NSF/ENG/ECCS-BSF: Sensing and Estimation under Energy and Communication Constraints

Stanford University, Stanford CA

Investigators

Abstract

Many of the sophisticated electronic devices ubiquitous today have been enabled by digital signal processing (DSP) that converts the analog signals associated with the physical world to the digital domain. Moore's law allows such digitized signals to be processed and communicated with small, low-cost energy-efficient digital hardware. Yet fundamental questions regarding the performance limits and tradeoffs associated with the sampling, quantization, communication, and reconstruction of analog data with respect to both fidelity and overall energy consumption remain open. Better understanding of these performance limits and tradeoffs will significant enhance capabilities for collection, processing, and communication of analog sensor data beyond the current state of the art. These capabilities are particularly acute for emerging sensor network applications in health and wellness, security, energy-efficient infrastructures, and smart cities, where many low-cost low-energy analog sensors will be collecting large amounts of data and transmitting it to remote locations for processing. The proposed research will investigate the interplay between sampling, quantization, communication and reconstruction of analog signals under memory constraints, communication constraints, and energy constraints. The goal of the proposed work is to develop a fundamental rate-distortion theory for the sampling, quantization, and reconstruction of analog data subject to these constraints. Specific Shannon-theoretical limits for the performance of combined sampling and source coding - the tradeoff between the digitizer's sampling rate and quantization precision in terms of distortion will be investigated. In addition, the optimal fidelity in the reconstruction of analog data from a sequence of samples will be derived. Fundamental limits on communication under energy constraints, where an analog sensor must digitize and communication its data under finite energy constraints, will be determined. Methods used will draw from prior work in Shannon capacity, rate-distortion theory, joint source-channel coding and separation, sampling, estimation, and statistics. In particular, after extending existing results on rate-distortion theory to incorporate sub-Nyquist sampling, joint source-channel coding techniques applied to the sampled analog data transmitted over a rate-limited channel will be developed. Energy constraints will be incorporated based on information-theoretic models for computation energy along with recent results on finite-block-length codes and minimum energy-per-bit capacity.