WADNet: Improving Direction-of-Arrival Estimation in Multipath Underwater Settings Using Wavelet Scattering Transform and Self-Attention Mechanism

Abstract

Accurately determining the direction of arrival (DoA) for multiple underwater sources in noisy and multipath conditions is a major challenge in underwater acoustics. Conventional approaches often struggle with noise and multipath interference, leading to underdetermined scenarios and reduced accuracy. This study introduces the wavelet-attention DoA network (WADNet), a deep neural network that combines a multihead self-attention mechanism with a wavelet scattering transform to generate robust feature maps. The WADNet effectively captures global variations through self-attention and localized distortions via the 2-D wavelet transform, isolating multipath-induced artifacts that are often obscured in global covariance matrix analyses. The model is trained on a comprehensive simulated data set incorporating noise and varying multipath signals in a shallow isotropic channel, utilizing multipath-resistant covariance features to mitigate noise and multipath effects. WADNet’s performance is assessed using root-mean-square error and resolution probability (${P}_{\text{rp}}$) across diverse ranges, signal-to-noise ratios, and multipath conditions. Furthermore, the WADNet exhibits strong generalization in real-time testing during the SWellEx-96 experiment, surpassing traditional methods in single-source ($S5$) and double-source ($S59$) scenarios. It delivers higher resolution and precise DoA estimates without needing domain adaptation or transfer learning, effectively bridging the gap between simulation and real-world applications.