Performance analysis of GEVD-based source separation with second-order statistics

One of the simplest (and earliest) approaches to blind source separation is to estimate the mixing matrix from the generalized eigenvalue decomposition (GEVD), or Exact Joint Diagonalization, of two target-matrices. In a second-order statistics (SOS) framework, these target-matrices are two different correlation matrices (e.g., at different lags, taken over different time-intervals, etc.), attempting to capture the diversity of the sources (e.g., diverse spectra, different nonstationarity profiles, etc.). More generally, such matrix pairs can be constructed as generalized correlation matrices, whose structure is prescribed by two selected association-matrices. In this paper, we provide a small-errors performance analysis of GEVD-based separation in such SOS frameworks. We derive explicit expressions for the resulting interference-to-source ratio (ISR) matrix in terms of the association-matrices and of the sources' temporal covariance matrices. The validity of our analysis is illustrated in simulation.