  In this paper, the adoption of an intelligent reflecting surface (IRS) for
multiple single-antenna source terminal (ST)-DT pairs in two-hop networks is
investigated. Different from the previous studies on IRS that merely focused on
tuning the reflection coefficient of all the reflection elements at IRS, in
this paper, we consider the true reflection resource management. Specifically,
the true reflection resource management can be realized via trigger module
selection based on our proposed IRS architecture that all the reflection
elements are partially controlled by multiple parallel switches of controller.
As the number of reflection elements increases, the true reflection resource
management will become urgently needed in this context, which is due to the
non-ignorable energy consumption. Moreover, the proposed modular architecture
of IRS is designed to make the reflection elements part independent and
controllable. As such, our goal is to maximize the minimum
signal-to-interference-plus-noise ratio (SINR) at DTs via a joint trigger
module subset selection, transmit power allocation of STs, and the
corresponding passive beamforming of the trigger modules, subject to per ST
power budgets and module size constraint. Whereas this problem is NP-hard due
to the module size constraint, to deal with it, we transform the hard module
size constraint into the group sparse constraint by introducing the mixed row
block norm, which yields a suitable semidefinite relaxation. Additionally, the
parallel alternating direction method of multipliers (PADMM) is proposed to
identify the trigger module subset, and then subsequently the transmit power
allocation and passive beamforming can be obtained by solving the original
minimum SINR maximization problem without the group sparse constraint via
partial linearization for generalized fractional programs.
