Stochastic approach to square timing estimation with frequency uncertainty

This paper addresses the problem of non-data-aided (NDA) symbol timing estimation in presence of carrier frequency errors. For that purpose, a novel stochastic maximum likelihood (ML) estimator is derived following a Bayesian approach by considering the carrier frequency error an unknown deterministic parameter constrained within a certain range. Further on, it will be exploited the cyclostationary nature of the received data for obtaining an ML symbol timing estimator. In this way, it is found that the weighted cyclic autocorrelation function of the received data is sufficient statistic of the problem and thus, an optimal ML symbol timing estimator is derived for low signal-to-noise ratios (SNR). As a consequence of the study, the well-known Oerder and Meyr ("square timing") method becomes a particular case of this new general solution.