Cyclic Detectors in the Fraction-of-Time Probability Framework

Abstract

The signal detection problem for cyclostationary signals is addressed within the fraction-of-time probability framework, where statistical functions are constructed starting from a single time series, without introducing the concept of stochastic process. Single-cycle detectors and quadratic-form detectors based on measurements of the Fourier coefficients of the almost-periodically time-variant cumulative distribution and probability density functions are proposed. The adopted fraction-of-time approach provides both methodological and implementation advantages for the proposed detectors. For single-cycle detectors, the decision statistic is a function of the received signal and the threshold is derived using side data under the null hypothesis. For quadratic-form detectors, the decision statistic can be expressed as a function of the received signal without using side data, at the cost of some performance degradation. The threshold can be derived analytically. Performance analysis is carried out using Monte Carlo simulations in severe noise and interference environments, where the proposed detectors provide better performance with respect to the analogous detectors based on second- and higher-order cyclic statistic measurements.