Stochastic Graph Filtering Under Asymmetric Links in Wireless Sensor Networks

Abstract

Wireless sensor networks (WSN s) are often characterized by random and asymmetric packet losses due to the wireless medium, leading to network topologies that can be modeled as random, time-varying and directed graphs. Most of existing works related to graph filtering in the context of WSNs assume that the probability of delivering an information from one node to a neighbor node is the same as in the reverse direction. This assumption is not realistic due to the typical link asymmetry in WSNs caused by interferences and background noise. In this work, we analyze the problem of applying stochastic graph filtering over random time-varying asymmetric network topologies. We show that it is possible to perform stochastic graph filtering under asymmetric links with node-variant graph filters, while optimizing a trade-off between the expected error (bias) and the variance of the error, with respect to performing graph filtering over a fixed static topology given by a certain connectivity radius of the nodes.