  Distributed intelligent reflecting surfaces (IRSs) deployed in multi-user
wireless communication systems promise improved system performance. However,
the signal-to-interference-plus-noise ratio (SINR) analysis and IRSs
optimization in such a system become challenging, due to the large number of
involved parameters. The system optimization can be simplified if users are
associated with IRSs, which in turn focus on serving the associated users. We
provide a practical theoretical framework for the average SINR analysis of a
distributed IRSs-assisted multi-user MISO system, where IRSs are optimized to
serve their associated users. In particular, we derive the average SINR
expression under maximum ratio transmission (MRT) precoding at the BS and
optimized reflect beamforming configurations at the IRSs. A successive
refinement (SR) method is then outlined to optimize the IRS-user association
parameters for the formulated max-min SINR problem which motivates
user-fairness. Simulations validate the average SINR analysis while confirming
the superiority of a distributed IRSs system over a centralized IRS system as
well as the gains with optimized IRS-user association as compared to random
association.
