Multivariate Multiscale Sample Entropy for Multi-Channel Underwater Acoustic Signal Analysis

Multi-channel time series collected by arrays are prevalent in underwater acoustic signal processing and are crucial for uncovering the intrinsic characteristics of the observed system. This paper introduces the multivariate multiscale sample entropy (MMSE) to assess the complexity information in multi-channel underwater acoustic signals. Simulation analysis is employed to validate the effectiveness of the MMSE algorithm in extracting both within-channel and cross-channel information from multi-channel signals. Various types of simulated ship-radiated noise are generated to illustrate the MMSE algorithm's capability to differentiate between signals. Additionally, we employ MMSE to analyze various real-world signals, including ship-radiated noise, ambient noise, and interface reverberation. The MMSE results demonstrate its proficiency in differentiating various underwater acoustic signals compared to traditional frequency domain methods.