# Deep Learning-Based Signal Detection for Underwater Acoustic OTFS Communication
## 4 Numerical Results  
### System Set-Up  
Both the simulation channel and experimental channel were used to evaluate the performance of the proposed signal detection scheme. The OTFS frame size was set to \((N,M)=(8,64)\), which means each frame had 8 symbols and 64 subcarriers in the TF domain. The carrier frequency was set to 6 kHz. The maximum multi-path delay in the sea  
Figure 5: Training loss of several optimizers.  
experiment was about 100 ms, so the subcarrier spacing was set to \(\Delta f=1/\tau_{max}=10\) Hz. The sound speed was set to \(c=1500\) m/s. Binary phase shift keying (BPSK) was utilized for symbol constellation mapping.  
The proposed model was implemented on the DL framework of TensorFlow and Keras for training and testing. The parameters of the neural network are listed in Table 2. In the proposed SC-CNN-BiLSTM, there are \(2 MN\) input neurons, where \((M,N)\) is the frame size of the OTFS. For the output of the SC-CNN-BiLSTM-based OTFS detector, every 32 bits of transmitted data were grouped and predicted according to the separately trained model and then serially converted to the final output. In the proposed SC-CNN-BiLSTM, the former three convolutional layers used 4, 8 and 16 filters and the rectified linear unit (ReLU) activation function, the convolutional kernels were 4, 2 and 2, and the stride sizes were 4, 2 and 2, respectively. The latter three deconvolution layers had 8, 4 and 2 filters, the convolutional kernels were 2, 2 and 4, and the stride sizes were 2, 2 and 4, respectively. BiLSTM includes three BiLSTM layers with 30, 20, and 16 hidden units, and layer normalization (LN) was added between each BiLSTM layer to accelerate convergence and prevent overfitting. The BiLSTM layers used a hyperbolic tangent (tanh) activation function. For the output, there was one FC-DNN layer with 32 neurons and a logistic sigmoid activation function. The logistic sigmoid function mapped the output values of [0,1] as soft bits, which would be then processed to obtain the target sent bits. The output layer used the regression sigmoid function to find the predicted values of the transmitted symbols [33].  
We generated 60,000 OTFS frame samples under time-varying delay-Doppler channels. The data samples were divided into the training set, validation set and test set at a ratio of 4:1:1.  
The BER performance of the following signal detection methods will be compared:  
* Proposed SC-CNN-BiLSTM: The proposed SC-CNN-BiLSTM signal detection method for UWA OTFS;
* 2D-CNN: The DL OTFS signal detection based on the 2D-CNN proposed for wireless radio communication [32];
* FC-DNN: The FC-DNN-based signal detection method for UWA OTFS [33];
* MP: Message-passing nonlinear signal detection method for OTFS [13];
* LMMSE: Classical linear minimum mean square error (LMMSE) [12] signal detection method for OTFS;
* ZF: Classical zero-forcing (ZF) [11] linear signal detection method for OTFS.  
We will evaluate the performance of SC-CNN-BiLSTM in both the simulation and experimental channels with the above system settings and also consider the non-ideal factor of signal processing in practical underwater acoustic communication.