On the Secrecy Capacity of a MIMO Gaussian Wiretap Channel with a Cooperative Jammer

TL;DR

This paper investigates the secrecy capacity of a multi-antenna Gaussian wiretap channel with a helper, proposing convex optimization-based solutions and analyzing the secure degrees of freedom to enhance understanding of secure communication limits.

Contribution

It introduces a convex optimization framework for secrecy capacity calculation and derives closed-form solutions for the helper-assisted MIMO wiretap channel.

Findings

Secrecy capacity can be computed via convex optimization and search methods.

Maximal secure degrees of freedom are characterized in closed-form.

Proposed schemes demonstrate effectiveness through numerical results.

Abstract

We study the secrecy capacity of a helper-assisted Gaussian wiretap channel with a source, a legitimate receiver, an eavesdropper and an external helper, where each terminal is equipped with multiple antennas. Determining the secrecy capacity in this scenario generally requires solving a nonconvex secrecy rate maximization (SRM) problem. To deal with this issue, we first reformulate the original SRM problem into a sequence of convex subproblems. For the special case of single-antenna legitimate receiver, we obtain the secrecy capacity via a combination of convex optimization and one-dimensional search, while for the general case of multi-antenna legitimate receiver, we propose an iterative solution. To gain more insight into how the secrecy capacity of a helper-assisted Gaussian wiretap channel behaves, we examine the achievable secure degrees of freedom (s.d.o.f.) and obtain the maximal achievable s.d.o.f. in closed-form. We also derive a closed-form solution to the original SRM problem which achieves the maximal s.d.o.f.. Numerical results are presented to illustrate the efficacy of the proposed schemes.