Using Shaping Filter for Deriving Analytical Models of Spectral Correlation Functions Describing Pulse-Modulated Cyclostationary Random Processes

Abstract

The paper proposes an extension of the shaping filter method for modeling cyclostationary random processes (CSRP) belonging to the subclass of pulse-amplitude modulated signals. The proposed method consists in utilizing an elementary process with cyclostationary properties followed by its subsequent transformation using a linear time-invariant (LTI) system with a known impulse response. The elementary CSRP is chosen to be an infinite sequence of Dirac delta functions uniformly distributed over the time dimension with a constant period. The weights of the Dirac deltas are modeled as independent identically distributed random variables so that it preserves the structural periodicity of the pulse process. The transformation of the sequence by means of the LTI system described by its impulse response makes it possible to obtain the desired shape of the pulses forming the process whose spectral properties can be described by means of its spectral correlation function (SCF). As an simulation example, the derivation of the analytical expression for SCF components is carried out for the sequence modulated with Barker code; the comparison to an uncoded random amplitude pulse modulated sequence is conducted.