Characterization of cyclostationary random signal processes

Many communication and control systems employ signal formats that involve some form of periodic processing operation. Signals produced by samplers, scanners, multiplexors, and modulators are familiar examples. Often these signals are appropriately modeled by random processes that are cyclostationary (CS), i.e., processes with statistical parameters, such as mean and autocorrelation, that fluctuate periodically with time. In this paper we examine two methods for representing nonstationary processes that reveal the special properties possessed by CS processes. These representations are the harmonic series representation (HSR) and the translation series representation (TSR). We show that the HSR is particularly appropriate for characterizing the structural properties of CS processes and that the TSR provides natural models for many types of communication signal formats. The advantages gained by modeling signals as CS processes rather than stationary processes is illustrated by consideration of the optimum filtering problem. We present general solutions for filters that minimize mean-square error for continuous-waveform estimation, and we discuss several specific examples for the particular case of additive noise. These examples demonstrate improvement in performance over that of filter designs based on stationary models for the signal processes.