Impact of Relay’s Eavesdropping on Untrusted Amplify-and-Forward Networks Over Nakagami- $m$ Fading

Abstract

We investigate the impact of eavesdropping on the secrecy outage performance of dual-hop amplify-and-forward networks with a single untrusted relay, in which cooperative jamming technique is employed at the destination to realize positive secrecy rate. Under Nakagami-m fading channels, we derive tight closed-form and asymptotic expressions for the lower and upper bounds of the secrecy outage probability (SOP). Our results explicitly show that a secrecy diversity order of min(m <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> , m <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> /2) in terms of the SOP is achieved, where m <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> and m <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> are the respective integer fading parameters of the source-relay and relay-destination links. Afterwards, we propose an asymptotically optimal power allocation (OPA) scheme that minimizes the SOP. Numerical and simulation results show that the proposed OPA offers significant improvement on the SOP performance, especially in the case of m <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> > m <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> /2.