# A Method for Extracting Acoustic Water Surface Waves Based on Phase Compensation
## 4 Simulation and Experiment
### Experiment  
To verify the effectiveness of the proposed method, we built a microwave acoustic cross-medium uplink communication platform in the laboratory, as shown in Figure 13: (a) is a schematic diagram of the experiment and (b) is the experiment scene. The underwater transmitter converts the 2 FSK signal, which is transmitted into sound waves by the computer. The sound waves excite the water surface to generate acoustic  
Figure 12: Results when significant wave height is 0.1 m: (**a**) range–time graph, (**b**) range bin and the phase history before/after compensation, (**c**) acoustic water surface waves using different methods. (**d**) STFT: Wavelet–Kalman Filtering; (**e**) STFT: compensation with a threshold; (**f**) STFT: the proposed method. Figure 13: (**a**) Experimental schematic diagram; (**b**) experimental scene. water surface waves, simultaneously using wave makers to simulate natural ocean waves by generating water surface waves. The radar AWR1843 emits microwaves. The echoes are transmitted to the computer through the ADC1000 EDM acquisition board. The data are then processed on the MATLAB platform. The experimental parameters are listed in Table 4.  
Range FFT is performed to obtain a range-time graph, as shown in Figure 14a. Then, the phase history is extracted. It can be found that sea surface interference causes discontinuity in the phase history. In Figure 14b, the green dot represents the range bin where the water surface is located within a certain pulse. For example, at t = 1.1 s, the water surface is located at the 13 th range bin of the radar. The black curve in Figure 14b represents the phase history without phase compensation and the red curve represents the phase history after phase compensation. In Figure 14c, the black curve represents the phase difference without phase compensation, and the red curve represents the phase difference after phase compensation. Experimental data show that phase jump occurs when the range bin changes, and even when the range bin remains unchanged, there is also a phase history discontinuity, which may be caused by factors such as data loss, abnormal waves, and multipath effects. Figure 15 illustrates the advantages of phase compensation based on range bins compared to thresholds. If the absolute value of the phase difference is greater than a certain threshold, the subsequent phase history will uniformly increase or decrease the phase difference. This is the principle of phase compensation based on a threshold. A \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Value** \\ \hline Start frequency & 77 GHz \\ Bandwidth & 4 GHz \\ Samples & 256 \\ PRF & 1000 Hz \\ Sound pressure level & 170 dB \\ Significant wave height & 0.03 m \\ Spectral peak period & 1 m \\ Height of the radar & 0.5 m \\ Depth of the underwater transmitter & 0.3 m \\ Frequency of the underwater transmitter & 100 Hz, 200 Hz \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Experimental Parameters. Figure 14: Experiment: (**a**) range–time graph, (**b**) range bin and the phase history before/after compensation, (**c**) the difference in phase history before/after compensation. limitation of this method is that the threshold is manually selected and not a fixed value. If the threshold is particularly small, some of the original phase history will be reduced to 0, as shown by the black dashed line in Figure 15. The blue line in Figure 15 represents the initial phase history. The red line represents the compensation result based on the range bin's change. This method can reduce the discontinuous points in the initial phase history. The blue line in Figure 16 represents the result of Wavelet-Kalman Filtering without phase compensation, the red line represents the result of High-pass Filtering after phase compensation, and the orange line represents the result of the proposed method.