Physics-based Modeling and Scalable Optimization of Large Intelligent\n Reflecting Surfaces

Intelligent reflecting surfaces (IRSs) have the potential to transform\nwireless communication channels into smart reconfigurable propagation\nenvironments. To realize this new paradigm, the passive IRSs have to be large,\nespecially for communication in far-field scenarios, so that they can\ncompensate for the large end-to-end path-loss, which is caused by the\nmultiplication of the individual path-losses of the transmitter-to-IRS and\nIRS-to-receiver channels. However, optimizing a large number of sub-wavelength\nIRS elements imposes a significant challenge for online transmission. To\naddress this issue, in this paper, we develop a physics-based model and a\nscalable optimization framework for large IRSs. The basic idea is to partition\nthe IRS unit cells into several subsets, referred to as tiles, model the impact\nof each tile on the wireless channel, and then optimize each tile in two\nstages, namely an offline design stage and an online optimization stage. For\nphysics-based modeling, we borrow concepts from the radar literature, model\neach tile as an anomalous reflector, and derive its impact on the wireless\nchannel for a given phase shift by solving the corresponding integral equations\nfor the electric and magnetic vector fields. In the offline design stage, the\nIRS unit cells of each tile are jointly designed for the support of different\ntransmission modes, where each transmission mode effectively corresponds to a\ngiven configuration of the phase shifts that the unit cells of the tile apply\nto an impinging electromagnetic wave. In the online optimization stage, the\nbest transmission mode of each tile is selected such that a desired\nquality-of-service (QoS) criterion is maximized. We show that the proposed\nmodeling and optimization framework can be used to efficiently optimize large\nIRSs comprising thousands of unit cells.\n