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arXiv 1402.5326cs.ITmath.IT
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矢量空间干扰对齐所需的信道分集

Channel Diversity needed for Vector Space Interference Alignment

Cheuk Ting Li, Ayfer Özgür

摘要:

我们认为矢量空间的干扰对齐策略在$K$ -用户干扰信道,并得出一个上限的可实现的自由度作为信道分集的函数$L$,其中信道分集是由$L$实值并行信道与系数从一个非退化的联合分布。Cadambe和Jafar的开创性工作表明,当$L$是无界的时,矢量空间干扰对齐可以实现每个用户的$1/2$自由度,而与用户的数量$K$无关。然而,无线信道实际上具有有限的分集,这由它们的相干时间和带宽决定,并且重要的问题是在有限$L$处可实现的自由度的数量。当$K=3$和如果$L$是有限的,Bresler等人表明,矢量空间干涉对准可实现的自由度的数量是有界的远离$1/2$,和间隙减小成反比于$L$。在本文中,我们表明,当$K\geq4$,差距明显较大。特别地,与每个用户的最佳$1/2$自由度的间隙最多可以像$1/\sqrt{L}$那样减小,并且当$L$小于$2^{(K-2)(K-3)}$的量级时,它最多像$1/\sqrt[4]{L}$那样衰减。

英文摘要:

We consider vector space interference alignment strategies over the $K$-user interference channel and derive an upper bound on the achievable degrees of freedom as a function of the channel diversity $L$, where the channel diversity is modeled by $L$ real-valued parallel channels with coefficients drawn from a non-degenerate joint distribution. The seminal work of Cadambe and Jafar shows that when $L$ is unbounded, vector space interference alignment can achieve $1/2$ degrees of freedom per user independent of the number of users $K$. However wireless channels have limited diversity in practice, dictated by their coherence time and bandwidth, and an important question is the number of degrees of freedom achievable at finite $L$. When $K=3$ and if $L$ is finite, Bresler et al show that the number of degrees of freedom achievable with vector space interference alignment is bounded away from $1/2$, and the gap decreases inversely proportional to $L$. In this paper, we show that when $K\geq4$, the gap is significantly larger. In particular, the gap to the optimal $1/2$ degrees of freedom per user can decrease at most like $1/\sqrt{L}$, and when $L$ is smaller than the order of $2^{(K-2)(K-3)}$, it decays at most like $1/\sqrt[4]{L}$.

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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