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In this paper, we study an intelligent reflecting surface (IRS)-aidedcommunication system with single-antenna transmitter and receiver, underimperfect channel state information (CSI). More specifically, we deal with therobust selection of binary (on/off) states of the IRS elements in order tomaximize the worst-case energy efficiency (EE), given a bounded CSIuncertainty, while satisfying a minimum signal-to-noise ratio (SNR). Inaddition, we consider not only continuous but also discrete IRS phase shifts.First, we derive closed-form expressions of the worst-case SNRs, and thenformulate the robust (discrete) optimization problems for each case. In thecase of continuous phase shifts, we design a dynamic programming (DP) algorithmthat is theoretically guaranteed to achieve the global maximum with polynomialcomplexity $O(L\,{\log L})$, where $L$ is the number of IRS elements. In thecase 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, numericalsimulations provide useful insights and confirm the theoretical results. Inparticular, the proposed algorithms are several orders of magnitude faster thanthe exhaustive search when $L$ is large, thus being highly scalable andsuitable for practical applications. Moreover, both algorithms outperform abaseline scheme, namely, the activation of all IRS elements.

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