New information processing theory and methods for exploiting sparsity in wireless systems

The work presented in this dissertation revolves around three major research thrusts: (i) efficient acquisition of data from physical sources, (ii) reliable transmission of data from one point to another, and (iii) optimal extraction of meaningful information from given data. The common theme underlying these (often intertwined) research thrusts is what can be termed as the "blessing of sparsity": while real-world data might live in a very high-dimensional space, the critical information conveyed by that data is often embedded in a much lower-dimensional (often non-linear) manifold of the observation space.The thesis of this dissertation is that "Joint exploitation of the sparsity of real-world data by the acquisition, transmission, and information extraction (processing) operations allows design of new computationally efficient and nearly optimal information processing algorithms that---despite being agnostic to the underlying information embeddings---can reduce the amount of data collected without incurring any reduction in the information content as measured by some fidelity criterion." In order to support our thesis, we have developed new theory and methods in the dissertation for some of the fundamental problems arising in wireless systems that involve sparse (or approximately sparse) data. In the process, we have also made a number of significant scholarly contributions in the diverse areas of compressed sensing, wireless communications, and wireless sensor networks.First, we have proved in the dissertation that collections of "structured sensing vectors" given by the rows of either Toeplitz matrices, Gabor matrices, or "low-rank projections" of unitary matrices can successfully encode and decode high-dimensional sparse data. Second, we have developed new framework in the dissertation for estimating sparse multipath channels in time, frequency, and space, and established that the proposed channel estimation framework---which is based on our work on structured sensing vectors---achieves a target reconstruction error using far less energy and, in many instances, latency and bandwidth than that dictated by the traditional training-based channel estimation methods. Finally, we have proposed and analyzed new distributed algorithms in the dissertation that are capable of efficiently accomplishing the task of information extraction in resource-constrained wireless sensor networks using minimal energy and bandwidth.