On the performance limits of data-aided synchronization

This paper addresses data-aided (DA) synchronization, in which the reference parameter acquisition is aided by a training sequence known to the receiver. The Cramer-Rao lower bound (CRB) for the DA timing and/or carrier phase recovery is presented. For DA parameter estimation, the CRB typically varies with the training sequence. This indicates that different training sequences offer fundamentally different performance. In the literature, the widely cited closed-form CRB for timing and carrier phase recovery was derived under the assumption that the training sequence is independent and identically distributed (i.i.d.) and sufficiently long. We derive a closed-form CRB for timing and carrier phase recovery with respect to an arbitrary training sequence and pulse shaping function for the over and under sampling cases. It turns out that the CRB is a weighted summation of the aperiodic correlation of the training sequence and the weighting factor is determined by the pulse shaping filter. Therefore, this paper reveals the fundamental link between a training sequence and its corresponding performance limit.