Efficient Gridless Wideband Direction-of-Arrival Estimation From Many Frequencies

This paper addresses gridless direction-of-arrival (DOA) estimation for unknown source signals across a wide frequency range. While processing signals jointly across multiple frequencies can improve DOA estimation accuracy, it significantly increases computational complexity as the model size expands, rendering traditional methods impractical for handling many frequencies. To improve computational efficiency, we apply the Hankel matrix lifting technique, casting the DOA estimation as a nonconvex low-rank Hankel matrix recovery problem. A crucial aspect of our method is that the optimization matrix variable possesses both low-rank and Hankel structures, which allows for efficient computations of matrix-vector products, truncated singular value decomposition (SVD), and gradient and Newton direction evaluations. By leveraging a modern second-order nonconvex optimization technique, our approach achieves a low computational cost per iteration and a fast overall convergence rate. We quantify the per-iteration complexity of our method, and demonstrate its superiority compared with benchmark approaches. Numerical simulations confirm that our approach not only reduces computational complexity but also improves empirical DOA estimation accuracy.