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Robust Resource Allocation for STAR-RIS Assisted SWIPT Systems

Guangyu Zhu, Xidong Mu, Li Guo, Ao Huang, Shibiao Xu

Abstract

A simultaneously transmitting and reflecting reconfigurable intelligent surface (STAR-RIS) assisted simultaneous wireless information and power transfer (SWIPT) system is proposed. More particularly, an STAR-RIS is deployed to assist in the information/power transfer from a multi-antenna access point (AP) to multiple single-antenna information users (IUs) and energy users (EUs), where two practical STAR-RIS operating protocols, namely energy splitting (ES) and time switching (TS), are employed. Under the imperfect channel state information (CSI) condition, a multi-objective optimization problem (MOOP) framework, that simultaneously maximizes the minimum data rate and minimum harvested power, is employed to investigate the fundamental rate-energy trade-off between IUs and EUs. To obtain the optimal robust resource allocation strategy, the MOOP is first transformed into a single-objective optimization problem (SOOP) via the ε-constraint method, which is then reformulated by approximating semi-infinite inequality constraints with the S-procedure. For ES, an alternating optimization (AO)-based algorithm is proposed to jointly design AP active beamforming and STAR-RIS passive beamforming, where a penalty method is leveraged in STAR-RIS beamforming design. Furthermore, the developed algorithm is extended to optimize the time allocation policy and beamforming vectors in a two-layer iterative manner for TS. Numerical results reveal that: 1) deploying STAR-RISs achieves a significant performance gain over conventional RISs, especially in terms of harvested power for EUs; 2) the ES protocol obtains a better user fairness performance when focusing only on IUs or EUs, while the TS protocol yields a better balance between IUs and EUs; 3) the imperfect CSI affects IUs more significantly than EUs, whereas TS can confer a more robust design to attenuate these effects.

Robust Resource Allocation for STAR-RIS Assisted SWIPT Systems

Abstract

A simultaneously transmitting and reflecting reconfigurable intelligent surface (STAR-RIS) assisted simultaneous wireless information and power transfer (SWIPT) system is proposed. More particularly, an STAR-RIS is deployed to assist in the information/power transfer from a multi-antenna access point (AP) to multiple single-antenna information users (IUs) and energy users (EUs), where two practical STAR-RIS operating protocols, namely energy splitting (ES) and time switching (TS), are employed. Under the imperfect channel state information (CSI) condition, a multi-objective optimization problem (MOOP) framework, that simultaneously maximizes the minimum data rate and minimum harvested power, is employed to investigate the fundamental rate-energy trade-off between IUs and EUs. To obtain the optimal robust resource allocation strategy, the MOOP is first transformed into a single-objective optimization problem (SOOP) via the ε-constraint method, which is then reformulated by approximating semi-infinite inequality constraints with the S-procedure. For ES, an alternating optimization (AO)-based algorithm is proposed to jointly design AP active beamforming and STAR-RIS passive beamforming, where a penalty method is leveraged in STAR-RIS beamforming design. Furthermore, the developed algorithm is extended to optimize the time allocation policy and beamforming vectors in a two-layer iterative manner for TS. Numerical results reveal that: 1) deploying STAR-RISs achieves a significant performance gain over conventional RISs, especially in terms of harvested power for EUs; 2) the ES protocol obtains a better user fairness performance when focusing only on IUs or EUs, while the TS protocol yields a better balance between IUs and EUs; 3) the imperfect CSI affects IUs more significantly than EUs, whereas TS can confer a more robust design to attenuate these effects.
Paper Structure (23 sections, 2 theorems, 38 equations, 9 figures, 1 table, 3 algorithms)

This paper contains 23 sections, 2 theorems, 38 equations, 9 figures, 1 table, 3 algorithms.

Table of Contents

  1. Introduction
  2. Prior Works
  3. Motivations and Contributions
  4. Organization and Notations
  5. System Model and Problem Formulation
  6. STAR-RIS Protocols and Models
  7. Signal Transmission Model
  8. CSI Error Model
  9. Problem Formulation
  10. Solutions of Robust Resource Allocation Problems
  11. Proposed Solution for ES
  12. Proposed Solution for TS
  13. Computational Complexity and Convergence Analysis
  14. Numerical Results
  15. Simulation Setup
  16. ...and 8 more sections

Key Result

Lemma 1

(General S-Procedure convex): Define the quadratic functions of the variable $\mathbf{x} \in \mathbb{C}^{N\times 1}$: where $\mathbf{A}_i$ is the complex symmetric matrix, i.e., $\mathbf{A}_i=\mathbf{A}_i^{H}$. Then the $\{f_i(\mathbf{x})\geq 0\}_{i=1}^{K}\Rightarrow{f_0({\mathbf{x})\geq 0}}$ holds if and only if there exists $\forall i, \lambda_i \geq 0$ satisfying with

Figures (9)

  • Figure 1: Illustration of the STAR-RIS assisted SWIPT systems
  • Figure 2: Simulation setup
  • Figure 3: Convergence of Algorithm 2.
  • Figure 4: System performance versus number of AP antennas for $M=16$, $\rho_G=\rho_H=0.01$
  • Figure 5: System performance versus number of STAR-RIS elements for $N=4$, $\rho_G=\rho_H=0.01$
  • ...and 4 more figures

Theorems & Definitions (3)

  • Lemma 1
  • Theorem 1
  • proof