# Energy-Efficient Secure Communications for Wireless-Powered Cognitive Radio Networks

## Abstract

**:**

## 1. Introduction

## 2. System Model and Problem Statement

## 3. Energy-Efficient Transmit Power Control Algorithm

Algorithm 1 Proposed energy-efficient transmit power control algorithm. |

1:$$Initialize $\overrightarrow{p}$, $\overrightarrow{\lambda}$, $\overrightarrow{\mu}$, and $\overrightarrow{\kappa}$ randomly 2:$$ repeat3:$$Set $\overrightarrow{x}={\overrightarrow{r}}^{s}/{\overrightarrow{p}}^{\mathrm{CE}}$ 4:$$ repeat5:$$${\overrightarrow{p}}_{\mathrm{old}}\leftarrow \overrightarrow{p}$ 6:$$ for $i=1$ to N9:$$ end for10:$$$\overrightarrow{p}=\{{p}_{1},{p}_{2},\cdots ,{p}_{N}\}$ 11:$$ until $\parallel \overrightarrow{p}-{\overrightarrow{p}}_{\mathrm{old}}\parallel <\u03f5$12:$$Update ${\overrightarrow{r}}^{s}$ and ${\overrightarrow{p}}^{\mathrm{CE}}$ with $\overrightarrow{p}$ 13: until $\parallel {\overrightarrow{r}}^{s}-\overrightarrow{x}{\overrightarrow{p}}^{\mathrm{CE}}\parallel <\delta $ |

## 4. Simulation Results and Discussion

- Optimal scheme: under the assumption of perfect channel state information (CSI), the near-optimal performance can be determined by brute-force search, in which all combinations are evaluated by quantizing $\overrightarrow{p}$ into $M=100$ equally spaced values. Therefore, the computational complexity of this scheme increases exponentially with N, i.e., $O\phantom{\rule{-0.166667em}{0ex}}\left({M}^{N}\right)$.
- Proposed scheme: the transmit powers of SU Txs are determined using Algorithm 1.
- SR max. scheme: the transmit powers of SU Txs are determined to maximize the average SR, $\frac{1}{N}{\sum}_{i\in \mathbb{N}}{r}_{i}^{s}$, which is determined by brute-force search.
- On–off scheme [21]: the transmit powers of SU Txs are determined to be either ${P}_{\mathrm{max}}$ or 0 so as to maximize the average SEE.
- Equally reduced power (ERP) scheme [22]: all SU Txs use the same transmit power that maximizes the average SEE while satisfying all constraints, and the optimal value of the transmit power is determined by one-dimensional brute-force search.
- Max. power scheme: the transmit powers of SU Txs are determined as ${P}_{\mathrm{max}}$.

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Haykin, S. Cognitive radio: Brain-empowered wireless communications. IEEE J. Sel. Commun.
**2005**, 23, 201–220. [Google Scholar] [CrossRef] - Xie, S.; Liu, Y.; Zhang, Y.; Yu, R. A parallel cooperative spectrum sensing in cognitive radio networks. IEEE Trans. Veh. Technol.
**2010**, 59, 4079–4092. [Google Scholar] [CrossRef] - Ji, Z.; Liu, K.J.R. Dynamic spectrum sharing: A game theoretical overview. IEEE Commun. Mag.
**2007**, 45, 88–94. [Google Scholar] [CrossRef] [Green Version] - Cheng, S.; Ao, W.C.; Chen, K. Efficiency of a cognitive radio link with opportunistic interference mitigation. IEEE Trans. Wirel. Commun.
**2011**, 10, 1715–1720. [Google Scholar] [CrossRef] - Kpojime, H.O.; Safdar, G.A. Interference mitigation in cognitive-radio-based femtocells. IEEE Commun. Surv. Tutor.
**2015**, 17, 1511–1534. [Google Scholar] [CrossRef] - Haider, F.; Wang, C.; Haas, H.; Hepsaydir, E.; Ge, X.; Yuan, D. Spectral and energy efficiency analysis for cognitive radio networks. IEEE Trans. Wirel. Commun.
**2015**, 14, 2969–2980. [Google Scholar] [CrossRef] - Wang, Y.; Xu, W.; Yang, K.; Lin, J. Optimal energy-efficient power allocation for OFDM-based cognitive radio networks. IEEE Commun. Lett.
**2012**, 16, 1420–1423. [Google Scholar] [CrossRef] - Mao, J.; Xie, G.; Gao, J.; Liu, Y. Energy efficiency optimization for OFDM-based cognitive radio systems: A water-filling factor aided search method. IEEE Trans. Wirel. Commun.
**2013**, 12, 2366–2375. [Google Scholar] [CrossRef] - Ren, J.; Zhang, Y.; Zhang, N.; Zhang, D.; Shen, X. Dynamic channel access to improve energy efficiency in cognitive radio sensor networks. IEEE Trans. Wirel. Commun.
**2016**, 15, 3143–3156. [Google Scholar] [CrossRef] - Chen, X.; Ng, D.W.K.; Yu, W.; Larsson, E.G.; Al-Dhahir, N.; Schober, R. Massive access for 5G and beyond. IEEE J. Sel. Areas Commun.
**2021**, 39, 615–637. [Google Scholar] [CrossRef] - Lu, X.; Wang, P.; Niyato, D.; Kim, D.I.; Han, Z. Wirel. networks with RF energy harvesting: A contemporary survey. IEEE Commun. Surv. Tutor.
**2015**, 17, 757–789. [Google Scholar] [CrossRef] [Green Version] - Yin, S.; Qu, Z.; Wang, Z.; Li, L. Energy-efficient cooperation in cognitive Wirel. powered networks. IEEE Commun. Lett.
**2017**, 21, 128–131. [Google Scholar] [CrossRef] - Zhao, W.; She, R.; Bao, H. Energy efficiency maximization for two-way relay assisted CR-NOMA system based on SWIPT. IEEE Access
**2019**, 7, 72062–72071. [Google Scholar] [CrossRef] - Wang, X.; Na, Z.; Lam, K.Y.; Liu, X.; Gao, Z.; Li, F.; Wang, L. Energy efficiency optimization for NOMA-based cognitive radio with energy harvesting. IEEE Access
**2019**, 7, 139172–139180. [Google Scholar] [CrossRef] - Lee, K.; Yoon, C.; Jo, O.; Lee, W. Joint optimization of spectrum sensing and transmit power in energy harvesting-based cognitive radio networks. IEEE Access
**2018**, 6, 30653–30662. [Google Scholar] [CrossRef] - Ding, X.; Zou, Y.; Zhang, G.; Chen, X.; Wang, X.; Hanzo, L. The security–reliability tradeoff of multiuser scheduling-aided energy harvesting cognitive radio networks. IEEE Trans. Commun.
**2019**, 67, 3890–3904. [Google Scholar] [CrossRef] [Green Version] - Ni, L.; Da, X.; Hu, H.; Huang, Y.; Xu, R.; Zhang, M. Outage constrained robust transmit design for secure cognitive radio with practical energy harvesting. IEEE Access
**2018**, 6, 71444–71454. [Google Scholar] [CrossRef] - Chen, X.; Guo, L.; Li, X.; Dong, C.; Lin, J.; Mathiopoulos, P.T. Secrecy rate optimization for cooperative cognitive radio networks aided by a Wirel. energy harvesting jammer. IEEE Access
**2018**, 6, 34127–34134. [Google Scholar] [CrossRef] - Ouyang, J.; Lin, M.; Zou, Y.; Zhu, W.; Massicotte, D. Secrecy energy efficiency maximization in cognitive radio networks. IEEE Access
**2017**, 5, 2641–2650. [Google Scholar] [CrossRef] - Ni, L.; Da, X.; Hu, H.; Zhang, M.; Cumanan, K. Outage constrained robust secrecy energy efficiency maximization for EH cognitive radio networks. IEEE Wirel. Commun. Lett.
**2020**, 9, 363–366. [Google Scholar] [CrossRef] [Green Version] - Gjendemsjø, A.; Gesbert, D.; Øien, G.E.; Kiani, S.G. Binary power control for sum rate maximization over multiple interfering links. IEEE Trans. Wirel. Commun.
**2008**, 7, 3164–3173. [Google Scholar] [CrossRef] [Green Version] - Lee, W.; Ban, T.; Jung, B.C. Distributed transmit power optimization for device-to-device communications underlying cellular networks. IEEE Access
**2019**, 7, 87617–87633. [Google Scholar] [CrossRef] - Kalamkar, S.S.; Banerjee, A. Secure communication via a Wirel. energy harvesting untrusted relay. IEEE Trans. Veh. Technol.
**2017**, 66, 2199–2213. [Google Scholar] [CrossRef] [Green Version] - Lee, K.; Hong, J.P.; Lee, W. Deep learning framework for secure communication with an energy harvesting receiver. IEEE Trans. Veh. Technol.
**2021**, 70, 10121–10132. [Google Scholar] [CrossRef] - Lee, W.; Lee, K. Resource allocation scheme for guarantee of QoS in D2D communications using deep neural network. IEEE Commun. Lett.
**2021**, 25, 887–891. [Google Scholar] [CrossRef] - Wyner, A.D. The wire-tap channel. Bell Syst. Tech. J.
**1975**, 54, 1355–1387. [Google Scholar] [CrossRef] - Yu, W.; Lui, R. Dual methods for nonconvex spectrum optimization of multicarrier systems. IEEE Trans. Commun.
**2006**, 54, 1310–1321. [Google Scholar] [CrossRef] [Green Version] - Dinkelbach, W. On nonlinear fractional programming. Manag. Sci.
**1967**, 13, 492–498. [Google Scholar] [CrossRef] - Fliege, J.; Vaz, A.I.F.; Vicente, L.N. Complexity of gradient descent for multiobjective optimization. Optim. Methods Softw.
**2018**, 34, 949–959. [Google Scholar] [CrossRef] [Green Version] - Venturino, L.; Prasad, N.; Wang, X. Coordinated scheduling and power allocation in downlink multicell OFDMA networks. IEEE Trans. Veh. Technol.
**2009**, 58, 2835–2848. [Google Scholar] [CrossRef]

**Figure 2.**Comparison of performances of five considered schemes as a function of maximum transmit power (${P}_{\mathrm{max}}$). (

**a**) Average SEE vs. ${P}_{\mathrm{max}}$. (

**b**) Average SR vs. ${P}_{\mathrm{max}}$. (

**c**) Average transmit power vs. ${P}_{\mathrm{max}}$.

**Figure 3.**Comparison of performances of five considered schemes as a function of constraints of ${I}_{\mathrm{th}}$ and ${Q}_{\mathrm{min}}$. (

**a**) Average SEE vs. ${I}_{\mathrm{th}}$. (

**b**) Average SEE vs. ${Q}_{\mathrm{min}}$.

**Figure 4.**Comparison of performances of five considered schemes as a function of number of SU pairs (N). (

**a**) Average SEE vs. N. (

**b**) Computation time vs. N.

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**MDPI and ACS Style**

Lee, K.
Energy-Efficient Secure Communications for Wireless-Powered Cognitive Radio Networks. *Sensors* **2021**, *21*, 8040.
https://doi.org/10.3390/s21238040

**AMA Style**

Lee K.
Energy-Efficient Secure Communications for Wireless-Powered Cognitive Radio Networks. *Sensors*. 2021; 21(23):8040.
https://doi.org/10.3390/s21238040

**Chicago/Turabian Style**

Lee, Kisong.
2021. "Energy-Efficient Secure Communications for Wireless-Powered Cognitive Radio Networks" *Sensors* 21, no. 23: 8040.
https://doi.org/10.3390/s21238040