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1Connectivity of Confined Dense Networks: Boundary Effects and Scaling Laws
"... 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 app ..."
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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.
On the asymptotic connectivity of random networks under the random connection model
- in IEEE INFOCOM
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Connectivity in Dense Networks Confined within Right Prisms
"... Abstract—We consider the probability that a dense wireless network confined within a given convex geometry is fully con-nected. We exploit a recently reported theory to develop a system-atic methodology for analytically characterizing the connectivity probability when the network resides within a co ..."
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Abstract—We consider the probability that a dense wireless network confined within a given convex geometry is fully con-nected. We exploit a recently reported theory to develop a system-atic methodology for analytically characterizing the connectivity probability when the network resides within a convex right prism, a polyhedron that accurately models many geometries that can be found in practice. To maximize practicality and applicability, we adopt a general point-to-point link model based on outage probability, and present example analytical and numerical re-sults for a network employing 2 × 2 multiple-input multiple-output (MIMO) maximum ratio combining (MRC) link level transmission confined within particular bounding geometries. Furthermore, we provide suggestions for extending the approach detailed herein to more general convex geometries. Index Terms—Connectivity, percolation, outage, MIMO, diver-sity, power scaling.
