Comments on "Precoding and Artificial Noise Design for Cognitive MIMOME Wiretap Channels"

TL;DR

This paper critically reviews and corrects previous work on secrecy rate maximization in cognitive MIMOME wiretap channels, providing rigorous convergence proofs for the proposed algorithm and clarifying its optimality conditions.

Contribution

It identifies errors in prior work, offers corrected proofs, and establishes convergence and optimality properties of the secrecy rate maximization algorithm.

Findings

The algorithm generates an increasing, bounded sequence of secrecy rates.

Convergence to a KKT point is proven for the algorithm.

Global optimality is confirmed if the original problem is convex.

Abstract

Several gaps and errors in [1] are identified and corrected. While accommodating these corrections, a rigours proof is given that the successive convex approximation algorithm in [1] for secrecy rate maximization (SRM) does generate an increasing and bounded sequence of true secrecy rates and hence converges. It is further shown that its convergence point is a KKT point of the original SRM problem and, if the original problem is convex, this convergence point is globally-optimal, which is not necessarily the case in general. An interlacing property of the sequences of the true and approximate secrecy rates is established.