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Recently proposed adaptive networks assume perfect communication among the nodes. In this correspondence, we extend existing analysis to study the performance of incremental least mean square (LMS) adaptive networks in a more realistic case in which communication links between nodes are considered noisy. More precisely, using weighted spatial-temporal energy conservation relation, we arrive a variance relation which contains moments that represent the effects of noisy links. We evaluate these moments and derive closed-form expressions for the mean-square deviation (MSD), excess mean-square error (EMSE) and mean-square error (MSE) to explain the steady-state performance at each individual node. The derived expressions have good match with simulations. However, the main result is that unlike the ideal link case, the steady-state MSD, EMSE, and MSE curves are not monotonically increasing functions of the step-size parameter when links are noisy. We illustrate this behavior and also find the optimal step-size in a closed-form (for a special case) which minimizes the steady-state values of MSD, EMSE, and MSE in each node. Simulations are also provided to clarify the derived theoretical results.
Date of Publication: May 2011