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NOMA-Based Cooperative Relaying with Receive Diversity in Nakagami-m Fading Channels

Vaibhav Kumar, Barry Cardiff, Mark F Flanagan

TL;DR

This work analyzes NOMA-based cooperative relaying with receive diversity under Nakagami-$m$ fading, deriving closed-form ergodic-rate and outage expressions for SC and MRC receivers, along with high-SNR approximations. It reveals that CRS-NOMA with receive diversity outperforms CRS-OMA even in the low-SNR regime and proves that the system achieves full diversity order dependent on the Nakagami shape parameter $m$ and the number of receive antennas. The study also optimizes power allocation to minimize outage and demonstrates a 0.5 slope in the high-SNR ergodic-rate growth for both SC and MRC, providing practical design insights for B5G networks. The results are validated via tight numerical agreement, underscoring the potential of receive-diverse CRS-NOMA for enhanced spectral efficiency with Nakagami-$m$ fading.

Abstract

Non-orthogonal multiple access (NOMA) is being widely considered as a potential candidate to enhance the spectrum utilization in beyond fifth-generation (B5G) communications. In this paper, we derive closed-form expressions for the ergodic rate and outage probability of a multiple-antenna-assisted NOMA-based cooperative relaying system (CRS-NOMA). We present the performance analysis of the system for two different receive diversity schemes - selection combining (SC) and maximal-ratio combining (MRC), in Nakagami-m fading. We also evaluate the asymptotic behavior of the CRS-NOMA to determine the slope of the ergodic rate and diversity order. Our results show that in contrast to the existing CRS-NOMA systems, the CRS-NOMA with receive diversity outperforms its orthogonal multiple access (OMA) based counterpart even in the low-SNR regime, by achieving higher ergodic rate. Diversity analysis confirms that the CRS-NOMA achieves full diversity order using both SC and MRC schemes, and this diversity order depends on both the shape parameter m and the number of receive antennas. We also discuss the problem of optimal power allocation for the minimization of the outage probability of the system, and subsequently use this optimal value to obtain the ergodic rate. An excellent match is observed between the numerical and the analytical results, confirming the correctness of the derived analytical expressions.

NOMA-Based Cooperative Relaying with Receive Diversity in Nakagami-m Fading Channels

TL;DR

This work analyzes NOMA-based cooperative relaying with receive diversity under Nakagami- fading, deriving closed-form ergodic-rate and outage expressions for SC and MRC receivers, along with high-SNR approximations. It reveals that CRS-NOMA with receive diversity outperforms CRS-OMA even in the low-SNR regime and proves that the system achieves full diversity order dependent on the Nakagami shape parameter and the number of receive antennas. The study also optimizes power allocation to minimize outage and demonstrates a 0.5 slope in the high-SNR ergodic-rate growth for both SC and MRC, providing practical design insights for B5G networks. The results are validated via tight numerical agreement, underscoring the potential of receive-diverse CRS-NOMA for enhanced spectral efficiency with Nakagami- fading.

Abstract

Non-orthogonal multiple access (NOMA) is being widely considered as a potential candidate to enhance the spectrum utilization in beyond fifth-generation (B5G) communications. In this paper, we derive closed-form expressions for the ergodic rate and outage probability of a multiple-antenna-assisted NOMA-based cooperative relaying system (CRS-NOMA). We present the performance analysis of the system for two different receive diversity schemes - selection combining (SC) and maximal-ratio combining (MRC), in Nakagami-m fading. We also evaluate the asymptotic behavior of the CRS-NOMA to determine the slope of the ergodic rate and diversity order. Our results show that in contrast to the existing CRS-NOMA systems, the CRS-NOMA with receive diversity outperforms its orthogonal multiple access (OMA) based counterpart even in the low-SNR regime, by achieving higher ergodic rate. Diversity analysis confirms that the CRS-NOMA achieves full diversity order using both SC and MRC schemes, and this diversity order depends on both the shape parameter m and the number of receive antennas. We also discuss the problem of optimal power allocation for the minimization of the outage probability of the system, and subsequently use this optimal value to obtain the ergodic rate. An excellent match is observed between the numerical and the analytical results, confirming the correctness of the derived analytical expressions.

Paper Structure

This paper contains 16 sections, 4 theorems, 44 equations, 8 figures.

Table of Contents

  1. INTRODUCTION
  2. System Model
  3. CRS-NOMA with SC
  4. Ergodic rate
  5. High-SNR approximation of the ergodic rate
  6. Outage probability
  7. Diversity analysis
  8. CRS-NOMA with MRC
  9. Ergodic rate
  10. High-SNR approximation of the ergodic rate
  11. Outage probability
  12. Diversity analysis
  13. Results and Discussion
  14. Conclusion
  15. Proof of Theorem \ref{['Theorem-SC_Cs1']}
  16. ...and 1 more sections

Key Result

Theorem 1

A closed-form expression for the ergodic rate for symbol $s_1$ in Nakagami-$m$ fading using SC in CRS-NOMA is given by C_s1_SC_Closed_Nak, shown on the next page, where $\tau = \sum_{\mu = 0}^{m_{sr} - 1} \mu k_{\mu + 1}$, $\omega = \sum_{\nu = 0}^{m_{sd} - 1} \nu l_{\nu + 1}$, $\Psi_{k_0, l_0}~=~\f

Figures (8)

  • Figure 1: System model for CRS-NOMA with multiple receive antennas.
  • Figure 2: Outage probability for CRS-NOMA. Here solid lines represent the analytical results, and the value of $N$ and $m$ are indicated in the form $(N, m)$.
  • Figure 3: Optimal value of $a_2$ to minimize the outage probability of CRS-NOMA with SC for $m = 2$, $N = 2$ and $\rho = 2$ dB.
  • Figure 4: Optimal value of $a_2$ to minimize the outage probability of CRS-NOMA with SC for $m = 2$, $N = 2$ and $\rho = 20$ dB.
  • Figure 5: Ergodic rate for $m = 2$ and different values of $N$. The analytical results are represented using solid lines.
  • ...and 3 more figures

Theorems & Definitions (8)

  • Theorem 1
  • proof
  • Proposition 1
  • proof
  • Theorem 2
  • proof
  • Proposition 2
  • proof