# Model-Driven Deep-Learning-Based Underwater Acoustic OTFS Channel Estimation
## 1 Introduction
However, its performance is highly dependent on the quality and quantity of the training data. In actual communication systems, obtaining high-quality datasets is often challenging [16; 17]. In OTFS investigation, data-driven DL-based methods have been explored for signal detection [18; 19; 20]. In the classic block-based OTFS communication system, a two-dimensional convolutional neural network (CNN) is utilized for substituting the signal detection process [18]. In order to construct the dataset, the data augmentation technology is used to enhance the dataset for learning. The use of ResNet, DenseNet, and RDN for OTFS signal detection is proposed and compared in [19], respectively. The three network structures can mitigate the gradient explosion and gradient disappearance problems existing in FC-DNN and CNN, consequently yielding superior performance outcomes. In UWA OTFS, the authors have proposed a cascaded neural network structure for signal detection, consisting of a skip connection (SC)-CNN and bidirectional long short-term memory (BiLSTM) network [20]. Through the evaluation in both simulation and experimental UWA channels, the proposed neural network exhibits better performance compared with the classic linear-, nonlinear-, DNN-, and CNN-based signal detection methods. Model-driven DL utilizes prior knowledge, which requires smaller datasets than data-driven DL-based methods. In wireless radio communication, model-driven DL-based channel estimation is investigated for MIMO based on a deep residual network [21] and YOLO network [22]. The neural networks can refine the preliminary channel matrix to be more accurate. The thought of image super-resolution can be also used for channel estimation, considering the estimated channel of pilots as a low-resolution image. With the preprocessing of interpolation, the proposed ChannelNet [23] can reconstruct the complete high-resolution channel impulse response (CIR) from the low-resolution CIR of pilots. Further, a enhanced super-resolution CNN-based channel estimation method, named SRDnNet, was introduced in [24]. The enhanced SRDnNet can directly learn from the input to determine the appropriate interpolation relationship, enabling the generation of a raw channel estimation matrix without interpolation. By employing an element-wise subtraction structure, SRDnNet leverages the denoising mechanism to recover the accurate channel coefficients from the raw channel matrix. However, the super-resolution-based methods are not suitable for UWA OTFS channel estimation due to channel sparsity. With the aim of alleviating the performance degradation of OMP channel estimation in UWA OTFS, this paper proposes a model-driven DL-based UWA OTFS channel estimation method. Our main contributions are as follows:  
* We address the design of system parameters for enabling effective UWA OTFS communication, considering the specific characteristics of the UWA channel. We discuss the configuration of subcarrier spacing, the number of subcarriers per symbol, and the number of symbols per frame in the delay-Doppler domain, taking into account the influence of multipath and Doppler effects. * We propose a model-driven deep learning technique for UWA OTFS channel estimation. Considering the more pronounced Doppler effect in the UWA channel compared with the radio channel, the channel information often deviates from the compressed sensing sparsity assumption typically assumed in the classical OMP estimation algorithm. To address this issue, our method incorporates the OMP algorithm and denoising convolutional neural network (DnCNN) collaboration for channel estimation. The use of a lightweight DnCNN network with a single residual block reduces computational complexity while still preserving the accuracy of the neural network. The proposed method can obtain better channel estimation results by denoising the preliminary channel estimation. The rest of this paper is organized as follows. Section 2 presents UWA OTFS system and typical channel estimation model.