Outage probability of wireless networks with directional antennas

In this paper, we consider wireless networks with directional antennas using slotted ALOHA medium access control. The channel model incorporates the effects of propagation loss and shadowing with Rayleigh fading. By deriving the cumulative distribution function of the signalto-interference-and-noise ratio of a certain link in the network, the outage probability of the link is analyzed. In particular, the analysis works for arbitrary beam patterns of the directional antennas used in the networks. Moreover, we propose a new parameter, the array interference factor (AIF), which fully characterizes the performance of any beam pattern in a wireless network over fading channels. Using a beam pattern with smaller AIF will give a better performance than other beam patterns with larger AIF values. The analysis of this paper enables us to find the optimal mobile density and the most efficient transmission power setting for such wireless networks.