Hybrid Cooperative Beamforming and Jamming for Physical-Layer Security of Two-Way Relay Networks

TLDR: A penalty function method incorporating the rank-1 constraint into the objective function is proposed and an efficient iterative algorithm to solve the so-obtained problem, which is a convex SDP problem, thus it can be efficiently solved using the interior point method.

Abstract: In this paper, we propose a hybrid cooperative beamforming and jamming scheme to enhance the physical-layer security of a single-antenna-equipped two-way relay network in the presence of an eavesdropper. The basic idea is that in both cooperative transmission phases, some intermediate nodes help to relay signals to the legitimate destination adopting distributed beamforming, while the remaining nodes jam the eavesdropper, simultaneously, which takes the data transmissions in both phases under protection. Two different schemes are proposed, with and without the instantaneous channel state information of the eavesdropper, respectively, and both are subjected to the more practical individual power constraint of each cooperative node. Under the general channel model, it is shown that both problems can be transformed into a semi-definite programming (SDP) problem with an additional rank-1 constraint. A current state of the art technique for handling such a problem is the semi-definite relaxation (SDR) and randomization techniques. In this paper, however, we propose a penalty function method incorporating the rank-1 constraint into the objective function. Although the so-obtained problem is not convex, we develop an efficient iterative algorithm to solve it. Each iteration is a convex SDP problem, thus it can be efficiently solved using the interior point method. When the channels are reciprocal such as in TDD mode, we show that the problems become second-order convex cone programming ones. Numerical evaluation results are provided and analyzed to show the properties and efficiency of the proposed hybrid security scheme, and also demonstrate that our optimization algorithms outperform the SDR technique.