Extensions on `A Convex Scheme for the Secrecy Capacity of a MIMO Wiretap Channel with a Single Antenna Eavesdropper'

TL;DR

This paper extends previous work on the secrecy capacity of MIMO wiretap channels, demonstrating that the problem can be efficiently solved using convex optimization techniques by analyzing the convexity properties beyond a certain cutoff point.

Contribution

The paper introduces an extension to the convex scheme for MIMO secrecy capacity, addressing the region beyond the cutoff point where the problem transitions from concave to convex.

Findings

The scheme is concave up to a cutoff point.

Beyond the cutoff, the scheme becomes convex.

Efficient solutions are achievable using convex optimization software.

Abstract

One key metric for physical layer security is the secrecy capacity. This is the maximum rate that a system can transmit with perfect secrecy. For a Multiple Input Multiple Output (MIMO) system (a newer technology for 5G, 6G and beyond) the secrecy capacity is not fully understood. For a Gaussian MIMO channel, the secrecy capacity is a non-convex optimisation problem for which a general solution is not available. Previous work by the authors showed that the secrecy capacity of a MIMO system with a single eavesdrop antenna is concave to a cut off point. In this work, which extends the previous paper, results are given for the region beyond this cut off point. It is shown that, for certain parameters, the presented scheme is concave to a point, and convex beyond it, and can therefore be solved efficiently using existing convex optimisation software.