Connectivity Analysis of Wireless Ad Hoc Networks With Beamforming

In this paper, we present an analytical model for evaluating the impact of shadowing and beamforming on the connectivity of wireless ad hoc networks accommodating nodes equipped with multiple antennas. We consider two simple beamforming schemes: random beamforming, where each node selects a main beam direction randomly with no coordination with other nodes, and center-directed beamforming, where each node points its main beam toward the geographical center of the network. Taking path loss, shadowing, and beamforming into account, we derive an expression for the effective coverage area of a node, which is used to analyze both the local network connectivity (probability of node isolation) and the overall network connectivity (1-connectivity and path probability). We verify the correctness of our analytical approach by comparing with simulations. Our results show that the presence of shadowing increases the probability of node isolation and reduces the 1-connectivity of the network, although moderate shadowing can improve the path probability between two nodes. Furthermore, we show that the impact of beamforming strongly depends on the level of the channel path loss. In particular, compared with omnidirectional antennas, beamforming improves both the local and the overall connectivity for a path loss exponent of alpha < 3. The analysis in this paper provides an efficient way for system designers to characterize and optimize the connectivity of wireless ad hoc networks with beamforming.