Estimation and Deconvolution of Second Order Cyclostationary Signals

Specifically, in wide-sense second-order cyclo-stationary (CS2) signals, the first two moments change periodically [1]. These signals are prevalent in numerous domains, including telecommunications, telemetry, radar, sonar, mechanics, radio astronomy, econometrics, and atmospheric science [2]. In the field of mechanics, the rotation of machinery is a significant source of such periodicity. Early signs of faults in gears, bearings, or components of internal combustion engines are represented by CS2 signals, typically detected using vibration, acoustic, or pressure sensors [3]. In telecommunications, telemetry, radar, and sonar, the periodicity in statistics stems from processes such as modulation, sampling, multiplexing, and coding. In radio astronomy, periodicity is observed due to phenomena like planetary revolution, rotation, and star pulsations. Econometrics encounters periodicity induced by seasonality, while atmospheric science studies periodic variations resulting from the Earth's rotation and revolution [4]. In the literature, two types of CS2 detectors are distinguished: one that identifies the presence of a CS2 signal amidst noise [5], and another that estimates CS2 signals, assuming prior knowledge about the cycle period or signal's sparsity [6]. However, in real-world situations, this information might not be available.