Two-User SIMO Interference Channel with Treating Interference as Noise: Improper Signaling Versus Time-Sharing

In the two-user Gaussian interference channel with Gaussian inputs and treating interference as noise (TIN), improper complex signals can be beneficial if time-sharing is not allowed or if only the data rates are averaged over several transmit strategies (convex hull formulation). On the other hand, proper (circularly symmetric) signals have recently been shown to be optimal if coded time-sharing is considered, i.e., if both the data rates and the transmit powers are averaged. In this paper, we show that both conclusions remain the same if single-input multiple-output (SIMO) systems with multiple antennas at the receivers are considered. The proof for the case with coded time-sharing is via a novel enhanced channel concept for the two-user SIMO interference channel, which turns out to deliver a tight outer bound to the TIN rate region with coded time-sharing. The result for the case without coded time-sharing is demonstrated by studying specific examples in which a newly proposed composite real gradient-projection method for improper signaling can outperform the globally optimal proper signaling strategy. In addition, we discuss how the achievable TIN rate region with coded time-sharing can be computed numerically.