Estimation of second-order cross-moments of generalized almost-cyclostationary processes

In this paper, the problem of estimating second-order cross-moments of generalized almost-cyclostationary (GACS) processes is addressed. GACS processes have statistical functions that are almost-periodic functions of time whose (generalized) Fourier series expansions have both frequencies and coefficients that depend on the lag shifts of the processes. The class of such nonstationary processes includes the almost-cyclostationary (ACS) processes which are obtained as a special case when the frequencies do not depend on the lag shifts. ACS processes filtered by Doppler channels and communications signals with time-varying parameters are further examples. It is shown that the second-order cross-moment of two jointly GACS processes is completely characterized by the cyclic cross-correlation function. Moreover, it is proved that the cyclic cross-correlogram is an asymptotically Normal, mean-square consistent, estimator of the cyclic cross-correlation function. Furthermore, it is shown that well-known consistency results for ACS processes can be obtained by specializing the results of this paper.