Power Efficiency, Overhead, and Complexity Tradeoff in IRS-Assisted\n Communications -- Quadratic Phase-Shift Design

In this paper, we focus on large intelligent reflecting surfaces (IRSs) and\npropose a new codebook construction method to obtain a set of predesigned\nphase-shift configurations for the IRS unit cells. Since the overhead for\nchannel estimation and the complexity of online optimization for IRS-assisted\ncommunications scale with the size of the phase-shift codebook, the design of\nsmall codebooks is of high importance. We show that there exists a fundamental\ntradeoff between power efficiency and the size of the codebook. We first\nanalyze this tradeoff for baseline designs that employ a linear phase-shift\nacross the IRS. Subsequently, we show that an efficient design for small\ncodebooks mandates higher-order phase-shift variations across the IRS.\nConsequently, we propose a quadratic phase-shift design, derive its\ncoefficients as a function of the codebook size, and analyze its performance.\nOur simulation results show that the proposed design yields a higher power\nefficiency for small codebooks than the linear baseline designs.\n