The wasserstein vector spectrum for underwater acoustic target recognition

Underwater Acoustic Target Recognition (UATR) is a challenging task due to the complex underwater environments, the received acoustic signal is severely contaminated by environmental noise and broadband cavitation noise. Although deep learning methods based on time frequency spectrogram features have been widely used for UATR, conventional TF representations tend to show unstable behavior in complex environments and few-shot scenarios, resulting in limited robustness and generalization performance. To address these issues, we propose a distribution geometry representation learning framework for UATR. The core of this framework is the Wasserstein Vector Spectrum (WVS), a feature representation that captures the statistical energy characteristics of narrowband processes, yielding a more robust and representative description of underwater acoustic signals formed by their superposition. Building on WVS, we introduce WVS-Net as a lightweight parallel one-dimensional architecture to demonstrate the practical effectiveness of the proposed feature in target characterization tasks. Each WVS component is processed by an independent branch, enabling efficient extraction of discriminative multiband information. In addition, a Rényi divergence based distributional consistency constraint module is introduced to enforce consistency among the embedding features learned by the parallel subnetworks. Experiments on the open source underwater acoustic benchmarks show that the proposed framework achieves a significant improvement over existing baselines in few-shot scenarios, demonstrating its strong advantage under limited sample conditions. Even with sufficient training data, the framework still attains high accuracy, surpassing state-of-the-art methods and confirming its overall robustness and generalization capability.