Secure Cognitive Reactive Decode-and-Forward Relay Networks: With and Without Eavesdropper

Abstract

In this paper, we study performances of cooperative relay networks in cognitive radio with reactive multiple decode-and-forward (DF) relays. In particular, we first derive exact and asymptotic expressions of outage probability for the considered scheme with K-th best relay selection over Rayleigh fading channel. Next, in the presence of an eavesdropper and the same relay selection scheme, secrecy performance of the cognitive relay network is also evaluated, in terms of average secrecy capacity. We then perform Monte-Carlo simulations to verify the theoretical derivations. Our results have presented the significance of using relay networks to enhance the system and secrecy performance of cognitive reactive DF relay networks.

Appendix: A Detailed Derivation of (31)

Using Eqs. (25), (26), and (30), the corresponding asymptotic outage probability of (17) is given by

$$\begin{aligned} \tilde{P}_1^\mathrm{out}&\mathop \approx \limits ^{\rho _p \rightarrow 0} \mathop {\mathop {\sum }\limits _{{Q_1},{Q_2}}}\limits _{{N < K}} \prod \limits _{t = K}^M {{\lambda _{s{j_t}}}} (\rho _P)^{M-K+1} \nonumber \\&\qquad \times \left( 1 - \exp (- \lambda _{sp}\mu )+ \frac{{\varGamma ( {M - K + 2,{\lambda _{sp}}\mu })}}{{{{( {{\lambda _{sp}}\mu })}^{M - K + 1}}}} \right) . \end{aligned}$$

(56)

Using again Eqs. (56) and (30) for (19), we get (57) as

$$\begin{aligned} \tilde{P}_2^\mathrm{out}&\mathop \approx \limits ^{\rho _p \rightarrow 0} \mathop {\mathop {\sum }\limits _{{Q_1},{Q_2}}}\limits _{{N \ge K}} \prod \limits _{t = N + 1}^M {{\lambda _{s{j_t}}}} \left( 1 - \exp \left( { - {\lambda _{sp}}\mu } \right) +\frac{{\varGamma \left( {M - N + 1,{\lambda _{sp}}\mu } \right) }}{{{{\left( {{\lambda _{sp}}\mu } \right) }^{M - N}}}} \right) \nonumber \\&\qquad \times \mathop {\mathop {\sum }\limits _{\scriptstyle c = 1}}\limits _{\scriptstyle {j_t} = b} ^N {\frac{1}{{N - K + 1}}\left( {{\lambda _{bd}} + \frac{{{\lambda _{bd}}\exp \left( { - {\lambda _{bp}}\mu } \right) }}{{{\lambda _{bp}}\mu }}} \right) } \nonumber \\&\qquad \times \sum \limits _{{W_1},{W_2}}^{} \prod \limits _{v = K + 1}^N \left( {{\lambda _{{z_v}d}} + \frac{{{\lambda _{{z_v}d}}\exp ( { - {\lambda _{{z_v}p}}\mu })}}{{{\lambda _{{z_v}p}}\mu }}} \right) \rho _P^{M - K + 1}. \end{aligned}$$

(57)

Thus, combining (56) and (57), we can obtain $\tilde{P}_\mathrm{out}$. Similarly, an asymptotic expression for $\tilde{P}_\mathrm{H,out}$ in the homogeneous networks can be readily computed as $\tilde{P}_\mathrm{H,out}$ in (31).