Blind separation of Gaussian sources via second-order statistics with asymptotically optimal weighting

Blind separation of Gaussian sources with different spectra can be attained using second-order statistics. The second-order blind identification (SOBI) algorithm, proposed by Belouchrani et al. (1997), uses approximate joint diagonalization. We show that substantial improvement over SOBI can be attained when the joint diagonalization is transformed into a properly weighted nonlinear least squares problem. We provide an iterative solution and derive the optimal weights for our weights-adjusted SOBI (WASOBI) algorithm. The improvement is demonstrated by analysis and simulations.