## 1 Introduction  
In recent years, the importance of wireless communication at sea has increased, particularly in areas such as managing ship operations, utilizing marine resources, and ensuring safety. A stable communication network is essential for these purposes [1; 2]. However, maritime communication faces unique challenges, as radio waves from terrestrial base stations have difficulty reaching offshore areas, making it challenging to establish a stable and wide-range communication network [3]. Ships are constantly moving, and fluctuations on the sea surface cause irregular positional changes, making it difficult to maintain a stable communication environment. Consequently, there is a growing demand for low-cost and highly efficient communication methods, which has become a significant challenge in maritime wireless communication today [4]. Traditional mainstream solutions include satellite communication, long-range Wi-Fi, and offshore base stations. Satellite communication offers wide coverage and high reliability. However, it is costly to operate, and communication latency is often an issue, especially with high-altitude geostationary satellites [5]. However, long-range Wi-Fi systems are relatively cost-effective but have limited signal coverage, making them insufficient for vast maritime areas [6]. Offshore base stations, such as antennas mounted on ships, are effective in specific areas but require significant installation and maintenance efforts, limiting their applicability to wide-area coverage [1; 7]. To address these challenges, this paper proposes the use of tethered balloons deployed at altitudes of several hundred meters, serving as low- to mid-altitude aerostat (LMA) base stations [8]. By deploying these aerostats at high altitudes over the sea, they can achieve wider communication coverage compared to terrestrial base stations, while offering lower operational costs than satellite communication [9]. Furthermore, they provide a more efficient and wider coverage solution compared to short-range wireless technologies [8]. This study focuses on downlink communication from the tethered balloon to maritime users, aiming to optimize the communication to improve both cost efficiency and reliability. Downlink communication is the process of directly transmitting signals from the base station (tethered balloon) to ships and maritime users, playing a crucial role in improving network performance. However, in dynamic and unstable environments, the quality of downlink signals is significantly affected [10]. This paper focuses on the instability of the tethered balloon's position due to weather conditions and maritime environmental factors, as well as the continuous movement of maritime users influenced by both their own motion and sea surface fluctuations [11]. To address these issues, this study proposes a communication method leveraging active beamforming (ABF) technology. ABF enables the real-time tracking of receiver positions and focuses the signal on the optimal direction, thereby extending the communication range and improving signal quality [12]. Specifically, in the Multiple-Input-Multiple-Output (MIMO) system, this study explores an optimized power allocation strategy for transmitting antennas. Conventional power allocation methods, such as equal power allocation and proportional allocation based on channel state information (CSI), are commonly used in static communication environments. However, in dynamic maritime environments, these traditional approachesface significant limitations, making it difficult to guarantee optimal communication quality under constant movement and unpredictable fluctuations [13]. To overcome these challenges, this paper proposes a nonlinear power allocation method based on CSI. This approach nonlinearly allocates transmission power according to the channel gain of each antenna, assigning more power to antennas with higher gains while suppressing power to those with lower gains.