## 1 Introduction  
With the increasing requirements for an Internet of Things in the oceans, efficient data processing and transmission become critical for ensuring the instantaneity for the underwater environment monitoring [1, 2] and emergency rescue [3]. Orthogonal frequency division multiplexing (OFDM) has been a viable method in bandwidth-constrained underwater acoustic communications [4, 5], as a result of its high spectral efficiency and ability to resist frequency selective fading. Nonetheless, the selective channels decided by variant parameters, such as distribution of sound speed [6], bottom reflection coefficient and surface waves [7], limit the performance improvement of the underwater acoustic (UWA) OFDM system [8, 9]. To better detect the OFDM signals from UWA channels, variable equalizers have been applied, e.g., linear equalizers including zero-forcing (ZF) and minimum mean square error (MMSE) equalizers [10], and decision feedback equalizer (DFE) such as the Turbo equalizer [11, 12]. The linear equalizers with simple structures are widely used in terrestrial communication links [13, 14], whose performances rely on accurate channel estimations. Although the DFEs show satisfactory performance without a channel estimator, it is at the expense of the requirement for higher computational complexity and extra channel coding [15; 16]. In practice, real-time underwater acoustic communications (UAC) do not allow for a large number of online iterations [17; 18; 19], which still require linear equalizers. However, the noise amplification problem occurs when applying the ZF equalizer. Although MMSE equalizer overcomes this problem by considering the signal-to-noise ratio (SNR), it is hard to estimate the statistical values of the noise in real underwater environments including non-Gaussian and colored noise [20; 21]. To further optimize the equalizer, deep learning (DL) and neural network (NN) have been developed [22; 23; 24; 25; 26]. With enough samples, a DL-based receiver can statistically learn to detect the symbols from the channel and other interference. [PERSON] et al. proposed a DL-based OFDM receiver [22], which used three fully connected layers to deal with a 64-subcarrier OFDM symbol with a block-type pilot. The bit error rate (BER) of the NN-based receiver was lower than the least square (LS) and MMSE estimation and detector in the simulation. To further obtain higher detecting accuracy, researchers have tried to substitute the whole communication system for the end-to-end networks [22; 24; 25; 27]. The traditional digital modulation and subcarrier mapping has been replaced by the autoencoder (AE) [24]. A blind receiver without the pilot has been built with a convolutional neural network (CNN), which showed better performance compared with the traditional baselines. Similarly, an AE has been designed [25] to provide a modulation scheme for the multicarrier system. This work fed the decoder with both the channel state information (CSI) and received symbol, constructing a data-driven model for symbol detection. The simulations showed significant BER performance in additive white Gaussian noise (AWGN) channels. In [PERSON]'s work [28], a super-resolution channel reconstruction network was combined with AE for the marine communication system, proving its effectiveness in slow fading channels. [PERSON] et al. [29], [PERSON] et al. [30], and [PERSON] et al. [31] proposed different network structures for the UWA OFDM receiver, and trained them with the WATERMARK dataset. These studies focused on designing specific network structures to improve the performance of the OFDM receiever. Nevertheless, the theoretical explanation of the networks remains limited. There is no quantitative analysis for the hyperparameters. Although the above NN-based communication systems show good performances in simulations, it is difficult to practically implement them, particularly in underwater acoustic channels because of the heavy computations and complex structures. For instance, Refs. [29; 30; 31] did not conduct sea trials.