Hybrid CNN-Transformer-based Modulation Optimization for UWA Communications with High Mobility

Abstract

Reliable underwater acoustic (UWA) communications are essential for emerging space-air-ground-underwater integrated networks, yet modulation scheme design remains challenging due to the severe Doppler scaling spread in UWA environments. Recent data-driven modulation optimization with the Siamese architecture provides a promising alternative to designed modulation schemes under practical equalization frameworks, but still remains limited by restricted network expressiveness and fixed loss weighting, resulting in slow optimization and limited convergence behavior. To solve this problem, this paper proposes a convolutional neural network (CNN)-Transformer-based modulation optimization framework for UWA communications under the assumption of linear minimum mean-square error (LMMSE) equalization. Specifically, the CNN module extracts local structures from the channel matrix, while the Transformer encoder captures long-range inter-stream dependencies associated with the dense inverse term in the LMMSE error covariance, enabling a better representation for modulation matrix optimization. Around this network backbone, an inverse discrete Fourier transform (IDFT)-based residual parameterization is introduced to stabilize training and a maximum mean-square error (MSE) penalty is adopted to guide worst-case per-symbol MSE equalization. Simulation results demonstrate that the proposed scheme achieves lower bit error rate (BER) than representative baseline modulation methods and exhibits strong generalization to out-of-distribution UWA channels.