标题： 具有 Gaussian MIMO 窃听信道的安全通信最优信号传输 显示英文标题

标题： Optimal Signaling for Secure Communications over Gaussian MIMO Wiretap Channels

摘要： 研究了在总发射功率约束下高斯MIMO窃听信道上的最优信号传输。 当信道严格退化时，得到了一个最优发射协方差矩阵的显式解。 结合秩-1解，这提供了两个发射天线情况下最优协方差的完整表征。 考虑了弱窃听者和高信噪比的情况。 结果显示，在高信噪比情况下，最优协方差不会收敛到缩放的单位矩阵。 对于一般情况，建立了必要的最优条件，并给出了最优协方差矩阵秩的紧上界，同时还给出了保密容量的下界，该下界在许多场景中是紧的。 显示英文摘要

摘要： Optimal signalling over the Gaussian MIMO wire-tap channel is studied under the total transmit power constraint. A closed-form solution for an optimal transmit covariance matrix is obtained when the channel is strictly degraded. In combination with the rank-1 solution, this provides the complete characterization of the optimal covariance for the case of two transmit antennas. The cases of weak eavesdropper and high SNR are considered. It is shown that the optimal covariance does not converge to a scaled identity in the high-SNR regime. Necessary optimality conditions and a tight upper bound on the rank of an optimal covariance matrix are established for the general case, along with a lower bound to the secrecy capacity, which is tight in a number of scenarios.