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中文摘要：
针对双向多天线中继系统中存在多个单天线窃听者的场景,在保证两个源节点安全速率情况下,提出了两种中继节点发送功率最小化方案：人工噪声辅助的波束成形（artificial noise aided beamforming,ANAB）方案和零空间波束成形（null space beamforming,NSB）方案。ANAB采用半定松弛（semidefinite relaxation,SDR）技术和连续的凸估计（successive convex approximation,SCA）算法,得到局部最优的波束成形和人工噪声协方差矩阵。考虑到中继节点的天线个数大于窃听节点个数,设计了低复杂度NSB方案,在等效窃听信道矩阵的零空间中发送保密信息,通过求解一个SDP问题得到波束成形解。仿真结果表明,所提的安全发送方法可以有效地降低中继节点的发送功率。
英文摘要：
For two-way multi-antenna relay systems in the presence of multiple eavesdroppers e- quipped with a single antenna, two schemes are proposed to minimize the relay power while satisfying individual secrecy rate constraints. For the proposed ANAB scheme, the locally optimal beam-forming and artificial noise covariance matrices are obtained by using the semidefinite relaxation （SDR） technique and the successive convex approximation algorithm. Considering the special case where there are more antennas at the relay than the number of eavesdroppers, the NSB scheme with a lower computation complexity is proposed. The confidential messages are transmitted in the null space of the equivalent eavesdroppers＇ channel, and the beamforming solution can be obtained by solving a semidefinite programming （SDP）. Simulation results demonstrate that the proposed meth- ods can decrease the consumed power at the relay subject to the given secrecy rate constraints.
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