This paper explores the network simplification problem for Gaussian full-duplex relay networks with arbitrary topology. Particularly, given an $N$ -relay Gaussian full-duplex network, the network simplification problem seeks to find fundamental guarantees on the capacity of the best subnetwork, among a particular class of subnetworks, as a fraction of the full-network capacity. The focus of this work is the case when the selected subnetwork class is a path from the source to the destination. The main result of the paper shows that for an $N$ -relay Gaussian networks with arbitrary topology, the best route can in the worst case guarantee an approximate fraction $\frac {1}{ \lfloor N/2 \rfloor + 1}$ of the capacity of the full network, independently of the channel coefficients and/or operating SNR. Furthermore, this guarantee is shown to be fundamental, i.e., it is the highest worst-case guarantee that can be provided for routing in relay networks. A key step in the proof of the main result lies in the derivation of a simplification result for antenna selection in MIMO channels that may also be of independent interest. To the best of our knowledge, this is the first result that characterizes the performance of routing in comparison to physical layer cooperation techniques that approximately achieve the network capacity for general wireless network topologies. The results in this paper show that routing can, in the worst case, result in an unbounded gap from the network capacity - or reversely, physical layer cooperation can offer unbounded gains over routing.

中文翻译：

---

无线网络简化：路由性能

本文探讨了 网络简化具有任意拓扑结构的高斯全双工中继网络问题。特别地，给定一个 $N$ -relay Gaussian 全双工网络，网络简化问题寻求找到最佳子网络容量的基本保证，在特定类别的子网络中，作为全网络容量的一小部分。这项工作的重点是所选子网类是从源到目标的路径的情况。论文的主要结果表明，对于一个 $N$ -具有任意拓扑结构的中继高斯网络，最佳路由在最坏情况下可以保证近似分数 $\frac {1}{ \lfloor N/2 \rfloor + 1}$ 整个网络的容量，与信道系数和/或操作 SNR 无关。此外，这种保证被证明是基本的，即它是可以为中继网络中的路由提供的最高最坏情况保证。证明主要结果的关键步骤在于推导出 MIMO 信道中天线选择的简化结果，这也可能是独立感兴趣的。据我们所知，与物理层协作技术相比，这是表征路由性能的第一个结果，物理层协作技术大致实现了一般无线网络拓扑的网络容量。本文中的结果表明，在最坏的情况下，路由会导致与网络容量的无限差距 - 或者相反，