Optimal quadratic non-assisted parameter estimation for digital synchronisation

This paper deals with the optimal design of quadratic non-data-aided (NDA) open- and closed-loop estimators. The new approach supplies the best quadratic unbiased estimator (BQUE), i.e., that one with the minimum variance, without the need of assuming a given statistic 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 UGCRB asymptotically. Afterwards, the BQUE deduction is applied to obtain robust NDA estimators of the signal parameters in the presence of a frequency-selective channel. Finally, the quadratic analysis is naturally extended to higher-order techniques which exhibit a better performance for high SNR.