Identifiability of multichannel linear systems driven by colored inputs and its application to blind signal separation

This paper deals with the problem of identification of multichannel linear systems driven by unobservable colored inputs based on higher-order statistics of the outputs. Let S be the set of scalar stable transfer functions. We define the notion of a generalized permutation matrix (g-matrix) over S and that of a shift matrix (s-matrix). It is shown that the transfer function matrix of an unknown system is identified up to post-multiplication of the product of a g-matrix and a s-matrix. This result is applied to identifying FIR systems for blind signal separation