## 4 Simulation Results and Discussions
### BER under Simulated Underwater Channel  
In this subsection, the BER of BC-UAC-TD and BC-UAC-FS is verified with the BELLHOP simulated channel model. The parameter settings of the BELLHOP channel are listed in Table 4, and the corresponding normalized CIR is illustrated in Figure 10. In the simulated shallow water channel, the largest time-delay of the multipath is about 0.5 s, and its amplitude is about 0.15. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Value** & **Parameter** & **Value** \\ \hline Distance & 5 km & Depth & 50 m \\ Sound speed & 1543–1546 m/s & Wave height & 0.6 m \\ Seawater acoustic absorption coefficient & 6.94 \(\times\) 10\({}^{-5}\) dB/km & Seafloor acoustic absorption coefficient & 0.5 dB/km \\ Seafloor density & 1810 kg/m\({}^{3}\) & Seawater density & 1021 kg/m\({}^{3}\) \\ Transmitter transducer depth & 25 m & Receiver transducer depth & 25 m \\ Number of beams & 10 & Transducer beam angle & 0–30\({}^{\circ}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: BELLHOP parameters. Figure 10: The impulse response of the BELLHOP channel. Figure 11 shows the impact of the symbol length (\(T_{\text{sym}}\)) on the BER of BC-UAC-TD and BC-UAC-FS, where \(M=4\), \(\Delta f=200\) Hz in BC-UAC-TD and \(\Delta f_{0}=200\) Hz in BC-UAC-FS. From Figure 11, we observe that the BER of the proposed BC-UAC method decreases along with the increase in \(T_{\text{sym}}\). This is because the larger the \(T_{\text{sym}}\), the more energy each symbol has. As the SNR increases, the performance of the channel estimation and equalization module is improved. From Figure 11a, we observe that the error platform of the BER is eliminated by the EC technique in BC-UAC-TD. Comparing Figure 11a with Figure 11b, one finds that the performance in terms of the BER of BC-UAC-FS is better than that of BC-UAC-TD under the same conditions. The reason for this phenomenon is that the signal energy utilization rate of BC-UAC-FS is greater than that of BC-UAC-TD. For BC-UAC-TD, only part of the energy in the corresponding delayed segment is used. Moreover, with a given \(T_{\text{sym}}\), as \(M\) increases, the difference of energy utilization between BC-UAC-TD and BC-UAC-FS becomes greater. Using the VTRM in (8), the multipath effect is mitigated effectively, and the energy of the main path signal increases. Figure 12 shows the impact of the frequency offset on the BER of BC-UAC-TD (\(\Delta f\)) and BC-UAC-FS (\(\Delta f_{0}\)), where \(M=4\) and \(T_{\text{sym}}=0.066\) s. From Figure 12, we observe that the BER of the proposed BC-UAC method decreases gradually along with the increase in the frequency offset. This is because the larger the frequency offset, the higher the frequency resolution. Moreover, from Figure 12, we observe that the BER can be decreased using the EC technique in BC-UAC-TD, and the VTRM technique for channel equalization in the proposed BC-UAC method. In addition, with a given \(T_{\text{sym}}\) and different \(\Delta f\) in BC-UAC-TD or \(\Delta f_{0}\) in BC-UAC-FS, the performance in terms of the BER of BC-UAC-FS is better than that of BC-UAC-TD. Figure 13 shows the impact of the modulation order (\(M\)) on the BER of the proposed BC-UAC method, where \(T_{\text{sym}}=0.066\) s, \(\Delta f=200\) Hz in BC-UAC-TD and \(\Delta f_{0}=200\) Hz in the BC-UAC-FS. From Figure 13, we observe that as \(M\) increases, the BER of the proposed BC-UAC method increases. The BER of BC-UAC-TD increases more than that of BC-UAC-FS. This is because the delay segment of a symbol in BC-UAC-TD becomes smaller as \(M\) increases, which results in a smaller signal energy used for modulation information. However, as \(M\) increases, the frequency band used for modulation information in BC-UAC-FS becomes larger, and the signal energy remains unchanged. Since the frequency resolution remains unchanged, the influence of \(M\) on the BER of BC-UAC-FS is relatively small. Figure 11: The impact of \(T_{\text{sym}}\) on the BER of the BC-UAC method under the simulated channel. (**a**) BC-UAC-TD.