  In this paper, we propose an optimization framework for rate splitting (RS)
techniques in multiple-input multiple-output (MIMO) reconfigurable intelligent
surface (RIS)-assisted systems, possibly with I/Q imbalance (IQI). This
framework can be applied to any optimization problem in which the objective
and/or constraints are linear functions of the rates and/or transmit covariance
matrices. Such problems include minimum-weighted and weighted-sum rate
maximization, total power minimization for a target rate, minimum-weighted
energy efficiency (EE) and global EE maximization. The framework may be applied
to any interference-limited system with hardware impairments. For the sake of
illustration, we consider a multicell MIMO RIS-assisted broadcast channel (BC)
in which the base stations (BSs) and/or the users may suffer from IQI. Since
IQI generates improper noise, we consider improper Gaussian signaling (IGS) as
an interference-management technique that can additionally compensate for IQI.
We show that RS when combined with IGS can substantially improve the spectral
and energy efficiency of overloaded networks (i.e., when the number of users
per cell is larger than the number of transmit/receive antennas).
