Fundamental Properties of Wireless Mobile Ad-hoc Networks

Abstract

Wireless mobile ad-hoc networks are formed by mobile devices that set up a possibly short-lived network for communication needs of the moment. Ad-hoc networks are decentralized, self-organizing networks capable of forming a communication network without relying on any fixed infrastructure. Each node in an ad-hoc network is equipped with a radio transmitter and receiver which allows it to communicate with other nodes over wireless channels. All nodes can function, if needed, as relay stations for data packets to be routed to their final destination. In other words, ad-hoc networks allow for multi-hop transmission of data between nodes outside the direct radio reach of each other. Ad-hoc networks have distinct advantages over traditional communication networks. For example, ad-hoc networks can be more economical as they eliminate fixed infrastructure costs, and they can be more robust because of their non-hierarchical distributed control and management mechanisms. Ad-hoc networks increase mobility and flexibility, as they can be brought up and torn down in a very short time. Ad-hoc networks form a relatively new and very diverse field of research. In this thesis we focus our attention on the fundamental properties of ad-hoc networks. For an ad-hoc network to function properly in the first place it must be connected, or mostly connected. Otherwise the network would consist of scattered isolated islands and could not support networking applications. Secondly, the ad-hoc network must have enough capacity to transport the required amount of data between network nodes. By fundamental properties we mean those properties of the network that directly and substantially affect the connectivity or the capacity of the network. In this thesis we have introduced a new mathematical model for ad-hoc networks which is based on realistic assumptions for radio propagation. By using this model we were able to modify connectivity theorems for wireless ad-hoc networks, and have contributed substantially to a better understanding of degree distribution and hopcount in ad-hoc networks. Another novel aspect in this thesis is a new method proposed for the calculation of interference statistics. Also, we have shown that interference in ad-hoc networks is upper bounded and have derived a mathematical formula for this upper bound. Our interference calculation methods have allowed us to investigate the capacity of ad-hoc networks. We have found capacity limits for ad-hoc networks and have established that in multi-hop ad-hoc networks there is a trade-off between the network size and the maximum input bit rate possible per node. Large ad-hoc networks, consisting of thousands of nodes, can only support low-bit-rate applications.