An Optimization Paradigm for Sustainable RIS-Assisted Cell-Free Networks

Abstract

—Reconfigurable intelligent surface (RIS)-assisted wireless networks offer significant performance gains; however, energy-efficiency maximization in such systems remains fundamentally challenging due to the coupled active–passive beamforming design and the fractional nature of the objective function. Existing studies typically rely on semidefinite relaxation or optimize surrogate spectral-efficiency metrics, without establishing theoretical equivalence to the original fractional formulation or providing formal convergence guarantees. This paper addresses this gap by formulating joint transmit and RIS phase optimization as a non-convex fractional program with unit-modulus constraints, which is NP-hard. We develop a unified optimization framework that integrates Dinkelbach fractional programming, a rigorously derived weighted minimum mean square error (WMMSE) reformulation, second-order cone programming (SOCP), and Riemannian manifold optimization within a provably convergent alternating structure. Unlike prior approaches, the proposed method preserves stationary-point equivalence to the original fractional objective and is proven to converge to a Karush–Kuhn–Tucker (KKT) point under standard constraint qualification conditions. A detailed per-stage computational complexity analysis is provided, together with empirical runtime evaluation. Simulation results, averaged over 1000 independent Monte Carlo realizations with 95% confidence intervals, demonstrate up to 40.9% improvement in energy efficiency compared with state-of-the-art benchmark schemes under identical system assumptions with 95% confidence interval (CI) [38 . 7% , 43 . 1%] . Sensitivity analysis further confirms robustness with respect to RIS size, user density, transmit power, and phase quantization resolution. These results establish both the theoretical soundness and practical scalability of the proposed framework for energy-efficient RIS-assisted communications.