On the effect of low-quality node observation on learning over incremental adaptive networks

In this paper, we study the impact of low-quality node on the performance of incremental least mean square (ILMS) adaptive networks. Adaptive networks involve many nodes with adaptation and learning capabilities. Low-quality mode in the performance of a node in a practical sensor network is modeled by the observation of pure noise (its observation noise) that leads to an unreliable measurement. Specifically, we consider ILMS networks with different number of low-quality nodes and compare their performance in two different cases including (i) ideal and (ii) noisy links in homogeneous and inhomogeneous environments. We show that in the case of ideal links among nodes, one node with low-quality mode degrades the estimation performance significantly and increasing the variance of observation noise does not degrade the performance anymore. Even with increasing node numbers with low-quality mode in network, estimation performance does not divergence. On the other hand, in the presence of noisy links, different behavior is observed and degradation is dependent on variance of noisy links and it may go unstable. Simulation results are provided to illustrate the discussions.