Design of Energy-efficient Sensing Systems with Direct Computations on Compressively-sensed Data

The aim of this thesis is to explore the energy limits that can be achieved by signal-processing systems when they explicitly utilize signal representations that encode information efficiently. Compressive sensing is one method that enables us to efficiently represent data. The challenge, however, is that in compressive sensing, signals get substantially altered due to the random projections involved, posing a challenge for signal analysis. Moreover, due to the high energy costs, reconstructing signals before analysis is also often infeasible. In this thesis, we develop methodologies that enable us to directly perform analysis on embedded signals that are compressively sensed. Thus, our approach helps potentially reduce the energy and/or resources required for computation, communication, and storage in sensor networks. We specifically focus on transforming linear signal-processing computations so that they can be applied directly to compressively-sensed signals. We show that this can be achieved by solving a system of linear equations, where we solve for a projection of the processed signals as opposed to the processed signals themselves. This opens up two approaches: (1) when the projection matrix is the random projection matrix used in compressive sensing, where we show that the linear equations can be solved with a least-squares approximation, and (2) when the projection matrix is an auxiliary matrix, where we show that the equations become underdetermined, allowing us to obtain either high-accuracy or low-energy solutions based on two designer-controllable knobs. We study our methodologies through information metrics, validating their generality, and through application to biomedical detectors, utilizing clinical patient data. Through a prototype IC implementation, we also demonstrate a hardware architecture that exploits the two knobs for power management. Further, we also explore options for hardware specialization through architectures based on custom-instruction and coprocessor computations. We identify the limitations in the former and propose a co-processor based platform, which exploits parallelism in computation as well as voltage scaling to operate at a subthreshold minimum-energy point. We show that the optimized coprocessor reduces the computational energy of an embedded signal-analysis platform by over three orders of magnitude compared to that of a low-power processor with custom instructions alone.