Robust IRS-Element Activation for Energy Efficiency Optimization in IRS-Assisted Communication Systems With Imperfect CSI

TL;DR

This paper proposes robust algorithms for activating IRS elements in IRS-assisted communication systems with imperfect CSI, optimizing energy efficiency and SNR under practical constraints, and demonstrates their effectiveness through theoretical analysis and simulations.

Contribution

It introduces a polynomial-time dynamic programming algorithm for continuous phase shifts and a convex relaxation method for discrete shifts, improving scalability and performance over existing schemes.

Findings

Algorithms outperform baseline schemes in simulations.

Proposed methods are significantly faster than exhaustive search.

Both algorithms achieve near-optimal energy efficiency and SNR.

Abstract

In this paper, we study an intelligent reflecting surface (IRS)-aided 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). In addition, we consider not only continuous but also discrete IRS phase shifts. First, we derive closed-form expressions of the worst-case SNRs, and then formulate the robust (discrete) optimization problems for each case. In the case of continuous phase shifts, we design 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. In the case of discrete phase shifts, we develop a convex-relaxation-based method (CRBM) to obtain a feasible (sub-optimal) solution in polynomial time $O(L^{3.5})$, with a posteriori performance guarantee. Furthermore, numerical simulations provide useful insights and confirm the theoretical results. In particular, the proposed algorithms are several orders of magnitude faster than the exhaustive search when $L$ is large, thus being highly scalable and suitable for practical applications. Moreover, both algorithms outperform a baseline scheme, namely, the activation of all IRS elements.