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.

翻译：载波间干扰(ICI)与噪声抑制对于水声差分正交频分复用(DOFDM)通信系统中信号的精确检测至关重要。本文采用Transformer设计了一种名为TransDetector的检测器，该检测器能在无需任何导频的情况下显著隐式抑制ICI并显式抑制噪声。与标准Transformer相比，我们提出了三项创新设计：首先，打破标准Transformer中多头注意力(MHA)的内编码器计算范式，设计了一种全新的编码器间注意力机制——交互式MHA，该机制能显著提升性能并加速收敛；其次，为降低接收信号中的噪声分量，设计了一种自动感知降噪结构，使网络能够学习接收信号中的噪声分布；第三，为更好匹配DOFDM信号特性并选择性聚焦于指定位置的数据，我们提出梯形位置编码(PE)以替代Transformer中原有的正弦-余弦PE。在实际水声信道和仿真信道上的实验结果表明，TransDetector在误码率(BER)和均方误差(MSE)方面均优于传统$\mathcal{X}$-FFT算法及DNNDetector。例如，基于实际信道时，当信噪比$\text{SNR}=0$~dB时，TransDetector的BER较PS-FFT和DNNDetector分别降低$27.21\%$和$12.50\%$；当$\text{SNR}=20$~dB时，则分别降低$47.44\%$和$33.49\%$。