Effects of Beamforming on the Connectivity of AdHoc Networks

Abstract

This paper analyzes the effects of beamforming on the connectivity of wireless ad hoc networks. We study different beamforming techniques using the uniform circular array as the antenna model. In particular, we study centre directed beamform- ing and greedy beamforming. In centre directed beamforming each node points its main beam toward the geometric centre of the network. The greedy beamforming method allows each node to choose the beamforming direction based on knowledge of other node positions. We investigate the connectivity of each beamforming scheme and compare their performances to that of omnidirectional antennas. The percentages of connection and isolated nodes are used as metrics for connectivity. We also show that greedy beamforming is robust against errors in node position information. between any two nodes contributes to the connectivity of the entire network. Some papers have investigated the relationship between connectivity and node transmission range based on omnidirectional antennas (5), (6). It has been shown that beamforming using smart antennas can significantly improve the connectivity (7). Different beamforming techniques have also been proposed for application to ad hoc networks. The use of randomized beamforming has been studied in (7). The randomized beamforming technique allows each node in the network to direct its main beam in a direction from a uniform distribution on (0, 2�). This simple technique does not require knowledge about location of neighbouring nodes, and it is shown to give significant improvement in the connectivity of ad hoc networks. In this paper we propose two beamforming methods, one called centre directed beamforming and the other called greedy beamforming. In centre directed beamforming all nodes ori- entate their main beam towards the geometric centre of the network, assuming the location of the centre is known. Greedy beamforming allows each node to choose the direction of its main beam based on knowledge of the locations of other nodes, such that the maximum number of one hop connections for the node is achieved. In the greedy beamforming scheme, each node assumes that others are equipped with omnidirec- tional antennas with known locations and performs a simple calculation to decide the direction of the main beam which maximizes its local connectivity. We study the connectivity of an ad hoc network using both techniques. For greedy beam- forming we consider the cases of nodes having perfect and imperfect knowledge of the positions of other nodes. We show that centre directed beamforming has certain advantages over random beamforming, and greedy beamforming outperforms both random and centre directed beamforming.