Aided Opportunistic Jammer Selection for Secrecy Improvement in Underlay Cognitive Radio Networks

Abstract

In this paper, we consider the physical-layer security for the primary system in an underlay cognitive radio model which comprises of a primary source–destination pair, a secondary receiver (SR), K secondary transmitters (ST_i, i = 1,…,K) and an eavesdropper (E). To protecting the transmission confidentiality of the primary transmission system against eavesdropping, we propose secondary transmitter (ST) aided opportunistic jamming transmission protocols. In our protocols, the selection of ST plays a crucial role. To this end, we propose the optimal secondary transmission selection (OSTS) and the Optimal Cooperative Jammer Selection (OCJS), respectively. For the non-security management, OSTS, OCJS schemes, we derive the closed-form expressions of the outage probability and the intercept probability for primary system, respectively. Furthermore, we also derive the closed-form expressions of the outage probability for the secondary user for the selective schemes. Numerical results show that the OCJS scheme has the best security performance and the conventional non-security management scheme has the worst security performance for primary system. In addition, the outage performances of OSTS and OCJS are better than the conventional non-security protocol in high secondary transmitting SNR region.

Appendix

Let $X_{1}$,$X_{2}$, $X_{3}$ and $X_{4}$ be exponentially variables with parameters ${1 \mathord{\left/ {\vphantom {1 {\sigma_{\text{P}}^{2} }}} \right. \kern-0pt} {\sigma_{\text{P}}^{2} }}$, ${1 \mathord{\left/ {\vphantom {1 {\sigma_{{{\text{S}}_{i} {\text{P}}}}^{2} }}} \right. \kern-0pt} {\sigma_{{{\text{S}}_{i} {\text{P}}}}^{2} }}$, ${1 \mathord{\left/ {\vphantom {1 {\sigma_{\text{PE}}^{2} }}} \right. \kern-0pt} {\sigma_{\text{PE}}^{2} }}$ and ${1 \mathord{\left/ {\vphantom {1 {\sigma_{{{\text{S}}_{j} {\text{E}}}}^{2} }}} \right. \kern-0pt} {\sigma_{{{\text{S}}_{j} {\text{E}}}}^{2} }}$, respectively. Moreover, letting $\tilde{X}_{2} = \beta X_{2} + {{N_{0} } \mathord{\left/ {\vphantom {{N_{0} } {P_{\text{S}} }}} \right. \kern-0pt} {P_{\text{S}} }}$, $\tilde{X}_{3} = X_{3} + {{N_{0} } \mathord{\left/ {\vphantom {{N_{0} } {P_{\text{S}} }}} \right. \kern-0pt} {P_{\text{S}} }}$, $Y_{1} = {{X_{1} } \mathord{\left/ {\vphantom {{X_{1} } {\tilde{X}_{2} }}} \right. \kern-0pt} {\tilde{X}_{2} }}$, and $Y_{2} = {{X_{4} } \mathord{\left/ {\vphantom {{X_{4} } {\tilde{X}_{3} }}} \right. \kern-0pt} {\tilde{X}_{3} }}$. The probability distribution and density of random variables $\tilde{X}_{2}$ can be derived as (43) and (44), respectively.

$$F_{{\tilde{X}_{2} }} \left( {\tilde{x}_{2} } \right) = \Pr \left\{ {\tilde{X}_{2} < \tilde{x}_{2} } \right\} = \Pr \left\{ {\beta X_{2} < \tilde{x}_{2} - \frac{{N_{0} }}{{P_{\text{S}} }}} \right\} = \int_{0}^{{\frac{{\tilde{x}_{2} }}{\beta } - \frac{{N_{0} }}{{\beta P_{\text{S}} }}}} {\frac{1}{{\sigma_{{{\text{S}}_{i} {\text{P}}}}^{2} }}e^{{ - \frac{{x_{2} }}{{\sigma_{{{\text{S}}_{i} {\text{P}}}}^{2} }}}} } dx_{2} = 1 - e^{{\frac{{N_{0} }}{{\beta P_{\text{S}} \sigma_{{{\text{S}}_{i} {\text{P}}}}^{2} }} - \frac{{\tilde{x}_{2} }}{{\beta \sigma_{{{\text{S}}_{i} {\text{P}}}}^{2} }}}} ,$$

(43)

$$f_{{\tilde{X}_{2} }} \left( {\tilde{x}_{2} } \right) = \frac{1}{{\beta \sigma_{{{\text{S}}_{i} {\text{P}}}}^{2} }}e^{{\frac{{N_{0} }}{{\beta P_{\text{S}} \sigma_{{{\text{S}}_{i} {\text{P}}}}^{2} }} - \frac{{\tilde{x}_{2} }}{{\beta \sigma_{{{\text{S}}_{i} {\text{P}}}}^{2} }}}} .$$

(44)

By using (44), the probability distribution and density of random variables $Y_{1}$ can be derived as (45) and (46) respectively.

$$\begin{aligned} F_{{Y_{1} }} \left( {y_{1} } \right) & = \Pr \left\{ {\frac{{X_{1} }}{{\tilde{X}_{2} }} < y_{1} } \right\} = \Pr \left\{ {X_{1} < \tilde{X}_{2} y_{1} } \right\} \\ & = e^{{\frac{{N_{0} }}{{\beta P_{\text{S}} \sigma_{{{\text{S}}_{i} {\text{P}}}}^{2} }}}} \int_{{{{N_{0} } \mathord{\left/ {\vphantom {{N_{0} } {P_{\text{S}} }}} \right. \kern-0pt} {P_{\text{S}} }}}}^{\infty } {\frac{1}{{\beta \sigma_{{{\text{S}}_{i} {\text{P}}}}^{2} }}e^{{ - \frac{{\tilde{x}_{2} }}{{\beta \sigma_{{{\text{S}}_{i} {\text{P}}}}^{2} }}}} \int_{0}^{{\tilde{x}_{2} y_{1} }} {\frac{1}{{\sigma_{\text{P}}^{2} }}e^{{ - \frac{{x_{1} }}{{\sigma_{\text{P}}^{2} }}}} } dx_{1} d\tilde{x}_{2} } = 1 - \frac{{\sigma_{\text{P}}^{2} }}{{\beta \sigma_{{{\text{S}}_{i} {\text{P}}}}^{2} y_{1} + \sigma_{\text{P}}^{2} }}e^{{ - \frac{{N_{0} }}{{P_{\text{S}} \sigma_{\text{P}}^{2} }}y_{1} }} , \\ \end{aligned}$$

(45)

$$f_{{Y_{1} }} \left( {y_{1} } \right) = \frac{{{{N_{0} } \mathord{\left/ {\vphantom {{N_{0} } {P_{\text{S}} }}} \right. \kern-0pt} {P_{\text{S}} }}}}{{\beta \sigma_{{{\text{S}}_{i} {\text{P}}}}^{2} y_{1} + \sigma_{\text{P}}^{2} }}e^{{ - \frac{{N_{0} }}{{P_{\text{S}} \sigma_{\text{P}}^{2} }}y_{1} }} + \frac{{\beta \sigma_{\text{P}}^{2} \sigma_{{{\text{S}}_{i} {\text{P}}}}^{2} }}{{\left( {\beta \sigma_{{{\text{S}}_{i} {\text{P}}}}^{2} y_{1} + \sigma_{\text{P}}^{2} } \right)^{2} }}e^{{ - \frac{{N_{0} }}{{P_{\text{S}} \sigma_{\text{P}}^{2} }}y_{1} }} .$$

(46)

The probability distribution and density of random variables $\tilde{X}_{2}$ can be derived as (47) and (48), respectively.

$$F_{{\tilde{X}_{3} }} \left( {\tilde{x}_{3} } \right) = \Pr \left\{ {X_{3} < \tilde{X}_{3} - \frac{{N_{0} }}{{P_{\text{S}} }}} \right\} = \int_{0}^{{\tilde{x}_{3} - \frac{{N_{0} }}{{P_{\text{S}} }}}} {\frac{1}{{\sigma_{{{\text{S}}_{i} {\text{E}}}}^{2} }}e^{{ - \frac{{x_{3} }}{{\sigma_{{{\text{S}}_{i} {\text{E}}}}^{2} }}}} } dx_{3} = 1 - e^{{\frac{{N_{0} }}{{P_{\text{S}} \sigma_{{{\text{S}}_{i} {\text{E}}}}^{2} }}}} e^{{ - \frac{{\tilde{x}_{3} }}{{\sigma_{{{\text{S}}_{i} {\text{E}}}}^{2} }}}} ,$$

(47)

$$f_{{\tilde{X}_{3} }} \left( {\tilde{x}_{3} } \right) = \frac{1}{{\sigma_{{{\text{S}}_{i} {\text{E}}}}^{2} }}e^{{\frac{{N_{0} }}{{P_{\text{S}} \sigma_{{{\text{S}}_{i} {\text{E}}}}^{2} }}}} e^{{ - \frac{{\tilde{x}_{3} }}{{\sigma_{{{\text{S}}_{i} {\text{E}}}}^{2} }}}} .$$

(48)

By using (48), the probability distribution and density of random variables $Y_{2}$ can be derived as (49) and (50) respectively.

$$\begin{aligned} F_{{Y_{2} }} \left( {y_{2} } \right) & = \Pr \left\{ {\frac{{X_{4} }}{{\tilde{X}_{3} }} < y_{2} } \right\} = \Pr \left\{ {X_{4} < \tilde{X}_{3} y_{2} } \right\} \\ & = e^{{\frac{{N_{0} }}{{P_{\text{S}} \sigma_{{{\text{S}}_{i} {\text{E}}}}^{2} }}}} \int_{{{{N_{0} } \mathord{\left/ {\vphantom {{N_{0} } {P_{\text{S}} }}} \right. \kern-0pt} {P_{\text{S}} }}}}^{\infty } {\frac{1}{{\sigma_{{{\text{S}}_{i} {\text{E}}}}^{2} }}e^{{ - \frac{{\tilde{x}_{3} }}{{\sigma_{{{\text{S}}_{i} {\text{E}}}}^{2} }}}} \int_{0}^{{\tilde{x}_{3} y_{2} }} {\frac{1}{{\sigma_{\text{PE}}^{2} }}e^{{ - \frac{{x_{4} }}{{\sigma_{\text{PE}}^{2} }}}} dx_{4} } d\tilde{x}_{3} } = 1 - \frac{{\sigma_{\text{PE}}^{2} }}{{\sigma_{\text{PE}}^{2} + \sigma_{{{\text{S}}_{i} {\text{E}}}}^{2} y_{2} }}e^{{ - \frac{{N_{0} }}{{P_{\text{S}} \sigma_{{P{\text{E}}}}^{2} }}y_{2} }} , \\ \end{aligned}$$

(49)

$$f_{{Y_{2} }} \left( {y_{2} } \right) = \frac{{\sigma_{{{\text{S}}_{i} {\text{E}}}}^{2} \sigma_{\text{PE}}^{2} }}{{\left( {\sigma_{{{\text{S}}_{i} {\text{E}}}}^{2} y_{2} + \sigma_{\text{PE}}^{2} } \right)^{2} }}e^{{ - \frac{{N_{0} }}{{P_{\text{S}} \sigma_{{P{\text{E}}}}^{2} }}y_{2} }} + \frac{{{{N_{0} } \mathord{\left/ {\vphantom {{N_{0} } {P_{\text{S}} }}} \right. \kern-0pt} {P_{\text{S}} }}}}{{\sigma_{{{\text{S}}_{i} {\text{E}}}}^{2} y_{2} + \sigma_{\text{PE}}^{2} }}e^{{ - \frac{{N_{0} }}{{P_{\text{S}} \sigma_{{P{\text{E}}}}^{2} }}y_{2} }} .$$

(50)