## 5 Conclusions  
Since underwater acoustic channels have severe ISI caused by multi-path, propagation loss, and Doppler effects, multi-band techniques with spreading are essential in a low SNR environment for reliable underwater communications. In multi-band configuration, the performance loss occurs because specific inferior band affects to entire band. It is very important to decide which band is the inferior one. In order to decide the inferior band, we proposed the EC-BER algorithm which estimates the reliability of the received data by checking the how many differences between re-encoded and demodulated symbols. The EC-BER has a close relationship with the performance of each band. Therefore, we can improve the performance as allocate lower weight to inferior band. The benefits of the proposed EC-BER algorithm are low computational complexity and exact performance prediction of coded data field for time-varying channel compared to state-of-the art such as ESNR and PES.  
Through the simulations, we optimized weighting values using the proposed EC-BER, and we confirmed performance gain was obtained compared to conventional one. To prove the effectiveness of the EC-BER algorithm, a lake trial was conducted by employing four bands, a spread 4-PSK modulation, and turbo codes with rate of one-third. The experimental results show that the performance was improved by increasing the number of chips and iterations of the turbo equalization. However, some packets still failed to decode even though the turbo equalization reached five times. We applied optimized weighting values of the EC-BER to the failed packets. As a result, failed packets are successfully decoded, and we confirmed that the EC-BER algorithm drastically improved the reliability of the system, resulting in minimal to zero errors. Through the lake experimental results, the proposed algorithm is a useful technology for reliable underwater channels. For future studies, based on the proposed algorithm, we will apply it to the exact Doppler estimation. Finally, it will be applied to long-range underwater communication that will further increase the distance between the transceivers.  
Conceptualization, H.-W.J.; methodology, J.-W.J.; software, H.-W.J.; validation J.-W.J.; formal analysis, J.-W.J.; data curation, H.-W.J.; writing--original draft preparation, H.-W.J.; writing--review and editing, J.-W.J.; supervision, J.-W.J.; project administration, J.-W.J. All authors have read and agreed to the published version of the manuscript.  
This work was supported by the Agency for Defense Development (contract No. UD200010 DD). The authors acknowledge with thanks the Agency for Defense Development for its technical and financial support.  
Not applicable.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Packet Number**} & \multirow{2}{*}{\begin{tabular}{c} **Band of** \\ **Frequency** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Estimation** \\ **Error Rate (\%)** \\ \end{tabular} } & \multirow{2}{*}{\
\begin{tabular}{c} **Weighting** \\ **Value** \\ \end{tabular} } & \multicolumn{3}{c}{
\begin{tabular}{c} **Decoded BER According to** \\ **Number of Turbo Iterations** \\ \end{tabular} } \\ \cline{3-6}  & & & & **1** & **3** & **5** \\ \hline \multirow{4}{*}{3} & \(f_{1}\) & 45 & 0.2 & & & \\ \cline{2-6}  & \(f_{2}\) & 49 & 0.2 & & & \\ \cline{2-6}  & \(f_{3}\) & 6 & 1.0 & & & \\ \cline{2-6}  & \(f_{4}\) & 53 & 0.2 & & & \\ \hline \multirow{4}{*}{5} & \(f_{1}\) & 42 & 0.4 & & & \\ \cline{2-6}  & \(f_{2}\) & 38 & 0.4 & & & \\ \cline{2-6}  & \(f_{3}\) & 7 & 1.0 & & & \\ \cline{1-1} \cline{2-6}  & \(f_{4}\) & 6 & 1.0 & & & \\ \hline \hline \end{tabular}
\end{table}
Table 5: Performance analysis according to weighting. (\(N_{c}=32,\ N_{b}=4\)).