Globally Optimal Max-Min Rate Joint Channel and Power Allocation for Hybrid NOMA-OMA Downlink Systems

This work proposes a globally optimal solution algorithm to the joint power allocation (PA) and channel allocation (CA) problem for downlink hybrid NOMA-OMA systems with the objective of maximizing the minimum user rate. In the hybrid NOMA-OMA scenario, the users are divided into clusters, each cluster shares one channel using NOMA (Non-Orthogonal Multiple Access), while different clusters are assigned channels orthogonally. The optimization problem is converted to the problem of maximizing the user rate under the constraint that all rates be equal. It is further decomposed into PA and CA subproblems, which are solved iteratively. The PA subproblem is handled by first deriving an analytical expression of the total power as a function of the common user rate, and then solving it via bisection search. The CA subproblem keeps the equal-rate assignment fixed and aims to find the CA that minimizes the total power. We prove that the CA subproblem is equivalent to a minimum bipartite graph matching problem, for which efficient algorithms exist. Finally, we demonstrate that the proposed iterative algorithm converges to the globally optimal solution after a finite number of iterations. In addition, we prove that the number of iterations is at most three when the power budget is sufficiently large. Extensive experiments demonstrate the effectiveness of the proposed scheme.