Underwater acoustic communication has currently become a popular field of research. Underwater Acoustic Channels (UACs) are characterized by severe effects like multipath propagation, Doppler shift and scaling, intersymbol interference (ISI), frequency dependent attenuation and ocean noise. This paper addresses Doppler shift, in the presence of ocean noise and attenuation while using OFDM to transmit data. Frequency dependent attenuation, ocean noise and Doppler Effect have been simulated, on MATLAB (v2015a), to represent the UAC. At the receiver, a method to estimate and compensate this Doppler Effect has been developed. It uses two banks of parallel self-correlators for coarse followed by fine estimation and compensation. This method enables online receiver operation for multicarrier underwater acoustic communication. The same is verified on a Zynq board (ZC702).