Ruey-Wen Liu

Indeterminacy and identifiability of blind identification

Blind identification of source signals is studied from both theoretical and algorithmic aspects. A mathematical structure is formulated from which the acceptable indeterminacy is represented by an equivalence relation. The concept of identifiability is then defined. Two identifiable cases are shown along with blind identification algorithms. The performance of FOBI (fourth-order blind identification), EFOBI (extended FOBI), and AMUSE algorithms is evaluated by some heuristic arguments and simulation results. It is shown that EFOBI outperforms the FOBI algorithm, and the AMUSE algorithm performs better than EFOBI in the case of nonwhite source signals. AMUSE is applied to a speech extraction problem and shown to have promising results. >

Waveform-preserving blind estimation of multiple independent sources

The problem of blind estimation of source signals is to estimate the source signals without knowing the characteristics of the transmission channel. It is shown that the minimum-variance unbiased estimates can be obtained if and only if the transmission channel can be identified blindly. It is shown that the channel can be blindly identified if and only if there is not more than one Gaussian source. This condition suggests that waveform-preserving blind estimation can be achieved over a wide range of signal processing applications, including those cases in which the source signals have identical nonGaussian distributions. The constructive proof of the necessary and sufficient condition serves as a foundation for the development of waveform-preserving blind signal estimation algorithms. Examples are presented to demonstrate the applications of the theoretical results. >

AMUSE: a new blind identification algorithm

The mathematical formulation of the blind identification problem is presented. Various theoretical properties are discussed. The AMUSE algorithm is derived on the basis of the necessary condition of source identifiability and shown to have good performance and wide application.<<ETX>>

A system-theoretic foundation for blind equalization of an FIR MIMO channel system

The system-theoretic foundation for blind equalization of a finite-impulse response (FIR) MIMO channel system in the channel-filter setting is investigated. In this setting, a general definition of equalizable channel system is presented, and its characterization is given: Every equalizable channel system has an FIR irreducible-paraunitary factorization. Based on this fact, we show that any equalizable channel system can be reduced to a paraunitary FIR system by a filter, called a whitener. It is shown that one such whitener can be designed by a linear prediction-based approach. It is also shown that if the original FIR channel system has no transmission zero at the origin, then the above paraunitary FIR channel system is a static system.

A finite-step global convergence algorithm for the parameter estimation of multichannel MA processes

An iterative algorithm for the identification of multichannel moving average (MA) processes using higher-order statistics is proposed. It is shown that the algorithm has a finite-step global convergence property. Three multichannel MA models, including one nonminimum-phase MA model, are estimated by this algorithm with satisfactory performances. >

A subspace method for estimating sensor gains and phases

The problem of array signal processing under model errors is studied. A signal subspace constraint is used to obtain a simple way for computing a set of sensor gains and phases consistent with a given set of DOA angles. Then the issue of uniqueness of the set of sensor gains and phases and DOA angles is addressed. >

A simple algorithm for finding all solutions of piecewise-linear networks

An efficient algorithm is presented for the searching of all solutions of a piecewise-linear (PWL) resistive network. Let P/sub /n be the number of largest segments of PWL resistors, and P/sub /n/sub -1/ the second largest. The algorithm presented is better than the brute-force method by a factor of P/sub /n*P/sub /n/sub -1/ and the Chua and Ying method, the most efficient method at the present time, by a factor of at least P/sub /n/sub -1/. The algorithm is based on a PWL network theorem, which is also introduced. >

Blind signal processing: an introduction

After a brief introduction to blind signal separation, the problem of blind signal processing is formulated, which provides an enlarged scope of blind signal separation. As such, it includes within its scope blind channel identification, blind identification of medium with layered structures, array signal processing, and computerized tomography. An application to early fault detection of analog circuits is also presented.

An extended fourth order blind identification algorithm in spatially correlated noise

An eigenstructure-based method called extended fourth-order blind identification (EFOBI) is presented for the problem of blind decomposition of multiple source signals in spatially correlated noise. Estimates of the source signals and the unknown model parameters are computed by the algorithm. The method is applied to a speech enhancement problem and to the direction-of-arrival problem in array signal processing under sensor gain uncertainties and shows improved performance over traditional methods such as MUSIC.<<ETX>>

Blind equalization of MIMO-FIR channels driven by white but higher order colored source signals

The goal of the article is to find a minimal amount of statistical information (or a much weaker condition) about source signals for which blind equalization is possible for multiple-input multiple-output finite-impulse response (MIMO-FIR) channels. First, a sufficiently broad framework is set up within which such a theoretical problem is well posed. Within this framework, it is shown that second-order statistics (SOS) alone are not sufficient for blind equalization when the source signals are white. Additional higher order statistics (HOS) are needed. Then we show that the only additional higher order statistical information needed is spatial fourth-order cumulants. Though it has not yet been proved to be minimal, it is interesting to note that this is the same as the weakest known condition on the source signals even for an instantaneous mixture. We then show a necessary and sufficient condition for blind equalization when the source signals are white and spatially fourth-order uncorrelated. Based on this condition, criterion (A) for blind equalization of MIMO-FIR channels is developed by exploiting the temporal fourth-order statistics. Finally, based on this criterion, a new necessary and sufficient condition in terms of cumulants for the blind equalization of MIMO-FIR channels is obtained.