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On the performance of downlink NOMA in underlay spectrum sharing

Vaibhav Kumar, Zhiguo Ding, Mark F. Flanagan

TL;DR

This paper analyzes downlink NOMA performance in an underlay spectrum-sharing setting with a multi-antenna secondary network, deriving closed-form average sum-rate and outage expressions under five CSI scenarios (IntICSI, IntSCSI, PowIntICSI, PowIntSCSI, One-Bit Feedback). It shows that NOMA significantly outperforms OMA in both rate and reliability, and quantifies how information loss on the ST--PR link degrades performance, especially in interference-constrained regimes; optimal power allocations are provided for the single-antenna case and extended numerically for multi-antenna users. The results offer practical insights into how CSI quality, peak-power and interference constraints, and feedback limitations shape system performance, with analytical results validated by simulations. Overall, the work demonstrates the robustness and gains of NOMA in underlay sharing and provides tractable design formulas across diverse CSI and power-budget scenarios.

Abstract

Non-orthogonal multiple access (NOMA) and spectrum sharing are two potential technologies for providing massive connectivity in beyond fifth-generation (B5G) networks. In this paper, we present the performance analysis of a multi-antenna-assisted two-user downlink NOMA system in an underlay spectrum sharing system. We derive closed-form expressions for the average achievable sum-rate and outage probability of the secondary network under a peak interference constraint and/or peak power constraint, depending on the availability of channel state information (CSI) of the interference link between secondary transmitter (ST) and primary receiver (PR). For the case where the ST has a fixed power budget, we show that performance can be divided into two specific regimes, where either the interference constraint or the power constraint primarily dictates the performance. Our results confirm that the NOMA-based underlay spectrum sharing system significantly outperforms its orthogonal multiple access (OMA) based counterpart, by achieving higher average sum-rate and lower outage probability. We also show the effect of information loss at the ST in terms of CSI of the link between the ST and PR on the system performance. Moreover, we also present closed-form expressions for the optimal power allocation coefficient that minimizes the outage probability of the NOMA system for the special case where the secondary users are each equipped with a single antenna. A close agreement between the simulation and analytical results confirms the correctness of the presented analysis.

On the performance of downlink NOMA in underlay spectrum sharing

TL;DR

This paper analyzes downlink NOMA performance in an underlay spectrum-sharing setting with a multi-antenna secondary network, deriving closed-form average sum-rate and outage expressions under five CSI scenarios (IntICSI, IntSCSI, PowIntICSI, PowIntSCSI, One-Bit Feedback). It shows that NOMA significantly outperforms OMA in both rate and reliability, and quantifies how information loss on the ST--PR link degrades performance, especially in interference-constrained regimes; optimal power allocations are provided for the single-antenna case and extended numerically for multi-antenna users. The results offer practical insights into how CSI quality, peak-power and interference constraints, and feedback limitations shape system performance, with analytical results validated by simulations. Overall, the work demonstrates the robustness and gains of NOMA in underlay sharing and provides tractable design formulas across diverse CSI and power-budget scenarios.

Abstract

Non-orthogonal multiple access (NOMA) and spectrum sharing are two potential technologies for providing massive connectivity in beyond fifth-generation (B5G) networks. In this paper, we present the performance analysis of a multi-antenna-assisted two-user downlink NOMA system in an underlay spectrum sharing system. We derive closed-form expressions for the average achievable sum-rate and outage probability of the secondary network under a peak interference constraint and/or peak power constraint, depending on the availability of channel state information (CSI) of the interference link between secondary transmitter (ST) and primary receiver (PR). For the case where the ST has a fixed power budget, we show that performance can be divided into two specific regimes, where either the interference constraint or the power constraint primarily dictates the performance. Our results confirm that the NOMA-based underlay spectrum sharing system significantly outperforms its orthogonal multiple access (OMA) based counterpart, by achieving higher average sum-rate and lower outage probability. We also show the effect of information loss at the ST in terms of CSI of the link between the ST and PR on the system performance. Moreover, we also present closed-form expressions for the optimal power allocation coefficient that minimizes the outage probability of the NOMA system for the special case where the secondary users are each equipped with a single antenna. A close agreement between the simulation and analytical results confirms the correctness of the presented analysis.

Paper Structure

This paper contains 31 sections, 8 theorems, 87 equations, 11 figures, 1 table.

Table of Contents

  1. Introduction
  2. System Model
  3. Secondary Performance for IntICSI
  4. Average achievable sum-rate
  5. Outage probability
  6. Optimal power allocation
  7. Secondary Performance for IntSCSI
  8. Average achievable sum-rate
  9. Outage probability
  10. Optimal power allocation
  11. Secondary Performance for PowIntICSI
  12. Average achievable sum-rate
  13. Outage probability
  14. Optimal power allocation
  15. Secondary Performance for PowIntSCSI
  16. ...and 16 more sections

Key Result

Theorem 1

For the case of IntICSI, the average achievable sum-rate for the NOMA system is given by Sec_IntCSI_CapClosed, shown on the next page, where $\Omega \triangleq \Omega_n \Omega_f / (\Omega_n + \Omega_f)$ and $G(\cdot)$ denotes Meijer's G-function.

Figures (11)

  • Figure 1: System model for underlay spectrum sharing. Here $U_n$ and $U_f$ are the secondary-user receivers.
  • Figure 2: Outage probability for the IntICSI and IntSCSI systems. Here solid lines are plotted using \ref{['Sec_IntCSI_OutClosed']} and \ref{['Sec_IntNoCSI_OutClosed']}. The constant-slope dotted lines show the slope of $\mathbb P_{\mathrm{out}}$ for large $I$.
  • Figure 3: Outage probability for the PowIntICSI system. The solid lines are drawn using \ref{['Sec_PowIntCSI_OutClosed']}. The tuples in the parenthesis denote $(N, P_{\mathrm{peak}})$, and the horizontal dotted lines drawn using \ref{['Sec_PowIntCSI_OutClosed_Asymptotic']} denote the asymptotic $\mathbb P_{\mathrm{out}}$ for the NOMA system.
  • Figure 4: Outage probability for the PowIntSCSI system. The solid lines are drawn using \ref{['Sec_IntNoCSI_OutClosed']} with $P_t^*$ given by \ref{['Sec_PowIntNoCSI_PtOptimal']}. The tuples in the parenthesis denote $(N, P_{\mathrm{peak}})$, and the horizontal dotted lines drawn using \ref{['Sec_PowIntNoCSI_OutClosed_Asymptotic']} denote the asymptotic $\mathbb P_{\mathrm{out}}$ for the NOMA system.
  • Figure 5: Outage probability for the PowIntOneBit system. The solid lines are drawn using \ref{['Sec_OneBit_OutClosed']}. The tuples in the parenthesis denote $(N, P_{\mathrm{peak}})$, and the horizontal dotted lines drawn using \ref{['Sec_OneBit_OutClosed_Asymptotic']} denote the asymptotic $\mathbb P_{\mathrm{out}}$ for the NOMA system.
  • ...and 6 more figures

Theorems & Definitions (15)

  • Theorem 1
  • proof
  • Theorem 2
  • proof
  • Theorem 3
  • proof
  • Theorem 4
  • proof
  • Theorem 5
  • proof
  • ...and 5 more