Reconfigurable Intelligent Surface: MIMO or radiating sheet?

A Reconfigurable Intelligent Surface (RIS) redirects and possibly modifies the properties of incident waves, with the aim to restore non-line-of-sight communication links. Composed of elementary scatterers, the RIS has been so far treated as a collection of point scatterers with properties similar to antennas in an equivalent massive MIMO communication link. Despite the discrete nature of the RIS, current design approaches often treat the RIS as a continuous radiating surface, which is subsequently discretized. Here we investigate the connection between the two approaches in an attempt to bridge the two seemingly opposite perspectives. We analytically find the factor that renders the two approaches equivalent and we demonstrate our findings with examples of RIS elements modeled as antennas with commonly used radiation patterns and properties consistent with antenna theory. The equivalence between the two theoretical approaches is analyzed with respect to design aspects of the RIS elements, such as gain and directivity, with the aim to provide insight into the observed discrepancies, the understanding of which is crucial for assessing the RIS efficiency.