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In this paper, we focus on orthogonal frequency-division multiplexing (OFDM) receiver designs for underwater acoustic (UWA) channels with user- and/or path-specific Doppler scaling distortions. The scenario is motivated by the cooperative communications framework, where distributed transmitter/receiver pairs may experience significantly different Doppler distortions, as well as by the single-user scenarios, where distinct Doppler scaling factors may exist among different propagation paths. The conventional approach of front-end resampling that corrects for common Doppler scaling may not be appropriate in such scenarios, rendering a post-fast-Fourier-transform (FFT) signal that is contaminated by user- and/or path-specific intercarrier interference. To counteract this problem, we propose a family of front-end receiver structures that utilize multiple-resampling (MR) branches, each matched to the Doppler scaling factor of a particular user and/or path. Following resampling, FFT modules transform the Doppler-compensated signals into the frequency domain for further processing through linear or nonlinear detection schemes. As part of the overall receiver structure, a gradient-descent approach is also proposed to refine the channel estimates obtained by standard sparse channel estimators. The effectiveness and robustness of the proposed receivers are demonstrated via simulations, as well as emulations based on real data collected during the 2010 Mobile Acoustic Communications Experiment (MACE10, Martha's Vineyard, MA) and the 2008 Kauai Acomms MURI (KAM08, Kauai, HI) experiment.