Unifying Sum Rate Analysis and Optimization of RIS-Assisted MU-MIMO Networks: An Operator-Valued Free Probability Approach

The fundamental performance limit of wireless systems is closely related to the transmission strategy of the transceivers as well as the wireless channels. As the channels are determined by the intrinsic characteristics of the environments, traditional system design is transceiver-centric, which adapts the transmit signals to the environments. Sharply different from the transceiver-centric design, by introducing the reconfigurable intelligent surface (RIS) into wireless systems, both the transceivers and the channels can be designed by properly adjusting the deployment of RIS panels as well as the phase-change and amplification of the RIS elements. However, as the RIS induces structural changes to the wireless channels, it is difficult to analyze and optimize the RIS-assisted systems in a unified framework. In this paper, we adopt the operatorvalued free probability theory to analyze the ergodic sum rate of an uplink MU-MIMO communication systems assisted by multiple cascaded RIS panels, where the sum rate is derived for rather generic system configurations, allowing arbitrary number of transceivers' antennas, number of RIS panels, and a generic fading model. The obtained sum rate expression also enables a unified optimization framework that jointly designs the multi-antenna transceivers and the RIS configurations. Finally, numerical results are provided to verify the accuracy of the derived ergodic sum rate, and to show the performance of the joint optimization algorithms.