Critical Sensor Density for Partial Coverage under Border Effects in Wireless Sensor Networks

Coverage is an important metric to measure the quality of service of a wireless sensor network monitoring a field of interest (FoI). From an energy perspective, it is often very important to maintain the desired coverage ratio with a minimum number of sensors. The literature on determining the critical sensor density (CSD) for the desired coverage ratio assumes that the FoI is unbounded or toroidal in shape. Although it is not a realistic assumption, it eliminates the border effects in analysis. Since the entire sensing area of the sensors near the boundary may not be useful for the coverage, the CSD estimated without the border effects is lower than the actual value. In this paper, we assume that the sensors are deployed uniformly at random in a convex polygon-shaped FoI and consider the border effects to derive the expected sensing area of a sensor used in the coverage. Next, we estimate the CSD required for the desired coverage ratio. We validate the analysis and demonstrate the impact of border effects on CSD using numerical results. Results show that our approach estimates the CSD better than another one that does not consider the exact geometry of the FoI.