# Deep Learning-Based Signal Detection for Underwater Acoustic OTFS Communication
## 4 Numerical Results
### Experimental Results  
We further evaluated the performance of SC-CNN-BiLSTM-based OTFS signal detection under multiple channels from a sea experimental dataset [34]. For evaluation of the proposed scheme, we used UWA experimental channels from the WATEMMARK dataset. WATEMMARK is a benchmark dataset driven by at-sea measurements of the time-varying impulse response. In this paper, we employed the raw CIR measured at Norway-Oslofjord (NOF) and Kauai 1 (KAU1). The parameter settings of the experiments are shown in Table 4.  
The CIRs of the NOF channel in the time domain and DD domain are shown in Figures 7 and 8. As shown in Figure 7, the CIR of NOF in the time domain had an obvious time-varying multi-path. Figure 8 presents the corresponding CIRs in the DD domain, where the Doppler shift for each path can be observed. As shown in Figure 9, the BER performance of the proposed SC-CNN-BiLSTM-based signal detection method was compared with other methods. Similar to the results in the simulation channel, the proposed SC-CNN-BiLSTM-based signal detection showed the best performance under the NOF UWA experimental channel. The proposed method had 5 dB, 2.5 dB and 2 dB gains at a BER of \(1\times 10^{-3}\) compared with MP-, FC-DNN- and 2D-CNN-based signal detection methods. Compared with the 2D-CNN, SC-CNN-BiLSTM enhanced the performance by employing skip connections for data reuse and BiLSTM in an RNN for time series data processing. Specifically, in SC-CNN-BiLSTM, skip connections with the CNN can provide more efficient information through the interactions of the convolutional and deconvolutional layers. After the SC-CNN extracts the features of the input vector, LSTM can further focus on effective information in the data sequences to mitigate ICI and ISI. A single CNN can only extract local features and cannot process time series data as efficiently as an RNN. Compared with DNN-based signal detection, our proposed method utilized a CNN and BiLSTM cascaded network for better data fitting than a single neural network. There are non-convex optimization and gradient disappearance problems in the FC-DNN, which limit its robustness. Compared with nonlinear MP detection, SC-CNN-BiLSTM can converge to the optimum, whereas MP may get trapped in local optimum and have high complexity during iteration. Compared with linear-based methods, such as LMMSE and ZF, the SC-CNN-BiLSTM signal detection method can use nonlinear operations in the neural network to better fit data in the DD domain. The CIR of the KAU1 channel in the time and DD domains are shown in Figures 10 and 11, respectively. In both the time and DD domains, the CIR structure was more complex than that for NOF. The channel variations were also more obvious than those for NOF. In the DD domain, it can be seen that the maximum Doppler shift of KAU1 was larger than that for NOF, which was about 4 Hz. Note that in these two sea experiments, although the transmitter and receiver were deployed in fixed locations, the Doppler shift was still evident. The Doppler shift in practical UWA channels is severe and complex, and it is caused by the multiple unique characteristics of the UWA environment. For example, the movement of seawater can cause the transceiver to move. Figure 8: CIR in DD domain under NOF experiment. Figure 11: CIR in DD domain under KAU1 experiment. Figure 10: CIR in time domain under KAU1 experiment. Figure 9: BER performance comparison for NOF experiment. In Figure 12, the BER performance of multiple signal detection methods is similar to that of the NOF channel. In the KAU1 experimental channel, SC-CNN-BiLSTM-based signal detection could achieve 4.5 dB, 2.5 dB and 1.5 dB SNR gains at a BER of \(1.5\times 10^{-3}\) compared with the MP, FC-DNN and 2D-CNN methods, respectively. Owing to the specific design of the neural network, our proposed method outperformed both DL-based signal detection and conventional linear or nonlinear signal detection methods.