Optimal Design of Nearfield Wideband Beamformers Robust Against Errors in Microphone Array Characteristics

Nearfield wideband beamformers for microphone arrays have wide applications, such as hands-free telephony, hearing aids, and speech input devices to computers. The existing design approaches for nearfield wideband beamformers are highly sensitive to errors in microphone array characteristics, i.e., microphone gain, phase, and position errors, as well as sound speed errors. In this paper, a robust design approach for nearfield wideband beamformers for microphone arrays is proposed. The robust nearfield wideband beamformers are designed based on the minimax criterion with the worst case performance optimization. The design problems can be formulated as second-order cone programming and be solved efficiently using the well-established polynomial time interior-point methods. Several interesting properties of the robust nearfield wideband beamformers are derived. Numerical examples are given to demonstrate the efficacy of the proposed beamformers in the presence of errors in microphone array characteristics.     

Subband design of fixed wideband beamformers based on the least squares approach

Subband method is an effective way to reduce the computational complexity of a wideband system and in this paper we study the subband design problem for fixed wideband beamformers, with an emphasis on the design of frequency invariant beamformers (FIBs). We first express the equivalent fullband beam response as a function of the subband beamformer coefficients and then formulate the design problem based on the least squares approach. One direct least squares formulation is first proposed for the design of a general wideband beamformer, and then extended to the FIB design case, followed by three further variations.     

基于子带SDL的宽带自适应波束形成

针对宽带波束形成通常需要大量阵元或延迟线所带来的硬件开销较大,波束形成效率相对较低的问题,提出一种基于子带阵元延迟线（SDL）的宽带自适应波束形成算法。该算法首先建立子带SDL模型,然后利用分析滤波器组将阵元接收的宽带信号分解为子带信号并进行相应的子带线性约束最小方差（LCMV）波束形成,最后通过综合滤波器组得到全带的波束形成。仿真结果表明,子带波束形成不仅具有比全带波束形成更高的效率,更好的频率不变性,更强的抗干扰能力及更快的收敛速度,而且可以大大降低硬件开销。      

Robust microphone arrays using subband adaptive filters

A new adaptive beamformer which combines the idea of subband processing and the generalised sidelobe canceller structure is presented. The proposed subband beamformer has a blocking matrix that uses coefficient-constrained subband adaptive filters to limit target cancellation within an allowable range of direction of arrival. Simulations comparing the fullband and subband adaptive beamformers show that the subband beamformer has better performance than the fullband beamformer when the target and/or interfering signals are coloured. In reverberant environments, the proposed subband beamformer also performs better than its fullband counterpart     

Wideband Beamspace Processing Using Orthogonal Modal Beamformers

We introduce a novel beamspace processing structure that can be used for narrowband or wideband sources located either in nearfield or farfield of a sensor array. Main features of the new structure are: (i) a single parameter is used to steer the processor to any desired radial distance; (ii) a set of fixed frequency invariant orthogonal beamformers are used to transform array data into beamspace; and (iii) consequently, only a single set of beamspace weights are needed to process wideband beamspace data. The utility of the novel structure is illustrated by applications in interference cancellation and direction/range estimation.     

A Competitive Mean-Squared Error Approach to Beamforming

We treat the problem of beamforming for signal estimation where the goal is to estimate a signal amplitude from a set of array observations. Conventional beamforming methods typically aim at maximizing the signal-to-interference-plus-noise ratio (SINR). However, this does not guarantee a small mean-squared error (MSE), so that on average the resulting signal estimate can be far from the true signal. Here, we consider strategies that attempt to minimize the MSE between the estimated and unknown signal waveforms. The methods we suggest all maximize the SINR but at the same time are designed to have good MSE performance. Since the MSE depends on the signal power, which is unknown, we develop competitive beamforming approaches that minimize a robust MSE measure. Two design strategies are proposed: minimax MSE and minimax regret. We demonstrate through numerical examples that the suggested minimax beamformers can outperform several existing standard and robust methods, over a wide range of signal-to-noise ratio (SNR) values. Finally, we apply our techniques to subband beamforming and illustrate their advantage in estimating a wideband signal.     

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.     

A User Parameter-Free Robust Adaptive Beamformer Based on General Linear Combination in Tandem with Steering Vector Estimation

If there is a mismatch between the assumed steering vector (SV) and the real value, the performance of adaptive beamforming methods is degraded. When the signal SV is known exactly but the sample size is small, the performance degradation can also occur. The second kind of degradation is mainly due to the mismatch between the sample covariance matrix and the real one. Almost all existing robust adaptive beamformers are proposed to improve the robustness against these two types of mismatch. Indeed, most of them are user parameter dependent, and the user parameter-free robust beamformers are scarce. As one of the shrinkage methods, the general linear combination (GLC) based beamformer is a good user parameter-free robust beamformer. However, it is only suitable for the scenarios with low sample size and/or small SV mismatch. In this paper, we propose a new robust beamformer, and it is based on general linear combination in tandem with SV estimation (GLCSVE). The proposed approach is superior to GLC in two aspects. One is that the GLCSVE beamformer performs well not only with small but also with large sample size. The other is that the GLCSVE can effectively deal with a large range of SV mismatch. Moreover, the proposed GLCSVE approach is a user parameter-free robust beamformer, and is more suitable for application than the parameter dependent approaches. The idea of our method can also be used to enhance other shrinkage based beamformers.     

Robust optimization of transmit/receive beamformer for MIMO downlink with imperfect CSI at base station

A robust scheme is proposed to jointly optimize transmit/receive beamformers for Multiple Input Multiple Output （MIMO） downlinks where the available Channel State Information （CSI） at Base Station （BS） （CSIBS） is imperfect. The criterion is to minimize the sum Mean Square Error （sum-MSE） over all users under a constraint on the total transmit power, which is a non-convex and non-linear problem. Observing from the first order optimization condition that the optimal transmit/receive beamformers are mutually dependent, the transmit/receive beamformers for each user are updated iteratively until the sum-MSE is minimized. Simulation results indicate that the proposed scheme can effectively mitigate the system performance loss induced by imperfect CSIBS.     

l2 and l1 beamformers: recursiveimplementation and performance analysis

Studies array beamformers as optimal waveform estimators. The authors apply an inverse problem formulation, presenting an integrated design to quadratic (l₂) and least absolute value (l₁ ) beamformers. The general solution of the l₂ beamformers is parameterized by a regularizing parameter that weights the confidence placed by the designer on prior knowledge versus the quality of the measurements. This regularizing parameter is used to establish an equivalence between alternative l₂ beamformers. The authors then develop time-recursive implementations of the l₂ and l₁ beamformers. The performance of these beamformers is studied next. The authors show that 1) in the presence of correlated arrivals, the MMSE beamformer uses constructively the correlation between incoming signals in reconstructing the estimated field, while rejecting the uncorrelated returns, and 2) the l₁ beamformer has the ability to adjust itself to unexpected noise conditions because it is considerably more robust than the l₂ beamformers to unmodeled impulsive noise or to the occurrence of malfunctioning sensors. The analysis is confirmed by simulated studies     

Applications of RF aperture-array spatially-bandpass 2-D IIR filters in sub-Nyquist spectrum sensing,wideband doppler radar and radio astronomy beamforming

The application of two-dimensional (2-D) infinite impulse response (IIR) spatially-bandpass (SBP) filters as a digital beamformer for a wide spectrum of practical applications spanning wireless cognitive radio communications, doppler radar, and radio astronomy instrumentation is discussed. The paper starts with an introduction of the recently proposed 2-D SBP filter. The first application is a spectrum sensing scheme for dynamic spectrum access based cognitive radios. A 2-D IIR SBP filter is used in conjunction with a sub-Nyquist wideband signal reconstruction technique to achieve aperture-array directional spectrum sensing using sub-Nyquist sparse sampling based on the recently reported Eldar algorithm. The second application is related to wideband pulse and continuous-wave frequency modulated Doppler radar sensing. The SBP filter is integrated with a wideband radar back-end connected to an electronically-steerable aperture antenna. A a low-complexity directional localization algorithm is presented, which estimates the range and angle of a target scatterer with a signal to interference ratio improvement of 10 dB. We also present applications of 2-D IIR SBP in the fields of classification and remote sensing of unmanned aerial vehicles. Finally, a digital aperture-array wideband beamforming model using the 2-D IIR SBP filters is presented for radio telescope systems based on dense aperture arrays and time-domain beamforming. A well-known example is the study of pulsar astrophysics using a highly-directional aperture antenna system. The 2-D IIR SBP beamformer is simulated as the digital backend of the time-domain beamforming system with array signals synthesized using measured time-domain signatures from the Crab pulsar obtained from the GAVRT. The SBP filter shows a gain of 12.3 dB with an order of magnitude lower circuit complexity compared to traditional phased-array digital beamformers. To obtain comparable levels of SINR improvement, the wideband phased-array beamformers require 48-point FFTs per antenna. Assuming the optimum three real-multiplications per complex multiplication for the Gauss algorithm, it is discovered that the proposed 2-D IIR SBP beamformers are more than 97 % lower in digital multiplier complexity compared to traditional FIR phased-array FFT-beamformers.     

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。     

Broadband beamforming using Laguerre filters

Space-time processing is a well-substantiated method for designing broadband beamformers. In the conventional Frost space-time beamformer, tapped delay line (TDL) filters are used in each branch of the array to create a wideband response for interference suppression. In this article a new space-time beamforming method is introduced in which Laguerre filters replace the traditional TDL filters in the Frost beamformer. The Laguerre filters are fundamentally IIR filters but with only one pole in their structure. Unlike other IIR-based space-time beamforming methods, the proposed method does not need an adaptive procedure for the pole adjustment and is inherently stable. Simulation results show superior performance of the proposed method compared to the Frost beamformer and comparable results against other IIR-based beamformers with much less computational complexity and guaranteed stability.     

A new delayless subband adaptive filter structure

Adaptive subband techniques have been developed to reduce complexity and slow convergence problems of the traditional fullband high-order adaptive filters. Some of the disadvantages often encountered in most of the proposed architectures are the effect of aliasing associated with the multirate structure, which is a source of error in the modeling of the unknown system, and the delay introduced in the signal path. We present a new delayless maximally decimated structure where the optimal subband filters are related to the wideband system in a closed form. They make use of a special DFT analysis filterbank where the polyphase components of the prototype filter represent fractional delays so that there is no need for adaptive cross-filters, and the unknown system can modeled perfectly in a closed-loop scheme. We interpret the proposed structure as a special case of a block adaptive filter with lower computational complexity than the conventional fullband LMS algorithm. Some computer simulations are presented in order to verify the good features of the proposed structure     

Efficient wideband source localization using beamforming invariancetechnique

A novel scheme for wideband direction-of-arrival (DOA) estimation is proposed. The technique performs coherent signal subspace transformation by a set of judiciously constructed beamforming matrices. The beamformers are chosen to transform each of the narrowband array manifold vectors into the one corresponding to the reference frequency, regardless of the actual spatial distribution of the sources. The focused data correlation matrix can thus be obtained without any preliminary DOA estimation or iteration. A simplified version of the beamspace Root-MUSIC algorithm is developed and used in conjunction with the proposed method to efficiently localize multiple wideband sources with a linear, equally spaced array. Numerical simulations are conducted to demonstrate the efficacy of the new scheme     

Design of broadband beamformers robust against gain and phase errors in the microphone array characteristics

Fixed broadband beamformers using small-size microphone arrays are known to be highly sensitive to errors in the microphone array characteristics. The paper describes two design procedures for designing broadband beamformers with an arbitrary spatial directivity pattern, which are robust against gain and phase errors in the microphone array characteristics. The first design procedure optimizes the mean performance of the broadband beamformer and requires knowledge of the gain and the phase probability density functions, whereas the second design procedure optimizes the worst-case performance by using a minimax criterion. Simulations with a small-size microphone array show the performance improvement that can be obtained by using a robust broadband beamformer design procedure.     

宽带聚焦数字波束形成技术

分析了宽带信号波束形成研究的应用背景，并概述其国内外研究现状以及所提出方法的基本思路和应用范围。根据最近提出的频率域频率不变波束形成技术需要进行方位角初次估计和进行多次奇异值分解的问题，提出了在任意传感器阵列存在误差和互耦的情况下，基于摄动方法的宽带信号方位估计算法。该方法在考虑阵列位置、增益和相位测量误差和阵元之间存在互耦的情况下，提出了聚焦矩阵的摄动算法；最后，利用聚焦求和窄带方位估计的方法对宽带信号进行方位估计。     

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。     

Broadband beamforming with power complementary filters

This paper addresses the design of broadband finite impulse response (FIR) beamformers with a power complementarity property. The power complementarity requirement is needed to preserve the whiteness of the channel noise at the beamformer output, which allows the application of optimum trellis-based equalizers to the output signal. The power complementarity property imposes non-negative definite quadratic constraints on the beamforming filters so that the beamformer design is expressed as a constrained quadratic optimization problem. Two approaches are proposed to solve this problem. The first method is a Lagrangian relaxation technique, which exploits the fact that the dual mathematical problem reduces to the unconstrained minimization of a convex function over a convex domain. A second approach employs a cascaded lattice representation of the power complementary filterbank and performs the beamformer design incrementally, one lattice stage at a time