Trade-offs in Estimating Maximum of Sensor Readings in Energy Harvesting Wireless Networks

Computing the maximum of the sensor readings across a wireless sensor network (WSN) has applications in environmental, health, and industrial monitoring. We characterize the novel trade-offs that arise when green energy harvesting (EH) WSNs are deployed for computing the maximum. In these WSNs, the nodes harvest random amounts of energy from the environment for communicating their readings to a fusion node over time-varying wireless channels that undergo fading. The fusion node then periodically estimates the maximum. For a transmission schedule in which randomly selected sensor nodes are scheduled for transmission in each sensor data collection round, we derive closed-form expressions for the mean absolute error (MAE), which is defined as the expectation of the absolute difference between the maximum sensor reading and that estimated by the fusion node in a data collection round. We optimize the transmit energy and the number of nodes that should transmit in each round. Our analysis holds for any probability distribution of the sensor readings, and for the general class of stationary and ergodic energy harvesting random processes. Our results show that the optimal number of nodes that transmit in each round and their transmit powers depend on the average rate of energy harvesting and the number of nodes in the WSN.