  In this paper, we study the performance of reconfigurable intelligent
surfaces (RISs) in a multicell broadcast channel (BC) that employs improper
Gaussian signaling (IGS) jointly with non-orthogonal multiple access (NOMA) to
optimize either the minimum-weighted rate or the energy efficiency (EE) of the
network. We show that although the RIS can significantly improve the system
performance, it cannot mitigate interference completely, so we have to employ
other interference-management techniques to further improve performance. We
show that the proposed NOMA-based IGS scheme can substantially outperform
proper Gaussian signaling (PGS) and IGS schemes that treat interference as
noise (TIN) in particular when the number of users per cell is larger than the
number of base station (BS) antennas (referred to as overloaded networks). In
other words, IGS and NOMA complement to each other as interference management
techniques in multicell RIS-assisted BCs. Furthermore, we consider three
different feasibility sets for the RIS components showing that even a RIS with
a small number of elements provides considerable gains for all the feasibility
sets.
