Optimization of Energy-Constrained IRS-NOMA Using a Complex Circle Manifold Approach

This work investigates the performance of intelligent reflective surfaces (IRSs) assisted uplink non-orthogonal multiple access (NOMA) in energy-constrained networks. Specifically, we formulate and solve two optimization problems, one for minimizing the users' sum transmit power and another for maximizing the energy efficiency (EE) of the system. The two problems are solved by jointly optimizing the users' transmit powers and the passive beamforming coefficients at the IRS reflectors subject to the users' individual uplink rate constraints. A novel algorithm is developed to optimize the IRS passive beamforming coefficients by optimizing the objective function over the \textit{complex circle manifold} (CCM), exploiting the manifold optimization technique. The proposed manifold optimization-based solution is bench-marked against the rather \textit{standard} semi-definite relaxation method (SDR). The results show that the manifold optimization-based algorithm achieves significantly better performance for both transmit power minimization and EE maximization problems at a computational complexity lower than the SDR approach. The results also reveal that IRS-NOMA is superior to the orthogonal multiple access (OMA) counterpart only when the users' target achievable rate requirements are relatively high.