Percolation for D2D networks on street systems

We study fundamental characteristics for the connectivity of multi-hop D2D networks. Devices are randomly distributed on street systems and are able to communicate with each other whenever their separation is smaller than some connectivity threshold. We model the street systems as Poisson-Voronoi or Poisson-Delaunay tessellations with varying street lengths. We interpret the existence of adequate D2D connectivity as percolation of the underlying random graph. We derive and compare approximations for the critical device-intensity for percolation, the percolation probability and the graph distance. Our results show that for urban areas, the Poisson Boolean Model gives a very good approximation, while for rural areas, the percolation probability stays far from 1 even far above the percolation threshold

Continuum Line-of-Sight Percolation on Poisson-Voronoi Tessellations

In this work, we study a new model for continuum line-of-sight percolation in a random environment driven by the Poisson-Voronoi tessellation in the $d$-dimensional Euclidean space. The edges (one-dimensional facets, or simply 1-facets) of this tessellation are the support of a Cox point process, while the vertices (zero-dimensional facets or simply 0-facets) are the support of a Bernoulli point process. Taking the superposition $Z$ of these two processes, two points of $Z$ are linked by an edge if and only if they are sufficiently close and located on the same edge (1-facet) of the supporting tessellation. We study the percolation of the random graph arising from this construction and prove that a 0-1 law, a subcritical phase as well as a supercritical phase exist under general assumptions. Our proofs are based on a coarse-graining argument with some notion of stabilization and asymptotic essential connectedness to investigate continuum percolation for Cox point processes. We also give numerical estimates of the critical parameters of the model in the planar case, where our model is intended to represent telecommunications networks in a random environment with obstructive conditions for signal propagation.Comment: 30 pages, 4 figures. Accepted for publication in Advances in Applied Probabilit

Achievable Throughput in Two-Scale Wireless Networks

We propose a new model of wireless networks which we refer to as "two-scale networks." At a local scale, characterised by nodes being within a distance r, channel strengths are drawn independently and identically from a distance-independent distribution. At a global scale, characterised by nodes being further apart from each other than a distance r, channel connections are governed by a Rayleigh distribution, with the power satisfying a distance-based decay law. Thus, at a local scale, channel strengths are determined primarily by random effects such as obstacles and scatterers whereas at the global scale channel strengths depend on distance. For such networks, we propose a hybrid communications scheme, combining elements of distance-dependent networks and random networks. For particular classes of two-scale networks with N nodes, we show that an aggregate throughput that is slightly sublinear in N, for instance, of the form N/ log^4 N is achievable. This offers a significant improvement over a throughput scaling behaviour of O(√N) that is obtained in other work

Coordinated control of mixed robot and sensor networks in distributed area exploration

Recent advancements in wireless communication and electronics has enabled the development of multifunctional sensor nodes that are small in size and communicate untethered in short distances. In the last decade, significant advantages have been made in the field of robotics, and robots have become more feasible in systems design. Therefore, we trust that a number of open problems with wireless sensor networks can be solved or diminished by including mobility capabilities in agents

Intrinsically secure communication in large-scale wireless networks

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2010.Cataloged from PDF version of thesis.Includes bibliographical references (p. 169-181).The ability to exchange secret information is critical to many commercial, governmental, and military networks. Information-theoretic security - widely accepted as the strictest notion of security - relies on channel coding techniques that exploit the inherent randomness of the propagation channels to significantly strengthen the security of digital communications systems. Motivated by recent developments in the field, this thesis aims at a characterization of the fundamental secrecy limits of large-scale wireless networks. We start by introducing an information-theoretic definition of the intrinsically secure communications graph (iS-graph), based on the notion of strong secrecy. The iS-graph is a random geometric graph which captures the connections that can be securely established over a large-scale network, in the presence of spatially scattered eavesdroppers. Using fundamental tools from stochastic geometry, we analyze how the spatial densities of legitimate and eavesdropper nodes influence various properties of the Poisson iS-graph, such as the distribution of node degrees, the node isolation probabilities, and the achievable secrecy rates. We study how the wireless propagation effects (e.g., fading and shadowing) and eavesdropper collusion affect the secrecy properties of the network. We also explore the potential of sectorized transmission and eavesdropper neutralization as two techniques for enhancing the secrecy of communications. We then shift our focus to the global properties of the iS-graph, which concern secure connectivity over multiple hops. We first characterize percolation of the Poisson iS-graph on the infinite plane. We show that each of the four components of the iS-graph (in, out, weak, and strong component) experiences a phase transition at some nontrivial critical density of legitimate nodes. Operationally, this is important because it implies that long-range communication over multiple hops is still feasible when a security constraint is present. We then consider full-connectivity on a finite region of the Poisson iS-graph. Specifically, we derive simple, explicit expressions that closely approximate the probability of a node being securely connected to all other nodes inside the region. We also show that the iS-graph is asymptotically fully out-connected with probability one, but full in-connectivity remains bounded away from one, no matter how large the density of legitimate nodes is made. Our results clarify how the spatial density of eavesdroppers can compromise the intrinsic security of wireless networks. We are hopeful that further efforts in combining stochastic geometry with information-theoretic principles will lead to a more comprehensive treatment of wireless security.by Pedro C. Pinto.Ph.D