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On the Capacity Region of Reconfigurable Intelligent Surface Assisted Symbiotic Radios

Qianqian Zhang, Hu Zhou, Ying-Chang Liang, Sumei Sun, Wei Zhang, H. Vincent Poor

TL;DR

This work characterizes the capacity region of RIS-assisted symbiotic radio under a blocked direct link, addressing a multiplicative MAC induced by the RIS. By analyzing two passive-reflection constraints, it derives optimal input distributions for primary and secondary transmissions, identifies infinite sum-rate boundary points, and shows that RIS amplitude control enlarges the capacity region and the secondary DOF. Under phase-only reflection, the secondary DOF is reduced by half at high SNR, whereas allowing amplitude adjustments yields concentric-circle (discrete-amplitude) or Rayleigh-like primary-input distributions for boundary points. The study provides both analytic insights and numerical validation of the region structure and boundary points, offering design guidelines for RIS-enabled SR systems with peak/average power and passive-constraint considerations. Overall, the paper advances fundamental limits for multiplicative MACs with passive hardware constraints and highlights when RIS amplitude flexibility yields substantial performance gains.

Abstract

In this paper, we are interested in a reconfigurable intelligent surface (RIS)-assisted symbiotic radio (SR) system, where an RIS assists a primary transmission by passive beamforming and simultaneously acts as an information transmitter by periodically adjusting its reflection coefficients. The above RIS functions innately enable a new multiplicative multiple access channel (M-MAC), where the primary and secondary signals are superposed in a multiplicative manner. To pursue the fundamental performance limits of M-MAC, we focus on the characterization of the capacity region for such a system when the direct link is blocked. Due to the reflection nature of RIS, the signal transmitted from the RIS should satisfy a passive reflection constraint. We consider two types of passive reflection constraints, one for the case that only the phases of the RIS can be adjusted, while the other for the case that both the amplitude and the phase can be adjusted. Under the passive reflection constraints at the RIS as well as the average power constraint at the primary transmitter (PTx), we characterize the capacity region of RIS-assisted SR. It is observed that: 1) the number of sum-rate-optimal points on the boundary of the capacity region is infinite; 2) for the rate pairs with the maximum sum rate, the optimal distribution of the amplitude of the primary signal is a continuous Rayleigh distribution, while for the remaining rate pairs on the capacity region boundary, the optimal amplitude of the primary signal is discrete; 3) the adjustment of the amplitude for the RIS can enlarge the capacity region as compared to the phase-adjusted-only case.

On the Capacity Region of Reconfigurable Intelligent Surface Assisted Symbiotic Radios

TL;DR

This work characterizes the capacity region of RIS-assisted symbiotic radio under a blocked direct link, addressing a multiplicative MAC induced by the RIS. By analyzing two passive-reflection constraints, it derives optimal input distributions for primary and secondary transmissions, identifies infinite sum-rate boundary points, and shows that RIS amplitude control enlarges the capacity region and the secondary DOF. Under phase-only reflection, the secondary DOF is reduced by half at high SNR, whereas allowing amplitude adjustments yields concentric-circle (discrete-amplitude) or Rayleigh-like primary-input distributions for boundary points. The study provides both analytic insights and numerical validation of the region structure and boundary points, offering design guidelines for RIS-enabled SR systems with peak/average power and passive-constraint considerations. Overall, the paper advances fundamental limits for multiplicative MACs with passive hardware constraints and highlights when RIS amplitude flexibility yields substantial performance gains.

Abstract

In this paper, we are interested in a reconfigurable intelligent surface (RIS)-assisted symbiotic radio (SR) system, where an RIS assists a primary transmission by passive beamforming and simultaneously acts as an information transmitter by periodically adjusting its reflection coefficients. The above RIS functions innately enable a new multiplicative multiple access channel (M-MAC), where the primary and secondary signals are superposed in a multiplicative manner. To pursue the fundamental performance limits of M-MAC, we focus on the characterization of the capacity region for such a system when the direct link is blocked. Due to the reflection nature of RIS, the signal transmitted from the RIS should satisfy a passive reflection constraint. We consider two types of passive reflection constraints, one for the case that only the phases of the RIS can be adjusted, while the other for the case that both the amplitude and the phase can be adjusted. Under the passive reflection constraints at the RIS as well as the average power constraint at the primary transmitter (PTx), we characterize the capacity region of RIS-assisted SR. It is observed that: 1) the number of sum-rate-optimal points on the boundary of the capacity region is infinite; 2) for the rate pairs with the maximum sum rate, the optimal distribution of the amplitude of the primary signal is a continuous Rayleigh distribution, while for the remaining rate pairs on the capacity region boundary, the optimal amplitude of the primary signal is discrete; 3) the adjustment of the amplitude for the RIS can enlarge the capacity region as compared to the phase-adjusted-only case.
Paper Structure (15 sections, 3 theorems, 64 equations, 8 figures)

This paper contains 15 sections, 3 theorems, 64 equations, 8 figures.

Table of Contents

  1. Introduction
  2. RIS-assisted SR
  3. System Model
  4. Definition of Capacity Region
  5. Capacity Region Characterization with Constraint $|X_2|=1$
  6. Maximum Achievable Rate of Primary Transmission
  7. Maximum Achievable Rate of Secondary Transmission
  8. Maximum Achievable Sum Rate
  9. Rate Pairs on Boundary ${\mathbf{A}}$-${\mathbf{B}}$
  10. Rate Pairs on Boundary ${\mathbf{B}}$-${\mathbf{C}}$
  11. Capacity Region Characterization with Constraint $|X_2|\leq1$
  12. Maximum Achievable Rate of Secondary Transmission
  13. Rate Pairs on Boundary ${\mathbf{B}}$-${\mathbf{C}}$
  14. Performance Evaluation
  15. Conclusions

Key Result

Theorem 1

The mutual information $I(X_2;Y|X_1 = x_1)$ can be calculated by where $\kappa(r) = \exp\left(-\frac{{r}^2+|hx_1|^2}{\sigma^2}\right)I_0\left(\frac{2{r}|hx_1|}{\sigma^2}\right)$ and $I_0(x) = \frac{1}{2\pi}\int_{-\pi}^{\pi}e^{x\cos\theta}d\theta$.

Figures (8)

  • Figure 1: System model.
  • Figure 2: Structure of capacity region of RIS-assisted SR.
  • Figure 3: Examples of the phase PDFs of $X_1$, $X_2$, and $X$.
  • Figure 4: An example of the optimal input distribution with passive reflection constraint.
  • Figure 5: The optimized locations of the mass points versus the corresponding probabilities of $f_a^*$ with constraint $|X_2| = 1$.
  • ...and 3 more figures

Theorems & Definitions (3)

  • Theorem 1
  • Theorem 2
  • Theorem 3