Distributed Beamforming for Physical-Layer Security of Two-Way Relay Networks

In this paper, we address the security of a two-way relay network in the presence of an eavesdropper, where each node is only equipped with single antenna. We propose two-phase distributed analog network coding, or distributed beamforming and power allocation to enhance the secrecy sum rate of the data exchange. In the first phase, the two terminals broadcast their information data simultaneously to all the relay nodes. In the second phase, three different security schemes are proposed: optimal beamforming, null-space beamforming, and artificial noise beamforming. In the first scheme, the objective is to achieve the maximum secrecy sum rate of the two terminals. Mathematically, the objective function is difficult to optimize. In the second scheme, we maximize the total information exchanged while we eliminate the information leakage completely, subject to the total transmission power constraint. We show that the problem has a unique and global optimum, which can be solved using bisection method. When the instantaneous channel state information of the eavesdropper is not available, we propose an artificial noise beamforming in the third scheme. We minimize the information transmission power so that the artificial noise power is maximized to eliminate information leakage, under the constraints of quality of service (QoS) required by terminals. It is a second-order convex cone programming (SOCP) problem, thus can be efficiently solved using interior point methods. Numerical results are provided and analyzed to show the properties and efficiency of the proposed designs.