Spatial networks with wireless applications

Many networks have nodes located in physical space, with links more common between closely spaced pairs of nodes. For example, the nodes could be wireless devices and links communication channels in a wireless mesh network. We describe recent work involving such networks, considering effects due to the geometry (convex,non-convex, and fractal), node distribution, distance-dependent link probability, mobility, directivity and interference.Comment: Review article- an amended version with a new title from the origina

Fundamentals of Large Sensor Networks: Connectivity, Capacity, Clocks and Computation

Sensor networks potentially feature large numbers of nodes that can sense their environment over time, communicate with each other over a wireless network, and process information. They differ from data networks in that the network as a whole may be designed for a specific application. We study the theoretical foundations of such large scale sensor networks, addressing four fundamental issues- connectivity, capacity, clocks and function computation. To begin with, a sensor network must be connected so that information can indeed be exchanged between nodes. The connectivity graph of an ad-hoc network is modeled as a random graph and the critical range for asymptotic connectivity is determined, as well as the critical number of neighbors that a node needs to connect to. Next, given connectivity, we address the issue of how much data can be transported over the sensor network. We present fundamental bounds on capacity under several models, as well as architectural implications for how wireless communication should be organized. Temporal information is important both for the applications of sensor networks as well as their operation.We present fundamental bounds on the synchronizability of clocks in networks, and also present and analyze algorithms for clock synchronization. Finally we turn to the issue of gathering relevant information, that sensor networks are designed to do. One needs to study optimal strategies for in-network aggregation of data, in order to reliably compute a composite function of sensor measurements, as well as the complexity of doing so. We address the issue of how such computation can be performed efficiently in a sensor network and the algorithms for doing so, for some classes of functions.Comment: 10 pages, 3 figures, Submitted to the Proceedings of the IEE

On Topological Properties of Wireless Sensor Networks under the q-Composite Key Predistribution Scheme with On/Off Channels

The q-composite key predistribution scheme [1] is used prevalently for secure communications in large-scale wireless sensor networks (WSNs). Prior work [2]-[4] explores topological properties of WSNs employing the q-composite scheme for q = 1 with unreliable communication links modeled as independent on/off channels. In this paper, we investigate topological properties related to the node degree in WSNs operating under the q-composite scheme and the on/off channel model. Our results apply to general q and are stronger than those reported for the node degree in prior work even for the case of q being 1. Specifically, we show that the number of nodes with certain degree asymptotically converges in distribution to a Poisson random variable, present the asymptotic probability distribution for the minimum degree of the network, and establish the asymptotically exact probability for the property that the minimum degree is at least an arbitrary value. Numerical experiments confirm the validity of our analytical findings.Comment: Best Student Paper Finalist in IEEE International Symposium on Information Theory (ISIT) 201

Connectivity of confined 3D Networks with Anisotropically Radiating Nodes

Nodes in ad hoc networks with randomly oriented directional antenna patterns typically have fewer short links and more long links which can bridge together otherwise isolated subnetworks. This network feature is known to improve overall connectivity in 2D random networks operating at low channel path loss. To this end, we advance recently established results to obtain analytic expressions for the mean degree of 3D networks for simple but practical anisotropic gain profiles, including those of patch, dipole and end-fire array antennas. Our analysis reveals that for homogeneous systems (i.e. neglecting boundary effects) directional radiation patterns are superior to the isotropic case only when the path loss exponent is less than the spatial dimension. Moreover, we establish that ad hoc networks utilizing directional transmit and isotropic receive antennas (or vice versa) are always sub-optimally connected regardless of the environment path loss. We extend our analysis to investigate boundary effects in inhomogeneous systems, and study the geometrical reasons why directional radiating nodes are at a disadvantage to isotropic ones. Finally, we discuss multi-directional gain patterns consisting of many equally spaced lobes which could be used to mitigate boundary effects and improve overall network connectivity.Comment: 12 pages, 10 figure

Connectivity in Dense Networks Confined within Right Prisms

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 point-to-point link model based on outage probability, and present example analytical and numerical results for a network employing $2 \times 2$ 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.Comment: 8 pages, 6 figures. arXiv admin note: text overlap with arXiv:1201.401

Analysis of Intermittent Distributed Connectivity in Urban Areas

Analysis of hypothetical connectivity of wirelessly interconnected networks and infrastructures deployed over a one-square kilometre of the Brussels Metropolitan area is presented. Upper and lower margins of wireless transceiver range are considered with a view to characterise representative interconnectivity profiles. Graph and percolation analyses of intermittent connectivity and its implications for resilience and vulnerability of the network are discussed. Based on these findings the report presents a proposal for the dimensioning of connectivity profiles for generic areas based on intrinsic algebraic network properties.JRC.E.4-Safety and Security of Building

Achieving Small World Properties using Bio-Inspired Techniques in Wireless Networks

It is highly desirable and challenging for a wireless ad hoc network to have self-organization properties in order to achieve network wide characteristics. Studies have shown that Small World properties, primarily low average path length and high clustering coefficient, are desired properties for networks in general. However, due to the spatial nature of the wireless networks, achieving small world properties remains highly challenging. Studies also show that, wireless ad hoc networks with small world properties show a degree distribution that lies between geometric and power law. In this paper, we show that in a wireless ad hoc network with non-uniform node density with only local information, we can significantly reduce the average path length and retain the clustering coefficient. To achieve our goal, our algorithm first identifies logical regions using Lateral Inhibition technique, then identifies the nodes that beamform and finally the beam properties using Flocking. We use Lateral Inhibition and Flocking because they enable us to use local state information as opposed to other techniques. We support our work with simulation results and analysis, which show that a reduction of up to 40% can be achieved for a high-density network. We also show the effect of hopcount used to create regions on average path length, clustering coefficient and connectivity.Comment: Accepted for publication: Special Issue on Security and Performance of Networks and Clouds (The Computer Journal