The canonical decomposition and blind identification with more inputs than outputs : Some algebraic results

In this paper we link the blind identification of a MIMO Moving Average (MA) system to the calculation of the Canonical Decomposition (CD) in multilinear algebra. This conceptually allows for the blind identification of systems tha t have many more inputs than outputs. We also derive a new theorem guaranteeing uniqueness of a high-rank CD and an algebraic algorithm for its computation.

[1]  Nikos D. Sidiropoulos,et al.  Almost sure identifiability of multidimensional harmonic retrieval , 2001, 2001 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings (Cat. No.01CH37221).

[2]  Nikos D. Sidiropoulos,et al.  Blind PARAFAC receivers for DS-CDMA systems , 2000, IEEE Trans. Signal Process..

[3]  J. Kruskal.  Three-way arrays: rank and uniqueness of trilinear decompositions, with application to arithmetic complexity and statistics , 1977 .

[4]  Alle-Jan van der Veen,et al.  Joint diagonalization via subspace fitting techniques , 2001, ICASSP.

[5]  Arie Yeredor,et al.  Non-orthogonal joint diagonalization in the least-squares sense with application in blind source separation , 2002, IEEE Trans. Signal Process..

[6]  Joos Vandewalle,et al.  Jacobi-Algorithm for Simultaneous Generalized Schur Decomposition in Higher-Order-Only ICA , 1998 .

[7]  Joos Vandewalle,et al.  Independent component analysis of largely underdetermined mixtures , 2003 .

[8]  Nikos D. Sidiropoulos,et al.  Generalizing Carathéodory's uniqueness of harmonic parameterization to N dimensions , 2001, IEEE Trans. Inf. Theory.

[9]  Jean-Francois Cardoso,et al.  Super-symmetric decomposition of the fourth-order cumulant tensor. Blind identification of more sources than sensors , 1991, [Proceedings] ICASSP 91: 1991 International Conference on Acoustics, Speech, and Signal Processing.

[10]  Joos Vandewalle,et al.  Computation of the Canonical Decomposition by Means of a Simultaneous Generalized Schur Decomposition , 2005, SIAM J. Matrix Anal. Appl..

[11]  Pierre Comon,et al.  Decomposition of quantics in sums of powers of linear forms , 1996, Signal Process..

[12]  Arogyaswami Paulraj,et al.  An analytical constant modulus algorithm , 1996, IEEE Trans. Signal Process..

[13]  L. Lathauwer,et al.  Signal Processing based on Multilinear Algebra , 1997 .