Two-Dimensional Thompson Sampling for Joint Beam and Power Control for Uplink Maritime Communications

In a cellular maritime communication system, ocean buoys are essential to enable environmental monitoring, offshore platform management, and disaster response. Therefore, energy-efficient transmission from the buoys is a key requirement to prolong their operational time. A fixed uplink beamforming can be considered to save energy by leveraging its beam gain while managing the target link reliability. However, the dynamic condition of ocean waves causes buoys’ random orientation, leading to frequent misalignment of their predefined beam direction aimed at the base station, which degrades both the link reliability and energy efficiency. To address this challenge, we propose a wave-adaptive beamforming framework to satisfy data-rate demands within limited power budgets. This strategy targets scenarios where sea state information is unavailable, such as in network-assisted systems. We propose a Two-Dimensional Thompson Sampling (2DTS) scheme that jointly selects beamwidth and transmit power to satisfy the target-rate constraint with minimal power consumption and thus achieve maximal energy efficiency. This adaptive learning approach effectively balances exploration and exploitation, enabling efficient operation in uncertain and changing sea conditions. In simulation, under a moderate sea state, 2DTS achieves an energy efficiency of 1.26 × 104 bps/Hz/J at round 600, which is 73.7% of the ideal (1.71 × 104), and yield gains of 96.9% and 447.8% over exploration-based TS and conventional TS, respectively. Under a harsh sea state, 2DTS attains 3.09 × 104 bps/Hz/J (85.6% of the ideal 3.61 × 104), outperforming the exploration-based and conventional TS by 83.9% and 113.1%, respectively. The simulation results demonstrate that the strategy enhances energy efficiency, confirming its practicality for maritime communication systems constrained by limited power budgets.