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.

本文涉及在双向多天线中继网络中最大化可达到的最小保密速率，其中两个单天线节点旨在借助一些结合了放大和转发 (AF) 策略的多天线中继来交换其机密消息，而单天线无源窃听者试图窃听交换的信息。通信在两跳中进行。在第一跳期间，两个源节点传输它们的信息，因此，中继获得传输信号的组合。然后，在整个第二跳中，每个中继将波束成形矩阵应用于其接收到的信号向量，并将结果信号向量广播到发送端。此外，窃听者还窃听了两跳的交换信息。当前工作的主要目标是在中继处设计适当的波束成形策略以提高最小保密率。该问题被视为优化问题，其中表明潜在问题通常不是凸的。因此，设计了两种次优方法，称为零空间 (NS) 和干扰泄漏对齐 (ILA)，其中使用所谓的半定松弛 (SDR) 和 Charnes-Cooper 变换技术，将潜在问题表述为可以数值求解的半定规划 (SDP) 问题。