## 5 Sea Experiment
### Result Analysis  
In this subsection, we report the results of the communication performance evaluation driven by different channel estimators. Figure 7 and Table 2 show the SRER results and the average SRER of the CE-DFE for different channel estimation algorithms, respectively. We observe that compared with the benchmark algorithms, the BS-CS algorithm achieves the highest SRER output with an average gain of 4.33 dB by LSQR, 0.92 dB by OMP, 0.64 dB by BOMP, 1.22 dB by BS-RLS, 0.52 dB by KF-CS, and 0.38 dB by SDD-CS. Affected by the considerable estimation noise, the LSQR estimator performs the worst for the SRER output. Moreover, due to the underrated of block and time-varying sparsity of the UWA channel, other CS-based benchmark algorithms display an obvious performance degradation when compared with the BS-CS algorithm. Next, Figure 8 and Table 2 show a histogram for the BER and the average BER of the CE-DFE for different channel estimation algorithms, respectively. Observing the results in Figure 8, we can see that the proposed BS-CS estimator outperforms the benchmark estimators in BER with an average gain of 6.59%, 0.57%, 0.50%, 0.63%, 0.25%, and 0.17% over LSQR, OMP, BOMP, RLS-CS, KF-CS, and SDD-CS, respectively. Due to the limitation of the length of the training sequence, BS-RLS has the second-worst BER performance. By exploiting the block sparsity, BOMP performs better than OMP; however, the time-varying \begin{table}
\begin{tabular}{l l} \hline \hline
**Description** & **Value** \\ \hline Length of training sequence for BS-RLS & 400 \\ Channel sparsity for OMP and KF-CS & 6 \\ Block size for BOMP, BS-RLS, and BS-CS & 2 \\ Block sparsity for BOMP, BS-RLS, and BS-CS & 3 \\ Continuous measurement number for SDD-CS & 2 \\ The addition threshold for KF-CS, SDD-CS, and BS-CS & 0.07 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: _Cont._  
Figure 6: Response of UWA channels associated with four receiving elements. (**a**) Channel 1. (**b**) Channel 2. (**c**) Channel 3. (**d**) Channel 4.  
feature of the UWA channel would cause performance degradation severely for the classic CS-based algorithm. Moreover, compared with OMP and BOMP estimators, KF-CS has relatively stable performance due to the time-varying sparsity exploitation of the UWA channel, but there is still a room for improvement for KF-CS as the limited role for block sparsity exploitation. Although the performance of SDD-CS is better than that of KF-CS by modeling the UWA channel as hybrid sparsity, the block sparse time-varying feature of the channel would also cause the model mismatch and performance degradation for SDD-CS. It is evident that the proposed BS-CS estimator can simultaneously exploit the time-varying characteristics and block sparsity for the UWA channel, and achieves the best estimation performance in the block sparse time-varying channel. Finally, Figure 9 shows the constellation outputs driven by the LSQR, OMP, BOMP, BS-RLS, KF-CS, SDD-CS, and BS-CS estimators. We observe that the six CS-based estimators generally outperforms the LSQR estimator that does not exploit the channel sparsity. Compared with the LSQR estimator, the constellations obtained by OMP, BOMP, BS-RLS, and KF-CS have different degrees of performance improvement due to the exploitation of sparsity, block sparsity, block sparsity, and time-varying sparsity, respectively. Moreover, the SDD-CS achieves the second-highest constellation results by exploiting the hybrid  
Figure 8: The BER output of CE-DFE. Figure 7: The SRER output of CE-DFE. sparsity of the UWA channel. Furthermore, it is obvious that BS-CS outperforms the other five sparse estimators with respect to the constellation results. Thus, we conclude that due to the exploitation of time-varying characteristics and the block sparsity in the UWA channel, the proposed BS-CS algorithm achieves the communication performance improvement for the block sparse time-varying channel.