A Mathematical Proof of the Superiority of NOMA Compared to Conventional OMA (1612.01069v1)

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.

• The paper provides a rigorous mathematical proof demonstrating NOMA's sum rate superiority over OMA, even when both systems employ optimal resource allocation.
• It derives a closed-form solution for NOMA's optimal sum rate and proves NOMA requires lower minimum power under fairness constraints than OMA variants.
• Numerical results show NOMA enhances sum rates and lowers outage probability, with benefits increasing with more users and heterogeneous channel conditions.

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

The paper "A Mathematical Proof of the Superiority of NOMA Compared to Conventional OMA" provides a rigorous mathematical analysis to substantiate the claim that Non-Orthogonal Multiple Access (NOMA) can outperform Orthogonal Multiple Access (OMA) in terms of sum rate performance, even when optimal resource allocation is performed for both systems. While previous studies have suggested NOMA's superiority in scenarios with fixed resource allocations, this paper addresses the gap concerning the comparison under optimal resource distribution, a crucial consideration for advanced wireless communication systems.

Key Contributions and Mathematical Formulations

1. Optimization Formulation: The paper presents optimization problems for both NOMA and OMA systems, assessing user fairness by incorporating minimum rate constraints into the performance analysis. This approach ensures a comprehensive evaluation of NOMA's potential, especially in scenarios where user equity is important.
2. Closed-Form Solution for NOMA: By leveraging the power splitting strategy, the authors derive a closed-form expression for the optimal sum rate of NOMA systems. This innovation helps establish a baseline for the performance enhancement potential of NOMA when optimal power allocation is performed.
3. Contrasting NOMA with OMA Variants: The paper considers two types of OMA systems:
   • OMA-TYPE-I: OMA with optimal power allocation but fixed time/frequency allocation.
   • OMA-TYPE-II: OMA systems optimizing both power and time/frequency allocation. The manuscript meticulously proves that NOMA maintains a performance advantage over these OMA configurations, with the benefit more pronounced when channel conditions among users vary significantly.
4. Mathematical Proofs: Through rigorous mathematical derivations, the paper demonstrates that:
   • The required minimum power to support reliable transmission under fairness constraints is lower for NOMA compared to OMA-TYPE-I and OMA-TYPE-II.
   • The optimal sum rate achieved by NOMA is consistently higher than that of either OMA variant, highlighting the efficiency of using NOMA in scenarios with varying channel conditions.

Numerical Results and Implications

The authors bolster their theoretical analyses with simulations, illustrating how NOMA achieves superior ergodic sum rates and lower outage probabilities compared to OMA counterparts across different channel conditions. The results under Rayleigh fading channels notably reveal that NOMA's performance benefit augments with increased user count and heterogeneous channel conditions.

Implications and Future Directions

The findings indicate several critical implications for the design and deployment of next-generation cellular networks:

• Network Efficiency: By corroborating the spectral efficiency gains of NOMA over OMA, this paper suggests practical pathways for implementing NOMA in future communication standards, such as 5G and beyond, where resource efficiency and user fairness are prioritized.
• User Pairing and Resource Allocation Strategies: Given NOMA's performance under varying conditions, further research could explore dynamic resource allocation strategies and user pairing mechanisms that maximize these benefits in real-world deployments.
• Advanced Network Architectures: The paper sets a foundation for integrating NOMA with MIMO and other advanced transmission technologies, particularly beneficial in dense urban environments where user diversity and channel variability are prevalent.

In conclusion, this paper substantiates the potential of NOMA to significantly surpass traditional OMA in performance, even when optimal conditions are assumed for the latter, thereby laying a robust ground for further explorations into its integration into cutting-edge communication systems.