Optimal Power Allocation for Multi-Group Non-Orthogonal Multiple Access Systems

Non-orthogonal multiple access (NOMA) is recognized as a pivotal technology for enhancing spectral efficiency and facilitating massive connectivity in wireless communications. In practice, users are often divided into groups that occupy different resource blocks, while the users in the same group share the same resource through power-domain multiplexing, leading to multi-group NOMA (MG-NOMA). Hence, the full benefit of MG-NOMA relies on optimum power allocation, which, unfortunately, leads to difficult optimization problems that have not been well solved so far. This work investigates the optimal power allocation to achieve the maximum spectral efficiency and energy efficiency with quality-of-service (QoS) requirements and arbitrary user weights in MG-NOMA. We show that the complicated MG-NOMA power allocation problems can be decomposed into two layers, the lower layer for power allocation within each group and the upper layer for the power budget allocation among groups. More importantly, we reveal that, although quite difficult, the two-layer problems both contain the hidden convexity, indicating the achievability of the globally optimal solution. Then, we derive the optimal power allocation in either closed or semi-closed form for the maximum spectral efficiency and energy efficiency in MG-NOMA, respectively. The simulation results demonstrate the superiority of the proposed optimal power allocation schemes.