Rate region boundary of the SISO Z-interference channel with improper signaling

TL;DR

This paper characterizes the boundary of the achievable rate region for the SISO Z-interference channel using improper Gaussian signaling, providing conditions for optimality and insights into when impropriety enhances performance.

Contribution

It offers a complete characterization of the Pareto boundary with improper signaling, including a necessary and sufficient condition for optimality and a closed-form expression for the circularity coefficient.

Findings

Improper signaling can outperform proper signaling under certain interference conditions.

A threshold on the interference channel coefficient determines the optimality of improper signaling.

Closed-form expression for the optimal circularity coefficient is derived.

Abstract

This paper provides a complete characterization of the boundary of an achievable rate region, called the Pareto boundary, of the single-antenna Z interference channel (Z-IC), when interference is treated as noise and users transmit complex Gaussian signals that are allowed to be improper. By considering the augmented complex formulation, we derive a necessary and sufficient condition for improper signaling to be optimal. This condition is stated as a threshold on the interference channel coefficient, which is a function of the interfered user rate and which allows insightful interpretations into the behavior of the achievable rates in terms of the circularity coefficient (i.e., degree of impropriety). Furthermore, the optimal circularity coefficient is provided in closed form. The simplicity of the obtained characterization permits interesting insights into when and how improper signaling outperforms proper signaling in the single-antenna Z-IC. We also provide an in-depth discussion on the optimal strategies and the properties of the Pareto boundary.