Generalizations of Cyclostationary Signal Processing: Spectral Analysis and Applications

2.1 Introduction

In the past two decades, a huge effort has been devoted to analysis and exploitation of the properties of the almost-cyclostationary (ACS) processes. In fact, almost-all modulated signals adopted in communications can be modeled as ACS (Gardner 1994), (Gardner and Spooner 1994), (Spooner and Gardner 1994), (Gardner et al. 2006). For an ACS process, multivariate statistical functions are almost-periodic functions of time and can be expressed by (generalized) Fourier series expansions whose coefficients depend on the lag shifts of the processes and whose frequencies, referred to as cycle frequencies, do not depend on the lag shifts. Almost-cyclostationarity properties have been widely exploited for analysis and synthesis of communications systems. In particular, they have been exploited to develop signal selective detection and parameter estimation algorithms, blind-channel-identification and synchronization techniques, and so on (Gardner 1994), (Gardner et al. 2006). Moreover, ACS processes are encountered in econometrics, climatology, hydrology, biology, acoustics, and mechanics (Gardner 1994), (Gardner et al. 2006).

More recently, wider classes of nonstationary processes extending the class of the ACS processes have been considered in (Izzo and Napolitano (1998a), (Izzo and Napolitano (2002a,b, 2003, 2005), (Napolitano 2003, 2007a, 2009), (Napolitano and Tesauro 2011).

In (Izzo and Napolitano 1998a), the class of the generalized almost-cyclostationary (GACS) processes ...