# Model-Driven Deep-Learning-Based Underwater Acoustic OTFS Channel Estimation
## 4 Numerical Results
### System Performance under Experimental UWA Channel  
The system validation utilized the UWA experimental channels from the sea trial dataset named WATERMARK [30], which is a benchmark dataset characterized by time-varying impulse response measurements at sea. The raw CIRs measured at Norway-Oslofjord (NOF) and Kauai 1 (KAU1) were employed. Table 4 lists the parameter settings of the two experimental channels. Figures 5 and 6 show the CIR of the NOF channel in both the time domain and DD domain. In Figure 5, the time-domain CIR of the NOF channel exhibits clear time-varying \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameters** & **NOF** & **KAU1** \\ \hline Environment & Fjord & Shelf \\ Range & 750 m & 1080 m \\ Water depth & 10 m & 100 m \\ Transmitter deployment & Bottom & Towed \\ Receiver deployment & Bottom & Suspended \\ Doppler coverage & 7.8 Hz & 7.8 Hz \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Parameters of channel dataset. Figure 4: MSE performance under simulated channel, 8 multipaths. multipaths. Correspondingly, Figure 6 presents the DD domain CIR, where the Doppler shift of each path can be observed. The Doppler range spans from \(-4\) to \(4\). Figures 7 and 8 show the CIR of the KAU1 channel in the time domain and DD domain. Compared with the NOF channel, the KAU1 channel exhibits a more complex CIR structure and pronounced variation in both the time and DD domain. In the DD domain, the maximum Doppler shift of KAU1 is larger than that of NOF. The larger Doppler shift in the KAU1 channel is attributed to the combined effects of tugboat motion and the movement of seawater. In the UWA channel, the presence of Doppler effects is noticeable even when the transmitter and receiver are not moving fast. Multiple unique characteristics in the actual UWA environment can cause complex varying Doppler shifts, including seawater motion, distributed bubble layer, and inhomogeneous sea surface and seabed. The complex varying UWA channels are often difficult to model accurately, but the  
Figure 5: CIR in time domain under NOF experiment. Figure 6: CIR in DD domain under NOF experiment. potential to learn and capture the specific UWA channel characteristics and then fit a more effective UWA channel model. Figures 9 and 10 show the MSE of the three channel estimation methods applied to the NOF and KAU1 channels, respectively. For threshold-based OTFS channel estimation, the threshold is set to \(3\sqrt{\sigma_{p}^{2}}\) according to the paper that proposed threshold-based OTFS channel estimation [8], where \(\sigma_{p}^{2}\) denotes the effective noise power of the pilot signal. From the two figures, the MSE performance of the proposed DnCNN-based channel estimation method performs better than the OMP-based channel estimation method. And the OMP channel estimation is better than the threshold-based channel estimation method. In Figure 9, the DnCNN-based channel estimation requires 5 dB lower SNR than the OMP-based channel estimation method at MSE of \(0.65\times 10^{-3}\). This significant im  
Figure 8: CIR in DD domain under KAU1 experiment. Figure 7: CIR in time domain under KAU1 experiment. provement in SNR requirements highlights the superior performance of the DnCNN-based method in accurate channel estimation. Similarly, in Figure 10, focusing on the more complex KAU1 channel, the DnCNN-based channel estimation method demonstrates enhanced performance, with approximately 1 dB lower SNR requirements compared with the OMP channel estimation method at the MSE of \(10^{-3}\). The DnCNN-based method employs denoising through DnCNN with residual blocks for fine estimation. By leveraging a well-trained model, this method effectively addresses non-Gaussian errors and noise, enabling a closer approximation to the optimal solution and resulting in enhanced accuracy in channel estimation.