RIS Beamforming under Element-Level Variations: Statistical Characterization and Robust Design

In this paper, a novel analytical framework to characterize the impact of element-level variations on the radiation characteristics of reconfigurable intelligent surfaces (RISs) is introduced. Specifically, a statistical model is proposed to capture the effects of varactor capacitance fluctuations on the RIS reflection coefficients, and, subsequently, on the resulting power radiation pattern; both low- and large-variance independent perturbation scenarios, are investigated. Leveraging the proposed statistical model, a low complexity greedy optimization methodology is presented, having the goal to optimize the expected RIS radiation power, thereby, generating inherently robust configurations. Furthermore, the analytical proposed model serves as an efficient alternative to computationally expensive Monte Carlo simulations, enabling the quantification of element sensitivity to manufacturing and operational tolerances. As demonstrated, optimizing the mean power pattern significantly enhances system performance under element-level variations. For typical RIS sizes (e.g., 32x32 or 64x64), a main lobe gain exceeding 2 dB and a sidelobe suppression of approximately 10 dB are achieved.