# Robust Improper Signaling for Two-user SISO Interference Channels

## TL;DR

This paper investigates the robustness of improper Gaussian signaling (IGS) in two-user SISO interference channels under imperfect channel state information, proposing closed-form robust designs that outperform non-robust solutions.

## Contribution

It introduces robust IGS designs for interference channels with imperfect CSI, ensuring performance gains and robustness against channel uncertainties.

## Key findings

- Robust IGS designs outperform non-robust solutions.
- Closed-form solutions are derived for both IC and Z-IC scenarios.
- Performance is maintained or improved under channel uncertainty.

## Abstract

It has been shown that improper Gaussian signaling (IGS) can improve the performance of wireless interference-limited systems when perfect channel state information (CSI) is available. In this paper, we investigate the robustness of IGS against imperfect CSI on the transmitter side in a two-user single-input single-output (SISO) interference channel (IC) as well as in a SISO Z-IC, when interference is treated as noise. We assume that the true channel coefficients belong to a known region around the channel estimates, which we call the uncertainty region. Following a worst-case robustness approach, we study the rate-region boundary of the IC for the worst channel in the uncertainty region. For the two-user IC, we derive a robust design in closed-form, which is independent of the phase of the channels by allowing only one of the users to transmit IGS. For the Z-IC, we provide a closed-form design for the transmission parameters by considering an enlarged uncertainty region and allowing both users to employ IGS. In both cases, the IGS-based designs are ensured to perform no worse than proper Gaussian signaling. Furthermore, we show, through numerical examples, that the proposed robust designs significantly outperform non-robust solutions.