Robust Reflective Beamforming for Aerial Reconfigurable Intelligent Surface

This paper addresses the reflective beamforming design for aerial reconfigurable intelligent surface (ARIS), where the RIS is mounted on an aerial platform at a certain height. Different from the terrestrial counterpart, the ARIS provides additional deployment flexibility but it is susceptible to perturbations such as wind effect and imperfect flight control. Consequently, the reflective beam from the ARIS may not provide the highest signal quality to the intended user. Since random perturbations are not known in prior, we adopt a deterministic uncertainty model where the deviation of the ARIS position from the desired one is bounded in a certain range. Based on this uncertainty model, the reflective beamforming design for maximizing the received signal-to-noise ratio (SNR) is formulated that contains a nonconvex objective function and infinitely many constraints. Two approaches are proposed to find the the phase shifts on the ARIS for constructing robust reflective beams. One resorts to the semi-definite relaxation (SDR) approach and the other leverages the subarray based beam broadening and flattening technique. Simulation results are shown to demonstrate the performance of the proposed robust reflective beamforming.