A NEW METHOD BASED ON ESPRIT FOR ESTIMATING QUADRATIC PHASE COUPLING

This paper presents a new method based on ESPRIT for estimating the quadrati-cally coupled frequency pairs (QC pairs). This method constructs an ESPRIT matrix pencil by exploiting frequency symmetry property of complex third-order cumulants, QC pairs are yielded by evaluating the generalized eigenvalues of this matrix pencil. A simple analysis is provided to show the method is simpler. The accuracy and the high-resolution performance of this method are verified by simulations.     

Nonminimum-phase FIR channel estimation using cumulant matrix pencils

This paper studies the blind estimation of single-input-single-output channels with finite impulse response (FIR) and nonminimum phase. Based on higher order statistics, we introduce a new algorithm that exploits a matrix pencil constructed from a set of cumulant matrices. By solving a generalized eigenvalue problem, channel estimates (up to a scalar ambiguity) can be obtained from nontrivial generalized eigenvectors of this cumulant matrix pencil. With multiple estimation results available, different schemes are given to extract channel information effectively. The proposed algorithm does not require exact knowledge of the channel length and can function properly under channel length overestimation. Numerical simulations demonstrate the robustness of this new algorithm to various adverse conditions.     

Estimation of frequencies and damping factors by two-dimensionalESPRIT type methods

In this paper, we consider two-dimensional (2-D) signals modeled by the sum of damped cisoids. We propose two high-resolution approaches to estimate their frequencies and damping factors. Both high-resolution methods are based on the shift-invariance structure of the signal subspace related to each dimension. The first one estimates the frequency components in both dimensions as in the matrix enhancement and matrix pencil (MEMP) method before pairing them with a new algorithm. The second one consists of the direct estimation of the signal frequency pairs without an additional step to pair the frequencies related to each dimension. We show how these methods can estimate the scattering points of radar images     

Matrix-based higher order spectral analysis for three-wave couplingprocesses

Composite linear and quadratic systems produce three-wave coupling when stimulated by random phase input sinusoids. Due to the nonlinearity of the system, the output frequencies are arithmetically related to the input. Using third-order cumulant statistics and their associated bispectrum, techniques are devised based on phase-insensitive matrix structures for detection and frequency estimation of coupling frequencies. The separation of the third-order cumulant series into symmetric and skew-symmetric portions allows one to exploit their characteristic eigendecompositions for frequency estimation. After symmetrization, biphases can be easily extracted as coefficients of the cumulant sequence. Using a generalized eigenvector representation, one can relate symmetric and skew-symmetric bases by a subspace rotation algorithm. Biphases can be estimated directly from generalized eigenvalues of the matrix pencil formed by symmetric and skew-symmetric matrices. The dimensionality of the matrices can be reduced through the use of cumulant projections that yield a slice of the bispectrum. The Radon transform procedure is related to bispectral processing through an isotropic radial-slice Volterra filter. The compact third-order Kronecker product matrix formulation and algorithms for coupling frequency estimation can also be converted for use in biphase estimation. Simulations showing the performance of the above procedures are also presented for both synthetic and biomedical time series     

四元数和超复数在二维二次非线性相位耦合分析中的应用

针对二维二次非线性相位耦合分析中的分维配对问题,本文首先对一般二维谐波信号模型进行变换,构造了符合四元数结构的新的信号模型.接着讨论了Hamilton四元数、三维超复数及"新四元数"在估计二维谐波频率中的可能性.最后根据上述模型利用特殊的三阶累积量切片分析了加性高斯有色噪声中二维二次非线性相位耦合及联合Hamilton四元数和超复数在二维二次非线性相位耦合中的应用前景.此方法避免了在复数模型的二维二次非线性相位耦合分析中构造复杂的增广矩阵,并从根本上解决了通过分维求取频率之后,频率配对中所有可能产生的错误频率对,以及有可能产生的两维频率估计精度的不平衡性.仿真实验验证了本文的理论.     

Utilization of a unitary transform for efficient computation in the matrix pencil method to find the direction of arrival

In this study, we use the matrix pencil (MP) method to compute the direction of arrival (DOA) of the signals using a very efficient computational procedure in which the complexity of the computation can be reduced significantly by using a unitary matrix transformation. This method applies the technique directly to the data without forming a covariance matrix. Simulation results show that the variance of the estimate approaches to the Cramer-Rao lower bound. Using real computations through the unitary transformation for the MP method leads to a very efficient computational methodology for real time implementation on a digital signal processor chip. A unitary transform can convert the complex matrix to a real matrix along with their eigenvectors and thereby reducing the computational cost at least by a factor of four without sacrificing accuracy. This reduction in the number of computations is achieved by using a transformation, which maps centro-hermitian matrices to real matrices. This transformation is based on Lee's work on centro-hermitian matrices.     

超宽带系统中同步和信道参数的闭式估计算法

提出超宽带系统中同步和信道参数的新型估计算法。首先对接收信号进行傅立叶变换,由傅立叶变换系数构造两个矩阵,把信道时延估计转化成矩阵束的特征值求解问题。在求解出时延后再进一步求解信道参数。算法的最大特点是能得到多径时延和多径增益的闭式解,避免现有算法普遍存在的搜索和迭代求解。     

A quasi-Newton adaptive algorithm for generalized symmetriceigenvalue problem

We first recast the generalized symmetric eigenvalue problem, where the underlying matrix pencil consists of symmetric positive definite matrices, into an unconstrained minimization problem by constructing an appropriate cost function. We then extend it to the case of multiple eigen-vectors using an inflation technique. Based on this asymptotic formulation, we derive a quasi-Newton-based adaptive algorithm for estimating the required generalized eigen-vectors in the data case. The resulting algorithm is modular and parallel, and it is globally convergent with probability one. We also analyze the effect of inexact inflation on the convergence of this algorithm and that of inexact knowledge of one of the matrices (in the pencil) on the resulting eigenstructure. Simulation results demonstrate that the performance of this algorithm is almost identical to that of the rank-one updating algorithm of Karasalo (1986). Further, the performance of the proposed algorithm has been found to remain stable even over 1 million updates without suffering from any error accumulation problems     

新型自适应广义特征向量估计算法及其特性分析

为了发展快速稳定的广义特征向量估计算法,该文提出基于神经网络的新型单维广义特征向量估计算法;通过分析该算法的所有平衡点证明了当且仅当神经网络权向量等于最小广义特征值对应的广义特征向量时该算法达到稳定状态;利用确定性离散时间分析方法完成了所提算法的动态特性分析,给出了保证算法收敛的边界条件;通过膨胀技术将单维算法扩展为多维广义特征向量估计算法,该算法可以根据实际需要增加提取广义特征向量的数量。仿真实验表明所提算法具有很好地收敛性,而且收敛速度优于一些现有算法。     

基于矩阵束的MIMO雷达低仰角快速估计方法

针对多径效应的影响,提出了一种基于矩阵束的MIMO雷达低仰角快速估计方法。该方法同时考虑了发射多径信号和接收多径信号,采用单样本数信号矢量构造了一个前后向矩阵束,并利用两个酉矩阵对该矩阵束进行降维处理,最后采用广义特征值分解的总体最小二乘法来估计目标角度。算法不需要估计数据协方差矩阵,可在低信噪比和单样本数情况下,有效地克服多径效应,实现同时多目标低仰角估计,相比最大似然算法,避免了谱峰搜索,计算量小。仿真结果验证了该算法的有效性。     

基于时空极化导向矢量的阵列信号多维参数联合估计

通过对极化敏感阵列的时域采样构造了具有旋转不变结构的矩阵对,该矩阵对分解的特征值与对应特征向量分别是旋转矩阵和阵列的时空导向矢量,利用该导向矢量和旋转矩阵直接得到信号的频率、二维波达方向和极化的联合估计,该多维参数计算方法具有虚拟阵元和较高的估计精度。简述了多维ESPRIT方法的基本原理,其配对方法采用了多个矩阵束具有相同的特征向量,两种方法均利用了的相同信息-矩阵束的特征值和特征向量,仿真实验验证和比较了两种方法的性能。     

Improved spectral resolution

Two new methods are presented for the estimation of the frequencies of closely spaced complex valued sinusoidal signals in the presence of noise. The most effective method is a computationally efficient method for realization of maximum likelihood or maximum posterior probability estimates of the frequencies. The second method is a class of algorithms for removing some of the deficiencies of present adaptive filtering and correlation-estimation approaches to estimation of frequencies, such as the forward-backward linear prediction method. In both of these new methods one is fitting a signal model to data. In method 1 the data are the observed samples of two complex sinusoids plus noise. In the second method the data are elements of an estimated correlation matrix, or of some of its eigenvectors, obtained from the observed samples.     

A two-stage algorithm for MIMO blind deconvolution of nonstationarycolored signals

A new two-stage algorithm is proposed for the deconvolution of multi-input multi-output (MIMO) systems with colored input signals. While many blind deconvolution algorithms in the literature utilize high order statistics of the output signal for white input signals, the additional information contained in colored input signals allows the design of second-order statistical algorithms. In fact, practical signal sources such as speech signals do have distinct, nonstationary, colored power spectral densities. We present a two-stage signal separation approach in which the first step utilizes a matrix pencil between output auto-correlation matrices at different delays, whereas the second stage adopts a subspace method to identify and deconvolve MIMO systems     

Minimum norm mutual coupling compensation with applications in direction of arrival estimation

This paper introduces a new mutual coupling compensation method based on the minimum norm solution to an underdetermined system of equations. The crucial advantage over previous techniques is that the formulation is valid independent of the type of antenna element and provides good results in situations where signal strengths vary considerably. In using the matrix pencil algorithm to estimate the directions of arrival, the examples show that the proposed method results in significantly lower bias than the traditional open circuit method. The analysis of mutual coupling is also applied in the context of a code division multiple access communication system.     

广义网络法分析复杂孔缝耦合问题

本文利用广义网络法结合连接算法分析复杂孔缝耦合问题.首先根据孔缝的结构及填充特点将其内腔体分为适当的几段,利用边界元法分别计算每段的广义导纳矩阵,再借助连接算法将各段连接起来得到整个孔缝的口径导纳矩阵,最后由广义网络法求解孔缝的口径磁流、散射及传输场.该方法不仅在计算效率方面取得了较大突破,也使复杂填充孔缝的分析得到很大简化.     

针对相干信号DOA估计的改进MUSIC算法

针对相干信号波达方向(Direction of Arrival, DOA)估计,提出了一种改进的多重信号分类(Multiple Signal Classification, MUSIC)算法。首先,利用信号协方差矩阵的两个最大特征值所对应的特征向量,构造出两个Toeplitz矩阵;然后,利用前后向空间平滑思想得到这两个矩阵的无偏估计并求和;最后,利用MUSIC算法从中估计出相干信号DOA。和已有方法相比,该方法无需损失阵列孔径且具有更优的DOA估计性能。     

Noise covariance incorporated MEG-MUSIC algorithm: a method formultiple-dipole estimation tolerant of the influence of background brainactivity

This paper proposes a method of localizing multiple current dipoles from spatio-temporal biomagnetic data. The method is based on the multiple signal classification (MUSIC) algorithm and is tolerant of the influence of background brain activity. In this method, the noise covariance matrix is estimated using a portion of the data that contains noise, but does not contain any signal information. Then, a modified noise subspace projector is formed using the generalized eigenvectors of the noise and measured-data covariance matrices. The MUSIC localizer is calculated using this noise subspace projector and the noise covariance matrix. The results from a computer simulation have verified the effectiveness of the method. The method was then applied to source estimation for auditory-evoked fields elicited by syllable speech sounds. The results strongly suggest the method's effectiveness in removing the influence of background activity     

A restoration–segmentation algorithm based on flexible Arnoldi–Tikhonov method and Curvelet denoising

In this paper, we illustrate a two-stage algorithm consisting of restoration and segmentation to reach binary segmentation from the noisy and blurry image. The results of our method can be applied in main fields of the image processing such as object extraction. In the first stage, we have a linear discrete ill-posed problem with a noise-contaminated right-hand side, arising from the image restoration. We consider problems in which the coefficient matrix is the sum of Kronecker products of matrices and present a global flexible Arnoldi–Tikhonov method coupled with the generalized cross-validation for the computation of the regularization parameter at each iteration. The proposed algorithm is based on the global Arnoldi method that allows using a more flexible solution subspace. In the second stage, we segment the restored image in order to reach a binary image in which the target object is emphasized. In our segmentation method, we use Gaussian scale-space technique to compute discrete gradients of the restored image for pre-segmenting. Also, in order to denoise, we use a tight frame of Curvelet transforms and thresholding which is based on the principle obtained by minimizing Stein’s unbiased risk estimate. This algorithm has an iterative part based on the iterative part of TFA (Cai et al. in SIAM J Imaging 6(1):464–486, 2013), but we use eigenvectors of Hessian matrix of image for improving this part. Theoretical properties of the method of both stages and numerical experiments are presented.     

On SVD for estimating generalized eigenvalues of singular matrixpencil in noise

Several algorithms for estimating generalized eigenvalues (GEs) of singular matrix pencils perturbed by noise are reviewed. The singular value decomposition (SVD) is explored as the common structure in the three basic algorithms: direct matrix pencil algorithm, pro-ESPRIT, and TLS-ESPRIT. It is shown that several SVD-based steps inherent in the algorithms are equivalent to the first-order approximation. In particular, the Pro-ESPRIT and its variant TLS-Pro-ESPRIT are shown to be equivalent, and the TLS-ESPRIT and its earlier version LS-ESPRIT are shown to be asymptotically equivalent to the first-order approximation. For the problem of estimating superimposed complex exponential signals, the state-space algorithm is shown to be also equivalent to the previous matrix pencil algorithms to the first-order approximation. The second-order perturbation and the threshold phenomenon are illustrated by simulation results based on a damped sinusoidal signal. An improved state-space algorithm is found to be the most robust to noise     

Estimating two-dimensional frequencies by matrix enhancement andmatrix pencil

A new method, called the matrix enhancement and matrix pencil (MEMP) method, is presented for estimating two-dimensional (2-D) frequencies. In the MEMP method, an enhanced matrix is constructed from the data samples, and then the matrix pencil approach is used to extract out the 2-D sinusoids from the principal eigenvectors of the enhanced matrix. The MEMP method yields the estimates of the 2-D frequencies efficiently, without solving the roots of a 2-D polynomial or searching in a 2-D space. It is shown that the MEMP method can be faster than a 2-D FFT method if the number of the 2-D sinusoids is much smaller than the data set. Simulation results are provided to show that the accuracy of the MEMP method can be very close to the Cramer-Rao lower bound