# Deep Learning-Based Signal Detection for Underwater Acoustic OTFS Communication
## 3 SC-CNN-BiLSTM-Based Signal Detection for UWA-OTFS
### Architecture of the Proposed SC-CNN-BiLSTM Detector  
For UWA OTFS with severe Doppler effect, a DL-based channel detection method is designed by cascading the skip connection CNN and BiLSTM. The architecture of SC-CNN-BiLSTM for UWA OTFS is shown in Figure 2. It includes the following layers:  
* **SC-CNN layer** : The SC-CNN layer extracts local signal features and learns the hidden relationship between the input and output. * **BiLSTM layer**: The BiLSTM layer can extract features of time series data from both the forward and backward directions and keep correlated and ignore uncorrelated information by the gates structure. It can mitigate interference for UWA OTFS. * **FC layer**: A fully connected layer with a sigmoid activation function is used to output soft bits for signal detection. **SC-CNN layer:**  
The CNN is a type of feedforward neural network structure with convolution calculations. With the advantage of convolution operation, the CNN can extract and express the internal complex correlation of signals, which plays the role of the mapping function. Meanwhile, its weight-sharing structure significantly reduces the number of weights and network complexity. In the SC-CNN layer of the proposed SC-CNN-BiLSTM network, the CNN consists of three convolutional neural network layers and three deconvolutional neural network (DeCNN) layers. The multiple convolutional layers are used to extract the signal features and internal correlations. The hidden layers in the neural network do not output the exact value. The output of the previous layer is the input of the next hidden layer. Accordingly, the output of the CNN can be expressed as  
\[\tilde{x}=f_{6}(f_{5}(...f_{1}(y))), \tag{7}\]  
where \(y\) is the input data, \(\tilde{x}\) is the output of the CNN, and the function \(f_{n}(\cdot)\) represents the operation in each convolutional layer. In the neural network structure, SC can create short paths from previous layers to later layers. Not only can they reuse information for training, but they also can ease the gradient disappearance problem in network backpropagation. In the proposed SC-CNN layer, we add symmetrical skip connections to transfer learned feature mapping from the previous layer to the current layer. Each DeCNN not only takes the output from the previous layer as input but is also skip connected to the previous CNN layers. This mechanism enhances feature reusability. With the output in the same dimensionality from the earlier layers, the  
Figure 2: Deep learning-aided UWA OTFS communication. SC-CNN can learn more effective information through the interactions of layers. As shown in Figure 2, in SC-CNN-BiLSTM, the first DeCNN layer takes the output of the previous CNN layer as its input. Starting from the second DeCNN layer, the fused feature vector of the SC-CNN can be expressed as  
\[DeCNN_{l}=g(DeCNN_{l-1}+CNN_{n+1-l}), \tag{8}\]  
where the function \(g(\cdot)\) represents the feature fusion of different network layers, \(n\) is the number of layers for the CNN or DeCNN and the total number of layers is \(2n\), while \(l\) represents the \(l\)th CNN or DeCNN layer. The input of \(DeCNN_{l}\) is the fusion of output of \(DeCNN_{n-1}\) and \(CNN_{n+1-l}\). **BiLSTM layer**:  
As shown in Figure 3, in an SC-CNN-BiLSTM cascaded neural network, the BiLSTM layer includes two LSTM networks in different directions: LSTM-F and LSTM-B. The input sequences are passed into LSTM-F in the forward direction and LSTM-B in the backward direction. These two LSTM cells are cascaded and passed to more Bi-LSTM layers. In the forward layer, the calculation is performed from the start time to the time \(t\), and the output of the forward hidden layer at each time is obtained and saved. The backward layer is calculated in reverse along the time axis, and the output of the backward hidden layer at each time is also obtained and saved.