Signal leakage neutralisation in instantaneous non-regenerative relaying networks under channel uncertainty

In a multi-user wireless network, physical layer security is an important issue, especially when some of the served users are malicious. As these users actively participate in the network, their channel state information can be estimated or feedback, although not perfectly known. With this channel uncertainty, the worst-case signal leakage to eavesdropping users´ needs to be managed. The authors propose a robust instantaneous relay design that improves the worst-case secrecy rate performance, and decompose the problem into two sub-problems: First, the achievable signal leakage or leakage-to-noise ratio region is studied. Second, for fixed signal leakage constraints, the achievable secrecy rate region is computed. To approach the non-convex optimisation problems, the authors propose to iteratively solve for the phases and magnitudes of the equivalent channel matrix, a function of the relay matrix. The numerical simulations illustrate that the proposed alternating optimisation algorithm achieves higher secrecy rates than those in a system without an instantaneous relay.