  This paper presents two different low-complexity methods for obtaining the
secrecy capacity of multiple-input multiple-output (MIMO) wiretap channel
subject to a sum power constraint (SPC). The challenges in deriving
computationally efficient solutions to the secrecy capacity problem are due to
the fact that the secrecy rate is a difference of convex functions (DC) of the
transmit covariance matrix, for which its convexity is only known for \emph{the
degraded case}. In the first method, we capitalize on the accelerated DC
algorithm, which requires solving a sequence of convex subproblems. In
particular, we show that each subproblem indeed admits a water-filling
solution. In the second method, based on the equivalent convex-concave
reformulation of the secrecy capacity problem, we develop a so-called partial
best response algorithm (PBRA). Each iteration of the PBRA is also done in
closed form. Simulation results are provided to demonstrate the superior
performance of the proposed methods.
