Comparison of Simplistic System-Level RIS Models and Diffraction-Theory Solutions

We discuss and compare two recently published path-loss models for reconfigurable intelligent surfaces (RIS) derived from the electromagnetic and communication theory points of view. The electromagnetic model considers the RIS as a whole, taking into account field interactions of all metasurface elements, whereas the communication model is based on an assumption that each array element is an independent relay. The estimations given by the two models are rather different but, surprisingly, we find that the simplistic model gives the same result as the electromagnetic calculation for perfectly functioning anomalous reflectors if one replaces the effective areas of the unit cells by their geometrical areas, scaled by the corresponding angular factors. Simulation results validate our analysis and show the numerical differences between the two models when we vary the frequency and the number of elements in RISs.