## 4 Simulation and Experiment
### Experiment and Results  
The simulation results highlight that the improved method can more accurately estimate the frequency than the periodogram. Thus, this section evaluates the proposed method's effectiveness on measured data. Specifically, we designed a cross-media communication system, which includes an underwater sound source device that transmits underwater signals, a millimeter wave radar that receives radio frequency signals, and a host for signal processing. The actual measurement experiment aims to verify the advantages of the improved RELAX algorithm for WSAW detection. The transmitting end of the cross-media communication system is a USW-015 underwater sound source, connected to the audio output port of the host through a power  
Figure 6: The underwater sound source sends four different frequency signals. The results of different frequency estimation algorithms based on (**a**) periodogram that presents large side lobes, (**b**) RELAX that misses the 300 Hz signal, and (**c**) improved RELAX, which has estimated results consistent with the frequency of the transmitted sound source. Figure 7: (**a**) Generalized inner product value of each sample, and (**b**) time–frequency analysis result of simulation data. amplifier. The power level of the cross-media communication system is consistent with the standard power acoustic transducer used in the underwater communication process. The signal frequency band of the loudspeaker is set to 100-500 Hz, a typical communication frequency band in underwater communication [32]. The experiment is conducted in a large pool, with Figure 8 illustrating the measurement scene and equipment setup. The transmitting and receiving antennas illuminate the water surface vertically, each placed 0.8 m away from the water surface. The underwater sound source is 0.45 m away from the water surface, and the antenna phase center is aligned with the center of the underwater sound source. The radar prototype applied in this WSAW detection is designed by the research of the National Key Laboratory of Microwave Imaging Technology, Chinese Academy of Sciences. The radar is a Ka-band FMCW radar, utilizing the two-horn antenna type presented in Figure 8. The radar's key parameters are presented in Table 3.  
The underwater sound source excites the water surface to form a WSAW, which carries the sound source information. Then we transmit a radar signal and receive the echo signal from the FMCW radar. Finally, we extract the phase of the reflected signal to unwrap and filter it to obtain the WSAW vibration signal. The measured signal is sinusoidal, consistent with the underwater sound source model established above. In this section, we set up two experiments to verify the effectiveness of the improved algorithm. The first experiment considers the first algorithm improvement presented in Section 3. This trial comprises three parts. First, to verify the algorithm's minimum detectable time, we set the duration of each frequency to 0.001 s, 0.005 s, 0.01 s, 0.05 s, and  
Figure 8: Cross-media communication platform construction. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Value** \\ \hline center frequency & 34.6 GHz \\ pulse repetition frequency (PRF) & 50 kHz/125 kHz \\ fast-time sampling points & 400/1000 \\ slow-time sampling points & 60,000 \\ antenna gain & 25 dB \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Radar parameters. 0.1 s and compare it with the periodogram to improve the cross-media communication rate. Second, we set the frequency of the underwater sound source to send two signals with a significant difference in frequency simultaneously. Since the amplitude of the WSAW is inversely proportional to the frequency, it is verified that the algorithm can detect the weak signal even when the strong signal covers the weak signal. Third, the minimum detectable frequency range of the proposed algorithm is compared with the periodogram.