## 4 Simulation Results and Analyses
### Comparison between Different Channel Estimation  
This subsection mainly compares the performance of the proposed scheme with other channel estimations. The UWAC channel used in this section is the first channel in Figure 4b. The IPNLMS, ZA-IPNLMS, RZA-IPNLMS, \(l_{0}\)-IPNLMS, SZA-IPNLMS, and a hybrid channel estimation are compared. The proposed channel estimation is made up of the SZA-IPNLMS and SM SZA-DIPNLMS. The common parameters of channel estimation for all schemes are set as step size \(\mu=0.2\), adjustment factor \(\alpha=0\), and regular factor \(\delta=0.01\). The norm constraint parameter of the ZA-IPNLMS, RZA-IPNLMS, and \(l_{0}\)-IPNLMS is \(\kappa=5\times 10^{-6}\), and the one for the SZA-IPNLMS and SM SZA-DIPNLMS, is set as \(\kappa=6\times 10^{-5}\). The hard threshold for \(l_{0}\)-IPNLMS is set as \(\beta=10\), the proportionate threshold of the SZA-IPNLMS and SM SZA-DIPNLMS is set as \(\beta=0.1\), and the update period of SM SZA-DIPNLMS is \(L/4\). The norm constraint parameter and the proportionate \begin{table}
\begin{tabular}{c c c} \hline \hline
**Experiment** & **SPACE’08** & **MACE’10** \\ \hline Carrier Frequency (kHz) & 13 & 13 \\ \hline Bandwidth [kHz] & 9 & 5 \\ \hline The Depth of Water [m] & 10 & 100 \\ \hline Transmitter Height [m] & 4 & 80 \\ \hline Receiver Height [m] & 2, 6 & 80, 70, 60, 50 \\ \hline Distance between Tx and Rx [km] & 1 & 0.5–4 \\ \hline Relative Velocity between Tx and Rx [m/s] & 0 & 1 \\ \hline Spread Factor & 1.7 & \\ \hline Bottom Density [g/m\({}^{3}\)] & 1.269 & \\ \hline Auto Regression (AR) Factor & 0.9 & \\ \hline Sampled Delay Points & 148 & \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Parameters of SPACE’08 and MACE’10 in UWAC simulations. threshold of the proposed IFDTE scheme are configured identically to those of the SZA-IPNLMS and SM SZA-DIPNLMS. Thus, it equivalently provides enough information for the simulation of the proposed IFDTE scheme for performance verification. Finally, the curves of the MSE and BER are simulated and shown in Figures 5 and 6. In Figure 5, the MSE performance for different channel estimations is presented. Under the same SNR, both the SZA-IPNLMS and the proposed algorithm have a lower MSE than those of other channel estimation schemes and they are almost overlapped together. MSE is the exact performance indication for the equalization since it illustrates the difference between the estimated values and the true ones. With the increase in SNR to 3.5 dB, the floor of the SZA-IPNLMS is lower than other channel estimations. Different from the traditional hard threshold, the SZA-IPNLMS gives a dynamical norm penalty term in terms of the ratio of channel coefficients to the maximum one in (4) and (5). The performance of the SZA-IPNLMS is better as the small coefficients of the UWAC channel estimate precisely. In Figure 6, the BER curves of the same equalization with different channel estimations are presented. The proposed IFDTE scheme obtains the same and best BER performance as those of the SZA-IPNLMS among all schemes, where it obtains a BER of \(7.15\times 10^{-4}\), \(1.35\times 10^{-4}\) and \(3.65\times 10^{-5}\) at SNR of 3 dB, 3.5 dB, and 4 dB, respectively. The BER performance for the equalization with the SZA-IPNLMS under the same SNR is better than others because the SZA-IPNLMS provides more precise CSI. Under the same BER, BER = \(1\times 10^{-3}\), and the SZA-IPNLMS has 1.9 and 0.5 dB compared with the IPNLMS and \(l_{0}\)-IPNLMS, respectively. Thus, utilizing the SZA-IPNLMS effectively promotes the performance of the equalization. In Figures 5 and 6, the curve of the proposed scheme is in accordance with the one of the SZA-IPNLMS. Here, the mean square error curve of the proposed algorithm is identical to that of the best SZA-IPNLMS scheme and the proposed algorithm obtains the best performance among these schemes. Thus, the proposed scheme has minimal influence on the performance of the SZA-IPNLMS.