Critical Sensor Density

Abstract

Before network deployment, one may want to know how many sensor nodes are needed such that every point of the sensor field can be covered by at least one sensor. Sensor density is defined as the number of nodes per unit area. In a homogeneous sensor network, the critical sensor density (CSD) provides an insight on the minimal number of nodes required for complete area coverage. In deterministic sensor placement, it is desirable to know not only the minimal number of nodes but also their locations. For a homogeneous network, a basic placement pattern can be repeated to tile-up the whole sensor field. A placement pattern is optimal if it requires the minimal number of nodes to completely cover the sensor field, and an optimal placement pattern determines the CSD for deterministic sensor placements. In random sensor deployments, the analysis for CSD often applies an asymptotic approach, but its result provides a lower bound of CSD for a sensor field with finite area: The number of nodes should be no smaller than the area of the sensor field times the critical sensor density to ensure complete area coverage (almost surely) in each deployment. In particular, the following questions are addressed in this chapter: