Cooperative Secure Transmission Relying on Optimal Power Allocation in the Presence of Untrusted Relays, A Passive Eavesdropper and Hardware Impairments

In this work, by considering a variety of realistic hardware impairments, we aim to enhance the security of a cooperative relaying network, where a source intends to transmit its confidential information to a destination in the presence of a group of untrusted amplify-and-forward relays, as potential eavesdroppers (Eves), and an entirely passive multiple-antenna aided Eve. Our goal is to safeguard the information against these two types of eavesdropping attacks, while simultaneously relying on the untrusted relays to boost both the security and reliability of the network. To reach this goal, we propose a novel joint cooperative beamforming, jamming and power allocation policy to safeguard the confidential information while concurrently achieving the required quality-of-service at the destination. We also take into account both the total power budget constraint and a practical individual power constraint for each node. Our optimization problem can be split into two consecutive sub-problems. In the first sub-problem, we are faced with a non-convex problem which can be transformed into the powerful difference of convex (DC) program. A low-complexity iterative algorithm is proposed to solve the DC program, which relies on the constrained concave-convex procedure (CCCP). We further introduce a novel initialization method, which is based on a feasible point of the original problem obtained from a novel iterative feasibility search procedure, rather than an arbitrary (infeasible) point as in the conventional CCCP. The second sub-problem of our optimization problem is a convex optimization problem and can be solved efficiently adopting the classic interior point method. The numerical results provided illustrate that although the trusted relaying scenario outperforms the untrusted relaying for small and medium total power budgets, however, by increasing the total power budget, the secrecy performances of both the trusted and untrusted relaying converge to the same. Additionally, by equally sharing the total impairments at the relays between the transmitter and the receiver the best secrecy performance is presented.