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arXiv 0905.1745cs.ITmath.IT
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O(1)内一类对称SIMO高斯干扰信道的容量

Capacity of a Class of Symmetric SIMO Gaussian Interference Channels within O(1)

Tiangao Gou, Syed A. Jafar

摘要:

研究了N+1用户、1 × N单输入多输出(SIMO)高斯干扰信道,其中每个发射机有一个单天线,每个接收机有N个天线。O(1)内的对称容量针对对称情况来表征,其中所有直接链路具有相同的信噪比(SNR),并且所有不期望的链路具有相同的干扰噪声比(INR)。精确容量的间隙是一个常数,与SNR和INR无关。为了得到这一结果,我们首先推广了由El Gamal和Costa引入的确定性干扰信道来建模具有多个天线的干扰信道。我们推导出这种确定性干扰信道的容量区域。基于确定性信道提供的见解,我们描述了高斯情况下的广义自由度(GDOF),这直接导致O(1)的容量近似。在可扩展性方面,一个有趣的结论是,在N+1用户、1 × N SIMO情况下,发现将干扰视为噪声的广义自由度(GDOF)机制在2用户干扰信道中是最优的。在相反的方面,新的多用户外部边界出现在这项工作中,并不直接遵循2用户的情况。除了GDOF区域之外,外部边界还标识了建立容量区域的强干扰机制。

英文摘要:

The N+1 user, 1 x N single input multiple output (SIMO) Gaussian interference channel where each transmitter has a single antenna and each receiver has N antennas is studied. The symmetric capacity within O(1) is characterized for the symmetric case where all direct links have the same signal-to-noise ratio (SNR) and all undesired links have the same interference-to-noise ratio (INR). The gap to the exact capacity is a constant which is independent of SNR and INR. To get this result, we first generalize the deterministic interference channel introduced by El Gamal and Costa to model interference channels with multiple antennas. We derive the capacity region of this deterministic interference channel. Based on the insights provided by the deterministic channel, we characterize the generalized degrees of freedom (GDOF) of Gaussian case, which directly leads to the O(1) capacity approximation. On the achievability side, an interesting conclusion is that the generalized degrees of freedom (GDOF) regime where treating interference as noise is found to be optimal in the 2 user interference channel, does not appear in the N+1 user, 1 x N SIMO case. On the converse side, new multi-user outer bounds emerge out of this work that do not follow directly from the 2 user case. In addition to the GDOF region, the outer bounds identify a strong interference regime where the capacity region is established.

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