Reconfigurable intelligent surfaces (RIS) are a promising tool for optimization of propagation channels for advanced  wireless communication systems. These tools are especially relevant for high-frequency (millimeter-band) links where directive antennas are used. RIS panels act as high-gain passive repeaters, whose reflected waves interfere with the waves reflected from the illuminated spots at  supporting walls, creating a complex field pattern in the far zone. In this work, we develop a simple link-budget model for non-line-of-sight channels via reflections from a finite size metasurface designed as a perfect anomalous reflector. The developed model takes into account diffraction at  the RIS panel edges as well as interference with reflections from supporting structures. We take into account realistic losses and confirm the validity of results by numerical simulations.

The use of reconfigurable intelligent surfaces (RISs) for optimization of propagation channels is one of the most promising and revolutionizing techniques for improving the efficiency of the next generation of communications systems. In this work, we combine the physical optics approximation and the theory of diffraction gratings to study the scattering properties of finite-size metasurfaces mounted on partially reflecting walls and illuminated by directive antennas. We consider both reflective and refractive metasurfaces designed to control both reflection and transmission of waves. We start the analysis under the assumption of uniform, plane-wave illumination, and then discuss non-uniform illuminations by directive antennas.