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In this paper, we design transmit beamforming for a full duplex base station (FD-BS) considering both self-interference mitigation and physical-layer security. The proposed design is formulated as minimizing the power consumption of FD-BS under different signal-to-interference-and-noise-ratio (SINR) constraints. Semidefinite relaxation (SDR) is used to convert the initial nonconvex optimization to be a convex semidefinite programming (SDP) problem. Then the optimality of SDR is strictly proved by showing the existence of the rank-one optimal solutions. To reduce the computational complexity, we develop zero forcing beamforming-based suboptimal algorithms, where the solutions can be obtained using golden search and closed-form solutions can be derived in each step. Simulation results are then provided to verify the efficiency of the proposed algorithms.
Zhu et al. (Tue,) studied this question.