[Paper Review] Optimal Power Allocation Scheme for Non-Orthogonal Multiple Access with $α$-Fairness

Peng Xu, Kanapathippillai Cumanan|arXiv (Cornell University)|Aug 3, 2017

Advanced Wireless Communication Technologies35 references4 citations

TL;DR

This paper proposes an optimal power allocation scheme for non-orthogonal multiple access (NOMA) systems under α-fairness constraints, enabling flexible trade-offs between spectral efficiency and user fairness. Using both statistical and perfect channel state information at the transmitter (CSIT), it formulates sum-throughput maximization problems and develops a simple alternate optimization (AO) algorithm that achieves optimal performance, demonstrating NOMA's significant spectral gain over conventional orthogonal MA across all fairness levels.

ABSTRACT

This paper investigates the optimal power allocation scheme for sum throughput maximization of non-orthogonal multiple access (NOMA) system with $α$-fairness. In contrast to the existing fairness NOMA models, $α$-fairness can only utilize a single scalar to achieve different user fairness levels. Two different channel state information at the transmitter (CSIT) assumptions are considered, namely, statistical and perfect CSIT. For statistical CSIT, fixed target data rates are predefined, and the power allocation problem is solved for sum throughput maximization with $α$-fairness, through characterizing several properties of the optimal power allocation solution. For perfect CSIT, the optimal power allocation is determined to maximize the instantaneous sum rate with $α$-fairness, where user rates are adapted according to the instantaneous channel state information (CSI). In particular, a simple alternate optimization (AO) algorithm is proposed, which is demonstrated to yield the optimal solution. Numerical results reveal that, at the same fairness level, NOMA significantly outperforms the conventional orthogonal multiple access (MA) for both the scenarios with statistical and perfect CSIT.

Motivation & Objective

• To address the limitation of existing NOMA fairness models that either enforce absolute fairness or require complex weighting vectors.
• To enable a unified, scalable fairness mechanism using a single scalar α to control the efficiency-fairness trade-off.
• To design an optimal power allocation scheme that maximizes sum throughput under α-fairness constraints for both statistical and perfect CSIT scenarios.
• To develop a low-complexity, convergent alternate optimization (AO) algorithm for the perfect CSIT case.

Proposed method

• Formulates sum-throughput maximization under α-fairness as a constrained optimization problem for both statistical and perfect CSIT assumptions.
• Characterizes the optimal power allocation solution for statistical CSIT by deriving key properties of the Karush-Kuhn-Tucker (KKT) conditions.
• Proposes a simple alternate optimization (AO) algorithm for the perfect CSIT case, iteratively updating power allocations to converge to the optimal solution.
• Uses function $ f_{2,K-1}(x) $ and recursive relations involving $ \tilde{c}_k^{(t)} $ and $ \tilde{\tilde{c}}_k^{(t)} $ to prove monotonic convergence of the AO algorithm.
• Employs reduction to absurdity and inductive reasoning to mathematically prove that the power allocation vector increases monotonically across iterations.
• Validates the optimality and convergence of the AO algorithm through rigorous theoretical proofs in Appendices D–F.

Experimental results

Research questions

• RQ1 How can α-fairness be effectively applied to NOMA systems to enable a continuous trade-off between spectral efficiency and user fairness?
• RQ2 What is the optimal power allocation policy for NOMA under α-fairness when only statistical CSIT is available?
• RQ3 Can a low-complexity, convergent algorithm be designed for optimal power allocation under perfect CSIT in NOMA with α-fairness?
• RQ4 How does the proposed NOMA scheme with α-fairness compare to conventional orthogonal MA in terms of sum throughput and fairness?

Key findings

• The proposed NOMA scheme with α-fairness achieves significantly higher sum throughput than conventional orthogonal multiple access (MA) across all fairness levels, particularly under both statistical and perfect CSIT.
• The alternate optimization (AO) algorithm converges to the optimal solution for the perfect CSIT case, as proven via inductive and contradiction-based arguments in the theoretical analysis.
• For statistical CSIT, the optimal power allocation is derived by characterizing the KKT conditions, ensuring that users with poorer channel gains receive higher power allocation.
• The AO algorithm exhibits monotonic convergence in power allocation, with each user’s power increasing iteratively until convergence.
• Numerical results confirm that NOMA with α-fairness outperforms conventional MA in both ergodic sum rate and outage capacity, especially at moderate to high fairness levels (α > 1).
• The use of a single scalar α to control fairness enables a unified and scalable framework, avoiding the need for complex weighting vectors as in prior work.