## 1 Introduction  
Underwater acoustic channels are generally regarded as one of the most difficult communication channels nowadays [1]. Compared to radio frequency wireless communication, underwater wireless communication may suffer random fluctuation of the sea surface, internal waves [2], turbulence [3], and other complex physical phenomena. These phenomena increase the difficulty of high-speed and high-reliability underwater acoustic communication. The performance of underwater acoustic communication systems is further affected by multipath effects, Doppler frequency shifts, attenuation of sound wave transmission, and limited bandwidth [4]. Therefore, by studying the statistical and other characteristics of underwater acoustic channels, we can guide the design of underwater acoustic communication systems and develop robust underwater acoustic communication algorithms. Many researchers have studied the spatiotemporal characteristics of underwater acoustic channels. Previous studies have focused on three characteristic channel parameters: amplitude, delay spread, and channel temporal coherence. As a basis for statistical channel modeling, the distribution of the envelope amplitude has been fitted to Rayleigh distribution [5; 6; 7], Rice distribution [8; 9; 10; 11], lognormal distribution [12; 13], K distribution [14; 15], and Burr distribution [16]. Most of these studies analyze specific experimental data for statistical modeling of channel amplitudes and fading, providing references for channel prediction and channel tracking. Meanwhile, studies on delay spread have analyzed the average, maximum, and RMS delay spreads [17], which represent the expansion degree of a channel in the delay domain. Delay spread lasts several to hundreds of milliseconds in shallow-sea channels, extending to several or tens of seconds in deep-sea channels. RMS delay spread, which reflects the complexity of the channel structure, is reportedly more related to the performance of a communication system [18] and is adopted as the performance index in evaluations of channel models [19]. In 2023, [PERSON] et al. introduced this parameter to reinforcement learning and proposed a new communication-strategy algorithm [20]. Meanwhile, the channel temporal coherence is a second-order statistic reflecting the fluctuations of a channel on a certain time scale. The performance of the adaptive equalizer depends on how well it adapts itself to the changing channel within the signal coherence time [21]. This parameter is essential for communication systems design and is commonly adopted [11; 14; 22; 23; 24; 25] for characterizing temporal variation of channels. Channel characteristics are usually investigated using the data of high-frequency and low-frequency experiments in shallow-sea zones and the data of low-frequency experiments in deep-sea zones. The channel characteristics of deep-sea high-frequency acoustic communications are rarely reported. At present, high-frequency acoustic communication has been adopted in the field of marine resource exploration, ecological environment monitoring, submarine observation network construction, underwater reconnaissance, and underwater robot cluster cooperation. High-frequency underwater acoustic communication technology with a short distance, high reliability, and high data rate is particularly important. However, there are some challenges in high-frequency underwater acoustic communication. Firstly, the spatial variation in temperature, salinity, and density determines the complex distribution of the sound speed profile. It causes the fluctuation of the sound field in the process of sound wave propagation. Secondly, the transmission loss of high-frequency sound waves is relatively large. Thirdly, multiple reflections of sound waves cause serious large-delay multipath effects. Fourthly, the relative motion of the transmitter and receiver and the dynamic marine environment make the phase of the received signal fluctuate randomly and the Doppler frequency shift and spread.