[论文解读] Interference Mitigation in Large Random Wireless Networks

Matthew Aldridge|arXiv (Cornell University)|Sep 6, 2011

Wireless Communication Security Techniques参考文献 70被引用 3

一句话总结

该论文通过遍历干扰对齐，建立了大规模随机密集高斯干扰网络的渐近和容量。证明了在一般幂律路径损耗和随机节点分布下，随着网络规模增大，平均用户容量以概率收敛于 $\frac{1}{2}\mathbb{E}\log(1+2\mathtt{SNR})$，解决了大规模无线网络容量极限中的一个关键开放问题。

ABSTRACT

A central problem in the operation of large wireless networks is how to deal with interference -- the unwanted signals being sent by transmitters that a receiver is not interested in. This thesis looks at ways of combating such interference. In Chapters 1 and 2, we outline the necessary information and communication theory background, including the concept of capacity. We also include an overview of a new set of schemes for dealing with interference known as interference alignment, paying special attention to a channel-state-based strategy called ergodic interference alignment. In Chapter 3, we consider the operation of large regular and random networks by treating interference as background noise. We consider the local performance of a single node, and the global performance of a very large network. In Chapter 4, we use ergodic interference alignment to derive the asymptotic sum-capacity of large random dense networks. These networks are derived from a physical model of node placement where signal strength decays over the distance between transmitters and receivers. (See also arXiv:1002.0235 and arXiv:0907.5165.) In Chapter 5, we look at methods of reducing the long time delays incurred by ergodic interference alignment. We analyse the tradeoff between reducing delay and lowering the communication rate. (See also arXiv:1004.0208.) In Chapter 6, we outline a problem that is equivalent to the problem of pooled group testing for defective items. We then present some new work that uses information theoretic techniques to attack group testing. We introduce for the first time the concept of the group testing channel, which allows for modelling of a wide range of statistical error models for testing. We derive new results on the number of tests required to accurately detect defective items, including when using sequential `adaptive' tests.

研究动机与目标

• 在现实路径损耗和衰落模型下，确定大规模随机密集无线网络的根本和容量极限。
• 解决此类网络中渐近用户容量表征的开放问题。
• 证明遍历干扰对齐在密集随机网络中可实现最优标度。
• 通过瓶颈链路论证和概率计数，提供容量标度的严格信息论证明。
• 将先前关于和容量的结果推广至更广泛的空间分布和衰落模型，超越均匀分布和瑞利衰落。

提出的方法

• 将网络建模为具有时变衰落系数和距离相关路径损耗的 $n$-用户高斯干扰信道。
• 采用遍历干扰对齐，其中信道系数中的随机相位使得干扰在时间上得以对齐，从而在接收端实现干扰消除。
• 应用 Jafar 提出的瓶颈链路论证，通过识别限制整体网络吞吐量的关键链路来上界和容量。
• 使用概率计数方法，证明在随机网络中，大量此类瓶颈链路以高概率存在。
• 通过熵功率不等式和瓶颈链路容量的互信息界，推导直接的反向证明。
• 采用一般幂律衰减模型，其中信号功率随距离衰减，不限于均匀节点分布。

实验结果

研究问题

• RQ1 在一般路径损耗和随机节点分布下，大规模随机密集无线网络的渐近和容量是多少？
• RQ2 遍历干扰对齐能否在该类网络中实现最优和容量标度？
• RQ3 当用户数 $n$ 趋近于无穷大时，平均用户容量如何变化？
• RQ4 瓶颈链路在限制大规模干扰网络和容量方面起什么作用？
• RQ5 一般衰落模型和非均匀节点分布如何影响容量标度律？

主要发现

• 在一般幂律衰减和独立随机节点分布下，平均用户容量 $C_{\Sigma}/n$ 以概率收敛于 $\frac{1}{2}\mathbb{E}\log(1+2\mathtt{SNR})$，当 $n \to \infty$ 时。
• 该结果适用于发射机和接收机的任意空间分布，不限于单位正方形上的均匀分布。
• 遍历干扰对齐实现了最优和容量标度，与通过瓶颈链路分析导出的理论上限完全匹配。
• 证明通过瓶颈链路的概率计数和其容量的信息论界，建立了紧致的反向证明。
• 该结果推广了 Jafar 和 Johnson 等人的先前发现，将其扩展至非均匀节点分布和任意路径损耗函数。
• 在给定衰落和路径损耗假设下，渐近容量与网络几何无关，仅取决于期望信噪比 $\mathtt{SNR}$。