Communication Networks An Optimization, Control, and Stochastic Networks Perspective

In earlier chapters, we considered distributed resource allocation algorithms for ad hoc wireless networks. We showed that there exist algorithms, called throughput-optimal algorithms, that maximize the network throughput. However, we do not yet have a simple expression for the total amount of information that can be transferred in an ad hoc wireless network. The problem of computing such an expression is challenging due to interference caused by simultaneous wireless transmissions. This chapter focuses on understanding the limitations on network throughput imposed by wireless interference. We will introduce geometric random graph models of wireless networks, in which n wireless nodes are distributed over a geographical area. Two nodes can communicate if the distance between them is smaller than a threshold and if no nodes near the receiver are transmitting at the same time. The capacity region of such a network is difficult to characterize exactly. Therefore, we will study the network capacity when the number of wireless nodes becomes large. We will show that, in such an asymptotic regime, one can obtain expressions for the network capacity that are asymptotically correct in a sense that will be made precise. A key insight of this chapter is that the throughput per source diminishes as the number of wireless nodes (in a fixed geographical area) increases because of wireless interference. The following questions will be addressed in this chapter.