Impact of Reconfigurable Intelligent Surface Geometry on Communication Performance

When beamforming is applied at the transmitter, only part of reconfigurable intelligent surfaces (RISs) will be active, and it becomes indispensable to study the impact of RIS geometry. This letter aims at evaluating RIS geometry, ranging from linear (1D), and planar (2D), to cylindrical (3D) structures. We first derive the effective illuminated surface of different RIS topologies and determine the resulting signal-to-noise ratio (SNR) and outage probability. Then, we investigate the optimal RIS location to trade off active area versus received power considering near-field propagation. Numerical results quantify the benefit of RIS geometric compactness and provide their applicable ranges.