  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.
