A general framework for second-order blind separation of stationary colored sources

This paper focuses on the blind separation of stationary colored sources using the second-order statistics (SOS) of their instantaneous mixtures. We first start by presenting a brief overview of existing contributions in that field. Then, we present necessary and sufficient conditions for the identifiability and partial identifiability using a finite set of correlation matrices. These conditions depend on the autocorrelation function of the unknown sources. However, it is shown here that they can be tested directly from the observation through the decorrelator output. This issue is of prime importance to decide whether the sources have been well separated. If that is not the case then, further treatments will be needed. We then propose an identifiability testing based on resampling (jackknife) technique that is validated by simulation results. Secondly, we present an iterative blind source separation method using SOS and natural gradient technique. This algorithm has a number of attractive properties including its simplicity and “easy” generalization to adaptive or convolutive schemes. Asymptotic performance analysis of this method is performed. Several numerical simulations are presented, to assess the theoretical results w.r.t. the “separability” testing, to demonstrate the effectiveness of the gradient-type decorrelation method and to validate the theoretical expression of the asymptotic performance index.