Mathematical Model and Real-World Demonstration of Multi-Beam and Wide-Beam Reconfigurable Intelligent Surface

In this paper, a mathematical model is proposed to govern the phase distribution on a reconfigurable intelligent surface (RIS) for anomalously reflecting the beam towards the directions of interest. To this end, two operational modes are defined with respect to the reflected pattern. In the first mode, the RIS is configured to form multi-reflected beams toward the directions of interest capable of being controlled independently. The second mode is when the RIS provides a wide reflected beam. Regarding to each mode, a cost function is derived and then, in order to enhance the reflected pattern characteristics, a genetic algorithm (GA) is employed to the model as optimization method. To validate the practicality of the method, the proposed model is applied to a fabricated RIS to assess its performance in a real-world outdoor scenario. In the first mode, an asymmetric dual-beam reflected pattern is obtained and tested with tilt angles of <inline-formula> <tex-math notation="LaTeX">$\theta _{0}=60^{\circ }$ </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">$\theta _{1}=135^{\circ }$ </tex-math></inline-formula>. Furthermore, a wide-reflected beam is generated in the second mode with half-power beamwidth of <inline-formula> <tex-math notation="LaTeX">$\theta _{HPBW}=30^{\circ }$ </tex-math></inline-formula> and tilt angle of <inline-formula> <tex-math notation="LaTeX">$\theta _{0}=75^{\circ }$ </tex-math></inline-formula>. At both modes, the measured data are well aligned with the simulated results.