Optimized random deployment of large-scale energy-harvesting sensors for field reconstruction

This work examines the large-scale deployment of energy-harvesting sensors for the purpose of sensing and reconstruction of a spatially correlated Gaussian random field. The sensors are assumed to be deployed randomly according to a spatially non-homogeneous Poisson point process and our goal is to determine the optimal spatially-dependent sensor density to minimize the field reconstruction error. During each observation period, each sensor takes a local sample of the random field and transmits a scaled version of its observation to the sink node. The sink node then performs reconstruction of the random field based on the received information. The transmit power of each sensor is converted from ambient energy and thus, depends highly on the energy arrival at each location. For the purpose of field reconstruction, the sensors should, on the one hand, be deployed uniformly in space to gather more informative samples, but should, on the other hand, be placed at locations with large energy arrival or large channel gain to the sink node to increase the reliability of data transmission. The optimal sensor intensity and the optimal energy-aware transmission policy, which maximizes the effectiveness of energy usage at the sensors, are determined by minimizing an upper bound of the average mean-square reconstruction error. The efficacy of the proposed scheme is demonstrated through numerical simulations.