Optimal power allocation for achieving perfect secrecy capacity in MIMO wire-tap channels

In this paper, we investigate optimal power allocation to achieve perfect secrecy capacity in Gaussian MIMO wire-tap channels. The number of antennas in the MIMO wire-tap channel is arbitrary at the transmitter, the intended receiver, and the eavesdropper. For this challenging non-convex optimization problem, we design a novel global optimization algorithm called branch-and-bound with reformulation and linearization technique (BB/RLT). As opposed to convex programming methods that only yield local optimal solutions, our proposed BB/RLT method guarantees finding a global optimal solution. The main contribution in this paper is that our proposed BB/RLT algorithm is the first method that solves the optimal power allocation problem for achieving perfect secrecy capacity problem in MIMO wire-tap channels. Numerical examples are also given to demonstrate the efficacy of the proposed algorithm.