Inteference mitigation in large random wireless networks

A central problem in the operation of large wireless networks is how to deal with interference -- the unwanted signals being sent by transmitters that a receiver is not interested in. This thesis looks at ways of combating such interference. In Chapters 1 and 2, we outline the necessary information and communication theory background. We define the concept of capacity -- the highest rate at which information can be sent through a network with arbitrarily low probability of error. We also include an overview of a new set of schemes for dealing with interference known as interference alignment, paying special attention to a channel-state-based strategy called ergodic interference alignment. In Chapter 3, we consider the operation of large regular and random networks by treating interference as background noise. We consider the local performance of a single node, and the global performance of a very large network. In Chapter 4, we use ergodic interference alignment to derive the asymptotic sum-capacity of large random dense networks. These networks are derived from a physical model of node placement where signal strength decays over the distance between transmitters and receivers. In Chapter 5, we look at methods of reducing the long time delays incurred by ergodic interference alignment. We decrease the delay for full performance of the scheme, and analyse the tradeoff between reducing delay and lowering the communication rate. In Chapter 6, we outline a problem of discovering which users interfere with which; a situation that is equivalent to the problem of pooled group testing for defective items. We then present some new work that uses information theoretic techniques to attack group testing. We introduce for the first time the concept of the group testing channel, which allows for modelling of a wide range of statistical error models for testing. We derive new results on the number of tests required to accurately detect defective items, including when using sequential `adaptive' tests. Chapter 7 concludes and gives pointers for further work.