Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Degree-of-Freedom of Modulating Information in the Phases of Reconfigurable Intelligent Surface

Hei Victor Cheng, Wei Yu

TL;DR

The paper establishes the information-theoretic DoF limits of RIS-aided channels when the RIS phases carry information in addition to passive reflection. By linking the RIS channel to a MIMO channel with phase noise and employing information-dimension analysis, it derives DoF expressions for both joint transmitter-RIS transmission and RIS-assisted multiple access, including scenarios with and without direct paths. It further provides practical symbol-level precoding and ML decoding strategies to approach these DoF limits, and validates the theory via simulations showing phase-transition behavior as the RIS size grows. The results indicate substantial DoF gains over conventional MIMO when $N$ is large and, crucially, show that phase modulation at the RIS can emulate additional input dimensions, enabling higher data rates with limited RF hardware. This work thus highlights a novel, information-theoretic role for RIS in wireless systems with potential for low-cost MIMO-like performance enhancements.

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

Degree-of-Freedom of Modulating Information in the Phases of Reconfigurable Intelligent Surface

TL;DR

The paper establishes the information-theoretic DoF limits of RIS-aided channels when the RIS phases carry information in addition to passive reflection. By linking the RIS channel to a MIMO channel with phase noise and employing information-dimension analysis, it derives DoF expressions for both joint transmitter-RIS transmission and RIS-assisted multiple access, including scenarios with and without direct paths. It further provides practical symbol-level precoding and ML decoding strategies to approach these DoF limits, and validates the theory via simulations showing phase-transition behavior as the RIS size grows. The results indicate substantial DoF gains over conventional MIMO when is large and, crucially, show that phase modulation at the RIS can emulate additional input dimensions, enabling higher data rates with limited RF hardware. This work thus highlights a novel, information-theoretic role for RIS in wireless systems with potential for low-cost MIMO-like performance enhancements.

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 antennas to a receiver with antennas through an RIS with 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 as compared to the DoF of 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.
Paper Structure (38 sections, 12 theorems, 99 equations, 7 figures, 2 algorithms)

This paper contains 38 sections, 12 theorems, 99 equations, 7 figures, 2 algorithms.

Table of Contents

  1. Introduction
  2. Prior Works
  3. Main Contributions
  4. Paper Organization and Notation
  5. System Model and Problem Formulation
  6. Channel Model
  7. RIS as Passive Beamformer
  8. Joint Transmission Model
  9. Multiple Access Model
  10. DoF of RIS System without Direct Path
  11. SISO Channel
  12. Joint Transmission in MIMO Channel with $(\mathbf{X},\mathbf{\Theta})$ as Input
  13. MIMO Channel with Deterministic $\mathbf{X}$
  14. Multiple Access Channel with $\mathbf{X}$ and $\mathbf{\Theta}$ as Inputs
  15. DoF of RIS System with Direct Path
  16. ...and 23 more sections

Key Result

Theorem 1

Consider the channel model with $(\mathbf{X,\Theta})$ as the input where $\mathbf{X}\in \mathbb{C}^M$ has a power constraint $\mathbb{E}[\|\mathbf{X}\|_2^2]\leq 1$ and ${\boldsymbol{{\Theta}}}={\text{diag}}([e^{j\theta_1},e^{j\theta_2},\cdots,e^{j\theta_{{N}}}])$, and $\mathbf{Y}\in\mathbb{C}^K$ as the output, and $\mathbf{Z} This DoF can be achieved using independent $\mathbf{X}$ and $\mathbf{\T

Figures (7)

  • Figure 1: Channel model for a RIS assisted point-to-point MIMO communication system in which $(\mathbf{X},\mathbf{\Theta})$ jointly transmit as an input to the channel
  • Figure 2: DoF region of the SISO multiple access channel model
  • Figure 3: Examples of DoF region for the multiple access channel without a direct path under different values of $M$, $N$ and $K$.
  • Figure 4: Examples of DoF region for the multiple access channel with a direct path of rank $r$ under different values of $M$, $N$ and $K$.
  • Figure 5: The feasible region of $y$ for synthesizing $\mathbf{Y}=[y,y,y,y]$ at $M=2$, $K=4$, $P=1$, and $N$ ranging from 4 to 6 for channels without the direct path. Color yellow means that a point is feasible while color blue means that a point is infeasible.
  • ...and 2 more figures

Theorems & Definitions (14)

  • Theorem 1
  • Theorem 2
  • Theorem 3
  • Theorem 4
  • Theorem 5
  • Theorem 6
  • Definition 1
  • Lemma 1: Wu2015,Stotz2016
  • Definition 2
  • Lemma 2
  • ...and 4 more