# A Cross-Medium Uplink Communication Model Merging Acoustic and Millimeter Waves
## 2 Model of Cross-Medium Communication Channel
### Verification of Cross-Medium Communication Channel Model
#### 2.4.2 SNR under Different Water Depths with an Acoustic Signal  
Water surface waves produced by an acoustic signal with a frequency of 146 Hz were detected within the depth range from 10 cm to 60 cm. The sampling interval was set at 5 cm, and the experiment needed to be repeated four times for each group. Figure 5 displays the time domain and frequency domain plots of the surface waves when the water depth was 20 cm. The measured results indicate an SNR of 1.7 dB. Although the SNR value appears low, a distinct peak is clearly observable in Figure 5 following the Fourier transformation. The utilization of peak extraction allowed for effective information decoding, thereby demonstrating the efficacy of the communication model even under lower SNR conditions.  
The SNR values were measured at different water depths in multiple experiments are shown in Figure 6. Measured data are visualized as red dots, while the model solution is represented by blue lines. Under the premise of water surface waves at the hundred-micron level, applying the model from Equation (5) directly, the calculated amplitude value differs from the actual value by three orders of magnitude, as this model was established under linear microamplitude wave conditions. Through nonlinear correction and environmental factor adjustments, our model achieved a high degree of correlation with the experimental data. The coefficient of determination, which quantifies the agreement between the measured data and the model calculations, was 0.982. This high \(R^{2}\) value significantly underscores the strong correlation between the observed data and the model predictions, showcasing the robustness and accuracy of our model in simulating the real-world scenario. In the results, the correction coefficient for multipath attenuation, \(\zeta\), was determined to be 1.267 in the modeling equation. The energy correction coefficient for  
Figure 4: Analysis of noise at the silent source. (**a**) Time domain diagram. (**b**) Frequency domain diagram.  
the box vibration, \(\varepsilon\), was determined to be 2.607 \(\times\) 10\({}^{-14}\). The correction coefficient for second-order nonlinearity, \(\eta\), was determined to be 2.234 \(\times\) 10\({}^{-10}\). This indicates that the measured results were in high agreement with the model, verifying that the model we built demonstrates high reliability and predictive capability.  
Figure 5: Surface wave in a water depth of 20 cm with acoustic signal. (**a**) Time domain diagram. (**b**) Frequency domain diagram.  
Figure 6: Test results of SNR changing with water depth and model curve.  
In general scenarios, obtaining these coefficients necessitates model fitting. During model fitting, it is imperative to accurately constrain the range of correction coefficients based on the specific experimental conditions to ensure the authenticity and reliability of the coefficients. The range of correction factors based on our experimental conditions, hardware facilities, and identified sources of error is shown in Table 1 below. This required multiple iterations of calculations to find the optimal correction coefficient values that suited the experimental conditions.  
According to the experimental results cited in reference [22], it is observed that the amplitude of the surface wave decreased significantly when the frequency exceeded 300 Hz. This reduction in amplitude can have a negative impact on communication quality and lead to an increase in the bit error rate (BER). In order to achieve higher quality cross-medium communication, it is recommended to use a carrier frequency below 300 Hz. Additionally, setting the high cut-off frequency of the filter to 300 Hz will help ensure a better communication performance.