A variable step-size diffusion LMS algorithm over networks with noisy links

Abstract The variable step-size (VSS) diffusion least mean square (LMS) algorithms for wireless sensor networks (WSNs) exhibit accelerated initial convergence rate and decreased steady-state deviation compared with the conventional constant step-size counterparts. However, the performance of the VSS diffusion LMS algorithms would be deteriorated if the network links are contaminated by noise. By explicitly considering the link noise impact, we develop a locally sub-optimal step-size scheme for the diffusion LMS algorithm, originated from which we propose an asymptotically locally sub-optimal (ALSO) step-size scheme as well as a VSS diffusion LMS algorithm. The proposed VSS diffusion LMS algorithm is verified through simulations to significantly outperform the current VSS diffusion algorithm in the networks with moderate and high link noise profiles. Simulation results further validate that the proposed VSS diffusion LMS algorithm is superior to the current VSS algorithm in the networks with correlated link noise.