Energy-Efficient Wireless Sensing for Level Set Estimations

Level set estimation (LSE) is the process of using noisy observations of an unknown function to estimate the region(s) where the function values lie above a given threshold. It has a wide range of applications in many scientific and engineering areas, such as spectrum sensing or environment monitoring. In this paper, we study the energy-efficient LSE of a time-varying random field under a total power constraint. The fusion center of a wireless sensing system performs LSE by using discrete-time samples collected by a sensor. An accurate LSE usually requires a large number of samples to be collected and transmitted. However, most wireless sensing systems operate with a stringent power constraint that may not be able to meet the high energy demands imposed by the large amount of data. The gap between energy demands and supplies is a direct result of the so-called big data problem. It is critical to develop energy-efficient sampling schemes that can bridge this gap by reducing the amount of data required by LSE. Two sampling schemes are considered in this paper: 1) a dynamic active sampling scheme that sequentially and adaptively selects the next sampling instant in a myopic manner with knowledge learned from previous samples and 2) a uniform sampling scheme that employs a fixed sampling rate to minimize the LSE error probability in the long term. The exact analytical cost functions and their respective upper bounds of both sampling schemes are developed by using an optimum thresholding-based LSE algorithm. The design parameters of both sampling schemes are optimized by minimizing their respective cost functions. The analytical and simulation results demonstrate that both sampling schemes can significantly reduce the amount of data collected by the system while obtain accurate LSE under a stringent power constraint. In addition, the uniform sampling scheme slightly outperforms the dynamic active sampling scheme.