Abstract: 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).

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