Second-order blind separation of first- and second-order cyclostationary sources-application to AM, FSK, CPFSK, and deterministic sources
All modulated signals used in digital communication activities are cyclostationary, because their autocorrelation function contains some temporal periodicities known as cyclic periods. In the frequency domain, their spectral components are correlated every time they are spaced apart by the inverse of a cyclic period, called a cyclic frequency. A number of signal processing algorithms applied to telecommunications can take advantage of the spectral correlation of the signals to be considered (detection, equalisation, source separation, ...). Furthermore, the knowledge of the theoretical expression of the spectral correlation of the signal to be received is often necessary in order to derive the optimal processing. The theoretical spectral correlation of modulated signals has already been the subject of some publications. However, until now there was no comprehensive reference concerning the large family of continuous phase modulations (CPM). The aim of this two-part paper is to give the theoretical expression of the spectral correlation for binary CPM signals. The first part is devoted to the study of rectangular, full-response binary CPM modulations, also called continuous phase frequency shift keying modulations (CPFSK). It gives the exact analytical expression for their spectral correlation. The second part presents a simple computation method valid for the whole class of binary CPM modulations. This method only requires the computation of some double numerical integrations over finite intervals.