  In this paper, we analyze the effects of random sampling on adaptive
diffusion networks. These networks consist in a collection of nodes that can
measure and process data, and that can communicate with each other to pursue a
common goal of estimating an unknown system. In particular, we consider in our
theoretical analysis the diffusion least-mean-squares algorithm in a scenario
in which the nodes are randomly sampled. Hence, each node may or may not adapt
its local estimate at a certain iteration. Our model shows that, if the nodes
cooperate, a reduction in the sampling probability leads to a slight decrease
in the steady-state Network Mean-Square Deviation (NMSD), assuming that the
environment is stationary and that all other parameters of the algorithm are
kept fixed. Furthermore, under certain circumstances, this can also ensure the
stability of the algorithm in situations in which it would otherwise be
unstable. Although counter-intuitive, our findings are backed by simulation
results, which match the theoretical curves well.
