Robust Cooperative Beamforming and Artificial Noise Design for Physical-Layer Secrecy in AF Multi-Antenna Multi-Relay Networks

This paper is concerned with an optimization problem in a two-hop relay wiretap channel, wherein multiple multi-antenna relays collaboratively amplify and forward (AF) information from a single-antenna source to a single-antenna destination, and at the same time emit artificial noise (AN) to improve physical-layer information security in the presence of multiple multi-antenna eavesdroppers (or Eves). More specifically, the problem is to simultaneously optimize the AF matrices and AN covariances for secrecy rate maximization, with robustness against imperfect channel state information of Eves via a worst-case robust formulation. Such a problem is nonconvex, and we propose a polynomial-time optimization solution based on a two-level optimization approach and semidefinite relaxation (SDR). In particular, while SDR is generally an approximation technique, we prove that SDR is optimal in the specific context here. This desirable result is obtained by careful reformulation and Karush-Kuhn-Tucker optimality analysis, where, rather interestingly, AN is found to be instrumental in providing guarantee of SDR optimality. Simulation results are provided, and the results show that the proposed joint AF-AN solution can attain considerably higher achievable secrecy rates than some existing suboptimal designs.