive beamformer demonstrates the advantages of better output signal-to-interference plus noise ratio performance and less sensitivity to pointing error over conventional ESB beamformers without any specific training bits. In conjugation with particle swam optimization assisted scheme to obtain more correct desired user’s transmitted bits from the output of the ESB, the more correct steering vector of the desired user can be reconstructed for DD-ESB adaptive beamforming in the presence of larger pointing error and relatively low interference-to-noise ratio. Computer simulations are provided to illustrate the effectiveness of the proposed approach.     

基于二次型约束的鲁棒自适应波束形成算法

针对期望信号方向向量存在偏差会导致自适应波束形成算法的性能急剧下降这一问题,该文提出了一种基于二次型约束的鲁棒自适应波束形成算法。通过对期望信号波达方向附近范围内的方向向量的误差模值进行约束,来提高算法的鲁棒性,并在此约束条件下对权重向量进行优化求解,且优化解中的参数能够准确求出。该算法可有效地控制波束主瓣区域内信号的畸变,并能够抑制方向向量偏差所带来的影响,提高了系统的鲁棒性,同时使干扰和噪声的功率输出最小,保证了对干扰信号的抑制能力,改善了阵列输出的信干噪比,使其更接近最优值。仿真结果验证了所提算法的有效性与优越性。     

基于幅相线性约束的自适应和差波束形成方法研究

阵列雷达自适应和差波束单脉冲测角面临信号对消、训练样本有限、波束保形及零点约束困难等问题.针对上述问题,本文提出基于幅相线性约束的自适应和差波束形成方法.该方法通过增加对主瓣临近角度的幅相线性约束条件,有效的克服和波束信号对消的现象;通过引入相位约束条件,使得差波束的在主瓣方向逼近静态差波束,具有良好的稳健性.同时通过合理的设计幅相约束条件实现了单脉冲和差波束测角二维解耦合.仿真实验验证了本文方法的有效性.     

Robust Adaptive Beamformers Based on Worst-Case Optimization and Constraints on Magnitude Response

In this paper, novel robust adaptive beamformers are proposed with constraints on array magnitude response. With the transformation from the array output power and the magnitude response to linear functions of the autocorrelation sequence of the array weight, the optimization of an adaptive beamformer, which is often described as a quadratic optimization problem in conventional beamforming methods, is then reformulated as a linear programming (LP) problem. Unlike conventional robust beamformers, the proposed method is able to flexibly control the robust response region with specified beamwidth and response ripple. In practice, an array has many imperfections besides steering direction error. In order to make the adaptive beamformer robust against all kinds of imperfections, worst-case optimization is exploited to reconstruct the robust beamformer. By minimizing array output power with the existence of the worst-case array imperfections, the robust beamforming can be expressed as a second-order cone programming (SOCP) problem. The resultant beamformer possesses superior robustness against arbitrary array imperfections. With the proposed methods, a large robust response region and a high signal-to-interference-plus-noise ratio (SINR) enhancement can be achieved readily. Simple implementation, flexible performance control, as well as significant SINR enhancement, support the practicability of the proposed methods.     

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     

A Robust Space-Time Generalized Sidelobe Canceller

This paper deals with adaptive array beamforming based on a two-dimensional generalized sidelobe canceller (GSC) with robust capability. It has been known that the performance of conventional GSC is quite sensitive even to pointing error. In conjunction with the joint desired user’s code-aid and signal subspace estimating approach, the proper quiescent weight vector and blocking matrix of GSC can be obtained to suppress the leakage of desired signal. However, space signature is estimated by exploiting the knowledge of the spreading code of the user of interest and the orthogonality between noise and signal subspaces. In this paper, the space-time signature estimation can be integrated jointly. Therefore, the desired signal cancellation does not occur; even the pointing error is relatively large. Computer simulation results show the effectiveness of the proposed approach.     

Robust adaptive array beamforming for cyclostationary signals undercycle frequency error

This paper deals with the problem of robust adaptive array beamforming for cyclostationary signals. By exploiting the signal cyclostationarity, the SCORE algorithms presented by Agee, Schell and Gardner (1990) have been shown to be effective in performing adaptive beamforming without requiring the direction vector of the desired signal. However, these algorithms suffer from severe performance degradation even if there is a small mismatch in the cycle frequency of the desired signal. In this paper, we first evaluate the performance of the SCORE algorithms in the presence of cycle frequency error (CFE). An analytical formula is derived to show the behavior of the performance degradation due to CFE. Based on the theoretical result, we then develop an efficient method in conjunction with the SCORE algorithms to achieve robust adaptive beamforming against the CFE. Several simulation examples for confirming the theoretical analysis and showing the effectiveness of the proposed method are also presented     

Efficient robust adaptive beamforming for cyclostationary signals

This paper deals with the problem of robust adaptive array beamforming for cyclostationary signals. By exploiting the signal cyclostationarity, the LS-SCORE algorithm presented in a paper by Agee et al. (1990) has been shown to be effective in performing adaptive beamforming without requiring the direction vector of the desired signal. However, this algorithm suffers from severe performance degradation even if there is a small mismatch in the cycle frequency of the desired signal. In this paper, we first evaluate the performance of the LS-SCORE algorithm in the presence of cycle frequency error (CFE). An analytical formula is derived to show the behavior of the performance degradation due to CFE. An efficient method is then developed based on the fact that the array output power approaches its maximum as the CFE is reduced. We formulate the problem as an optimization problem for reducing the CFE iteratively to achieve robust adaptive beamforming against the CFE. Simulation examples for confirming the theoretical analysis and showing the effectiveness of the proposed method are provided     

SVM自适应波束成形算法

在天线阵列过载,以及强干扰与期望用户信号夹角过近的情况下,传统的线性阵列信号处理算法,如MMSE(minimum mean-squareerror)、NLMS(Normalized Least Mean Squares)等表现并不理想。SVM(SupportVectorMachine)是机器学习领域的最新成果,有较强的泛化能力,收敛快以及低复杂度等优点。本文提出了在上行波束成形中使用SVM算法,提高空域滤波的分辨率,与其他相关算法相比较,系统性能有了明显的改进。     

基于可变对角载入的鲁棒自适应波束形成算法

针对传统算法对方向向量偏差敏感的缺点,提出了一种基于可变对角载入的鲁棒自适应波束形成算法.为了提高算法的鲁棒性,采用非线性约束条件下的最优化阵列输出功率对信号方向向量进行优化求解,且优化解中的参量能够准确求出.为了减少计算量,采用递推算法求逆矩阵并利用泰勒级数展开,推导出基于可变对角载入的权重向量公式.该算法可有效地抑制方向向量偏差所带来的影响,降低了计算量易于实时实现,提高了系统的鲁棒性,改善了阵列输出的信干噪比,使其更接近最优值.仿真结果表明,该算法相对传统算法可以获得更好的性能.     

Modified constant modulus algorithm for digital signal processingadaptive antennas with microwave analog beamforming

This paper proposes a novel algorithm, called modified constant modulus algorithm (M-CMA), which is able to give adaptability to microwave beamforming phased array antennas. Since microwave analog beamformers basically require much fewer RF devices than digital beamformers, microwave analog beamformers based on M-CMA, that is, adaptive microwave beamformers, can be cheaply fabricated. Therefore, they are very suitable for mobile communication systems where both miniaturization and low cost are required for the mobile terminals. M-CMA obtains a gradient vector by a combination of analytical calculation and perturbation of the microwave beamforming control voltage. Though M-CMA is implemented with a digital signal processor, M-CMA controls the microwave analog beamformer by utilizing the gradient vector. The microwave analog beamformer based on M-CMA is analyzed to have the following characteristics: (1) the beamformer can point its main beam to the desired direction in additive white Gaussian noise (AWGN) channels; (2) although the beamformer may possibly fail in ill solutions in cochannel interference (CCI) channels, M-CMA can converge to the optimum solution when the desired direction is roughly a priori known     

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     

Adaptive beam forming using split-polarity transformation forcoherent signal and interference

Split-polarity transformation (SPT), which is incorporated into conventional linearly constrained minimum variance (LCMV) beamformers to decorrelate the desired signal from interference, is presented. The SPT processor does not distort the direction vectors associated with wave fronts impinging on the array, but it does reverse the phase of the signal coming from a specified direction. With the aid of SPT processing, the signal cancellation due to correlation between the desired signal and interference is almost eliminated. The design of a robust SPT processor for combating the effects of mismatch between idealized array model and actual scenario arising from causes such as sensor location, amplitude, and phase errors is discussed. A detailed performance study of the SPT-LCMV beamformer shows it to be robust against direction uncertainty in the assumed look direction. Numerical results are presented to demonstrate the effectiveness of the SPT-LCMV beamforming scheme is a coherent interference environment     

Robust cyclic adaptive beamforming using a compensation method

This paper deals with the problem of robust adaptive array beamforming using signal cyclostationarity. The constrained cyclic adaptive beamforming (C-CAB) algorithm presented by Wu and Wong (1996) [6] has been shown to be effective in performing adaptive beamforming without requiring the direction vector or the waveform of the desired signal. However, this algorithm suffers from severe performance degradation even if there is a small mismatch in the cycle frequency of the desired signal. In this paper, we first evaluate the performance degradation of the C-CAB algorithm in the presence of cycle frequency error (CFE). A novel compensation method in conjunction with the subspace projection is then proposed to tackle the problem due to CFE. We reconstruct the required cyclic conjugate correlation matrix by using a compensation matrix to cope with the deterioration of its dominant singular value when CFE exists. Finally, several simulation examples are provided to show the effectiveness of the proposed algorithm.