Robust beamforming design for secure DM-based relay networks with self-sustained jammers

In this paper, we propose to use self-sustained jammers to generate artificial noise with the aim of enhancing the physical layer security of a directional modulation (DM) relay system. To this end, we specifically tackle an optimization problem of designing beamforming vectors at the source, relay, and jammers to maximize a lower bound on the average secrecy rate of the considered system. Due to that the optimization problem is non-convex and the optimization variables are coupled, and so we cannot directly solve this problem. As such, we first develop a centralized scheme to achieve the near-optimal beamforming vectors with the aid of semidefinite relaxation, successive convex approximation, and an alternating iterative algorithm. The tightness of the incurred relaxation and the convergence of the involved algorithm are proved. To reduce the overhead and complexity of the centralized scheme, we also develop two decentralized schemes with partial cooperation and without cooperation among devices to obtain suboptimal beamforming vectors. Our examination shows that the developed centralized scheme can achieve similar performance as the optimal beamforming vectors, which can only be obtained through exhaustive numerical search. Our examination also specifies the conditions under which the decentralized schemes can achieve similar or significantly worse performance relative to the centralized scheme. Furthermore, our examination demonstrates that the developed three schemes are robust to the angle estimation errors in practical DM systems.