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

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

Towards a System Theoretic Approach to Wireless Network Capacity in Finite Time and Space

In asymptotic regimes, both in time and space (network size), the derivation of network capacity results is grossly simplified by brushing aside queueing behavior in non-Jackson networks. This simplifying double-limit model, however, lends itself to conservative numerical results in finite regimes. To properly account for queueing behavior beyond a simple calculus based on average rates, we advocate a system theoretic methodology for the capacity problem in finite time and space regimes. This methodology also accounts for spatial correlations arising in networks with CSMA/CA scheduling and it delivers rigorous closed-form capacity results in terms of probability distributions. Unlike numerous existing asymptotic results, subject to anecdotal practical concerns, our transient one can be used in practical settings: for example, to compute the time scales at which multi-hop routing is more advantageous than single-hop routing

Connectivity scaling laws in wireless networks

We present scaling laws that dictate both local and global connectivity properties of bounded wireless networks. These laws are defined with respect to the key system parameters of per-node transmit power and the number of antennas exploited for diversity coding and/or beamforming at each node. We demonstrate that the local probability of connectivity scales like $\mathcal{O}(z^\mathcal C)$ in these parameters, where $\mathcal C$ is the ratio of the dimension of the network domain to the path loss exponent, thus enabling efficient boundary effect mitigation and network topology control.Comment: 4 pages, 1 figur

Stability Oriented Routing in Mobile Ad-Hoc Networks Based on Simple Automatons

International audienceSince wireless ad-hoc networks with mobile nodes have not stable topology, the classical network functions as the routing are difficult to realize. The router nodes and the links between them are not stable and can appear and disappear randomly. So, classic routing algorithms can not be used successfully. New approaches should be used which deals with these dynamic changes. To avoid frequent route requests and volatile routes due to uncertain information, the objective of the routing can correspond to the route stability. The route computation can be based on random variables and becomes probabilistic routing. Our book chapter focuses on modeling the resilience of these information for ad hoc networks where topology information is uncertain. Our model is based on a dynamic graph where the existence of the nodes and the communication capability between them are modeled by simple two state automaton where the transitions are initiated by random events

Cross-layer Optimization in Wireless Multihop Networks

In order to meet the increasing demand for higher data rates, next generation wireless networks must incorporate additional functionalities to enhance network throughput. Multihop networks are considered as a promising alternative due to their ability to exploit spatial reuse and to extend coverage. Recently, industry has shown increased interest in multihop networks as they do not require additional infrastructure and have relatively low deployment costs. Many advances in physical and network layer techniques have been proposed in the recent past and they have been studied mostly in single-hop networks. Very few studies, if any, have tried to quantify the gains that these techniques could provide in multihop networks. We investigate the impact of simple network coding, advanced physical layer and cooperative techniques on the maximum achievable throughput of wireless multihop networks of practical size. We consider the following advanced physical layer techniques: successive interference cancellation, superposition coding, dirty-paper coding, and some of their combinations. We achieve this by formulating several cross-layer frameworks when these techniques are jointly optimized with routing and scheduling. We also formulate power allocation subproblems for the cases of continuous power control and superposition coding. We also provide numerous engineering insights by solving these problems to optimality