Efficient Numerical Methods for Secrecy Capacity of Gaussian MIMO Wiretap Channel

TL;DR

This paper introduces two low-complexity algorithms for efficiently computing the secrecy capacity of Gaussian MIMO wiretap channels under power constraints, leveraging convex optimization and reformulation techniques.

Contribution

The paper proposes novel accelerated DC and partial best response algorithms that simplify and speed up secrecy capacity calculations for MIMO wiretap channels.

Findings

Both methods outperform existing approaches in computational efficiency.

Water-filling solutions are derived for each convex subproblem.

Simulation results confirm the superior performance of the proposed algorithms.

Abstract

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.