How is the capacity of ad hoc networks improved with directional antennas?

The capacity of wireless ad hoc networks is constrained by the interference caused by the neighboring nodes. Gupta and Kumar have shown that the throughput for such networks is only Θ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(\frac{W}{\sqrt{n}})$$\end{document} bits per second per node in a unit area domain when omnidirectional antennas are used [1]. In this paper we investigate the capacity of ad hoc wireless networks using directional antennas. Using directional antennas reduces the interference area caused by each node, thus increases the capacity of the network. We will give an expression for the capacity gain and we argue that in the limit, when the beam-width goes to zero the wireless network behaves like the wired network. In our analysis we consider both arbitrary networks and random networks where nodes are assumed to be static. We have also analyzed hybrid beamform patterns that are a mix of omnidirectional/directional and a better model of real directional antennas. Simulations are conducted for validation of our analytical results.