Maximum Secrecy-Key Capacity Design for Amplify-and-Forward Relays in Secure Cooperative Networks

摘要

In this paper, we study the secret-key capacity of the secure cooperative network using the collaborative amplify-andforward (AF) relays to form a beamforming system through the physical layer. The closed-form expression of secret-key capacity is firstly given to prove the the secret-key capacity is not only achievable but can be designed and optimized by beamforming vector formed by AF relays. Furthermore, three beamforming solutions are proposed to maximize the secret-key capacity under the total relay power constraint. The first solution, maximum secret-key capacity (MSKC) beamforming solution, is aimed towards two-level optimization problems and performed by using the semidefinite relaxation (SDR) technique. This solution is the closest to the optimal solution of original problem, but its complexity is very high because of the SDPs. To decrease the complexity, the signals at all eavesdroppers are forced to be zero, producing the second solution named zero-forcing (ZF) beamforming solution. However, the ZF beamforming solution does not work when the number of eavesdroppers is larger than that of relays. The third solution, lower bound maximum secretkey capacity (LB-MSKC) beamforming solution, is designed to make up the loss. It simplifies the original problem to a one-level optimization problem by relaxing the eavesdroppers, and it can still work well when the number of eavesdroppers is larger than that of relays. Simulation results are presented to illustrate the proposed solutions.