On the behavior of current second and higher order blind source separation methods for cyclostationary sources

Most of the second-order (SO) and higher order (HO) blind source separation methods developed in the 1990s aim at blindly separating statistically independent sources that are assumed zero-mean, stationary, and ergodic. Nevertheless, in many situations of practical interest, such as in radiocommunication contexts, the sources are nonstationary and very often (quasi)-cyclostationary (digital modulations). In these conditions, it becomes important to wonder whether the performance of these current SO and HO blind source separation methods, which have been developed for stationary sources, may be affected by the potential nonstationarity of the latter. Limiting the analysis to the SO and fourth-order (FO) cumulant-based blind source separation methods, the purpose of this paper is to bring some answers to this important question through the behavior analysis of the empirical SO and FO cumulants estimator in the presence of zero-mean (quasi)-cyclostationary sources