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.     

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.     

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.     

一种改进的稳健波束形成算法

针对期望信号的实际方向与约束方向有误差这一问题,提出了信号子空间投影与非线性约束条件下最小化输出功率相结合的一种改进波束形成算法。该方法能缩小期望信号导向矢量的误差范围,避免导向矢量误差过大引起的波束形成算法性能下降,而且能使收敛速度更快,对信号导向矢量偏差较大的波束形成有很强的稳健性。     

基于子空间的线性约束最小二乘恒模算法

线性约束最小二乘恒模算法能够有效克服恒模算法中存在的干扰捕获问题,然而,在实际的系统中,由于受到来自噪声子空间分量的影响,从而导致性能下降。针对这一问题,该文提出了一种基于子空间方法的线性约束最小二乘恒模(SLSCM)多用户检测算法并对其性能进行了理论分析。该算法收敛速度快,信道跟踪能力强,有较好的输出信干噪比和误码率性能。理论分析和仿真实验验证了该文算法的有效性和优越性。     

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。     

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.     

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。     

The Linearly Constrained LSCMA for Blind Multi-user Detection

The least square constant modulus algorithm (LSCMA) is a popular constant modulus algorithm (CMA) because of its global convergence and stability. But the performance will degrade when it is affected by the problem of interference capture in the MC-CDMA system that has several constant modulus signals. In order to overcome this shortage, a linearly constrained LSCMA multiuser detection algorithm is proposed by using the spreading code of the desired user to impose linear constraint on the LSCMA. The proposed algorithm ensures the algorithm convergence to the desired user. Thus the performance of the system is improved. The simulation results demonstrate that the proposed algorithm offers faster convergence rate and provides better output signal-to-interference-plus-noise-ratio (SINR) and bit error rate (BER) performance compared with the traditional LSCMA.     

The performance of an adaptive array combining reference signal and steering vector

Using the knowledge of signal arrival direction and the stochastic characteristics of the steering vector and reference signal, the performance of an adaptive array combining reference signal and steering vector algorithms is presented. Expressions for output signal power, interference power, and noise power are obtained to show that the array sensitivity to the random steering vector error is reduced. Computational results of signal-to-interference-plus-noise ratio (SINR) as a function of random steering vector error are presented, showing that the sensitivity is reduced.     

一种空间色噪声环境下的鲁棒自适应波束

该文提出了一种基于对角加载的鲁棒自适应波束形成算法,以提高空间色噪声环境中自适应波束对方向矢量误差的鲁棒性。该算法首先利用噪声协方差矩阵对阵列相关矩阵进行预白化,同时定义了一个与噪声矩阵相对应的椭圆方向矢量模糊集,然后,通过在该模糊集内进行最坏情况性能优化来确定对角加载因子。和现有的通过迭代求解加载因子的方法不同,该文给出了最优加载因子的近似解析表达式,降低了运算量,揭示了哪些因素可以影响最优加载因子,以及如何影响。仿真结果表明,在空间色噪声环境中,该算法具有很好的鲁棒性,并且,给出的加载因子表达式是其真实最优解的一个准确近似。     

存在阵列导引向量误差时的自适应波束形成算法

提出了一种存在阵列导引向量误差时的自适应波束形成算法。首先,文章提出了一个由接收信号协方差矩阵的噪声子空间和带有随机误差的期望信号导引向量构成的代价函数。然后基于非线性约束条件对此代价函数进行优化。新算法在期望信号导引向量存在误差的情况下仍能提供较好的输出SINR。仿真证明了新算法的有效性。     

基于半正定秩松弛方法的稳健波束形成

现有的向量加权稳健波束形成方法只有在指向误差较小的情况下才能有效估计目标的信号功率;矩阵加权波束形成方法在指向误差较大时,虽然可以估计目标的信号功率,但是它的系统实现复杂度与向量加权稳健波束形成方法相比较大。针对以上问题,该文提出基于半正定秩松弛(SDR)方法的稳健波束形成,该方法优化模型中的目标函数与Capon算法的目标函数相同,优化变量为加权向量的协方差矩阵,并约束方向图的主瓣幅度波动范围、旁瓣电平,协方差矩阵的秩为1。应用SDR方法求得加权向量的协方差矩阵,将该矩阵中的每一行(列)转化为加权向量,然后选择使得方向图主瓣与0 dB之间失真最大值最小的一个加权向量。该方法的系统实现复杂度与传统向量加权方法一致,对信号功率的估计性能与矩阵加权方法相当。仿真实验验证了该文方法可以得到理想的方向图形状,并且可以在大指向误差条件下有效估计信号功率。     

基于谱分析的稳健自适应波束形成算法

针对在导向矢量存在误差情况下,自适应波束形成算法性能下降问题,提出一种基于谱分析的稳健自适应波束形成(SA-RAB)算法。算法利用空域与频域的对称性,根据真实导向矢量与理想导向矢量之间的误差,运用谱分析(SA)技术确定波束主瓣宽度,最后利用二阶锥规划(SOCP)技术在主瓣宽度内形成平顶响应,并在副瓣区域内进行干扰抑制。仿真结果表明:该算法可有效地抑制干扰,并输出理想的信号干扰噪声比(SINR),且提高了波束形成针对导向矢量误差的稳健性,验证了算法的有效性和优越性。     

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.     

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。     

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。     

基于最差性能最优的稳健STAP算法

导向矢量失配和协方差矩阵失配是影响空时自适应处理(STAP)性能的两大主要因素,基于在最差情况下的性能最优,提出了一种稳健的STAP算法.通过对原始问题的数学描述,建立了基于最差性能最优的稳健STAP算法模型,并将原始模型进行等价转换成可以处理的加载样本矩阵求逆(LSMI)算法,得到了加权矢量的具体表达式,通过对Lagrange乘数λ的准确计算,从而给出了LSMI算法中准确的加载量,解决了对角加载技术中加载量估计的难题.仿真分析表明了该算法的正确性和有效性.     

频分MIMO雷达分解迭代稳健自适应波束形成算法

频率分集雷达因其独特的距离依赖波束特性而受到广泛关注。针对频率分集雷达稳健波束形成问题,本文建立了二维频分子孔径MIMO(FDS-MIMO)雷达阵列信号模型,理论导出了基于等效载频的权向量分解解析解,提出了一种分解迭代的稳健自适应波束形成算法。为解决距离依赖波束栅瓣导致的周期性输出信干燥比(SINR)损失的问题,进一步提出了一种沿平面阵两方向互质的频率偏置方案。仿真结果表明,与传统算法相比在导向矢量存在失配的情况下,本文所提方法能够有效抑制输出SINR周期性损失,且具有计算复杂度低,训练样本需求少,抗导向误差失配稳健性强等优点。