Abstract
In multi-hop wireless networks, communication quality depends on the selection of a path between source and destination nodes from several candidate paths. Exploring how path selection affects communication quality is important to characterize the best path. To do this, in [1], we used expected transmission count (ETX) as a metric of communication quality and theoretically characterized minimum route ETX, which is the ETX of the best path, in a static one-dimensional random multi-hop network. In this paper, we characterize minimum route ETX in static two-dimensional multi-hop networks. We give the exact formula of minimum route ETX in a two-dimensional network, assuming that nodes are located with lattice structure and that the ETX function satisfies three conditions for simplifying analysis. This formula can be used as an upper bound of minimum route ETX without two of the three conditions. We show that this upper bound is close to minimum route ETX by comparing it with simulation results. Before deriving the formula, we also give the formula for a one-dimensional network where nodes are located at constant intervals. We also show that minimum route ETX in the lattice network is close to that in a two-dimensional random network if the node density is large, based on a comparison between the numerical and simulation results.
