# 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

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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