Asymptotic Connectivity in Wireless Networks Using Directional Antennas

Connectivity is a crucial issue in wireless networks. Gupta and Kumar show that with omnidirectional antennas, the critical transmission range for a wireless network to achieve asymptotic connectivity is O(radiclog n/n) if n nodes are uniformly and independently distributed in a disk of unit area. In this paper, we investigate the connectivity problem when directional antennas are used. We find that there also exists a critical transmission range, which corresponds to a critical transmission power. We show that in the same propagation environment, when directional antennas use the optimal antenna pattern, the critical transmission power could be much smaller than that in networks using omnidirectional antennas. Moreover, to achieve asymptotic connectivity, it is known that each node has to have O(log n) neighbors when using omnidirectional antennas. We show that even using the transmission power level at which each node has only O(1) neighbors when using omnidirectional antennas, we can still achieve the asymptotic connectivity with directional antennas.