Analysis of a Reduced-Communication Diffusion LMS Algorithm

In diffusion-based algorithms for adaptive distributed estimation, each node of an adaptive network estimates a target parameter vector by creating an intermediate estimate and then combining the intermediate estimates available within its closed neighborhood. We analyze the performance of a reduced-communication diffusion least mean-square (RC-DLMS) algorithm, which allows each node to receive the intermediate estimates of only a subset of its neighbors at each iteration. This algorithm eases the usage of network communication resources and delivers a trade-off between estimation performance and communication cost. We show analytically that the RC-DLMS algorithm is stable and convergent in both mean and mean-square senses. We also calculate its theoretical steady-state mean-square deviation. Simulation results demonstrate a good match between theory and experiment.

💡 Research Summary

The paper addresses the communication bottleneck inherent in diffusion‑based adaptive networks, where each node traditionally receives intermediate estimates from all of its neighbors at every iteration. To alleviate this load, the authors propose a Reduced‑Communication Diffusion LMS (RC‑DLMS) algorithm. In RC‑DLMS, at each time instant each node selects only a subset of its neighboring nodes—according to a predefined probability or schedule—and combines the intermediate estimates from this subset together with its own estimate. This selective reception reduces the average number of transmitted packets while still allowing the network to converge to the true parameter vector.

The authors develop a rigorous theoretical framework for RC‑DLMS. They first decompose the algorithm into an adaptation step (local LMS update) and a combination step (weighted averaging of selected intermediate estimates). By defining the global error vector and taking expectations, they derive a mean‑error recursion of the form (\mathbb{E}