Asymptotic equivalence between the unconditional maximum likelihood and the square-law nonlinearity symbol timing estimation

Abstract—This paper provides a systematic approach to the problem of nondata aided symbol-timing estimation for linear modulations. The study is performed under the unconditional maximum likelihood framework where the carrier-frequency error is included as a nuisance parameter in the mathematical derivation. The second-order moments of the received signal are found to be the sufficient statistics for the problem at hand and they allow the provision of a robust performance in the presence of a carrier-frequency error uncertainty. We particularly focus on the exploitation of the cyclostationary property of linear modulations. This enables us to derive simple and closed-form symbol-timing estimators which are found to be based on the well-known square timing recovery method by Oerder and Meyr. Finally, we gen-eralize the OM method to the case of linear modulations with offset formats. In this case, the square-law nonlinearity is found to provide not only the symbol-timing but also the carrier-phase error. Index Terms—Cyclostationarity, nondata aided, phase estima-tion, second-order statistics, synchronization, timing. I