Robust Reflective Beamforming For Non-Terrestrial Networks Under Thermal Deformations

Abstract

In this paper, we present a beamforming method that is robust against thermal deformations for non-terrestrial reconfigurable intelligent surfaces (RIS). We analytically derive the expressions for the worst-case bound on perturbations of the covariance matrix and the corresponding steering vectors as functions of possible displacements of RIS elements. We apply these bounds during the optimization procedure to find the beamforming coefficients that are robust to thermal deformations. Moreover, we present a simple heuristic to obtain the constant modulus beamforming coefficients from the optimal beamforming via an array thinning operation. The simulation results confirm the robustness of the proposed solution against random but bounded perturbations caused by thermal deformations of the reflective surface.