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Global Optimization of Energy Efficiency in IRS-Aided Communication Systems via Robust IRS-Element Activation

Christos N. Efrem, Ioannis Krikidis

TL;DR

The paper tackles maximizing worst-case energy efficiency in an IRS-aided single-antenna link under bounded CSI uncertainty. It derives a closed-form worst-case SNR and casts a robust discrete optimization over binary IRS activation, then introduces a polynomial-time dynamic programming algorithm that guarantees a global optimum with complexity ${O}(L \log L)$. Numerical results show the DP solution matches exhaustive search and significantly outperforms an all-on IRS baseline, with EE degraded by CSI uncertainty. The work offers a scalable, rigorously optimal approach for energy-efficient IRS design under CSI errors, with potential extensions to discrete phase shifts and broader network settings.

Abstract

In this paper, we study an intelligent reflecting surface (IRS) assisted communication system with single-antenna transmitter and receiver, under imperfect channel state information (CSI). More specifically, we deal with the robust selection of binary (on/off) states of the IRS elements in order to maximize the worst-case energy efficiency (EE), given a bounded CSI uncertainty, while satisfying a minimum signal-to-noise ratio (SNR). The IRS phase shifts are adjusted so as to maximize the ideal SNR (i.e., without CSI error), based only on the estimated channels. First, we derive a closed-form expression of the worst-case SNR, and then formulate the robust (discrete) optimization problem. Moreover, we design and analyze a dynamic programming (DP) algorithm that is theoretically guaranteed to achieve the global maximum with polynomial complexity $O(L \log L)$, where $L$ is the number of IRS elements. Finally, numerical simulations confirm the theoretical results. In particular, the proposed algorithm shows identical performance with the exhaustive search, and significantly outperforms a baseline scheme, namely, the activation of all IRS elements.

Global Optimization of Energy Efficiency in IRS-Aided Communication Systems via Robust IRS-Element Activation

TL;DR

The paper tackles maximizing worst-case energy efficiency in an IRS-aided single-antenna link under bounded CSI uncertainty. It derives a closed-form worst-case SNR and casts a robust discrete optimization over binary IRS activation, then introduces a polynomial-time dynamic programming algorithm that guarantees a global optimum with complexity . Numerical results show the DP solution matches exhaustive search and significantly outperforms an all-on IRS baseline, with EE degraded by CSI uncertainty. The work offers a scalable, rigorously optimal approach for energy-efficient IRS design under CSI errors, with potential extensions to discrete phase shifts and broader network settings.

Abstract

In this paper, we study an intelligent reflecting surface (IRS) assisted communication system with single-antenna transmitter and receiver, under imperfect channel state information (CSI). More specifically, we deal with the robust selection of binary (on/off) states of the IRS elements in order to maximize the worst-case energy efficiency (EE), given a bounded CSI uncertainty, while satisfying a minimum signal-to-noise ratio (SNR). The IRS phase shifts are adjusted so as to maximize the ideal SNR (i.e., without CSI error), based only on the estimated channels. First, we derive a closed-form expression of the worst-case SNR, and then formulate the robust (discrete) optimization problem. Moreover, we design and analyze a dynamic programming (DP) algorithm that is theoretically guaranteed to achieve the global maximum with polynomial complexity , where is the number of IRS elements. Finally, numerical simulations confirm the theoretical results. In particular, the proposed algorithm shows identical performance with the exhaustive search, and significantly outperforms a baseline scheme, namely, the activation of all IRS elements.
Paper Structure (12 sections, 7 theorems, 31 equations, 3 figures, 1 algorithm)

This paper contains 12 sections, 7 theorems, 31 equations, 3 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. System Model
  3. Signal Transmission Model
  4. Imperfect CSI Model and Assumptions
  5. IRS Phase-Shift Design
  6. Power Consumption Model
  7. Formulation of Robust Optimization Problem
  8. Global Optimization Using Dynamic Programming
  9. Numerical Results
  10. Conclusion and Future Work
  11. Proof of Theorem \ref{['theorem:Worst-case_SNR']}
  12. Proof of Theorem \ref{['theorem:DP_algorithm']}

Key Result

Proposition 1

Assumption assumption:CSI-uncertainty_radius_2 implies Assumption assumption:CSI-uncertainty_radius_1.

Figures (3)

  • Figure 1: Worst-case energy efficiency versus the number of IRS elements, for several CSI-uncertainty radii ($\delta = \tau {\widehat{\alpha}_{\min}}$).
  • Figure 2: Worst-case energy efficiency versus the transmit power, for different CSI-uncertainty radii ($\delta = \tau {\widehat{\alpha}_{\min}}$).
  • Figure 3: Worst-case energy efficiency versus the minimum-SNR control parameter, for various CSI-uncertainty radii ($\delta = \tau {\widehat{\alpha}_{\min}}$).

Theorems & Definitions (10)

  • Proposition 1
  • Theorem 1
  • Remark 1
  • Proposition 2
  • Proposition 3
  • Remark 2
  • Proposition 4
  • Remark 3
  • Theorem 2
  • Lemma 1