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.     

一种分解迭代二阶锥规划鲁棒自适应波束形成算法

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,该文提出了一种最差性能最优的分解迭代鲁棒自适应波束形成算法。该算法对非凸的幅度响应约束问题进行分解处理,将问题转化为迭代的二阶锥规划问题,从而可对鲁棒响应区的波束宽度和纹波水平进行自由控制,并可得到较高的输出信干噪比。此外,与现有大部分该类鲁棒波束形成方法相比,提出的算法直接对权矢量进行优化,无需使用谱分解算法,避免了阵列结构的限制,可适用于任意阵形。仿真结果验证了算法的正确性和有效性。     

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 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.     

基于稀疏约束和SRV约束的宽带自适应波束形成

针对传统的宽带MVDR自适应波束形成中,抑制干扰的同时会抬高旁瓣电平,且过多的线性约束会导致波束输出的SINR性能下降的问题,提出了一种基于SRV约束和稀疏约束的低旁瓣、高增益宽带自适应波束形成方法.该方法在窄带MVDR自适应波束形成基础上,通过增加波束图稀疏约束来降低波束的旁瓣电平,同时利用空间响应偏差(SRV)约束将窄带算法推广到宽带MVDR 自适应波束形成中,极大地降低了算法的复杂度,改善了波束输出的SINR 性能.与传统方法相比,该方法在降低宽带波束的旁瓣电平的同时,还具有良好的干扰抑制效果.数值仿真实验验证了该方法的有效性.     

非完备杂波先验知识场景下MIMO-STAP稳健波形设计

本文考虑了色高斯干扰条件下MIMO STAP稳健波形优化问题以提高非完备杂波先验知识条件下多输入多输出（MIMO）雷达体制下空时自适应处理（STAP）最坏情况下探测性能。由于高斯干扰（包括杂波、干扰以及热噪声）场景下最大化系统输出信干噪比（SINR）等价于最大化MIMO STAP检测性能,因而在本文所建立杂波协方差估计误差的模型基础上,总功率发射以及参数不确定凸集约束下,经推导可得稳健波形优化问题。为求解得到的复杂非线性问题,本文提出了一种迭代算法以优化发射波形相关阵（WCM）从而最大化凸不确定集上最差情况下的输出SINR进而改善最差情况下MIMO STAP的检测性能。通过利用对角加载（DL）方法,所提算法中的每个迭代步骤皆可表示为能获得高效求解的半定规划（SDP）问题。与非稳健方法及非相关波形相比,数值实验验证了本文所提方法的有效性。      

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.     

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。     

A Novel Adaptive Antenna Array for DS/CDMA Code Acquisition

Equipped with an adaptive beamformer, existing adaptive array code acquisition still relies on the correlator structure. Due to the inherent property of the associated serial-search scheme, its mean acquisition time is large, especially in strong interference environments. In this paper, we propose a novel adaptive filtering scheme to solve the problem. The proposed scheme comprises two adaptive filters, an adaptive spatial and an adaptive temporal filter. With a specially designed structure, the spatial filter can act as a beamformer suppressing interference, while the temporal filter can act as a code-delay estimator. A mean squared error (MSE) criterion is proposed such that these filters can be simultaneously adjusted by a stochastic gradient descent method. The performance as well as the convergence behavior of the proposed algorithm are analyzed in detail. Closed-form expressions for optimum filter weights, optimum beamformer signal-to-interference-plus-noise ratio (SINR), steady-state MSE, and mean acquisition time are derived for the additive white Gaussian noise (AWGN) channel. Computer simulations show that the mean acquisition time of the proposed algorithm is much shorter than that of the correlator-based approach, and the derived theoretical expressions are accurate.     

相位响应固定幅度响应约束的稳健波束形成方法

传统的幅度约束波束形成器是一个非凸问题,需将原始模型化为线性规划进行间接求解。该文针对均匀线阵提出一种相位响应固定幅度响应约束(PFMC)的稳健波束形成方法。利用权矢量逆序列对应的传递函数与阵列响应函数只差一个相位因子这一性质,将阵列响应的相位设置为固定的线性相位,仅对阵列响应的实数幅度进行约束,从而得到一个凸的代价函数,最优权矢量可以利用内点法求出。同时考虑到协方差矩阵误差,利用最坏(WC)情况性能最优原理提出PFMC-WC算法改善PFMC的性能。与传统幅度约束波束形成器相比,减少了约束个数并省掉了恢复权矢量过程,从而降低了计算量。此外,由于相位响应得到保证,该文算法相对于传统算法具有更好的性能。仿真实验验证了该文算法的有效性。     

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.     

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.     

Waveform optimization for MIMO-STAP to improve the detection performance

In this letter, we address the problem of waveform optimization for multi-input multi-output (MIMO) space-time adaptive processing (STAP) in the presence of colored Gaussian disturbance. A novel diagonal loading (DL) based method is proposed to optimize the waveform covariance matrix (WCM) for maximizing the output signal-interference-noise ratio (SINR) of MIMO-STAP such that the detection performance can be maximized. The resultant nonlinear optimization problem is reformulated as a semidefinite programming (SDP) one, which can be solved very efficiently. Simulation results show that the output SINR of MIMO-STAP can be improved considerably by the proposed method, as compared to that of uncorrelated waveforms.     

转弯畸变拖曳阵声呐鲁棒Capon波束形成方法

针对柔性拖曳阵转弯机动过程,在积累时间内阵形变化导致自适应波束形成性能下降的问题,该文提出一种基于时变阵形聚焦和降维处理的低复杂度鲁棒波束形成方法。首先,基于阵列Water-Pulley模型估计时变阵形,以基准阵形为参考采用预成导向方法对阵形进行聚焦,消除数据中阵形模型偏差;然后,以阵形聚焦后数据协方差矩阵的共轭梯度方向矢量构成降维矩阵,构造大孔径阵列降维鲁棒Capon波束形成器。仿真结果表明:所提方法能够提高转弯机动拖曳阵波束形成输出信号-干扰噪声比(SINR)。海试验证表明:该方法能够提高测向空间谱上目标输出信噪比,提高大孔径阵列机动状态下对弱目标检测能力,同时能区分目标左右舷。     

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。     

MIMO雷达稳健的发射波束形成算法

针对发射导向矢量存在未知误差的问题,该文提出了一种MIMO雷达稳健的发射波束形成算法(Robust Transmitting Beamforming, RTB)。该算法在稳健的接收波束形成算法的基础上,以最大化最差情况输出信干噪比为优化准则,对发射导向矢量误差做稳健的发射波束形成。RTB算法属于对角加载方法。仿真结果表明,相比于已有算法,RTB算法的稳健性更好、计算复杂度更低、收敛速度更快。     

Low-Complexity Iterative Adaptive Linearly Constrained Minimum Variance Beamformer

The closed-form solution of linearly constrained minimum variance (CF-LCMV) suffers heavy computational burden from two-matrix inversion when computing the optimal vector. CF-LCMV is not an adaptive beamformer and performs poorly with low signal-to-interference-plus-noise-ratio (SINR) and small number of snapshots. In this study, we derive a low-complexity iterative adaptive LCMV (IA-LCMV) algorithm based on conjugate gradient (CG) technique with threefold advantages: first, IA-LCMV can remarkably alleviate the complexity of CF-LCMV; second, IA-LCMV can adjust output adaptively with comparable convergence speed. Finally, it shows robust performance against low SINR and small number of snapshots. Simulation results demonstrate the efficacy of our proposed algorithms.     

高低轨频率共存卫星通信系统鲁棒波束成形算法研究

针对静止轨道(Geostationary Earth Orbit, GEO)卫星系统和低轨道(Low Earth Orbit, LEO)卫星系统频率共享时存在的干扰问题,本文基于低轨分布式卫星编队提出了一种鲁棒自适应波束成形算法,从空间域功率隔离角度解决了高低轨卫星通信系统上行链路共用频谱时GEO用户对于LEO卫星共线干扰问题。算法中综合考虑卫星通信系统长传播时延导致的阵列导向矢量存在一定误差,在基于线性约束最小方差(LCMV)准则的自适应波束成形器中设计了考虑系统最恶劣误差情况的鲁棒性约束,并采用泰勒级数逼近法求解波束成形器加权矢量。仿真结果表明本文的鲁棒波束成形算法在卫星通信环境下适应度较高,能够有效地缓解高低轨卫星通信系统频率共享带来的同频干扰问题。      

非线性能量收集下的鲁棒性波束赋形

在无线信息能量同步传输系统中,考虑实际电路实现中的非线性能量收集模型,提出了一种具有鲁棒性的波束赋形设计方案。为了提升系统用户间的公平性,对最小的用户信干噪比进行优化,并构建了一个非凸的优化问题。针对问题的非凸特性以及引入信道估计误差带来的限制条件,基于S过程对问题进行变形,并通过半定松弛技术对问题进行凸化,提出了一种基于二分法的迭代波束赋形算法。仿真结果表明,相比于非鲁棒性算法,所提的算法能够获得25%到50%的性能增益。因此,所提算法更加适用于实际系统中的非理想信道环境。仿真结果还表明所提算法相比于线性能量收集模型或迫零波束赋形等方法,能够取得更好的公平性能。