Robust Beamforming and Power Allocation for Secrecy in DF Relay Networks With Imperfect Channel State Information

We address a robust beamforming design and power allocation problem for a one-way multi-antenna relay network, where the multi-antenna source implements communication with the multi-antenna destination via a decode-and-forward (DF) relay in the presence of the multiple single-antenna eavesdroppers. The eavesdroppers can only overhear the information flowed from the relay to the destination in the second hop. We aim to maximize the worst-case secrecy rate in the condition that the global channel state information (CSI) is imperfect. To this end, we propose the joint beamforming and power allocation design for the worst-case secrecy rate maximization. However, our proposed design constitutes a non-convex problem, which involves an infinite number of constraints because of the imperfect CSI. To make the problem more tractable, we approximate the problem into several tractablesemidefinite programs by semidefinite relaxation, successive convex approximation, and S-procedure techniques, and we propose an iterative algorithm to solve the problem. Furthermore, we show that the proposed algorithm is also applicable for the case the Gaussian wiretap model, where only the eavesdroppers' CSI is imperfect. Simulation results validate the effectiveness of the proposed algorithm.