Multiple Scattering Model for Beam Synthesis With Reconfigurable Intelligent Surfaces

This article presents a method of synthetic beamforming for reconfigurable intelligent surfaces (RIS). The method uses a
$T$
-matrix-based multiple scattering model to compute the scattering from the RIS. We assume that the elements of the RIS are infinite circular cylinders. This allows us to make the model 2-D. Furthermore, we assume that the RIS elements satisfy the impedance boundary condition (IBC), the complex parameter of which adjusts the phase shift of the scattered field. We synthesize the beam both analytically and numerically. Both approaches rely on an approximation that assumes RIS elements that are small compared to the wavelength. We demonstrate the efficacy of the beam synthesis by applying it in a test case that features a linear array of RIS elements.