Sequential Statistical Signal Processing with Applications to Distributed Systems

Detection and estimation, two classical statistical signal processing problems with wellestablished theories, are traditionally studied under the fixed-sample-size and centralized setups, e.g., Neyman-Pearson target detection, and Bayesian parameter estimation. Recently, they appear in more challenging setups with stringent constraints on critical resources, e.g., time, energy, and bandwidth, in emerging technologies, such as wireless sensor networks, cognitive radio, smart grid, cyber-physical systems (CPS), internet of things (IoT), and networked control systems. These emerging systems have applications in a wide range of areas, such as communications, energy, the military, transportation, health care, and infrastructure. Sequential (i.e., online) methods suit much better to the ever-increasing demand on time-efficiency, and latency constraints than the conventional fixed-sample-size (i.e., offline) methods. Furthermore, as a result of decreasing device sizes and tendency to connect more and more devices, there are stringent energy and bandwidth constraints on devices (i.e., nodes) in a distributed system (i.e., network), requiring decentralized operation with low transmission rates. Hence, for statistical inference (e.g., detection and/or estimation) problems in distributed systems, today's challenge is achieving high performance (e.g., time efficiency) while satisfying resource (e.g., energy and bandwidth) constraints. In this thesis, we address this challenge by (i) first finding optimum (centralized) sequential schemes for detection, estimation, and joint detection and estimation if not available in the literature, (ii) and then developing their asymptotically optimal decentralized versions through an adaptive non-uniform sampling technique called level-triggered sampling. We propose and rigorously analyze decentralized detection, estimation, and joint detection and estimation schemes based on level-triggered sampling, resulting in a systematic theory of event-based statistical signal processing. We also show both analytically and numerically that the proposed schemes significantly outperform their counterparts based on conventional uniform sampling in terms of time efficiency. Moreover, they are compatible with the existing hardware as they work with discrete-time observations produced by conventional A/D converters. We apply the developed schemes to several problems, namely spectrum sensing and dynamic spectrum access in cognitive radio, state estimation and outage detection in smart grid, and target detection in multi-input multi-output (MIMO) wireless sensor networks.