Weighted Sum-Rate Maximization for Large-Scale RIS-Assisted Multi-User MISO Systems

We present a low-complexity algorithm for jointly designing active and passive beamforming to maximize the weighted sum-rate (WSR) in downlink RIS-assisted communication systems. We exploit an equivalent, lower-dimensional reformulation of the WSR maximization problem to derive a closed-form solution for active beamforming optimization using the successive convex approximation (SCA) framework. For passive beamforming, we propose a scaled projected gradient method (SPGM) algorithm and a novel line search technique to improve performance. Notably, we demonstrate that the complexity of the proposed method scales linearly with the number of BS antennas and RIS reflective elements. Extensive numerical experiments demonstrate that our proposed algorithm significantly reduces both run time and computational complexity, while enhancing WSR performance over known benchmarks.