A comparison of soft and hard decision-directed feedforward phase estimators

This paper is devoted to the comparison of hard and soft decision directed feedforward phase estimators based on the maximum likelihood principle. The particular structure of these estimators is taken into account to derive a new lower bound on the estimation variance for a constant phase error. Equivalent noise bandwidths for decision directed estimators are also studied. They allow us to characterize the estimator behaviour for the tracking of a time varying phase error. Simulation results are finally proposed, comparing the root mean square errors of the different estimators, for a constant phase error and for a time varying phase error respectively.