Quantized Phase Alignment by Discrete Phase Shifts for Reconfigurable Intelligent Surface-Assisted Communication Systems

Reconfigurable intelligent surface (RIS) has aroused a surge of interest in recent years. In this paper, we investigate the joint phase alignment and phase quantization on discrete phase shift designs for RIS-assisted single-input single-output (SISO) system. Firstly, the phenomena of phase distribution in far field and near field are respectively unveiled, paving the way for discretization of phase shift for RIS. Then, aiming at aligning phases, the phase distribution law and its underlying degree-of-freedom (DoF) are characterized, serving as the guideline of phase quantization strategies. Subsequently, two phase quantization methods, dynamic threshold phase quantization (DTPQ) and equal interval phase quantization (EIPQ), are proposed to strengthen the beamforming effect of RIS. DTPQ is capable of calculating the optimal discrete phase shifts with linear complexity in the number of unit cells on RIS, whilst EIPQ is a simplified method with a constant complexity yielding sub-optimal solution. Simulation results demonstrate that both methods achieve substantial improvements on power gain, stability, and robustness over traditional quantization methods. The path loss (PL) scaling law under discrete phase shift of RIS is unveiled for the first time, with the phase shifts designed by DTPQ due to its optimality. Additionally, the field trials conducted at 2.6 GHz and 35 GHz validate the favourable performance of the proposed methods in practical communication environment.