基于雷达系统抗干扰的卷积盲分离算法研究

如何提高雷达系统的抗干扰能力一直是雷达信号处理中比较关注的问题。卷积混合盲分离技术是当前盲分离研究的热点和难点。文中用卷积混合盲分离算法来分离雷达系统接收的信号,把卷积混合的干扰信号和有用信号分离开来,以实现雷达系统抗干扰的目的。该方法使用基于Householder变换的高阶累积量的联合对角化的频域方法来分离卷积混合的雷达接收信号。计算机仿真表明,该抗干扰方法可把卷积混合的雷达信号和干扰信号分离出来,且达到较好的分离效果。     

Blind Signal Separation Using Steepest Descent Method

A method that significantly improves the convergence rate of the gradient-based blind signal separation (BSS) algorithm for convolutive mixtures is proposed. The proposed approach is based on the steepest descent algorithm suitable for constrained BSS problems, where the constraints are included to ease the permutation effects associated with the convolutive mixtures. In addition, the method is realized using a modified golden search method plus parabolic interpolation, and this allows the optimum step size to be determined with only a few calculations of the cost function. Evaluation of the proposed procedure in simulated environments and in a real room environment shows that the proposed method results in significantly faster convergence for the BSS when compared with a fixed step-size gradient-based algorithm. In addition, for blind signal extraction where only a main speech source is desired, a combined scheme consisting of the proposed BSS and a postprocessor, such as an adaptive noise canceller, offers impressive noise suppression levels while maintaining low-target signal distortion levels.     

An MSE-Based Method to Avoid Permutation/Gain Indeterminacy in Frequency-Domain Blind Source Separation

This paper presents a novel technique for separating convolutive mixtures of statistically independent non-Gaussian signals without resorting to an a priori knowledge of the sources or the mixing system. This problem is solved in the frequency domain by transforming the convolutive mixture into several instantaneous mixtures which are independently separated using blind source separation (BSS) algorithms. First, the instantaneous mixture at one frequency is solved using the joint approximate diagonalization of eigenmatrices (JADE) technique, and the other mixtures are then separated using the mean squared error (MSE) criterion. As a special case of this method, we consider the separation of non-Gaussian temporally white signals transmitted in blocks with zero padding between them.     

Blind source separation for convolutive mixtures based on the joint diagonalization of power spectral density matrices

This paper studies the problem of blind separation of convolutively mixed source signals on the basis of the joint diagonalization (JD) of power spectral density matrices (PSDMs) observed at the output of the separation system. Firstly, a general framework of JD-based blind source separation (BSS) is reviewed and summarized. Special emphasis is put on the separability conditions of sources and mixing system. Secondly, the JD-based BSS is generalized to the separation of convolutive mixtures. The definition of a time and frequency dependent characteristic matrix of sources allows us to state the conditions under which the separation of convolutive mixtures is possible. Lastly, a frequency-domain approach is proposed for convolutive mixture separation. The proposed approach exploits objective functions based on a set of PSDMs. These objective functions are defined in the frequency domain, but are jointly optimized with respect to the time-domain coefficients of the unmixing system. The local permutation ambiguity problems, which are inherent to most frequency-domain approaches, are effectively avoided with the proposed algorithm. Simulation results show that the proposed algorithm is valid for the separation of both simulated and real-word recorded convolutive mixtures.     

MIMO-AR System Identification and Blind Source Separation for GMM-Distributed Sources

The problem of blind source separation (BSS) and system identification for multiple-input multiple-output (MIMO) auto-regressive (AR) mixtures is addressed in this paper. Two new time-domain algorithms for system identification and BSS are proposed based on the Gaussian mixture model (GMM) for sources distribution. Both algorithms are based on the generalized expectation-maximization (GEM) method for joint estimation of the MIMO-AR model parameters and the GMM parameters of the sources. The first algorithm is derived under the assumption of unstructured input signal statistics, while the second algorithm incorporates the prior knowledge about the structure of the input signal statistics due to the statistically independent source assumption. These methods are tested via simulations using synthetic and audio signals. The system identification performances are tested by comparison between the state transition matrix estimation using the proposed algorithms and the well-known multidimensional Yule-Walker solution followed by an instantaneous BSS method. The results show that the proposed algorithms outperform the Yule-Walker based approach. The BSS performances were compared to other convolutive BSS methods. The results show that the proposed algorithms achieve higher signal-to-interference ratio (SIR) compared to the other tested methods.     

盲信号分离及盲信号抽取研究

盲信号分离技术是将混合信号中的源信号分离出来的一种功能强大的信号处理方法,已成为信号处理领域的研究热点。阐述了盲信号分离的发展现状,介绍了盲信号分离问题的数学模型,给出了盲源分离的基本思想。对盲信号分离算法进行了研究,阐述了盲信号分离几种典型算法的特点及性能,对与盲信号分离紧密相关的盲信号抽取算法进行了总结,并对盲信号分离的进一步研究进行了展望。     

Penalty function-based joint diagonalization approach for convolutive blind separation of nonstationary sources

A new approach for convolutive blind source separation (BSS) by explicitly exploiting the second-order nonstationarity of signals and operating in the frequency domain is proposed. The algorithm accommodates a penalty function within the cross-power spectrum-based cost function and thereby converts the separation problem into a joint diagonalization problem with unconstrained optimization. This leads to a new member of the family of joint diagonalization criteria and a modification of the search direction of the gradient-based descent algorithm. Using this approach, not only can the degenerate solution induced by a unmixing matrix and the effect of large errors within the elements of covariance matrices at low-frequency bins be automatically removed, but in addition, a unifying view to joint diagonalization with unitary or nonunitary constraint is provided. Numerical experiments are presented to verify the performance of the new method, which show that a suitable penalty function may lead the algorithm to a faster convergence and a better performance for the separation of convolved speech signals, in particular, in terms of shape preservation and amplitude ambiguity reduction, as compared with the conventional second-order based algorithms for convolutive mixtures that exploit signal nonstationarity.     

Convolutive blind source separation based on joint block Toeplitzation and block-inner diagonalization

This paper takes a close look at the block Toeplitz structure and block-inner diagonal structure of auto correlation matrices of source signals in convolutive blind source separation (BSS) problems. The aim is to propose a one-stage time-domain algorithm for convolutive BSS by explicitly exploiting the structure in autocorrelation matrices of source signals at different time delays and inherent relations among these matrices. The main idea behind the proposed algorithm is to implement the joint block Toeplitzation and block-inner diagonalization (JBTBID) of a set of correlation matrices of the observed vector sequence such that the mixture matrix can be extracted. For this purpose, a novel tri-quadratic cost function is introduced. The important feature of this tri-quadratic contrast function enables the development of an efficient algebraic method based on triple iterations for searching the minimum point of the cost function, which is called the triply iterative algorithm (TIA). Through the cyclic minimization process in the proposed TIA, it is expected that the JBTBID is achieved. The source signals can be retrieved. Moreover, the asymptotic convergence of the proposed TIA is analyzed. Convergence performance of the TIA and the separation results are also demonstrated by simulations in comparison with some other prominent two-stage time-domain methods.     

Noninvasive fetal electrocardiogram extraction: blind separation versus adaptive noise cancellation

The problem of the fetal electrocardiogram (FECG) extraction from maternal skin electrode measurements can be modeled from the perspective of blind source separation (BSS). Since no comparison between BSS techniques and other signal processing methods has been made, we compare a BSS procedure based on higher-order statistics and Widrow's multireference adaptive noise cancelling approach. As a best-case scenario for this latter method, optimal Wiener-Hopf solutions are considered. Both procedures are applied to real multichannel ECG recordings obtained from a pregnant woman. The experimental outcomes demonstrate the more robust performance of the blind technique and, in turn, verify the validity of the BSS model in this important biomedical application.     

卷积混叠信号盲分离

本文讨论了卷积混叠信号盲分离问题，证明了一系列基于高阶谱的判据，指出了盲辨识和盲分离的充分条件，利用判据，发展了若干算法，模拟实验证实了判据的正确性和算法的有效性。     

Preconditioned optimization algorithms solving the problem of the non unitary joint block diagonalization: application to blind separation of convolutive mixtures

This article addresses the problem of the Non Unitary Joint Block Diagonalization (\(\mathsf {NU-JBD}\)) of a given set of complex matrices for the blind separation of convolutive mixtures of sources. We propose new different iterative optimization schemes based on Conjugate Gradient, Preconditioned Conjugate Gradient, Levenberg–Marquardt and Quasi-Newton methods. We perform also a study to determine which of these algorithms offer the best compromise between efficiency and convergence speed in the studied context. To be able to derive all these algorithms, a preconditioner has to be computed which requires either the calculation of the complex Hessian matrices or the use of an approximation to these Hessian matrices. Furthermore, the optimal stepsize is also computed algebraically to speed up the convergence of these algorithms. Computer simulations are provided in order to illustrate the behavior of the different algorithms in various contexts: when exactly block-diagonal matrices are considered but also when these matrices are progressively perturbed by an additive Gaussian noise. Finally, it is shown that these algorithms enable solving the blind separation of the convolutive mixtures of sources problem.     

A near real-time approach for convolutive blind source separation

In this paper, we propose an algorithm for real-time signal processing of convolutive blind source separation (CBSS), which is a promising technique for acoustic source separation in a realistic environment, e.g., room/office or vehicle. First, we apply an overlap-and-save (sliding windows with overlapping) strategy that is most suitable for real-time CBSS processing; this approach can also aid in solving the permutation problem. Second, we consider the issue of separating sources in the frequency domain. We introduce a modified correlation matrix of observed signals and perform CBSS by diagonalization of the matrix. Third, we propose a method that can diagonalize the modified correlation matrix by solving a so-called normal equation for CBSS. One desirable feature of our proposed algorithm is that it can solve the CBSS problem explicitly, rather than stochastically, as is done with conventional algorithms. Moreover, a real-time separation of the convolutive mixtures of sources can be performed. We designed several simulations to compare the effectiveness of our algorithm with its counterpart, the gradient-based approach. Our proposed algorithm displayed superior convergence rates relative to the gradient-based approach. We also designed an experiment for testing the efficacy of the algorithm in real-time CBSS processing aimed at separating acoustic sources in realistic environments. Within this experimental context, the convergence time of our algorithms was substantially faster than that of the gradient-based algorithms. Moreover, our algorithm converges to a much lower value of the cost function than that of the gradient-based algorithm, ensuring better performance.     

Underdetermined Anechoic Blind Source Separation via $ell^{q}$-Basis-Pursuit With $q≪1$

In this paper, we address the problem of underdetermined blind source separation (BSS) of anechoic speech mixtures. We propose a demixing algorithm that exploits the sparsity of certain time-frequency expansions of speech signals. Our algorithm merges lscr^q -basis-pursuit with ideas based on the degenerate unmixing estimation technique (DUET) [Yiotalmaz and Rickard, "Blind Source Separation of Speech Mixtures via Time-Frequency Masking," IEEE Transactions on Signal Processing, vol. 52, no. 7, pp. 1830-1847, July 2004]. There are two main novel components to our approach: 1, our algorithm makes use of all available mixtures in the anechoic scenario where both attenuations and arrival delays between sensors are considered, without imposing any structure on the microphone positions, and 2, we illustrate experimentally that the separation performance is improved when one uses lscr^q-basis-pursuit with q < 1 compared to the q = 1 case. Moreover, we provide a probabilistic interpretation of the proposed algorithm that explains why a choice of 0.1 les q les 0.4 is appropriate in the case of speech. Experimental results on both simulated and real data demonstrate significant gains in separation performance when compared to other state-of-the-art BSS algorithms reported in the literature.     

联合非高斯性和非线性自相关的有噪盲源分离算法

现有的盲源分离算法往往利用信号某一方面的统计特性来分离信号,例如:利用信号的非高斯特性,或者利用信号的时序特性。在实际应用中,信号往往是具有这两种特性信号的混合,采用信号某一方面的特性往往不能够成功的分离出信号。现有的盲源分离算法往往不考虑噪声的影响,但在实际应用中,噪声的影响是不可避免的。当源信号具有非高斯性和非线性自相关特性时,提出了联合非高斯性和非线性自相关特性的有噪盲源分离算法。计算机仿真表明了提出算法的有效性,和现有的基于非高斯性和非线性自相关特性的有噪盲源分离算法相比,提出算法具有更好的信号分离性能。      

一种新型的卷积混和盲信号分离算法

本文提出了一种新的卷积混合盲信号分离算法。首先将卷积混合模型进行等价简化,再用理论推导论证了卷积混合盲分离问题等价于最优化Wiener滤波器问题,给出了一种去相关分离准则函数。最后,对两个源信号卷积混合的情况,用标准自适应LMS算法使分离准则函数达到最小值,从而得到了两个信号混合的分离算法;然后,推广到多个源信号混合得到了相应分离算法。通过计算机仿真试验验证了本算法的有效性和可行性。     

Blind Deconvolution of DS-CDMA Signals by Means of Decomposition in Rank-$(1,L,L)$ Terms

In this paper, we present a powerful technique for the blind extraction of direct-sequence code-division multiple access (DS-CDMA) signals from convolutive mixtures received by an antenna array. The technique is based on a generalization of the canonical or parallel factor decomposition (CANDECOMP/PARAFAC) in multilinear algebra. We present a bound on the number of users under which blind separation and deconvolution is guaranteed. The solution is computed by means of an alternating least squares (ALS) algorithm. The excellent performance is illustrated by means of a number of simulations. We include an explicit expression of the Cramer-Rao bound (CRB) of the transmitted symbols.     

A Novel and Fast Algorithm for Solving Permutation in Convolutive BSS,Based on Real and Imaginary Decomposition

In this paper, a new fast method for solving the permutation problem in convolutive BSS is presented. Typically, by transferring signals to the frequency domain, the convolutive BSS problem is converted to an instantaneous BSS, and deconvolution takes place in each frequency bin. However, another major problem arises which is permutation ambiguity in the frequency domain. Solving the permutation ambiguity for N sources in frequency domain needs N! comparisons between adjacent frequency bins. This drastically increases the overall computational complexity of the convolutive BSS. In our new approach, the complex-valued signals are decomposed into real and imaginary parts in each frequency bin. We show that the ideal mixing matrix has to possess a simple and symmetric structure. Accordingly, the structure can be exploited for solving the permutation ambiguity in frequency domain. Although separation in subband is accomplished by the FastICA algorithm, the proposed method requires modification of the separation algorithm, and a new structure is imposed on the mixing matrix. After that signals are separated by means of the FastICA, the permutation correction takes place only by N comparisons, decreasing the computational complexity. Comparing to five competitive methods, we experimentally demonstrate that permutation ambiguity is resolved accurately by this very fast approach while substantially decreasing the order of calculations. In terms of the separation performance and signal quality, the proposed method is superior to four of the compared methods and almost similar to the best of them.     

一种充分利用变量结构的解卷积 混合盲源分离新方法

 针对卷积混合盲源分离问题,提出一种基于接收信号不同延时下自相关矩阵组的联合块内对角化方法.为了求解表征联合块内对角化近似程度的基于最小二乘的三二次代价函数,给出基于梯度下降法的三迭代算法.该算法在充分利用混迭矩阵的块Toeplitz结构和源信号相关矩阵的块内对角化结构的基础上,交替估计代价函数中的三组待定参数,搜索代价函数最小点,从而得到混迭矩阵的估计,实现信道的盲均衡和源信号的盲分离.分析了三迭代算法的收敛性能,证明即使存在估计误差时,该算法依然全局渐进收敛.仿真结果表明,与其他经典的两步算法相比,提出的一步算法能够更好地估计混迭矩阵并恢复出源信号,有效地解决了卷积混合盲源分离问题.     

非线性盲源分离的原理及算法综述

本文主要阐述了非线性盲源分离(BSS)/独立成分分析(ICA)模型的基本数学原理、分离算法、算法性能及其应用。首先对线性和非线性BSS/ICA的数学模型作了介绍,重点介绍了非线性BSS/ICA解的不确定性,然后在此基础上对近十年来出现的各种非线性BSS/ICA算法进行简单综述,着重分析了一类可解且应用比较广泛的非线性BSS/ICA模型-后非线性BSS/ICA模型及其分离算法。最后对非线性BSS/ICA存在的问题和发展趋势进行了总结。     

Blind separation of independent sources for virtually any sourceprobability density function

The blind source separation (BSS) problem consists of the recovery of a set of statistically independent source signals from a set of measurements that are mixtures of the sources when nothing is known about the sources and the mixture structure. In the BSS scenario, of two noiseless real-valued instantaneous linear mixtures of two sources, an approximate maximum-likelihood (ML) approach has been suggested in the literature, which is only valid under certain constraints on the probability density function (pdf) of the sources. In the present paper, the expression for this ML estimator is reviewed and generalized to include virtually any source distribution. An intuitive geometrical interpretation of the new estimator is also given in terms of the scatter plots of the signals involved. An asymptotic performance analysis is then carried out, yielding a closed-form expression for the estimator asymptotic pdf. Simulations illustrate the behavior of the suggested estimator and show the accuracy of the asymptotic analysis. In addition, an extension of the method to the general BSS scenario of more than two sources and two sensors is successfully implemented