Data-Driven Modulation Optimization with LMMSE Equalization for Reliability Enhancement in Underwater Acoustic Communications

Ultra-reliable underwater acoustic (UWA) communications serve as one of the key enabling technologies for future space-air-ground-underwater integrated networks. However, the reliability of current UWA transmission is still insufficient since severe performance degradation occurs for conventional multicarrier systems in UWA channels with severe delay-scale spread. To solve this problem, we exploit learning-inspired approaches to optimize the modulation scheme under the assumption of linear minimum mean square error (LMMSE) equalization, where the discrete representation of waveforms is adopted by utilizing Nyquist filters. The optimization problem is first transferred into maximizing the fairness of estimation mean square error (MSE) for each data symbol since the total MSE is invariant considering the property of orthogonal modulation. The Siamese architecture is then adopted to obtain consistent optimization results across various channel conditions, which avoids the overhead of online feedback, cooperation, and deployment of neural networks and guarantees generalization. The overall scheme including the loss function, neural network structure, and training process is also investigated in depth in this paper. The excellent performance<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sup> and robustness of the proposed modulation scheme are verified by carrying out the bit error rate test over various UWA channels with severe delay-scale spread.<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sup>Open-source codes of this paper are available at https://github.com/neatlyw/UWA_moduOptimization_ICCC2025.