This paper investigates the information theoretic limit of a reconfigurable intelligent surface (RIS) aided communication scenario in which the RIS and the transmitter either jointly or independently send information to the receiver. The RIS is an emerging technology that uses a large number of passive reflective elements with adjustable phases to intelligently reflect the transmit signal to the intended receiver. While most previous studies of the RIS focus on its ability to beamform and to boost the received signal-to-noise ratio (SNR), this paper shows that if the information data stream is also available at the RIS and can be modulated through the adjustable phases at the RIS, significant improvement in the {degree-of-freedom} (DoF) of the overall channel is possible. For example, for an RIS system in which the signals are reflected from a transmitter with $M$ antennas to a receiver with $K$ antennas through an RIS with $N$ reflective elements, assuming no direct path between the transmitter and the receiver, joint transmission of the transmitter and the RIS can achieve a DoF of $\min\left(M+\frac{N}{2}-\frac{1}{2},N,K\right)$ as compared to the DoF of $\min(M,K)$ for the conventional multiple-input multiple-output (MIMO) channel. This result is obtained by establishing a connection between the RIS system and the MIMO channel with phase noise and by using results for characterizing the information dimension under projection. The result is further extended to the case with a direct path between the transmitter and the receiver, and also to the multiple access scenario, in which the transmitter and the RIS send independent information. Finally, this paper proposes a symbol-level precoding approach for modulating data through the phases of the RIS, and provides numerical simulation results to verify the theoretical DoF results.

翻译：本文研究了可重构智能表面（RIS）辅助通信场景的信息论极限，其中RIS与发射机可联合或独立地向接收机发送信息。RIS是一种新兴技术，它利用大量具有可调相位的无源反射单元，将发射信号智能地反射至目标接收机。以往大多数RIS研究主要关注其波束成形能力和提升接收信噪比（SNR）的作用，本文则证明：若信息数据流在RIS端同样可用，并能通过RIS的可调相位进行调制，则整个信道的自由度（DoF）可获得显著提升。例如，在一个RIS系统中，信号从具有$M$根天线的发射机通过具有$N$个反射单元的RIS反射至具有$K$根天线的接收机，假设发射机与接收机之间无直射路径，发射机与RIS的联合传输可实现$\min\left(M+\frac{N}{2}-\frac{1}{2},N,K\right)$的自由度，而传统多输入多输出（MIMO）信道的自由度仅为$\min(M,K)$。该结论通过建立RIS系统与含相位噪声MIMO信道的关联，并利用投影下信息维度的表征结果而获得。本文进一步将结果扩展至存在发射机-接收机直射路径的场景，以及发射机与RIS发送独立信息的多址接入场景。最后，本文提出一种通过RIS相位调制数据的符号级预编码方法，并提供数值仿真结果以验证理论自由度结论。