# Channel Estimation and Iterative Decoding for Underwater Acoustic OTFS Communication Systems
## 5 Performance Evaluation  
In this section, the performance of our approach is evaluated. Table 1 shows the parameters used in the simulation experiments. The UWA channels were modeled following the methodology described in [33]. The water depth was set to 100 m, with the transmitter positioned at a depth of 30 m and the receiver at 50 m. The horizontal distance between the transmitter and receiver was 2 km. The sound speed profile utilized for channel simulation is illustrated in Figure 5. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Value** \\ \hline Modulation mode & QPSK \\ \hline Channel coding & 1/2 LDPC \\ \hline Carrier frequency & 10 kHz \\ \hline Bandwidth & 4 kHz \\ \hline Max path delay \(\tau_{\text{max}}\) & 35 ms \\ \hline Relative speed of transmitter and receiver \(v\) & 5 kn/10 kn \\ \hline Number of subcarriers \(M\) & 384/512 \\ \hline Number of OTFS symbols \(N\) & 24/16 \\ \hline Sampling frequency & 48 kHz \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Simulation parameters. Figure 6a illustrates the CIR without Doppler compensation with relative movement speed \(v=10\) kn. It is evident that the maximum channel delay spread exceeds 15 ms. The relative motion between the receiver and transmitter results in strong time variation in the UWA channel. Figure 6b depicts the Doppler dispersion in the DD domain distributed from 2 Hz to 3 Hz, indicating an overspread UWA channel. After Doppler compensation, Figure 6c shows that the CIR in the DD domain becomes sparser compared to the DT domain, confirming that the modeled channel becomes underspread. Figure 7 compares the BER performance with different values of \(N\) and \(M\) under varying \(v\). The frame lengths were identical, and the communication rates were set to the same value of 2.333 kbps. The relative speed between the transmitter and receiver was specified as \(v=5\) kn and \(v=10\) kn. In the \(v=5\) kn or \(v=10\) kn cases, OTFS frames with larger values of \(N\) exhibited higher performance due to their higher Doppler tolerance, provided \(M\) is large enough to avoid significant fractional delay. As the Doppler spread increases, the system with larger \(N\) shows substantial superiority. Figure 5: Sound speed profile. Figure 6: The same UWA Channel in (**a**) DT domain, (**b**) DD domain, and (**c**) DD domain after Doppler compensation. Based on these analyses, setting \(M=384\) and \(N=24\) proved to be effective, allowing the system to better handle large Doppler spreads and obtain enhanced performance while maintaining a reasonable frame size. Figure 8 compares the obtained performance based on different ZP lengths when setting the value of \(L_{g}\) to 3 dB, 7 dB, or 10 dB. The communication rate with maximum ZP length \(L_{max}\), maximum additional delay \(L_{10 dB}\), maximum additional delay \(L_{7 dB}\), and maximum additional delay \(L_{3 dB}\) were 2.3333 kbps, 2.5197 kbps, 2.8329 kbps, and 2.9579 kbps, respectively. We can see that setting \(L_{g}\) to the maximum additional delay resulted in a higher communication rate than when using the maximum delay. As \(\beta\) in Equation (10) decreases, the communication rate improves. However, when \(\beta\) dB decreases, the ZP length may not sufficiently prevent inter-block interference, thereby diminishing its effectiveness and increasing the BER. In this simulation, setting \(L_{g}=L_{10 dB}\) improved the communication rate while ensuring communication reliability. Therefore, subsequent simulations used the parameters \(M=384\), \(N=24\), and \(L_{g}=L_{10 dB}\). Figure 8: BER comparison of OTFS frames with different ZP lengths. Figure 7: BER comparison of OTFS frames with different \(M\) and \(N\) under different relative speeds. Figure 9 shows the BER performance of the IDF-MP algorithm with different numbers of outer-loop iterations. The outer-loop iteration number \(n_{out}\) was set to 0, 1, 2, or 3, and the relative speed \(v\) was set to 5 kn or 10 kn.