PC-FFT： A Time-Frequency-Cooperative ICI Mitigation Method for Differential Underwater Acoustic OFDM Signals

‍ ‍Inter-carrier interference （ICI） is a bottleneck factor that restricts the detection performance of differential underwater acoustic （UWA） orthogonal frequency division multiplexing （OFDM） signals. This paper presents a novel ICI mitigation method， named Partially-Single-Frequency-Corrected Fast Fourier Transform （PC-FFT）， which utilizes time-frequency synergy to suppress ICI. In this paper， we propose a novel ICI mitigation method， referred to as the partially-single-frequency-corrected fast Fourier transform （PC-FFT）， which cooperates with the time domain and frequency domains. Specifically， in the time domain， it first performs non-overlapping and uniform segmentation on the received signal within an OFDM symbol duration， converting the fast-varying signal into several quasi-static signals. Secondly， in the frequency domain， compensation is applied to each segment of the short signal at a specific frequency. Finally， the Fourier transform outputs of the compensated short signals are linearly weighted and fed into the differential detector. Subsequently， to determine the weights and compensation frequencies， this paper establishes an optimization problem with both variables and aims to minimize the mean square error （MSE） of signal detection. In this problem， there is a high coupling between the weights and the compensation frequencies， resulting in it being severely non-convex. To reduce the complexity， we design a coordinate rotation descent solution algorithm， which solves the weights and compensation frequencies based on the eigenvalue decomposition and the gradient descent method， respectively， and these two are executed alternately until convergence. The results in both the simulated and the actual-measured UWA channels indicate that compared to the existing methods such as partial fast Fourier transform （P-FFT）， fractional fast Fourier transform （F-FFT）， and partially-shifted fast Fourier transform （PS-FFT）， the PC-FFT exhibits better ICI mitigation performance in larger Doppler shift scenarios. Specifically， the MSE of the PC-FFT is reduced by 55.08%~67.64% compared to the PS-FFT， in the case that the signal-to-noise ratio （SNR） ranges from 10 dB to 30 dB with a carrier number of 1024 and a Doppler factor reaching 3.5×10^-4， while the P-FFT and F-FFT are almost unable to work.