Connectivity of Wireless Ad Hoc Networks with Random Beamforming: An Analytical Approach

Random beamforming, where each node selects a main beam direction without any coordination with other nodes, has been proposed as a simple technique to improve connectivity in wireless ad hoc networks. This paper presents an analytical model for evaluating the impact of random beamforming on the connectivity of wireless ad hoc networks in the presence of path loss and shadowing effects. We investigate the connectivity with random beamforming from the view points of a single node and the entire network. The correctness of our analytical approach is validated by comparing the analytical results with simulations. We show that for a path loss exponent of alpha < 3, irrespective of shadowing effects, random beamforming improves both the local and overall connectivity compared to omnidirectional antennas.