A Deep Shrinkage Network for Direction-of-Arrival Estimation with Sparse Prior

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Direction-of-arrival (DOA) estimation of underwater multipath signals plays a indispensable role in both military and civilian underwater applications. Despite its importance, accurately estimating DOA under multipath conditions is challenging due to the proximity of paths in the spatial domain. Current methods struggle with this problem in passive detection scenarios. To address these limitations, this study proposes a deep learning (DL)-based DOA estimation framework leveraging sparse representation. First, the approach models the array covariance matrix as an undersampled linear measurement of the spatial spectrum. Then, a super-resolution deep shrinkage reconstruction network (SDSR-Net) is designed to map the sparse representation of the covariance matrix directly to the DOA. The network integrates a shrinkage module as nonlinear transformation layers, promoting sparsity and enhancing the discrimination of features. Simulations and experimental evaluations validated the effectiveness of the proposed method, showing that the DOA estimation accuracy was significantly improved and able to achieve a resolution of 0.2° in the spatial spectrum. Compared with existing methods, SDSR-Net achieved superior performance by effectively utilizing a sparsity prior, maintaining a high-resolution performance at signal-to-noise ratios higher than −10 dB. This work contributes a robust and efficient solution to DOA estimation challenges in underwater environments.