Asymptotic normality of cyclic autocorrelation estimate with estimated cycle frequency

For an almost-cyclostationary signal, mean-square consistent and asymptotically complex normal estimators of the cyclic statistics exist, provided that the signal has finite or practically finite memory and the cycle frequency is perfectly known. In the paper, conditions are derived to obtain a mean-square consistent and asymptotically complex normal estimator of the cyclic autocorrelation function with estimated cycle frequency. For this purpose, a new lemma on conditioned cumulants of complex-valued random variables is derived. As an example of application, the problem of detecting a rapidly moving source emitting a cyclostationary signal is addressed and the case of a low Earth orbit satellite considered.