Suppressing the inter-carrier interference (ICI) is crucial for differentially coherent detection in underwater acoustic (UWA) orthogonal frequency division multiplexing (OFDM) systems due to the fact that the UWA channel is inherently violently Doppler-shifted. In this paper, we propose a new ICI suppression method, referred to as the partially-shifted fast Fourier transform (PS-FFT), which eliminates the ICI from both the time and frequency domains. Specifically, the PS-FFT first divides the received signal in the entire block duration into several short non-overlapping ones to reduce the channel variation in the time domain. It then applies the Fourier transform at several predefined frequencies to the received signal in each of these intervals to compensate Doppler shifts in the frequency domain. Finally, it weightedly combines the multiple demodulator outputs at each carrier as one output for symbol detection, with the combiner weights being solved by the stochastic gradient algorithm. Simulation results show that the PS-FFT dramatically outperforms the existing classical methods, the partial fast Fourier transform (P-FFT) and the fractional fast Fourier transform (F-FFT), for both medium and high Doppler factors and large carrier numbers in terms of the 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 input signal-to-noise ratio (SNR) at the receiver ranges from 10 dB to 30 dB at a Doppler factor of $\bf{3\times 10^{-4}}$ and a carrier number of 1024 where the P-FFT even cannot work.

翻译：由于UWA 频道本质上是暴力多普勒转换的,因此在水下声学(UWA) 或远方频率多路分解(OFDM) 系统中,抑制设备间干扰(ICI)对于不同一致地探测水下声学(UWA) 或远方频率分解(OFDM) 系统至关重要。 在本文中,我们提出了一个新的 ICI 抑制方法, 称为半变式快速 Fleier 变换( PS- FFT), 将 ICI 从时间和频域中消除。 具体地说, PS- FFT 将整个区段内接收的信号分解为几个较短的非重叠信号, 以减少时间域内的频道变换。 然后, 将 Fourier 以几个预定义的频率变换换到每个间隔内的信号。 最后, 将每个载体的多振动器输出( PS- FFT) 作为符号检测的一个输出, 由Stochastelex lex lex lex lex laft-T 和 NFFFT 快速变换MS- 的输出( Pal- MA- fal- fal- mal- mess- mess) 10- fal- fal- mess- messal- fal- mess) 10- mess) 和 10- fal- fal- fal- fal- fal- fal- sl) 10- fal- fal- fal- 和 的缩算法的缩数。