Graph Filtering of Time-Varying Signals over Asymmetric Wireless Sensor Networks

Abstract

In many applications involving wireless sensor networks (WSNs), the observed data can be modeled as signals defined over graphs. As a consequence, an increasing interest has been witnessed to develop new methods to analyze graph signals, leading to the emergence of the field of Graph Signal Processing. One of the most important processing tools in this field is graph filters, which can be easily implemented distributedly over networks by means of cooperation among the nodes. Most of previous works related to graph filters assume the same connection probability in both link directions when transmitting an information between two neighboring nodes. This assumption is not realistic in practice due to the typical random link asymmetry in WSNs caused by interferences and background noise. This paper proposes solutions to cope with the problem of graph filtering of noisy time-varying input graph signals over random time-varying asymmetric WSNs. We design an extension to node-variant graph filters that can provide a trade-off between the expected error and variance, by optimizing the filter coefficients adaptively, resulting in an accurate graph filtering. Numerical experiments carried out over different random WSNs illustrate the efficiency of the proposed solutions.