Best Quadratic Unbiased Estimator (bque) for Timing and Frequency Synchronization

This paper deals with the optimal design of quadratic NonData-Aided (NDA) openand closed-loop estimators. The new approach supplies the minimumvariance, unbiasedNDA quadratic estimators, without the need of assuming a 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 closedloop 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 UCRBG asymptotically. Finally, the quadratic analysis is naturally extended to higher-order techniques which exhibit a better performance for high SNRs.