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In this paper, a time varying Doppler-shift compensation scheme for wideband orthogonal frequency division multiplexing (OFDM) suitable for shallow water communications is proposed. This scheme accommodates a channel model having velocity that accelerate and de-accelerate during a packet of multiple OFDM frames. Furthermore, it assumes that the Doppler-shift varies linearly during the symbol time. To deal with this variation, the time expansion/compression is measured within a fraction of the sample period and then compensated using sample-by-sample interpolation. The Doppler-shift and its residual are frequently estimated during the symbol time to mitigate the inter-carrier interference (ICI) by estimating the first order moment of the cyclic prefix correlation. Additionally, in this technique, the fractional deviation of the sub-carrier spacing, which is considered to be the source of ICI, is estimated by exploiting the fractional part of the normalized sampling frequency offset. The proposed algorithm performance is investigated with real data obtained from an experiment that took place in the North Sea in 2009. In addition, results show that the technique is robust and more pragmatic than existing cyclic prefix (CP)-based algorithms.