Gaussian Half-Duplex Diamond Networks: Ratio of Capacity the Best Relay Can Achieve
Gaussian Half-Duplex Diamond Networks: Ratio of Capacity the Best Relay Can Achieve
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DOI：
10.1109/twc.2021.3066527
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发表时间：
2021-08
影响因子：
10.4
通讯作者：
Sarthak Jain;S. Mohajer;Martina Cardone
中科院分区：
文献类型：
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作者：
Sarthak Jain;S. Mohajer;Martina Cardone
本文考虑高斯半双工菱形$n$中继网络，其中源与目的地通过跳频信息通过一层$n$非通信中继，在半双工工作。主要的焦点包括调查以下问题：什么是一个单一的继电器对整个网络的近似容量的贡献？特别地，近似容量是指在仅取决于$n$的加性间隙内近似香农容量的量，并且与信道参数无关。本文回答了上述问题，提供了一个基本的约束之间的比率的近似容量的最高性能的单个中继和整个网络的近似容量，为任何数量$n$。令人惊讶的是，它表明，这样的比例保证是$f = 1/（2+2\cos（2\pi /（n+2）$，这是一个正弦函数的$n$，这减少了$n$增加。还表明，上述比率保证是严格的，即，存在高斯半双工菱形中继网络，其中最高性能中继具有等于整个网络的近似容量的一个分数的近似容量。
This paper considers Gaussian half-duplex diamond $n$ -relay networks, where a source communicates with a destination by hopping information through one layer of $n$ non-communicating relays that operate in half-duplex. The main focus consists of investigating the following question: What is the contribution of a single relay on the approximate capacity of the entire network? In particular, approximate capacity refers to a quantity that approximates the Shannon capacity within an additive gap which only depends on $n$ , and is independent of the channel parameters. This paper answers the above question by providing a fundamental bound on the ratio between the approximate capacity of the highest-performing single relay and the approximate capacity of the entire network, for any number $n$ . Surprisingly, it is shown that such a ratio guarantee is $f = 1/(2+2\cos (2\pi /(n+2)))$ , that is a sinusoidal function of $n$ , which decreases as $n$ increases. It is also shown that the aforementioned ratio guarantee is tight, i.e., there exist Gaussian half-duplex diamond $n$ -relay networks, where the highest-performing relay has an approximate capacity equal to an $f$ fraction of the approximate capacity of the entire network.