# A Method for Extracting Acoustic Water Surface Waves Based on Phase Compensation
In 2023, [PERSON] et al. from Tianjin University proposed a signal-to-noise ratio (SNR) channel model for evaluating the performance metrics of an uplink communication system for the first time [10]. In 2023, [PERSON] et al. from Zhejiang University successfully detected acoustic water surface waves using wavelet transform [11]. But, neither of them considered the influence of waves on uplink communication. In the same year, [PERSON] et al. from the National University of Defense Technology proposed the Wavelet-Kalman Filtering algorithm to filter out water surface interference and radar phase noise and conducted sea experiments for the first time to verify the effectiveness of the proposed algorithm in first-level sea conditions. Through semi-physical simulation experiments, its effectiveness in second-level sea conditions was verified [12]. In 2023, [PERSON] et al. from the National Key Laboratory of Microwave Imaging Technology proposed a method of Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN) and wavelet transform based on the mechanism of an acoustic water surface wave [13], which realized effective communication under the laboratory conditions with wave interference, providing a relatively rich theoretical support for microwave acoustic cross-medium uplink communication technology. In 2023, [PERSON] et al. from Nanjing University of Aeronautics and Astronautics discovered the phenomenon of random phase jumps [14] and proposed a method with multi-angle coherent accumulation and phase compensation based on a threshold to suppress random phase jumps. However, this method relies on threshold selection and is not robust enough in engineering applications. To sum up, how to effectively extract acoustic water surface waves from water surface fluctuations is one of the key problems in microwave acoustic cross-medium uplink communication. When the sea surface fluctuates greatly, the extraction of acoustic water surface waves becomes more difficult. First, the sea surface will span multiple range bins, making it difficult to calculate the phase changes in different range bins uniformly. Second, when the dip angle of the sea surface is large, the reflected echo is beyond the antenna receiving range, causing the interruption of the received signal. Third, the fluctuation of the sea surface results in multiple reflections of radar echoes, resulting in the incorrect selection of the target range bin and destroying the continuity and effectiveness of the phase history. To solve this problem, the authors of reference [12] pointed out that the frequency of sea surface fluctuations is lower than the communication frequency. They proposed the Wavelet-Kalman Filtering Method. Wavelet transform is used to separate the acoustic water surface waves that are mixed in the sea surface fluctuations, and the radar additive phase noise is filtered out through the Kalman filter. By reducing the value of the low-frequency coefficient, the acoustic water surface waves can be reconstructed. However, the wavelet coefficients at a point may be affected by the signal values far away from the point. The Kalman filter cannot effectively eliminate the wavelet denoising results at the discontinuous points, which leads to an increase in the bit error rate (BER) and it being unable to achieve effective communication. In [14], the authors proposed a phase compensation algorithm based on a threshold. The principle is to compensate for discontinuous points where the phase difference is greater than the threshold to suppress random phase jumps. This method depends on the threshold. If the threshold is too large, random phase jumps cannot be compensated for effectively. If the threshold is too small, it is easy to overcompensate and lose the vibration information of acoustic water surface waves, making it difficult to accurately extract acoustic water surface waves. Therefore, it has poor robustness in engineering applications.