# Underwater-Acoustic-OFDM Channel Estimation Based on Deep Learning and Data Augmentation
## 4 Experiments and Evaluations
### MSE and BER Performance for the Different Number of Pilot Symbols  
Below, we analyzed the performance of MSE and BER under different pilot symbols. The above simulation used two symbols, occupying the 2 nd and 14 th OFDM symbols, respectively. The following situation combined the four pilot symbols, to occupy the 2 nd, 6 th, 10 th, and 14 th OFDM symbols, respectively. We first analyzed the case of MSE, as shown in Figures 13 and 14. It can be seen that because the input-channel pattern features corresponding to the added pilot symbols were richer, the performance of using four pilot symbols rather than two pilot symbols was significantly better in the high SNR. In the low-SNR case, the results of the LS-4 symbols were inferior to the LS-2-symbols case. The reason for this result is mainly attributable to the elements in the UWA-CSI matrix averaging in the order of \(10^{-4}\) after the square, while the MSE in these cases was also of the same order. When the error is compared to itself, it is not surprising that anyone's MSE is better than the others, as their performance was disappointing.  
The analysis of BER under different pilot symbols is shown in Figures 15 and 16. We can see that compared to the case of two symbols, four symbols can bring very excellent BER performance. It can also be seen from the figure that, whether in the KAU1 or NOF1 scenarios, our proposed algorithm can still maintain excellent performance, even with fewer pilot symbols. This result holds significant implications for the UWA-OFDM system within the repository. By conserving time-frequency resources for data transmission, we can notably enhance data rates.  
We performed ablation experiments for the proposed CAD module, to demonstrate the effectiveness of the module. Our method took into account the uncertainty of the underwater environment for the channel estimation and did not directly estimate the channel information, but instead used the attention mechanism to denoise the channel. The experimental results are shown in Figure 17. We considered the effect of w/- or w/o-CAD modules on the model under two different pilot signals. With the pilot signal of two and the low SNR = 5 dB, w/CAD improved the model performance by about 130% compared to w/o CAD. With the pilot signal of four and a high SNR = 25 dB, w/CAD was about 109% better than w/o CAD. This proves that CAD modules can further optimize channel information, and can selectively focus on or reinforce the information of the specific water-acoustic channel, especially in a low-SNR environment.  
From the above simulation results, we know that the normalization amplitude of the channel estimated by our proposed algorithm was close to the actual channel. The performance of MSE and BER was better than the comparison algorithm, and it had better performance for underwater-acoustic channels of different complexity, especially for complex multi-path-structure scenarios in the performance comparison. For the small number of pilots, the proposed channel-estimation algorithm could also maintain better performance and help to enhance the data rate. However, because the samples of the experiment came from the enhanced samples generated by the CWGAN-CP model, which was close to the characteristics of the real samples, but had fine ambiguity compared to the real samples, the models trained in this paper may still have had a weak gap for the models trained with real data.  
Figure 15: BER vs. SNR for different number of pilot symbols in KAU1 channel.