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

TL;DR

This paper develops a robust optimization framework for IRS-assisted communication systems to maximize energy efficiency under imperfect CSI, introducing a polynomial-time dynamic programming algorithm that achieves global optimality.

Contribution

It proposes a novel robust binary IRS element activation method with a polynomial-time algorithm for worst-case energy efficiency maximization under CSI uncertainty.

Findings

The DP algorithm achieves the same performance as exhaustive search.

The proposed scheme outperforms activating all IRS elements.

Numerical results validate the robustness and efficiency of the method.

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.