Best quadratic unbiased estimator (BQUE) for timing and frequency synchronization

This paper deals with the optimal design of quadratic non-data-aided (NDA) open- and closed-loop estimators. The new approach supplies the minimum variance, unbiased NDA quadratic estimators, without the need of assuming given statistics for the nuisance parameters, that is, avoiding the common adoption of the Gaussian assumption, which does not apply in digital communications. Alternatively, if the unbiased constraint is relaxed, a Bayesian open-loop estimator is presented and its performance compared with the open-loop BQUE solution. On the other hand, the closed-loop BQUE is developed, showing that it outperforms the well-known ´ad hoc´ Gaussian stochastic maximum likelihood (GSML) scheme for short observation windows, that is, for low-complexity implementations, only converging to the Gaussian unconditional Cramer-Rao bound (UCRBG) asymptotically. Finally, the quadratic analysis is naturally extended to higher-order techniques which exhibit a better performance for high SNRs