Inter-carrier interference (ICI) and noise mitigation is crucial for precise signal detection in underwater acoustic (UWA) differential orthogonal frequency division multiplexing (DOFDM) communication systems. In this paper, we adopt the Transformer to design a detector, referred to as the TransDetector, which can dramatically mitigate ICI implicitly and noise explicitly, even without requiring any pilot. Compared with the standard Transformer, we come up with three creative designs. Firstly, we break the inner-encoder computation paradigm of the multi-head attention (MHA) in the standard Transformer, and design a brand new inter-encoder attention mechanism, referred to as the interactive MHA, which can significantly improve the performance, as well as accelerate the convergence rate. Secondly, to reduce the noise component attached to the received signal, we design an auto-perception denoising structure, which allows the network to learn the noise distribution in received signals. Thirdly, to better match the characteristics of DOFDM signals and selectively focus on the data at specified locations, we propose a trapezoidal positional encoding (PE), instead of adopting the original sine-cosine PE in the Transformer. Experimental results on both the realistic underwater channel and the simulation channel show that the TransDetector outperforms the classical $\mathcal{X}$-FFT algorithms and the DNNDetector in terms of the BER and the MSE. For example, the BER achieved by the TransDetector is reduced by $27.21\%$ and $12.50\%$ when the signal-to-noise ratio $(\text{SNR})=0$~dB and by $47.44\%$ and $33.49\%$ when $\text{SNR}=20$~dB against the PS-FFT and the DNNDetector based on the realistic channel, respectively.

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