On the Performance of the Relay Selection in Multi-hop Cluster-based Wireless Networks with Multiple Eavesdroppers Under Equally Correlated Rayleigh Fading

The performance of multi-hop cluster-based wireless networks under multiple eavesdroppers is investigated in the present work. More precisely, we derive the outage probability (OP) of the considered networks under two relay selection schemes: the channel-gain-based scheme and the random scheme. Although equally correlated Rayleigh fading is taken into consideration, the derived mathematical framework remains tractable. Specifically, we represent the exact expression of the OP under the channel-based scheme in series form, while the OP under the random scheme is computed in a closed-form expression. Additionally, we propose a novel power allocation for each transmitter that strictly satisfies the given intercept probability. Numerical results based on the Monte Carlo method are provided to verify the correctness of the derived framework. These results are also used to identify the influences of various parameters, such as the number of clusters, the number of relays per cluster, and the transmit power.