受限稠密网络的连通性：边界效应和缩放定律
Connectivity of Confined Dense Networks: Boundary Effects and Scaling Laws
摘要：
在本文中，我们研究的概率，一个稠密的网络限制在一个给定的几何是完全连通的。我们采用统计物理中常用的集群扩展方法来分析几何形状的边界对连通性的影响。为了最大限度地提高实用性和适用性，我们采用了四个重要的点对点链路模型中断概率的基础上，在我们的分析：单输入单输出（SISO），单输入多输出（SIMO），多输入单输出（MISO），和多输入多输出（MIMO）。此外，我们推导出多样性和权力缩放定律，规定如何边界效应可以减轻（领先秩序）在封闭的密集网络，这些模型。最后，为了证明我们的理论的多功能性，我们分析了密集网络的边界效应，包括限制在一个正确的棱柱，多面体，准确地模拟许多几何形状，可以在实践中找到MIMO点对点链接。我们提供了这个例子的数值结果，验证了我们的分析结果。
英文摘要：
In this paper, we study the probability that a dense network confined within a given geometry is fully connected. We employ a cluster expansion approach often used in statistical physics to analyze the effects that the boundaries of the geometry have on connectivity. To maximize practicality and applicability, we adopt four important point-to-point link models based on outage probability in our analysis: single-input single-output (SISO), single-input multiple-output (SIMO), multiple-input single-output (MISO), and multiple-input multiple-output (MIMO). Furthermore, we derive diversity and power scaling laws that dictate how boundary effects can be mitigated (to leading order) in confined dense networks for each of these models. Finally, in order to demonstrate the versatility of our theory, we analyze boundary effects for dense networks comprising MIMO point-to-point links confined within a right prism, a polyhedron that accurately models many geometries that can be found in practice. We provide numerical results for this example, which verify our analytical results.
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