## 5 Lake Trials  
To investigate the performance of the proposed method in a real environment, lake trials were conducted at Kyungcheon Lake, Munyeong City. The first and second experiments were conducted at the beginning and end of May 2018, respectively. The water depth of the lake was approximately 30-40 m, and the transmitters were located approximately 5 m from the boat. The receiver was located at a depth of 30 m, and the boat was steered randomly from 100 m to approximately 400 m from the receiver. The boat moved at speeds of 2 knots and 4 knots, and the configuration of the signals used was the same as those of the previous simulations. However, in the second experiment, which was conducted at the end of May, the hopping rate designed a half-spacing signal for each hopping frequency. Because of the overlap of the hopping frequencies, the ISI can degrade the communication performance due to multipath delay. However, this can be overcome by using the FrFT and bandpass filtering. Additionally, by designing with the above method, the frequency band can be used more efficiently. A Neptune D/17/BB model projector was used as the transmitter and a B&K 8106 hydrophone was used as the receiver. The Neptune D/17/BB model that was used as a transmitter is a broadband projector with a bandwidth of approximately 10 kHz [34; 35]. Figure 13 shows the channel impulse response and Figure 14 shows the scattering function used for the Doppler estimation. Figure 13a shows the measured channel response in the first experiment performed at the beginning of May, and Figure 13b is the result of the second experiment performed at the end of May. As shown in Figure 13, the difference in the reception time occurs as the transmitter moves, which generates a slope. Figure 13b shows there are more complex delay profiles. Figure 14a \begin{table}
\begin{tabular}{c c c} \hline \hline
**SNR (dB)** & **Non-Sync Method** & **Sync Method** \\ \hline
15 & 0.49 & 0.000 \\
10 & 0.48 & 0.002 \\
5 & 0.49 & 0.004 \\
0 & 0.48 & 0.050 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Uncoded bit error rate in the simulation. Figure 12: Simulation result using Watermark benchmark model. shows that the Doppler frequency is approximately \(-16\) Hz to \(-22\) Hz, and Figure 14b shows that the Doppler frequency is approximately \(-10\) Hz to \(-5\) Hz, where the (\(-\)) sign means that the distance between the transceivers gradually increased. However, there seems to be an issue with the scattering function in Figure 14b, as a main Doppler shift cannot be detected and the multipath arrival is entirely smeared. This was a result of the increased level of noise due to minor equipment problems and because the channel conditions in the second experiment were relatively poor due to stronger winds. Figures 15a and 16a show spectrograms of the transmitted signal, and Figures 15b and 16b show spectrograms of the received signal through the lake experiments. From the figures, we can see that there is considerable fading in the received signals due to multipath propagation delay. Figure 14: Scattering function for the Doppler frequency estimation for (**a**) the first lake trial and (**b**) the second lake trial. Figure 15: Spectrogram of (**a**) the transmitted signal, and (**b**) the received signal in the first trial. Since the received signal experiences substantial fading as it passes through the underwater channel, the delay due to multipath propagation or the slope change due to the Doppler frequency should be considered. Therefore, it is necessary to calculate the range adjacent to the optimal transform order for the application of the FrFT scheme at the receiver. Figure 17 shows the accumulation of the spectra of the received signal that is obtained from the optimal transform order to the adjacent range. When the optimal transform order is \(\alpha_{opt}=0.996\), the spectrum is spread by the delay caused by multipath propagation in the range adjacent to the order.