Topology control with Hexagonal Tessellation

Reducing energy consumption has been a recent focus of wireless sensor network research. Topology control explores the potential that a dense network has for energy savings. One such approach is Geographic Adaptive Fidelity (GAF) (Xu et al., 2001). GAF is proved to be able to extend the lifetime of self-configuring systems by exploiting redundancy to conserve energy while maintaining application fidelity. However the properties of the square grid topology in GAF have not been fully studied. In this paper it is shown that there exists an unreachable corner in the GAF grid architecture. Using an analytical model, we are able to calculate the probability associated with an unreachable node and analyse its impacts on data delivery. After investigating a few lossless topologies, we propose to replace the square grid of GAF with a Hexagonal Tessellation virtual mesh (GAF-h). We then proceed to prove that GAF-h is able to achieve zero loss with little extra cost when compared to the original GAF scheme. The Hexagonal Tessellation cell placement and node association algorithm is also proposed for efficient implementation. This algorithm is proved to integrate with the original GAF protocol with little computing overhead.