Critical Density for Connectivity in 2D and 3D Wireless Multi-Hop Networks

In this paper we investigate the critical node density required to ensure that an arbitrary node in a large-scale wireless multi-hop network is connected (via multi-hop path) to infinitely many other nodes with a positive probability. Specifically we con

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

Characterization of the fundamental properties of wireless CSMA multi-hop networks

A wireless multi-hop network consists of a group of decentralized and self-organized wireless devices that collaborate to complete their tasks in a distributed way. Data packets are forwarded collaboratively hop-by-hop from source nodes to their respective destination nodes with other nodes acting as intermediate relays. Existing and future applications in wireless multi-hop networks will greatly benefit from better understanding of the fundamental properties of such networks. In this thesis we explore two fundamental properties of distributed wireless CSMA multi-hop networks, connectivity and capacity. A network is connected if and only if there is at least one (multi-hop) path between any pair of nodes. We investigate the critical transmission power for asymptotic connectivity in large wireless CSMA multi-hop networks under the SINR model. The critical transmission power is the minimum transmission power each node needs to transmit to guarantee that the resulting network is connected aas. Both upper bound and lower bound of the critical transmission power are obtained analytically. The two bounds are tight and differ by a constant factor only. Next we shift focus to the capacity property. First, we develop a distributed routing algorithm where each node makes routing decisions based on local information only. This is compatible with the distributed nature of large wireless CSMA multi-hop networks. Second, we show that by carefully choosing controllable parameters of the CSMA protocols, together with the routing algorithm, a distributed CSMA network can achieve the order-optimal throughput scaling law. Scaling laws are only up to order and most network design choices have a significant effect on the constants preceding the order while not affecting the scaling law. Therefore we further to analyze the pre-constant by giving an upper and a lower bound of throughput. The tightness of the bounds is validated using simulations

Characterization of the fundamental properties of wireless CSMA multi-hop networks

A wireless multi-hop network consists of a group of decentralized and self-organized wireless devices that collaborate to complete their tasks in a distributed way. Data packets are forwarded collaboratively hop-by-hop from source nodes to their respective destination nodes with other nodes acting as intermediate relays. Existing and future applications in wireless multi-hop networks will greatly benefit from better understanding of the fundamental properties of such networks. In this thesis we explore two fundamental properties of distributed wireless CSMA multi-hop networks, connectivity and capacity. A network is connected if and only if there is at least one (multi-hop) path between any pair of nodes. We investigate the critical transmission power for asymptotic connectivity in large wireless CSMA multi-hop networks under the SINR model. The critical transmission power is the minimum transmission power each node needs to transmit to guarantee that the resulting network is connected aas. Both upper bound and lower bound of the critical transmission power are obtained analytically. The two bounds are tight and differ by a constant factor only. Next we shift focus to the capacity property. First, we develop a distributed routing algorithm where each node makes routing decisions based on local information only. This is compatible with the distributed nature of large wireless CSMA multi-hop networks. Second, we show that by carefully choosing controllable parameters of the CSMA protocols, together with the routing algorithm, a distributed CSMA network can achieve the order-optimal throughput scaling law. Scaling laws are only up to order and most network design choices have a significant effect on the constants preceding the order while not affecting the scaling law. Therefore we further to analyze the pre-constant by giving an upper and a lower bound of throughput. The tightness of the bounds is validated using simulations

A Framework for Analysis of Connectivity and Performance Bounds in Ad Hoc Networks and Its Application to a Slotted-ALOHA Scenario

In this paper, a framework is proposed to analyse the problems of connectivity and performance in ad-hoc networks through an analytical approach. To this aim, available results regarding the application of percolation theory to the study of connectivity in ad-hoc networks are exploited jointly with communication theory models in order to derive the configuration of network parameters that ensures long range connectivity among nodes and the corresponding available capacity on the wireless medium. The framework is then applied to a slotted ALOHA ad-hoc network. Theoretical and numerical results validate the approach and allow the derivation of interesting design principles for ad-hoc networks that consider the impact of physical and MAC-level parameters on network connectivity and end-to-end performance

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