arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 1506.03319cs.ITmath.IT
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$K$ -用户高斯干扰信道的容量界

Capacity Bounds for the $K$-User Gaussian Interference Channel

Junyoung Nam

摘要:

$K$ -用户高斯干扰信道(GIC)的容量域是一个长期存在的公开问题,甚至容量的外界一般都知之甚少。$K$ -用户GIC的自由度(DoF)分析(一阶容量近似)的重大进展为高信噪比(SNR)限制下的感兴趣问题提供了新的重要见解。然而,已经观察到这种容量近似在预测\emph{finite} SNR下的容量时具有一些限制。在这项工作中,我们开发了一种新的上限技术,利用一种新的类型的精灵信号和应用\emph{time sharing}精灵信号在$K$接收器。基于这种技术,我们推导出新的上限上的三个用户的GIC与恒定的,复杂的信道系数的总和容量,然后推广到$K$ -用户的情况下,以更好地了解在有限的SNR和速率的行为。我们还提供了封闭形式的表达式,我们的上限上的容量的$K$ -用户对称GIC容易计算\emph{any} $K$。从我们的结果的角度来看,在有限的SNR的一些总和速率的行为是符合已知的自由度的结果给出的见解,而其他一些则不是。特别地,对于几乎所有恒定实信道系数可实现的公知的$K/2$ DoF在$K$ -用户对称实情况下,特别是对于\emph{large} $K$,在一定范围的交叉信道系数上没有体现为实质的性能增益。我们进一步研究了直接信道系数和交叉信道系数之间的相位偏移对三用户\emph{complex} GIC的和速率上界的影响。因此,我们的目标是提供新的发现,不能预测的自由度的GIC的先前的工作。

英文摘要:

The capacity region of the $K$-user Gaussian interference channel (GIC) is a long-standing open problem and even capacity outer bounds are little known in general. A significant progress on degrees-of-freedom (DoF) analysis, a first-order capacity approximation, for the $K$-user GIC has provided new important insights into the problem of interest in the high signal-to-noise ratio (SNR) limit. However, such capacity approximation has been observed to have some limitations in predicting the capacity at \emph{finite} SNR. In this work, we develop a new upper-bounding technique that utilizes a new type of genie signal and applies \emph{time sharing} to genie signals at $K$ receivers. Based on this technique, we derive new upper bounds on the sum capacity of the three-user GIC with constant, complex channel coefficients and then generalize to the $K$-user case to better understand sum-rate behavior at finite SNR. We also provide closed-form expressions of our upper bounds on the capacity of the $K$-user symmetric GIC easily computable for \emph{any} $K$. From the perspectives of our results, some sum-rate behavior at finite SNR is in line with the insights given by the known DoF results, while some others are not. In particular, the well-known $K/2$ DoF achievable for almost all constant real channel coefficients turns out to be not embodied as a substantial performance gain over a certain range of the cross-channel coefficient in the $K$-user symmetric real case especially for \emph{large} $K$. We further investigate the impact of phase offset between the direct-channel coefficient and the cross-channel coefficients on the sum-rate upper bound for the three-user \emph{complex} GIC. As a consequence, we aim to provide new findings that could not be predicted by the prior works on DoF of GICs.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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