QoS Constrained Optimization for Multi-Antenna AF Relaying With Multiple Eavesdroppers

In this letter, we study physical-layer secure transmission for a multi-antenna relay system in the presence of multiple eavesdroppers, with emphasis on quality-of-service (QoS) based optimization. In particular, our ultimate goal is to minimize relay transmit power and meanwhile guarantee the fulfillment of QoS constraints with regard to both legitimate receiver and eavesdroppers. Instead of directly dealing with this intricate problem, we first prove that the optimal relay precoder possesses a generalized channel matching structure, which allows us to transform the original problem into a tractable semi-definite programming (SDP). We then rigorously verify the optimality of this approach, and further discuss its extension to the scenario with only channel statistics. Simulations are finally performed to demonstrate the superiority of the proposed optimal design.