Generalized Identifiability Conditions for Blind Convolutive MIMO Separation

• Published in: IEEE transactions on signal processing Vol. 57; no. 7; pp. 2846 - 2852
• Main Authors: Castella, M., Moreau, E.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.07.2009; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Applied sciences; Array signal processing; Biological system modeling; Blind source separation; Blinds; Bridges; Computer Science; contrast functions; Detection, estimation, filtering, equalization, prediction; Engineering Sciences; Exact sciences and technology; Higher order statistics; Independent component analysis; Information, signal and communications theory; Matrices; MIMO; MIMO convolutive mixtures; MIMO identification; Miscellaneous; Reactive power; Reference signals; reference system; semi-blind methods; Separation; Signal and communications theory; Signal and Image processing; Signal processing; Signal, noise; Simulation; Source separation; Statistics; Telecommunications and information theory; MIMO system; Second order; Parameter estimation; Identifiability; Source separation; Independent component analysis; Signal estimation; semi-blind methods; Order statistic; Blind source separation; higher order statistics; Higher order statistic; MIMO identification; Blind separation; Statistical method; contrast functions; Simulation; Reference system; Signal processing; MIMO convolutive mixtures; Semi-blind methods; Contrast functions; Higher order statistics
• ISSN: 1053-587X; 1941-0476
• DOI: 10.1109/TSP.2009.2016259

This correspondence deals with the problem of source separation in the case where the output of a multivariate convolutive mixture is observed: we propose novel and generalized conditions for the blind identifiability of a separating system. The results are based on higher-order statistics and are valid in the case of stationary but not necessarily i.i.d. signals. In particular, we extend recent results based on second-order statistics only. The approach relies on the use of so called reference signals. Our new results also show that only weak conditions are required on the reference signals: this is illustrated by simulations and opens up the possibility of developing new methods.