A gradient descent implementation of the adaptive robust narrowband constrained LMS beamformer

Classical adaptive beamforming strategies have been shown to exhibit a substantial performance degradation if an error exists in the estimation of the angle of arrival (AOA). The optimization problem can be modified to incorporate an improved constraint allowing for robustness to AOA imperfections. In this paper, we propose a gradient descent implementation of the robust adaptive beamformer whereby a direct relation is established between the Lagrange multiplier and the adaptation step size. This allows for the heuristic approximation of one of the parameters while establishing a valid range for the other. Computer simulations have been used to confirm the findings of this study and illustrate the performance of the developed algorithm.     

A robust adaptive beamformer for microphone arrays with a blockingmatrix using constrained adaptive filters

This paper proposes a new robust adaptive beamformer applicable to microphone arrays. The proposed beamformer is a generalized sidelobe canceller (GSC) with a new adaptive blocking matrix using coefficient-constrained adaptive filters (CCAFs) and a multiple-input canceller with norm-constrained adaptive filters (NCAFs). The CCAFs minimize leakage of the target-signal into the interference path of the GSC. Each coefficient of the CCAFs is constrained to avoid mistracking. The input signal to all the CCAFs is the output of a fixed beamformer. In the multiple-input canceller, the NCAFs prevent undesirable target-signal cancellation when the target-signal minimization at the blocking matrix is incomplete. The proposed beamformer is shown to be robust to target-direction errors as large as 200 with almost no degradation in interference-reduction performance, and it can be implemented with several microphones. The maximum allowable target-direction error can be specified by the user. Simulated anechoic experiments demonstrate that the proposed beamformer cancels interference by over 30 dB. Simulation with real acoustic data captured in a room with 0.3-s reverberation time shows that the noise is suppressed by 19 dB. In subjective evaluation, the proposed beamformer obtains 3.8 on a five-point mean opinion score scale, which is 1.0 point higher than the conventional robust beamformer     

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。     

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.     

The output SINR of the linearly constrained beamformer

The authors derive expressions of the output signal-to-interference plus noise ratio (SINR) of the linearly constrained narrowband beamformer in noncoherent situations using a vector approach. Numerical results are included     

Time-delay- and time-reversal-based robust Capon beamformers for ultrasound imaging

Currently, the nonadaptive delay-and-sum (DAS) beamformer is extensively used for ultrasound imaging, despite the fact that it has lower resolution and worse interference suppression capability than the adaptive standard Capon beamformer (SCB) if the steering vector corresponding to the signal of interest (SOI) is accurately known. The main problem which restricts the use of SCB, however, is that SCB lacks robustness against steering vector errors that are inevitable in practice. Whenever this happens, the performance of SCB may hecome worse than that of DAS. Therefore, a robust adaptive beamformer is desirable to maintain the robustness of DAS and adaptivity of SCB. In this paper we consider a recent promising robust Capon beamformer (RCB) for ultrasound imaging. We propose two ways of implementing RCB, one based on time delay and the other based on time reversal. RCB extends SCB by allowing the array steering vector to be within an uncertainty set. Hence, it restores the appeal of SCB including its high resolution and superb interference suppression capabilities, and also retains the attractiveness of DAS including its robustness against steering vector errors. The time-delay-based RCB can tolerate the misalignment of data samples and the time-reversal-based RCB can withstand the uncertainty of the Green's function. Both time-delay-based RCB and time-reversal-based RCB can be efficiently computed at a comparable cost to SCB. The excellent performances of the proposed robust adaptive beamforming approaches are demonstrated via a number of simulated and experimental examples.     

基于稳健Capon波束形成技术的矢量相关测向方法

为了弥补阵列天线导向矢量失配对测向性能的影响,提出基于稳健Capon波束形成技术的矢量相关测向方法。与直接使用相位差的常规相关干涉测向技术不同,该方法首先利用稳健Capon波束形成技术估计目标信号的真实导向矢量;然后通过导向矢量的相关拟合确定目标信号方向。通过仿真分析,得出了以测向为衡量标准时不确定集约束参数的选择原则。仿真结果表明该方法能够弥补阵列流型失配的影响、准确测量目标信号方向。     

最大稀疏稳健恒定束宽波束形成器设计

为了降低宽带阵列恒定束宽的实现复杂性,在分析宽带阵列稀疏性的基础上,构造了以阵元和抽头延迟线(TDL, tapped delay line)稀疏性的凸组合为目标函数,满足恒定束宽约束的波束形成器优化模型,降低了所需的阵元和TDL个数。引入重加权机制,通过序列凸优化,使稀疏性递增并收敛到最大值,证明了保证波束形成器稳健性的范数约束与最大TDL稀疏目标函数之间的等价性。仿真结果表明,可用较少的阵元及TDL个数获得相同的恒定束宽性能,具有工程实用价值。     

Neural minor component analysis approach to robust constrained beamforming

Since the pioneering work of S.-I. Amari (1977) and E. Oja (1982; 1989; 1992), principal component neural networks and their extensions have become an active adaptive signal processing research field. One of such extensions is minor component analysis (MCA), that proves to be effective in tasks such as robust curve/surface fitting and noise reduction. The aims of the paper are to give a detailed and homogeneous review of one-unit first minor/principal component analysis and to propose an application to robust constrained beamforming. In particular, after a careful presentation of first/minor component analysis algorithms based on a single adaptive neuron, along with relevant convergence/steady-state theorems, it is shown how the adaptive robust constrained beamforming theory by H. Cox et al. (see IEEE Trans. Acoust. Speech. Sig. Process., vol.34, no.3, p.393-8, 1986; vol.35, no.10, p.1365-76, 1987) may be advantageously recast into an MCA setting. Experimental results obtained with a triangular array of microphones introduced in a teleconference context help to assess the usefulness of the proposed theory.     

Blind concurrent beamformer

The electronically steerable parasitic array radiator (ESPAR) is a smart antenna based on the adjustment of reactances at parasitic elements. A new blind beamformer is presented, for use with reactance domain arrays, such as the ESPAR. Two stochastic gradient algorithms work concurrently so that two distinct cost functions are simultaneously minimised. Results show that the new blind beamformer presents a faster convergence and a lower steady-state mean squared error     

Capon estimation of covariance sequences

Estimating the covariance sequence of a wide-sense stationary process is of fundamental importance in digital signal processing (DSP). A new method, which makes use of Fourier inversion of the Capon spectral estimates and is referred to as theCapon method, is presented in this paper. It is shown that the Capon power spectral density (PSD) estimator yields an equivalent autoregressive (AR) or autoregressive moving-average (ARMA) process; hence, theexact covariance sequence corresponsing to the Capon spectrum can be computed in a rather convenient way. Also, without much accuracy loss, the computation can be significantly reduced via an approximate Capon method that utilizes the fast Fourier transform (FFT). Using a variety of ARMA signals, we show that Capon covariance estimates are generally better than standard sample covariance estimates and can be used to improve performances in DSP applications that are critically dependent on the accuracy of the covariance sequence estimates.This work was supported in part by National Science Foundation Grant MIP-9308302, Advanced Research Project Agency Grant MDA-972-93-1-0015, the Senior Individual Grant Program of the Swedish Foundation for Strategic Research and the Swedish Research Council for Engineering Sciences (TFR).     

基于模约束的稳健Capon波束形成算法

针对Capon波束形成器在导向矢量失配存在时的较差指向性能,利用模约束来提高算法的稳健性.详细分析了模不等式约束Capon波束形成器(NICCB)解的存在情况,给出了NICCB中模不等式约束参数的选择范围.由于模等式约束远远强于不等式约束,所以模等式约束Capon波束形成器(NECCB)的稳健性要远远优于NICCB,故提出NECCB并进行了有效的求解.仿真分析验证了理论分析的正确性,当模约束参数在允许的范围内选择时,最优NICCB和NECCB的波束指向性能变化不是很明显,但是NECCB的性能要明显优于NICCB.     

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。     

基于半实值Capon的高效波达方向估计算法

子空间类超分辨波达方向(DOA)估计算法需预先估计信号个数,当信号个数估计错误时,其性能会严重下降。该文提出一种新颖的半实值Capon(SRV-Capon)DOA估计算法。该算法继承了Capon算法无需信号个数估计的优点并克服了现存实值算法仅适用于中心对称阵列(CSA)的缺点。相比于Capon算法,SRV-Capon仅利用阵列接收数据协方差矩阵的实部求逆构建空间谱函数,实现了谱值计算的半实值化并将谱搜索的范围压缩至原来的一半,从而至少降低约75%的计算量。理论分析和仿真实验证明了该算法的有效性。     

Computationally efficient two-dimensional Capon spectrum analysis

We present a computationally efficient algorithm for computing the 2-D Capon (1969) spectral estimator. The implementation is based on the fact that the 2-D data covariance matrix will have a Toeplitz-block-Toeplitz structure, with the result that the inverse covariance matrix can be expressed in closed form by using a special case of the Gohberg-Heinig (1974) formula that is a function of strictly the forward 2-D prediction matrix polynomials. Furthermore, we present a novel method, based on a 2-D lattice algorithm, to compute the needed forward prediction matrix polynomials and discuss the difference in the so-obtained 2-D spectral estimate as compared with the one obtained by using the prediction matrix polynomials given by the Whittle-Wiggins-Robinson (1963, 1965) algorithm. Numerical simulations illustrate the improved resolution as well as the clear computational gain in comparison to both the well-known classical implementation and the method published by Liu et al.(see IEEE Trans. Aerosp. Electron. Syst., vol.34, p.1314-19, 1998)     

Adaptive beamformer orthogonal rejection test

Research in the area of signal detection in the presence of unknown interference has resulted in a number of adaptive detection algorithms. Examples of such algorithms include the adaptive matched filter (AMF), the generalized likelihood ratio test (GLRT), and the adaptive coherence estimator (ACE). Each of these algorithms results in a tradeoff between detection performance for matched signals and rejection performance for mismatch signals. This paper introduces a new detection algorithm we call the adaptive beamformer orthogonal rejection test (ABORT). Our test decides if an observation contains a multidimensional signal belonging to one subspace or if it contains a multidimensional signal belonging to an orthogonal subspace when unknown complex Gaussian noise is present. In our analysis, we use a statistical hypothesis testing framework to develop a generalized likelihood ratio decision rule. We evaluate the performance of this decision rule in both the matched and mismatched signal cases. Our results show that for constant power complex Gaussian noise, if the signal is matched to the steering vector, ABORT, GLRT, and AMF give approximately equivalent probability of detection, higher than that of ACE, which trades detection probability for an extra invariance to scale mismatch between training and test data. Of these four tests, ACE is most selective and, therefore, least tolerant of mismatch, whereas AMF is most tolerant of mismatch and, therefore, least selective, ABORT and GLRT offer compromises between these extremes, with ABORT more like ACE and with GLRT more like AMF     

Minimum-noise-variance beamformer with an electromagnetic vectorsensor

We study the performance of the minimum-noise-variance beamformer employing a single electromagnetic (EM) vector sensor that is capable of measuring the complete electric and magnetic fields induced by EM signals at one point. Two types of signals are considered: one carries a single message, and the other carries two independent messages simultaneously. The state of polarization of the interference under consideration ranges from completely polarized to unpolarized. We first obtain explicit expressions for the signal to interference-plus-noise ratio (SINR) in terms of the parameters of the signal, interference, and noise. Then, we discuss some physical implications associated with the SINR expressions. These expressions provide a basis for effective interference suppression as well as generation of dual-message signals of which the two message signals have minimum interference effect on one another. We also analyze the characteristics of the main-lobe and side-lobe of the beampattern of an EM vector sensor and compare them with other types of sensor arrays     

频域宽带波束形成器优化设计

将常规频域宽带波束形成运用到电子战侦察系统存在一个问题：分块DFT处理会造成时域输出波形在块衔接处产生周期性失真,影响系统对信号时域参数的检测。为解决上述问题,在分析失真产生原因的基础上提出采用交叠DFT处理对传统方案予以改进,该方法首先对预处理数据进行交叠分段,再完成DFT运算及后续窄带处理。最后的仿真通过对比改进前后方案时域输出波形的保真度,验证改进后方法能有效缓解时域输出波形失真对系统的影响,并为工程实现提供了依据。     

基于特征空间的相干干扰抑制技术

该文把多线性约束和特征空间技术相结合,提出了基于特征空间的多约束最小方差波束形成器(EM-CMVB),该波束形成器可以有效抑制相干干扰。EMCMVB是利用估计得到的相干干扰方向和阵列信号相关矩阵特征分解来得到修改的信号子空间,再把多约束最小方差波束形成器(MCMVB)的权矢量向修改的信号子空间投影来得出新的权矢量。经分析表明,EMCMVB的性能优于MCMVB的性能。最后,给出了计算机仿真结果,证实了EMCMVB的优越性。     

Analysis of a decision directed beamformer

Studies a technique for using decision direction to extract digital signals from antenna array data. The algorithm alternates between 1) estimating and demodulating the received signals and 2) using the resulting bit decisions to regenerate the signal waveforms and recompute the beamformer weights. An analysis of the (asymptotic) symbol error rate performance of the algorithm for the case of M-ary PSK signals is included, along with several representative simulation examples