Blind source estimation of FIR channels for binary sources: a grouping decision approach

Authors:
Yuanqing Li;Andrzej Cichocki;Liqing Zhang
Affiliations:
Laboratory for Advanced Brain Signal Processing, RIKEN Brain Science Institute, Wako-Shi, Saitama 3510198, Japan and Automation Science and Engineering Institute, Southchina University of Technolo ...;Laboratory for Advanced Brain Signal Processing, RIKEN Brain Science Institute, Wako-Shi, Saitama 3510198, Japan and The Department of Electrical Engineering, Warsaw University of Technology, Pola ...;Department of Computer Science and Engineering, Shanghai Jiaotong University, Shanghai 200030, China
Venue:
Signal Processing
Year:
2004

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Abstract

This paper proposes a novel grouping decision approach for blind source estimation of FIR. (finite impulse response) channels with binary sources. First, solvability is discussed for single-input systems and multi-input systems. Necessary and sufficient conditions for recoverability are derived. For single-input systems, a new deterministic algorithm based on grouping and decision is proposed to recover the source up to a delay. The algorithm is easy to implement and has several advantages. For instance, when the solvability conditions are satisfied, it can be applied to cases in which: (i) the channel has zeros on the unit circle or outside of the unit circle; (ii) there are fewer sensors than sources; (iii) the source is temporarily dependent. To improve noise tolerance and reduce computational cost, the algorithm is further elaborated for highly noisy channels and high-order FIR channels, respectively. For the channels with high unimodal noise, fewer peaks appear in the probability density function (pdf) of the outputs compared to the pdf of the outputs of channels with a higher SNR. After the peaks representing cluster centers are estimated using a maximum likelihood (ML) approach, the deterministic algorithm can be used. Similar to highly noisy channels, the algorithm is also effective for high-order, exponentially decaying channels after fewer cluster centers are estimated. Furthermore, blind source estimation for multi-input systems also can be carried out as with the case of single input systems. Two deflation algorithms are presented for temporarily dependent sources and i.i.d. sources. Based on the source estimation and deflation algorithms, the sources can be obtained one by one. Finally, the validity and performance of the algorithms are illustrated by several simulation examples.