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.
Highlights
It is widely known that proper Gaussian signals are capacityachieving in different wireless communication networks, such as the point-to-point, broadcast and multiple-access channels
We have analyzed the benefits of improper signaling in the single-antenna Z interference channel (Z-interference channel (IC))
Under the assumption that interference is treated as Gaussian noise, we have derived a complete and insightful characterization of the Pareto boundary of the rate region, and the corresponding transmit powers and circularity coefficients in closed-form
Summary
It is widely known that proper Gaussian signals are capacityachieving in different wireless communication networks, such as the point-to-point, broadcast and multiple-access channels. Less complex non-linear techniques have been studied (see, e.g., the characterization of the rate region boundary of the 2-user IC with successive interference cancellation at the receivers [35]) Even for such techniques, it is not known whether proper signaling is optimal. The inclusion of the spatial dimension makes a complete analytical assessment intractable, which is why the authors proposed an heuristic scheme to optimize the widely linear operation at the transmitter, which permits a trade-off between the rates of both users This way, [19] obtained an achievable rate region that is larger than that obtained by proper signaling. We adopt the augmented complex model to provide a complete and insightful characterization of the optimal rate region boundary, called the Pareto boundary, of the single-antenna Z-IC, when users may transmit improper Gaussian signals, assuming that interference is treated as noise. By adopting the augmented complex formulation, we provide, for each point of the boundary, closed-form
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