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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 pointtopoint link models based on outage probability in our analysis: singleinput singleoutput (SISO), singleinput multipleoutput (SIMO), multipleinput singleoutput (MISO), and multipleinput multipleoutput (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 pointtopoint 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 connected. We exploit a recently reported theory to develop a systematic 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 connected. We exploit a recently reported theory to develop a systematic 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 pointtopoint link model based on outage probability, and present example analytical and numerical results for a network employing 2 × 2 multipleinput multipleoutput (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, diversity, power scaling.