Adaptive networks are well suited to perform distributed estimation task where the observations collected by nodes of a network are used to estimate a common network-wide desired parameter. Although the benefits of cooperation are clear for the networks with ideal links, in the presence of noisy links their behavior changes considerably. Thus, it is important to analyze, in this case, when and to what extent the cooperation improves the estimation performance. In this paper, we study the influence of noisy links on the effectiveness of cooperation for two important types of adaptive networks, i.e. incremental LMS adaptive network (ILMS) and diffusion LMS (DLMS). We first define the concept of cooperation gain and compute it for the ILMS and the DLMS algorithms with ideal and noisy links. We show that when the links are ideal, both ILMS and DLMS algorithms provide increased performance in comparison with the non-cooperative solution. On the other hand, in the presence of noisy links, the cooperation gain is not always influential, and based on the channel and data statistics, for some values of step-size, a non-cooperative scheme outperforms the ILMS and DLMS algorithms. We present some simulation results to clarify the discussions.
