Conditions on sources and mixing matrix for solving the permutation indeterminacy in 2×2 instantaneous blind signal separation

This paper describes a closed-form solution for 2×2 instantaneous blind signal separation (IBSS) that is based on second order statistics and explicitly exploits the nonstationarity and the coloredness (difference between spectra) of the source signals. A criterion is derived which specifies the requirements on the statistics of the source signals for which the proposed method will work. This criterion unifies the nonstationarity and coloredness criteria encountered separately in other work. Moreover, it is shown that if this criterion is satisfied a condition on the scalar mixing coefficients can be derived under which the permutation indeterminacy is solved. This is very important, since it makes it possible to predict for which of the two resulting solutions the sources are permuted. The algorithm is based on the division of available data into two different time blocks each time the de-mixing system is estimated. For each block, certain correlation values are computed that are subsequently combined to provide two separating solutions. One of these solutions provides the sources in the original order and the other in the reversed order.