Blind two-input-two-output FIR channel identification based on frequency domain second-order statistics

We present an analytical solution to the two-input-two-output blind crosswise mixture identification based on eigenvalue decomposition of second-order spectra correlations. The sources are independent and non-white, but otherwise, we consider their statistics to be unknown. We show that the cross channels cannot be uniquely determined by the analysis of the frequency domain covariance alone due to the unknown eigenvector permutations. However, the problem can be attacked with the help of two invariant indices that are immune to these permutations. Using these indices together with standard reconstruction-from-phase techniques, we show that the channels can be uniquely determined. Our theoretical results lead to a novel frequency domain second-order algorithm that identifies the unknown channels