RIS with insufficient phase shifting capability: Modeling, beamforming, and experimental validations

Most research works on reconfigurable intelligent surfaces (RIS) rely on idealized models of the reflection coefficients, i.e., uniform reflection amplitude for any phase and sufficient phase shifting capability. In practice however, such models are oversimplified. This paper introduces a realistic reflection coefficient model for RIS based on measurements. The reflection coefficients are modeled as discrete complex values that have non-uniform amplitudes and suffer from insufficient phase shift capability. We then propose a group-based query algorithm that takes the imperfect coefficients into consideration while calculating the reflection coefficients. We analyze the performance of the proposed algorithm, and derive the closed-form expressions to characterize the received power of an RIS-aided wireless communication system. The performance gains of the proposed algorithm are confirmed in simulations. Furthermore, we validate the proposed theoretical results by experiments with our fabricated RIS prototype systems. The simulation and measurement results match well with the theoretical analysis.