Blind identification of linear multi-input-multi-output systems driven by colored inputs with applications to blind signal separation

The blind identification problem of a linear multi-input-multi-output system is widely noticed by many researchers in diverse fields due to its relevance to blind signal separation. However, such a problem is ill-posed and has no unique solution. Therefore, we can only find a solution of the problem within an equivalent class. In this paper, we clarify the equivalent classes in the blind identification problem utilizing higher-order statistics, called cumulants. Let S be the set of stable scalar transfer functions and let us define the notion of a generalized permutation matrix (abbreviated by g-matrix) over S. Then it is shown that the blind identification problem cannot be solved uniquely even if we assume input signal are white, and that we can identify the transfer function matrix only up to post-multiplication of a g-matrix. This result is applied to identifying finite impulse response systems for blind signal separation.