Optimal Power Allocation in Downlink Multicarrier NOMA Systems: Theory and Fast Algorithms

In this work, we address the problem of finding globally optimal power allocation strategies to maximize the users sum-rate (SR) as well as system energy efficiency (EE) in the downlink of single-cell multicarrier non-orthogonal multiple access (MC-NOMA) systems. Each NOMA cluster includes a set of users in which the well-known superposition coding (SC) combined with successive interference cancellation (SIC) technique is applied among them. By obtaining the closed-form expression of intra-cluster power allocation, we show that MC-NOMA can be equivalently transformed to a virtual orthogonal multiple access (OMA) system, where the effective channel gain of these virtual OMA users is obtained in closed-form. Then, the SR and EE maximization problems are solved by using very fast water-filling and Dinkelbach algorithms, respectively. The equivalent transformation of MC-NOMA to the virtual OMA system brings new theoretical insights, which are discussed throughout the paper. The extensions of our analysis to other scenarios, such as considering users rate fairness, admission control, long-term performance, and a number of future next-generation multiple access (NGMA) schemes enabling recent advanced technologies, e.g., reconfigurable intelligent surfaces are discussed. Extensive numerical results are provided to show the performance gaps between single-carrier NOMA (SC-NOMA), OMA-NOMA, and OMA.