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

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-tonoise 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.