On the Maximum-Likelihood based data-aided frequency offset and channel estimates

We consider transmission over a frequency-selective channel. We focus on the data-aided joint and directed maximum-likelihood estimation of the carrier frequency offset and of the dispersive channel. The directed estimators correspond to the frequency offset estimator assuming the channel known, as well as the channel estimator assuming the frequency offset known. A comparison of directed and non-directed estimators based on asymptotic (large sample) analysis is addressed and shows that the performance of the joint estimates and the directed estimates is not so different.