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Robust Transmission Design for Active RIS-Aided Systems

Jinho Yang, Hyeongtaek Lee, Junil Choi

TL;DR

The paper tackles robust transmission design for an active RIS‑aided MU‑MISO downlink under statistical CSI error. It derives the minimum per‑user rate $R_{ ext{min},k}$ under the error model and formulates the objective $R_{ ext{sum}}= abla_{k=1}^K R_{ ext{min},k}$ to be maximized by jointly optimizing the BS beamformer ${f F}$ and RIS weights ${f w}$ under power constraints, incorporating RIS noise. A tractable lower bound based on a weighted MMSE surrogate is developed, and an alternating optimization procedure solves the resulting convex subproblems. Numerical results show substantial sum-rate gains of the robust design over non-robust baselines, especially under higher CSI uncertainty, larger RIS amplification, and higher transmit power, demonstrating improved reliability in practical imperfect-CSI regimes.

Abstract

Different from conventional passive reconfigurable intelligent surfaces (RISs), incident signals and thermal noise can be amplified at active RISs. By exploiting the amplifying capability of active RISs, noticeable performance improvement can be expected when precise channel state information (CSI) is available. Since obtaining perfect CSI related to an RIS is difficult in practice, a robust transmission design is proposed in this paper to tackle the channel uncertainty issue, which will be more severe for active RIS-aided systems. To account for the worst-case scenario, the minimum achievable rate of each user is derived under a statistical CSI error model. Subsequently, an optimization problem is formulated to maximize the sum of the minimum achievable rate. Since the objective function is non-concave, the formulated problem is transformed into a tractable lower bound maximization problem, which is solved using an alternating optimization method. Numerical results show that the proposed robust design outperforms a baseline scheme that only exploits estimated CSI.

Robust Transmission Design for Active RIS-Aided Systems

TL;DR

The paper tackles robust transmission design for an active RIS‑aided MU‑MISO downlink under statistical CSI error. It derives the minimum per‑user rate under the error model and formulates the objective to be maximized by jointly optimizing the BS beamformer and RIS weights under power constraints, incorporating RIS noise. A tractable lower bound based on a weighted MMSE surrogate is developed, and an alternating optimization procedure solves the resulting convex subproblems. Numerical results show substantial sum-rate gains of the robust design over non-robust baselines, especially under higher CSI uncertainty, larger RIS amplification, and higher transmit power, demonstrating improved reliability in practical imperfect-CSI regimes.

Abstract

Different from conventional passive reconfigurable intelligent surfaces (RISs), incident signals and thermal noise can be amplified at active RISs. By exploiting the amplifying capability of active RISs, noticeable performance improvement can be expected when precise channel state information (CSI) is available. Since obtaining perfect CSI related to an RIS is difficult in practice, a robust transmission design is proposed in this paper to tackle the channel uncertainty issue, which will be more severe for active RIS-aided systems. To account for the worst-case scenario, the minimum achievable rate of each user is derived under a statistical CSI error model. Subsequently, an optimization problem is formulated to maximize the sum of the minimum achievable rate. Since the objective function is non-concave, the formulated problem is transformed into a tractable lower bound maximization problem, which is solved using an alternating optimization method. Numerical results show that the proposed robust design outperforms a baseline scheme that only exploits estimated CSI.

Paper Structure

This paper contains 10 sections, 1 theorem, 22 equations, 4 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. System Model
  3. Proposed Robust Transmission Design
  4. Problem Formulation
  5. Problem Transformation
  6. Alternating Optimization
  7. Algorithm Description and Complexity Analysis
  8. Numerical Results
  9. Conclusion
  10. Derivation of $R_{\mathrm{min}, k}$

Key Result

Proposition 1

For any $v_k \in \mathbb{R}_{++}$ and $u_k \in \mathbb{C}$, the following inequality holds where $e_k(u_k, {\mathbf{F}}, {\mathbf{w}}) = \mathbb{E}\left[ (s_k - u_k^\mathrm{H} y_k)(s_k - u_k^\mathrm{H} y_k)^\mathrm{H} \right]$ is the MSE for the $k$-th user, and $c$ is constant, which are given by

Figures (4)

  • Figure 1: An active RIS-aided downlink system with $N$ BS antennas, $M$ RIS elements, and $K$ single-antenna users.
  • Figure 2: Average sum-rate performance according to $P_\mathrm{B}$ with $a_{\mathrm{max}} = 30 \ \mathrm{dB}$ and $\delta = 0.3$.
  • Figure 3: Average sum-rate performance according to $\delta$ with $P_\mathrm{B} = 30 \ \mathrm{dBm}$ and $a_{\mathrm{max}} = 30 \ \mathrm{dB}$.
  • Figure 4: Average sum-rate performance according to $a_\mathrm{max}$ with $P_{\mathrm{B}} = 30 \ \mathrm{dBm}$ and $\delta = 0.3$.

Theorems & Definitions (2)

  • Proposition 1
  • proof