[论文解读] Degree-of-Freedom of Modulating Information in the Phases of Reconfigurable Intelligent Surface

Hei Victor Cheng, Wei Yu|arXiv (Cornell University)|Dec 27, 2021

Advanced Wireless Communication Technologies参考文献 43被引用 4

一句话总结

本文研究了在可重构智能表面（RIS）通过其可调相移调制信息时，RIS辅助通信中的自由度（DoF）增益。通过将RIS视为主动信息调制器而非仅被动波束成形器，作者表明，发射机与RIS的联合传输可实现自由度为 $\min(M + \frac{N}{2} - \frac{1}{2}, N, K)$，显著超过传统MIMO的自由度 $\min(M, K)$。

ABSTRACT

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 $\min\left(M+\frac{N}{2}-\frac{1}{2},N,K ight)$ 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.

研究动机与目标

• 研究当RIS通过其相移主动调制信息时，RIS辅助通信的信息论极限。
• 量化当RIS与发射机联合传输数据时，与仅通过RIS增强信噪比相比，自由度（DoF）的增益。
• 将自由度分析扩展至存在发射机与接收机之间直射链路的场景。
• 研究在RIS与发射机发送独立数据流的多址接入场景下的自由度。
• 提出并评估一种符号级预编码策略，以实现RIS上基于相位的信息调制的实际应用。

提出的方法

• 作者通过建立RIS辅助信道与存在相位噪声的MIMO信道之间的数学联系，分析投影下的信息维数。
• 通过将RIS建模为通过相移调制数据的联合发射机，推导出带有RIS的点对点MIMO系统的自由度。
• 利用信息维数理论和投影性质，推导出自由度表达式 $\min(M + \frac{N}{2} - \frac{1}{2}, N, K)$。
• 在多址接入场景中，分析在发射机与RIS独立发送数据时的自由度，接收端采用联合检测。
• 提出一种符号级预编码算法，联合优化发射波束成形与RIS相位偏移，以逼近理论自由度。
• 采用黎曼共轭梯度法求解非凸优化问题，并利用重投影映射与传输映射以保持RIS相位的单位模约束。

实验结果

研究问题

• RQ1 当RIS通过其相移主动调制信息时，在RIS辅助的MIMO系统中可实现的最大自由度（DoF）是多少？
• RQ2 当RIS与发射机联合传输数据时，RIS辅助系统的自由度与传统MIMO相比如何？
• RQ3 当发射机与接收机之间存在直射链路时，RIS辅助系统中的自由度如何变化？
• RQ4 在发射机与RIS分别发送独立数据流的多址接入场景中，自由度是多少？
• RQ5 一种实用的符号级预编码方案能否实现RIS辅助通信中的理论自由度极限？

主要发现

• 发射机与RIS的联合传输可实现自由度 $\min(M + \frac{N}{2} - \frac{1}{2}, N, K)$，超过传统MIMO的自由度 $\min(M, K)$。
• 自由度增益源于RIS通过相位调制承载信息的能力，有效提升了系统的复用增益。
• 在存在发射机与接收机之间直射链路的情况下，自由度仍优于传统MIMO，尽管表达式依赖于信道条件。
• 在独立数据流的多址接入场景中，自由度由两个信源的自由度之和决定，受RIS相位约束限制。
• 数值结果表明，所提出的符号级预编码方法可逼近理论自由度极限，验证了信息论分析的正确性。
• 采用适当重投影与传输映射的黎曼共轭梯度法能有效求解非凸优化问题，同时保持RIS相位偏移的单位模约束。