LAUSR

In this paper, we consider transmission optimization in a multiple-input-single-output downlink network, in which each user is wiretapped by a specific eavesdropper. Particularly, we aim to minimize the total transmit power and maximize the sum secrecy rate (SSR) of the system simultaneously, under the assumption that the channel state information (CSI) of the eavesdroppers is not perfectly known at the transmitter. Considering the conflict between two objectives, a multi-objective optimization (MOO) framework based on the weighted Tchebycheff approach is proposed. The formulated MOO problem is non-convex and intractable. To tackle it, several auxiliary variables are introduced and the corresponding Taylor series expansion is employed to linearize the term related to each auxiliary variable. Then, the non-convexity resulting from the CSI errors is recast as a convex one with the aid of ${S}$ -procedure and Cauchy–Schwarz inequality. Based on above treatments, a robust iterative algorithm is proposed to solve the original problem. Simulation results not only demonstrate the effectiveness of the proposed design, but also unveil the tradeoff between the total transmit power and the SSR.