Practical hardware limitations often impose a reduced number of available phase shifts at the elements of a reconfigurable intelligent surface (RIS). Most works often assume continuous phase-shits at the RIS elements for the transmit and passive beamforming optimization, which can lead to substantial performance loss. Therefore, to harvest the gains of RIS-assisted multi-stream multiple-input multiple-output (MIMO) communications under realistic phase shifts, this letter proposes a problem formulation for the maximization of the achievable rate over the transmit precoder and RIS elements, which avoids an explicit discrete constraint while still incorporating its effect. To efficiently tackle the resulting problem when considering large arrays and RIS panels, an iterative algorithm is derived which comprises a sequence of simple projections. Simulation results demonstrate that the proposed design can be very effective, especially with low-resolution phase-shifts.

翻译：实际硬件限制通常会导致可重构智能表面（RIS）元件的可用移相器数量减少。大多数研究工作通常假设RIS元件具有连续移相能力以优化发射波束赋形与无源波束赋形，但这种假设可能导致显著的性能损失。因此，为在现实移相器条件下获取RIS辅助多流多输入多输出（MIMO）通信的增益，本文提出一种最大化可达速率的问题建模方案，该方案同时优化发射预编码器与RIS元件配置，通过隐含方式规避显式离散约束的同时保留其物理效应。针对大规模天线阵列与RIS面板场景下的优化问题，本文推导出一种包含序列化简单投影的迭代算法。仿真结果表明，所提设计方法具有显著有效性，尤其适用于低分辨率移相器场景。