  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.
