Non unitary joint block diagonalization of complex matrices using a gradient approach

Authors:
Hicham Ghennioui;Nadège Thirion-Moreau;Eric Moreau;Abdellah Adib;Driss Aboutajdine
Affiliations:
STD, ISITV, La Valette du Var Cedex, France and GSCM-LRIT, FSR, Rabat, Maroc;STD, ISITV, La Valette du Var Cedex, France;STD, ISITV,La Valette du Var Cedex, France;GSCM-LRIT, FSR, Rabat, Maroc and DPG, IS, Rabat, Maroc;GSCM-LRIT, FSR, Rabat, Maroc
Venue:
ICA'07 Proceedings of the 7th international conference on Independent component analysis and signal separation
Year:
2007

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Abstract

This paper addresses the problem of the non-unitary approximate joint block diagonalization (NU - JBD) of matrices. Such a problem occurs in various fields of applications among which blind separation of convolutive mixtures of sources and wide-band signals array processing. We present a new algorithm for the non-unitary joint block-diagonalization of complex matrices based on a gradient-descent algorithm whereby the optimal step size is computed algebraically at each iteration as the rooting of a 3rd-degree polynomial. Computer simulations are provided in order to illustrate the effectiveness of the proposed algorithm.