Steady-State Analysis of Incremental LMS Adaptive Networks With Noisy Links

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.