Connectivity analysis of wireless ad-hoc networks

Connectivity is one of the most fundamental properties of wireless ad-hoc networks as most network functions are predicated upon the network being connected. Although increasing node transmission power will improve network connectivity, too large a power level is not feasible as energy is a scarce resource in wireless ad-hoc networks. Thus, it is crucial to identify the minimum node transmission power that will ensure network connectivity with high probability. It is known that there exists a critical level transmission power such that a suitably larger power will ensure network connectivity with high probability. A small variation across this threshold level will lead to a sharp transition of the probability that the network is connected. Thus, in order to precisely estimate the minimum node transmission power, not only do we need to identify this critical threshold, but also how fast this transition takes place. To characterize the sharpness of transition, we define weak, strong and very strong critical thresholds associated with increasing transition speeds. In this dissertation, we seek to estimate the minimum node transmission power for large scale one-dimensional wireless ad-hoc networks under the Geometric Random Graph (GRG) models. Unlike in previous works where nodes are taken to be uniformly distributed, we assume a more general node distribution. Using the methods of first and second moments, we theoretically prove the existence of a very strong critical threshold when the density function is everywhere positive. On the other hand, only weak thresholds are shown to exist when the density function contains vanishing densities. We also study the connectivity of two-dimensional wireless ad-hoc networks under the random connection model, which accounts for statistical channel variations. With the help of the Stein-Chen method, we derive a closed form formula for the limiting probability that there are no isolated nodes under a very general assumption of channel variations. The node transmission power to ensure the absence of isolated nodes provides a tight lower bound on the transmission power needed to ensure network connectivity

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

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

Communication Over a Wireless Network With Random Connections

A network of nodes in which pairs communicate over a shared wireless medium is analyzed. We consider the maximum total aggregate traffic flow possible as given by the number of users multiplied by their data rate. The model in this paper differs substantially from the many existing approaches in that the channel connections in this network are entirely random: rather than being governed by geometry and a decay-versus-distance law, the strengths of the connections between nodes are drawn independently from a common distribution. Such a model is appropriate for environments where the first-order effect that governs the signal strength at a receiving node is a random event (such as the existence of an obstacle), rather than the distance from the transmitter. It is shown that the aggregate traffic flow as a function of the number of nodes n is a strong function of the channel distribution. In particular, for certain distributions the aggregate traffic flow is at least n/(log n)^d for some d≫0, which is significantly larger than the O(sqrt n) results obtained for many geometric models. The results provide guidelines for the connectivity that is needed for large aggregate traffic. The relation between the proposed model and existing distance-based models is shown in some cases

Percolation in Multi-hop Wireless Networks

To be adde

Percolation and Connectivity in the Intrinsically Secure Communications Graph

The ability to exchange secret information is critical to many commercial, governmental, and military networks. The intrinsically secure communications graph (iS-graph) is a random graph which describes the connections that can be securely established over a large-scale network, by exploiting the physical properties of the wireless medium. This paper aims to characterize the global properties of the iS-graph in terms of: (i) percolation on the infinite plane, and (ii) full connectivity on a finite region. First, for the Poisson iS-graph defined on the infinite plane, the existence of a phase transition is proven, whereby an unbounded component of connected nodes suddenly arises as the density of legitimate nodes is increased. This shows that long-range secure communication is still possible in the presence of eavesdroppers. Second, full connectivity on a finite region of the Poisson iS-graph is considered. The exact asymptotic behavior of full connectivity in the limit of a large density of legitimate nodes is characterized. Then, simple, explicit expressions are derived in order to closely approximate the probability of full connectivity for a finite density of legitimate nodes. The results help clarify how the presence of eavesdroppers can compromise long-range secure communication.Comment: Submitted for journal publicatio

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