Atom-constrained Gridless DOA Refinement with Wirtinger Gradients

This paper proposes gridless sparse direction-of-arrival (DOA) refinement using gradient-based optimization. The objective function minimizes the fit between the sample covariance matrix (SCM) and a reconstructed covariance matrix. The latter is constrained to contain only a few atoms, but otherwise maximally matches the SCM. This reconstruction enables analytic derivatives with respect to DOA using Wirtinger gradients. The sensitivity of the solution to local minima is addressed by initializing near the true DOAs, where a user-input-free gridded sparse Bayesian learning is employed. Numerical results validate the effectiveness of the DOA refinement using analytic gradients, demonstrating its ability to reach the Cramér-Rao bound and achieve higher resolution compared to conventional gridless DOA estimation methods. The approach is validated by considering different numbers of DOAs, grid sizes, DOAs on/off the grid, fewer (even a single) snapshots, coherent arrivals, closely separated DOAs, and many DOAs.