Reconfigurable Coding Design for Programmable Metasurface-Based DOA Estimation via Riemannian Manifold Optimization

Programmable metasurface (PMS) has effective control over amplitude and phase, presenting a cost-efficient solution for direction-of-arrival (DOA) estimation. However, its performance is significantly influenced by the design of the PMS’s reconfigurable coding. In this letter, we propose a reconfigurable coding design method for PMS-based DOA estimation problem based on Riemannian manifold optimization. Specifically, we cast the reconfigurable coding design as a mutual coherence minimization problem, and reformulate it as a Frobenius norm minimization problem, aiming to reduce the difference between the identity matrix and the Gram matrix of the sensing matrix. To address this non-convex optimization problem, we propose an alternating optimization framework that combines positive semidefinite programming with Riemannian manifold optimization to obtain the reconfigurable coding matrix. Simulation results validate that the proposed method outperforms the existing methods in DOA estimation accuracy with fewer measurements.