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In this letter, we design joint communication and artificial jamming beamforming to guarantee both downlink multi-user (MU) communication and proactive eavesdropping for a full-duplex base-station (FD-BS). Specifically, we aim to maximize the weighted sum-rate (WSR) of legitimate communication users (CUs) under the total power budget constraint and successful eavesdropping constraint. The equivalence between the weighted mean squared error (MSE) minimization problem and the original non-convex WSR maximization problem is strictly proved. First-order Taylor approximation is applied to relax the non-convex constraint. Then an alternating optimization framework based on block coordinate descent (BCD) algorithm is proposed to solve the weighted MSE minimization problem iteratively. Simulation results are provided to illustrate the effectiveness of the proposed beamforming design.
Jing et al. (2025) studied this question.