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

Full Connectivity: Corners, edges and faces

We develop a cluster expansion for the probability of full connectivity of high density random networks in confined geometries. In contrast to percolation phenomena at lower densities, boundary effects, which have previously been largely neglected, are not only relevant but dominant. We derive general analytical formulas that show a persistence of universality in a different form to percolation theory, and provide numerical confirmation. We also demonstrate the simplicity of our approach in three simple but instructive examples and discuss the practical benefits of its application to different models.Comment: 28 pages, 8 figure

Research on Wireless Multi-hop Networks: Current State and Challenges

Wireless multi-hop networks, in various forms and under various names, are being increasingly used in military and civilian applications. Studying connectivity and capacity of these networks is an important problem. The scaling behavior of connectivity and capacity when the network becomes sufficiently large is of particular interest. In this position paper, we briefly overview recent development and discuss research challenges and opportunities in the area, with a focus on the network connectivity.Comment: invited position paper to International Conference on Computing, Networking and Communications, Hawaii, USA, 201

Extremal Properties of Three Dimensional Sensor Networks with Applications

In this paper, we analyze various critical transmitting/sensing ranges for connectivity and coverage in three-dimensional sensor networks. As in other large-scale complex systems, many global parameters of sensor networks undergo phase transitions: For a given property of the network, there is a critical threshold, corresponding to the minimum amount of the communication effort or power expenditure by individual nodes, above (resp. below) which the property exists with high (resp. a low) probability. For sensor networks, properties of interest include simple and multiple degrees of connectivity/coverage. First, we investigate the network topology according to the region of deployment, the number of deployed sensors and their transmitting/sensing ranges. More specifically, we consider the following problems: Assume that $n$ nodes, each capable of sensing events within a radius of $r$, are randomly and uniformly distributed in a 3-dimensional region $\mathcal{R}$ of volume $V$, how large must the sensing range be to ensure a given degree of coverage of the region to monitor? For a given transmission range, what is the minimum (resp. maximum) degree of the network? What is then the typical hop-diameter of the underlying network? Next, we show how these results affect algorithmic aspects of the network by designing specific distributed protocols for sensor networks

Percolation in Multi-hop Wireless Networks

To be adde

Performance Evaluation of Connectivity and Capacity of Dynamic Spectrum Access Networks

Recent measurements on radio spectrum usage have revealed the abundance of under- utilized bands of spectrum that belong to licensed users. This necessitated the paradigm shift from static to dynamic spectrum access (DSA) where secondary networks utilize unused spectrum holes in the licensed bands without causing interference to the licensed user. However, wide scale deployment of these networks have been hindered due to lack of knowledge of expected performance in realistic environments and lack of cost-effective solutions for implementing spectrum database systems. In this dissertation, we address some of the fundamental challenges on how to improve the performance of DSA networks in terms of connectivity and capacity. Apart from showing performance gains via simulation experiments, we designed, implemented, and deployed testbeds that achieve economics of scale. We start by introducing network connectivity models and show that the well-established disk model does not hold true for interference-limited networks. Thus, we characterize connectivity based on signal to interference and noise ratio (SINR) and show that not all the deployed secondary nodes necessarily contribute towards the network\u27s connectivity. We identify such nodes and show that even-though a node might be communication-visible it can still be connectivity-invisible. The invisibility of such nodes is modeled using the concept of Poisson thinning. The connectivity-visible nodes are combined with the coverage shrinkage to develop the concept of effective density which is used to characterize the con- nectivity. Further, we propose three techniques for connectivity maximization. We also show how traditional flooding techniques are not applicable under the SINR model and analyze the underlying causes for that. Moreover, we propose a modified version of probabilistic flooding that uses lower message overhead while accounting for the node outreach and in- terference. Next, we analyze the connectivity of multi-channel distributed networks and show how the invisibility that arises among the secondary nodes results in thinning which we characterize as channel abundance. We also capture the thinning that occurs due to the nodes\u27 interference. We study the effects of interference and channel abundance using Poisson thinning on the formation of a communication link between two nodes and also on the overall connectivity of the secondary network. As for the capacity, we derive the bounds on the maximum achievable capacity of a randomly deployed secondary network with finite number of nodes in the presence of primary users since finding the exact capacity involves solving an optimization problem that shows in-scalability both in time and search space dimensionality. We speed up the optimization by reducing the optimizer\u27s search space. Next, we characterize the QoS that secondary users can expect. We do so by using vector quantization to partition the QoS space into finite number of regions each of which is represented by one QoS index. We argue that any operating condition of the system can be mapped to one of the pre-computed QoS indices using a simple look-up in Olog (N) time thus avoiding any cumbersome computation for QoS evaluation. We implement the QoS space on an 8-bit microcontroller and show how the mathematically intensive operations can be computed in a shorter time. To demonstrate that there could be low cost solutions that scale, we present and implement an architecture that enables dynamic spectrum access for any type of network ranging from IoT to cellular. The three main components of this architecture are the RSSI sensing network, the DSA server, and the service engine. We use the concept of modular design in these components which allows transparency between them, scalability, and ease of maintenance and upgrade in a plug-n-play manner, without requiring any changes to the other components. Moreover, we provide a blueprint on how to use off-the-shelf commercially available software configurable RF chips to build low cost spectrum sensors. Using testbed experiments, we demonstrate the efficiency of the proposed architecture by comparing its performance to that of a legacy system. We show the benefits in terms of resilience to jamming, channel relinquishment on primary arrival, and best channel determination and allocation. We also show the performance gains in terms of frame error rater and spectral efficiency