On Secure Cooperative Non-orthogonal Multiple Access Network with RF Power Transfer

Abstract

In this paper, we investigate the secrecy performance of the cooperative non-orthogonal multiple access (NOMA) network with radio frequency (RF) power transfer. Specifically, this considered network consists of one RF power supply station, one source and multiple energy constrained NOMA users in the presence of a passive eavesdropper. The better user helps the source to forward the message to worse user by using the energy harvested from the power station. The expression of secrecy outage probability for the scenario of wiretaping from user-to-user link is derived by using the statistical characteristics of signal-to-noise ratio (SNR) and signal-to-interference-plus-noise ratio (SINR) of transmission links. In order to understand more detail about the behaviour of this considered system, the numerical results are provided according to the system key parameters, such as the transmit power, number of users, time switching ratio and power allocation coefficients. The simulation results are also provided to confirm the correctness of our analysis.

Appendices

Appendix A - Proof of Proposition 1

Here, we derive the expression of the joint CDF of $\gamma _{mn}$ and $\gamma _{D_mE}$ as follows

$$\begin{aligned} F_{\gamma _{mn},\gamma _{D_mE}}(x,y)= & {} \int _{0}^{\infty }{F_{\gamma _{mn},\gamma _{D_mE}|X_1}(x,y|z)f_{X_1}(z)dz} \nonumber \\= & {} \int _{0}^{\infty }{F_{\gamma _{mn}|X_1}(x|z)F_{\gamma _{D_mE}|X_1}(y|z)f_{X_1}(z)dz} \nonumber \\= & {} \int _{0}^{\infty }\left( 1-e^{-\frac{x}{c_1\lambda _{mn}z}}\right) \left( 1-e^{-\frac{y}{c_2\lambda _{D_mE}z}}\right) \frac{1}{\lambda _{PD_m}}e^{-\frac{z}{\lambda _{PD_m}}}dz \nonumber \\= & {} 1-u\mathcal {K}_1(u)-v\mathcal {K}_1(v)+t\mathcal {K}_1(t), \end{aligned}$$

(17)

where $u=2\sqrt{\frac{x}{c_1\lambda _{PD_m}\lambda _{mn}}}$, $v=2\sqrt{\frac{y}{c_2\lambda _{PD_m}\lambda _{D_mE}}}$, $t=2\sqrt{\frac{c_2\lambda _{D_mE}x+c_1\lambda _{mn}y}{c_1c_2\lambda _{PD_m}\lambda _{mn}\lambda _{D_mE}}}$. This concludes the proof.

Appendix B - Proof of Theorem 1

By means of (15), $\varPhi _1$ and $\varPhi _2$ are respectively calculated as follows

$$\begin{aligned} \varPhi _1= & {} \Pr \left( \frac{b_2X_2}{b_1X_2 + 1}<\gamma _t\right) = F_{X_2}\left( \frac{\gamma _t}{b_2 - b_1\gamma _t}\right) \\= & {} \left\{ {\begin{array}{*{20}{c}} {\frac{M!}{(M-m)!(m-1)!}\overset{m-1}{\underset{k=0}{\sum }}(-1)^k C^{m-1}_k\frac{1}{M-m+k+1}\left[ 1 - e^{- \frac{\gamma _t(M-m+k+1)}{(b_2 - b_1\gamma _t)\lambda _{SDm}}}\right] ,\mathrm{{ }}}&{}{{\gamma _t} < {\frac{a_n}{a_m}}} \\ {1,\mathrm{{ }}}&{}{{\gamma _t} > \frac{a_n}{a_m}} \end{array}} \right. \end{aligned}$$

$$\begin{aligned} \varPhi _2= & {} \Pr \left( \frac{1+\gamma _{mn}}{1 + \gamma _{D_mE}}< \varOmega _S\right) = \int _{0}^{\infty } \left[ \frac{\partial F_{\gamma _{mn},\gamma _{D_mE}}(x,y)}{\partial y}\right] _{x=\varOmega _S(1+y)-1}dy \nonumber \\= & {} -\frac{2}{c_2 \lambda _{PD_m} \lambda _{D_mE}} \int _{0}^{\infty } \mathcal {K}_0\left( \sqrt{\frac{y}{c_2\lambda _{PD_m}\lambda _{D_mE}}}\right) dy \nonumber \\&+\frac{2}{c_2 \lambda _{PD_m} \lambda _{D_mE}} \int _{0}^{\infty } \mathcal {K}_0\left( \sqrt{\frac{(c_1\lambda _{mn}+c_2\lambda _{D_mE}\varOmega _S)y+c_2\lambda _{D_mE}(\varOmega _S-1)}{c_1c_2\lambda _{PD_m}\lambda _{mn}\lambda _{D_mE}}}\right) dy \nonumber \\= & {} \int _{0}^{\infty }v\mathcal {K}_0(v)dv - \frac{2c_1\lambda _{mn}}{c_1\lambda _{mn}+c_2\lambda _{D_mE}\varOmega _S} \int _{2\sqrt{\frac{\varOmega _S-1}{c_1\lambda _{PD_m}\lambda _{mn}}}}^{\infty } s\mathcal {K}_0(s)ds \nonumber \\= & {} 1-\frac{2c_1 \lambda _{mn}}{c_1\lambda _{mn}+c_2\lambda _{D_mE}\varOmega _S} \sqrt{\frac{\varOmega _S-1}{c_1\lambda _{PD_m}\lambda _{mn}}} \mathcal {K}_1\left( 2\sqrt{\frac{\varOmega _S-1}{c_1\lambda _{PD_m}\lambda _{mn}}}\right) , \end{aligned}$$

(18)

where $\varOmega _S=2^{\frac{2R_S}{1-\alpha }}$, $s = \sqrt{\frac{(c_1\lambda _{mn}+c_2\lambda _{D_mE}\varOmega _S)y+c_2\lambda _{D_mE}(\varOmega _S-1)}{c_1c_2\lambda _{PD_m}\lambda _{mn}\lambda _{D_mE}}}$.

This is the end of our proof.