On the True Cramer-Rao Lower Bound for the DA Joint Estimation of Carrier Phase and Timing Offsets

This paper concerns the Cramer-Rao lower bound (CRB) for the data-aided (DA) timing and/or phase recovery, i.e., the synchronization parameter acquisition is aided by a training sequence known to the receiver. For the DA parameter estimation, the CRB typically varies with the training sequence. This indicates that different training sequences offer fundamental different performance. In this manuscript, we derive a closed-form formula of the CRB for timing and phase recovery with respect to any particular training sequence. The bound illustrates the close relation between the training sequence and the fundamental limit on timing and phase synchronization. It provides additional insights on the training sequence design.