Proportionally Fair Joint Power and Channel Allocation for Hybrid NOMA-OMA Downlink Systems

We consider a downlink multiuser transmission system that divides users into clusters, each cluster shares one channel using non-orthogonal multiple access (NOMA), while different clusters are assigned orthogonal channels. To achieve high system efficiency while guaranteeing fairness, we propose a joint power allocation (PA) and channel allocation (CA) framework with the proportional fairness (PF) objective, which maximizes the sum of logarithmic rates. The problem is decoupled into the PA and CA subproblems, which are solved iteratively. For the PA subproblem, we prove that although it is not convex, strong duality holds and the problem can be solved globally optimally by solving the KKT conditions. We further propose a $O(T(\log\frac{1}{\epsilon})^{2})$ time algorithm for this purpose, where $T$ is the number of users and $\epsilon$ is the tolerance threshold. The PA problem with the PF objective was considered before only for one NOMA group. When specialized to this case, our algorithm is much faster than in prior work. For the CA subproblem, we prove that it is equivalent to a bipartite graph matching problem, for which efficient solution algorithms exist. We show empirically that the proposed joint PA-CA approach performs very close to exhaustive search for small number of users. Extensive experiments demonstrate that our framework significantly outperforms several benchmark schemes in both system efficiency and fairness.