## Ad Hoc Wireless Networks With Noisy Links (2003)

Citations: | 12 - 0 self |

### BibTeX

@MISC{Booth03adhoc,

author = {Lorna Booth and Jehoshua Bruck and Matthew Cook and Massimo Franceschetti},

title = {Ad Hoc Wireless Networks With Noisy Links},

year = {2003}

}

### Years of Citing Articles

### OpenURL

### Abstract

Models of ad-hoc wireless networks are often based on the geometric disc abstraction: transmission is assumed to be isotropic, and reliable communication channels are assumed to exist (apart from interference) between nodes closer than a given distance. In reality communication channels are unreliable and communication range is generally not rotationally symmetric. In this paper we examine how these issues affect network connectivity. Using ideas from percolation theory, we compare networks of geometric discs to other simple shapes, including probabilistic connections, and we find that when transmission range and node density are normalized across experiments so as to preserve the expected number of connections (ENC) enjoyed by each node, the discs are the "hardest" shape to connect together. In other words, anisotropic radiation patterns and spotty coverage allow an unbounded connected component to appear at lower ENC levels than perfect circular coverage allows. This indicates that connectivity claims made in the literature using the geometric disc abstraction will in general hold also for the more irregular shapes found in practice.

### Citations

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(Show Context)
Citation Context ... has been a growing interest in modeling global properties of these networks as a function of the node population, and basic results on connectivity and throughput capacity have been obtained [5] [6] =-=[7]-=- [8]. These works typically assume that nodes are randomly located and that they are able to reliably relay messages to sufficiently close neighbors. A first stochastic model that exploited these idea... |

1917 |
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(Show Context)
Citation Context ...ly, the idea that some longer connections help to reach percolation at a lower density of points is also related to the small world networks described, for example, in the paper by Watts and Strogatz =-=[16]-=-. � ||x|| 2sconnection probability g s g shift s Fig. 3. Shifting and squeezing Thesfunction is shifted and squeezed to give thes¢¡ function £¥¤§¦©¨ � ¡ The dynamic coupling technique needed in the pr... |

840 | Mobility increases the capacity of ad hoc wireless networks
- Grossglauser, Tse
- 2002
(Show Context)
Citation Context ...y, there has been a growing interest in modeling global properties of these networks as a function of the node population, and basic results on connectivity and throughput capacity have been obtained =-=[5]-=- [6] [7] [8]. These works typically assume that nodes are randomly located and that they are able to reliably relay messages to sufficiently close neighbors. A first stochastic model that exploited th... |

392 | Critical power for asymptotic connectivity in wireless networks”, Stochastic Analysis, Control, Optimization and Applications: A Volume
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(Show Context)
Citation Context ...here has been a growing interest in modeling global properties of these networks as a function of the node population, and basic results on connectivity and throughput capacity have been obtained [5] =-=[6]-=- [7] [8]. These works typically assume that nodes are randomly located and that they are able to reliably relay messages to sufficiently close neighbors. A first stochastic model that exploited these ... |

210 |
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(Show Context)
Citation Context ...s appeared in the 1961 paper of Gilbert’s [3], who studied the problem of multi-hop connectivity of wireless broadcasting stations, establishing the foundations of the theory of Continuum Percolation =-=[10]-=-. In his formulation, points of a two-dimensional Poisson point process represent wireless transmitting stations of ranges¢¡ and he asks if the system can provide some longdistance communication. He s... |

113 | A deterministic approach to throughput scaling in wireless networks
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(Show Context)
Citation Context ... been a growing interest in modeling global properties of these networks as a function of the node population, and basic results on connectivity and throughput capacity have been obtained [5] [6] [7] =-=[8]-=-. These works typically assume that nodes are randomly located and that they are able to reliably relay messages to sufficiently close neighbors. A first stochastic model that exploited these ideas ap... |

102 |
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(Show Context)
Citation Context ...des are randomly located and that they are able to reliably relay messages to sufficiently close neighbors. A first stochastic model that exploited these ideas appeared in the 1961 paper of Gilbert’s =-=[3]-=-, who studied the problem of multi-hop connectivity of wireless broadcasting stations, establishing the foundations of the theory of Continuum Percolation [10]. In his formulation, points of a two-dim... |

39 | Covering Algorithms, Continuum Percolation and the Geometry of Wireless Networks
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(Show Context)
Citation Context ... possible. In the past forty years Gilbert’s model has received much attention from mathematicians and physicists and, recently, extensions relevant to wireless network design have also been proposed =-=[1]-=- [2] [14] [15]. In this paper we consider a further extension that is useful to model more realistic, unreliable and non-rotationally symmetric communication channels (see Fig 1). We consider a genera... |

14 | Critical probabilities for site and bond percolation models
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Citation Context ... (dynamic) coupling is not difficult to construct, and has been exploited in discrete percolation on graphs to prove the well known inequality � ¡������ � ¨�� � ¤ ¡���������¨ . We refer the reader to =-=[4]-=- for details. ¤ The theorem above has a certain depth. Essentially, it states that unreliable links are at least as good at providing connectivity as reliable links, if the average number of connectio... |

11 |
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(Show Context)
Citation Context ...Another way of looking at this is that the longer links introduced by stretching the connection function are making up for the increased unreliability of the connections. In some related work Penrose =-=[12]-=- has shown that (speaking roughly) as a connection function of effective area 1 gets more spread out, its critical density for percolation converges to 1. This can be seen as the limiting case of our ... |

10 | Designing a contact process: The piecewisehomogeneous process on a finite set with applications
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(Show Context)
Citation Context ...e. In the past forty years Gilbert’s model has received much attention from mathematicians and physicists and, recently, extensions relevant to wireless network design have also been proposed [1] [2] =-=[14]-=- [15]. In this paper we consider a further extension that is useful to model more realistic, unreliable and non-rotationally symmetric communication channels (see Fig 1). We consider a general random ... |

5 | Optimization of shape in continuum percolation
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(Show Context)
Citation Context ...lap each other. This means that if a node falls inside the shape of another node, then the reverse is true as well. This property does not hold for non-centrally symmetric shapes, see Fig 4. Jonasson =-=[9]-=- has shown that if any convex shape of area 1 percolates at at certain density, then triangles (that are not centrally symmetric) of area 1 will also do so. Roy and Tanemura [13] strengthened this res... |

5 | Wireless sensor network design via interacting particles
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(Show Context)
Citation Context ... the past forty years Gilbert’s model has received much attention from mathematicians and physicists and, recently, extensions relevant to wireless network design have also been proposed [1] [2] [14] =-=[15]-=-. In this paper we consider a further extension that is useful to model more realistic, unreliable and non-rotationally symmetric communication channels (see Fig 1). We consider a general random conne... |

3 |
Critical intensities of Boolean models with different underlying convex shapes
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(Show Context)
Citation Context ...s, see Fig 4. Jonasson [9] has shown that if any convex shape of area 1 percolates at at certain density, then triangles (that are not centrally symmetric) of area 1 will also do so. Roy and Tanemura =-=[13]-=- strengthened this result to show a strict inequality between the critical density of triangle and that of any other given convex shape of the same area. Jonasson [9] has also shown that the convex sh... |

1 |
Power requirements for connectivity in clustered wireless networks
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- 2002
(Show Context)
Citation Context ...sible. In the past forty years Gilbert’s model has received much attention from mathematicians and physicists and, recently, extensions relevant to wireless network design have also been proposed [1] =-=[2]-=- [14] [15]. In this paper we consider a further extension that is useful to model more realistic, unreliable and non-rotationally symmetric communication channels (see Fig 1). We consider a general ra... |

1 |
The random connection model in high dimensions. Statistics and Probability Letters 35,145153
- Meester, Penrose, et al.
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(Show Context)
Citation Context ...nection function of effective area 1 gets more spread out, its critical density for percolation converges to 1. This can be seen as the limiting case of our Theorem II.1. Meester, Penrose, and Sarkar =-=[11]-=- proved a similar result as the dimension tends to infinity. Philosophically, the idea that some longer connections help to reach percolation at a lower density of points is also related to the small ... |