Angle-Dependent Phase Shifter Model for Reconfigurable Intelligent Surfaces: Does the Angle-Reciprocity Hold?

The existing phase shifter models adopted for reconfigurable intelligent surfaces (RISs) have ignored the electromagnetic (EM) waves propagation behavior, thus cannot reveal practical effects of RIS on wireless communication systems. Based on the equivalent circuit, this paper introduces an angle-dependent phase shifter model for varactor-based RISs. To the best of our knowledge, this is the first phase shifter model which reveals that the incident angle of EM waves has influence on the reflection coefficient of RIS. In addition, the angle-reciprocity on RIS is investigated and further proved to be tenable when the reflection phase difference of adjacent RIS unit cells is invariant for an impinging EM wave and its reverse incident one. The angle-dependent characteristic of RIS is verified through full-wave simulation. According to our analysis and the simulation results, we find that the angle-reciprocity of varactor-based RIS only holds under small incident angles of both forward and reverse incident EM waves, thus limits the channel reciprocity in RIS-assisted TDD systems.