Exact Outage Probability Analysis of a Dual-Hop Cognitive Relaying Network Under the Overhearing of an Active Eavesdropper

Abstract

In this paper, we study the secure communication of dual-hop cognitive relaying networks. An eavesdropper can combine two received signals from two hops by using the maximum ratio combining technique. The data transmission from the secondary source to the secondary destination is assisted by the best decode-and-forward relay, which is selected from four relay selection schemes. The first scheme, MaSR, is based on the maximum channel gain from the source to the relays. In the second scheme, MaRD, the best relay is selected on the basis of the maximum channel gain from the relays to the destination. In the third scheme, MiRE, the gain to the eavesdroppers is instead minimized. Finally, optimal relay selection is considered as the fourth scheme. For these four schemes, we study the system security performance by deriving the exact analytical secrecy outage probability. These analytical expressions are then verified by comparing them with the results of Monte Carlo simulations. Herein, we evaluate and discuss the outage performance of the schemes while varying important system parameters: the number and locations of the relay nodes, primary user node, and eavesdropper; the transmit power threshold; and the target secure rate.

Appendix 1: Proof of Lemma 1

By setting $u = {\lambda _2}\theta \frac{{{x_3}}}{{{x_5}}}$, the integral ${I_1}$ can be rewritten by:

$$\begin{aligned} {I_1} = \frac{{{x_5}}}{{{\lambda _2}\theta }}\int _0^\infty {{{\left( {{\lambda _6} + {\lambda _2}\frac{{\theta - 1}}{\gamma } + u} \right) }^{ - 1}}{e^{ - \left( {{\lambda _3} + {\lambda _1}\theta } \right) \frac{{{x_5}}}{{{\lambda _2}\theta }}u}}} du \end{aligned}$$

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Using equation 3.382.4 in [22] ($\int _0^\infty {{{\left( {x + \beta } \right) }^v}{e^{ - \mu x}}dx} = {\mu ^{ - v - 1}}{e^{\beta \mu }}\Gamma \left( {v + 1,\beta \mu } \right)$), we obtain:

$$\begin{aligned} {I_1}= & {} \frac{{{x_5}}}{{{\lambda _2}\theta }}\int _0^\infty {{{\left( {{\lambda _6} + {\lambda _2}\frac{{\theta - 1}}{\gamma } + u} \right) }^{ - 1}}{e^{ - \left( {{\lambda _3} + {\lambda _1}\theta } \right) \frac{{{x_5}}}{{{\lambda _2}\theta }}u}}} du\nonumber \\= & {} \frac{{{x_5}}}{{{\lambda _2}\theta }}{e^{\left( {{\lambda _6} + {\lambda _2}\frac{{\theta - 1}}{\gamma }} \right) \left( {\frac{{{\lambda _3} + {\lambda _1}\theta }}{{{\lambda _2}\theta }}} \right) {x_5}}}\Gamma \left[ {0,\left( {{\lambda _6} + {\lambda _2}\frac{{\theta - 1}}{\gamma }} \right) \left( {\frac{{{\lambda _3} + {\lambda _1}\theta }}{{{\lambda _2}\theta }}} \right) {x_5}} \right] \end{aligned}$$

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This finishes the proof.