Performance Analysis and Energy-Efficient Optimization for Multiple Active RIS-Assisted MIMO Communication Systems

This paper investigates an uplink multi-user multiple-input multiple-output (MU-MIMO) system assisted by multiple active reconfigurable intelligent surfaces (ARISs). To analytically characterize the performance of multi-ARIS-assisted MIMO system under practical channel conditions, the operator-valued free probability theory is employed to derive closed-form expressions for the ergodic sum rate in spatially transceiver-correlated MIMO channels. Building on these expressions, an alternating optimization framework is developed to jointly design the transmit covariance matrices of the users and the phase-shift matrices of the ARISs, with the objective of maximizing the system energy efficiency (EE). The inherent non-convexity of the formulated problem is addressed by decomposing it into tractable subproblems, which are solved via the Dinkelbach algorithm and a gradient descent method. Simulation results verify the accuracy of the theoretical analysis and demonstrate that the proposed design achieves substantial EE gains and rapid convergence across a wide range of system configurations.