  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.
