Optimal Transmit Design at Relay Nodes for Secure AF Relay Networks

We study the transmit design at relay nodes for secure amplify-and-forward (AF) networks. Two joint cooperative relaying and jamming schemes, namely Secrecy Rate Maximization Scheme and Null-Space Jamming Scheme, are proposed. In the first scheme, optimal relaying weight vector and optimal covariance matrix associated with the artificial noise (AN) are obtained, which involves doing a one-dimensional search and solving a sequence of semidefinite programs(SDPs). In the second scheme, which is suboptimal but computationally much cheaper, AN is designed to decrease the rate at the eavesdropper while the relaying weight vector is determined to increase the rate at the destination. In addition, Power Allocation based on secrecy rate maximization provides a balance between these two goals. Numerical results show that the proposed Secrecy Rate Maximization Scheme outperforms the existing cooperative relaying without jamming scheme. Especially, when the power is large enough, the secrecy rate achieved by the proposed schemes approaches the maximal achievable rate for the no-eavesdropper case.