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Suppressing the inter-carrier interference (ICI) is crucial fordifferentially coherent detection in underwater acoustic (UWA) orthogonalfrequency division multiplexing (OFDM) systems due to the fact that the UWAchannel is inherently violently Doppler-shifted. In this paper, we propose anew ICI suppression method, referred to as the partially-shifted fast Fouriertransform (PS-FFT), which eliminates the ICI from both the time and frequencydomains. Specifically, the PS-FFT first divides the received signal in theentire block duration into several short non-overlapping ones to reduce thechannel variation in the time domain. It then applies the Fourier transform atseveral predefined frequencies to the received signal in each of theseintervals to compensate Doppler shifts in the frequency domain. Finally, itweightedly combines the multiple demodulator outputs at each carrier as oneoutput for symbol detection, with the combiner weights being solved by thestochastic gradient algorithm. Simulation results show that the PS-FFTdramatically outperforms the existing classical methods, the partial fastFourier transform (P-FFT) and the fractional fast Fourier transform (F-FFT),for both medium and high Doppler factors and large carrier numbers in terms ofthe mean squared error (MSE). Numerically, the MSE of the PS-FFT is reduced by$\bf{61.83\%-84.89\%}$ compared to that of the F-FFT when the inputsignal-to-noise ratio (SNR) at the receiver ranges from 10 dB to 30 dB at aDoppler factor of $\bf{3\times 10^{-4}}$ and a carrier number of 1024 where theP-FFT even cannot work.

Inter-Carrier Interference Mitigation for Differentially Coherent Detection in Underwater Acoustic OFDM Systems