Analytical Study of Connectivity in Wireless Ad hoc Networks with Random Beamforming

Random beamforming is a technique in which each node in a wireless ad hoc network directs its main bean towards a randomly chosen direction. This paper presents an analytical method for investigating the effect of random beamforming on the connectivity of wireless ad hoc networks. We derive analytically an expression for an effective beamforming gain, which we use to characterize the impact of random beamforming on the number of direct connections to an arbitrary node, i.e. the local connectivity. Result shows that for a path-loss model, random beamforming improves the local connectivity for pathloss exponent α < 3, while it degrades the local connectivity for larger values of α. The analytical method is validated by comparison with simulation results.