Diophantine approximation and applications in interference alignment
Diophantine approximation and applications in interference alignment
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丢番图近似及其在干涉对准中的应用
DOI：
10.1016/j.aim.2016.07.002
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发表时间：
2016
影响因子：
1.7
通讯作者：
Adiceam F
中科院分区：
文献类型：
--
作者：
Adiceam F
丢番图近似最近在电子学中的应用，特别是在快速发展的干涉对准领域的应用，激发了本文的研究。在这一领域的一些显著进展，很大程度上归功于基本的Khintchine-Groshev定理，特别是它对欧几里得空间子流形的深远推广。从上述应用的角度来看，这里我们引入并证明了rn的非退化子流形的Khintchine-Groshev定理的定量显式推广。这种定量表述的重要性在Jafar的专著[12，§4.7]中有明确的讨论。1]。
This paper is motivated by recent applications of Diophantine approximation in electronics, in particular, in the rapidly developing area of Interference Alignment. Some remarkable advances in this area give substantial credit to the fundamental Khintchine–Groshev Theorem and, in particular, to its far reaching generalisation for submanifolds of a Euclidean space. With a view towards the aforementioned applications, here we introduce and prove quantitative explicit generalisations of the Khintchine–Groshev Theorem for non-degenerate submanifolds of R n. The importance of such quantitative statements is explicitly discussed in Jafar's monograph [12, § 4.7. 1].