In this paper, fast fading Gaussian multiuser channels are considered. If the channel state information (CSI) is perfectly known to the transmitter, capacities have been derived for many cases in which the channels satisfy certain information-theoretic orders such as degradedness, or strong/very strong interference. We study the case when only the statistics of the CSI are known at the transmitter, which is an open problem in general. The main contributions of this paper are the following: First, we derive a sufficient condition to construct equivalent (having the same capacity region as the original channel) degraded Gaussian broadcast channels, which is based on the marginal distributions of the channel gains. To achieve this goal, we leverage three schemes: coupling, maximal coupling, and copulas, in addition to the same marginal property. The underlying idea of all schemes is to obtain an equivalent channel by changing the joint distribution in such a way that it satisfies a certain information-theoretic order while ensuring that the marginal distributions of the channels to different users are not changed. The construction of this equivalent multiuser channel allows us to directly apply existing capacity results. We then further derive the capacity regions of Gaussian interference channels with strong and very strong interferences, and also the secrecy capacity of Gaussian wiretap channels, while in all cases, the transmitters know only the statistics of the channels. Several practical examples such as Rayleigh fading and Nakagami-m fading illustrate the applicability of the derived results.

中文翻译：

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利用统计 CSIT 得出衰落高斯多用户信道的新容量结果


在本文中，考虑快衰落高斯多用户信道。如果发射机完全了解信道状态信息（CSI），则可以针对许多情况导出容量，其中信道满足某些信息论顺序，例如退化或强/非常强干扰。我们研究了发射机处仅知道 CSI 统计数据的情况，这通常是一个悬而未决的问题。本文的主要贡献如下：首先，我们推导了构造等效（与原始信道具有相同容量区域）退化高斯广播信道的充分条件，该条件基于信道增益的边际分布。为了实现这个目标，除了相同的边际属性之外，我们还利用了三种方案：耦合、最大耦合和 copula。所有方案的基本思想是通过改变联合分布来获得等效信道，使其满足一定的信息论顺序，同时确保信道对不同用户的边际分布不改变。这个等效多用户通道的构建使我们能够直接应用现有的容量结果。然后，我们进一步推导具有强和非常强干扰的高斯干扰信道的容量区域，以及高斯窃听信道的保密容量，而在所有情况下，发射机只知道信道的统计数据。瑞利衰落和Nakagami-m衰落等几个实际例子说明了推导结果的适用性。