MIMO Wiretap 频道保密率最大化的固定解决办法的最佳程度 (On the Optimality of the Stationary Solution of Secrecy Rate Maximization for MIMO Wiretap Channel)

To achieve perfect secrecy in a multiple-input multiple-output (MIMO) Gaussian wiretap channel (WTC), we need to find its secrecy capacity and optimal signaling, which involves solving a difference of convex functions program known to be non-convex for the non-degraded case. To deal with this, a class of existing solutions have been developed but only local optimality is guaranteed by standard convergence analysis. Interestingly, our extensive numerical experiments have shown that these local optimization methods indeed achieve global optimality. In this paper, we provide an analytical proof for this observation. To achieve this, we show that the Karush-Kuhn-Tucker (KKT) conditions of the secrecy rate maximization problem admit a unique solution for both degraded and non-degraded cases. Motivated by this, we also propose a low-complexity algorithm to find a stationary point. Numerical results are presented to verify the theoretical analysis.

翻译：为了在多投入多输出(MIMO)Gaussian窃听频道(WTC)实现完全保密,我们需要找到它的保密能力和最佳信号,这需要解决已知对非降级案件而言非解密的 convex 函数程序的差异。要解决这个问题,已经开发出一系列现有解决方案,但标准趋同分析只保证地方最佳性。有趣的是,我们广泛的数字实验表明,这些本地优化方法确实实现了全球最佳性。在本文中,我们为这一观察提供了分析证据。为了实现这一点,我们证明,保密率最大化问题的Karush-Kuhn-Tucker(KKKT)条件为退化和非降级案件提供了独特的解决办法。为此,我们还提出了低兼容性算法,以找到一个固定点。我们提出了数字结果,以核实理论分析。