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Generalized Almost-Cyclostationary Processes

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In Chapter 2, the class of the generalized almost-cyclostationary (GACS) processes is presented and characterized. GACS processes have multivariate statistical functions that are almost-periodic function of time. The (generalized) Fourier series of these functions have both coefficients and frequencies, named lag-dependent cycle frequencies, that depend on the lag shifts of the processes. Almost-cyclostationary processes are obtained as special case when the frequencies do not depend on the lag parameters. The problems of linear filtering and sampling of GACS processes are addressed. The cyclic correlogram is shown to be, under mild conditions, a mean-square consistent and asymptotically Normal estimator of the cyclic autocorrelation function. Such a function allows a complete second-order characterization in the wide-sense of GACS processes. Numerical examples of communications through Doppler channels due to relative motion between transmitter and receiver with constant relative radial acceleration are considered. Simulation results on statistical function estimation are carried out to illustrate the theoretical results. Proofs of the results in Chapter 2 are reported in Chapter 3.