Physical Layer Secrecy Enhancement for Non-orthogonal Multiple Access Cooperative Network with Artificial Noise

Abstract

In this paper, the physical layer secrecy performance of non-orthogonal multiple access (NOMA) in a downlink cooperative network is studied. This considered system consists of one source, multiple legitimate user pairs and presenting an eavesdropper. In each pair, the better user forwards the information from the source to the worse user by using the decode-and-forward (DF) scheme and assuming that the eavesdropper attempts to extract the worse user’s message. We propose the artificial noise - cooperative transmission scheme, namely ANCOTRAS, to improve the secrecy performance of this considered system. In order to evaluate the effectiveness of this proposed scheme, the lower bound and exact closed-form expressions of secrecy outage probability are derived by using statistical characteristics of signal-to-noise ratio (SNR) and signal-to-interference-plus-noise ratio (SINR). Moreover, we investigate the secrecy performance of this considered system according to key parameters, such as power allocation ratio, average transmit power and number of user pair to verify our proposed scheme. Finally, Monte- Carlo simulation results are provided to confirm the correctness of the analytical results.

Appendix A

Here, we derive the expression of SOP at $D_m$ in the case of with AN.

$$\begin{aligned} SOP_3= & {} \Pr \left( \frac{b_4X_1}{b_3X_1 + 1}<\gamma _t\right) + \left( 1-\Pr \left( \frac{b_4X_1}{b_3X_1 + 1}<\gamma _t\right) \right) \Pr \left( \frac{1+\gamma _{mn}}{1 + \gamma _{D_mE}}< 2^{R_S/(1-\alpha )}\right) \nonumber \\= & {} \varPhi _1 + (1-\varPhi _1)\int _{0}^{\infty }{F_{U_1}(2^{R_S/(1-\alpha )}(1+y)-1)f_{U_2}(y)dy} \nonumber \\= & {} \varPhi _1 + (1-\varPhi _1) \Bigg [ 1 - \frac{M!}{(M-n)!(n-1)!}\overset{n-1}{\underset{k=0}{\sum }}C^{n-1}_{k}(-1)^k\nonumber \\\times & {} \int _{0}^{\infty }\frac{c_1\lambda _{mn}}{c_3\lambda _{SDn}(2^{R_S/(1-\alpha )}(1+y)-1)+c_1\lambda _{mn}(M-n+k+1)}e^{-\frac{(2^{R_S/(1-\alpha )}(1+y)-1)}{c_1\lambda _{mn}}}\nonumber \\\times & {} \left( \frac{c_2c_4\lambda _{DmE}\lambda _{SE}}{(c_4\lambda _{SE}y+c_2\lambda _{DmE})^2}+\frac{1}{(c_4\lambda _{SE}y+c_2\lambda _{DmE})}\right) e^{-\frac{y}{c_2\lambda _{DmE}}}dy \Bigg ]\nonumber \\= & {} \varPhi _1 + (1-\varPhi _1)(1- \frac{M!}{(M-n)!(n-1)!}\overset{n-1}{\underset{k=0}{\sum }}C^{n-1}_{k}(-1)^k(\varPhi _2+\varPhi _3)), \end{aligned}$$

(30)

where $\gamma _t$ is the threshold to detect $s_n$ and $\varPhi _1, \varPhi _2, \varPhi _3$ are calculated as follows

$$\begin{aligned} \varPhi _1= & {} F_{X_1}\left( \frac{\gamma _t}{b_4 - b_3\gamma _t}\right) \\= & {} \left\{ {\begin{array}{*{20}{c}} {\frac{M!}{(M-m)!(m-1)!}\overset{m-1}{\underset{k=0}{\sum }}(-1)^k C^{m-1}_k\frac{1}{M-m+k+1}\left[ 1 - e^{- \frac{\gamma _t(M-m+k+1)}{(b_4 - b_3\gamma _t)\lambda _{SDm}}}\right] ,\mathrm{{ }}}&{}{{\gamma _t} < {\frac{a_n}{a_m}}}\\ {1,\mathrm{{ }}}&{}{{\gamma _t} > \frac{a_n}{a_m}} \end{array}} \right. \end{aligned}$$

$$\begin{aligned} \varPhi _2= & {} \int _{0}^{\infty }\frac{c_1\lambda _{mn}}{c_3\lambda _{SDn}(2^{R_S/(1-\alpha )}(1+y)-1)+c_1\lambda _{mn}(M-n+k+1)}e^{-\frac{(2^{R_S/(1-\alpha )}(1+y)-1)}{c_1\lambda _{mn}}}\nonumber \\\times & {} \frac{c_2c_4\lambda _{DmE}\lambda _{SE}}{(c_4\lambda _{SE}y+c_2\lambda _{DmE})^2}e^{-\frac{y}{c_2\lambda _{DmE}}}dy\nonumber \\= & {} c_1\lambda _{mn}c_2c_4\lambda _{DmE}\lambda _{SE}e^{-\frac{2^{R_S/(1-\alpha )}-1}{c_1\lambda _{mn}}}\!\int _{0}^{\infty }\!\frac{1}{(ay+b)^2}\frac{1}{cy+d}e^{-\left( \frac{1}{c_2\lambda _{DmE}}+\frac{2^{R_S/(1-\alpha )}}{c_1\lambda _{mn}}\right) y}dy\nonumber \\= & {} c_1\lambda _{mn}c_2c_4\lambda _{DmE}\lambda _{SE}e^{-\frac{2^{R_s}-1}{c_1\lambda _{mn}}}\Bigg [\int _{0}^{\infty }\frac{E_1}{cy+d}e^{-\mu y}dy+\int _{0}^{\infty }\frac{E_2}{ay+b}e^{-\mu y}dy \nonumber \\+ & {} \int _{0}^{\infty }\frac{E_3}{(ay+b)^2}e^{-\mu y}dy\Bigg ]\nonumber \\= & {} c_1\lambda _{mn}c_2c_4\lambda _{DmE}\lambda _{SE}e^{-\frac{2^{R_s}-1}{c_1\lambda _{mn}}}\Bigg [\frac{E_1}{c}e^{\frac{d}{c}\mu }\varGamma (0,\frac{d}{c}\mu )+\frac{E_2}{a}e^{\frac{b}{a}\mu }\varGamma (0,\frac{b}{a}\mu ) \nonumber \\+ & {} \frac{E_3}{a^2}\mu e^{\frac{b}{a}\mu }\varGamma (-1,\frac{b}{a}\mu )\Bigg ]. \end{aligned}$$

(31)

$$\begin{aligned} \varPhi _3= & {} \int _{0}^{\infty }\frac{c_1\lambda _{mn}}{c_3\lambda _{SDn}(2^{R_s}(1+y)-1)+c_1\lambda _{mn}}e^{-\frac{(2^{R_s}(1+y)-1)}{c_1\lambda _{mn}}}\\\times & {} \frac{1}{(c_4\lambda _{SE}y+c_2\lambda _{DmE})}e^{-\frac{y}{c_2\lambda _{DmE}}}dy\\= & {} c_1\lambda _{mn}e^{-\frac{2^{R_s}-1}{c_1\lambda _{mn}}}\int _{0}^{\infty }\frac{1}{ay+b}\frac{1}{cy+d}e^{-\left( \frac{1}{c_2\lambda _{DmE}}+\frac{2^{R_s}}{c_1\lambda _{mn}}\right) y}dy\\= & {} c_1\lambda _{mn}e^{-\frac{2^{R_s}-1}{c_1\lambda _{mn}}}\Bigg [\int _{0}^{\infty }\frac{F_1}{cy+d}e^{-\mu y}dy+\int _{0}^{\infty }\frac{F_2}{ay+b}e^{-\mu y}dy\Bigg ]\\= & {} c_1\lambda _{mn}e^{-\frac{2^{R_s}-1}{c_1\lambda _{mn}}}\Bigg [\frac{F_1}{c}e^{\frac{d}{c}\mu }\varGamma (0,\frac{d}{c}\mu )+\frac{F_2}{a}e^{\frac{b}{a}\mu }\varGamma (0,\frac{b}{a}\mu )\Bigg ] \end{aligned}$$

Denoted that $a = c_4\lambda _{SE}, b = c_2\lambda _{DmE}, c = c_3\lambda _{SDn}2^{R_S/(1-\alpha )}, d = c_3\lambda _{SDn}(2^{R_S/(1-\alpha )}-1)+c_1\lambda _{mn}(M-n+k+1), \mu = \frac{2^{R_S/(1-\alpha )}}{c_1\lambda _{mn}}+\frac{1}{c_2\lambda _{DmE}}, E_1 = \frac{c^2}{(ad - bc)^2}, E_2 = - \frac{ac}{(ad - bc)^2}, E_3 = \frac{a}{(ad - bc)}, F_1 = - \frac{c}{ad-bc}, F_2 = \frac{a}{ad-bc}$.

Substituting $\varPhi _1, \varPhi _2, \varPhi _3$ into (30), we obtain the closed-form expression of SOP for the link $D_m-D_n$ in the case of using AN. This concludes the proof.