Optimized Random Deployment of Energy Harvesting Sensors for Field Reconstruction in Analog and Digital Forwarding Systems

This paper 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 powered solely by energy harvested from the environment and are deployed randomly according to a spatially non-homogeneous Poisson point process whose density depends on the energy arrival statistics at different locations. Random deployment is suitable for applications that require deployment over a wide and/or hostile area. During an observation period, each sensor takes a local sample of the random field and reports the data to the closest data-gathering node if sufficient energy is available for transmission. The realization of the random field is then reconstructed at the fusion center based on the reported sensor measurements. For the purpose of field reconstruction, the sensors should, on one hand, be more spread out over the field to gather more informative samples, but should, on the other hand, be more concentrated at locations with high energy arrival rates or large channel gains toward the closest data-gathering node. This tradeoff is exploited in the optimization of the random sensor deployment in both analog and digital forwarding systems. More specifically, given the statistics of the energy arrival at different locations and a constraint on the average number of sensors, the spatially-dependent sensor density and the energy-aware transmission policy at the sensors are determined for both cases by minimizing an upper bound on the average mean-square reconstruction error. The efficacy of the proposed schemes are demonstrated through numerical simulations.