University of Minnesota Ph.D. dissertation. October 2019. Major: Electrical/Computer Engineering. Advisor: Georgios Giannakis. 1 computer file (PDF); x, 116 pages.The turn of the decade has trademarked the `global society' as an information society, where the creation, distribution, integration, and manipulation of information have significant political, economic, technological, academic, and cultural implications. Its main drivers are digital information and communication technologies, which have resulted in a "data deluge", as the number of smart and Internet-capable devices increases rapidly. Unfortunately, establishing information infrastructure to collect data becomes more challenging particularly as communication networks for those devices become larger, denser, and more heterogeneous to meet the quality-of-service (QoS) for the users. Furthermore, scarcity in spectral resources due to an increased demand for mobile devices urges the development of a new methodology for wireless communications possibly facing unprecedented constraints both on hardware and software. At the same time, recent advances in machine learning tools enable statistical inference with efficiency as well as scalability in par with the volume and dimensionality of the data. These considerations justify the pressing need for machine learning tools that are amenable to new hardware and software constraints, and can scale with the size of networks, to facilitate the advanced operation of next-generation communication systems. The present thesis is centered on analytical and algorithmic foundations enabling statistical inference of critical information under practical hardware/software constraints to design and operate wireless communication networks. The vision is to establish a unified and comprehensive framework based on state-of-the-art data-driven learning and Bayesian inference tools to learn the channel-state information that is accurate yet efficient and non-demanding in terms of resources. The central goal is to theoretically, algorithmically, and experimentally demonstrate how valuable insights from data-driven learning can lead to solutions that markedly advance the state-of-the-art performance on inference of channel-state information. To this end, the present thesis investigates two main research thrusts: i) channel-gain cartography leveraging low-rank and sparsity; and ii) Bayesian approaches to channel-gain cartography for spatially heterogeneous environment. The aforementioned research thrusts introduce novel algorithms that aim to tackle the issues of next-generation communication networks. Potential of the proposed algorithms is showcased by rigorous theoretical results and extensive numerical tests
