Scattering gain loss bounds for discretized reconfigurable intelligent surfaces

In this contribution, we study how the unavoidable discretization process affects the scattering gain of a Reconfigurable Intelligent Surface (RIS). We characterize the discretization as an equivalent random variable with a proper expected value and variance depending on the unit cell (UC) dimensions and the phase profile exhibited by the RIS. This consideration allows us to model the response of a discrete RIS as a continuous RIS perturbed by that random variable. From there, we evaluate the expected value on the radiation patterns and define the discrete RIS scattering gain loss. We numerically verify our model by comparing a discrete RIS with a continuous RIS whose phase is perturbed by a random variable with adequate statistical characteristics. The proposed model gives an interesting tool to evaluate the communication channel of a realistic RIS.