Uplink Sum-Rate Optimization in RIS-Assisted NOMA Systems via Conjugate Gradient Descent Method

With the evolution toward 6G wireless networks, new technologies such as reconfigurable intelligent surfaces (RIS) and non-orthogonal multiple access (NOMA) are considered to meet increasing demands for spectral efficiency, connectivity, and network reconfigurability. This paper investigates the uplink sum-rate optimization problem in RIS-assisted power-domain NOMA systems. We consider a scenario where a direct line-of-sight path between users and the base station (BS) is blocked, and communication is enabled exclusively via a passive RIS. The goal is to design the RIS phase shifts to maximize the achievable sum-rate under unit-modulus constraints, which leads to a challenging non-convex optimization problem with coupled variables. To address this, we propose an alternating optimization (AO) strategy, where RIS configurations are optimized for one user at a time while keeping others fixed. Each subproblem is tackled using a phase-only conjugate gradient method (CGM), adapted from adaptive array processing theory. This method preserves the phase-only constraint while iteratively maximizing the user-specific signal-to-interference-plus-noise ratio (SINR). Simulation results demonstrate that the proposed AO-CGM approach outperforms conventional strategies in terms of sum-rate and user fairness, while offering a practical and scalable solution for future 6G networks.