Performance Analysis of Distributed Incremental LMS Algorithm with Noisy Links

Recently proposed distributed adaptive estimation algorithms for wireless sensor networks (WSNs) do not consider errors due to noisy links, which occur during the transmission of local estimates between sensors. In this paper, we study the effect of noisy links on the performance of distributed incremental least-mean-square (DILMS) algorithm for the case of Gaussian regressors. More specifically, we derive theoretical relations which explain how steady-state performance of DILMS algorithm (in terms of mean-square deviation (MSD), excess mean-square error (EMSE), and mean-square error (MSE)) is affected by noisy links. In our analysis, we use a spatial-temporal energy conservation argument to evaluate the steady-state performance of the individual nodes across the entire network. Our simulation results show that there is a good match between simulations and derived theoretical expressions. However, the important result is that unlike the ideal links case, the steady-state MSD, EMSE and MSE are not monotonically increasing functions of step size parameter when links are noisy. In addition, the optimal step size is found in a closed form for a special case which minimizes the steady-state values of MSD, EMSE, and MSE in each node.