Cyclic statistic estimators with uncertain cycle frequencies

For almost-cyclostationary processes, sufficient conditions are derived such that estimates of second-order cyclic probabilistic functions with estimated cycle frequencies are mean-square consistent and asymptotically complex normal. (Conjugate) cyclic autocorrelation functions and (conjugate) cyclic spectra are considered. Under the derived conditions, asymptotically, as the data-record length approaches infinity, the estimates of cyclic statistics with estimated cycle frequencies have the same complex normal distribution as the case of exactly known cycle frequencies. The results are applied to the detection of a moving cyclostationary source in the presence of strong Doppler effect and for low values of SNR.