Second-Order Blind Separation of First- and Second-Order Cyclostationary Sources—Application to AM, FSK, CPFSK, and Deterministic Sources

Most of the second-order (SO) and higher order (HO) blind source separation (BSS) methods developed this last decade 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 radiocommunications contexts, the sources are nonstationary and very often cyclostationary (digital modulations). The behavior of the current SO and fourth-order (FO) cumulant-based BSS methods in the presence of cyclostationary sources has been analyzed, recently, in a previous paper by Ferréol and Chevalier, assuming zero-mean sources. However, some cyclostationary sources used in practical situations are not zero-mean but have a first-order (FIO) cyclostationarity property, which is, in particular, the case for some amplitude modulated (AM) signals and for some nonlinearly modulated digital sources such as frequency shift keying (FSK) or some continuous phase frequency shift keying (CPFSK) sources. For such sources, the results presented in the previous paper by Ferréol and Chevalier no longer hold, and the purpose of this paper is to analyze the behavior and to propose adaptations of the current SO BSS methods for sources that are both FIO and SO cyclostationary and cyclo-ergodic. An extension for deterministic sources is also proposed in the paper.