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A Simple Study on the Optimality of Hybrid NOMA

Zhiguo Ding

TL;DR

The paper analyzes a two-user TDMA-downlink where a legacy OMA network coexistence motivates hybrid NOMA. By formulating a total-power minimization with per-user rate constraints and decomposing into convex subproblems and KKT conditions, it demonstrates that the first user (${\rm U}_1$) always prefers OMA and that the overall optimum aligns with conventional hybrid NOMA, even when both users have equal access to bandwidth resources. Numerical results confirm that hybrid NOMA achieves the same total power as the optimal policy and yields larger gains when channel differences are pronounced. The findings indicate hybrid NOMA’s robustness for legacy compatibility and energy efficiency in the two-user regime, with future work needed for scenarios with more users or time-varying channels.

Abstract

The key idea of hybrid non-orthogonal multiple access (NOMA) is to allow users to use the bandwidth resources to which they cannot have access in orthogonal multiple access (OMA) based legacy networks while still guaranteeing its compatibility with the legacy network. However, in a conventional hybrid NOMA network, some users have access to more bandwidth resources than others, which leads to a potential performance loss. So what if the users can access the same amount of bandwidth resources? This letter focuses on a simple two-user scenario, and develops analytical and simulation results to reveal that for this considered scenario, conventional hybrid NOMA is still an optimal transmission strategy.

A Simple Study on the Optimality of Hybrid NOMA

TL;DR

The paper analyzes a two-user TDMA-downlink where a legacy OMA network coexistence motivates hybrid NOMA. By formulating a total-power minimization with per-user rate constraints and decomposing into convex subproblems and KKT conditions, it demonstrates that the first user () always prefers OMA and that the overall optimum aligns with conventional hybrid NOMA, even when both users have equal access to bandwidth resources. Numerical results confirm that hybrid NOMA achieves the same total power as the optimal policy and yields larger gains when channel differences are pronounced. The findings indicate hybrid NOMA’s robustness for legacy compatibility and energy efficiency in the two-user regime, with future work needed for scenarios with more users or time-varying channels.

Abstract

The key idea of hybrid non-orthogonal multiple access (NOMA) is to allow users to use the bandwidth resources to which they cannot have access in orthogonal multiple access (OMA) based legacy networks while still guaranteeing its compatibility with the legacy network. However, in a conventional hybrid NOMA network, some users have access to more bandwidth resources than others, which leads to a potential performance loss. So what if the users can access the same amount of bandwidth resources? This letter focuses on a simple two-user scenario, and develops analytical and simulation results to reveal that for this considered scenario, conventional hybrid NOMA is still an optimal transmission strategy.
Paper Structure (9 sections, 24 equations, 4 figures)

This paper contains 9 sections, 24 equations, 4 figures.

Table of Contents

  1. Introduction
  2. System Model
  3. Conventional Hybrid NOMA
  4. An Extension of Hybrid NOMA
  5. Optimality of Hybrid NOMA
  6. ${\rm U}_2$ Chooses the Pure OMA Mode
  7. ${\rm U}_2$ Chooses the Hybrid NOMA Mode
  8. Numerical Results
  9. Conclusions

Figures (4)

  • Figure 1: Illustration for the three considered transmission strategies.
  • Figure 2: Total power consumption required by the three considered transmission strategies as a function of the transmit signal-to-noise ratio (SNR), denoted by $\rho$, where the order users' channel gains are obtained from two independent and identically complex Gaussian distributed random variables with zero mean and variance $\rho$.
  • Figure 3: Total power consumption required by the three considered transmission strategies as a function of the target data rate in nats per channel use (NPCU). With Case I, the ordered users' channels are obtained from two independent and identically complex Gaussian distributed random variables with zero mean and unit variance. With Case II, the variances of two random variables are $\frac{1}{2}$ and $1$, respectively.
  • Figure 4: Analysis of the optimal solution of problem \ref{['pb:3']}, where $R=3$ NPCU. In the two subfigures, two random realizations are used for the users' channels, by assuming that the ordered users' channels are obtained from two independent and identically complex Gaussian distributed random variables with zero mean and unit variance.