Fundamental Limits on Sensing Capacity for Sensor Networks and Compressed Sensing
Shuchin Aeron, Manqi Zhao, Venkatesh Saligrama · arXiv (Cornell University) · 2008
Modern applications of signal processing problems arising in sensor networks require efficient sensing of multi-dimensional data or phenomena. In this context it becomes important to understand fundamental performance limits of both sensing and communication between sensors. In this paper we focus primarily on sensing aspects. We propose the notion of sensing capacity to characterize the performance and effectiveness of various sensing configurations. We define Sensing Capacity as the maximal number of signal dimensions reliably identified per sensor deployed. The inverse of sensing capacity is the compression rate, i.e., the number of measurements required per signal dimension for accurate reconstruction, a concept that is of interest in compressed sensing(CS). Using information theoretic arguments we quantify sensing capacity (compression rate) as a function of information rate of the event domain, SNR of the observations, desired distortion in the reconstruction and diversity of sensors. In this paper we consider fixed SNR linear observation models for sensor network (SNET) and CS scenarios for different types of distortions motivated by detection, localization and field estimation problems. The principle difference between the SNET and CS scenarios is the way in which the signal-tonoise