A CNN–Transformer-Based Beamforming Design for Maritime Downlink Systems With Imperfect CSI

With the rapid growth of the maritime Internet of Things (MIoT), cost-efficient maritime links with high spectral efficiency are becoming increasingly needed. This paper investigates hybrid analog-digital beamforming for a maritime downlink base station under imperfect channel state information (CSI). We propose a CNN–transformer neural network (CTNN) and auxiliary beamforming-guidance loss to learn constant-modulus analog beamformers and improve spectral efficiency. Simulations show that the CTNN improves spectral efficiency by 69% and 85% over manifold optimization (MO) and orthogonal matching pursuit (OMP), respectively, and by 17% over a fully connected beamforming neural network (BFNN). The CTNN also exhibits strong robustness to path-number mismatch.