Relay-and-Jammers Selection for Performance Improvement of Energy Harvesting Underlay Cognitive Networks

Abstract

This paper adopts a relay among available secondary relays and exploits non-selected relays as jammers to maintain and secure legitimate secondary source-to-destination communications in energy harvesting underlay cognitive networks (EHUCNs) as their direct communications is in outage. All relays harvest radio frequency energy in signals transmitted by primary and secondary transmitters and consume the harvested energy for their jamming-and-relaying operations. Under Rayleigh fading, peak transmission power restriction, interference power restriction, primary interference and power splitting-based energy scavenging method, we propose exact closed-form formulas of outage and intercept probabilities to promptly assess both security and reliability performances of the suggested relay-and-jammers selection in EHUCNs. The suggested expressions are corroborated by computer simulations. Numerous results indicate the efficacy of the relay-and-jammers selection in improving both security and reliability for source–destination communications. Moreover, the security and reliability performances are saturated at large maximum transmit/interference powers and considerably degraded by the primary interference. Furthermore, the reliability performance can be optimized by splitting appropriately the received power for information decoding and energy harvesting at the relays.

Appendix: Asymptotic Results when \(I_t \rightarrow \infty \)

When primary receivers tolerate any interference level from secondary transmitters, the case of $I_t \rightarrow \infty$ holds. For instance, secondary transmitters are distant from primary receivers so that interference caused by secondary transmitters upon primary receivers is negligible, and then, the interference power restriction relating to $I_t$ is relaxed. Another example is that secondary transmitters operate in the non-cognitive mode, and then, the interference power restriction is ignored.

This appendix shows asymptotic results for IP and OP when $I_t \rightarrow \infty$. In this asymptotic region, $P_s$ in (23), $P_{r_b}$ in (24) and ${\bar{P}}_s$ in (25) become $P_{sm}$, $P_{r_bm}$ and $P_{sm}$, respectively. Therefore, (55) is approximated as

$$\begin{aligned} I{^{\mathrm{asym}}} = 1 - I_1^{\mathrm{asym}}\sum \limits _{b = 1}^K {\left( {1 - I_{2111}^{\mathrm{asym}}} \right) I_{22}}, \end{aligned}$$

(72)

where $I_{22}$ is given by (49).

$I_1^{\mathrm{asym}}$ is obtained from $I_{1t}$ in (29) with the substitution of $P_s$ with $P_{sm}$, i.e.,

$$\begin{aligned} I_1^{\mathrm{asym}} = 1 - {e^{ - \frac{{{{{\bar{\gamma }} }_e}\sigma _e^2}}{{{P_{sm}}{\mu _{se}}}}}}{\left( {\frac{{{P_p}{{{\bar{\gamma }} }_e}{\mu _{pe1}}}}{{{P_{sm}}{\mu _{se}}}} + 1} \right) ^{ - 1}}. \end{aligned}$$

(73)

Similarly, $I_{2111}^{\mathrm{asym}}$ is obtained from (38) with the substitution of $P_{r_b}$ with $P_{r_bm}$, i.e.,

$$\begin{aligned} I_{2111}^{\mathrm{asym}} = {e^{ - \frac{{\sigma _e^2{{{\bar{\gamma }} }_e}}}{{{P_{{r_b}m}}{\mu _{{r_b}e}}}}}}\sum \limits _{k = 1}^K {{{\left( {\frac{{{{{\bar{\gamma }} }_e}{M_k}}}{{{P_{{r_b}m}}{\mu _{{r_b}e}}}} + 1} \right) }^{ - 1}}{L_k}}. \end{aligned}$$

(74)

In the asymptotic region, (71) is approximated as

$$\begin{aligned} {O^{\mathrm{asym}}} = 1 - \sum \limits _{b = 1}^K {O_1^{\mathrm{asym}}O_2^{\mathrm{asym}}}, \end{aligned}$$

(75)

where $O_2^{\mathrm{asym}}$ is computed in the same way as $I_1^{\mathrm{asym}}$, resulting in

$$\begin{aligned} O_2^{\mathrm{asym}} = {e^{ - \frac{{{{{\bar{\gamma }} }_d}\sigma _d^2}}{{{P_{{r_b}m}}{\mu _{{r_b}d}}}}}}{\left( {1 + \frac{{{P_p}{{{\bar{\gamma }} }_d}{\mu _{pd}}}}{{{P_{{r_b}m}}{\mu _{{r_b}d}}}}} \right) ^{ - 1}}. \end{aligned}$$

(76)

With the substitution of $P_s$ with $P_{sm}$, the event $\left\{ {{P_s} > \frac{{{{{\bar{\gamma }} }_d}}}{{{\phi _{{r_b}}}}}} \right\}$ in (58) is equivalent to $\left\{ {{\phi _{{r_b}}} > \frac{{{{{\bar{\gamma }} }_d}}}{{{P_{sm}}}}} \right\}$. Therefore, $O_1$ in (58) is approximated as

$$\begin{aligned} O_1^{\mathrm{asym}} = \int \limits _{\frac{{{{{\bar{\gamma }} }_d}}}{{{P_{sm}}}}}^\infty {\left\{ {\prod \limits _{j \in {{{\mathcal {J}}}}} {\left( {1 - {B_j}\frac{{{e^{ - {A_j}x}}}}{{x + {B_j}}}} \right) } } \right\} {f_{{\phi _{{r_b}}}}}\left( x \right) \mathrm{d}x} = {O_{11}}, \end{aligned}$$

(77)

where $O_{11}$ is given by (64).