Physical layer security in cooperative amplify-and-forward relay networks over mixed Nakagami-m and double Nakagami-m fading channels: performance evaluation and optimisation

The authors investigate the secrecy performance of a cooperative relaying network, wherein a fixed source communicates with a fixed destination via an amplify-and-forward mobile relay in the presence of a passive mobile eavesdropper. They assume that the source-to-relay channel and relay-to-destination channel experience Nakagami-m fading, whereas relay-to-eavesdropper link follows double Nakagami-m fading. Under such a mixed fading environment, they derive the novel tight closed-form expressions for the secrecy outage probability (SOP), probability of non-zero secrecy capacity, and intercept probability of the considered system. They also deduce the asymptotic secrecy outage and intercept probability expressions in the high signal-to-noise ratio regime to highlight the impact of fading parameters and channel conditions on the secrecy diversity order. It is shown that the system can achieve secrecy diversity order of min($m_{\rm SR}, m_{\rm RD}$mSR,mRD) in terms of SOP, and $m_{\rm RD}$mRD in terms of intercept probability, where $m_{\rm SR}$mSR and $m_{\rm RD}$mRD represent the fading severity parameters between source and relay and between relay and destination, respectively. They also formulate and investigate analytically two optimisation problems, namely, optimal relay location with fixed power allocation and optimal power allocation with fixed relay location, to minimise the system SOP. They verify analytical findings via numerical and simulation results.