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

In this correspondence, we analyze the effects of noisy links on the steady-state performance of diffusion least-mean-square (LMS) adaptive networks. Using the established weighted spatial-temporal energy conservation argument, we derive 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, supported by simulations, reveal 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. Moreover, the diffusion LMS adaptive network does not diverge due to noisy links.