时变混合系统的在线FastICA算法

现有的多数盲源分离（BSS,Blind Source Separation）算法都是假设混合系统是时不变的,然而在实际的通信系统中混合系统常常是时变的。传统的快速不动点（FastICA）算法具有快速收敛的优点,但是不能直接用于处理混合系统时变的盲源分离问题。为了提高盲源分离算法的收敛速度和对时变混合系统的跟踪性能,改进了传统FastICA算法,将混合信号分段,在各段样本中估计峭度并采用批处理的方法进行分离。仿真实验表明,改进后的FastICA算法能在时变环境中跟踪混合系统的时变,并能有效地抗多音干扰。     

Analysis of stochastic gradient tracking of time-varying polynomialWiener systems

This paper presents analytical and Monte Carlo results for a stochastic gradient adaptive scheme that tracks a time-varying polynomial Wiener (1958) system [i.e., a linear time-invariant (LTI) filter with memory followed by a time-varying memoryless polynomial nonlinearity]. The adaptive scheme consists of two phases: (1) estimation of the LTI memory using the LMS algorithm and (2) tracking the time-varying polynomial-type nonlinearity using a second coupled gradient search for the polynomial coefficients. The time-varying polynomial nonlinearity causes a time-varying scaling for the optimum Wiener filter for Phase 1. These time variations are removed for Phase 2 using a novel coupling scheme to Phase 1. The analysis for Gaussian data includes recursions for the mean behavior of the LMS algorithm for estimating and tracking the optimum Wiener filter for Phase 1 for several different time-varying polynomial nonlinearities and recursions for the mean behavior of the stochastic gradient algorithm for Phase 2. The polynomial coefficients are shown to be accurately tracked. Monte Carlo simulations confirm the theoretical predictions and support the underlying statistical assumptions     

基于时频分析的混合矩阵估计方法

在盲源分离信号处理中,尤其在欠定条件下(观测信号数目大于源信号数目),精确的估计混合矩阵是具有挑战性的问题。现存部分方法利用信号的稀疏性进行求解,并假设在时域或者时频域中源信号不重叠,然而这类方法在假设条件不满足,即源信号部分重叠情况下随着信号稀疏性降低性能恶化明显。本文针对具有较弱稀疏性的源信号,提出了一种基于时频分析的欠定盲源分离的混合矩阵估计方法。首先,利用源信号时频变换后系数实部与虚部比值的差异性选择单源点;其次,运用经典的聚类方法估计解混合矩阵的各向量。仿真结果表明:提出的方法简易可行并具有较好的估计性能。      

通信中的盲源分离问题及解决方案探讨

主要阐述了盲源分离技术应用于无线通信系统时面临的若干问题和解决方案的研究现状。在无线通信系统中,参与混合的源信号是射频通信信号和干扰,这些源信号往往具有循环平稳特性;完成源的混合的无线信道往往受环境影响而发生变化,即具有时变特性;受客观实际条件的限制,观测信号数目往往少于混合源的数目,即表现为欠定混合特性。因此,将盲源分离理论应用于无线通信系统中时,需要特别关注的是循环平稳源、时变、欠定等条件下的盲分离问题。     

Multichannel Convolution Blind Separation Algorithm for MIMO DSSS/CDMA System

Direct-sequence spread-spectrum (DSSS)/code division multiple access (CDMA) transmissions are now widely used for secure communications and multiple access. They can be transmitted at a low signal-to-noise ratio, and have a low probability of interception and capture. How to obtain the original users' signal in a noncooperative context or estimate the spreading sequence in blind conditions is a very difficult problem. Most of the signal sources are assumed to be instantaneous mixtures. In fact, the received CDMA signals are linearly convoluted. A more complicated blind source separation (BSS) algorithm is required to achieve better source separation. In this paper, a new BSS algorithm is proposed for separating linearly convolved signals in CDMA systems when the mixture coefficients of the signal and channel response are totally unknown, but some knowledge about the temporal model does exist. This algorithm is based on minimizing the squared cross-output-channel-correlation criterion. The simulation results show the effectiveness of the algorithm in the blind detection of DS-CDMA signals.     

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.     

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.     

On the LTI properties of adaptive feedforward systems with tapdelay-line regressors

It is shown that an adaptive system whose regressor is formed by tap delay-line (TDL) filtering of a multitone sinusoidal signal is representable as a parallel connection of a linear time-invariant (LTI) block and a linear time-varying (LTV) block. A norm-bound (induced 2-norm) is computed explicitly on the LTV block and is shown to decrease as N^-1, where N is the number of taps. Hence, the adaptive system becomes LTI in the limit as the number of taps goes to infinity. In the more realistic case where the number of taps N is finite, the new “LTI plus norm-bounded perturbation” representation renders, for the first time, the adaptive system analyzable by standard robust control methods     

Convolutive blind source separation algorithms applied to the electrocardiogram of atrial fibrillation: study of performance

The analysis of the surface electrocardiogram (ECG) is the most extended noninvasive technique in medical diagnosis of atrial fibrillation (AF). In order to use the ECG as a tool for the analysis of AF, we need to separate the atrial activity (AA) from other cardioelectric signals. In this matter, statistical signal processing techniques, like blind source separation (BSS), are able to perform a multilead statistical analysis with the aim to obtain the AA. Linear BSS techniques can be divided in two groups depending on the mixing model: algorithms where instantaneous mixing of sources is assumed, and convolutive BSS (CBSS) algorithms. In this work, a comparison of performance between one relevant CBSS algorithm, namely Infomax, and one of the most effective independent component analysis (ICA) algorithms, namely FastICA, is developed. To carry out the study, pseudoreal AF ECGs have been synthesized by adding fibrillation activity to normal sinus rhythm. The algorithm performances are expressed by two indexes: the signal to interference ratio (SIRAA) and the cross-correlation (RAA) between the original and the estimated AA. Results empirically prove that the instantaneous mixing model is the one that obtains the best results in the AA extraction, given that the mean SIRAA obtained by the FastICA algorithm (37.6 +/- 17.0 dB) is higher than the main SIRAA obtained by Infomax (28.5 +/- 14.2 dB). Also the RAA obtained by FastICA (0.92 +/- 0.13) is higher than the one obtained by Infomax (0.78 +/- 0.16).     

基于改进人工蜂群算法的盲源分离方法

 针对现有盲源分离方法大多存在收敛速度慢、分离精度低的问题,提出一种基于改进人工蜂群(Artificial Bee Colony,ABC)算法的盲信号分离方法.在ABC的邻域搜索公式中自适应调整步长,并加入全局最优解指导项,增强局部趋化性搜索能力.改进的ABC算法保持了ABC全局搜索和局部搜索之间的平衡,使ABC算法可以达到更好的寻优效果,从而提高盲源分离算法的分离精度和稳定性.实验结果表明,提出的改进盲源分离算法可以有效地分离线性瞬时混合信号.与其它算法相比,该算法具有更优异的分离性能,并具有更快的收敛速度.     

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.     

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.     

Blind separation of linear instantaneous mixtures of nonstationary surface myoelectric signals

Electromyographic (EMG) recordings detected over the skin may be mixtures of signals generated by different active muscles due to the phenomena related to volume conduction. Separation of the sources is necessary when single muscle activity has to be detected. Signals generated by different muscles may be considered uncorrelated but in general overlap in time and frequency. Under certain assumptions, mixtures of surface EMG signals can be considered as linear instantaneous but no a priori information about the mixing matrix is available when different muscles are active. In this study, we applied blind source separation (BSS) methods to separate the signals generated by two active muscles during a force-varying task. As the signals are non stationary, an algorithm based on spatial time-frequency distributions was applied on simulated and experimental EMG signals. The experimental signals were collected from the flexor carpi radialis and the pronator teres muscles which could be activated selectively for wrist flexion and rotation, respectively. From the simulations, correlation coefficients between the reference and reconstructed sources were higher than 0.85 for signals largely overlapping both in time and frequency and for signal-to-noise ratios as low as 5 dB. The Choi-Williams and Bessel kernels, in this case, performed better than the Wigner-Ville one. Moreover, the selection of time-frequency points for the procedure of joint diagonalization used in the BSS algorithm significantly influenced the results. For the experimental signals, the interference of the other source in each reconstructed source was significantly attenuated by the application of the BSS method. The ratio between root-mean-square values of the signals from the two sources detected over one of the muscles increased from (mean +/- standard deviation) 2.33 +/- 1.04 to 4.51 +/- 1.37 and from 1.55 +/- 0.46 to 2.72 +/- 0.65 for wrist flexion and rotation, respectively. This increment was statistically significant. It was concluded that the BSS approach applied is promising for the separation of surface EMG signals, with applications ranging from muscle assessment to detection of muscle activation intervals, and to the control of myoelectric prostheses.     

基于两步法稀疏分量分析的欠定盲源分离

分析了解决欠定盲源分离问题的稀疏分量分析方法。首先讨论了数据矩阵稀疏表示（分解）的方法,其次重点讨论了基于稀疏因式分解方法的盲源分离。该盲源分离技术分两步．一步是估计混合矩阵,第二步是估计源矩阵。如源信号是高度稀疏的,盲分离可直接在时域内实现。否则．对观测的混合矩阵运用小波包变换预处理后才能进行。仿真结果证明了理论分析的正确性。     

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     

A Non-Linear Blind Source Separation Method Based on Perceptron Structure and Conjugate Gradient Algorithm

The linear mixing model has been considered previously in most of the researches which are devoted to the blind source separation (BSS) problem. In practice, a more realistic BSS mixing model should be the non-linear one. In this paper, we propose a non-linear BSS method, in which a two-layer perceptron network is employed as the separating system to separate sources from observed non-linear mixture signals. The learning rules for the parameters of the separating system are derived based on the minimum mutual information criterion with conjugate gradient algorithm. Instead of choosing a proper non-linear functions empirically, the adaptive kernel density estimation is used in order to estimate the probability density functions and their derivatives of the separated signals. As a result, the score function of the perceptron’s outputs can be estimated directly. Simulations show good performance of the proposed non-linear BSS algorithm.     

MIMO Instantaneous Blind Identification Based on Second-Order Temporal Structure

Blind identification is a crucial subtask in signal processing problems such as blind signal separation (BSS) and direction-of-arrival (DOA) estimation. This paper presents a procedure for multiple-input multiple-output instantaneous blind identification based on second-order temporal properties of the signals, such as coloredness and nonstationarity. The procedure consists of two stages. First, based on assumptions on the second-order temporal structure (SOTS) of the source and noise signals, and using subspace techniques, the problem is reformulated in a particular way such that each column of the unknown mixing matrix satisfies a system of multivariate homogeneous polynomial equations. Then, this nonlinear system of equations is solved by means of a so-called homotopy method, which provides a general tool for solving (possibly nonexact) systems of nonlinear equations by smoothly deforming the known solutions of a simple start system into the desired solutions of the target system. Our blind identification procedure allows to estimate the mixing matrix for scenarios with more sources than sensors without resorting to sparsity assumptions, something that is often believed to be impossible when using only second-order statistics. In addition, since our algorithm does not require any assumption on the mixing matrix, also mixing matrices that are rank-deficient or even have identical columns can be identified. Finally, we give examples and performance results for speech source signals.      

Time-varying effects and averaging issues in models forcurrent-mode control

This paper investigates issues in modeling of current-mode control in converters. The effects of the current-sampling intrinsic to current-mode control are analyzed, and inadequately recognized limitations of linear time-invariant (LTI) models at high frequencies (where the system behavior is time-varying) are exposed. The paper also examines the geometric methods used to derive duty-ratio constraints in averaged models of current-mode control and points out the sources of discrepancies among various models. The conclusions are supported by simulation and experimental results     

A unifying criterion for instantaneous blind source separation based on correntropy

Correntropy has recently been introduced as a generalized correlation function between two stochastic processes, which contains both high-order statistics and temporal structure of the stochastic processes in one functional form. Based on this blend of high-order statistics and temporal structure in a single functional form, we propose a unified criterion for instantaneous blind source separation (BSS). The criterion simultaneously exploits both spatial and spectral characteristics of the sources. Consequently, the new algorithm is able to separate independent, identically distributed (i.i.d.) sources, which requires high-order statistics; and it is also able to separate temporally correlated Gaussian sources with distinct spectra, which requires temporal information. Performance of the proposed method is compared with other popular BSS methods that solely depend on either high-order statistics (FastICA, JADE) or second-order statistics at different lags (SOBI). The new algorithm outperforms the conventional methods in the case of mixtures of sub-Gaussian and super-Gaussian sources.     

FRFT-OFDM系统中FRFT域变换角度的估计

针对FRFT-OFDM(分数阶傅里叶域的正交多载波)系统,该文提出了一种基于信道时变传输函数的FRFT域角度参数的估计算法。该算法利用信道的时变传输函数,对信道的G-特征函数中时变频率和时间的关系进行了线性近似,理论分析和仿真都表明,相对于已有的角度参数估计方法,该方法具有较低的复杂度,在子载波个数为128的系统中,该方法比传统方法复杂度可降低104数量级。该方法适用于信道时变性较强、多普勒频偏较大的场合。