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。     

On robust Capon beamforming and diagonal loading

The Capon (1969) beamformer has better resolution and much better interference rejection capability than the standard (data-independent) beamformer, provided that the array steering vector corresponding to the signal of interest (SOI) is accurately known. However, whenever the knowledge of the SOI steering vector is imprecise (as is often the case in practice), the performance of the Capon beamformer may become worse than that of the standard beamformer. Diagonal loading (including its extended versions) has been a popular approach to improve the robustness of the Capon beamformer. We show that a natural extension of the Capon beamformer to the case of uncertain steering vectors also belongs to the class of diagonal loading approaches, but the amount of diagonal loading can be precisely calculated based on the uncertainty set of the steering vector. The proposed robust Capon beamformer can be efficiently computed at a comparable cost with that of the standard Capon beamformer. Its excellent performance for SOI power estimation is demonstrated via a number of numerical examples.     

四元数域干扰加噪声协方差矩阵重构鲁棒自适应波束形成

基于电磁矢量传感器阵列的四元数Capon波束形成器较传统的复数域Capon波束形成器有更好的性能。但是该方法在存在指向误差和极化失配的情况下性能急剧下降,甚至会出现信号相消现象。本文将协方差矩阵重构方法推广于四元数Capon波束形成中,通过利用Q-Capon的极化-角度谱估计得到干扰和噪声的功率来对干扰加噪声协方差矩阵进行重构,避免了对角加载方法中对对角加载因子的求解,而且能够有效克服指向误差与极化失配带来的性能下降。计算机仿真表明,该方法相较于其他四元数域的方法有着更好的性能。      

一种改进的迭代型鲁棒波束形成算法

为有效克服模型失配误差对自适应波束形成器的影响,该文提出了一种改进的迭代型鲁棒波束形成算法.该算法以导向矢量在期望信号来波方向区间宽度内、外的积分关系式构造新的终止条件,克服了迭代对角加载算法对终止条件参数鲁棒性不强的问题,从而进一步提高了波束形成器的输出信干噪比.仿真实验表明,提出的算法可以有效克服不同类型的模型失配误差带来的影响,能够处理较大范围的方向失配误差,且对算法中的来波方向区间宽度这一关键参数设置具有较强的鲁棒性.     

Sidelobe Suppression for Robust Beamformer Via the Mixed Norm Constraint

Applying a sparse constraint on the beam pattern has been suggested to suppress the sidelobe of the minimum variance distortionless response (MVDR) beamformer recently. To further improve the performance, we add a mixed norm constraint on the beam pattern. It matches the beam pattern better and encourages dense distribution in mainlobe and sparse distribution in sidelobe. The obtained beamformer has a lower sidelobe level and deeper nulls for interference avoidance than the standard sparse constraint based beamformer. Simulation demonstrates that the SINR gain is considerable for its lower sidelobe level and deeper nulling for interference, while the robustness against the mismatch between the steering angle and the direction of arrival (DOA) of the desired signal, caused by imperfect estimation of DOA, is maintained too.     

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     

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.     

柔性稀疏阵的稳健波束形成

本文将导向矢量失配时的稳健波束形成问题归结为二次锥规划问题,利用高效的内点法求解。该波束形成器成功地应用于存在阵元位置误差的柔性稀疏阵,相对于经典的对角线加载法、特征空间法,在不同的输入信噪比下获得了更好的输出信号干扰加噪声比。仿真结果表明对超稀疏分布的柔性阵,阵元位置误差对输出SINR起决定性影响,而阵列稀疏程度对其影响不大。     

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.     

一种加载量迭代搜索的稳健波束形成

当阵列的导向矢量并不精确已知时,自适应波束形成有较大的性能损失.为提高波束形成的稳健性,对角加载成为一种常用的方式.但困扰这类方法的核心问题是合适的加载量如何确定.粗估导向矢量经对角加载后得到修正的导向矢量,如果加载量合适,则修正后的导向矢量接近真实导向矢量,即与噪声子空间的正交性变好.基于以上分析,构造修正导向矢量向信号子空间和噪声子空间投影的加权代价函数来评价加载量的合适与否,进而提出一种迭代搜索合适加载量的方法.计算机仿真验证了方法的有效性,与同类方法对比显示其优越性.     

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.     

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     

Robust beamforming based on variable loading

A novel beamformer based on variable loading technique is presented. It is more robust than the widely used diagonal loading technique against steering errors or lack of training data. Computer results demonstrate good performance of the proposed beamformer.     

正交模约束的稳健波束形成算法

Capon波束形成算法在导向矢量存在误差或是在较少快拍数或高信噪比情况下,都会使波束产生严重的畸变。为了提高波束的稳健性,该文提出了一种正交模约束的稳健波束形成算法(OCCB),并通过二次求导得到阵列权值的具体数学表达式。该算法在Capon算法的基础上,增加对阵列权值和噪声子空间的正交模约束,实现了在不影响信号和干扰特征值的同时,完成对噪声特征值的加载,减小噪声特征值的扩散程度。分析了部分对角加载对期望信号、干扰和噪声的影响。该算法在导向矢量存在误差、采样快拍数较少和高信噪比情况下,都可使波束具有更低的旁瓣和更加准确的主瓣指向,同时对干扰能进行较好的抑制,仿真结果证实了方法的有效性。     

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.     

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.     

Sidelobe suppression for adaptive beamforming with sparse constraint on beam pattern

To suppress the sidelobe level of adaptive beamforming, sparse constraint on beam pattern is added to the conventional minimum variance distortionless response (MVDR) beamformer. The sparse constraint is an Lp-norm which can be explained as a diversity measure to evaluate the sparsity of the beam pattern. The proposed beamformer can not only reduce the sidelobe level, but also increase robustness against the mismatch problem caused by imprecise knowledge of the desired source.     

基于特征值分解的稳健波束形成技术

Capon 自适应波束形成中,导向矢量误差和协方差矩阵的估计误差均会导致波束形成器的性能下降。针对这一现象,提出一种基于特征值分解的稳健波束形成技术,即在将估计的协方差矩阵特征值分解后,直接对影响波束形成器稳健性能的噪声小特征值进行算术平均处理,以获得接近于理想波束形成器的稳健性能。同时根据试验仿真,给出了用于区分干扰和噪声特征值的门限计算公式,为准确构建特征子空间提供了思路。分析结果表明,与传统的对角加载方法相比,该方法能够达到同样的改善性能,在实际运用中更加直接和有效。     

MIMO阵列波束形成方法研究

相控阵雷达无法分辨一个波束宽度内的2个目标,多输入多输出(Multi-Input Multi-Output,MIMO)雷达阵列各阵元发射正交信号,提高了阵列系统的自由度,改善了雷达阵列系统分辨性能。文中给出了MIMO阵列相关滤波器组分离目标回波信号的原理框图,并进行了MIMO阵列常规波束形成器和最小方差无失真响应(MVDR)波束形成器理论分析和仿真实验。仿真结果表明,MIMO阵列比常规相控阵列具有更高的角度分辨率。     

迭代对角加载采样矩阵求逆鲁棒自适应波束形成

为有效克服导向矢量大失配误差对自适应波束形成器的影响,该文提出了一种迭代对角加载采样矩阵求逆鲁棒自适应波束形成算法。该算法对传统对角加载算法进行了迭代运算,基于Capon波束形成器的最优权矢量与假定导向矢量的基本关系,将每一步得到的权矢量,对应反解出一个比导向矢量假定值更为准确的导向矢量,并替代假定值,最终逼近真实的期望信号导向矢量。提出的方法在迭代过程中只需一步递推,无需对导向矢量建立不确定集,避免了在每步迭代中运用拉格朗日数值法或凸优化法,且明显提高了波束形成器的输出信干噪比。仿真结果验证了算法的正确性和有效性。