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

Abstract

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.

1. Introduction

The advancement of ocean exploration has underscored the pivotal role of cross-media air–ocean communication technology in facilitating marine ecological research, offshore oil exploration, and air–sea Internet infrastructure development [1,2,3]. Current cross-media communication primarily relies on relay modules, including buoys and ships. However, these modules possess limitations, such as weak anti-interference capabilities and substantial costs [4]. Communication technology, which operates without a relay node, has the potential to significantly address these prevailing issues.

Today, there are three prevalent cross-media wireless communication technologies that have been extensively researched: visible light direct communication, electromagnetic wave wireless communication, and underwater information identification via acoustic and microwave waves [5]. However, underwater optical communication technology is highly susceptible to the dynamic and complex marine environment, and it faces challenges in terms of misalignment issues caused by water refraction [6,7,8,9,10,11]. Electromagnetic wave signals experience significant loss and absorption underwater, resulting in limited propagation range and impaired transmission rates, particularly within the low-frequency range of 30~300 Hz [12,13]. Fortunately, a novel cross-media communication technology employing sound and millimeter waves has been introduced, boasting exceptional anti-interference capabilities and the potential to facilitate long-range communication.

Studies have shown that when an underwater source emits sound waves to the water–air interface, minute vibrations with identical frequencies to the sound source are induced on the water surface, referred to as water surface waves, which can be detected using laser sensors or millimeter-wave radar [14,15,16,17,18]. This technique can also be applied to ocean wave observations [19,20]. However, the identification of water surface ripples remains a significant challenge due to the complexities of surface tension and other influencing factors that govern their propagation. In recent years, scholars have devoted significant attention to and made progress in the development of detection technology for micro-vibrations on water surfaces. Lee [21] proposed the theory of laser wave amplitude modulation on the water surface for detecting underwater acoustic signals that induce vibrations on the water surface. Laser interference technology based on a Michelson interferometer was employed by Blackmon [22] to extract sound source information, while wavelet analysis and Fourier transform methods were effectively utilized to enhance the detection capability of weak underwater sound signals. Zhang [23] employed optical heterodyne detection technology to accurately measure the frequency of micro-amplitude waves on water surface amidst significant low-frequency interference. However, laser-acoustic detection technology requires precise alignment straightness and is susceptible to water absorption.

Consequently, some studies have proposed employing airborne radar for transmitting FMCW signals towards the water surface to detect minute vibrations on its surface. Tonolini [24] proposed a translational acoustic radio frequency (TARF) communication model, which utilizes millimeter-wave radar for emitting frequency modulated continuous waves to detect and demodulate surface wave displacement induced by underwater sound source signals in low-frequency bands. A mathematical modeling study was conducted by Qu [25] to investigate the channel performance of the TARF system using different signal carrier modes in the middle and low frequency bands. Qian [26] proposed a multi-input and single-output cross-media-focused phased array (CMFPA) model, which effectively expands the radar detection area, enhances the overall water surface amplitude, reduces alignment requirements among communication nodes, and optimizes the performance of cross-media information transmission. Deng [27] proposed a wavelet–Kalman filter method for detecting microwave signals on water surface based on terahertz radar, which can effectively filter out water surface interference and radar phase noise. However, the signal transmission process still faces many challenges due to the dynamics wavy interface and equipment limitation, such as the process investigation of energy conversion between sound intensity and vibration amplitude, as well as multi-frequency complex signal transmission.

Underwater target recognition and marine communication possesses significant application value for environmental detection and ocean remote sensing. This paper investigates the integration of underwater sound source and millimeter wave radar for information transmission process to realize signal reconstruction. The main contributions of this paper can be summarized as follows. Firstly, a ECUAV methodology was devised to evaluate the amplitude of water surface micro-vibrations through sound source levels, based on the propagation characteristics of underwater sound signals, followed by the computation and analysis of the acquired data, to provide the AEIT system with better dynamic modulation characteristics. Subsequently, the fundamental principle of utilizing millimeter-wave radar ranging technology for the detection of micro vibrations on water surfaces was analyzed. Finally, an experiment was designed to detect the surface perturbations of the sound source in the low frequency range of 100~300 Hz. Concurrently, an optimal frequency band was chosen for the recognition of BFSK underwater modulation signals, thereby providing experimental and theoretical reference for the further advancements in cross-medium water–air wireless communication.

2. Signal Reconstruction Model Across the Water–Air Interface

To achieve underwater acoustic information transmission, it is indispensable to construct a theoretical model that considers various physical processes. The impact of parameters like source frequency and underwater depth on the channel should be clearly demonstrated. In practical applications, the evaluation and prediction of channel quality can be conducted simultaneously, enabling superior dynamic adjustment characteristics. Figure 1 illustrates the uplink signal transmission process between water and air, utilizing the AEIT system as its foundation. The underwater acoustic signal is transmitted to the surface through a transducer in the form of pressure waves, inducing minor vibrations on the surface. The millimeter-wave radar emits a frequency modulated continuous wave towards the water surface, receives the reflected echo signal, and subsequently processes it to reconstruct the sound source information.

2.1. Acoustically Induced Water Surface Microwaves

The propagation of underwater acoustic signals is subject to attenuation processes, primarily due to spreading losses and absorption losses. Spread loss typically refers to the attenuation of sound intensity caused by the expansion of the wave front in the propagation process. This attenuation is closely associated with the frequency of the sound signal and the geometric radiation field within the soundscape. Absorbing losses refers to the physical attenuation within the medium band. The transmission of acoustic signals underwater occurs in the form of pressure waves P(ω, r, t), which vary with time t and distance r [28], and can be expressed as follows:

$$P(\omega ,r,t)=A(\omega )e^{j\omega (t-r/v_W)}$$

(1)

$$A(r,\omega )=A_0(\omega )e^{-\alpha r}/r$$

(2)

$$SPL=20\lg (P/P_0)$$

(3)

where the amplitude of the signal is A; A₀ represents the initial amplitude; α is the attenuation coefficient of underwater sound; ω denotes the angular frequency; and v_w represents the propagation speed of acoustic signals in water. The sound pressure level (SPL) is usually used to express the relative intensity of a sound source in dB, and the underwater reference sound pressure P₀ = 1 μPa. The definition of α is presented below [29]:

$$\alpha (f,h)=({\displaystyle \frac{0.109f^2}{1+f^2}}+{\displaystyle \frac{40.7f^2}{4100+f^2}}+3.01\times {10}^{-4}{f}^2)(1-6.67\times {10}^{-5}h)$$

(4)

where f represents the frequency of underwater sound waves, and h is the depth of the sound source.

The acoustic pressure wave is a type of longitudinal wave. When the underwater acoustic wave propagates to the water–air interface, it induces a minute displacement on the water surface. Set the two coordinate axes of the mathematical model established in Equation (5) return to the origin, that is, x = y = 0. At this time, the sound wave is vertically incident on the water–air interface, and the amplitude of the water surface caused by it reaches the maximum value δ_MAX, which is negatively correlated with f and positively correlated with P [23]:

$$\delta (x,y)={\displaystyle \frac{2P}{\omega \rho v_W}}{e}^{-{\alpha }_0\sqrt{x^2+y^2}}\cos (k\sqrt{x^2+y^2}-\omega t)$$

(5)

$${\delta }_{MAX}(P,f)={\displaystyle \frac{P}{\pi \rho v_W\cdot f}}={\displaystyle \frac{A_0(\omega )e^{-\alpha r}}{\pi v_W\rho r\cdot f}}$$

(6)

where k is the wave number of the surface wave, α₀ is the attenuation coefficient of the surface wave amplitude, ρ is the density of the water medium, and x and y are the coordinates on the horizontal plane, respectively.

2.2. Detection of Surface Acoustic Wave by Radar

The process of radar signal detection and IF signal generation is illustrated in Figure 2a. The frequency change rate of the FM signal is denoted as S, the time delay is represented by τ, and T_c refers to the duration of a single pulse. The initial frequency of the continuous FM wave is designated as f_c, while B represents its bandwidth, and λ denotes the wavelength of the radar-transmitted signal. Figure 2b shows the FMCW signal structure of one chirp pulse, which includes an idle part, an analog-to-digital conversion (ADC) preparation interval, an ADC sampling interval for recording the main detection information, and a margin buffer. When performing radar detection, multiple chirps constitute a data frame, and multiple frames constitute a single complete FMCW transmission signal.

A radar transmits a linear FMCW signal for target detection, and the received echo signal exhibits a certain time delay compared to the transmitted one. The intermediate frequency signal is generated by a mixer, whose frequency and phase encode the displacement information of the object under measurement. The IF signal is denoted as:

$$X(t)=M\cos \left(2\pi \mathsf{\Delta }ft+\mathsf{\Delta }\phi \right)$$

(7)

where M represents the amplitude, Δf denotes the frequency difference between the transmitted and received signals, and Δφ signifies the phase difference.

When a displacement change, δ(t), occurs in the detection target, it can be readily inferred that the phase difference of the signal can be expressed as:

$$\mathsf{\Delta }\phi (t)={\displaystyle \frac{4\pi \delta (t)}{\lambda }}$$

(8)

By substituting Equations (5) and (6) into Equation (8), we obtain:

$$\mathsf{\Delta }\phi (t)={\displaystyle \frac{8\pi P}{\omega \rho v_W\lambda }}{e}^{-{\alpha }_0\sqrt{x^2+y^2}}\cos (k\sqrt{x^2+y^2}-\omega t)$$

(9)

$$\mathsf{\Delta }{\phi }_{MAX}={\displaystyle \frac{4P}{\lambda \rho v_W\cdot f}}={\displaystyle \frac{4A_0(\omega )e^{-\alpha r}}{\lambda \rho v_W\cdot rf}}$$

(10)

To represent the formation process of water surface ripples from the perspective of changes in underwater acoustic wave energy propagation, we substitute Equation (3) with Equation (9), and we obtain:

$$\mathsf{\Delta }{\phi }_{MAX}={\displaystyle \frac{4P_0\times {10}^{0.05SPL}}{\lambda \rho v_W\cdot f}}$$

(11)

Nonetheless, advancements in underwater acoustic technology have empowered researchers to directly ascertain the intensity of the sound field, thereby facilitating the derivation and subsequent verification of a mathematical model that assesses surface amplitude, grounded in the sound source level, as elaborated below, which can significantly enhance the transmission efficiency for the AEIT system.

2.3. ECUAV Evaluation Model

Sound source level refers to the decibel value of the sound intensity emitted at 1 m from the sound source along its axis, relative to the reference sound intensity, which can be expressed as:

$$SL=10\lg {\displaystyle \frac{I}{I_{ref}}}$$

(12)

where I represents the sound intensity at 1 m from the equivalent sound center of the source, and I_ref is the reference sound intensity, typically chosen as the plane wave corresponding to the sound intensity with a root mean square (RMS) sound pressure of 1 μPa, i.e., $I_{ref}={\displaystyle \frac{{(1.0\times {10}^{-6})}^2}{\rho v_W}}=0.67\times {10}^{-18}$ W/m², where ρ is the density of the water medium, usually equal to 1 × 10³ kg/m³, and v_w represents the propagation speed of acoustic signals in water, usually equal to 1500 m/s.

The sound pressure P and sound intensity I are known to be satisfied as

$$I={\displaystyle \frac{P^2}{\rho v_W}}$$

(13)

By combining Equations (12) and (13), the relation between SL and P can be obtained as follows:

$$P=\sqrt{{10}^{0.1SL+\lg I_{ref}}}\sqrt{\rho v_W}$$

(14)

By substituting Equation (14) into Equation (6), the maximum surface acoustic wave amplitude information can be calculated through the current frequency and the directly measurable SL. Then, the AEIT system is coordinated to improve the detection efficiency.

$${\delta }_{LMAX}(SL,f)={\displaystyle \frac{\sqrt{{10}^{0.1SL+\lg I_{ref}}}}{\sqrt{\rho v_W}\cdot \pi f}}$$

(15)

The surface amplitude is observed to be directly proportional to the SL and inversely proportional to the frequency. Neglecting propagation loss, the amplitude of surface vibration caused by vertically incident low-frequency acoustic signals is in the order of microns. Figure 3a illustrates the relationship between interface vibration amplitude versus SL and frequency within a range of 100 dB to 180 dB for SL and 50 Hz to 500 Hz for vibration frequency. By setting the parameters of the mathematical model in Equation (5) to f = 50 Hz and converting the sound pressure value to SPL = 145 dB using Equation (3), the sound field measurement scenario can be restored more intuitively. And the wavy states of the water surface with fixed frequency and sound pressure levels are shown in Figure 3b, Figure 3c, and Figure 3d, which, respectively, represent the three-dimensional vibration distribution, top-down information, and the vibration profile state vertical to the water–air interface. It can be observed that the maximum amplitude of the water surface can reach 76.5 nm and gradually decays to nearly zero on the horizontal plane under the action of water surface tension.

The energy conversion process during the transmission of underwater sound waves to the surface can be clearly observed. The instrument in underwater acoustic detection, such as hydrophones, converts underwater acoustic signals into analog voltage values to facilitate the determination of sound source parameters.

Additionally, short-time Fourier transform (STFT) offers the ability to analyze the temporal variations in signal frequency, along with instantaneous frequency and amplitude at each moment. This frequency information is obtained by applying a sliding window to the signal under analysis and performing Fourier transform. The STFT is computed as follows:

$$STFT(t,f)={\displaystyle {\int }_{-\infty }^{\infty }x(\tau )h(\tau -t)e^{-j2\pi f\tau }d\tau }$$

(16)

where x represents the initial signal and h (τ − t) denotes the analysis window function.

According to the above equations, once the frequency and underwater SL are determined, it becomes possible to acquire the amplitude information regarding water surface perturbations, which can be effectively discerned through the adjustment of channel configuration.

The reconstruction process of cross water–air medium signal based on AEIT system established in this paper can be divided into three channels, including underwater acoustic channel, water–air interface, and airborne millimeter-wave channel. In practice, the underwater node can be composed of multiple autonomous underwater vehicles (AUVs) carrying sound sources and detection devices, and the aerial node can be carried by the drone radar kit and communicate with the ground through electromagnetic waves. The key point of the ECUAV model established in this paper is to accurately detect SL value, which is the inherent characteristic of the underwater sound field. Considering the impact of the vibration amplitude on radar detection efficiency, the sound source is coordinated to complete a more perfect energy conversion. This will require device binding by placing a detection device such as a hydrophone near the source node. Another idea is to place the detection equipment in a certain sequence to form a network of sound sources in the array structure of multiple superimposed sound sources.

3. Experimental Setup

To verify the feasibility of the above vibrations assessment scheme across the water–air media, an information transmission system based on underwater low-frequency sound source and aerial millimeter wave radar was built in the water tank environment, as shown in Figure 4a. It was mainly composed of an EV-UW30 underwater loudspeaker and a power amplifier, an RHSA-5 spherical hydrophone, an NI-cDAQ-9185 data acquisition card, an AWR1642 millimeter wave radar board by NI (linear frequency modulation range is 77~81 GHz), and a DCA1000 acquisition card. The experimental environment of the water tank is shown in Figure 4b. The underwater sound source was placed at a depth of 0.3 m from the water surface and was located in the center of the tank. Anechoic cotton was used to reduce propagation loss and vibration of the water tank. The aerial radar was at a height of 0.35 m above the water surface, and the hydrophone was placed 1 m away from the equivalent sound center of the sound source. The tank was 1.2 m in length by 0.8 m in width and 0.5 m in height. Detailed parameters are shown in

Table 1. Experimental environment.

Parameters	Value
Millimeter-radar frequency band	77~81 GHz
Single-chirp ADC samples	128
Total FMCW frames	4096
Radar aerial height	0.35 m
Tank size	1.2 m length, 0.8 m width, 0.5 m height.

.

In the previous study of the physical process of acoustic surface microwaves, it was shown that the vibration amplitude was in the range of several micrometers or even nanometers. A key aspect of micro-vibration detection technology was to match the wavelength of the detection wave with the vibration amplitude of the object being measured. According to Equation (8) and the FMCW ranging principle, when the displacement is in the micrometer order, a relatively large detection wavelength (such as a few centimeters of Wi-Fi signal) will cause a tiny phase change and reduce the robustness to environmental noise. On the other hand, choosing a very short wavelength (such as a sub-micrometer of terahertz) will lead to rapid phase wrapping, thereby reducing the ability to track surface vibrations. Therefore, the detection wave frequency that is ultimately suitable for the AEIT system was selected as being in the range of 77~81 GHz with a wavelength between 3 mm and 4 mm. In addition, the data acquisition card should have a relatively good sampling rate.

In the second part, the propagation characteristics of underwater sound were studied. After adding anechoic cotton, the water tank used in the experiment was able to meet the requirements of signal transmission and detection within the allowable error range. However, subsequent application scenarios of AEIT should be expanded to more complex water environments, such as those with low-frequency wave interference. This calm water tank experiment has sufficient preliminary verification for subsequent cross-interface signal restoration in larger bodies of water.

4. Experiment for Cross-Medium Information Transmission

4.1. Surface Perturbations Assessment by ECUAV Model

After successfully establishing the AEIT system, for experimental purposes, a low-frequency sound source ranging from 100 Hz to 300 Hz was selected to evaluate the system performance. The evaluation of the vibration state of acoustically induced surface microwaves was conducted through the SL model. The obtained results are presented in Figure 5. Based on our measurements and calculations, the following conclusions can be drawn.

Figure 5a illustrates a measured non-linear distribution of sound source level within the frequency, with a peak value of 181.5 dB near the 135 Hz source by combining Equation (15) with I_ref for reference. Subsequently, there is a significant decrease in the sound source level beyond 200 Hz. Figure 5b illustrates the distribution of maximum amplitude vibrations on the water surface calculated from the SL, which aligns with the observed pattern of SL. The peak vibration amplitude of 1.89 μm can be achieved at a frequency of 135 Hz, and the amplitude decreases significantly for source frequencies exceeding 150 Hz. The experimental results demonstrate that, under a fixed loudspeaker driving power, the appropriate low-frequency acoustic signal can induce a larger amplitude of surface vibrations through the universal underwater acoustic environment, thereby facilitating the detection of micro-vibrations on water surfaces.

The essence of ECUAV is from the perspective of energy transmission and conversion. Its input judgment encompasses frequency, sound source level, and other pertinent parameters, while its output yields the amplitude of water surface ripples induced by the prevailing sound field, as depicted in Figure 3a. Predominantly, it utilizes a millimeter-wave phase ranging technology to discern between signal sources and ambient noise. The details are as follows.

Initially, within the AEIT system devised in this paper, the amplitude of acoustic ripples on the water surface are measured in microns or less, which is far from the noise interference caused by sea breeze and other environmental factors, such as waves and turbulence. Furthermore, although the propagation of sound waves underwater exhibits a 1/f distribution characteristic, as far as the current AEIT technology is concerned, the sound signals in the frequency band of several hundred to several thousand hertz still have a high degree of reproducibility, which is also highly distinguishable compared with the inherent environmental noise of the ocean (usually several to tens of hertz).

In addition, for the millimeter waves in the 77~81 GHz frequency band in the article, the water surface ripple vibrations generated by the above-mentioned sound wave frequency band can be easily identified with a resolution accurate to a single hertz. Finally, in the specific application of signal transmission across the water–air interface, taking frequency modulation as an example, the increase in communication rate corresponds to the reduction in the conversion interval of different coding frequencies. At the same time, setting correction measures such as parity bits and acknowledgement responses during signal modulation can effectively resist various environmental interferences and eliminate the impact of dynamic changes on the water surface.

4.2. Low Frequency Signal Detection and Reconstruction

While the SL determination is conducted using a hydrophone, the millimeter-wave radar board transmits a series of RF signals to the water surface. Subsequently, the digital sampling of the IF signal is performed by the data acquisition card, followed by digital signal processing. The number of samples per pulse is 256, and the phase information of the IF signals undergo Butterworth high-pass digital filtering to eliminate ambient low-frequency noise. Furthermore, it is evident from the principle of water surface vibration that the frequency of underwater acoustic signals plays a crucial role in the recognition process of aerial radar. The predominant noise in the ocean is primarily composed of low-frequency interference. Excessively high frequency will diminish the efficiency of signal transmission. Hence, enhancing the channel quality can be achieved through the implementation of a signal band-pass filtering process in practical applications. We recommend a low frequency threshold of 30 Hz and a high frequency threshold of 200 Hz.

The phase characteristics of the initial detection signals of surface rippling under a 135 Hz sound source frequency are illustrated in Figure 6a, while Figure 6b displays the processed signal after applying a filter with a cut-off frequency of 30 Hz. By effectively removing low-frequency interference, the restored sound source information can be observed in the time domain. The calculation of Equation (15) reveals that the measured vibration amplitude of the water surface falls within the range of 0.4 to 10 μm, which aligns closely with the theoretical value depicted in Figure 5. The disparity between them can be attributed primarily to echo interference within the water tank and environmental influences on the millimeter wave measurement process.

After distinguishing the signal source from the noise, the surface tiny perturbations generated at 135 Hz and 150 Hz sound frequencies were detected, and the filtered 1024-point fast Fourier transform of the phase information is illustrated in Figure 7, with a sampling frequency Fs = 1000 Hz. The frequency response in the vicinity of the selected frequency point is excellently exhibited in the frequency domain, thereby enabling the accurate identification of underwater sound source information. The normalization of the frequency domain amplitude in 100 Hz~300 Hz is illustrated in Figure 8. The observation reveals that the surface rippling in the frequency domain exhibits a peak amplitude when the underwater sound source operates at approximately 150 Hz, followed by a decrease as the frequency increases. This behavior aligns with the propagation characteristics of underwater pressure waves and demonstrates a certain correlation with the sound source level distribution depicted in Figure 5.

The experimental results indicate a high detection efficiency can be achieved within the low frequency range of 130 Hz~150 Hz. The maximum peak of the vibrations was observed at 135 Hz, while the highest amplitude response in the frequency domain occurred at 150 Hz, aligning with the propagation characteristics of underwater acoustic waves. And the amplitude of the water surface vibrations is nonlinearly and positively correlated with the sound source level.

4.3. BFSK-Encoded Signal Transmission Across Water–Air Media

The experiments conducted in Section 4.2 have successfully demonstrated the feasibility of water–air signal transmission through the AEIT system using single frequency acoustic signals. Simultaneously, an approach is proffered to enhance detection efficiency through the utilization of the ECUAV model. However, to cater to the practical demands of cross-media communication, it is imperative to transmit complex underwater information, such as terrain and oil resources, to the air node for processing in a precise and timely manner. Additionally, to ensure the confidentiality of the communication process, the encoding and modulation of the generated signal are crucial.

Therefore, a straightforward coded signal transmission experiment was devised, utilizing BFSK modulation. In this experiment, considering the transfer rate requirements, 150 Hz was represented as ‘0’, while 210 Hz was denoted as ‘1’. Figure 9a,b depict the phase information of the radar-based vibration measurement IF signal, before and after filtering, respectively. It can be observed that after digital filtering, the small amount of vibration information is completely preserved in the phase variation of the IF signal.

To illustrate the restoration process of underwater modulated sound signals more vividly across varying signal-to-noise ratios (SNRs), Figure 10a presents the frequency domain response of the radar signal within the initial experimental setup, featuring a SNR of −15 dB. Notably, the peaks of the two modulation bands are distinctly discernible in the frequency domain. However, upon analyzing the time–frequency representation via STFT analysis in Figure 10b, it becomes evident that the intended signal is overshadowed by pronounced low-frequency noise, making it challenging to discern. After digitally filtering the radar signal, Fourier transform is executed, yielding the result depicted in Figure 10c, where the interference from environmental noise is significantly mitigated. At this juncture, the SNR attains a value of −8 dB. Subsequently, upon signal amplification, a distinct and clear restoration of the BFSK modulated signal along the time axis becomes evident, as illustrated in Figure 10d. It is evident that the modulated acoustic signal can be accurately discerned by the airborne millimeter-wave radar. This enables the restoration of underwater sound source information over time while maintaining signal precision.

After computation, the key performance metrics of BFSK are presented in

Table 2. The performance of underwater acoustic signal restoration after filtering, modulated by BFSK.

Performance	Value
Bit error rate	0
Actual transmission rate	3 bps
Signal duration	4.09 s
Signal-to-noise ratio	−8 dB

. Effective signal extraction and reconstruction are achievable under stable channel conditions, thereby facilitating the formulation of strategies for tackling more intricate scenarios requiring a heightened information transmission index.

5. Conclusions

In this paper, we employed millimeter-wave radar FMCW phase ranging technology to measure acoustic microwaves propagating over the water surface, thereby enabling cross water–air interface signal transmission and reconstruction. A comprehensive mathematical model ECUAV that illustrates the energy conversion process of underwater signals to air channel signals is also presented. In the experimental environment of the water tank, the control speaker operates at a constant power level, enabling the precise measurement of the surface vibration amplitude by SL through the ECUAV model. Disregarding the disturbances imparted by the tank vibrations, the observed trend aligns seamlessly with theoretical predictions, revealing the energy conversion mechanisms during channel signal transmission. Notably, the peak vibration amplitude reaches 1.89 μm when the experimental frequency band is probed at 135 Hz. Thus, it is proven that the cross-interface information transmission exhibits frequency selectivity; in particular, the detection efficiency of radar is positively correlated with SL and negatively correlated with acoustic frequency. The acoustic signal utilizing BFSK with modulation frequencies of 150 Hz and 210 Hz is capable of precisely reconstructing the information transmitted by the underwater transmitting node through the AEIT system. This study validates the possibility of multi-frequency and phase-continuous acoustic signal transmission across the water–air medium.

However, there are still more potential development opportunities for the subsequent development of cross-media water–air information transmission. Firstly, in view of the actual needs of cross-interface communication, it is necessary to carry out verification work in larger bodies of water with more complex environments to study the anti-interference ability of AEIT to environmental interference, such as ocean waves. Secondly, for underwater signal sources, equipment with better response in the appropriate frequency band is needed to transmit richer modulated signals. In addition, more stable signal modulation methods should be used to resist multipath interference, such as orthogonal frequency division multiplexing (OFDM) and hyperbolic frequency modulation (HFM). Faced with these limitations and challenges, we hope that the research in this paper will inspire future studies in the field of cross-media water–air communications.