  This paper studies an intelligent reflecting surface (IRS)-aided
multi-antenna simultaneous wireless information and power transfer (SWIPT)
system where an $M$-antenna access point (AP) serves $K$ single-antenna
information users (IUs) and $J$ single-antenna energy users (EUs) with the aid
of an IRS with phase errors. We explicitly concentrate on overloaded scenarios
where $K + J > M$ and $K \geq M$. Our goal is to maximize the minimum
throughput among all the IUs by optimizing the allocation of resources
(including time, transmit beamforming at the AP, and reflect beamforming at the
IRS), while guaranteeing the minimum amount of harvested energy at each EU.
Towards this goal, we propose two user grouping (UG) schemes, namely, the
non-overlapping UG scheme and the overlapping UG scheme, where the difference
lies in whether identical IUs can exist in multiple groups. Different IU groups
are served in orthogonal time dimensions, while the IUs in the same group are
served simultaneously with all the EUs via spatial multiplexing. The two
problems corresponding to the two UG schemes are mixed-integer non-convex
optimization problems and difficult to solve optimally. We propose efficient
algorithms for these two problems based on the big-M formulation, the penalty
method, the block coordinate descent, and the successive convex approximation.
Simulation results show that: 1) the non-robust counterparts of the proposed
robust designs are unsuitable for practical IRS-aided SWIPT systems with phase
errors since the energy harvesting constraints cannot be satisfied; 2) the
proposed UG strategies can significantly improve the max-min throughput over
the benchmark schemes without UG or adopting random UG; 3) the overlapping UG
scheme performs much better than its non-overlapping counterpart when the
absolute difference between $K$ and $M$ is small and the EH constraints are not
stringent.
