Manifold-Based Sum Rate Maximization for Uplink RIS-MIMO-NOMA With Imperfect SIC

In this paper, we investigate the uplink sum rate maximization problem in an intelligent reflecting surface (IRS)-assisted multiple-input multiple-output (MIMO) non-orthogonal multiple access (NOMA) network with direct links. Modelling IRS phase shifts and user precoders on complex-circle and complex-sphere manifolds, we enforce rate and power constraints via an exact-penalty (EP) reformulation and tackle the resulting product-manifold problem using joint conjugate gradient descent (JCGD). The unconstrained variant scales linearly with the number of reflecting elements, while the rate-constrained version requires outer and inner iterations. Simulation results confirm its superiority over existing methods.