Accurate Graph Filtering in Wireless Sensor Networks
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Wireless sensor networks (WSNs) are considered as a major technology enabling the Internet of Things (IoT) paradigm. The recent emerging Graph Signal Processing field can also contribute to enabling the IoT by providing key tools, such as graph filters, for processing the data associated with the sensor devices. Graph filters can be performed over WSNs in a distributed manner by means of a certain number of communication exchanges among the nodes. But, WSNs are often affected by interferences and noise, which leads to view these networks as directed, random and time-varying graph topologies. Most of existing works neglect this problem by considering an unrealistic assumption that claims the same probability of link activation in both directions when sending a packet between two neighboring nodes. This work focuses on the problem of operating graph filtering in random asymmetric WSNs. We show first that graph filtering with finite impulse response graph filters (node-invariant and node-variant) requires having equal connectivity probabilities for all the links in order to have an unbiased filtering, which can not be achieved in practice in random WSNs. After this, we characterize the graph filtering error and present an efficient strategy to conduct graph filtering tasks over random WSNs with node-variant graph filters by maximizing accuracy, that is, ensuring a small bias-variance trade-off. In order to enforce the desired accuracy, we optimize the filter coefficients and design a cross-layer distributed scheduling algorithm at the MAC layer. Extensive numerical experiments are presented to show the efficiency of the proposed solution as well as the cross-layer distributed scheduling algorithm for the denoising application.
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