Optimal signal design strategy with improper Gaussian signaling in the Z-interference channel

本文提出一种用于在干扰被视为加性高斯噪声的假设下在Z干扰信道(z-interference channel,Z-IC)上实现非正则高斯信号(IGS)的Pareto边界(可实现速率区域的边界)。具体来说,文章表明了帕累托边界可由某个用户的传输速率的两个区域表征,由传输信号的方差与伪协方差的两个变化路径决定。为每个用户发送的非正则信号的最优协方差和伪协方差设计推导出简明闭合的表达式。为此,我们通过仿真试验有力证明了所提出的最优信号设计策略的有效性,同时直观地展现出IGS较正则高斯信号(proper Gaussian signaling,PGS)的优越性。此外,我们提出的最优信号设计策略提供了实现所需速率区域的简单方法。利用该方法,我们得到了一个闭合形式的解决方案,用于快速确定最大和速率的信号设计方案。最后,我们深入讨论了帕累托边界的特征,定性分析了信道系数以及两个用户发送的信号的协方差和伪协方差与其的关系。

We propose a thoroughly optimal signal design strategy to achieve the Pareto boundary （boundary of the achievable rate region） with improper Gaussian signaling （IGS） on the Z-interference channel （Z-IC） under the assumption that the interference is treated as additive Gaussian noise. Specifically, we show that the Pareto boundary has two different schemes determined by the two paths manifesting the characteristic of improperly transmitted signals. In each scheme, we derive several concise closed-form expressions to calculate each user＇s optimally transmitted power, covariance, and pseudo-covariance of improperly transmitted signals. The effectiveness of the proposed optimal signal design strategy is supported by simulations, and the results clearly show the superiority of IGS. The proposed optimal signal design strategy also provides a simple way to achieve the required rate region, with which we also derive a closed-form solution to quickly find the circularity coefficient that maximizes the sum rate. Finally, we provide an in-depth discussion of the structure of the Pareto boundary, characterized by the channel coefficient, the degree of impropriety measured by the covariance, and the pseudo-covaxiance of signals transmitted by two users.