Distributed Spatial Filtering in Wireless Sensor Networks

Wireless sensor networks (WSNs) paved the way for accessing data previously unavailable by deploying sensors in various locations in space, each collecting local measurements of a target source signal. By exploiting the information resulting from the multitude of signals measured at the different sensors of the network, various tasks can be achieved, such as denoising or dimensionality reduction which can in turn be used, e.g., for source localization or detecting seizures from electroencephalography measurements. Spatial filtering consists of linearly combining the signals measured at each sensor of the network such that the resulting filtered signal is optimal in some sense. This technique is widely used in biomedical signal processing, wireless communication, and acoustics, among other fields. In spatial filtering tasks, the aim is to exploit the correlation between the signals of all sensors in the network, therefore requiring access to all signals collected at the nodes. Due to the high energy cost of transmitting these signals to a central processing unit, many applications require a fully distributed approach to solve spatial filtering problems in order to reduce the energy and bandwidth requirements. Although various distributed signal processing methods already exist, many of them are not designed to solve spatial filtering problems, which makes them either impractical or not usable in this setting. On the other hand, existing methods for distributed spatial filtering are tailored for specific problems. The aim of this thesis is therefore to provide a generic framework for designing distributed algorithms for such spatial filtering problems. In the first part, we derive the steps of the proposed Distributed Adaptive Signal Fusion (DASF) framework, which allows us to design adaptive and distributed algorithms to solve spatial filtering problems in a WSN context. The framework can be used to solve a large family of optimization problems including many commonly used spatial filtering criteria such as minimum mean square error, principal component analysis, trace ratio optimization, minimum variance beamforming, and canonical correlation analysis, among others. We provide a technical analysis of the convergence properties of the proposed method and show that convergence to an optimal solution is achieved in most practical scenarios while also discussing solutions for the very contrived cases where convergence is not guaranteed. In the second part, the focus is on improving the DASF framework and extending it to larger problem families. More specifically, we describe an approach for improving the adaptivity properties of the framework while keeping the amount of additional data transmission required for this low. We also extend the DASF framework to node-specific problems where each node has a different task to solve. Finally, a computationally efficient variant of the DASF framework is provided for fractional programs, significantly reducing the computational burden at each node of the network. The DASF framework and its extensions presented in this thesis therefore fill the gap in the existing literature on distributed spatial filtering problems for which traditional distributed signal processing methods are usually not suited. The framework also unifies existing distributed algorithms for specific spatial filtering problems without having to design a tailored approach for each instance. To summarize, this thesis provides a generic unified framework to solve spatial filtering problems in an adaptive and distributed fashion, in order to cope with the energy and bandwidth limitations of wireless sensor networks. The proposed distributed algorithms converge to the optimal solution of the problems of interest under mild conditions generally satisfied in practice as demonstrated in various simulations.