## 1 Introduction  
The ocean parameter (velocity and wave height) inversion based on remote sensing means has a wide range of applications in many fields [1, 2]. Among these, cross-water-air interface acoustic and electromagnetic integrated communication (AEIC) technology considers an underwater target sending sound signals, which excite the water surface to vibrate. The aerial platform sends radio frequency signals to detect the vibration, restoring underwater information. In recent years, human exploration activities in the ocean have increased, and therefore AEIC has great applications in maritime communication, including water body detection [3, 4, 5, 6], underwater resource exploration [7, 8, 9], marine biological population monitoring [10, 11, 12], and underwater target location [13, 14, 15]. Currently, cross-water-air communication technology is divided into three categories:  
1. Buoy technology [16, 17], where acoustic-electro conversion and signal processing are realized by setting buoys to complete information transmission from underwater to water. However, this technology suffers from low concealment and high volume power consumption. 2. Opto-acousto communication technology [18, 19, 20], where the underwater target sends sound signals to excite the water surface to form the water surface micro-amplitude wave (WSAW). Then, laser interference technology is used to detect the WSAW. 3. Acoustic-electromagnetic communication technology [21], unlike opto-acousto communication technology, uses radar signals instead of laser to measure the WSAW. Compared with the opto-acousto communication technology, it has the features of all-weather, large irradiation area, and minimal requirements regarding the measurement platform's stability. This paper primarily considers acoustic-electromagnetic cross-media communication technology. In acoustic-electromagnetic communication technology, the information of underwater sound source is inversed by detecting the WSAW. This is because the vibration frequency of the WSAW is identical to the underwater sound source's frequency, and cross-media communication can be achieved by frequency estimation [22]. Since the WSAW amplitude is only in the order of micrometers [22; 23], an accurate spectrum estimation algorithm has an important influence on the WSAW frequency estimation accuracy. In recent years, some research groups use the traditional periodogram (FFT) method to estimate the WSAW frequency based on their radar prototypes [21; 24; 25]. For instance, in [21], [PERSON] designed the translational acoustic-RF communication (TARF) with a carrier frequency of 60 GHz, which was used to estimate the WSAW frequency. In [24], the radar's center frequency was set to 0.33 THz and was exploited to detect the WSAW. After unwrapping and filtering, the vibration change form of the WSAW was calculated utilizing the periodogram. However, the periodogram naturally suffers from smearing and spectrum leakage. The smearing problem does not allow the separation of two similar signals, while the spectrum leakage causes the side lobes of the strong signal to overwhelm the weak signal. Thus, the periodogram typically fails to obtain accurate results of the frequency spectrum estimation of minute vibrations [26; 27; 28]. The periodogram is typically used in cross-media communication, but the periodogram method will fail in the following cases. First, to increase the communication rate, the shorter the signal frequency duration, the higher the communication rate. Short sampling duration will reduce frequency resolution, leading to inaccurate frequency and increasing the communication bit-error rate. Second, the communication frequency band of the underwater speaker is a narrow band range. In order to use multiple frequencies coding in the narrow band, signals of similar frequencies must be separated as much as possible.