A Fast Two-Dimensional Direction-of-Arrival Estimator Using Array Manifold Matrix Learning

Sparsity-based methods for two-dimensional (2D) direction-of-arrival (DOA) estimation often suffer from high computational complexity due to the large array manifold dictionaries. This paper proposes a fast 2D DOA estimator using array manifold matrix learning, where source-associated grid points are progressively selected from the set of predefined angular grids based on marginal likelihood maximization in the sparse Bayesian learning framework. This grid selection reduces the size of the manifold dictionary matrix, avoiding large-scale matrix inversion and resulting in reduced complexity. To overcome grid mismatch errors, grid optimization is established based on the marginal likelihood, with a dichotomizing-based solver provided that is applicable to arbitrary planar arrays. For uniform rectangular arrays, we present a 2D zoom fast Fourier transform as an alternative to the dichotomizing-based solver by transforming the manifold vector in a specific form, thus accelerating the computation without compromising accuracy. Simulation results verify the superior performance of the proposed methods in terms of estimation accuracy, computational efficiency, and angle resolution compared to state-of-the-art methods for 2D DOA estimation.