Physics-based Modeling of Large Intelligent Reflecting Surfaces for Scalable Optimization

In this paper, we develop a physics-based model that allows a scalable optimization of large intelligent reflecting surfaces (IRSs). The basic idea is to partition the IRS unit cells into several subsets, referred to as tiles, and model the impact of each tile on the wireless channel. Borrowing concepts from the radar literature, we model each tile as an anomalous reflector, and derive its impact on the wireless channel for given unit cell phase shifts by solving the corresponding integral equations for the electric and magnetic vector fields. Based on this model, one can design the phase shifts of the unit cells of a tile offline for the support of several transmission modes and then select the best mode online for a given channel realization. Therefore, the number of tiles and transmission modes in the proposed model are design parameters that can be adjusted to trade performance for complexity.