# Multiple Access-Enabled Relaying with Piece-Wise and Forward NOMA: Rate Optimization under Reliability Constraints

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## Abstract

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## 1. Introduction

**PF-NOMA**: We propose a PF-NOMA scheme—NOMA-based cooperative relaying scheme using PF protocol—for a coexisting primary–secondary IoT setup, and develop rate formulations for the two systems considering their cooperation time and power allocations within a time slot under the adaptive threshold of PF protocol.**Rate optimization under reliability constraints**: We formulate a rate maximization problem for the secondary link under reliability (i.e., guaranteed rate) constraints of both the primary and secondary links. We obtain the optimal time splitting and power splitting factors by decomposing the original optimization problem into two sub-problems leading to closed-form feasible boundary regions and developing an algorithm.**Results**: Based on extensive simulations, our analysis shows that, using the PF-NOMA scheme with optimal time-/power-splitting, the secondary link can achieve a higher rate than the baseline approaches (i.e., AF-NOMA and DF-NOMA). Moreover, PF-NOMA provides a higher degree-of-freedom in relay-location selections to support the primary and secondary rate requirements compared to the baseline schemes.

## 2. System Model

#### 2.1. PF-NOMA

#### 2.2. Deriving SNR at the Receivers for PF-NOMA

#### 2.3. Rate Regions for PF-NOMA Protocol

## 3. Maximizing Rate at the Secondary Receiver

#### 3.1. Solving OP-1

#### 3.2. Solving OP-2

#### 3.2.1. $\left|\mathfrak{R}\right({y}_{PS}\left)\right|\ge \Gamma $

#### 3.2.2. $\left|\mathfrak{R}\right({y}_{ps}\left)\right|<\Gamma $

#### 3.3. Optimal Rate from OP-1 and OP-2

Algorithm 1. Optimization Algorithm for PF-NOMA |

## 4. Analytical Results

#### 4.1. Rate Regions

#### 4.2. Secondary Rate Maximization

#### 4.3. Implementation Considerations of PF-NOMA

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Appendix A

## Appendix B

## Appendix C

## Appendix D

## References

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**Figure 1.**The cooperative network consisted of a primary user and secondary user. The secondary transmitter used PF as a relaying protocol.

**Figure 4.**Achievable rate at the secondary receiver (${R}_{s}$) versus achievable rate at the primary receiver (${R}_{p}$) for PF-NOMA, AF-NOMA, and DF-NOMA schemes at different locations of the secondary transmitter.

**Figure 5.**Maximizing rate at the second receiver (SR) by finding the optimum value for time fraction ($\beta $) and power fraction ($\omega $) in the PF-NOMA protocol.

**Figure 6.**Maximizing rate at the second receiver (SR) by finding the optimum value for time fraction ($\beta $) and power fraction ($\omega $) in the AF-NOMA protocol.

**Figure 7.**Maximizing rate at the second receiver (SR) by finding the optimum value for time fraction ($\beta $) and power fraction ($\omega $) in the DF-NOMA protocol.

**Figure 8.**A comparison of the locations that PF-NOMA, DF-NOMA and AF-NOMA can cover for the rate greater than or equal to 0.5 bit/s/Hz at the second receiver (SR).

Condition | Constraint | ||
---|---|---|---|

${\mathbf{R}}_{\mathbf{s}}\ge {\mathbf{R}}_{\mathbf{0}}$ | ${\mathbf{R}}_{\mathbf{p}}\ge {\mathbf{R}}_{\mathbf{m}}$ | $\mathbf{0}<\mathbf{\beta}<\mathbf{1}$ | |

${C}_{1}$ | $\beta \le 1-{\displaystyle \frac{{R}_{0}}{{log}_{2}(1+{\gamma}_{22})}}$ | $\beta \ge {\displaystyle \frac{{R}_{m}-{v}_{2}}{{v}_{1}-2{v}_{2}}}$ | $0<\beta <\frac{1}{2}$ |

${C}_{2}$ | − | $\beta \le {\displaystyle \frac{{R}_{m}-{v}_{2}}{{v}_{1}-2{v}_{2}}}$ | − |

${C}_{3}$ | − | $\beta \ge {\displaystyle \frac{{R}_{m}+{v}_{3}-{v}_{1}}{2{v}_{3}-{v}_{1}}}$ | $\frac{1}{2}\le \beta <1$ |

${C}_{4}$ | − | $\beta \le {\displaystyle \frac{{R}_{m}+{v}_{3}-{v}_{1}}{2{v}_{3}-{v}_{1}}}$ | − |

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**MDPI and ACS Style**

Khodakhah, F.; Mahmood, A.; Österberg, P.; Gidlund, M.
Multiple Access-Enabled Relaying with Piece-Wise and Forward NOMA: Rate Optimization under Reliability Constraints. *Sensors* **2021**, *21*, 4783.
https://doi.org/10.3390/s21144783

**AMA Style**

Khodakhah F, Mahmood A, Österberg P, Gidlund M.
Multiple Access-Enabled Relaying with Piece-Wise and Forward NOMA: Rate Optimization under Reliability Constraints. *Sensors*. 2021; 21(14):4783.
https://doi.org/10.3390/s21144783

**Chicago/Turabian Style**

Khodakhah, Farnaz, Aamir Mahmood, Patrik Österberg, and Mikael Gidlund.
2021. "Multiple Access-Enabled Relaying with Piece-Wise and Forward NOMA: Rate Optimization under Reliability Constraints" *Sensors* 21, no. 14: 4783.
https://doi.org/10.3390/s21144783