Two-Timescale Design for Uplink Systems: How Many IRS Beamforming Patterns Are Needed?

Abstract

In this paper, we develop a new dynamic intelligent reflecting surface (IRS) beamforming (BF) framework for an IRS aided energy-constrained Internet-of-Things system, where multiple IRS BF patterns are employed to assist uplink transmission. To alleviate the channel estimation overhead incurred by the IRS, a novel two-timescale scheme is proposed to maximize the ergodic sum-rate. Specifically, multiple IRS BF patterns are first optimized based on the statistical channel state information (CSI). Under the obtained IRS BF patterns, the transmit power and time allocation for devices in each channel coherence interval are optimized based on the instantaneous CSI. By characterizing the lower bound of the objective value, we further analytically quantify the performance degradation incurred by using less IRS BF patterns to shed light on the fundamental performance-overhead tradeoff. Simulation results validate the effectiveness of our proposed design and demonstrate that only <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$33\%$</tex-math></inline-formula> of the total IRS BF patterns are needed to maintain <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$95\%$</tex-math></inline-formula> of the maximum achieved ergodic sum-rate.