Blind feedforward cyclostationarity-based timing estimation for linear modulations

By exploiting a general cyclostationary (CS) statistics-based framework, this letter develops a rigorous and unified asymptotic (large sample) performance analysis setup for a class of blind feedforward timing epoch estimators for linear modulations transmitted through time nonselective flat-fading channels. Within the proposed CS framework, it is shown that several estimators proposed in the literature can be asymptotically interpreted as maximum likelihood (ML) estimators applied on a (sub)set of the second- (and/or higher) order statistics of the received signal. The asymptotic variance of these ML estimators is established in closed-form expression and compared with the modified Cramer-Rao bound. It is shown that the timing estimator proposed by Oerder and Meyr achieves asymptotically the best performance in the class of estimators which exploit all the second-order statistics of the received signal, and its performance is insensitive to oversampling rates P as long as P greater than or equal to 3. Further, an asymptotically best consistent estimator, which achieves the lowest asymptotic variance among all the possible estimators that can be derived by exploiting jointly the second- and fourth-order statistics of the received signal, is also proposed.