This paper includes some of the results obtained by Daniel G. Tiglea during the period he was working to obtain the Ph.D. Degree.

Here, we present a theoretical analysis of 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 a reduction in the sampling probability leads to a noticeable deterioration in the convergence rate, and, if the nodes cooperate, 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.

The PDF file can be obtained in this page.