A Mathematical Proof of the Superiority of NOMA Compared to Conventional OMA

TL;DR

This paper provides a rigorous mathematical proof that NOMA consistently outperforms conventional OMA in sum rate, even with optimal resource allocation, supported by analytical derivations and simulations.

Contribution

It offers the first proof that NOMA's superiority persists under optimal resource allocation, advancing understanding of NOMA's fundamental advantages.

Findings

NOMA always outperforms OMA with optimal resource allocation

Closed-form expression for NOMA's maximum sum rate derived

Simulations confirm analytical results

Abstract

While existing works about non-orthogonal multiple access (NOMA) have indicated that NOMA can yield a significant performance gain over orthogonal multiple access (OMA) with fixed resource allocation, it is not clear whether such a performance gain will diminish when optimal resource (Time/Frequency/Power) allocation is carried out. In this paper, the performance comparison between NOMA and conventional OMA systems is investigated, from an optimization point of view. Firstly, by using the idea of power splitting, a closed-form expression for the optimum sum rate of NOMA systems is derived. Then, with rigorous mathematical proofs, we reveal the fact that NOMA can always outperform conventional OMA systems, even if both are equipped with the optimal resource allocation policies. Finally, computer simulations are conducted to validate the accuracy of the analytical results.