  Intelligent reflecting surface (IRS) is deemed as a promising solution to
improve the spectral and energy efficiency of wireless communications
cost-effectively. In this paper, we consider a wireless network where multiple
base stations (BSs) serve their respective users with the aid of distributed
IRSs in the downlink communication. Specifically, each IRS assists in the
transmission from its associated BS to user via passive beamforming, while in
the meantime, it also randomly scatters the signals from other co-channel BSs,
thus resulting in additional signal as well as interference paths in the
network. As such, a new IRS-user/BS association problem arises pertaining to
optimally balance the passive beamforming gains from all IRSs among different
BS-user communication links. To address this new problem, we first derive a
tractable lower bound of the average signal-to-interference-plus-noise ratio
(SINR) at the receiver of each user, termed
average-signal-to-average-interference-plus-noise ratio (ASAINR), based on
which two ASAINR balancing problems are formulated to maximize the minimum
ASAINR among all users by optimizing the IRS-user associations without and with
BS transmit power control, respectively. We also characterize the scaling
behavior of user ASAINRs with the increasing number of IRS reflecting elements
to investigate the different effects of IRS-reflected signal versus
interference power. Moreover, to solve the two ASAINR balancing problems that
are both non-convex optimization problems, we propose an optimal solution to
the problem without BS power control and low-complexity suboptimal solutions to
both problems by applying the branch-and-bound method and exploiting new
properties of the IRS-user associations, respectively. Numerical results verify
our performance analysis and also demonstrate significant performance gains of
the proposed solutions over benchmark schemes.
