# Cooperative Secure Transmission in MISO-NOMA Networks

^{*}

## Abstract

**:**

## 1. Introduction

- Taking multiple eavesdroppers into consideration, we investigate physical layer security in cooperative MISO-NOMA networks. We first derive an accurate closed form expression for SOP. Then, we transform the objective function in the SRM problem under certain SOP into a strictly concave function through strict mathematical proofs.
- Different from the work of [21] in which only one user was served by Alice, in this paper, we investigate cooperative secure transmission in NOMA networks where a source (Alice) intends to transmit confidential messages to one legitimate user with high-level security requirement (LU1), and serve another normal one (LU2) simultaneously. In particular, we consider the upper bound of the power Alice allocates to LU2 to guarantee the QoS constraint at LU2. In addition, we have made a comprehensive discussion and developed an adaptive approach based on different cases to obtain the optimal power allocation factor for solving the SRM problem under certain SOP.
- Numerical results are provided to verify that the proposed scheme enables dynamic transmission. Both the effectiveness and flexibility of our scheme in achieving higher secrecy performance and effective EE have also been demonstrated.

**Notations:**Boldface upper and lower cases denote matrices and vectors, respectively. ${\mathbf{I}}_{N}$ represents $N\times N$ identity matrix. ${\mathbb{C}}^{n}$ denotes the n-dimensional complex space and circularly symmetric complex Gaussian random vector submits to $\mathcal{CN}(\mu ,\mathsf{\Lambda})$, with mean $\mu $ and covariance matrix $\mathsf{\Lambda}$. null(X) is the null space of X. Subscripts ${[\xb7]}^{+}$ stands for max-function max$(\xb7,0)$. $\mathbf{Pr}(\xb7)$ is the probability measure. Exponential distribution with parameter $\lambda $ and Gamma distribution with shape parameter $\alpha $ and rate parameter $\beta $ is denoted as $\mathrm{Exp}\left(\lambda \right)$ and $\mathsf{\Gamma}(\alpha ,\beta )$, respectively.

## 2. System Model and Problem Formulation

#### 2.1. System Model

#### 2.2. Problem Formulation

## 3. Proposed Solution for SRM Problem under Certain SOP Constraint

#### 3.1. Solution for SOP Constraint

**Proposition**

**1.**

**Proof.**

#### 3.2. Power Allocation Optimization for LU1

**Lemma**

**1.**

**Proof.**

**Lemma**

**2.**

**Proof.**

**Proposition**

**2.**

**Proof.**

- (a)
- ${R}_{s}^{\prime}\left(0.5\right)\ge 0$. $\zeta >\rho \left(0.5\right)$ can be easily verified. Thus, we have ${a}_{1}^{*}=0.5,\phantom{\rule{4pt}{0ex}}{R}_{s}^{*}\left({a}_{1}\right)={R}_{s}\left(0.5\right)$, if ${a}_{1}^{U}=0.5$; otherwise, ${a}_{1}^{*}={a}_{1}^{U},\phantom{\rule{4pt}{0ex}}{R}_{s}^{*}\left({a}_{1}\right)={R}_{s}\left({a}_{1}^{U}\right)$.
- (b)
- ${R}_{s}^{\prime}\left(0.5\right)<0\phantom{\rule{0.166667em}{0ex}}\&\phantom{\rule{0.166667em}{0ex}}{R}_{s}^{\prime}\left(0\right)>0$. Based on the characteristics of the concave function, there must exist a unique ${a}_{1,opt}$. Hence, if ${a}_{1,opt}\le {a}_{1}^{U}$, we have ${a}_{1}^{*}={a}_{1,opt},\phantom{\rule{4pt}{0ex}}{R}_{s}^{*}\left({a}_{1}\right)={R}_{s}\left({a}_{1,opt}\right)$; otherwise, ${a}_{1}^{*}={a}_{1}^{U},\phantom{\rule{4pt}{0ex}}{R}_{s}^{*}\left({a}_{1}\right)={R}_{s}\left({a}_{1}^{U}\right)$.
- (c)
- ${R}_{s}^{\prime}\left(0\right)\le 0$. According to (25), we have $\zeta <\rho \left(0\right)$, and it is optimal for Alice to stop secure transmission, which leads to ${a}_{1}^{*}={0}^{+}$ and ${R}_{s}^{*}\left({a}_{1}\right)={R}_{s}\left({0}^{+}\right)$.

Algorithm 1 Solution to the SRM problem in (12). | |

Input:$\epsilon $, ${P}_{a}$, ${P}_{c}$, ${N}_{a}$, ${N}_{c}$, ${h}_{a1}$, ${h}_{a2}$, ${h}_{ae}$, ${h}_{ce}$, ${R}_{th}$; | |

Output:${R}_{s}^{*}\left({a}_{1}\right)={R}_{s}\left({a}_{1}^{*}\right)$; | |

1: | calculate ${a}_{1}^{U}$ according to (26); |

2: | if ${a}_{1}^{U}\le 0$, |

Alice stops serving LU2. In addition, the CJ scheme in [21] is carried out at Alice to guarantee secure transmission for LU1; | |

3: | else if ${a}_{1}^{U}>0.5$, |

the CJ scheme in [21] is implemented to solve the SRM problem in (12); | |

4: | else |

the solution to obtain ${a}_{1}^{*}$ has been discussed in Case 3; | |

5: | end if |

6: | return${a}_{1}^{*}$; |

## 4. Numerical Results

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Dai, L.; Wang, B.; Yuan, Y.; Han, S.; I, C.; Wang, Z. Non-orthogonal multiple access for 5G: Solutions, challenges, opportunities, and future research trends. IEEE Commun. Mag.
**2015**, 53, 74–81. [Google Scholar] [CrossRef] - Anwar, A.; Seet, B.C.; Hasan, M.A.; Li, X.J. A Survey on Application of Non-Orthogonal Multiple Access to Different Wireless Networks. Electronics
**2019**, 8, 1135. [Google Scholar] [CrossRef][Green Version] - Ding, Z.; Lei, X.; Karagiannidis, G.K.; Schober, R.; Yuan, J.; Bhargava, V.K. A Survey on Non-Orthogonal Multiple Access for 5G Networks: Research Challenges and Future Trends. IEEE J. Sel. Areas Commun.
**2017**, 35, 2181–2195. [Google Scholar] [CrossRef][Green Version] - Wang, C.; Chen, H.; Yin, Q.; Feng, A.; Molisch, A.F. Multi-User Two-Way Relay Networks with Distributed Beamforming. IEEE Trans. Wirel. Commun.
**2011**, 10, 3460–3471. [Google Scholar] [CrossRef] - Chen, Y.; Zhang, Z. UAV-Aided Secure Transmission in MISOME Wiretap Channels With Imperfect CSI. IEEE Access
**2019**, 7, 98107–98121. [Google Scholar] [CrossRef] - Jameel, F.; Wyne, S.; Kaddoum, G.; Duong, T.Q. A Comprehensive Survey on Cooperative Relaying and Jamming Strategies for Physical Layer Security. IEEE Commun. Surv. Tutur.
**2019**, 21, 2734–2771. [Google Scholar] [CrossRef][Green Version] - Ding, Z.; Peng, M.; Poor, H.V. Cooperative Non-Orthogonal Multiple Access in 5G Systems. IEEE Commun. Lett.
**2015**, 19, 1462–1465. [Google Scholar] [CrossRef][Green Version] - Jiao, R.; Dai, L.; Zhang, J.; MacKenzie, R.; Hao, M. On the Performance of NOMA-Based Cooperative Relaying Systems Over Rician Fading Channels. IEEE Trans. Veh. Technol.
**2017**, 66, 11409–11413. [Google Scholar] [CrossRef][Green Version] - Chen, B.; Chen, Y.; Chen, Y.; Cao, Y.; Zhao, N.; Ding, Z. A Novel Spectrum Sharing Scheme Assisted by Secondary NOMA Relay. IEEE Wirel. Commun. Lett.
**2018**, 7, 732–735. [Google Scholar] [CrossRef][Green Version] - Le, C.B.; Do, D.T.; Voznak, M. Wireless-powered Cooperative MIMO NOMA Networks: Design and Performance Improvement For Cell-Edge Users. Electronics
**2019**, 8, 328. [Google Scholar] [CrossRef][Green Version] - Nomikos, N.; Trakadas, P.; Hatziefremidis, A. Full-Duplex NOMA Transmission with Single-Antenna Buffer-Aided Relays. Electronics
**2019**, 8, 1482. [Google Scholar] [CrossRef][Green Version] - Chen, J.; Yang, L.; Alouini, M. Physical Layer Security for Cooperative NOMA Systems. IEEE Trans. Veh. Technol.
**2018**, 67, 4645–4649. [Google Scholar] [CrossRef][Green Version] - Feng, Y.; Yan, S.; Liu, C.; Yang, Z.; Yang, N. Two-Stage Relay Selection for Enhancing Physical Layer Security in Non-Orthogonal Multiple Access. IEEE Trans. Inf. Forensics Secur.
**2019**, 14, 1670–1683. [Google Scholar] [CrossRef] - Lv, L.; Zhou, F.; Chen, J.; Al-Dhahir, N. Secure Cooperative Communications With an Untrusted Relay: A NOMA-Inspired Jamming and Relaying Approach. IEEE Trans. Inf. Forensics Secur.
**2019**, 14, 3191–3205. [Google Scholar] [CrossRef] - Zhou, F.; Chu, Z.; Sun, H.; Hu, R.Q.; Hanzo, L. Artificial Noise Aided Secure Cognitive Beamforming for Cooperative MISO-NOMA Using SWIPT. IEEE J. Sel. Areas Commun.
**2018**, 36, 918–931. [Google Scholar] [CrossRef] - Yu, C.; Ko, H.; Peng, X.; Xie, W.; Zhu, P. Jammer-aided Secure Communications for Cooperative NOMA Systems. IEEE Commun. Lett.
**2019**, 23, 1935–1939. [Google Scholar] [CrossRef] - Yuan, C.; Tao, X.; Li, N.; Ni, W.; Liu, R.P.; Zhang, P. Analysis on Secrecy Capacity of Cooperative Non-Orthogonal Multiple Access With Proactive Jamming. IEEE Trans. Veh. Technol.
**2019**, 68, 2682–2696. [Google Scholar] [CrossRef] - Cao, Y.; Zhao, N.; Pan, G.; Chen, Y.; Fan, L.; Jin, M.; Alouini, M. Secrecy Analysis for Cooperative NOMA Networks With Multi-Antenna Full-Duplex Relay. IEEE Trans. Commun.
**2019**, 67, 5574–5587. [Google Scholar] [CrossRef][Green Version] - Feng, Y.; Yan, S.; Yang, Z. Secure Transmission to the Strong User in Non-Orthogonal Multiple Access. IEEE Commun. Lett.
**2018**, 22, 2623–2626. [Google Scholar] [CrossRef] - Lv, L.; Ding, Z.; Ni, Q.; Chen, J. Secure MISO-NOMA Transmission With Artificial Noise. IEEE Trans. Veh. Technol.
**2018**, 67, 6700–6705. [Google Scholar] [CrossRef][Green Version] - Hu, L.; Wen, H.; Wu, B.; Tang, J.; Pan, F.; Liao, R. Cooperative-Jamming-Aided Secrecy Enhancement in Wireless Networks With Passive Eavesdroppers. IEEE Trans. Veh. Technol.
**2018**, 67, 2108–2117. [Google Scholar] [CrossRef] - Tran, T.N.; Voznak, M. Multi-Points Cooperative Relay in NOMA System with N-1 DF Relaying Nodes in HD/FD Mode for N User Equipments with Energy Harvesting. Electronics
**2019**, 8, 167. [Google Scholar] [CrossRef][Green Version] - Zhu, J.; Wang, Z.; Li, Q.; Chen, H.; Ansari, N. Mitigating Intended Jamming in mmWave MIMO by Hybrid Beamforming. IEEE Wirel. Commun. Lett.
**2019**, 8, 1617–1620. [Google Scholar] [CrossRef] - Yu, C.; Yu, L.; Wu, Y.; He, Y. Transmit-Power Minimization for NOMA-Enabled Traffic Offloading With Security Provisioning. IEEE Commun. Lett.
**2018**, 22, 986–989. [Google Scholar] [CrossRef] - Zhao, N.; Wang, W.; Wang, J.; Chen, Y.; Lin, Y.; Ding, Z.; Beaulieu, N.C. Joint Beamforming and Jamming Optimization for Secure Transmission in MISO-NOMA Networks. IEEE Trans. Commun.
**2019**, 67, 2294–2305. [Google Scholar] [CrossRef][Green Version] - Zhang, Z.; Chen, H.; Hua, M.; Li, C.; Huang, Y.; Yang, L. Double Coded Caching in Ultra Dense Networks: Caching and Multicast Scheduling via Deep Reinforcement Learning. IEEE Trans. Commun.
**2020**, 68, 1071–1086. [Google Scholar] [CrossRef] - Li, X.; Zhao, M.; Zhang, C.; Khan, W.U.; Wu, J.; Rabie, K.M.; Kharel, R. Security Analysis of Multi-Antenna NOMA Networks under I/Q Imbalance. Electronics
**2019**, 8, 1327. [Google Scholar] [CrossRef][Green Version] - Li, Y.; Yin, Q.; Sun, L.; Chen, H.; Wang, H. A Channel Quality Metric in Opportunistic Selection With Outdated CSI Over Nakagami- m Fading Channels. IEEE Trans. Veh. Technol.
**2012**, 61, 1427–1432. [Google Scholar] [CrossRef] - Boyd, S.; Vandenberghe, L. Convex Optimization; Cambridge University Press: Cambridge, UK, 2004. [Google Scholar]

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**MDPI and ACS Style**

Chen, Y.; Zhang, Z.; Li, B.
Cooperative Secure Transmission in MISO-NOMA Networks. *Electronics* **2020**, *9*, 352.
https://doi.org/10.3390/electronics9020352

**AMA Style**

Chen Y, Zhang Z, Li B.
Cooperative Secure Transmission in MISO-NOMA Networks. *Electronics*. 2020; 9(2):352.
https://doi.org/10.3390/electronics9020352

**Chicago/Turabian Style**

Chen, Yang, Zhongpei Zhang, and Bingrui Li.
2020. "Cooperative Secure Transmission in MISO-NOMA Networks" *Electronics* 9, no. 2: 352.
https://doi.org/10.3390/electronics9020352