Diffusion sign-error LMS algorithm: Formulation and stochastic behavior analysis

• The diffusion LMS algorithm may suffer from severely degraded convergence performance in impulsive interference environments.
• The proposed diffusion sign-error LMS algorithm is robust against impulsive interferences.
• The stochastic behavior of the diffusion sign-error LMS algorithm is analyzed based on Price's theorem.

In the case where the measurement noise involves impulsive interference, distributed estimation algorithms based on the mean-square error (MSE) criterion may suffer from severely degraded convergence performance or divergence. To address this problem, we modify the adapt-then-combine (ATC) diffusion LMS (DLMS) algorithm by applying the sign operation to the error signals at all agents to develop a diffusion sign-error LMS (DSE-LMS) algorithm. Furthermore, the stochastic behavior of the DSE-LMS algorithm is analyzed for Gaussian inputs and contaminated Gaussian noise based on Price's theorem. Simulation results show the robustness of the DSE-LMS algorithm against impulsive interference and validate the theoretical findings.