# Improving Performance of Far Users in Cognitive Radio: Exploiting NOMA and Wireless Power Transfer

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## Abstract

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## 1. Introduction

- Reliable transmission of AF relaying scheme required in such CR-NOMA system with a common relay and EH policy was studied. This implementation of two schemes is designed to satisfy the users’ condition in terms of channel quality with respect to the more reliable transmitted information. We intend to analyze the system performance of EH assisted CR-NOMA networks through the Rayleigh fading channels.
- The exact expressions of outage probability is presented and then throughput is further examined. From the achieved results, we analyze the effects of a number of factors including power allocation factors, transmit SNR, and the number of relays to prove the superiority of such CR NOMA model.
- As extended model, multiple relay selection in Scheme 2 is introduced in EH assisted CR NOMA to increase data rate and reliability of transmission compared to singe relay systems reported in Scheme 1. Moreover, the EH assisted CR-NOMA systems illustrate an improved performance as increasing the number of selected relays.

## 2. System Model

## 3. Performance Analysis in Scheme 1

#### 3.1. Calculation of SNR

#### 3.2. Outage and Throughput Performance Analysis

**Proposition**

**1.**

- If${\epsilon}_{PUrx1}\ge \frac{{l}_{D}}{{m}_{D}}$$$\begin{array}{c}\hfill O{P}_{out}^{PUrx1}=1.\end{array}$$
- If${\epsilon}_{PUrx1}<\frac{{l}_{D}}{{m}_{D}}$$$\begin{array}{cc}\hfill O{P}_{out}^{PUrx1}& =Pr\left({\gamma}_{x1}<{\epsilon}_{D}\right)\hfill \\ & =1-exp\left(-\frac{{\epsilon}_{PUrx1}{k}_{D}}{{\mathsf{\Omega}}_{g1}\left({l}_{D}-{m}_{D}{\epsilon}_{PUrx1}\right)}\right)\sqrt{\frac{4{\epsilon}_{PUrx1}}{{\mathsf{\Omega}}_{1}{\mathsf{\Omega}}_{g1}\left({l}_{D}-{m}_{D}{\epsilon}_{D}\right)}}{K}_{1}\left(\frac{4{\epsilon}_{PUrx1}}{{\mathsf{\Omega}}_{1}{\mathsf{\Omega}}_{g1}\left({l}_{D}-{m}_{D}{\epsilon}_{PUrx1}\right)}\right),\hfill \end{array}$$

**Proof.**

**Proposition**

**2.**

- If${\left|{g}_{2}\right|}^{2}<\frac{{\epsilon}_{SUrx1}{k}_{C}}{{l}_{C}}$$$\begin{array}{c}\hfill O{P}_{out}^{SUrx}=1.\end{array}$$
- If${\left|{g}_{2}\right|}^{2}>\frac{{\epsilon}_{SUrx1}{k}_{C}}{{l}_{C}}$$$\begin{array}{cc}\hfill O{P}_{out}^{SUrx}& =Pr\left({\gamma}_{x3}<{\epsilon}_{SUrx1}\right)\hfill \\ & =1-exp\left(-\frac{{\epsilon}_{SUrx1}{k}_{C}}{{l}_{C}{\mathsf{\Omega}}_{g2}}\right)\sqrt{\frac{4{\epsilon}_{SUrx1}}{{\mathsf{\Omega}}_{g2}{\mathsf{\Omega}}_{2}{l}_{C}}}{K}_{1}\left(\sqrt{\frac{4{\epsilon}_{SUrx1}}{{\mathsf{\Omega}}_{g2}{\mathsf{\Omega}}_{2}{l}_{C}}}\right),\hfill \end{array}$$

**Proof.**

#### 3.3. Consideration on Overall Performance in Terms of Outage Behavior and Throughput

## 4. Performance Analysis in Scheme 2

**Proposition**

**3.**

- If${\epsilon}_{PUrx1}\ge \frac{{l}_{D}}{{m}_{D}}$$$\begin{array}{c}\hfill O{P}_{out,II}^{PUrx1}=1.\end{array}$$
- If${\epsilon}_{PUrx1}<\frac{{l}_{D}}{{m}_{D}}$$$\begin{array}{c}\hfill O{P}_{out,II}^{PUrx1,k}=1-\sum _{k=1}^{K}\left(\begin{array}{c}K\hfill \\ k\hfill \end{array}\right){\left(-1\right)}^{k-1}exp\left(-\frac{k{\epsilon}_{PUrx1}{k}_{D}}{{\mathsf{\Omega}}_{g1,k}\left({l}_{D}-{\epsilon}_{PUrx1}{m}_{D}\right)}\right)\\ \hfill \times \sqrt{\frac{4k{\epsilon}_{PUrx1}}{{\mathsf{\Omega}}_{k,1}{\mathsf{\Omega}}_{g1,k}\left({l}_{D}-{\epsilon}_{PUrx1}{m}_{D}\right)}}{\mathrm{K}}_{1}\left(\frac{4k{\epsilon}_{PUrx1}}{{\mathsf{\Omega}}_{k,1}{\mathsf{\Omega}}_{g1,k}\left({l}_{D}-{\epsilon}_{PUrx1}{m}_{D}\right)}\right).\end{array}$$

**Proof.**

**Proposition**

**4.**

- If${\left|{g}_{2,k}\right|}^{2}<\frac{{\epsilon}_{SUrx}{k}_{C}}{{l}_{C}}$$$\begin{array}{c}\hfill O{P}_{out,II}^{SUrx,k}=1.\end{array}$$
- If${\left|{g}_{2,k}\right|}^{2}>\frac{{\epsilon}_{SUrx}{k}_{C}}{{l}_{C}}$$$\begin{array}{cc}\hfill O{P}_{out,II}^{SUrx,k}& =Pr\left({\gamma}_{x3,k}<{\epsilon}_{SUrx}\right)\hfill \\ & =1-\sum _{k=1}^{K}\left(\begin{array}{c}K\hfill \\ i\hfill \end{array}\right){\left(-1\right)}^{k-1}exp\left(-\frac{k{\epsilon}_{SUrx}{k}_{C}}{{l}_{C}{\mathsf{\Omega}}_{g2,k}}\right)\sqrt{\frac{4k{\epsilon}_{SUrx}}{{\mathsf{\Omega}}_{g2,k}{\mathsf{\Omega}}_{2,k}{l}_{C}}}{K}_{1}\left(\sqrt{\frac{4k{\epsilon}_{SUrx}}{{\mathsf{\Omega}}_{g2,k}{\mathsf{\Omega}}_{2,k}{l}_{C}}}\right).\hfill \end{array}$$

**Proof.**

## 5. Simulation Results

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Appendix A. Proof of Proposition 1

## Appendix B. Proof of Proposition 3

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**Figure 3.**Scheme 1: Outage performance of PUrx1 and SUrx versus transmit SNR at source when ${R}_{PUrx1}={R}_{SUrx}$ (${a}_{1}=$ 0.85, $\eta =1$).

**Figure 4.**Scheme 1: PUrx1 and SUrx and overall outage of system comparison with respect to varying both SNR and ${a}_{1}$ (${R}_{PUrx1}={R}_{SUrx}=0.3$).

**Figure 5.**Scheme 1: Outage performance of PUrx1 and SUrx under changing of ${a}_{1}^{2}$ and SNR (${R}_{PUrx1}={R}_{SUrx}=0.1$).

**Figure 8.**Scheme 2: Performance of PUrx1 and SUrx with ${a}_{1}$ as varying SNR (${R}_{PUrx1}={R}_{SUrx}$ = 0.1, $K=2$).

**Figure 10.**Comparison of two schemes and work in [14] in terms of outage performance.

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**MDPI and ACS Style**

Van Nguyen, M.-S.; Do, D.-T.; Voznak, M.
Improving Performance of Far Users in Cognitive Radio: Exploiting NOMA and Wireless Power Transfer. *Energies* **2019**, *12*, 2206.
https://doi.org/10.3390/en12112206

**AMA Style**

Van Nguyen M-S, Do D-T, Voznak M.
Improving Performance of Far Users in Cognitive Radio: Exploiting NOMA and Wireless Power Transfer. *Energies*. 2019; 12(11):2206.
https://doi.org/10.3390/en12112206

**Chicago/Turabian Style**

Van Nguyen, Minh-Sang, Dinh-Thuan Do, and Miroslav Voznak.
2019. "Improving Performance of Far Users in Cognitive Radio: Exploiting NOMA and Wireless Power Transfer" *Energies* 12, no. 11: 2206.
https://doi.org/10.3390/en12112206