Simplified Capacity Formulation and Phase Optimization in Large RIS-Aided MIMO Systems

Reconfigurable Intelligent Surface (RIS) technology is designed to improve channel propagation and, in turn, the performance of wireless communication systems. The extent of the improvement heavily relies on the phase shift optimization, a.k.a. passive beamforming design, at the RIS. This paper proposes novel approaches for simplifying this process in large RIS-aided multiple-input multiple-output (MIMO), a.k.a. MIMO-RIS, systems. More specifically, we derive two novel simplified closed-form approximations (CFAs) of the MIMO-RIS capacity expression in the large number of elements/antennas asymptotic regime and identify various scenarios for which they tightly approximate the classic MIMO-RIS capacity expression. We then design two novel simplified RIS phase optimization algorithms for lossless and practical metasurfaces with reduced computational complexity. We also demonstrate that, in certain practical scenarios, very simple guidelines can be used for setting the phases of MIMO-RIS systems. Numerical evaluations validate the accuracy of our CFAs and simplified RIS phase-shift optimization algorithms. They also show that our simplified approaches can deliver either similar or even better capacity performance than existing methods, especially for practical metasurfaces, in various scenarios.