Intelligent Reflecting Surface Networks with Multi-Order-Reflection Effect: System Modelling and Critical Bounds

Abstract

In this paper, we model, analyze and optimize the multi-user and multi-order-reflection (MUMOR) intelligent reflecting surface (IRS) networks. We first derive a complete MUMOR IRS network model that is applicable for arbitrary times of reflections, arbitrary size and number of IRSs/reflectors. The optimal condition for achieving sum-rate upper bound with one IRS in a closed-form function and the analytical condition to achieve interference-free transmission, are derived respectively. Leveraging this optimal condition, we obtain the MUMOR sum-rate upper bound of IRS network with different network topology, where the linear graph (LG), complete graph (CG) and null graph (NG) topologies are considered. Simulation results verify our theories and derivations and demonstrate that the sum-rate upper bounds of different network topologies is under a 𝐾-fold improvement given 𝐾-piece IRS.