Improper Signaling versus Time-Sharing in the Two-User Gaussian Interference Channel with TIN

TL;DR

This paper demonstrates that in the two-user Gaussian interference channel with treat interference as noise, allowing coded time-sharing makes proper signals optimal, contrasting previous findings with pure strategies.

Contribution

It extends the analysis of improper signaling by including coded time-sharing, showing proper signals become optimal in this more general setting.

Findings

Proper signals are optimal when coded time-sharing is allowed.

The rate region can be computed using a new algorithm.

Coded time-sharing changes the optimal signaling strategy.

Abstract

So-called improper complex signals have been shown to be beneficial in the single-antenna two-user Gaussian interference channel under the assumptions that all input signals are Gaussian and that we treat interference as noise (TIN). This result has been obtained under a restriction to pure strategies without time-sharing, and it was extended to the case where the rates, but not the transmit powers, may be averaged over several transmit strategies. In this paper, we drop such restrictions and discuss the most general case of coded time-sharing, where both the rates and the powers may be averaged. Since coded time-sharing can in general not be expressed by means of a convex hull of the rate region, we have to account for the possibility of time-sharing already during the optimization of the transmit strategy. By means of a novel channel enhancement argument, we prove a surprising result: proper signals are optimal if coded time-sharing is allowed. In addition to establishing this result, we present an algorithm to compute the corresponding achievable rate region.