Adaptive blind source separation and equalization formultiple-input/multiple-output systems

In this paper, we investigate adaptive blind source separation and equalization for multiple-input/multiple-output (MIMO) systems. We first analyze the convergence of the constant modulus algorithm (CMA) used in MIMO systems (MIMO-CMA). Our analysis reveals that the MIMO-CMA equalizer is able to recover one of the input signals, remove the intersymbol interference (ISI), and suppress the other input signals. Furthermore, for the MIMO finite impulse response (FIR) systems satisfying certain conditions, the MIMO-CMA FIR equalizers are able to perfectly recover one of the system inputs regardless of the initial settings. We then propose a novel algorithm for blind source separation and equalization for MIMO systems. Our theoretical analysis proves that the new blind algorithm is able to recover all system inputs simultaneously regardless of the initial settings. Finally, computer simulation examples are presented to confirm our analysis and illustrate the effectiveness of blind source separation and equalization for MIMO systems     

Macrocell multiple-input multiple-output system analysis

We develop a semi-deterministic semi-stochastic channel model for the multiple-input multiple-output (MIMO) system under the macrocell environment with local-to-mobile and local-to-base scatterers. We show that employing closely-spaced antennas (e.g., phased array) at the base station is capable of achieving diversity via the local-to-base scatterers, which avoids impractical large aperture requirement for the spatial diversity at the base station. We evaluate the system performance in terms of ergodic capacity, average pairwise error probability (PEP), and signal-to-noise ratio (SNR); derive closed-form expressions for lower and upper bounds on the capacity and PEP; and show that the capacity, multiplexing and diversity gains are limited by the number of multipaths around the base station. The base-station array affects the lower bound on the capacity and the upper bound on the error probability through the same metric; thus, optimal design of the base station array based on this metric will optimize the two different information theoretic measures simultaneously. The fading correlation matrix also appears in the two bounds in the same form. To improve the performance of the macrocell MIMO system, we propose using artificial scatterers and discuss optimal design issues. Numerical examples demonstrate the accuracy of our analytical results and tightness of performance bounds.     

Multistep linear predictors-based blind identification andequalization of multiple-input multiple-output channels

Channel estimation and blind equalization of multiple-input multiple-output (MIMO) communications channels is considered using primarily the second-order statistics of the data. Such models arise when single receiver data from multiple sources is fractionally sampled (assuming that there is excess bandwidth) or when an antenna array is used with or without fractional sampling. We consider the estimation of (partial) channel impulse response and design of finite-length minimum mean-square error (MMSE) blind equalizers. We extend the multistep linear prediction approach to MIMO channels where the multichannel transfer function need not be column reduced. Moreover, we allow infinite impulse response (IIR) channels as well as the case where the “subchannel” transfer functions have common zeros. In the past, this approach has been confined to SIMO finite impulse response (FIR) channels with no common subchannel zeros. A related existing approach applicable to MIMO channels is restricted to FIR column-reduced systems with equal length subchannels. In our approach, the knowledge of the nature of the underlying model (FIR or IIR) or the model order is not required. Our approach works when the “subchannel” transfer functions have common zeros, as long as the common zeros are minimum-phase zeros. The sources are recovered up to a unitary mixing matrix and are further “unmixed” using higher order statistics of the data. Illustrative computer simulation examples are provided     

Channel prediction for precoded spatial multiplexing multiple-input multiple-output systems in time-varying fading channels

Conventional precoded spatial multiplexing multiple-input multiple-output (MIMO) systems using limited feedback are mainly based on the notion of time invariant channels throughout transmission. Consequently, the precoding matrix can be found during the training symbols and used over the subsequent data symbols. In this study, the authors consider a more practical system where the channel varies from one block of symbols to another. In such a scenario, the precoding matrix designed at the receiver based on the previous training symbols becomes outdated, which results in significant system performance degradation. In order to avoid this problem and reduce performance degradation, the authors propose the use of a Kalman filter linear predictor at the receiver to provide the transmitter with the precoding matrix for the next block of symbols. The performance of this method is assessed using computer simulation, and the obtained results for the proposed channel prediction demonstrate improved bit error rate performance for time-varying Rayleigh fading channels.     

Adaptive blind source separation for virtually any sourceprobability density function

Blind source separation (BSS) aims to recover a set of statistically independent source signals from a set of linear mixtures of the same sources. In the noiseless real-mixture two-source two-sensor scenario, once the observations are whitened (decorrelated and normalized), only a Givens rotation matrix remains to be identified in order to achieve the source separation. In this paper an adaptive estimator of the angle that characterizes such a rotation is derived. It is shown to converge to a stable valid separation solution with the only condition that the sum of source kurtosis be distinct from zero. An asymptotic performance analysis is carried out, resulting in a closed-form expression for the asymptotic probability density function of the proposed estimator. It is shown how the estimator can be incorporated into a complete adaptive source separation system by combining it with an adaptive prewhitening strategy and how it can be useful in a general BSS scenario of more than two signals by means of a pairwise approach. A variety of simulations assess the accuracy of the asymptotic results, display the properties of the estimator (such as its robust fast convergence), and compare this on-line BSS implementation with other adaptive BSS procedures     

Adaptive nonlinear PCA algorithms for blind source separation without prewhitening

Blind source separation (BSS) aims at recovering statistically independent source signals from their linear mixtures without knowing the mixing coefficients. Besides independent component analysis, nonlinear principal component analysis (NPCA) is shown to be another useful tool for solving this problem, but it requires that the measured data be prewhitened. By taking into account the autocorrelation matrix of the measured data, we present in this paper a modified NPCA criterion, and develop a least-mean-square (LMS) algorithm and a recursive least-squares algorithm. They can perform the online BSS using directly the unwhitened observations. Since a natural gradient learning is applied and the prewhitening process is removed, the proposed algorithms work more efficiently than the existing NPCA algorithms, as verified by computer simulations on man-made sources as well as practical speech signals.     

On a whitening approach to partial channel estimation and blindequalization of FIR/IIR multiple-input multiple-output channels

Channel estimation and blind equalization of multiple-input multiple-output (MIMO) communications channels is considered using primarily the second-order statistics of the data. Such models arise when a single receiver data from multiple sources is fractionally sampled (assuming that there is excess bandwidth) or when an antenna array is used with or without fractional sampling. We consider estimation of (partial) channel impulse response and design of finite-length minimum mean-square error (MMSE) blind equalizers. The basis of the approach is the design of a zero-forcing equalizer that whitens the noise-free data. We allow infinite impulse response (IIR) channels. Moreover, the multichannel transfer function need not be column reduced. Our approaches also work when the “subchannel” transfer functions have common zeros as long as the common zeros are minimum-phase zeros. The channel length or model orders need not be known. The sources are recovered up to a unitary mixing matrix and are further “unmixed” using higher order statistics of the data. A linear prediction approach is also considered under the above conditions of possibly IIR channels, common subchannel zeros/factors, and not-necessarily column reduced channels. Four illustrative simulation examples are provided     

Superefficiency in blind source separation

Blind source separation is the problem of extracting independent signals from their mixtures without knowing the mixing coefficients nor the probability distributions of source signals and may be applied to EEG and MEG imaging of the brain. It is already known that certain algorithms work well for the extraction of independent components. The present paper is concerned with superefficiency of these based on the statistical and dynamical analysis. In a statistical estimation using t examples, the covariance of any two extracted independent signals converges to 0 of the order of 1/t. On-line dynamics shows that the covariance is of the order of η when the learning rate η is fixed to a small constant. In contrast with the above general properties, a surprising superefficiency holds in blind source separation under certain conditions where superefficiency implies that covariance decreases in the order of 1/t² or of η² . The paper uses the natural gradient learning algorithm and method of estimating functions to obtain superefficient procedures for both batch estimation and on-line learning. A standardized estimating function is introduced to this end. Superefficiency does not imply that the error variances of the extracted signals decrease in the order of 1/t² or η² but implies that their covariances (and independencies) do     

Low-complexity single-channel blind source separation

For the time-frequency overlapped signals, a low-complexity single-channel blind source separation (SBSS) algorithm is proposed in this paper. The algorithm does not only introduce the Gibbs sampling theory to separate the mixed signals, but also adopts the orthogonal triangle decomposition-M (QRD-M) to reduce the computational complexity. According to analysis and simulation results, we demonstrate that the separation performance of the proposed algorithm is similar to that of the per-survivor processing (PSP) algorithm, while its computational complexity is sharply reduced.     

Multistep linear predictors-based blind equalization of FIR/IIRsingle-input multiple-output channels with common zeros

The problem of blind equalization of single-input multiple-output (SIMO) communications channels is considered using only the second order statistics of the data. Such models arise when a single receiver data is fractionally sampled (assuming that there is excess bandwidth) or when an antenna array is used with or without fractional sampling. We extend the multistep linear prediction approach to infinite impulse response (IIR) channels as well as to the case where the “subchannel” transfer functions have common zeros. In the past, this approach has been confined to finite impulse response (FIR) channels with no common subchannel zeros. We focus on the design of finite-length minimum mean-square error (MMSE) blind equalizers. Knowledge of the nature of the underlying model (FIR or IIR) or the model order is not required. Our approach works when the “subchannel” transfer functions have common zeros as long as the common zeros are minimum-phase zeros. Illustrative simulation examples are provided     

Design of a mixed fuzzy controller for multiple-input multiple-output systems

Multiple-input multiple-output (MIMO) systems usually have characteristics of nonlinear dynamics coupling. Therefore, the difficulty in controlling MIMO systems is how to overcome the coupling effects between the degrees of freedom. The computational burden and dynamic uncertainty associated with MIMO systems make model-based decoupling impractical for real-time control. This work develops a mixed fuzzy controller (MFC) to solve this problem and improve control performance. This study first designs a traditional fuzzy controller (TFC) from the viewpoint of a single-input single-output (SISO) system for controlling each degree of freedom of a MIMO system. Then, an appropriate coupling fuzzy controller is also designed according to the characteristics of the system’s dynamics coupling and incorporated into a TFC to compensate for coupling effects between the degrees of freedom. This control strategy can not only simplify the implementation problem of fuzzy control, but also improve control performance. The state-space approach for analyzing the stability of fuzzy control systems is applied to evaluate the stability and robustness of this intelligent mixed fuzzy controller. To verify the applicability of the proposed mixed fuzzy controller, this work presents a two-link robotic manipulator with a complex dynamic model for a MIMO system to evaluate the stability and robustness of the MFC by numerical simulation, and to examine the control performance by comparing the simulation results of the MFC with those of a TFC for this MIMO system.     

General approach to blind source separation

This paper identifies and studies two major issues in the blind source separation problem: separability and separation principles. We show that separability is an intrinsic property of the measured signals and can be described by the concept of m-row decomposability introduced in this paper; we also show that separation principles can be developed by using the structure characterization theory of random variables. In particular, we show that these principles can be derived concisely and intuitively by applying the Darmois-Skitovich theorem, which is well known in statistical inference theory and psychology. Some new insights are gained for designing blind source separation filters     

Uncorrelated component analysis for blind source separation

The uncorrelated component analysis (UCA) of a stationary random vector process consists of searching for a linear transformation that minimizes the temporal correlation between its components. Through a general analysis we show that under practically reasonable and mild conditions UCA is a solution for blind source separation. The theorems proposed in this paper for UCA provide useful insights for developing practical algorithms. UCA explores the temporal information of the signals, whereas independent component analysis (ICA) explores the spatial information; thus UCA can be applied for source separation in some cases where ICA cannot. For blind source separation, combining ICA and UCA may give improved performance because more information can be utilized. The concept of single UCA (SUCA) is also proposed, which leads to sequential source separation.This work was supported in part by grants from the Research Grants Council of Hong Kong, grants HKU553/96M, HKU7036/97E, and HKUST776/96E.     

Compound noise separation in digital circuits using blind source separation

Analysis of individual noise sources in pre-nanometer circuits cannot take into account the evolving reality of multiple noise sources interacting with each other. Noise measurement made at an evaluation node will reflect the cumulative effect of all the active noise sources, while individual and relative severity of various noise sources will determine what types of remedial steps can be taken, pressing the need for development of algorithms that can analyze the contributions of different noise sources when a noise measurement is available. This paper addresses the cocktail-party problem inside integrated circuits with multiple noise sources. It presents a method to extract the time characteristics of individual noise source from the measured compound voltage in order to study the contribution and properties of each source. This extraction is facilitated by application of blind source separation technique, which is based on the assumption of statistical independence of various noise sources over time. The estimated noise sources can aid in performing timing and spectral analysis, and yield better circuit design techniques.     

Underdetermined blind source separation of temporomandibular joint sounds

The underdetermined blind source separation problem using a filtering approach is addressed. An extension of the FastICA algorithm is devised which exploits the disparity in the kurtoses of the underlying sources to estimate the mixing matrix and thereafter achieves source recovery by employing the ll-norm algorithm. Besides, we demonstrate how promising FastICA can be to extract the sources. Furthermore, we illustrate how this scenario is particularly appropriate for the separation of temporomandibular joint (TMJ) sounds.     

超定盲信号分离的半参数统计方法

研究观测信号的数目m不小于源信号的数目n情况下盲信号分离问题.首先证明若混合矩阵满列秩,则在本质相等意义下,存在唯一的m×m非奇异矩阵使得分离系统的输出除零信号外,其它非零信号即是希望提取的源信号.基于此,采用半参数统计方法构造超定盲信号分离的估计函数,给出相应的学习算法;理论证明了该算法具有等变化性和分离矩阵的非奇异特性,并借助于源信号数目未知且动态变化的计算机仿真验证了其有效性.     

A blind source separation technique using second-order statistics

Separation of sources consists of recovering a set of signals of which only instantaneous linear mixtures are observed. In many situations, no a priori information on the mixing matrix is available: The linear mixture should be “blindly” processed. This typically occurs in narrowband array processing applications when the array manifold is unknown or distorted. This paper introduces a new source separation technique exploiting the time coherence of the source signals. In contrast with other previously reported techniques, the proposed approach relies only on stationary second-order statistics that are based on a joint diagonalization of a set of covariance matrices. Asymptotic performance analysis of this method is carried out; some numerical simulations are provided to illustrate the effectiveness of the proposed method     

Deterministic blind modulation-induced source separation fordigital wireless communications

In this paper, we present a new simple deterministic blind source separation algorithm, which is based on modulating the same data symbol sequence with different code sequences and transmitting the resulting modulated data symbol sequences through different antennas. The algorithm does not exploit the finite alphabet property of the data symbols. As a result, no iterations are required, and convergence is not an issue. Instantaneous mixtures (frequency-flat fading), as well as convolutive mixtures (frequency-selective fading), can be handled. In the case of a convolutive mixture, the difficulties that occur when the users have unequal channel orders are avoided. Moreover, the proposed algorithm is robust against channel order underestimation     

Underdetermined blind source separation based on sparse representation

This paper discusses underdetermined (i.e., with more sources than sensors) blind source separation (BSS) using a two-stage sparse representation approach. The first challenging task of this approach is to estimate precisely the unknown mixing matrix. In this paper, an algorithm for estimating the mixing matrix that can be viewed as an extension of the DUET and the TIFROM methods is first developed. Standard clustering algorithms (e.g., K-means method) also can be used for estimating the mixing matrix if the sources are sufficiently sparse. Compared with the DUET, the TIFROM methods, and standard clustering algorithms, with the authors' proposed method, a broader class of problems can be solved, because the required key condition on sparsity of the sources can be considerably relaxed. The second task of the two-stage approach is to estimate the source matrix using a standard linear programming algorithm. Another main contribution of the work described in this paper is the development of a recoverability analysis. After extending the results in , a necessary and sufficient condition for recoverability of a source vector is obtained. Based on this condition and various types of source sparsity, several probability inequalities and probability estimates for the recoverability issue are established. Finally, simulation results that illustrate the effectiveness of the theoretical results are presented.