On Cycle-Period Estimation: A Bayesian Information Criterion

Abstract

Detection of cyclostationary (CS) signals has been addressed by means of generalized likelihood ratio test criteria. However, an accurate maximum likelihood estimator requires the estimation of cycle period (CP) as $a priori$ information, which has not yet been correctly addressed in the literature. In this correspondence, an estimator of CP is devised under the information theoretic criterion(ITC) framework for long observation regime. In particular, we formulate asymptotic log-likelihood function in discrete frequency domain. From the evidence that direct implementation of ITC leads to a high probability of CP overestimation, we reformulate ITC by Bayesian information criterion (BIC), and derive an accurate penalty function. The proposed BIC variant appears to be consistent as signal-to-noise ratio increases. Numerical simulations corroborate the feasibility of the proposed estimator and show its superiority over state-of-the-art schemes.