Second-Order Statistics of One-Sided CPM Signals

This letter deals with second-order statistics (SOS) of continuous-phase modulated (CPM) signals. To overcome some mathematical inconsistencies emerging from the idealized assumption that the CPM signal evolves from t = -∞, we consider a one-sided model for the signal, which starts from t = 0, noting also that such a model emerges naturally when building practical SOS estimators. On the basis of such a model, we first evaluate the SOS of the pseudosymbols, which arise when expressing a CPM signal in terms of its Laurent representation, as well as closed-form expressions of the cyclic autocorrelation and conjugate correlation functions of one-sided CPM signals.