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; the first aims at minimizing the sum of users' transmit power, while the second targets maximizing the system level energy efficiency (EE). The two problems are solved by jointly optimizing the users' transmit powers and the beamforming coefficients at IRS subject to the users' individual uplink rate and transmit power constraints. A novel and low complexity algorithm is developed to optimize the IRS beamforming coefficients by optimizing the objective function over a \textit{complex circle manifold} (CCM). To efficiently optimize the IRS phase shifts over the manifold, the optimization problem is reformulated into a feasibility expansion problem which is reduced to a max-min signal-plus-interference-ratio (SINR). Then, with the aid of a smoothing technique, the exact penalty method is applied to transform the problem from constrained to unconstrained. The proposed solution is compared against three semi-definite programming (SDP)-based benchmarks which are semi-definite relaxation (SDR), SDP-difference of convex (SDP-DC) and sequential rank-one constraint relaxation (SROCR). The results show that the manifold algorithm provides better performance than the SDP-based benchmarks, and at a much lower computational complexity for both the transmit power minimization and EE maximization problems. The results also reveal that IRS-NOMA is only superior to orthogonal multiple access (OMA) when the users' target achievable rate requirements are relatively high.

翻译：本研究探讨了能量受限网络中智能反射面辅助上行非正交多址接入系统的性能。具体而言，我们构建并求解了两个优化问题：第一个问题旨在最小化用户发射功率总和，第二个问题则以最大化系统级能量效率为目标。通过联合优化用户发射功率与智能反射面波束成形系数，在满足用户个体上行速率和发射功率约束的条件下求解这两个问题。本文提出了一种新颖的低复杂度算法，通过在\textit{复圆流形}上优化目标函数来实现智能反射面波束成形系数的优化。为在流形上高效优化智能反射面相移，将优化问题重构为可行性扩展问题，进而简化为最大最小信号加干扰噪声比优化问题。随后借助平滑技术，应用精确罚函数法将约束问题转化为无约束问题。所提方法与三种基于半定规划的基准方案（半定松弛法、半定规划-凸差法、序列秩一约束松弛法）进行了对比。结果表明：对于发射功率最小化与能量效率最大化两类问题，流形算法在计算复杂度显著降低的同时，均能提供优于半定规划基准方案的性能。研究还发现，仅当用户目标可达速率要求较高时，智能反射面辅助非正交多址接入系统才优于正交多址接入系统。