# Posterior Probability-Based Symbol Detection Algorithm for CPM in Underwater Acoustic Channels
## 6 Conclusions  
CPM was applied to improve the bandwidth and the power efficiency of UWA communication, and PS-FDE was proposed to further improve CPM signal detection performance compared with the traditional FDE. It has a lower complexity than the Viterbi algorithm and uses simple phase detection to extract preliminary information. Combined with the correlation function of CPM, PS-FDE effectively harnesses the inherent coding gain within CPM, ultimately improving the symbol detection performance. Simulations were conducted using MSK and GMSK signals over UWA channels, and the results show that PS-FDE significantly improves detection performance after 2-3 information mergings, compared with that of FDE [15]. The performance improvement for MSK signals ranged from 0.2 to 1.2 dB under different channel conditions, while for GMSK signals, it ranged  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**SNR (dB)**} & **Number of** & **Error Bit of** & \multicolumn{4}{c}{**Error Bit of the PS-FDE**} \\ \cline{3-6}  & **Frames** & **the FDE** & **\(k\) = 0** & **\(k\) = 1** & **\(k\) = 2** & \(k\) = 3 \\ \hline
5-10 & 22 & 212 & 212 & 206 & 188 & 182 \\
10-15 & 52 & 58 & 58 & 56 & 52 & 48 \\
15-20 & 72 & 8 & 8 & 6 & 4 & 4 \\ \textgreater{}20 & 64 & 0 & 0 & 0 & 0 & 0 \\ Total & 210 & 278 & 278 & 268 & 244 & 234 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Number of error bits of received signal frames in different received SNRs.  
Figure 9: Measured channel of MSK signal by OMP.  
from 0.3 to 2.3 dB. The results of the sea trial conducted to prove the effectiveness of the algorithms revealed that compared with that of FDE [15], the BER of PS-FDE exhibited a 15.83% reduction after the third information merging.  
Due to the time-varying nature of UWA channels, the FDE and OMP channel estimation algorithms used in this paper struggle to effectively track channel variations. Consequently, the BER of sea trials is relatively high. Due to the high compatibility of the symbol detection algorithm proposed in this paper with channel equalization, future work will consider integrating this symbol detection algorithm with channel equalization algorithms capable of tracking time-varying channels to enhance the capability to combat time-varying UWA channels.  
Conceptualization, R.H. and N.J.; methodology, R.H.; software, Y.L. and J.H.; validation, N.J.; formal analysis, R.H.; investigation, R.H.; resources, S.G.; data curation, S.Q.; writing--original draft preparation, R.H.; writing--review and editing, R.H. and N.J.; visualization, Y.L.; supervision, J.H.; project administration, S.G.; funding acquisition, N.J. and S.G. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the Youth Innovation Promotion Association, Chinese Academy of Sciences, grant number 2020024.  
The original contributions presented in this study are included in the article. Further inquiries can be directed to the corresponding author.  
Thanks to the personnel involved in the sea trial and the research vessel \"Shiyan 1\" for their contributions to data acquisition for the project.  
The authors declare no conflicts of interest.