Higher-order statistics for QAM signals: A comparison between cyclic and stationary representations

For a cyclostationary signal, the cumulant-based cyclic tri-correlation (fourth-order correlation) at cycle frequency zero should not be confused, in the general case, with the cumulant-based tricorrelation of the same signal after stationarization. The reasons for this unusual assertion are detailed; as an illustration, we show that if QAM signal classification is impossible using their fourth-order cyclic statistics, classification is however possible if a stationary modelling is adopted. Remarks on the estimation of both cyclic and stationary temporal cumulants are provided and consequently, the skip between the cyclic and the stationary models is enlightened. Theoretical expressions of cyclic and stationary tricorrelations are derived and computer simulations confirm the results.