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.

中文翻译：

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将干扰视为噪声的双用户 SIMO 干扰信道：不正确的信令与分时

在具有高斯输入且将干扰视为噪声 (TIN) 的双用户高斯干扰信道中，如果不允许分时或仅对几种传输策略（凸包公式）的数据速率进行平均，则不正确的复杂信号可能是有益的. 另一方面，如果考虑编码分时，即如果数据速率和发射功率均被平均，则适当的（圆对称）信号最近已被证明是最佳的。在本文中，我们表明，如果考虑在接收器处具有多个天线的单输入多输出 (SIMO) 系统，则两个结论都保持不变。编码分时情况的证明是通过一种新颖的增强型信道概念，用于双用户 SIMO 干扰信道，事实证明，它为具有编码分时的 TIN 速率区域提供了一个紧密的外部边界。通过研究新提出的针对不当信令的复合实梯度投影方法可以优于全局最优适当信令策略的具体例子，证明了没有编码分时的情况下的结果。此外，我们讨论了如何以数字方式计算具有编码分时的可实现 TIN 速率区域。