# Underwater-Acoustic-OFDM Channel Estimation Based on Deep Learning and Data Augmentation
###### Abstract
Although previous research has demonstrated the effectiveness of machine-learning methods in improving the overall performance of UWA channel estimation, there are still many key problems to be solved, regarding the specific application scenarios of UWA. One major challenge is the scarcity of samples. UWA communication faces limitations imposed by sea test conditions and other factors, resulting in low collection efficiency in the UWA environment and high acquisition costs for communication data. Therefore, with the sample size collected by UWA communication in a limited time, it is usually difficult to support the effective training of the model, thus causing overfitting of the model. Another hurdle is data-calibration difficulties. Existing models usually use the real channel impulse response as the training label. However, it is difficult to obtain the true value of the channel in real UWA communication in real time--that is, the calibration of the training labels cannot be realized, so the learning of the model usually needs to be conducted offline. Hence, there is a pressing need for research focused on enhancing UWA channel data. Traditional data-enhancement algorithms include replay technology based on the statistical characteristics of raw water-acoustic-channel-distribution and data-enhancement methods based on communication-signal-processing technology. Channel replay is able to generate data with the same statistical properties, based on a small number of measured UWA channels. Relevant studies have proposed a UWA channel simulator driven by measurement data, which assumes that in a specific time window the communication channel is a stochastic process [17]. In [18], the authors used Empirical-Mode-Decomposition-(EMD) technology to first dismantle the channel into the true part and the random part [19]. On the basis of ensuring the inherent characteristics of the UWA channel, the method extends the latter and recombines with the confirmed part, to generate new UWA channel data. With the help of disturbances and interference often occurring in UWA communication scenarios, such as synchronization error, Doppler offset, noise interference, etc., data enhancement based on communication-signal-processing technology can realize data expansion. Typical work includes applying a symbolic time shift to the raw data in the literature and a Doppler shift to achieve data enhancement [20]. Data-enhancement algorithms are needed in many application fields of deep learning, and the research from the perspective of deep learning provides a way for the reference of UWA channel estimation. Typical of these is Generative-Adversarial-Networks-(GANs) data enhancement. GANs have the powerful ability to produce simulated samples that capture the actual data distribution [21]. The training algorithm of GANs for generating simulated samples highly similar to the actual data distribution essentially involves a two-player minimax game with two adversarial networks and one discriminative network. The generator network \(G\) uses random latent variables, following a standard Gaussian distribution or a uniform distribution, to generate simulated samples with the goal of deceiving the discriminator network. Conversely, the discriminator network \(D\) aims to differentiate between the simulated samples generated by the network \(G\) and real samples that adhere to the actual data distribution. This implies that a trained GAN can effectively capture the complex distribution of a UWA channel. By using a GAN's generator network, we can obtain a large number of generated samples of simulated UWA channels. However, the training of GANs is usually unstable, with the problems of network convergence, mode collapse, and gradient vanishing [22], etc. Therefore, in this paper we propose a novel GAN variant to improve the training stability. After obtaining a rich sample of UWA channels, channel estimation is performed on the received signals passing through the UWA channels, using our proposed DL framework.