Analysis of stochastic k-coverage in wireless sensor networks with boundary deployment

Coverage is an important metric used to measure the quality of service of wireless sensor networks monitoring a field of interest (FoI). Existing literature on the coverage problem assumes that the sensors are deployed directly in the FoI. These results cannot be applied in some applications like canal water surface monitoring, because the sensors cannot be deployed on the water surface. In this paper, we analyze the coverage problem in applications where, the sensors are deployed uniformly at random outside the FoI near the boundary. We derive the expected value of the effective sensing area useful for k-coverage of the FoI using exact geometry. We demonstrate the utility of the analysis in estimation of the minimum number of sensors required for a desired level of coverage. With numerical results we show the impact of various parameters on the number of sensors.