Decentralized parameter and random field estimation with wireless sensor networks

In recent years, research on Wireless Sensor Networks (WSN) has attracted considerable attention. This is in part motivated by the large number of applications in which WSNs are called to play a pivotal role, such as parameter estimation (namely, moisture, temperature), event detection (leakage of pollutants, earthquakes, fires), or localization and tracking (for e.g. border control, inventory tracking), to name a few. This PhD dissertation is focused on the design of decentralized estimation schemes for wireless sensor networks. In this context, sensors observe a given phenomenon of interest (e.g. temperature). Consequently, sensor observations are conveyed over a wireless link to a Fusion Center (FC) for further processing. The ultimate goal of the WSN is the estimation or reconstruction of the phenomenon with minimum distortion. The problem is addressed from a signal processing and information-theoretical perspective. However, the interplay with some selected functionalities at the link layer of the OSI protocol stack (e.g. scheduling protocols) or network topologies (flat/hierarchical) are also taken into consideration where appropriate. First, this dissertation addresses the power allocation problem in amplify-and-forward wireless sensor networks for the estimation of a spatially-homogeneous parameter. This study is mainly devoted to the analysis of a class of Opportunistic Power Allocation (OPA) strategies which operate with low complexity and stringent signalling requirements. Several problems of interest in WSNs are considered: i) the minimization of distortion, ii) the minimization of transmit power and, iii) the enhancement of network lifetime. Finally, hierarchical network topologies are introduced for those situations where sensor-to-FC channel links suffer from severe path losses. In this context, the analysis is aimed to identify the power allocation strategy that provides the best performance trade-off between estimation accuracy and signalling requirements. Second, sensor nodes are allowed to transmit their observations digitally. In this setting, two encoding strategies are analyzed: Quantize-and-Estimate (Q&E) encoding and Compress-and-Estimate (C&E) encoding, which operate with and without side information at the decoder, respectively. This PhD dissertation addresses a number of issues of interest: i) the impact of different channel models (Gaussian, Rayleigh-fading channels with/without transmit CSI) on the accuracy of the estimates, ii) the optimal number of sensors to be deployed and, iii) the impact of realistic contention-based multiple-access protocols on the estimation distortion. Finally, this PhD dissertation focuses on the estimation of spatial random fields. In this scenario, the spatial variability of the parameter of interest is taken into account, rather than assuming the estimation of a single (i.e. spatially-homogeneous) parameter. Two different scenarios are considered, namely, delay-constrained networks and delay-tolerant networks. In addition, the case where sensors cannot acquire instantaneous transmit CSI (CSIT) is addressed. In this context, the outage events experienced in the sensors-to-FC links result in a random sampling effect which is investigated.