Fairness-oriented Joint Channel and Power Allocation for Hybrid NOMA-OMA Downlink Systems

Abstract

Hybrid NOMA-OMA (HMA) systems divide users into clusters, each cluster sharing one channel using non-orthogonal multiple access (NOMA), while different clusters are assigned orthogonal channels using orthogonal multiple access (OMA). Both system efficiency and fairness are important service objectives that should be considered in the design of HMA systems. However, they have conflicting objectives. An optimization criterion that strikes a balance between fairness and system efficiency in multi-user networks is proportional fairness (PF). On the other hand, the max-min rate (MMR) criterion aims at maximizing the minimum rate to achieve the highest degree of fairness. This dissertation introduces novel algorithms for optimal power allocation (PA), channel allocation (CA), and joint power and channel allocation (JPCA) in downlink hybrid NOMA-OMA (DHMA) systems, under the PF and MMR criteria. One of the main contributions of this dissertation is a globally optimal solution to the JPCA problem for DHMA systems under the MMR criterion. To the best of our knowledge, this is the first time the problem has been solved globally optimally. The optimization problem is first converted to the problem of maximizing the user rates while ensuring equal rates across all users and next it is decomposed into PA and CA subproblems, which are solved iteratively. The PA subproblem is addressed by deriving an analytical expression of the total power as a function of the common user rate and is solved via a bisection search. The CA subproblem is converted to a bipartite graph matching problem and is solved using known algorithms. It is further proved that the proposed JPCA algorithm converges to the globally optimal solution within a finite number of iterations, which equals at most three when the power budget is sufficiently large. In addition, for the flat fading case (where the CA problem reduces to user clustering), it is proven that the generalized Best Strong user with the Best Weak user (BSBW) clustering strategy is optimal under the MMR criterion. The dissertation also addresses the JPCA problem under the sum of logarithmic rates (sum-log-rate) criterion, aligning with the PF objective for DHMA systems. To the best of our knowledge, this is the first time this problem has been addressed. The problem is decoupled into 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 KarushKuhn-Tucker (KKT) conditions. Furthermore, we propose an efficient globally optimal solution algorithm to solve the KKT conditions. When specialized to a single NOMA group, our PA algorithm is proved to be significantly faster than previous approaches. The CA subproblem is proved to be equivalent to a maximum weight matching problem in a bipartite graph, for which optimal solution algorithms are known. The proposed JPCA algorithm performs very close to the global optimum achieved by the exhaustive search (ES). For the flat fading scenario with two users per channel, we prove that the BSBW pairing strategy is optimal, and therefore, we can also obtain a globally optimal solution to the JPCA problem with the sum-log-rate criterion for this special case. The experimental results demonstrate significant improvements in the proposed JPCA solutions over benchmark DHMA schemes in both fairness and system throughput.