V-RIS: Virtual-Aperture DoA Estimation with Sparse RIS

Large-aperture reconfigurable intelligent surfaces (RISs) enable high-resolution 2D direction-of-arrival (DoA) estimation, but existing approaches still tie hardware cost and control overhead to aperture size. To decouple the effective sensing aperture from the number of physically deployed RIS elements, we present V-RIS, a framework for virtual-aperture surface-field reconstruction and DoA estimation. V-RIS uses only four corner subarrays and a single-antenna receiver to reconstruct the virtual-aperture surface field from receiver observations collected under multiple RIS phase configurations, and then performs DoA estimation on the reconstructed virtual-aperture surface field. Our key observation is that, under far-field illumination, the discretized RIS surface field satisfies finite-order spatial recurrences along both aperture axes. We enforce data-level consistency through the RIS-coded receiver observations and propagation consistency through the far-field spatial recurrence, while using a four-corner deployment geometry that retains both contiguous local elements and long aperture baselines. To improve robustness in practical receiver observations, we adopt a bias-invariant receiver-domain loss that suppresses quasi-static hardware distortions and configuration-invariant multipath contributions. Extensive simulations show that V-RIS approaches the DoA accuracy of a full-aperture benchmark while producing cleaner spectra than matrix-completion and least-squares baselines. An outdoor prototype further validates the design: with only 25\% programmable elements, V-RIS keeps both elevation and azimuth errors within $1^\circ$ of the ground truth.