  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 applicable for the arbitrary
times of reflections, 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 the IRS network with different network topologies, 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 are
under a K-fold improvement given K-piece IRS.
