Chirp cyclic moment for chirp cyclostationary processes: Definitions and estimators

In high-mobility wireless communications and radar systems, a higher carrier frequency and higher moving speed/acceleration of terminals enhance the impact of the time-varying Doppler effect. This effect alters the cyclostationarity of the transmitted signal and characterizes the received signal as a chirp cyclostationary (CCS) signal. The generalized cyclic statistics of CCS signals are defined based on Fourier analysis, which is either zero-value or non-bandlimited, and is thus inefficient. In this study, the linear canonical transform (LCT), a generalized form of the Fourier transform, was used to address these issues. The moment function is a k-dimensional variable comprising a single time variable and k−1 lag variables. The chirp cyclic moment and the time-varying canonical spectrum were designed as the LCT of the moment with respect to the time and lag variables, respectively. Furthermore, an estimator of the chirp cyclic moment was defined, which is demonstrated to be asymptotic unbiased, asymptotic mean-square-consistent and asymptotic complex normal. Applications of the chirp cyclic moment in radar parameter estimation and electrocardiogram signal characterization were verified using simulated and real-life data.