EURASIP Journal on Applied Signal Processing 
Volume 2005 (2005), Issue 17, Pages 2828-2847
doi:10.1155/ASP.2005.2828

Separating More Sources Than Sensors Using Time-Frequency Distributions

Nguyen Linh-Trung,1 Adel Belouchrani,2 Karim Abed-Meraim,3 and Boualem Boashash4

 1Service Système Télécommunications Spatiales, Centre National d' Études Spatiales, 18 avenue Edouard Belin, Toulouse 31401, France
2Département d' Électronique, École Nationale Polytechnique, 10 avenue Hassen Badi, PB 182 EL Harrach, Algiers 16200, Algeria
3Département Traîtement du Signal et des Images, École Nationale Supérieure des Télécommunications, 46 rue Barrault, Paris Cedex 13 75634, France
4College of Engineering, University of Sharjah, P.O. Box 27272, Sharjah, United Arab Emirates
Received 8 July 2004; Revised 24 March 2005

Recommended by Kostas Berberidis

Abstract

We examine the problem of blind separation of nonstationary sources in the underdetermined case, where there are more sources than sensors. Since time-frequency (TF) signal processing provides effective tools for dealing with nonstationary signals, we propose a new separation method that is based on time-frequency distributions (TFDs). The underlying assumption is that the original sources are disjoint in the time-frequency (TF) domain. The successful method recovers the sources by performing the following four main procedures. First, the spatial time-frequency distribution (STFD) matrices are computed from the observed mixtures. Next, the auto-source TF points are separated from cross-source TF points thanks to the special structure of these mixture STFD matrices. Then, the vectors that correspond to the selected auto-source points are clustered into different classes according to the spatial directions which differ among different sources; each class, now containing the auto-source points of only one source, gives an estimation of the TFD of this source. Finally, the source waveforms are recovered from their TFD estimates using TF synthesis. Simulated experiments indicate the success of the proposed algorithm in different scenarios. We also contribute with two other modified versions of the algorithm to better deal with auto-source point selection.