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This paper addresses the problem of frequency-domain inter-carrierinterference (ICI) mitigation for differential orthogonal frequency-divisionmultiplexing (OFDM) systems. The classical fractional fast Fourier transform(F-FFT), adopting the fixed sampling interval, would suffer from the limitedaccuracy of ICI mitigation and low adaptability in dynamic Doppler spread. Totarget the above challenges, we propose an adaptive fractional Fouriertransform (A-FFT) demodulation method, in which an estimation algorithm basedon the coordinate descent approach is designed to compute the fiducialfrequency offset without increasing pilots. By means of compensating ICI atfractions of the fiducial frequency offset adapted to the time-varying Dopplershift, the A-FFT has the capability of tracking Doppler fluctuations over theunderwater acoustic channels, thus extending the application range offrequency-domain ICI mitigation. Simulation results show that the A-FFT issignificantly superior to the existing classical methods, the partial fastFourier transform (P-FFT) and the F-FFT, for both medium and high Dopplerfactors and large carrier numbers in terms of the mean squared error (MSE).Numerically, the MSE of the A-FFT is reduced by $\bf{39.88\%-72.14\%}$ comparedto that of the F-FFT with the input signal-to-noise ratio ranging from 10 dB to30 dB at a Doppler factor of $\bf{2.5\times 10^{-4}}$ and a carrier number of1024, while the P-FFT even cannot work well.

Adaptive F-FFT Demodulation for ICI Mitigation in Differential Underwater Acoustic OFDM Systems