[论文解读] Towards a Tractable Analysis of Localization Fundamentals in Cellular Networks

Javier Schloemann, Harpreet S. Dhillon+1 more|arXiv (Cornell University)|Feb 24, 2015

Indoor and Outdoor Localization Technologies参考文献 27被引用 6

一句话总结

本文提出了一种可处理的随机几何框架，通过将基站（BS）位置建模为泊松点过程（PPP），分析蜂窝网络定位性能，实现对检测到最少数量基站以实现定位的概率的解析评估。主要贡献是推导出一个闭式表达式，用于定位成功概率，该表达式综合考虑了路径损耗、干扰和基站协调，提供了一个通用且无偏的度量指标，与特定定位技术无关。

ABSTRACT

When dedicated positioning systems, such as GPS, are unavailable, a mobile device has no choice but to fall back on its cellular network for localization. Due to random variations in the channel conditions to its surrounding base stations (BS), the mobile device is likely to face a mix of both favorable and unfavorable geometries for localization. Analytical studies of localization performance (e.g., using the Cramér-Rao lower bound) usually require that one fix the BS geometry, and favorable geometries have always been the preferred choice in the literature. However, not only are the resulting analytical results constrained to the selected geometry, this practice is likely to lead to overly-optimistic expectations of typical localization performance. Ideally, localization performance should be studied across all possible geometric setups, thereby also removing any selection bias. This, however, is known to be hard and has been carried out only in simulation. In this paper, we develop a new tractable approach where we endow the BS locations with a distribution by modeling them as a Poisson point process (PPP), and use tools from stochastic geometry to obtain easy-to-use expressions for key performance metrics. In particular, we focus on the probability of detecting some minimum number of BSs, which is shown to be closely coupled with a network operator's ability to obtain satisfactory localization performance (e.g., meet FCC E911 requirements). This metric is indifferent to the localization technique (e.g., TOA, TDOA, AOA, or hybrids thereof), though different techniques will presumably lead to different BS hearability requirements. In order to mitigate excessive interference due to the presence of dominant interferers in the form of other BSs, we incorporate both BS coordination and frequency reuse in the proposed framework and quantify the resulting performance gains analytically.

研究动机与目标

• 解决在真实、随机网络条件下缺乏通用解析模型来评估蜂窝网络定位性能的问题。
• 消除以往研究中仅考虑有利于定位的几何结构所带来的选择偏差。
• 开发一个可处理的框架，捕捉随机BS分布、路径损耗和干扰对定位成功率的影响。
• 量化检测到实现可靠定位所需最少数量BS的概率，该概率与FCC E911要求相关。
• 通过调整干扰项并推导不同路径损耗指数下的SIR和$ \mathtt{P_L} $的闭式表达式，分析性评估在干扰受限场景中BS协调和频率复用带来的性能增益。

提出的方法

• 将基站位置建模为齐次泊松点过程（PPP），以捕捉蜂窝网络中的空间随机性。
• 利用随机几何工具推导到最近和次近基站距离的分布，实现可处理的分析。
• 通过考虑路径损耗、来自多个BS的干扰以及频率复用，构建移动终端处的信号干扰比（SIR）。
• 通过引入一个替代变量$ X $来近似距离比$ R_L / \hat{R}_1 $，将双重积分简化为单重积分。
• 通过在$ X $的分布上积分并基于干扰波束数$ \Omega $进行条件化，推导出定位成功概率$ \mathtt{P_L} $。
• 通过调整干扰项并推导不同路径损耗指数下SIR和$ \mathtt{P_L} $的闭式表达式，整合BS协调和频率复用。

实验结果

研究问题

• RQ1 在随机部署的蜂窝网络中，检测到至少最少数量基站用于定位的概率是多少？
• RQ2 基站的随机空间分布在多大程度上影响蜂窝定位的可靠性？
• RQ3 在干扰受限环境中，BS协调和频率复用能在多大程度上提升定位性能？
• RQ4 所提出的模型如何避免以往研究中假设有利、确定性几何结构所带来的偏差？
• RQ5 能否开发一个可处理的解析框架，在不依赖仿真或固定几何假设的前提下评估定位性能？

主要发现

• 本文推导出定位成功概率$ \mathtt{P_L} $的闭式表达式，其仅依赖于路径损耗指数、BS密度和干扰参数。
• 所推导的$ \mathtt{P_L} $表达式与具体定位技术（如TOA、TDOA、AOA）无关，具有广泛适用性。
• 对于路径损耗指数$ \alpha = 4 $的特殊情况，本文提供了依赖于干扰波束数$ \Omega $和SIR阈值的$ \mathtt{P_L} $的简化解析表达式。
• 模型表明，通过降低干扰功率，BS协调和频率复用显著提升了定位性能，该效果通过SIR表达式得以量化。
• 检测到足够数量用于定位的BS的概率对BS密度和路径损耗指数高度敏感，更高的BS密度可提升可靠性。
• 该框架可通过量化在真实网络条件下实现所需定位精度的可能性，实现对E911合规性的解析评估。