Element-Grouping Intelligent Reflecting Surface: Electromagnetic-Compliant Model and Geometry-Based Optimization

Abstract

Intelligent reflecting surface (IRS) is a promising solution for enabling the control of wireless environments. Most of existing works consider that an IRS consists of a large number of reconfigurable passive elements and each of them can reflect the signal independently. However, it is difficult and costly in practice to manufacture this kind of large-scale IRS. In this paper, we propose a practical electromagnetic-compliant reflection coefficient model for element-grouping IRS, which configures each <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">sub-surface</i> (including multiple homogeneous elements) but not each single element. Under this model, the reflection amplitude and the phase shift are coupled, which brings new challenges for optimizing the IRS configuration. We study a phase shift optimization problem to maximize the received power in an IRS-aided wireless system. As this problem is difficult to solve due to the complicated coupling in the practical model, we transform it into a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">vector composition</i> problem equivalently. By constructing a geometry-based phase analysis model, we analyze the relationship of the vectors in a two-dimensional space to maximize the length of the sum vector. By exploiting the geometrical properties, we propose a low-complexity phase control algorithm to find the optimal phase shifts of IRS. Simulation results reveal that substantial performance gains are achieved by the proposed algorithm compared to the conventional schemes.