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.

翻译：可重构智能表面（RIS）近年来引发了研究热潮。本文针对RIS辅助单输入单输出（SISO）系统，研究离散相移设计中的联合相位对齐与相位量化问题。首先，分别揭示了远场和近场中相位分布现象，为RIS相移离散化奠定基础。随后，以相位对齐为目标，刻画了相位分布规律及其内在自由度（DoF），作为相位量化策略的指导准则。继而，提出动态阈值相位量化（DTPQ）和等间隔相位量化（EIPQ）两种增强RIS波束赋形效应的相位量化方法。DTPQ能以RIS单元数量线性复杂度计算最优离散相移，而EIPQ作为简化方法，以恒定复杂度得到次优解。仿真结果表明，与经典量化方法相比，两种方法在功率增益、稳定性和鲁棒性方面均取得显著提升。首次揭示了基于DTPQ最优相移设计的RIS离散相移下路径损耗（PL）标度律。此外，在2.6 GHz和35 GHz频段开展的现场试验验证了所提方法在实际通信环境中的优异性能。