Acoustic Signal Reconstruction Across Water–Air Interface Through Millimeter-Wave Radar Micro-Vibration Detection

Water surface micro-amplitude waves (WSMWs) of identical frequency are elicited as acoustic waves propagating through water. This displacement can be translated into an intermediate frequency (IF) phase shift through transmitting a frequency modulated continuous wave (FMCW) towards the water surface by a millimeter-wave radar, and information transmission across the water–air interface is achieved via the signal reconstruction method. In this paper, a novel mathematical model based on energy conversion from underwater acoustic to vibration (ECUAV) is presented. This method was able to obtain WSMW vibration information directly by measuring the sound source level (SL). An acoustic electromagnetic wave-based information transmission (AEIT) system was integrated within the water tank environment. The measured distribution of SL within the frequency range of 100 Hz to 300 Hz exhibited the same amplitude variation trend as predicted by the ECUAV model. Thus, the WSMW formation process at 135 Hz was simulated, and the phase information was extracted. The initial vibration information was retrieved through a combination of phase unwinding and Butterworth digital filtering. Fourier transform was applied to the vibrational data to accurately reproduce the acoustic frequency of underwater nodes. Finally, the dual-band binary frequency shift keying (BFSK) modulated underwater encoding acoustic signal was effectively recognized and reconstructed by the AEIT system.