A new scheme for Doppler estimation and data detection for OFDM underwater acoustic communications is derived in this paper. We design the OFDM symbol as a concatenation of two sub-blocks. The first one is shorter and carries out few data with few subcarriers whereas the second one contains both informative and pilot symbols. The first sub-block serves to estimate the Doppler scaling factor while the pilots in the second sub-block are used for estimating the equivalent channel. Both estimation approaches are based on high resolution methods for solving harmonic retrieval problems in time and frequency domains respectively. Each sub-block contains a cyclic suffix, which allows having more data to be processed. The effectiveness of the proposed scheme is evaluated by means of simulation results.