Maximizing the minimum secrecy rate of two-way relay networks

This paper concerns maximizing the minimum achievable secrecy rate in a two-way multi-antenna relay network in which two single-antenna nodes aim at exchanging their confidential messages with the help of some multi-antenna relays incorporating the Amplify and Forward (AF) strategy, while a single-antenna passive eavesdropper attempts to overhear the exchanged information. The communication is carried out in two hops. During the first hop, two source nodes transmit their information, hence, the relays get a combination of transmitted signals. Then, throughout the second hop, each relay applies a beamforming matrix to its received signal vector and broadcasts the resulting signal vector to the transmitting ends. Also, the eavesdropper overhears the exchanged information of two hops. The main goal persuaded in the current work is to devise proper beamforming strategies at the relays to improve the minimum secrecy rate. The problem is cast as an optimization problem, where it is shown that the underlying problem is not convex in general. Hence, two suboptimal approaches, called null-space (NS) and interference-leakage alignment (ILA) are devised, where using the so-called semi-definite relaxation (SDR) and Charnes-Cooper transformation techniques, the underlying problems are formulated as semi-definite programming (SDP) problems which can be numerically solved.