In practical mobile communication systems, dataaided synchronization is performed before actual data exchanges, and synchronization methods are tailored to the pilot sequence. In this paper, we propose a framework for initial synchronization that works independently of the pilot sequence. We show that classical data-aided and blind techniques are particular cases of this general framework. We thoroughly study the specific problem of OFDM data-aided carrier frequency offset estimation. For the latter, we provide theoretical expressions of performance upper-bounds. Also, a practical thin CFO estimator for OFDM is provided under the form of a novel algorithm which is shown by simulations to perform better than classical pilot based methods.