Complexity Reduction in RIS Optimization: A User Grouping and Adaptive Beamforming Approach

Abstract

This paper addresses a critical challenge of high computational complexity in the optimization of reconfigurable intelligent surfaces (RISs), a bottleneck that currently prevents real-time implementation in practical wireless networks. Existing iterative algorithms often exceed the channel coherence time, necessitating a shift toward insight-driven, low-complexity solutions. Specifically, we observe that the multiplicative fading nature of passive RISs means their impact is localized; thus, users strongly dominated by the direct transmit source receive negligible gains from RIS optimization. Based on this, we propose a novel User Grouping (UG) framework that categorizes users into three or two groups (3-UG and 2-UG) according to their relative direct and reflected channel strengths. By optimizing RIS operations only for relevant user subsets, we significantly limit the number of computational constraints. Furthermore, we investigate a per-user multi-stream transmission problem involving mixed-integer log-sum expressions. We derive a geometric-mean (GM)-based convex formulation to handle these discrete variables and develop a multi-step alternating optimization (AO) algorithm. Finally, we extend the UG concept to point-to-point (P2P) multiple-input multiple-output (MIMO) by introducing Adaptive Selection Beamforming (ASB), a non-iterative method that selects between two low-complexity solution sets. Numerical results demonstrate that the proposed UG methods achieve up to a 77% reduction in computational complexity compared to traditional benchmarks. Additionally, the non-iterative ASB-MIMO scheme is found to be approximately 67%–85% less complex (depending on the MIMO size) than the most efficient existing closed-form solutions. In all scenarios, the proposed frameworks maintain near-optimal performance with negligible performance degradation.