## 6 Evaluation and Result Analysis
### Simulation Results  
Firstly, the proposed PB-CSBL and NC-CSCE algorithms were compared with the LS, OMP, SOMP and TMSBL for channel estimation. All paths are distributed in three non-overlapping clusters, and these clusters are set with three different temporal correlation \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameters** & **Notations** & **Values of the Simulations** & **Values of the Lake Trial** \\ \hline Bandwidth & \(B\) & 1.6 kHz & 5 kHz \\ Carrier frequency & \(f_{c}\) & 2.5 kHz & 20 kHz \\ Sampling frequency & \(f_{s}\) & 12.5 kHz & 100 kHz \\ Number of subcarriers & \(K\) & 256 & 256 \\ Number of data subcarriers & \(K_{d}\) & 218 & 193 \\ Number of pilot subcarriers & \(K_{p}\) & 14 & 32 \\ Number of null subcarriers & \(K_{n}\) & 24 & 31 \\ Symbol duration without CP & \(T\) & 160 ms & 51.2 ms \\ CP length & \(T_{cp}\) & 10 ms & 25.6 ms \\ Blocks in one frame & \(M\) & 4 & 5 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: UWA CP-OFDM settings. coefficients ranges over multiple OFDM blocks, which are \([0.1,0.3]\), \([0.5,0.7]\), \([0.8,1.0]\). The additive noise is assumed to be white Gaussian noise, and thus all subcarriers are divided into the same group (i.e., \(Q=1\)) for the proposed NC-CSCE algorithm. The transmitted data bits are mapped to QPSK or 16-QAM constellation symbols. The performance metrics used in the numerical simulations are the MSE of CIRs and BER of data bits, which are verified in 500 simulations for each value of SNR. Figure 3a,b show the MSE and BER performance of different channel estimation methods, respectively. LS performs worst, because the channel sparsity is not considered for this underdetermined system. Based on the joint estimation of multiple OFDM blocks, the SOMP makes full use of the strong temporal correlation of path delays and achieves better performance than the OMP. The delay and correlation of path gains are analyzed in the TMSBL, which makes it better than the SOMP. However, the proposed PB-CSBL performs even better, as it can learn different temporal correlation coefficients and reduce the interference among clusters. The proposed NC-CSCE algorithm utilizes all received pilot and data symbols for the channel estimation, which achieves the lowest BER close to the perfect CSI. When 16-QAM mapping is adopted, Figure 4 proves that the proposed algorithms still maintain good estimation performance. However, in the low SNR region from 0 to 10 dB, the NC-CSCE algorithm does not perform well. This is mainly because high-order modulation at low SNR is prone to symbol decision errors, which may be exacerbated in the iterative process of the NC-CSCE algorithm. Figure 4: The comparison of MSE and BER performance based on 16-QAM constellation mapping: **(a)** the comparison of MSE performance; and **(b)** the comparison of BER performance. Figure 3: The comparison of MSE and BER performance based on QPSK constellation mapping: **(a)** the comparison of MSE performance; and **(b)** the comparison of BER performance. Then, to verify the estimation performance of the proposed algorithms under extreme temporal correlation coefficients (i.e., \(\beta=0\) and \(\beta=1\)), the proposed algorithms are compared with their theoretical lower bounds. Multipaths are assumed to be sparse and share the same correlation coefficient. Then, under QPSK mapping and white Gaussian noise, the mean square error performance is presented in Figure 5. When \(\beta=0\), the MSE of the proposed algorithms is close to the theoretical lower bound in a high SNR region. A significant gap exists in the low SNR region, especially for the NC-CSCE algorithm. This is caused by imperfect hyperparameter estimation, as the lower bound is only reached when the perfect hyperparameters are obtained. When \(\beta=1\), the gap is more obvious in the whole SNR region because of the hyperparameter estimation error. However, the MSE performance with \(\beta=1\) is better than the MSE performance with \(\beta=0\) in a low SNR region.