Deep Unfolding of Atomic Norm Minimization for DoA Estimation

Direction-of-arrival (DoA) estimation is a critical problem in array signal processing with applications in radar sensing and mobile positioning. Among various approaches, atomic norm minimization (ANM) is an effective technique that promotes sparsity in the angular domain, making it well-suited for DoA estimation. However, the conventional ANM problem is typically solved using semi-definite programming (SDP), which is computationally intensive and limits its practical applicability. To address this challenge, we propose a novel DoA estimation approach based on deep unfolding of the ANM problem. Specifically, we introduce an approximate function for the atomic norm and solve the resulting problem using a deep unfolded projected gradient descent (PGD) method. In this framework, the step size of the PGD and the parameters of the approximated ANM function are optimized via data training to minimize the objective function efficiently. The proposed method unifies the PGD optimization with deep learning, delivering accurate DoA estimation with low complexity. Simulation results demonstrate that our method achieves competitive performance with state-of-the-art techniques while maintaining computational efficiency, making it a promising solution for practical DoA estimation.