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

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(LlogL), 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.