Generalized second order identifiability condition and relevant testing technique

This paper presents a generalized sufficient and necessary identifiability condition for second order statistics (SOS) based blind source separation (BSS). It is then shown that, even when this condition is not satisfied the sources are still partially identifiable (in blocks). Furthermore, although the identifiability condition depends on the autocorrelation coefficients of the unknown source signals, it can be tested directly from the observations. This issue is of prime importance to decide whether the sources have been well separated or else if further treatments are needed. Some simulation examples are given to assess our theoretical results.