Analytical Design of Low-Communication Diffusion Estimation Strategy Under Practical Noise Conditions

Communication efficiency is one of the essential elements in the Internet of Things. While most existing works mainly present energy-efficient methods for distributed estimation under ideal conditions, real-world environments involve imbalanced noise variances, such as input noise and measurement noise. In addition, disturbances from impulsive noise drive the system into instability. Thus, conventional methods result in degraded estimation performance when applied to practical environments. To address this issue, this work proposes an extended partial diffusion least-mean-square algorithm based on mean-square-deviation (MSD) analysis. Theoretical analysis shows that the MSD-based formulation extends a scalar-based combination coefficient to a matrix-based one, enabling flexible combinations that allow the network to achieve consensus with low communication cost. Furthermore, it presents an analytical design of an MSD-based optimal variable step size, considering practical noise components in adaptive networks. The simulation results validate the communication efficiency and estimation performance of the proposed algorithm under various noisy conditions.