Novel Second-Order Statistics of the Chirp Cyclostationary Signals

Abstract

In communications and radar/sonar systems, one of the most popular nonstationary stochastic signal models is the chirp cyclostationary (CCS) signal. Recently, the second-order statistics of complex CCS signals are defined based on the conjugate correlation function, which have shown to be more proper in linear canonical transform domain than in the frequency domain. However, the information provided by unconjugate correlation function is missing, which leads to an incomplete study of second-order CCS signals. In this letter, the unified conjugate and unconjugate correlation function of CCS signals is researched. In detail, the definitions of the novel second-order statistics, chirp cyclic correlation and chirp cyclic spectrum, are expounded. Then the properties of these statistics are investigated. Finally, the additional information provided by the correlation function with conjugate operation and the usefulness of the proposed statistics are introduced and explained by simulations.